Description
The International Finance Corporation (IFC) is an international financial institution which offers investment, advisory, and asset management services to encourage private sector development in developing countries.
ABSTRACT
Title of dissertation:
ESSAYS IN MACROECONOMICS AND INTERNATIONAL FINANCE
Daniel Hernaiz Diez de Medina, Doctor of Philosophy, 2012
Dissertation directed by:
Professors Boragan Aruoba and John Shea Department of Economics
This document is a collection of essays in two issues of interest in macroeconomics and international ?nance. Chapter 2 introduces price promotions in a monetary DSGE model where consumers di?er in their price sensitivity and look for promotions, and where ?rms choose their regular and promotional prices as well as the frequency of promotions. In this environment, regular and promotional prices coexist, ?rm-level prices show rigidity in the form of inertial reference values from which weekly prices temporarily deviate, and promotions provide a new channel of price adjustment in the face of shocks. As a result, the economy displays near neutrality with respect to monetary shocks, with an impact response of output equal to one third of the one obtained in a model with no promotions. This result contrasts sharply with those of similar studies which, using alternative rationales for price
promotions, ?nd that price promotions do not fundamentally alter the real e?ects of monetary shocks. Chapter 3 studies the currency substitution phenomenon and develops a two-currency model that introduces ”dollarization capital” as a means to capture the economy’s accumulated experience in using the foreign currency. The model is able to generate a low-in?ation-high-substitution equilibrium consistent the data, and explains 1/6 of the gap between the observed currency substitution ratios and those generated by a model with no dollarization capital dynamics. The model, however, does not generate asymmetries in the relationship between in?ation and currency substitution before and after high in?ation episodes. Therefore, Chapter 4 presents a simple framework that creates non-linearities between in?ation and currency substitution. The model has two consumers who can di?er in their distance from money exchange points provided by the ?nancial sector, who decides whether or not to pay a ?xed cost necessary to install these exchange points. In this environment, a sequence of episodes of high and moderate in?ation may push the ?nancial sector into expanding the number of available money exchange points, therefore permanently reducing the consumers’ cost of using the foreign currency and decreasing the in?ation threshold at which households are willing to substitute foreign for domestic currency.
ESSAYS IN MACROECONOMICS AND INTERNATIONAL FINANCE
by Daniel Hernaiz Diez de Medina
Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial ful?llment of the requirements for the degree of Doctor of Philosophy 2012
Advisory Commmittee: Professor Professor Assistant Professor Professor Boragan Aruoba, Co-Chair/Advisor John Shea, Co-Chair/Advisor Professor Sanjay Chugh Pallassana Kannan Carlos Vegh
c Copyright by Daniel Hernaiz Diez de Medina 2012
ACKNOWLEDGEMENTS
Above all I want to thank the Lord Jesus Christ, my savior, for making it possible for me to earn this degree. Without Him I could do nothing. Without Him I would be lost. Jesus, I have no words to tell you how much I appreciate all you have done for me. I have had a great dissertation committee. John Shea was willing to read every piece of work that I sent to him (even when he was not at UMD and was busy working at the Treasury Department!). Boragan Aruoba has been very patient, supportive and helpful. He is a terri?c advisor, inspiring and always willing to spend time with his students. Sanjay Chugh is the person that ?rst got me interested in monetary economics. His macro course was outstanding; my discussions with him were the seed of my job market paper. Carlos Vegh has been an inspiration, a mentor and a friend (gracias!). I also thank professor P.K. Kannan from the Robert H. Smith School of Business for accepting the invitation to be the Dean’s Representative in my committee. To all of you, thank you! I wish you all the best in your professional and personal lives. I would also like to thank Carmen Reinhart for all her support during her time at Maryland. Working as a research assistant for her and Carlos Vegh was an ii
extremely rewarding experience. Also, I’d like to thank Enrique Mendoza, Anton Korinek and Pablo D’Erasmo for all the helpful discussions that we had during the time of preparation of my job market paper. I also thank Tom Powers, Gerry Caprio, Peter Montiel, Peter Pedroni, Jon Bakija and Dukes Love from the Center for Development Economics and the Department of Economics at Williams College. I thank my family (Joaquin, Maricarmen and Viviana) for their love and support, and Carlos Echazu (closest thing I have to a blood brother) for always being there. I thank Avy, Carola, Cristina, Daniela, Chris, Danny, Ethan and Zoe, my Virginian family. I’ve had some really good days during my time in Maryland, but the ones I spend with Ethan and Danny were among the best. Five years ago I met two guys looking for a roommate. Today I see them as my brothers. Cesar and Gabo, aguante el Chateau!!! I thank Juandi and Caro for being like they are: two of the best people I’ve met in my life. I thank Pablo Cuba for his friendship (he is always willing to help somebody in need). I’m glad he came to Maryland and I expect him to be one of the best macroeconomists this university has produced. Finally, I thank Tim and Maria Belen, Teresa and Greg, and Abby for being such good friends.
iii
TABLE OF CONTENTS
List of Figures List of Tables Introduction A Monetary Model With Price Promotions
2.1
vii ix 1 6
1
2
The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.1.7 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 The Government . . . . . . . . . . . . . . . . . . . . . . . . . 24 The Economy’s Resource Constraint . . . . . . . . . . . . . . 25 Characterizing the Economy-wide Price Level . . . . . . . . . 26 Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . 28 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
iv
2.1.8 2.2 2.3
Price Discrimination in General Equilibrium . . . . . . . . . . 29
Solution Method and Parameter Values . . . . . . . . . . . . . . . . . 37 The Workings of the Model . . . . . . . . . . . . . . . . . . . . . . . 41 2.3.1 2.3.2 Individual Price Setting Behavior . . . . . . . . . . . . . . . . 41 Does Micro Flexibility Translates Into Higher Neutrality at the Macro Level? . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3
A Quantitative Analysis of Currency Substitution
3.1 3.2
60
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Currency Substitution in Two Selected Economies . . . . . . . . . . . 62 3.2.1 3.2.2 Currency substitution and in?ation . . . . . . . . . . . . . . . 62 Inverse velocities of money . . . . . . . . . . . . . . . . . . . . 66
3.3
A Model of Currency Substitution . . . . . . . . . . . . . . . . . . . . 67 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . 69 Transaction Costs . . . . . . . . . . . . . . . . . . . . . . . . . 69 Dollarization Capital . . . . . . . . . . . . . . . . . . . . . . . 70 Maximization Problem and Competitive Equilibrium . . . . . 71
3.4
IV. Solving the Model . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.4.1 Parametrization and Solution Method . . . . . . . . . . . . . . 75
v
3.4.2 3.5
Transitional Dynamics from High to Low in?ation
. . . . . . 79
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4
Investment Activity in the Financial Sector and the Relationship between In?ation and Currency Substitution
4.1 4.2
85
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 A simple three-agent model . . . . . . . . . . . . . . . . . . . . . . . 91 4.2.1 4.2.2 4.2.3 The environment . . . . . . . . . . . . . . . . . . . . . . . . . 91 Consumer’s problem . . . . . . . . . . . . . . . . . . . . . . . 92 The ?nancial sector’s investment problem . . . . . . . . . . . 98
4.3
Conclusion
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A
Appendix to Chapter 1
110
A.1 Calvo stickiness in regular prices . . . . . . . . . . . . . . . . . . . . . 110 A.2 Looking for f in the data . . . . . . . . . . . . . . . . . . . . . . . . . 116 A.3 The Firm’s Problem Under Perfect Price Discrimination (PPD) . . . 118 A.4 Monetary Model with Price Promotions: Impulse Response Functions 121
B
Appendix to Chapter 2
122 124
Bibliography
vi
LIST OF FIGURES
2.1 2.2 2.3 2.4
FIRMS PRICES IN THE ABSENCE OF MACRO SHOCKS . . . . . 35 PRICE EVOLUTION IN FOUR SELECTED PRODUCTS . . . . . . 44 SIMULATED PRICE FOR AN INDIVIDUAL FIRM . . . . . . . . . 45 SIMULATED PRICE FOR AN INDIVIDUAL FIRM: THE CASE OF POSITIVE STEADY STATE INFLATION . . . . . . . . . . . . 46
2.5 2.6 2.7 2.8
OUTPUT RESPONSE TO A MONETARY POLICY SHOCK . . . . 54 IMPULSE RESPONSE ANALYSIS . . . . . . . . . . . . . . . . . . . 55 TIME ALLOCATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 56 THE RESPONSE IN THE MODEL WITH PRICE PROMOTIONS COMPARED THAT OF A CALVO MODEL CALIBRATED TO DIFFERENT TIMES BETWEEN CHANGES . . . . . . . . . . . . . 56
3.1 3.2 3.3 4.1
CURRENCY SUBSTITUTION IN BOLIVIA AND PERU . . . . . . 65 TRANSITIONAL DYNAMICS . . . . . . . . . . . . . . . . . . . . . 80 TRANSITION WITH AND WITHOUT DOLLARIZATION CAPITAL 82 MODEL ENVIRONMENT . . . . . . . . . . . . . . . . . . . . . . . . 92
vii
4.2 4.3 4.4
CURRENCY SUBSTITUTION AND INFLATION . . . . . . . . . . 99 EXCHANGE POINTS AND THE INFLATION RATE . . . . . . . . 102 PATHS OF INFLATION AND CURRENCY SUBSTITUTION . . . 107
viii
LIST OF TABLES
2.1 2.2 3.1 3.2 3.3 3.4 4.1 4.2
Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Steady State Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Model Results and Calibration Targets . . . . . . . . . . . . . . . . . 77 Currency Substitution Ratios in High-in?ation Periods . . . . . . . . 79 Currency Substitution Ratios in High-in?ation Periods . . . . . . . . 83 In?ation Probabilities and the State of Exchange Points . . . . . . . . 103 In?ation Probabilities and Currency Substitution . . . . . . . . . . . 103
A.1 Fraction of Weeks by Department . . . . . . . . . . . . . . . . . . . . 117 A.2 Fraction of Weeks: Sample I . . . . . . . . . . . . . . . . . . . . . . . 118 A.3 Fraction of Weeks: Sample II . . . . . . . . . . . . . . . . . . . . . . 118 B.1 Data Series Used in the Document . . . . . . . . . . . . . . . . . . . 122 B.2 Money Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 B.3 In?ation Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
ix
Chapter 1
Introduction
This document is a collection of essays On two di?erent issues of interest in macroeconomics and international ?nance. The second chapter presents a study on the role of sale-induced high frequency price ?uctuations in monetary economics. The third and fourth chapters focus on the phenomenon of currency substitution observed in several developing countries and transition economies. Chapter 2 is motivated by recent microeconomic price evidence that shows that price promotions may have a signi?cant bearing on the measured frequency of price changes. This ?nding raises the question of whether micro price ?exibility caused by the presence of price promotions translates into macro neutrality to monetary shocks. The issue is addressed by introducing price promotions in a dynamic stochastic general equilibrium (DSGE) environment where agents di?er in their de-
1
gree of price sensitivity and face a time cost when looking for promotions. On the production side, ?rms optimally choose their regular and promotional prices as well as the frequency of promotions. In this framework, regular and promotional prices coexist and promotions provide a new source of ?rm-level price ?exibility. After introducing Calvo-stickiness in regular prices, individual price series behave similarly to those reported in recent empirical studies: regular prices are sticky; prices including promotions change very frequently, and realized prices show rigidity in the form of inertial reference values from which weekly prices temporarily deviate. In the aggregate, the economy displays near neutrality with respect to monetary shocks with a response of output that, on impact, is equal to one third of the one obtained from a standard Calvo model, a result that shows the importance of further exploration of ?rm-customer interactions in macroeconomic models. Chapter 2 is organized in ?ve sections. The ?rst one presents the introduction. The model is developed in the second section. The solution method, parameters and steady state values are discussed in the third section. The fourth section presents results on the model’s micro price behavior and the macroeconomic implications of price promotions, particularly on the responses to monetary shocks. The ?fth section concludes. Chapter 3 studies the phenomenon of currency substitution; that is, the use of foreign currency as a means of payment, as frequently observed in several developing countries and emerging economies. In several countries, currency substitution increases with in?ation during high in?ation periods and reaches its peak once the 2
economy has been stabilized, showing high persistence in the subsequent periods in spite of the downward trend in in?ation. The chapter focuses on two examples of this particular phenomenon: Bolivia and Peru. The chapter develops a perfect foresight two-currency model with exogenous production and transaction costs that is used to generate persistence in currency substitution. The model introduces ”dollarization capital” as a means to capture the economy’s accumulated experience in using the foreign currency. When parameters are set to replicate observed pre-hyperin?ation ratios in the two selected economies, the model is able to generate a low-in?ation-high-substitution equilibrium consistent with the post-stabilization behavior observed in various emerging markets and developing countries. The dollarization capital model explains from 1/6 of the gap between the observed currency substitution ratios and the ones generated by a model with no dollarization capital dynamics. As a result of quick and sizable changes in domestic currency real balances, the predicted post-stabilization currency substitution ratios adjust quickly in their path towards a low-in?ation equilibrium, a ?nding that suggests focusing future modeling e?orts on exploring plausible mechanisms that may introduce post-stabilization inertia in domestic currency holdings. Chapter 3 is organized in ?ve sections. After the introduction, the second section describes the pre and post high-in?ation pattern of currency substitution in Bolivia and Peru. The theoretical model is presented in the third section and solved in the fourth section. The ?fth section concludes. One of the limitations of the model analyzed in Chapter 3 is that it is not able to generate an asymmetric relationship between in?ation and currency substitution 3
before and after high in?ation episodes. This behavior is at odds with the data in several partially dollarized economies. Therefore, Chapter 4 explores a simple model that generates non-linearities in the relationship between currency substitution and in?ation. The chapter presents a simple three agent model with two consumers who can di?er in their distance, and therefore walking cost, from money exchange points provided by the third agent, the ?nancial sector, who is the only one that possesses the technology to exchange domestic for foreign currency. Money is used for transaction purposes and agents have an incentive to hold foreign currency balances for high enough levels of in?ation. The possibility of substitution, however, depends on whether or not the ?nancial sector pays a ?xed cost necessary to install money exchange points where consumers can buy currency exchange services. In this environment, a sequence of episodes of high and moderate in?ation may push the ?nancial sector into expanding the number of available money exchange points, therefore permanently reducing the consumers’ cost of using the foreign currency and decreasing the in?ation threshold at which households are willing to substitute foreign for domestic currency. From a theoretical point of view, the work presented in Chapter 4 constitutes an e?ort to provide a micro foundation for the emergence and functioning of network externality e?ects that have been explored as a possible explanation for high levels of currency substitution even after several years of low in?ation. Chapter 4 is organized in three sections. The ?rst section presents the introduction. The second section presents a simple three agent model used to study the 4
consumer’s optimal currency substitution behavior and the ?nancial sector’s optimal dollarization capital investment decision. The third section concludes.
5
Chapter 2
A Monetary Model With Price Promotions
Recent microeconomic price evidence shows that price promotions may have a signi?cant bearing on the measured frequency of price changes, a ?nding that raises the question of whether micro price ?exibility translates into macro neutrality to monetary shocks. This chapter addresses this issue by introducing price promotions in a dynamic stochastic general equilibrium (DSGE) environment where agents di?er in their degree of price sensitivity and face a time cost when looking for promotions. On the production side, ?rms optimally choose their regular and promotional prices as well as the frequency of promotions. Under this setting, regular and promotional prices coexist and promotions provide a new source of ?rm-level price ?exibility. After introducing Calvo-stickiness in regular prices, individual price series behave similarly to the ones reported in recent empirical studies: regular prices are sticky;
6
prices including promotions change very frequently, and realized prices show rigidity in the form of inertial reference values from which weekly prices temporarily deviate. In the aggregate, the economy displays near neutrality with respect to monetary shocks with a response of output that, on impact, is equal to one third of the one obtained from a standard Calvo model, a result that shows the importance of further exploration of ?rm-customer interactions in macroeconomic models. The exercise of studying price promotions in a macroeconomic context is motivated by recent empirical work showing that the treatment of price sales may have an important e?ect on the estimated frequency of individual price changes. An example of this is the in?uential work of Bils and Klenow (2004), who analyzed the frequency of price changes in di?erent components of the US Consumer Price Index (CPI), ?nding a median time between changes of 4.3 months. This estimate, which includes sale related price changes, is well below previous ones obtained using less comprehensive datasets. Given that the degree of price stickiness and, more speci?cally, the probability of price changes is an important element for the quantitative solution of New Keynesian models, the result has important implications for macroeconomic modeling. For example, when discussing Michael Woodford’s Interest and Prices, Green (2005) mentions that “at the very least [Bils and Klenow’s] study shows a need to recalibrate Woodford’s model.” Indeed, Bils and Klenow’s result has become a calibration reference used in well known DSGE studies such as Altig, Christiano, Eichenbaum and Linde (2005) and Golosov and Lucas (2007). Following Bils and Klenow’s seminal work, recent research by Nakamura and Steinsson (2008) and Klenow and Krystov (2008) uses a more detailed dataset (the 7
US CPI Research Database) and ?nds that the estimated time between price changes is sensitive to the inclusion of sale prices. Particularly, Nakamura and Steinsson ?nd median durations between 4.4 and 4.6 months when including sales, but between 8 and 11 months when excluding sales. This new evidence on price setting has been complemented by recent studies using higher frequency micro price datasets. Eichenbaum, Jaimovich and Rebelo (2011) analyze a new weekly scanner dataset for a major US retailer, ?nding that nominal rigidities take the form of inertia in reference prices with weekly prices ?uctuating around reference values that tend to remain constant over extended periods of time. Klenow and Malin (2010) ?nd that the reference price phenomenon documented by Eichenbaum et. al. (2011) extends to most items in the non-shelter CPI.1 These results suggest that promotional prices have a large impact on measures of the frequency of price changes, but also point to the need to explore the potential macroeconomic implications of price promotions.2 In the words of Klenow and
1
The shelter component of the CPI is composed of the following items: (i) Rent of primary
residence, (ii) Lodging away from home, (iii) Housing at school (excluding board), (iv) Other lodging away from home including hotels and motels, (v) Owners’ equivalent rent of primary residence and (vi) Tenants’ and household insurance.
2
This also seems to be the case outside the US. For example, Dhyne et. al. (2006) note
that the statistical treatment and report of sale prices may be an important factor in explaining the observed di?erences in the frequency of price adjustment across euro-area countries. Cavallo (2009), meanwhile, uses price scraped data for four Latin-American countries, ?nding that, in most cases, measured price durations are considerably increased by the exclusion of sales. Data scraping is the activity of extracting data from output intended for the screen or printer of a computer
8
Krystov (2008), “sales are not . . . [just] a discount from the regular price; they have a life of their own.” In relation to this point, Mackowiak and Smets’ (2008) survey paper on micro price evidence presents some interesting comments on the macromodeling implications of sales in micro price data. First, an optimizing model of sales will, in general, predict that the magnitude, frequency and duration of sales respond to macroeconomic shocks. The practice of excluding all sale-related price changes from macro models may therefore be unjusti?ed. Second, sale-related price changes in the Bureau of Labor Statistics (BLS) dataset are at least as sensitive to in?ation as are regular price changes (Klenow and Willis, 2007). Third, even if price promotions are caused by shocks orthogonal to the macroeconomy, the presence of sales may matter for the response of prices to macroeconomic shocks. The ?rst papers that incorporate sale prices into a macro model are Kehoe and Midrigan (2007, 2008). These papers modify the Golosov and Lucas (2007) menu cost model by explicitly including a motive for sales, allowing ?rms to pay for temporary price changes at a lower menu cost than that paid when changing their price permanently. The authors then use their sales model as a data generating process and evaluate the e?ects of ?tting a simple Calvo model (with no sales motive in it) in order to match the moments generated by the sales model. They consider two cases: one including temporary price changes (i.e. sales) from the price series generated by the benchmark sales model, and one excluding them. They ?nd that excluding sales overstates the real e?ects of monetary shocks by almost 70%, and including sales produces only 1/9 of the real e?ects of monetary policy in the bench(human-readable output) rather than from original ?les or databases (www.pcmag.com).
9
mark model. Kehoe and Midrigan’s exercise highlights the importance of explicitly developing a motive for temporary price changes in monetary models. More recently, Guimaraes and Sheedy (2011) and Kehoe and Midrigan (2010) focus on whether sale-related and temporary price changes translate into macroeconomic neutrality in a monetary DSGE environment. Guimaraes and Sheedy (2011) develop a framework in which sale prices are not linked to the existence of menu costs. They construct an environment with di?erentiated goods and di?erentiated brands for each good, with consumers willing to substitute between brands for some products, but not for others. Firms are not able to price discriminate between consumers, and therefore choose to o?er a regular price at some moments in time and a sale price at others. If a Calvo-type rigidity is introduced in regular prices, the model generates individual time series that behave similarly to those studied by Eichenbaum et al. (2011). When studying the e?ects of monetary shocks, the authors ?nd that output impulse responses are very similar to those of a model with no sales, implying that micro price ?exibility does not translate into macro ?exibility and, therefore, sales are essentially irrelevant for monetary analysis. This result is due to the fact that in their model, sales are strategic substitutes; that is, a ?rm’s incentive to have a sale is decreasing in the number of other ?rms having a sale. Continuing with their earlier work, Kehoe and Midrigan (2010) build an extension of the standard menu cost model adding features that make the predictions of the modi?ed environment consistent with the micro price data. In their model, prices are subject to both permanent and temporary shocks; retailers set a list price and a posted price and face two ?xed costs: one when changing the list price, and 10
another when the posted price temporarily di?ers from the listed one. In this environment, ?rms tend to change list prices in order to o?set permanent productivity shocks and monetary shocks and temporarily deviate from the list price in order to o?set transitory shocks. Given the menu cost friction on list prices, ?rms may recur to deviations from the listed price as a channel for o?setting transitory monetary shocks. However, since these deviations are temporary, this only allow ?rms to react temporarily to a monetary shock, so that economy presents a high degree of non neutrality even in the presence of frequent temporary price changes. Kehoe and Midrigan also show that this result does not arise from strategic interactions as in Guimaraes and Sheedy (2011) but solely from the special nature of temporary price changes in their model. A common characteristic of Kehoe and Midrigan (2007, 2008, 2010) and Guimaraes and Sheedy (2011) is that households have no choice over how often they look for price promotions. Sales are therefore exogenous from the consumer’s point of view. Letting consumers choose the time spent looking for price promotions creates a new intratemporal margin that has important implications for the model’s response to aggregate shocks. This is the line of work followed in this document.3
3
Two other models that can deliver sticky regular prices with frequent sales are Nakamura and
Steinsson (2009) and Albrecht et. al. (2010). Nakamura and Steinsson develop a habit persistence model where ?rms face a time inconsistency problem, having the incentive to promise low prices in the present and raise them once that households have developed a consumption habit. In this context, price stickiness can arise endogenously and optimally as a partial commitment device, with ?rms choosing a price cap and discretionally setting prices only when they are below the cap. Albrecht et. al. (2010), on the other hand, model shopping as a search process in a framework
11
The model presented here analyzes the behavior of a monopolistically competitive economy in which ?rms face di?erent market demands and maximize pro?ts by setting a regular price and a promotional strategy composed of a discount price and a promotion frequency. Following Banks and Moorthy (1999), the model allows for consumer heterogeneity by having agents with di?erent price elasticities of demand, and introduces a time cost of looking for price promotions. In this context, it is possible to make an explicit distinction between regular and promotional prices: regular prices are always available to anyone, while promotional prices are only available when o?ered and only to those who look for them. The approach here thus di?ers from previous work in the area in at least two important aspects. First, the de?nition of regular and promotional prices di?ers from previous work. Second, consumers choose optimally the time spent looking for price promotions. In this setting, heterogeneity in price sensitivity and the assumption that households must pay a time cost in order to take advantage of price promotions are enough to (i) ensure that household time choices interact with ?rm promotional strategies, creating an environment in which regular and promotional prices coexist and (ii) generate a new source of price ?exibility through movements in promotional prices.
similar to that used in the job search literature. The authors show that, in a model with a semidurable good and consumer heterogeneity, there is an equilibrium pattern in which ?rms choose to post a high price for a number of periods followed by a single period sale. The sale rationales developed in these papers have not been introduced in a more general monetary DSGE framework yet, so their macroeconomic implications remain to be explored.
12
Given this framework, the model generates a large degree of micro-level price movement even in the absence of macroeconomic shocks, with ?rm-level realized prices ?uctuating between the regular and promotional values in response to the ?rm’s optimal choice of the fraction of time at which its product will be o?ered on promotion and to consumers’ optimal choices of the time invested looking for those promotions. However, even though not every price movement is the result of a macroeconomic shock, the model’s rationale for promotions has e?ects on how the economy reacts to monetary shocks. When extended in order to allow for Calvostickiness in regular prices, the model generates individual price series that behave in a way consistent with recent empirical studies: (i) regular (non-promotional prices) are sticky; (ii) prices including promotions change very frequently; (iii) realized prices show rigidity in the form of inertia in reference prices around which weekly prices ?uctuate. When studying the e?ects of monetary shocks, the model displays output responses well below the ones obtained with a standard Calvo model calibrated to match the frequency of regular price changes. In this case, sales are important for macroeconomics since their existence creates a dynamic pricing arrangement in which the market can outsmart the Calvo fairy. More generally, this result points to the importance of further exploration on how consumer behavior and ?rm-customer interactions are designed in macroeconomic models. The remainder of the chapter is organized as follows. The model is developed in the second section. The solution method, parameters and steady state values are discussed in the third section. The fourth section presents results on the model’s 13
micro price behavior and the macroeconomic implications of price promotions, particularly on the responses to monetary shocks. The ?fth section concludes.
2.1
The Model
The model consists of households, ?rms and a government. Money is introduced as an argument of the utility function; households purchase goods for consumption, supply labor, spend time looking for price promotions and hold money and bonds, while ?rms hire labor and produce and sell a continuum of di?erentiated consumption goods produced in a monopolistically competitive market. Households di?er in the price elasticity parameter of the Dixit-Stiglitz consumption aggregator. Given this heterogeneity in consumption, each ?rm’s price setting decision includes a choice of a regular price, and a promotional strategy consisting of a promotional price and a promotion probability (the fraction of time that the good is o?ered at promotion prices).
2.1.1
Households
There is a measure one of in?nitely lived households divided in two possible types: measure h of high price elasticity consumers (HECs), and measure 1 ? h of low price elasticity consumers (LECs).
High Elasticity Consumers High elasticity households maximize the expected present discounted value of utility:
14
?
E0
t=0
? t u ch t +?
mh t Pth
h + v 1 ? nh t ? st
(2.1)
where u(.), ?(.), and v (.) are strictly increasing and strictly concave, mh are nominal balances, nh is the fraction of time spent working and sh is the fraction of time spent looking for price promotions. ch is a Dixit-Stiglitz composite consumption good de?ned as ?
? ? ?? 1
?h (ft ,sh t)
1
??1 ?
where the parameter ? > 1 governs the price elasticity of demand for individual goods, ?h (ft , sh t ) is the fraction of goods purchased at promotion prices (with
h h demanded quantities {chp jt }), and 1 ? ? (ft , st ) is the fraction of goods acquired at
? ch t = ?
(chp jt )
0
dj +
?h (ft ,sh t)
(chr jt )
??1 ?
? dj ?
(2.2)
regular prices (with demanded quantities {chr jt }). I do not consider any additional frictions between consumers and ?rms such as matching frictions, so ?h (f, sh t ) is given by ft · sh t where ft is the fraction of time that a ?rm o?ers its product at promotional prices.4 Notice that even though a ?rm can sell a good at promotional and regular prices simultaneously (this will become clear when presenting the problem of the ?rm), in each period of time a consumer can acquire a speci?c good at either the regular or promotional price, but not both. Therefore, ? in (2.2) has the same interpretation as it would in the standard Dixit-Stiglitz consumption aggregator
4
For simplicity, and anticipating a symmetric equilibrium, in the consumer’s problem I assume
fj,t = ft for every ?rm j .
15
and captures the elasticity of substitution between di?erentiated goods. The budget constraint for the household is
h h h h h h h nt + mh Pth wt t?1 + (1 + it?1 )Bt?1 + ?t + Tt = Pt ct + mt + Bt
(2.3)
h where Pth is the price of the consumption composite, wt is the real wage h received for labor services, Bt is the amount of nominal bonds, Tt is a nominal
transfer from the government, and ?t are nominal pro?ts from the di?erentiated ?rms that are assumed to be owned by the households.
hr From the ?rst order conditions for chp jt and cjt :
chp jt
=
pp jt Pth
??
ch t
(2.4)
chr jt
=
pr jt Pth
??
ch t
(2.5)
Then, the relationship between quantities of a good bought at regular and promotional prices is given by
chp jt = chr jt
pr jt pp jt
?
(2.6)
Replacing (2.4) and (2.5) in (2.2), the price index for aggregate consumption is given by ?
1 ? 1? ?
?h (f,sh t) 1?? (pp dj + jt ) 0
1
? Pth = ?
?h (f,sh t)
1?? ? ( pr dj ? jt )
(2.7)
16
Notice that using the demand equations (2.4) and (2.5) and the price aggregator (2.7) it can be shown that
?h (ft ,sh t) hp pp jt cjt dj 0
1
+
?h (ft ,sh t)
hr h h pr jt cjt dj = Pt ct
(2.8)
h h The ?rst order conditions for nh t , mt and Bt yield the standard intratemporal
and intertemporal optimality conditions:
h v (1 ? nh t ? st ) h = wt u ( ch ) t
(2.9)
t u ( ch t ) ? ? ( Ph ) t
mh
Pth
= ?Et
u (ch t+1 ) h Pt+1
(2.10)
(1 + it )u (ch u ( ch t+1 ) t) = ?E t h h Pt Pt+1
(2.11)
The introduction of a time cost in order to take advantage of price promotions, on the other hand, creates a new intratemporal optimal margin. The ?rst order condition for sh t is
h v (1 ? nh t ? st ) =
? ??1 +
hp h ? h ch t ?s (f, st ) c?h t
1
??1 ?
? chr ?h t
??1 ?
u (ch t) (2.12)
h ?s (f, sh t)
pr chr ? pp chp ?h t ?h t ?h t ?h t Pth
u (ch t)
Equation (2.12) implies that the high elasticity consumer will choose optimal sh t by equating the utility cost incurred when looking for promotions and the
17
marginal utility gain derived from spending an extra unit of time looking for promotions. The right hand side of (12) has two components. The ?rst one comes from a re-composition of the consumption bundle. From (2.6), chp ?h t
??1 ?
? chr ?h t
??1 ?
is greater
than zero, implying an increase in overall consumption coming from higher quantih (f, sh ties of additional goods (a fraction ?s t ) of them) now available at promotional
prices. The second component is negative and corresponds to the utility loss because of higher spending after increasing the consumer’s time searching for promotions. When a good previously consumed at regular prices is found at a lower price as a result of additional time looking for price promotions, the consumer increases her consumption in a quantity such that her new expenditure on that good is greater than previously. This is a direct result of the elastic demand assumption typical in monopolistic competition models (since ? is greater than one, pr chr ? pp chp is ?h t ?h t ?h t ?h t negative). Combining equations (2.9) and (2.12), we have
h wt =
? ??1 +
hp h ? h ch t ?s (f, st ) c?h t
1
??1 ?
? chr ?h t
??1 ?
h ?s (f, sh t)
pr chr ? pp chp ?h t ?h t ?h t ?h t Pth
(2.13)
The left hand side of (2.13) is the relative price of leisure in terms of forgone labor income, while the right hand side is the relative price of leisure in terms of forgone gains from additional time spent looking for price promotions. Then, in equilibrium, consumers optimally choose their labor and shopping time allocations by equating the two alternative opportunity costs of an additional unit of leisure. 18
High Elasticity Consumers Low elasticity consumers di?er from high elasticity ones only in the price elasticity parameter of their consumption aggregator. Their consumption aggregator is given by ?
? ? ?? 1
?l (ft ,sl t)
1
? ?1 ?
with ? > ? > 1.
? cl t = ?
(clp jt )
0
dj +
?l (ft ,sl t)
(clr jt )
? ?1 ?
? dj ?
(2.14)
The LEC set of optimality conditions is analogous to the HEC one but changing ”h” by ”l” superscripts and ? by ? when needed. The LEC price aggregator is given by ?
1 ? 1? ?
?l (f,sl t) 1?? (pp dj + jt ) 0
1
? Ptl = ?
?l (f,sl t)
1?? ? (pr dj ? jt )
(2.15)
2.1.2
Firms
Cost Minimization There is a measure one continuum of ?rms indexed by j . Firm j minimizes costs wt Njt , where wt is the real wage and Njt is total labor hired by the ?rm, subject to a production restriction summarizing the available technology where output, cjt , is a function of labor and a productivity shock: cjt = ezt Njt , with E (zt ) = 0. From the ?rm’s cost minimization problem, real marginal cost is given by mcjt = mct = wt /ezt .
19
Price Setting Decision Flexible Regular Prices. The ?rm’s price setting problem consists of choosing
p 5 pr jt , pjt and fjt to maximize nominal pro?ts:
h h hp r h h hr ?jt = pp jt h? (fjt , st )cjt + pjt h 1 ? ? (fjt , st ) cjt l l lp r l l lr + pp jt (1 ? h)? (fjt , st )cjt + pjt (1 ? h) 1 ? ? (fjt , st ) cjt hp h h hr ? mcjt Pt {h?h (fjt , sh t )cjt + h 1 ? ? (fjt , st ) cjt lp l l lr + (1 ? h)?l (fjt , sl t )cjt + (1 ? h) 1 ? ? (fjt , st ) cjt }
(2.16)
subject to the demand equations (2.4), (2.5), and their LEC counterparts.
p The ?rst order conditions for pr j , pj and fjt are
hr l l lr h 1 ? ?h (fjt , sh t ) cjt + (1 ? h) 1 ? ? (fjt , st ) cjt =
1?
Pt mct pr jt
hr l l lr h[1 ? ?h (fjt , sh t )]?cjt + (1 ? h)[1 ? ? (fjt , st )]?cjt
(2.17)
hp l l lp h?h (fjt , sh t )cjt + (1 ? h)? (fjt , st )cjt =
1?
5
Pt mct pp jt
lp hp l l h?h (fjt , sh t )?cjt + +(1 ? h)? (fjt , st )?cjt
(2.18)
A real world justi?cation for having ?rms choosing fjt may come from the existence of market-
ing agreements in which a producer speci?es the number of times in which a retailer can put the good on sale in a given period (i.e. 20 days in the next three months). Then, the exact moment of promotion is chosen by the retailer and the producer’s decision ends up being about the fraction of time that the good is on sale. Alternatively, the ?rm may have multiple retail outlets and may put the unit on sale at only a fraction of its stores.
20
pp jt ? mct Pt pr jt ? mct Pt
hp l lp l h (fjt , sh h?f t )cjt + (1 ? h)?f (fjt , st )cjt h hr l l lr h?f (fjt , sh t )cjt + (1 ? h)?f (fjt , st )cjt
= (2.19)
Equations (2.17) and (2.18) equate the marginal revenue obtained from a variation in demand because of a change in a speci?c price (regular or promotional), with the marginal production cost of satisfying that marginal demand. Equation (2.19), on the other hand, comes from the fact that ?rms choose the fraction of time that they put their good on promotion. The left hand side is the marginal pro?t obtained from demand at promotional prices when increasing fjt , while the right hand side is the marginal pro?t obtained from demand at regular prices when increasing fjt . Further intuition can be gained after some rearrangement in order to re-express (2.19) as
p hp p lp h r hr l r lr h?f (fjt , sh + (1 ? h)?f (fjt , sl t ) pjt cjt ? pjt cjt t ) pjt cjt ? pjt cjt lp hp h hr l lr + (1 ? h)?f (fjt , sl h?f (fjt , sh t )mct Pt cjt ? cjt t )mct Pt cjt ? cjt
= (2.20)
The two terms in the left hand side of (2.20) corresponds to the marginal revenue coming from increasing the probability with which the ?rm o?ers its good
h h l l l on promotion. ?f (fjt , sh t ) = st and ?f (fjt , st ) = st are the additional fractions
of consumers that ?nd the good at promotional prices after the ?rm increases ft ,
hp p lp r hr r lr and pp jt cjt ? pjt cjt and pjt cjt ? pjt cjt correspond to the additional revenue coming
21
from these new purchases.6 On the other hand, the two terms in the right hand side of the equation correspond to the marginal cost associated with increasing ft ,
lp hr lr with chp jt ? cjt and cjt ? cjt representing the change in production needed to satisfy
the higher demand coming from additional consumers able to acquire the good at promotional prices. Notice that the standard monopolistic competition model is nested in the model presented here. To see this, take (2.17) and let h tend to 1. The equation reduces to:
pr jt = Pt
? ??1
mcjt
(2.21)
With no consumer heterogeneity (h = 1), f = 0 and therefore ?h = 0. Regular prices then are the only ones in the economy and Pth in (2.7) is reduced to ?
1
1 ? 1? ?
With h = 1, Pt =
Pth ,
and (2.21) corresponds to the pricing optimality condi-
1?? ? Pth = ? (pr dj jt ) 0
(2.22)
tion of a model with monopolistic competition and ?exible prices. Sticky Regular Prices. For the exercises performed in the following sections, it will prove useful to amend the model by including a nominal rigidity in the regular price. For this purpose, it is assumed that regular prices are subject to Calvo staggering. There may be reasons to consider ridigity in promotional prices
6
Since ? > 1, revenue from sales of good j at promotional prices is greater than revenue from
hp p lp r hr r lr sales at regular prices, so the terms pp jt cjt ? pjt cjt and pjt cjt ? pjt cjt , are positive.
22
as well.7 However, there is evidence that sale prices are less sticky than regular ones (Klenow and Kryvtsov (2008)) and allowing for rigidities only on regular prices is a simple way of capturing this fact. Also, stickiness in regular prices su?ces to generate the type of reference price rigidity found in recent studies on micro price data like Eichenbaum et al. (2011) and Klenow and Malin (2010), and facilitates comparison with Guimaraes and Sheedy (2011) who also impose a Calvo rigidity only in regular prices and who argue that their exercise will provide an upper bound for price ?exibility in the aggregate if there is rigidity in promotional prices in reality. When the regular price is sticky, the price setting problem of the ?rm becomes
?
p pr jt ,pjt ,fjt
max Et
s= t
?
s? t
h h ?t+s/t {pp js h? (fjs , ss )
Psh pp js Psl pp js Psh ? pr jt Psl ? pr jt Psh pp js Psl pp js Psh ? pr jt Psl ? pr jt
? ?
?
ch s
?
+pp js (1 +
? pr jt h
? h)?
h
l
(fjs , sl s)
cl s
?
1??
(fjs , sh s)
ch s cl s}
?
? l l +pr jt (1 ? h) 1 ? ? (fjs , ss ) h
? mcjs Ps {h?
(fjs , sh s) (fjs , sl s)
ch s
?
+(1 ? h)? +h 1??
h
l
cl s
?
(fjs , sh s)
ch s cl s} (2.23)
+(1 ? h) 1 ? ?l (fjs , sl s)
Where ? is the probability of not being able to change the regular price in the period, and ?t+1/t is the ?rm’s stochastic discount factor for nominal payo?s.
7
For example, ?rms could be constrained in their ability to change their promotional strategy
because of contractual pricing arrangements between producers and retailers.
23
The ?rst order conditions for pp jt and fjt are the same as in the ?exible price
? scenario, and the ?rst order condition for pr jt is
? ? pr jt
(? ? 1)Et
t=s ?
hr ?s?t ?t+s/t h 1 ? ?h (fjs , sh js ) cjs
? + pr jt
(? ? 1)Et
t=s ?
lr ?s?t ?t+s/t (1 ? h) 1 ? ?l (fjs , sl js ) cjs
=
?Et
t=s ?
hr ?s?t ?t+s/t h 1 ? ?h (fjs , sh js ) cjs mcjs Ps
+ ?Et
t=s
lr ?s?t ?t+s/t (1 ? h) 1 ? ?l (fjs , sl js ) cjs mcjs Ps
(2.24)
Notice that when h = 1 (and therefore ft = 0) there is only one type of consumer in the economy and Pt = Pth . In this case this last equation collapses to
? pr jt
? Et t=s ?s?t ?t+s/t chr js Ps mcjs = ? s ? t ??1 Et t=s ? ?t+s/t chr js
?
(2.25)
Which is the standard optimal pricing equation in a model with Calvo rigidities and no capital. Further details on the solution of the sticky regular price case are provided in Appendix 1.
2.1.3
The Government
The Government Budget Constraint Each period, the government satis?es the following budget constraint:
(Bt ? Bt?1 ) + (Mt ? Mt?1 ) = Tt + it?1 Bt?1 24
(2.26)
where Tt are lump sum transfers.
Monetary Policy It is assumed that the Central Bank reacts to in?ation and output growth according to the following interest rate rule: ? ? ? ? ?
1 + it 1+i
=
e e?
?t
?1
yt yt?1
?2
1??R
1 + it?1 1+i
?R ?
e?R ?R,t
(2.27)
where ?t is the in?ation rate, yt is total output, ? and i are the steady state in?ation and interest rates, and ?R,t is a monetary policy shock. This speci?cation corresponds to the one used by Aruoba and Schorfheide (2011) with the exception that these authors also introduce a time varying in?ation target as part of the interest rate feedback rule.
2.1.4
The Economy’s Resource Constraint
The economy’s resource constraint can be recovered combining the consumers’ budget constraints, the government balanced budget equation and the expression for ?rms’ pro?ts. Pre-multiplying the HEC’s budget constraint (2.3) by h and the LEC’s budget constraint by 1 ? h and adding up we have:
h h h h h h h h Pth wt nt + mh t?1 + (1 + it?1 )Bt?1 + ?t + Tt ? Pt ct ? mt ? Bt =
(2.28)
(1 ? h)
l l Ptl wt nt
+
ml t?1
+ (1 +
l it?1 )Bt ?1
+ ?t + Tt ?
Ptl cl t
?
ml t
?
l Bt
Using equation (2.8) and its analogue for low elasticity consumers and applying symmetry yields: 25
h h h h Pth wt nt + mh t?1 + (1 + it?1 )Bt?1 + ?t + Tt p hp h h r hr h h ? h ?h (ft , sh t )pjt cjt + 1 ? ? (ft , st ) pjt cjt + mt + Bt l l l (1 ? h) Ptl wt nt + ml t?1 + (1 + it?1 )Bt?1 + ?t + Tt p lp l l r lr l l ? (1 ? h) ?l (ft , sl t )pjt cjt + 1 ? ? (ft , st ) pjt cjt + mt + Bt
=
(2.29)
De?ne the economy’s labor income in nominal terms as
h h l l l Pt wt Nt = hnh t Pt wt + (1 ? h)nt Pt wt l where Nt = Njt dj = hnh t + (1 ? h)nt . 0 1
(2.30)
Finally, plugging equations (2.26), (2.30) and the expressions for ?rms’ pro?ts and marginal costs into (2.29), we have:
h l ez t hnt + (1 ? h)nt
hp h h hr = h?h (ft , sh t )ct + h 1 ? ? (ft , st ) ct lp + (1 ? h)?l (ft , sl t )ct lr + (1 ? h) 1 ? ?l (ft , sl t ) ct
(2.31)
where (2.31) is the economy’s resource constraint.
2.1.5
Characterizing the Economy-wide Price Level
The ?nal equilibrium condition is the relationship between the economy wide price
r level, Pt , and the two types of prices faced by consumers, pp t and pt . In order to ?nd
this, de?ne the economy’s total consumption expenditure as 26
l l Pt ct = hPth ch t + (1 ? h)Pt ct
(2.32)
where
1
ct =
0
hp h h hr l l lp l l lr cjt = h?h (ft , sh t )ct + h[1 ? ? (ft , st )]ct +(1 ? h)? (ft , st )ct +(1 ? h)[1 ? ? (ft , st )]ct
Using equation (2.8) and its analogue for the LEC’s case, we have:
? P t ct = h ?
?
?h (ft ,sh t) hp pp jt cjt dj + 0
1
Assuming ?exible regular prices and applying symmetry, we have:
? + (1 ? h) ?
?
?h (ft ,sh t) ?l (ft ,sl t) lp pp jt cjt dj + 0
hr ? pr jt cjt dj ? 1
? ?
?l (ft ,sl t)
lr ? pr jt cjt dj ?
(2.33)
hp p h h hr r Pt ct = h?h (ft , sh t )ct pt + h 1 ? ? (ft , st ) ct pt lp p l l lr r + (1 ? h)?l (ft , sl t )ct pt + (1 ? h) 1 ? ? (ft , st ) ct pt
(2.34)
Rearranging, we have:
r Pt = ?t pp t + (1 ? ?t )pt
(2.35)
where
27
?t =
hp l l lp h?h (ft , sh t )ct + (1 ? h)? (ft , st )ct hp h hr l lp l lr h l l h?h (ft , sh t )ct + h 1 ? ? (ft , st ) ct + (1 ? h)? (ft , st )ct + (1 ? h) 1 ? ? (ft , st ) ct r Equation (2.35) de?nes Pt as a time-varying weighted average of pp t and pt ,
with the weights of each price given by the ratio of goods purchased at that price with respect to the total quantity of goods consumed in the economy. From (2.35) we can also write
1 = ?t mct
pp t Pt mct
+ (1 ? ?t )
pr t Pt mct
(2.36)
r where, from the ?rm’s ?rst order conditions for pp t and pt , the optimal real
markups associated with each price are given by
lp hp l l h?h (ft , sh pp t t )?ct + (1 ? h)? (ft , st )?ct = hp lp l l Pt mct h?h (ft , sh t )(? ? 1)ct + (1 ? h)? (ft , st )(? ? 1)ct
and
lr hr l l h 1 ? ?h (ft , sh pr t ) ?ct + (1 ? h) 1 ? ? (ft , st ) ?ct t = hr l lr l Pt mct h 1 ? ?h (ft , sh t ) (? ? 1)ct + (1 ? h) 1 ? ? (ft , st ) (? ? 1)ct
Then, equation (2.36) de?nes the economy-wide markup as a time-varying weighted average of the real markups associated with the two prices available in the economy.
2.1.6
Stochastic Processes
The stochastic process for productivity zt is given by 28
z zt+1 = ?z zt + ?t ;
z ?t ? i.i.d.(0, ?z )
(2.37)
Finally, it is assumed that the monetary policy shock ?R,t is serially uncorrelated with mean zero and variance one. Then, the autoregresive component in monetary shocks is given by the interest rate smoothing parameter ?R in (2.27).
2.1.7
Equilibrium
hr hp l lr An equilibrium for this economy is de?ned as a set of allocations {ch t , ct , ct , ct , ct , l h l h l h h l l h clp t , nt , nt , Nt , st , st , ft }, portfolio choices {mt , mt , Bt , Bt , Mt , Bt }, prices {Pt , Pt , Pt , p h l pr t , pt , wt , wt , wt , it }, and transfers {Tt , ?t } such that: hp h h h h i) {chr t , ct , nt , st , mt , Bt } solve the HEC utility maximization problem. lp l l l l ii) {clr t , ct , nt , st , mt , Bt } solve the LEC utility maximization problem. p iii) {pr t , pt , ft } are such that ?rms maximize pro?ts.
iv) Aggregation satis?es equations (2.2), (2.7), (2.14) , (2.15), (2.30) and (2.35). v) The government runs a balanced budget.
l h l vi) Markets clear: Nt = hnh t + (1 ? h)nt , Bt = hBt + (1 ? h)Bt , Mt = l hmh t + (1 ? h)mt .
2.1.8
Price Discrimination in General Equilibrium
As observed in the model’s equilibrium conditions, this economy has the feature that both regular and promotional prices coexist at the same time for each ?rm. The
29
key modeling element behind this result is the fact that consumers must spend time looking for price promotions. This is formally stated in the following propositions: Proposition 1: Given strictly increasing utility in consumption and leisure, in a general equilibrium with monopolistic competition (? > 1, ? > 1) and with
l consumers looking for price promotions (sh t ? (0, 1), st ? (0, 1)), ?rms always price p discriminate by setting a regular price greater than the promotional one (pr jt > pjt ). p Proof: Suppose not. That is, let pr jt ? pjt . Consider the HEC case; using the
demand equations (2.4) and (2.5), equation (2.12) can be re-expressed as:
v (1 ?
nh t
?
sh t)
=u
h h (ch t )?s (ft , st )
1 ??1
ch t
1?? 1?? pp ? pr jt jt
Pth
1??
(2.38)
p Given ? > 1 and the assumption that u(·) is strictly increasing, pr jt ? pjt
implies that the right hand side of equation (2.38) is lower or equal to zero, so (2.38) is satis?ed only when v (·) ? 0, a contradiction that violates the assumption that v (.) is strictly increasing. Proposition 2: Given strictly increasing utility in consumption and leisure, in a general equilibrium with monopolistic competition (? > 1, ? > 1) and with
l consumers looking for price promotions (sh t ? (0, 1), st ? (0, 1)), ?rms follow an
active promotional policy by making the promotional price available with a positive probability ft > 0. Proof: analogous to the one for Proposition 1. In this model, then, ?rms will always price discriminate; that is, they will set
p two di?erent prices for the same good (pr jt > pjt ), and they will always follow an
30
active promotional strategy (fjt > 0), making their promotional price available for consumers willing to spend the time needed to ?nd a promotion and take advantage of the lower price. The intuition behind this result is that there is a cost associated with ?nding a price promotion, and that cost is paid only by consumers and not by ?rms. If, in a given period, a ?rm decides not to o?er promotions (fjt = 0), it will charge only its regular price at every moment of time within that period without distinguishing between consumption demands. However, recognizing that looking for discounts is costly for consumers and that only a fraction of them will access price promotions, the ?rm can increase pro?ts by making the promotional price available with a given probability (fjt > 0) and therefore costlessly distinguishing between two di?erent types of demand: demand from consumers that ?nd the price promotion and demand from consumers that don’t.8 This follows the basic principle of using promotions for price discrimination purposes studied in the Industrial Organization and Marketing literature: when a ?rm wants to use a price promotion as a price discrimination tool, it should try to make it easy for some consumers to access the promotion, but harder for others; that is, the promotion must impose some cost on which consumers di?er, rewarding the people willing to bear that cost (see Banks and Moorthy (1999) and Lu and Moorthy (2007)).
8
The ?rm can price discriminate even if it puts its good on promotion all the time (ft = 1).
The reason for this is that since consumers do not spend all of their time looking for promotions
l h h l l (sh t < 1, st < 1), only fractions ? (ft , st ) and ? (ft , st ) of the ?rm’s good are sold at promotional
prices, with the complement transacted at the regular price.
31
The most salient real-world example of price promotions associated with consumer time costs is the use of coupons.9 Coupons are certainly an important promotional vehicle in the United States, but there are several other promotional arrangements that are associated with di?erent types of consumer costs; examples of these are mail-in rebates, cash-back o?ers, loyalty cards, reward programs and discount clubs.10
9
11
The mechanism developed here can be thought of as a reduced form
There are several types of time costs associated with the usage of coupons beyond the standard
“cut and clip” costs: (i) in order to take advantage of the promotion, the consumer may need to spend time looking for the coupon (i.e. going over mailed ?iers and newspapers, or browsing the internet); (ii) it may be necessary to prepare shopping lists so the coupon may be used in a future shopping trip before its expiration date; (iii) coupon redemption may be conditioned on some information exchange with the consumer (i.e. logging into a retailer’s web page and providing contact information, or participating in an on-line consumer survey).
10
According to NCH Marketing Services Inc., in 2009, 311 billion coupons were distributed by
consumer packaged-goods companies in the United States, 3.2 billion of these were redeemed, and the redemption value reached 3.5 billion dollars. Also, a recent consumer study by Inmar Inc. reports that 75% of the participants in a shopping habits survey conducted by the Food Marketing Institute stated that coupons had at least some in?uence on their decision to buy a product. Inmar also reports that in the ?rst half of 2009, 68% of US households participating in Nielsen’s Homescan Consumer Panel used at least one coupon.
11
An interesting fact about some of these promotional vehicles is that they are not used only by
grocery stores and supermarkets, which have received most of the attention in recent studies on the implications of micro price data for macroeconomic modeling. Mail-in rebates, for example, are widely used by home appliance providers and electronics retail stores, with o?ers ranging from small-ticket items like computer accessories to big-ticket ones like home entertainment systems. Di?erent types of cash-back options are also very common among automobile dealers. On the other hand, loyalty cards, typical in supermarkets and grocery stores, are also common among
32
capturing a broader fact with interesting implications when modeling price discrimination in monetary models: not every price promotion is realized, and whether a consumer ends up receiving a discount or not often depends endogenously on how much time, e?ort and money she is willing to invest in taking advantage of the o?ered promotion. This could be the case even for on-shelf promotions in the sense that even though there is no explicit consumer cost associated with them, a shopper may need to spend some time and attention comparing prices and brands before ?nally picking the products o?ered on discount.12 Thus, it is the fact that price promotions are costly for the consumer that ensures the coexistence of the two prices in the model economy. This will allow for a large amount of ?rm level transaction price variation over time even in the absence of shocks, a result consistent with Nakamura’s (2008) ?nding of a high amount of idiosyncratic price variation in product categories with temporary sales, suggesting that retail prices may vary largely as a consequence of dynamic pricing strategies on
book, music and electronics retailers, while service providers like banks and airlines often o?er loyalty programs associated with their products. Finally, discount clubs include warehouse clubs that sell grocery store and supermarket products, but also providers of big-ticket items like home furnishings. Also, wholesale clubs like Costco and BJ’s sell a variety of non-supermarket household goods, including TVs, books, clothes, etc.
12
Sometimes this may require shopping trips to di?erent locations in order to compare on-shelf
promotions between retailers. When the product is not o?ered at a physical location, taking advantage of price promotions may require spending time browsing the internet looking for the best available deals. Think, for example, about buying a plane ticket using kayak.com instead of visiting a speci?c airline, or ?nding discount lodging at hotwire.com instead of contacting a particular hotel.
33
the part of retailers or manufacturers. In the model, this dynamic pricing strategy consists of ?rms o?ering costly promotions and choosing the fraction of time at which they are available, but being indi?erent about the exact moment of time at which a promotion is realized. Consider for example a case with no shocks and zero in?ation in which ?rms choose to o?er their goods on promotion 50% of the time. Panel a) in Figure 2.1 shows a sample time path for the price strategy of an individual ?rm that randomly chooses when to o?er a price promotion, subject to ensuring that the the promotion is available half of the time. The regular price will be o?ered all the time, while the promotional price is o?ered only at intervals. Panel b) depicts the time series of the minimum price available, which is equal to
p pr t when no promotion is o?ered and pt when a promotion is in place.
The following sections show how this type of strategic combined pricing, with nominal rigidity in regular prices, helps in generating price behavior similar to that documented in the recent microeconomic evidence on price-setting, and how this pricing has important implications on the way real variables respond to monetary shocks. Among recent research on sale prices in monetary models, the Kehoe and Midrigan (2007, 2008, 2010) framework is an example of a model in which prices ?uctuate only in response to stochastic shocks and not to randomization decisions made for price discrimination purposes. In their setup, every period a ?rm can either pay a large ?xed cost and change their price permanently or pay a smaller cost and change their price only for one period. Kehoe and Midrigan’s models, therefore, require time varying shocks and price rigidities in order to generate temporary 34
Figure 2.1: FIRMS PRICES IN THE ABSENCE OF MACRO SHOCKS
movements away from the regular price. Closer in spirit to the model presented here is the work of Guimaraes and Sheedy (2011). They develop a model in which households consume a continuum of heterogeneous goods and a continuum of heterogeneous brands for each good. Consumers have di?erent price sensitivities with respect to di?erent sets of goods, being loyal to speci?c brands for a given measure of products (that is, they do not receive utility from consuming any alternative brand) but being bargain hunters willing to substitute between di?erent brands for the rest of the goods. Each ?rm 35
produces a brand speci?c product and faces a measure of loyal consumers and a measure of bargain hunters. Firms do not know the type of any individual consumer, and cannot practice price discrimination directly. Instead they follow the strategy of holding periodic sales in order to target the two types of consumers at di?erent moments of time. This is done by randomizing the timing of sales after choosing a fraction of time (i.e. a number of moments within a given period) at which the ?rm charges a lower price. At any one point in time, all consumers recive the same price. As in the framework presented in this document, Guimaraes and Sheedy’s (2011) setup is able to generate price ?uctuations even in the absence of the standard aggregate or idiosyncratic shocks included in DSGE models, as a result of the dynamic pricing strategy followed by ?rms that target di?erent types of customers. In contrast to Guimaraes and Sheedy, however, the model developed in this paper does feature price discrimination at many points in time as part of the ?rm’s optimal
p dynamic pricing strategy: for a fraction ft of the time, both pr t and pt coexist and
transactions are made using both prices. This paper’s framework thus allows for a distinction between price-quote and realized-price series. As I will show below, when combined with a nominal rigidity in the de?nition of regular prices, the model delivers individual price series with the type of rigidity recently found in studies on reference prices in micro price data, but with di?erent macroeconomic implications from those found by Guimaraes and Sheedy (2011).
36
2.2
Solution Method and Parameter Values
The model is solved around a zero-in?ation steady state applying Schmitt-Grohe and Uribe’s (2004a) local approximation algorithm. I assume the following functional forms:
h u(ch t ) = log (ct ) l u(cl t ) = log (ct )
t ?( P h ) = ?log t
mh
mh t h Pt ml t l Pt
?( P lt ) = ?log
t
ml
h h h v (1 ? nh t ? st ) = ?log 1 ? nt ? st l l l v (1 ? nl t ? st ) = ?log 1 ? nt ? st
There are fourteen parameters in the model: the intertemporal discount factor, ? ; the constants pre-multiplying the money and leisure utility terms, ? and ?; the measure of high elasticity consumers, h; the elasticities of substitution for HECs and LECs, ? and ? ; the probability of a ?rm not being able to change its regular price, ?; the interest rate smoothing parameter, ?R ; the in?ation and output growth weights in the Central Bank’s interest rate rule, ?1 and ?2 ; and the parameters governing the stochastic processes for productivity and monetary policy, ?z , ?z and ?R . The length of each period is one week, so the discount factor ? is set at 0.961/52 . The Calvo parameter, ?, is set at 0.974, implying that, on average, ?rms change their regular prices every 9 months (39 weeks); this time between changes is in the middle range of the estimates reported by Nakamura and Steinsson (2008). The values for the productivity stochastic process, ?z and ?z , correspond to the weekly counterparts
37
of the quarterly values used in Hansen (1985), while the parameters for the interest rate rule and the monetary policy stochastic process are taken from Aruoba and Schorfheide (2009): ?1 = 1.7, ?2 = 0.86, ?R = 0.611/13 , ?R = 0.0036/13. The values of ?, ?, ?, ? and h are chosen to match ?ve steady state calibration targets: average hours worked of 1/3, a weekly velocity of money of 0.15, a ratio of time spent looking for promotions with respect to hours worked of 1/4, a probability with which goods are o?ered on promotion of 0.7, and an average gross markup of 1.4. The target value for total hours worked, hnh + (1 ? h)nl , is standard in the literature. The value for money velocity was computed using the formula V = GDP/(52 · M 1), where M 1 is the weekly seasonally adjusted series for M1 of the Board of Governors of the Federal Reserve System, and GDP is annual nominal Gross Domestic Product. The 1975:1-2009:9 average is 0.15, close to the weekly analogue of the quarterly value calculated by Aruoba and Schorfheide (2009) using sweep-adjusted M 1 data. Time spent looking for price promotions is the only type of shopping time in the model. Therefore the target for the shopping/working time ratio is taken from US time surveys with information on daily time spent purchasing goods and services, and is close to the value used in Arseneau and Chugh (2007).13 The targeted markup is within the range of estimated values for the US and
13
The American Time Use Survey (ATUS) provides nationally representative estimates of how
and where Americans spend their time. Data ?les are available from 2003 to 2009 and can be accessed athttp://www.bls.gov/tus/.
38
close to values used in trade and macroeconomic studies such as Bernard et al. (2003) and Biblie et al (2007). The choice of the target value for f requires more elaboration. In the model, f is the fraction of time ?rms o?er their goods at promotional prices. Moreover, this is the only type of price promotion considered in the framework developed in Section 2. Given the model’s de?nition of promotional prices as only available when o?ered and only to those who look for them, the empirical counterpart of f should correspond to a type of promotion that is not always o?ered and that requires some search e?ort from the consumer in order to be realized. The James M. Kilts Center at the University of Chicago Booth School of Business provides data useful for constructing this target. The Booth School provides several publicly available datasets on weekly store-level transaction prices for over 100 stores operated by Dominick’s Finer Foods (DFF), which have been used in various macroeconomic studies such as Golosov and Lucas (2007), Midrigan (2008) and Kehoe and Midrigan (2007,2008). One of these datasets, the Customer Count Files, has information on total coupon redemption ?gures by DFF de?ned productcategory. Since sale coupons are a natural example of the type of promotion discussed in Section 2, I use this database to construct a proxy for the probability that ?rms o?er their goods at promotional prices in a given period. I proceed as follows: ?rst, for each product category I construct a dummy variable, dt , equal to 1 if at least one coupon was redeemed in a given week (that is, if the coupon redemption ?gure is di?erent from zero). Next, I compute the fraction of time at which category k was o?ered on promotion: 39
fk =
t
dt /(number of weeks).
Finally, I compute the average across product categories: f=
k
fk /(number of good categories).
The underlying assumption is that if a promotional price is available in a given week, then there is at least one person that takes advantage of it (alternatively, at least one coupon is redeemed). Therefore, I assume that if the coupon redemption ?gure in a given week is zero (dt = 0), then no coupons were o?ered that week. When considering a sample of all categories for which coupons were redeemed at least once in the sample period, the sales-weighted value for f is 0.87. When considering all product categories, the value is 0.7. Appendix 2 provides more details on these calculations. Of course, it would be ideal to perform a similar calculation for a broader range of goods and sectors. However, in spite of this limitation, and given the lack of richer data on non-shelf price promotions for other sectors and goods, the above described calculation provides an empirical benchmark consistent with the theoretical de?nition of f and with the model’s de?nition of promotional prices. Table 2.2 presents the model’s steady state under this parameterization, where pp and pr are relative prices with respect to the economy-wide price and ah and al are HEC and LEC real balances with respect to each consumer’s e?ective price index. HECs represent 9% of the economy’s population and spend a large fraction of their time working, and therefore are able to consume more than LECs: ?(f, sh )chp + 1 ? ?(f, sh ) chr = 0.84 ?(f, sl )clp + 1 ? ?(f, sl ) clr = 0.28 40
As expected, HECs spend a lower fraction of their time looking for price promotions. HECs are very price sensitive, and whey they ?nd a promotion they substitute a lot, buying very large quantities of a good when it is found on sale, so they are able to take advantage of price discounts even when spending only a very small fraction of time looking for them. LECs, on the other hand, substitute less when a good is on sale, and need to spend a higher fraction of time looking for promotions in order to take advantage of price discounts. Under the current parameterization, the ?rm sets an optimal discount of 31%, very close to the values reported by Nakamura and Steinsson (2008), 30%, and Klenow and Kryvtsov (2008), 25%. The discount price is available 70% of the time, but only 6% of total transactions are realized at promotional prices. This value is close to the expenditure-weighted fraction of price quotes that are sales reported by Nakamura and Steinsson (2008), 7.4%.
2.3
2.3.1
The Workings of the Model
Individual Price Setting Behavior
A ?rst step in evaluating the performance of the model is to assess its ability to generate individual price series similar to those reported in recent microeconomic studies of price setting. As mentioned in Section 1, a recently documented feature of the CPI data is that prices including sales tend to change roughly every quarter, while prices excluding sales tend to remain unchanged for two to three quarters
41
Table 2.1: Parameter Values
Parameter
Intertemporal discount factor Fraction of HECs Scale parameter leisure utility Scale parameter money utility HEC elasticity of substitution LEC elasticity of substitution Calvo parameter for regular prices Interest rate smoothing parameter In ation weight interest rate rule Output growth weight interest rate rule Standard deviation for monetary policy shocks Productivity autoregressive coe cient Standard deviation for productivity innovations
? h ? ? ? ?
Value
0.961/52
Comment
Length of a period = 1 week To match f
= 0.7
0.09 0.21 0.005 20.26 2.44 0.974
To match n = 1/3 To match V elocity = 0.15 To match s/n = 1/4 To match M arkup = 1.4 Implies a time between changes of 39 weeks Weekly analogue ofAruoba and Schorfheide's (2009) quarterly value From Aruoba and Schorfheide (2009)
?
?R
0.611/13
?1
1.7
?2
0.86
From Aruoba and Schorfheide (2009)
?R
0.0036/13
Weekly analogue ofAruoba and Schorfheide's (2009) quarterly value Weekly analogue of Hansen's (1985) quarterly value Weekly analogue of Hansen's (1985) quarterly value
?z
0.951/13
?z
0.007/13
(Nakamura and Steinsson, 2008; Klenow and Krystov, 2008; Klenow and Malin, 2010). Also, new evidence from high frequency scanner data has found that nominal rigidities take the form of inertia in reference (modal) prices, with weekly prices ?uctuating around a reference value that tends to remain constant over extended periods of time (see Kehoe and Midrigan (2007, 2008), and especially Eichenbaum
1
et al., (2011)). This point is illustrated in Figure 2.2, which displays the time series 42
Ì
Ä ¾ ÅÅÈÈ
Table 2.2: Steady State Values
? = ?h = ?l = 0
À
chr = 0.05 chp = 88.9 nh = 0.93 sh = 0.01 ? h (f, sh ) = 0.009
Ä
ÖÑ
pr = 1.11 pp = 0.77 discount = 0.31 f = 0.70 ? (f, s) = 0.06
clr
= 0.25
clp = 0.63 nl = 0.27 sl = 0.09 ? l (f, sl ) = 0.06
behavior of four selected DFF items. From the ?gure one can see that there seems to be an inertial reference price (i.e. the most observed price in a given time window) and prices tend to return to this reference value after having deviated from it. The model is able to replicate this type of behavior in prices, because it di?erentiates not only between regular and promotional prices, but also between pricequotes (like the ones recorded in CPI data) and realized transactions prices (like the ones recorded in scanner data). To see this, Figure 2.3 presents individual price simulations of the sticky regular price version of the model. Panel a) presents the regular and promotional price series of an individual ?rm for a simulation of 250 weeks.14 . The graph depicts the optimal regular price that the ?rm would set each period were it able to do so. However, the ?rm is subject to a Calvo friction and it is not able to adjust its regular price every period, so
14
The series is constructed by iterating forward the relative price optimal decision rules of the
linearized model for 250 periods, and then by simulating the behavior of an individual ?rm. Each period, there is a probability 1 ? ? that the ?rm will be able to set its price at the optimal price
r? r r level pr jt = pt , and a probability ? that the ?rm’s price will not change, pjt = pjt?1 .
43
Figure 2.2: PRICE EVOLUTION IN FOUR SELECTED PRODUCTS
its actual regular price, depicted by the dotted line, tends to remain unchanged for several periods, adjusting to the optimal value every time that the ?rm is allowed to change its price. Panel b) presents the evolution of the two prices available to consumers. The regular price is available in any period. The promotional price, however, is not always available, since the ?rm optimally chooses the fraction of time at which the price is o?ered. That is, in each period there is a probability ft that the lowest available price will correspond to pp jt and a probability 1 ? ft that the only available price will be pr jt . Consider the exercise of constructing a price quote series reporting the lowest available price in each period. In this case, the series will change almost every period, with frequent ?uctuations between the regular and promotional price and with occasional shifts to the regular one. The series of price quotes is presented in
44
Figure 2.3: SIMULATED PRICE FOR AN INDIVIDUAL FIRM
a) Regular Prices (optimal: solid line, realized: dashed line) and Optimal Promotional Prices (circle markers)
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.690
b) Available Prices (Regular: dashed line, Promotional: solid line)
1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.690 0.689
0.689
0.688 0.687 0.686 0.685
1 51 101 151 201
0.688
0.687 0.686
0.685
1 51 101 151 201
c) Minimum Available Price
1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999
1 51 101 151 201
d) Realized Price
1.000 1.000 1.000
1.000
1.000 1.000 1.000 0.999
1 51 101 151 201
0.690 0.690 0.689 0.689 0.688 0.688 0.687 0.687 0.686 0.686 0.685
1 51 101 151 201
0.690 0.690 0.689 0.689 0.688 0.688 0.687 0.687 0.686
1 51 101 151 201
panel (c). The price series described in panel (c), however, corresponds to quoted prices
45
Figure 2.4: SIMULATED PRICE FOR AN INDIVIDUAL FIRM: THE CASE OF POSITIVE STEADY STATE INFLATION
a) Regular Prices (optimal: solid line, realized: dashed line) and Optimal Promotional Prices (circle markers)
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1 51 101 151 201
b) Available Prices (Regular: dashed line, Promotional: solid line)
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1 51 101 151 201
c) Minimum Available Price
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1 51 101 151 201 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1 51
d) Realized Price
101
151
201
and not to the ones resulting from actual transactions. Each period, there is a probability ?t that the good will be purchased at the promotional price pp j , and a probability 1 ? ?t that it will be purchased at the ?rm’s regular price.15 The series of realized prices is presented in panel (d), showing the type of rigidity reported by Eichenbaum et. al. (2011). Realized prices show rigidity in the form of inertial reference values to which prices tend to return after having deviated from them.16
15 16 h l l ?t = h?t (fjt , sh t ) + (1 ? h)?t (fjt , st )
In terms of constructing the underlying price series from observed data, this exercise is more
consistent with the use of transaction-based datasets like supermarket scanner data than with price quotes like those recorded by BLS visitors. For example, think about a grocery store that uses loyalty cards in a way such that every week some of its products are o?ered on promotion and
46
The model with zero steady state in?ation is able to replicate the behavior of observed individual time series as long as these do not trend because of in?ation pressures. Since some individual price series seem to show an upward trend (see for example the Kellogg’s Corn Flakes example in Figure 2.2), the model was also solved around a 0.05 percent weekly steady state in?ation rate; this value corresponds to an annual cumulative in?ation rate of 3 percent (the post-Volker average in the US).17 The simulated price series are presented in panels (a) to (d) of Figure 2.4. The model, then, is able to deliver price-quote and realized-price series consistent with the microeconomic evidence. Because of the Calvo-type rigidity, the time series behavior of an individual ?rm’s regular price will be highly inertial. When including price promotions, on the other hand, prices will change very frequently. This behavior is consistent with the recent evidence on CPI price quotes that ?nds
their price tags display both the regular and promotional price. According to the BLS, a sale price must be temporarily lower than the regular price, be available to all consumers, and be usually identi?ed by a sign or statement on the price tag (Klenow and Krystov, 2008). In the speci?c case of loyalty cards, discounts are reported as only if the outlet con?rms that more than 50% of its customers use these cards (Nakamura and Steinsson, 2008). So, in this example, if the percent of customers using loyalty cards is lower to 50%, a price-quoting visitor will not even record the sales. But even if the sales were recorded, the visitor could gather data on both the regular and promotional price but she would have no information on the number of transactions closed at each price. A rich enough scanner dataset, on the other hand, would record both the regular and the promotional price as well as whether the loyalty card was used at the time of each transaction.
17
The pattern of steady state allocations when the model is solved around a positive in?ation
rate is similar to the one observed in the zero in?ation case but with a higher equilibrium discount, 0.45.
47
that the median frequency of price changes is sensitive to the inclusion or exclusion of sales (Nakamura and Steinsson, 2008; Klenow and Krystov, 2008; Klenow and Malin, 2010).
2.3.2
Does Micro Flexibility Translates Into Higher Neutrality at the Macro Level?
Figure 2.5 presents the responses of output to a monetary shock in the model with price promotions and sticky regular prices and in a standard model with no consumer heterogeneity and sticky prices. The latter model with no price promotions was calibrated to replicate the steady state hours, velocity and markup targets presented in Table 2.1 and with the same Calvo parameter used in the price promotions model. The model with price promotions presents a smaller and less persistent output response, with an impact deviation equal to one third of the one obtained with the standard Calvo model. Figure 2.6 helps in further understanding the intuition behind this result. Given the introduction of a New Keynesian interest rate rule, the model assumes that the impact of monetary policy on output operates through the real interest rate. There is thus a mapping between the time paths of output and the real interest rate. Panel (a) depicts the responses of these variables for both models. Real variables in the promotions model follow the same pattern as those of the Calvo model, but with smaller and less persistent responses. Panel (b) presents the responses of the relative regular and promotional prices,
48
p p r? r? ? pr t and pt , and the optimal promotional discount ((pt ? pt )/pt ).The graph also
shows the average price response constructed using ?t and 1 ? ?t as weights for the promotional regular price components respectively. After a shock to the interest rate, ?rms react mainly by reducing their promotional price and therefore increasing their optimal discount. Thus it is the possibility of adjusting their promotional price that provides ?rms with an alternative channel of adjustment when facing monetary shocks. Finally, panel (c) presents the responses of the probability of price promotions and the size of the promotion-economy (the share of real activity sold at promotional prices, ?t in equation 2.35) in response to a monetary policy shock. The graph shows that ?rms use the size of the promotional discount and not the frequency of promotions as a shock absorbing mechanism. Given the contraction in demand after the increase in the real interest rate, the share of the promotion economy also decreases and ?rms react by reducing the fraction of time at which they o?er price promotions.18 Why is it that ft decreases after a shock to the interest rate? To understand this, look at the two panels of Figure 2.7 which depict the time allocations of the two types of consumers. The shock a?ects consumers’ time-allocation decisions asymmetrically. HECs consumers take much more advantage from price promotions that LECs, and when they ?nd a promotion they substitute large quantities of goods at regular prices for good at promotional prices. Now that the size of the price discount has
18
The complete set of the models impulse response functions is presented in Appendix A.4.
49
increased, they do not need to spend as much time as they used to looking for price promotions (they ?nd less promotions but at larger discounts and they take full advantage of them) and they increase they labor time so they can have more resources dedicated to larger substitution of regular-price consumption for promotional-price consumption. Since LECs show a much lower degree of substitution when they ?nd a good on promotion, they have an incentive to increase the time they spent looking for price promotions (they do not substitute as much as HECs do, so they need to ?nd more promotions in order to take advantage of the increase in the price discount) and decrease their labor time. How does this a?ect the ?rms’ decisions about ft ? Since ?rms cannot distinguish between the two types of consumers, they price-discriminate by choosing a fraction of time at which they o?er their goods at promotional prices. As mentioned in previous sections, in doing so, the ?rms take advantage of that fact that promotions are costly in the sense that consumers have to spent time looking for promotions in other to take advantage of them. In a perfect price discrimination environment, the ?rms would be able to distinguish between types of consumers and charge a high price to LECs and a low price to HECs. In the model presented here, the ?rm could achieve perfect price discrimination if HECs looked for promotions all of their time (sh = 1) and HECs never looked for promotions (sl = 0). In that case, by setting ft = 1 the ?rm could completely distinguish between HECs and LECs and charge optimal perfect price discrimination prices (see Appendix A.3 for a formal treatment of this issue). A ?rm, then, has a larger incentive to discriminate (setting a higher ft ) when 50
l sh t /st increases. But, as explained in previous paragraphs, this is exactly the opposite
of what happens after a nominal shock when, given the asymmetric response of prices
l (the increase of the price discount) HECs decrease sh t and LECs increase st . Firms,
therefore have less incentive to price-discriminate and reduce ft . The ?rst panel in Figure 2.8 compares the output response of the model with price promotions presented in Figure 2.5 with several responses of the Calvo model calibrated to di?erent times between price changes. No Calvo response overlaps exactly with the one of the model with price promotions. The reason for this is that the model with price promotions combines features of both ?exible and sticky price models; the output response is small on impact but it dies out at a lower rate than those of the Calvo model. What is, then, the equivalent response in a Calvo model? The second panel of the ?gure presents two responses with the same cumulative impact on output. From the point of view of the overall e?ect of an interest rate shock on output, the model with price promotions calibrated to a time between regular price changes of nine months is equivalent to a Calvo model calibrated to a time between price changes of one month. The dynamics, however, are very di?erent; the response of the Calvo model shows a much higher initial impact but dies out almost twice as fast as the response of the model with price promotions. The near neutrality result contrasts with that obtained by Guimaraes and Sheedy (2011), who ?nd that even though their model delivers individual price paths similar to ones observed in the data, aggregate prices adjust by little in response to monetary shocks, which therefore have large e?ects on real variables. Since the 51
?exibility of prices at the micro level due to sales does not translate into ?exibility at the macro level, the authors conclude that sales are essentially irrelevant for monetary policy analysis. The key element behind Guimaraes and Sheedy’s (2011) non-neutrality result is that in their model sales are strategic substitutes; that is, a ?rm’s incentive to have a sale is decreasing in the number of other ?rms having a sale. For example, after a particular shock, an individual ?rm may have an incentive to have a sale and increase pro?ts coming from bargain hunters. However, if other ?rms follow the same strategy, targeting bargain hunters’ demand becomes a more competitive task, performed at the cost of charging a lower price to loyal customers willing to acquire the good at high prices. The ?rm then may ?nd it more pro?table to not have a sale, targeting only its demand from loyal customers. Guimaraes and Sheedy’s (2011) rationale for sales, then, implies a real rigidity constraining ?rms’ promotional strategies. As explained in an earlier version of their paper (Guimaraes and Sheedy, 2008), this strategic substitution implies that, following an expansionary monetary shock, an individual ?rm has an incentive to decrease sales, therefore increasing its average price. However, if all other ?rms pursue the same course of action, bargain hunters’ demand would be relatively neglected, increasing the returns to targeting non-loyal consumers. Then, in equilibrium, ?rms do not adjust sales by much in response to aggregate shocks, and monetary policy has large real e?ects. Guimaraes and Sheedy’s framework thus provides a well structured IO rationale for sales, consistent with micro price evidence on large amounts on price 52
variation due to idiosyncratic factors, and is able to generate realistic individual price series with inertial regular prices and frequent deviations from reference values. However, their model implies little adjustment in sales in response to aggregate shocks, which ends up being critical for their results on monetary non-neutrality. Is there any evidence on the response of ?rms’ promotional strategies to aggregate shocks? Chevalier et. al. (2003) use DFF data to study the behavior of prices in periods of high demand. They identify eight categories of products that a priori would seem susceptible to seasonal demand shifts, captured by dummy variables taking the value of 1 on determined holidays, as well as by temperature variables capturing weather-induced demand cycles. One of their exercises corresponds to evaluating the response of product advertising (price promotion) to demand peaks. The authors cite earlier evidence showing that high-demand items are more likely to be put on sale, and then regress the percentage of category revenues accounted for by items advertised by Dominick’s against the holiday and temperature high-demand variables. They ?nd that, in general, seasonally peaking items are signi?cantly more likely to be placed on sale.19 Even though Chevalier et. al. (2003) focus only on a small number of product categories (due to data limitations), their study ?nds evidence that sale promotions do respond to aggregate shocks, providing some ground for exploring alternatives
19
Chevalier et. al. argue that, if market share can be viewed as a proxy for high demand, then
the work of Nelson et. al. (1992) and Hosken and Rei?en (2001) shows a positive correlation between high-demand and the probability of being put on sale. Hosken and Rei?en (2004) also presents evidence that high-demand items are more likely to be placed on sale.
53
to Guimaraes and Sheedy’s dynamic pricing model.20 Figure 2.5: OUTPUT RESPONSE TO A MONETARY POLICY SHOCK
In the model presented in this document, ?rms have the alternative of o?ering regular and promotional prices at the same time, and randomize between moments of time in which only the regular price is available and moments of time in which both prices are available, implying a large amount of price ?uctuations even in a deterministic scenario as in Guimaraes and Sheedy (2011). Also, as in Guimaraes and
20
Working with a more comprehensive dataset (bimonthly observations of the CPI Research
Database), Klenow and Willis (2007) ?nd that sales seem to respond to macro information at least as much as regular price changes. Given the di?culty to identifying aggregate nominal shocks for the economy, the authors focus on the expected change in prices based only on current information about in?ation. For this purpose, they regress regular and sale individual prices against a measure of cumulative in?ation since the previous price change, ?nding that sales are at least as responsive to recent in?ation as are regular price changes.
54
Figure 2.6: IMPULSE RESPONSE ANALYSIS
(a) Output and Real Interest Rate Responses
0.0005 real int. rate response model with promotions real int. rate response Calvo Model 0.0000 1 -0.0005 6 11 16 21 26 31 36 41 46 51
output response model with promotions
-0.0010
-0.0015
output response Calvo model
-0.0020
(b) Relative Prices and Price Discount in the Model with Promotions (% deviations from steady state values)
0.04% price discount 0.03% 0.02% 0.01% 0.00% 1 -0.01% -0.02% 6 11 16 21 26 31 36 41 46 51
relativel regular price
relative promotional price average price response
(c) Size of the Promotion-Economy, Price Discount and Fraction of Time at Which Goods are Offered on Promotion (% deviations from steady state values)
0.06% 0.04% 0.02%
0.00% 1 6 11 16 21 26 31 36 41 46 51
price discount
-0.02% -0.04% -0.06% -0.08% -0.10% -0.12%
-0.14%
?t
ft
-0.16%
55
Figure 2.7: TIME ALLOCATIONS
HEC time allocations (% deviations from steady state values)
0.01%
LEC time allocations (% deviations from steady state values)
0.10% 0.05% 0.00% 1 -0.05% 6 11 16 21 26 31 36 41 46 51
nh
1 6 11 16 21 26 31 36 41 46 51
0.00% -0.01%
-0.02% -0.03%
sl
-0.10% -0.04% -0.15%
nl
-0.05% -0.06%
-0.07%
sh
-0.20% -0.25%
Figure 2.8: THE RESPONSE IN THE MODEL WITH PRICE PROMOTIONS COMPARED THAT OF A CALVO MODEL CALIBRATED TO DIFFERENT TIMES BETWEEN CHANGES
(a) Output Responses (Model with price promotions: solid line Standard Calvo Model: dashed line Units: % of steady state output)
1 0.00% 6 11 16 21 26 31 36 41 46 51 0.00%
-0.05%
(b) Two Equivalent Responses in Terms of Cumulative Effects (Units : % of steady state output)
1 6 11 16 21 26
-0.10% -0.10% -0.20% -0.15%
-0.20%
MPP TBRPC = 9 months half life: 6 weeks
-0.30%
CM TBPC = 1 month half life: 3 weeks
-0.25%
-0.40%
-0.30% -0.50% -0.35% -0.40%
-0.60%
Sheedy’s case, the inclusion of a nominal rigidity in regular prices allows the model to generate price series showing the type of reference price rigidity recently documented in the literature, providing also the opportunity of distinguishing between price quotes and realized prices. As regards e?ects of monetary policy, however, the type of price discrimination embedded in this paper provides a new source of price 56
?exibility that undermines the e?ect of nominal rigidities. When a monetary shock hits the economy and ?rms are not able to change their regular prices, they have the option of changing their promotional strategy (the promotional price and the fraction of time at which this is o?ered) in order to modify their average sale price. The key assumption behind this result is that the model’s rationale for sales relies on the use of price promotions for price discrimination, rather than on the assumption of customer loyalty. When consumers are given the possibility of endogenously determining the e?ort they want to invest to take advantage of price promotions, a new margin is created on the household side of the economy and, in a general equilibrium setting, ?rm’s and custumers’ choices interact, generating the coexistence of regular and promotional prices in a way such that the e?ects of nominal rigidities in regular prices are o?set by changes in promotional strategies. In this framework, sale prices end up being important for macroeconomics since their existence gives the market a way to outsmart the Calvo fairy. More generally, this result points out the importance of how consumer behavior is modelled. Indeed, since di?erent approaches to modeling ?rm-customer relationships may perform similarly in replicating features of the microeconomic data but di?er in their macro implications, further exploration of the interaction between ?rms and consumers may be a promising task for future research in macroeconomics.21
21
This line of research includes a wide range of possibilities such as modeling habit persistence
in di?erentiated goods as in Nakamura and Steinsson (2009), allowing for switching costs when consumers change sellers as in Kleshchelski and Vincent (2007), and modeling shopping as a search
57
2.4
Conclusion
This paper has introduced time looking for price promotions as part of the endogenous set of consumer choices. When price promotions are associated with a consumer time cost, the economy features the coexistence of regular and promotional prices. The exercise is relevant not only because of the recent evidence on micro price setting showing that the inclusion or exclusion of sale prices has bearing on the estimated frequency of price changes, but also because the rationale behind sale prices may a?ect the way in which real variables respond to aggregate shocks. When the model is complemented with a nominal rigidity in regular prices, individual price series behave in a way consistent with several features of the data: there is a large amount of price variation not associated with aggregate prices, price quotes rarely change when price promotions are excluded, and they change very often when price promotions are included. Moreover, the model allows a distinction between quoted and realized prices, with realized price series showing the type of rigidity recently found in studies using scanner data: there is inertia in reference prices, with frequent ?uctuations around the reference price. Regarding whether price rigidity at the ?rm level translates into monetary non-neutrality at the macro level, the results show that the type of price promotion considered in the model generates a new source of price ?exibility that o?sets the e?ect of nominal rigidity in regular prices. The economy thus features a dynamic
process as in Arsenau and Chugh (2007), Hall (2007), Levin and Yun (2008), and Albrecht et. al. (2010).
58
pricing arrangement in which the market is able to outmaneuver the Calvo fairy. This result is in contrast with the one recently obtained by Guimaraes and Sheedy (2011), showing the importance of how consumer behavior and ?rm-customer interactions are treated in macroeconomic models. Finally, the results suggest that gathering more empirical evidence on the relationship between price promotions and aggregate prices would be fruitful. How many goods in the economy are associated with price promotions? How many of these correspond to “o?-shelf” discounts? What types of customer costs are associated with accessing these promotions and how big are these costs? How much would these discounts a?ect estimates of the frequency of price changes? The answers to these questions could shed further light on the type and degree of price rigidity observed in the economy and on how this rigidity relates to aggregate ?uctuations.
59
Chapter 3
A Quantitative Analysis of Currency Substitution
3.1
Introduction
A striking feature of various emerging and developing economies is the high level of currency substitution observed even after several years of low in?ation. This paper focuses on two examples of this particular phenomenon: Bolivia and Peru. Data on the ratio of foreign currency deposits with respect to broad money, used as a proxy for total currency substitution, shows that the relationship between currency substitution and in?ation is not the same before and after high in?ation episodes. In both countries currency substitution increases with in?ation during high in?ation periods and reaches its peak once the economy has been stabilized, showing high persistence in the subsequent periods in spite of the downward trend in in?ation.
60
This persistence is also observed in other Latin American countries, as well as in many transition economies1 . Given that conventional monetary general equilibrium models cannot generate the hysteresis observed in the data, Uribe (1997) and Reding and Morales (2004) develop network externalities models that display low-in?ation - high-substitution steady states. Particularly, Uribe’s model proposes that the cost of buying goods with foreign currency is decreasing in the economy’s accumulated experience in transacting in the foreign currency. He refers to this accumulated experience as the economy’s “dollarization capital”. This chapter explores the quantitative implications of incorporating Uribe’s dollarization capital idea in a simple endowment economy model in which domestic and foreign currency balances are held because of their services in reducing transaction costs. Particularly, the model is used to generate a low in?ation-highsubstitution equilibrium and to compare the predicted currency substitution ratios to those observed in the data as well as those obtained using a model in which the dollarization capital mechanism is not present. When parameters are chosen as to replicate pre-hyperin?ation currency substitution levels, the model performs well in predicting high levels of currency substitution during high in?ation episodes, generating substitution ratios close to the ones observed in the data. The model also displays inertia in real foreign currency holdings during the transition towards a low-in?ation equilibrium and generates higher levels of currency substitution than a model with no dollarization capital dynamics. The model generates low in?ation currency substitution ratios that are be1
See Savastano (1996), Valev (2007) and Feige (2003).
61
tween 40% and 50% of those observed in post in?ation stabilization periods. Although the predicted currency substitution ratios are below the observed ones, the model is able to explain between 1/6 of the gap between the observed ratios and the ones generated by a model without dollarization capital dynamics. The fact that the predicted low-in?ation currency substitution ratios are below the ones observed in the data is a result of sizable post-stabilization impact e?ects on domestic currency holdings, a ?nding that suggests the need for future work on mechanisms that could induce inertia in domestic currency balances. Particularly, it would be interesting to study a model that displays uncertainty with respect to future in?ation, probably including a devaluation risk probability as in Mendoza and Uribe (1999, 2000). The rest of the chapter is organized as follows. The second Section describes the pre and post high-in?ation pattern of currency substitution in Bolivia and Peru. The theoretical model is presented in the third section and solved in the fourth section. The ?fth section concludes.
3.2
3.2.1
Currency Substitution in Two Selected Economies
Currency substitution and in?ation
The ?rst challenge in analyzing currency substitution in developing countries is constructing a relevant measure of the use of foreign currency in the domestic economy, often a di?cult task because of the lack of data on the amount of foreign currency
62
held by households outside the ?nancial system. Following Savastano (1996), a useful proxy for the total level of currency substitution in the economy is the ratio of foreign currency deposits (F CDs) to broad money. This measure, labeled F CD/BM ? , is represented by the dark gray areas in the left hand panels of Figure 3.1.2 The graphs also depict the behavior of the in?ation rate (in logarithmic scale for Bolivia and Peru). In the Bolivian case, this measure of currency substitution is not available for the 1981-1984 period when the central government imposed restrictions on the use of foreign currency in the ?nancial system, forcing the conversion of all bank liabilities into domestic currency. Therefore, this measure does not provide information on the behavior of currency substitution during the hyperin?ation period of the early eighties. When observing the 1985-2007 period, it is interesting to notice that the substitution ratio reached its peak in 1995 after several years of reductions in the annual in?ation rate, and decreased after that, even in the 2002-2008 period during which the in?ation rate gradually rose. Peruvian currency substitution follows a similar behavior. The substitution ratio was already high before 1988, with a 50% average for 1980-1987. The sharp decrease observed between 1984 and 1987 is related to the temporary prohibition
2
The broad money measure varies depending on the monetary aggregates classi?cation used
by each Central Bank. In the case of Bolivia the measure is constructed as the ratio of FCDs to M3’, the broadest monetary aggregate used by the Bolivian Central Bank, which includes short term and long term deposits denominated in local and foreign currency. In the cases of Peru , the measure is computed as the ratio of quasi-money denominated in foreign currency to total money and quasi-money.
63
of U.S. dollar denominated deposits (Rojas-Suarez, 1992). As in the Bolivian case, restrictions on F CDs limit the capacity of this measure to re?ect the relationship between in?ation and currency substitution during hyperin?ation episodes. During the post-restrictions period (1990 onwards) currency substitution remained high, achieving its peak in 1993 and showing a slow downward trend after that. Again following Savastano (1996), data limitations due to restrictions on FCDs in the domestic ?nancial system in Bolivia and Peru can be addressed by combining the F CD/BM ? substitution measure with information on foreign currency deposits held abroad (da). This new measure, labeled (F CD +da)/(BM ? +da), is represented by the light gray areas in the left hand panels of Figure 3.1. The measure was constructed using data on bank net foreign asset positions available at the Bank of International Settlements (BIS), taking the series of liabilities of BIS reporting banks against each country, converting them into domestic currency and adding them to the numerator and denominator of F CD/BM ? .3 The new and broader measure provides a clearer picture of the currency substitution - in?ation relationship before and after hyperin?ationary periods. In Bolivia, the broader substitution ratio was already high in 1980 (38%) and increased to 56% at the peak of the hyperin?ation episode in 1985, the same year in which F CD restrictions were eliminated. Currency substitution continued rising even after the hyperin?ation period ended, reaching a maximum of 83% in 1995. The reduction in the distance between the two substitution measures during the 1988-2008 pe3
BIS Banking Statistics. Table 6A: External positions of reporting banks vis--vis individual
countries, vis--vis all sectors.
64
Figure 3.1: CURRENCY SUBSTITUTION IN BOLIVIA AND PERU
riod shows that as in?ation was controlled and continually reduced, domestic agents changed the composition of their portfolios from assets held abroad to assets held in the domestic banking sector, but with little change in the currency composition of their monetary assets, relying heavily on F CDs. A similar pattern is observed in Peru, where both in?ation and the broader substitution measure were already high in the pre-hyperin?ation period. The broader ratio increased with in?ation in the 1987-1990 period, and reached its peak in 1993, by which time in?ation already presented a marked downward trend. As in the Bolivian case, once F CD restrictions were eliminated (1990) the portfolio composition shifted towards domestically held deposits, but with the currency composition still leaning towards U.S. dollar denominated monetary assets.
65
Thus, the left-hand side panels in Figure 3.1 summarize the ?rst main stylized fact that motivates the quantitative work presented later in the document: while dollarization increases quickly with in?ation during high-in?ation periods, it does not quickly revert once in?ation has been reduced and does not present a clear comovement with in?ation in the post-stabilization years.
3.2.2
Inverse velocities of money
This section describes the behavior of the Bolivian and Peruvian ?nancial systems by constructing di?erent inverse velocities of money as proxies of ?nancial deepness. Each of the right-hand side panels in Figure 3.1 presents in?ation (in logarithmic scale) and the inverse of three money velocity ratios: i) M/GDP , money over GDP, ii) BM/GDP , broad money over GDP, and iii) BM ? /GDP , broad money including foreign currency deposits over GDP.4 The top right panel shows a sharp decline in monetization ratios during the Bolivian hyperin?ation years (1984-1985); once that in?ation was controlled and F CD restrictions lifted, the inverse velocities of money in domestic currency remained relatively low for several years, while BM ? /GDP increased strongly until reaching a peak in 2001 (54%). The domestic currency ratios (M/GDP and BM/GDP ) increased in the 2004-2008 period, but this was not joined by a decrease in BM ? /GDP which increased from 43% in 2004 to 51% in 2007.
4
Bolivia:
M/GDP = M1/GDP, BM=M2/GDP, BM* = M3’/GDP. Peru:
M/GDP =
Money/GDP, BM = (Money + Quasimoney)/GDP, BM* = (Money + Quasimoney in domestic and foreign currency)/GDP. See Appendix 2.
66
In the case of Peru, there was a marked reduction in the three monetary ratios during the hyperin?ation period, followed by a strong increase in BM ? /GDP after in?ation was controlled and F CD restrictions eliminated. While both domestic currency inverse velocities followed an increasing trend, they remained well below BM ? /GDP which reached its historical peak of 30% in 2008. Overall, the right-hand side panels in Figure 3.1 summarize the second main stylized fact of interest in this document: if the inverse velocities of money presented in Figure 3.1 are understood as proxies of ?nancial deepness, then the graphs show that after high in?ation episodes, the ?nancial system recovery relies strongly on the use of the foreign currency. After the sharp decrease in monetization ratios, the post-hyperin?ation ?nancial sectors were rebuilt on the basis of the U.S. dollar instead of the national currency. The next section presents a simple perfect foresight model that seeks to capture the above mentioned stylized facts by introducing an accumulation externality in the use of the foreign currency.
3.3
A Model of Currency Substitution
The stylized facts analyzed in the previous section show that the relationship between currency substitution and in?ation follows di?erent patterns in pre-stabilization and post-stabilization periods, a type of asymmetry that is not captured by standard monetary general equilibrium models. Motivated by the high degree of persistence in currency substitution observed
67
in several developing countries, Uribe (1997) develops a cash in advance model in which the cost of buying goods with foreign currency is decreasing in the economy’s accumulated experience in transacting in foreign currency, a concept that Uribe calls the economy’s dollarization capital. Uribe’s framework delivers the possibility of an equilibrium in which the foreign currency circulates even in a low in?ation steady state. Building on Uribe’s work, Reding and Morales (2004) replace the exogenous dollarization capital assumption by modeling endogenous network externality e?ects in which the size of the foreign currency network increases with the number of agents whose foreign currency balances are larger than a given threshold. Their model also renders the possibility of high-substitution - low-in?ation equilibria by combining a learning e?ect (the acquisition of experience in the use of an alternative currency) with a size e?ect (the reduction in transaction costs caused by an increase in the number of agents with signi?cant foreign currency balances). Both of these works present heterogeneous agent models with complex dynamics and are not solved computationally. This section develops a simple representative agent monetary model incorporating Uribe’s (1997) dollarization capital idea; the model is then solved using numerical methods.
3.3.1
Preferences
Consider a perfect foresight endowment economy with income yt = y in every period and lifetime utility stream given by
68
?
? t u(ct )
t=0
(3.1)
where ? is the inter-temporal discount factor, u (ct ) > 0 and u (ct ) < 0.
3.3.2
Monetary Policy
The economy is open. It follows a predetermined exchange rate regime and the law of one price holds at any moment in time. That is, the nominal exchange rate
? St is given by St = pt /p? t , where pt and pt , are the domestic and international
price levels respectively. Therefore in?ation is given by ?t = ?t + ? ? where ? is the policy-determined devaluation rate and ? ? is international in?ation. Each period the government injects money in the economy through a transfer Tt = Mt+1 ? Mt , where Mt are nominal money balances. The transfer is such that it satis?es the law of one price and the model equilibrium conditions that will be derived below. The agent uses her resources either in consumption (ct ) or in acquiring domestic and foreign currency balances carried to the next period (mt , m? t ).
3.3.3
Transaction Costs
Money enters into the model because of its transaction cost reduction services. Each period the agent must cover a transaction cost given by
t ? ct , ? ( m ), ? ? pt
m? t , dt p? t m? t p? t
; ?c > 0, ?? < 0, ??? < 0
where
5
mt pt
and
are domestic and foreign real money balances respectively.5
? Notice that m? t are nominal foreign currency balances expressed in the foreign currency, mt St
69
The transaction cost reduction services provided by domestic currency real
t balances are given by ?( m ) with ? > 0, while the cost reduction services derived pt
from from holding foreign currency real balances are given by ??
m? t , dt p? t
, where dt
is the economy’s accumulated experience in using foreign currency (the dollarization
? ? capital) and ?m ? /p? > 0 , ?d > 0. t t
Under this structure, the agent’s budget constraint in period t is given by
y+
mt?1 m? mt m? 1 t + t? + ? + T = c + t t Pt Pt? Pt Pt mt + ? ct , ? , ?? Pt
m? t , dt Pt?
(3.2)
3.3.4
Dollarization Capital
I assume that the transaction cost reduction services provided by foreign currency depend not only on the amount of foreign currency real balances, but on the accumulated experience using this currency. The dollarization capital depreciates at ˜) and its accumulation is an increasing function of the current an exogenous rate (? level of currency substitution.
˜)dt + G dt+1 = (1 ? ? with G (.) > 0 and G (.) < 0.
m? t Pt
m? t ? Pt
+
mt Pt
(3.3)
are foreign currency balances expressed in domestic currency and currency balances expressed in real terms.
m? t St pt
t = pttp?t = p? are foreign t t
m? p
m?
70
3.3.5
Maximization Problem and Competitive Equilibrium
mt pt
Letting at =
and a? t =
m? t , p? t
the consumer’s problem is maximizing (3.1) subject
to (3.2) and (3.3), with ?rst order conditions given by
?
u (t + 1) u (t) = (1 + ?t+1 )[ (1 + ?? (t)? (t)) 1 + ?c (t + 1) 1 + ?c (t) a? + ?t G (t) ? t 2 ] (at + at )
(3.4)
?
u (t + 1) = 1 + ?c (t + 1)
u (t) ? (1 + ??? (t) ?a ? (t)) 1 + ?c (t) at ? ?t G (t) ? (at + at )2
? 1 + ?t +1 [
(3.5)
˜ ? ?t = ? ?t+1 1 ? ?
u (t + 1) ? ??? (t + 1) ?d (t + 1) 1 + ?c (t + 1)
(3.6)
where ?t is the multiplier on the dollarization capital accumulation equation, the expression (t) is used to denote that all the arguments of a given function are
? ? evaluated at period t, ?t = pt /pt?1 and ?t = p? t /pt?1 . Finally, when imposing market
clearing in the money market, that is Mt = mt , equation (3.2) is reduced to
m? t p? t
?
m? t?1 p? t
= y ? ct ? ? (t)
or
a? t ?
a? t?1 = y ? ct ? ? (t) ? 1 + ?t
(3.7)
71
? Notice that if the international price is normalized to one, ?t = 0 and this last
equation is reduced to
? a? t ? at?1 = [y ? ? (t)] ? ct
(3.8)
that is, an increase in real foreign currency balances held by domestic agents is ?nanced through a trade balance surplus, with the trade balance de?ned as the di?erence between output net of transaction costs, y ? ? (t), and consumption. Then, the model’s competitive equilibrium is de?ned as a list of sequences for consumption and dollarization capital {ct , dt }, portfolio choices {mt , m? t }, prices {pt , p? t }, and policy variables {Mt , ?t } such that: i) Equations (3.2), (3.3), (3.4), (3.5) and (3.6) solve the representative agent’s consumption maximization problem, ii) the monetary market clears (Mt = mt ) and iii) the Law of One Price is satis?ed in every period. The intuition behind the ?rst order conditions of the model is better understood by considering ?rst the case of a model without dollarization capital. The equilibrium conditions of such a model correspond to equations (3.4), (3.5) and (3.11), setting ?t = 0 and normalizing dt to one:
?
u (t + 1) 1 + ?c (t + 1)
1 1 + ?t+1
=
u (t) (1 + ?? (t) ? (t)) 1 + ?c (t)
(3.9)
?
u (t + 1) 1 + ?c (t + 1)
1 ? 1 + ?t +1
=
u (t) (1 + ??? (t) ?a? (t)) 1 + ?c (t)
(3.10)
72
a? t ?
a? t?1 = y ? ct ? ? (t) ? 1 + ?t
(3.11)
The left hand side of (3.9) is the marginal utility consuming one less unit of the good in period t and using those resources to increase domestic real balances at t + 1. In t + 1 these extra real balances are used for consumption, and the marginal utility of this future consumption is properly discounted by domestic in?ation and the marginal increase in transaction costs ?c (t + 1) . This expression is equated to the marginal utility of consuming the good in period t (right hand side of (3.9)), adjusted by the increase in transaction costs caused by additional consumption and by the opportunity cost of not carrying an extra unit of domestic real balances to the next period. This opportunity cost equals the marginal reduction in the transaction cost from carrying domestic real balances from period t to period t + 1 (remember that ?? (t) is negative). A similar interpretation is given to equation (3.10), where the left hand side is the marginal utility of carrying a unit of foreign currency real balances to the next period, while the right hand side is the marginal utility of consuming a unit of the good in the current period, including the increase in transaction costs caused by additional current consumption and by having one less unit of foreign real balances carried to the next period. Combining (3.9) and (3.10):
1 + ??? (t) ?a? (t) 1 + ?t+1 = ? 1 + ?? (t) ? (t) 1 + ?t +1
(3.12)
73
Equation (3.12) summarizes how the agent’s currency portfolio composition is a?ected by domestic and foreign in?ation in a model with no dollarization capital.
? When ?t = ?t , the opportunity cost (in transaction cost reduction terms) of not
carrying a unit of domestic real balances (?? (t) ? (t)) is equal, at an optimum, to the opportunity cost of not carrying a unit of foreign real balances (??? (t) ?a? (t)).
? When ?t+1 > ?t +1 ? ?1 however, 1 + ??? (t)?a? (t) > 1 + ?? (t)? (t).
Thus, in the absence of dollarization capital dynamics, discrepancies between domestic and foreign in?ation are immediately translated into changes in the current composition of the agent’s real balances portfolio. When endogenous accumulation of dollarization capital is introduced in the model, the equivalent of equation (3.12) is found by combining (3.4) and (3.5):
u (t) 1+?c (t)
at ? (1 + ??? (t) ?a ? (t)) ? ?t G (t) (a? +a )2
t t
u (t) 1+?c (t)
?t (1 + ?? (t) ? (t)) + ?t G (t) (a?a +a )2
t t
=
1 + ?t+1 ? 1 + ?t +1
(3.13)
This last expression implies new trade-o?s not present in (3.12). When ?t+1 =
? ?t +1 , (3.13) is reduced to:
u (t) ?t G (t) ? [??? (t) ?a ? (t) ? ?? (t) ? (t)] = 1 + ?c (t) a? t + at
(3.14)
where this last expression equates the marginal value of increasing the dollarization capital by holding a higher proportion of foreign real balances (right-hand side of 3.14) with the forgone marginal utility gain from reducing transaction costs by holding domestic balances over foreign ones and then spending the proceedings
? on consumption (left-hand side of 3.14, recalling that ??? (t) ?a ? (t) and ?? (t) ? (t)
74
are negative). In the absence of dollarization capital dynamics, the term in square brack? ets on the left-hand side of (3.14) would be zero when ?t+1 = ?t +1 (see equation
3.12), but now it is positive at an optimum. That is, the model with dollarization capital dynamics requires higher marginal transaction cost reduction services from holding domestic currency balances than would be required in a framework without dollarization capital (| ?? (t) ? (t) |>| ??? (t) ?a? (t) |). This framework thus introduces inertia through a substitution motive not present in the model without dollarization capital. Suppose that dollarization (the
? proportion of foreign real balances with respect to total real balances , a? t /(at + at ))
decreases. Then, for a given {?t , ct } pair, this would imply an increase in the right hand side of (3.14) because of the strict concavity of G(t). This, in turn, implies broadening the gap between | ?? (t) ? (t) | and | ??? (t) ?a? (t) | ( left hand side of (3.14) ), implying an increase in a? t and a decline in at .
3.4
3.4.1
IV. Solving the Model
Parametrization and Solution Method
The model is solved for the following functional forms: u (ct ) =
?? c1 t 1??
? (ct , ? (t) , ?? (t)) =
ct ?(t)?? (t)
?
ct ; ? > 0
? (t) = (at )? ; ? ? (0, 1)
75
1?? ?? (t) = (dt a? t)
G (t) =
a? t a? t +at mt Pt
?
; ? ? (0, 1)
m? t ?. Pt
where at =
and a? t =
The functional form for the transaction cost term is similar to that used in works like Mendoza and Uribe (1997,1999,2000) but replacing mt in the denominator
? 1?? by m? . t (dt mt )
Parameter
Table 3.1: Parameter Values Value
Bolivia Peru 0.96
Source
Calibration Target
-
Discount factor
? ? (0, 1)
0.96
Standard value in yearly models Reinhart and Vegh (95) Country Data Calibrated
c y
Risk Aversion Coe cient In ation Rate Exponential term: transaction cost function Exponential term: cost reduction services provided by the domestic currency Exponential term: Dollarization Capital accumulation function Dollariation Capital depreciation rate
C = Private Consumption
?>0
1.5
1.5
-
? ?>0
0.24 0.081
0.93 0.139
-
=
C GDP
? ? (1 2 , 1)
0.927
0.911
Calibrated
a y
=
N CSR GDP
? ? (0, 1)
0.689
0.490
Calibrated
a? y = DCSR?N CSR GDP
? ? (0, 1)
0.521
0.777
Calibrated
d=1
NCSR = Numerator in Currency Substitution Ratio (CSR) DCSR = Denominator in CSR
Given the predetermined exchange rate regime and normalizing p? to one, the in?ation rate is given by the devaluation rate, ?t = ?, taken as a policy parame76
Ì
Ä ¾ ËÈ È Ê
Table 3.2: Model Results and Calibration Targets
Ì
a/y a? /y c/y d CSR
ÅÓ Ð ¼º½ ¼º½½ ¼º ½º¼ ¼º¿
ÓÐ Ú Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
Ø ¼º½ ¼º½½ ¼º ¹ ¼º¿
Ë ØØ Ò Ô Ö Ñ Ø Ö× × ØÓ Ö ÔÐ ÅÓ Ð ¼º½ ¼º¾¼ ¼º ½º¼ ¼º ¼
Ì È ÖÙÚ Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
Ø ¼º½ ¼º¾¼ ¼º ¹ ¼º
Ø
ter that determines each steady state. The solution method consists of linearizing equations (3.3), (3.4), (3.5), (3.6) and (3.11) around alternative steady states using Schmitt-Grohe and Uribe’s (2004) perturbation algorithm. Regarding the values chosen for each parameter, y is normalized to one, while ? is set at a standard value of 0.96. ? is set at 1.5, in the middle of the range used in Mendoza’s (1991) study on real business cycles in small open economies; this value is also within the range estimated by Reinhart and Vegh (1995). Two sets of values for ?, ? , ? and ? are chosen to replicate the pre-hyperin?ation currency substitution ratio in Bolivia and Peru. The values for {?, ?, ?, ? } are jointly determined to match four calibration targets: ?rst, a consumption-output ratio (c/y ) equal to the observed consumptionGDP ratio in the pre-hyperin?ation period (1980-1981); second, a foreign real balances–output ratio (a? /y ) equal to the observed (F CD + da)/N GDP ratio in the pre-hyperin?ation period, where N GDP stands for nominal GDP, F CD stands for
¾
foreign currency deposits and da stands for deposits held abroad; third, a domestic real balances-output ratio (a/y ) equal to the observed (BM ? ? F CD)/GDP ratio in the pre-hyperin?ation period, where BM ? is the broad money measure used in
77
Section II; fourth, a dollarization capital value equal to one. By setting the above mentioned targets for a? /y and a/y , the model’s ratio of foreign monetary assets to output ( ay =
?
sm? ) py
corresponds to the ratio between
the numerator of the currency substitution measure used in Section II and nominal GDP (that is, the ratio of foreign currency monetary assets to nominal GDP), while the model’s ratio of domestic monetary assets to output ( a = y
m ) py
corresponds to
the ratio of the di?erence between the denominator and numerator terms of the currency substitution measure used in Section II to nominal GDP (that is, the ratio of domestic currency monetary assets to nominal GDP). Given these targets, the model’s ratio of foreign real monetary assets to total monetary assets (a? /(a? + a)) corresponds to the observed currency substitution measure discussed in Section II ((F CD + da)/(BM ? + da)). The target for dt is chosen to generate some similarity between the model’s pre-hyperin?ation equilibrium and that obtained in a model with no dollarization capital dynamics. In the two cases the value for ? is restricted to be greater than 1/2 in order to ensure that domestic real balances are greater than foreign currency when ?t+1 =
? ?t +1 and when there is no dollarization capital. To see this notice that under the
current functional forms equation (3.12) implies ? > 1/2 ensures at ¿a? t.
at a? t
=
? 1??
? when ?t+1 = ?t +1 , and
The four sets of parameter values are reported in Table 3.1. Table 3.2 presents the observed and model-generated values for each calibration target. Table 3.3 shows the performance of the model in matching the observed degree 78
of currency substitution during hyperin?ation episodes. Ì Ä ¿ ËÈ È Ê Table 3.3: Currency Substitution Ratios in High-in?ation Periods
Ë ØØ Ò Ô Ö Ñ Ø Ö× × ØÓ Ö ÔÐ
CSR d
ÅÓ Ð ¼º ¼ ½º ¼ ÅÓ Ð ¼º ½º½¼
Ì
ÓÐ Ú Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
Ø ½¶ ¼º ¹ Ø ½¶ ¼º ¼ ¹
Ø
Ø ¾¶¶ ¼º ¹ Ø ¾¶¶ ¼º ¹
Ì È ÖÙÚ Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
¶ ØØ Ô Ó Ø ¶¶ ÇÒ Ô Ö Ó Ø Ö Ø
CSR d
¹ Ò Ø ÓÒ Ô Ö Ó º ÝÔ Ö Ò Ø ÓÒº
The average value of Bolivian in?ation for the 1982-1985 period was 2700%. When in?ation is set at this value, the result is a 53% increase in dollarization capital and a currency substitution ratio of 70%, a little higher than the average between the ratio observed at the peak of the hyperin?ation and the one observed one period after the hyperin?ation. In the case of Peru, the average in?ation rate for the hyperin?ation period (1988-1991) was 4000%. When the model is solved for this in?ation rate, the dollarization capital level increases by 12% with respect to the pre-hyperin?ation period and the currency substitution ratio is 74%, seven to eight percentage points below the observed ratio.
3.4.2
Transitional Dynamics from High to Low in?ation
¿
As shown in Table 3.3, the model performs well in terms of generating high dollarization ratios for large values of in?ation. The model can also be used to study
79
transitional dynamics from a high-in?ation steady state to a low-in?ation one. Figure 3.2 presents impact and transitional e?ects of reducing in?ation from 2700% (the Bolivian post-hyperin?ation value) to 24% (the Bolivian pre-hyperin?ation value), and from 4000% (the Peruvian post-hyperin?ation value) to 90% (the Peruvian prehyperin?ation value). All series are expressed as percentage deviations from the original steady state. The adjustment in dollarization capital is slow, taking more than three years in every case, and the rapid adjustment in currency portfolios is mainly due to sharp changes in domestic currency balances. The much slower and less sizable adjustment in foreign currency balances is directly related to the inertia observed in dollarization capital dynamics. Currency substitution dynamics are shown in the third graph in each panel, with a high impact e?ect explained by the quick adjustment in domestic currency balances. Since money enters the model through a transaction cost function, the reduction in in?ation has a positive e?ect on consumption and therefore utility. Figure 3.2: TRANSITIONAL DYNAMICS
Dynamics from from High-Inflation Equilibrium Figure 2: Transitional Dynamics High-Inflation to to Low-Inflation Low-Inflation Equilibrium Equilibrium
a) Parameters set as to obtain the Bolivian pre-hyperinflation currency substitution ratio Money Balances Dollarization Capital, d
0.0 1 -0.1 -0.2 -0.3 -0.4 -0.5 4.0 0.0
a (-, left axis) a*(--, right axis)
6.0 0.2
0.2 0.1
Currency Substitution, a/(a+a*)
0.0 0.10
Consumption, c
0.08 0.06 0.04 0.02 0.00 1
Dollarization Capital, d
6.0 4.0
2.0
2
2
3
4
5
6
7
8
1
-0.2
2
3
4
5
6
7
8
-0.4 -0.6
-0.8
2.0 0.0 1 2
3 4 5 6 7 8
0.1 0.0
2
3
4
5
6
7
8
b) Parameters set as to obtain the pre-hyperinflation currency currency substitution substitution ratio ratio obtain the Peruvian Peruvian pre-hyperinflation Money Balances
a (-, left axis) a*(--, right axis)
0.1 0.1
0.0 0.0 8
Currency Substitution, a/(a+a*)
0.0 0.2
Consumption, c
1
-0.1 -0.2
3
4
5
6
7
1
-0.2
2
3
4
5
6
7
8 0.1
-0.3 -0.4
-0.4 -0.6
0.1 0.0 1
2
0.0
1 2
0.0 3 4 5 6 7 8
3
4
5
6
7
8
80
How does the model perform compared to one in which there is no dollarization capital? This question is answered by analyzing currency substitution transitional dynamics from the high-in?ation steady state to one in which in?ation equals the post-stabilization average. Panel a) in Figure 3.3 corresponds to a reduction in in?ation from 2700% (the Bolivian hyperin?ation average) to 11% (the Bolivian post stabilization average), while panel b) corresponds to a reduction in in?ation from 4000% (the Peruvian hyperin?ation average) to 17% (the Peruvian post stabilization average). Solid lines are used for the model with dollarization capital, while dashed lines are used for the model with no dollarization capital6 . In all cases the initial value is set at the high in?ation steady state in the model with dollarization capital. As expected, the dollarization capital model delivers higher post-stabilization ratios than those obtained with the model without dollarization capital.4. Panels a.1) to b.2) show the transition paths of domestic and foreign real balances. In the model with no dollarization capital foreign balances fall with respect to their levels in the previous equilibrium while they increase when dollarization capital is added to the model. However, as mentioned earlier, in both models the dynamics of the currency substitution ratio are not driven by the adjustment in foreign balances but by quick and very sizable variations in domestic balances. The currency substitution ratios of the model with dollarization capital are below the observed ratios, but still represent a large increase with respect to a more conventional model with no dollarization capital dynamics. The ratios generated by the dollarization capital model are between 40% and 50% of the observed ratios,
6
Dollarization capital dynamics are shut down by setting ? = 1 and ? = 0
81
Figure 3.3: TRANSITION WITH AND WITHOUT DOLLARIZATION CAPITAL
Inflation drops from 2700% (Bolivian 1982-1985 average) to 11% (Bolivian 1986-2008 average) Inflation drops from 3100% (Peruvian 1988-1991 average) to 17% (Peruvian 1992-2008 average)
a) Currency Substitution Ratio
0.80 0.70 0.60 0.80 0.70 0.60
b) Currency Substitution Ratio
a*/(a*+a)
0.40 0.30 0.20 0.10 0.00 1 2 3
a*/(a*+a)
4
5 6 7
0.50
0.50
0.40 0.30 0.20 0.10 0.00 1 2 3 4
5
6
7
a.1) a as % of st. st. value
700.00 600.00 500.00 400.00 600.00
b.1) a as % of st. st. value
500.00
400.00
300.00
300.00
200.00
100.00 0.00 1 20.00 15.00 10.00 5.00 0.00 1 -5.00 -10.00 -15.00 -20.00 -25.00 2 3 2 3
200.00
100.00
0.00
a.2) a* as % of st. st. value
10.00 5.00 0.00 1
Solid line: model with dollarization capital
explaining 1/6 of the gap between the observed currency substitution ratios and those obtained with a model with no dollarization capital. This is seen in Table 3.4, where the ?rst three columns in each panel present the post-stabilization currency substitution ratios obtained by models with and without dollarization capital, as well as the observed ratios. The fourth column presents the ratio between the di?erence in predicted currency substitution ratios with and without dollarization capital and the di?erence between the observed ratio and the 82
4 4
5 5
6 6
7 -5.00 7 -10.00
1
b.2) a* as % of st. st. value
2 2
3 3
4 4
5 5
6 6
7 7
-15.00
-20.00 -25.00
Dotted line: model with no dollarization capital
Ì
Ä
ËÈ È Ê
Ë ØØ Ò Ô Ö Ñ Ø Ö× × ØÓ Ö ÔÐ
Table 3.4: Currency Substitution Ratios in High-in?ation Periods
Ì
ÓÐ Ú Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
(iii)
Ø
(i)
(ii)
ÅÓ Ð
(dol capital) CSR
¼º¾
ÅÓ Ð ´no dol capitalµ ¼º¾½
(ii)
Ø ´ ¹¼ µ ¼º
(iii)
(i) (iii)
(i)?(ii) (iii)?(ii)
¶
¼º ¼
¼º½
Ì È ÖÙÚ Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
(i)
ÅÓ Ð
(dol capital) CSR
¶
Ô
ØÛ Ò (ii) Ò
¼º¿
ÅÓ Ð ´no dol capitalµ ¼º¿¼
(iii)
ÜÔÐ Ò
Ý (i)
Ø ´ ¾¹¼ µ ¼º
(i) (iii)
(iii)?(ii) (i)?(ii)
¶
¼º ¼
¼º½
one generated by the model without dollarization capital. Overall, the dollarization capital framework delivers high post-stabilization substitution ratios using a very simple structure, and leaving ample room for further additions to the model dynamics. These additions could focus on generating inertia in the adjustment process for domestic currency holdings in a way consistent with the behavior of the inverse velocities of money discussed in Section II. An interesting line of work in this regard would be the introduction of uncertainty about the future value of in?ation, by assigning a policy reversal probability as part of the agent’s information set as in Mendoza and Uribe (1999,2000)7 .
7
In the predetermined exchange rate regime environment of the present document, this fea-
ture could be added to the model by introducing a post-stabilization time-dependent devaluation probability as in Mendoza and Uribe (2000), or by making this probability an endogenous variable conditioned on foreign reserves as in Mendoza and Uribe (1999).
83
3.5
Conclusion
The present document has developed a simple endowment-economy monetary model able to generate high levels of currency substitution in low in?ation environments. The introduction of a dollarization capital variable to capture the economy’s accumulated experience in the use of foreign currency generates a motive for holding foreign currency balances even when in?ation is low. When applied to high-in?ation equilibria, the model is able to generate currency substitution ratios very close to those observed during hyperin?ation episodes, and it presents inertia in foreign currency real balances during the adjustment towards a low-in?ation steady state. In terms of the model’s predicted post-hyperin?ation dollarization levels, these are still below the observed ratios but represent a sizable increase with respect to those obtained using a more standard framework with no dollarization capital. The dollarization capital model generates post-hyperin?ation currency substitution ratios that are between 40% and 50% of the observed ratios and is able to explain 1/6 of the gap between the observed substitution ratios and those generated by a model with no dollarization capital dynamics. Further model building e?orts could focus on introducing frictions that reduce the size of impact e?ects on post-stabilization domestic currency holdings. An important step in this direction may be the introduction of devaluation risk dynamics along the lines of Mendoza and Uribe (1999, 2000).
84
Chapter 4
Investment Activity in the Financial Sector and the Relationship between In?ation and Currency Substitution
4.1
Introduction
As shown in the previous chapter, the dollarization capital model generates a higher steady state currency substitution ratio than that obtained with a model with no dollarization capital in it. There are, however, three important limitations that a?ect the model’s ability to study currency substitution dynamics. First, the dollarization capital variable was introduced in an ad hoc manner as a stock variable entering the transaction cost function. Second, the model has a representative household, and
85
the dollarization capital variable is optimally chosen by the consumer taking into account an accumulation law of motion in which dollarization capital increases with the currency substitution ratio. In this environment, the consumer fully internalizes the e?ect of currency substitution on the dollarization capital variable, leaving no room for network externality e?ects like the ones developed in Uribe (1997) and Reding and Morales (2004). Third, the model is not able to generate an asymmetric relationship between in?ation and currency substitution before and after high in?ation episodes. This behavior is at odds with the data in several partially dollarized economies. This chapter presents a framework that provides a micro foundation for a quantitative model able to deal with the above mentioned limitations. Developing and solving such a model is beyond the scope of this chapter. The chapter rather focuses on exploring the theoretical elements needed to generate di?erent in?ationsubstitution patterns before and after high in?ation episodes. The main idea is that in an environment in which consumers show some heterogeneity in their ability to access the ?nancial sector’s money exchange services, a su?ciently high level of in?ation can induce the ?nancial sector to make a ?xed cost investment that decreases this heterogeneity by permanently reducing money exchange costs. More formally, this chapter presents a simple model of two consumers who use money to buy a consumption good. The consumers can hold either domestic or foreign currency, but they do not have the technology to transform domestic balances for foreign ones, so to do so they must use a money exchange point owned by the ?nancial sector. The only di?erence between consumers is that they may be located 86
at di?erent distances from the nearest exchange point, and they obtain disutility from walking that distance. The ?nancial sector provides only one service, money exchange, and decides on whether or not to construct money exchange points at a given ?xed cost. The ?nancial sector makes its optimal exchange point construction decision anticipating the consumers’ substitution decisions under di?erent levels of in?ation. For su?ciently high levels of in?ation, the ?nancial sector will construct new exchange points, changing consumers’ distance to the closest exchange point and therefore permanently reducing currency substitution costs. It could be said then that in this framework the dollarization capital variable corresponds to the number of exchange points set by the ?nancial sector. This seems like a plausible example of the type of investment decisions made by the ?nancial sector in developing countries as agents increase their usage of foreign currency. Think, for example, of a bank in a high-in?ation developing country deciding on whether to o?er money exchange services in some or all of its agencies. Provided that there are no legal restrictions, the bank may also decide to o?er foreign currency high liquidity services (i.e. checking accounts denominated in dollars), an action that may be associated with di?erent types of one-time costs, such as training personnel in the use of the foreign currency and setting up accounting and software systems that handle both currencies. For an example directly related to the concepts of distance and accessibility, think of banks investing in ATM machines and deciding whether to provide ATM services only in domestic currency or allowing them to work in foreign currency as well. The ?nancial system may be willing to pay these investment costs during periods of high in?ation (or of high in?ation expectations) with 87
the purpose of taking advantage of the increase in household’s demand for foreign currency. However, this investment permanently reduces household’s costs in terms of accessing foreign currency services and therefore induces currency substitution at lower levels of in?ation in the future. The combination of consumer heterogeneity and ?xed costs in exchange point construction generate in?ation regions with di?erent intensities in terms of investment in new exchange points. Particularly, starting from a state in which there are no exchange points in the economy, an episode of high in?ation will push the ?nancial sector into action in terms of expanding the economy’s dollarization capital, by installing one exchange point which will be more closely located to one consumer than to the other. For a su?ciently high in?ation rate, both consumers will be willing to walk to the exchange point, therefore eliminating any incentive of the ?nancial sector to invest in a second exchange point. If in subsequent periods in?ation declines to a level that is low enough to discourage the more distant consumer from walking to the exchange point, the ?nancial sector will have an incentive to invest in a second money exchange point. This decision will locate both consumers at the same distance from an exchange point, eliminating heterogeneity in terms of access to ?nancial services, and lowering the in?ation threshold at which the second consumer is willing to substitute foreign for domestic currency. Thus, the model presented here is able to generate an equilibrium in which the relationship between in?ation and currency substitution is path dependent and di?ers before and after periods of high in?ation. From a theoretical point of view, the work presented here constitutes a step 88
along the lines of Guidotti and Rodrigues (1992), Uribe (1997) and Reding and Morales (2004) in terms explaining non-linearities in the relationship between in?ation and currency substitution. Guidotti and Rodrigues (1992) present a model in which agents may choose the currency in which purchases are denominated, but they must pay a cost every time they decide to switch the currency denomination of their transactions. Switching is optimal when the in?ation rate is su?ciently high; when in?ation drops back to a low level, inaction becomes optimal, generating a low-in?ation - high-currency-substitution equilibrium. Uribe (1997) remarks that Guidotti and Rodriguez (1992) ignores the possibility that hysteresis in currency substitution is likely to involve network e?ects. Therefore, he develops a model in which the economy’s accumulated experience in using a foreign currency as a means of payment reduces the cost of buying goods with foreign currency. Chapter 3 of this dissertation studies a model similar to Uribe’s but solved computationally. Uribe models this accumulated experience in using a foreign currency as a dollarization capital variable that is strictly increasing in the degree of dollarization of the economy. Reding and Morales (2004) depart from Uribe’s approach by not relying on a dollarization capital variable with exogenous dynamics, but rather trying to model explicitly the network e?ects related to the use of foreign currency. They assume agents are heterogeneous with respect to the transaction cost they face when they wish to use foreign currency as a means of payment. In turn, this cost is decreasing in the size of a foreign currency network, comprised of all agents whose balances in dollars are higher than an exogenous threshold. 89
The framework presented here can be seen as an e?ort to provide a micro foundation for the emergence and functioning of such a foreign currency network. This is done by considering an aspect not studied in the papers described so far: the role of the ?nancial sector in developing the economy’s dollarization capital. When thinking about the experience of several partially dollarized developing countries, it seems that the emergence of a network of foreign currency users is highly a?ected by the decision of the ?nancial sector to provide services in foreign currency. As mentioned earlier, this is very likely to be associated with di?erent types of investment costs (some of them ?xed). In the model presented here, a network of foreign currency users emerges only after the ?nancial sector has made the proper sunk investment. In this context, and in contrast to Uribe (1997), the economy’s dollarization capital corresponds to actual physical capital (the number of available exchange points), and, in contrast to Reding and Morales (2004), the currency substitution network is not composed of agents that have foreign currency holdings above some exogenous level, but by the ?nancial sector and those agents that have access to money exchange services. Further, whether an agent has access to ?nancial sector services or not depends on the consumer’s endogenous in?ation threshold for currency substitution and on the ?nancial sector’s endogenous optimal investment decision. Network expansion e?ects, then, are the result of interactions between optimal decisions on the consumer side and on the ?nancial sector side. Consumers de?ne their substitution behavior based on the level of in?ation and the availability 90
of exchange points (the level of dollarization capital), and do not internalize the impact that their demand for currency exchange services may have on the ?nancial sector’s decision to expand the number of exchange points. The ?nancial sector makes its optimal investment decision based on the potential demand that it would face if consumers had access to the proper level of dollarization capital (the pro?t maximizing number of exchange points). The rest of this chapter is organized as follows. The second section presents a simple three agent model used to study the consumer’s optimal currency substitution behavior and the ?nancial sector’s optimal dollarization capital investment decision. The third section concludes.
4.2
4.2.1
A simple three-agent model
The environment
The world consists of a local economy given by a horizontal space of measure one, as depicted in the top panel of Figure 4.1, and an external economy (the rest of the world). Prices in the local economy are not necessarily the same as those of the rest of the world. There are three agents in the local economy: a ?nancial sector that provides only one service, money exchange, and two consumers that start each period located on positions one and two. If these consumers want to acquire foreign currency they need to walk to the closest money exchange point constructed by the ?nancial sector. There can be at most two exchange points, and these can only be
91
located in positions A and B. Figure 4.1: MODEL ENVIRONMENT
4.2.2
Consumer’s problem
Each period consumers derive utility from consumption and disutility from walked distance. Preferences then are given by u(c) ? v (D) Where u(·) and v (·) are strictly increasing Bernoulli utility functions, c is 92
consumption and D is walked distance. The consumer’s problem is an intratemporal one, so time subscripts are ignored for simplicity. Each period starts with an initial price level (PI ) and ?nishes with a ?nal price level (PF ). At the beginning of each period, each consumer receives a real endowment y . As mentioned above, consumers receive utility from consumption and it is assumed that they need domestic money to buy the consumption good. That is, consumers cannot directly change their endowment y for consumption, but need money in order to perform the transaction. Therefore, after receiving their real endowment, consumers change it for nominal balances; at the end of the period, these balances are used to buy the consumption good. For simplicity, it is assumed that there is no savings technology; therefore, at the end of each period all currency balances must be exchanged for the consumption good. Then, the consumer’s problem consists solely of choosing the currency denomination of the nominal balances that she holds within the period. The sequence of actions is clari?ed by the graph presented in the second panel of Figure 4.1. The consumer starts the period with a real endowment y , which is immediately exchanged for domestic money at the initial price level. If the consumer has access to the money exchange services provided by the ?nancial sector (that is, if there is a money exchange point located either at position A or B or both), the consumer decides whether to keep these domestic currency balances or change them for foreign currency. If she chooses not to substitute, then the consumer gets to the end of the period with the initial amount of domestic money holdings and uses them to ?nance consumption at the end of period price level. In this case the consumer’s 93
utility is given by u(c) ? v (0). If the consumer instead decides to hold foreign currency balances, she needs to walk to the closest available money exchange point (located at distance D = d or D = 2d). There she pays a real fee f in order to change her domestic currency balances for foreign ones that she holds until the end of the period, when these are once again changed for domestic money and used to ?nance consumption. In this case the consumer’s utility is u(c) ? v (D). Let ? be the set of positions where the ?nancial sector has built a money exchange point. Then, the consumers’ substitution decision can be analyzed under three case: no exchange points, ? = { }, one exchange point, ? = {A} or ? = {B }, and two exchange points, ? = {A, B }.
Case 1. No Exchange Points Available, ? = { } This is a trivial problem since none of the consumers has a choice on the denomination of her currency holdings. At the beginning of each period, each consumer receives the real endowment y , which she changes for money holdings MI = yPI , where PI is the beginning-ofperiod domestic price level. At the end of the period, these money holdings are used to ?nance real consumption c =
MI , PF
where PF is the end-of-period domestic price
PF PI
level. De?ne gross in?ation, 1 + ? =
. Then, real consumption in terms of the
yPI PF
original endowment will be given by c =
y the period is u( 1+ ) ? v (0). ?
=
y 1+?
and the consumer’s utility in
94
Case 2 One exchange point available, ? = {A} or ? = {B } Consider the case in which there is a money exchange point available at point A. Let’s start by considering agent one, who is closest to A. After exchanging its real endowment y for money balances MI = yPI , the agent must decide whether to substitute MI for foreign currency or not. As derived in Case 1, if she decides not
y to substitute her utility will be u( 1+ ) ? v (0). ?
If she wants to substitute MI for foreign currency, she ?rst needs to walk to the exchange point, deriving disutility v (d), and then pay a real fee ?y , ? ? (0, 1), before
?1 obtaining M ? = SI (M ? ?yPI ), where SI = PI ? PI
is the initial nominal exchange
rate and PI? is the begeining-of-period foreign price level. Then, foreign currency holdings are given by M ? = (1 ? ? )yPI? . At the end of the period M ? is changed for domestic currency at the end-of-period exchange rate and real consumption is c=
M ? SF PF
=
(1?? )y , 1+? ?
?? )y where the consumer’s utility is u( (1 ) ? v (d). 1+? ?
Let s? 1 be a variable that indicates whether the consumer substitutes or not: ? ? ? ? 1 if consumer 1 substitutes s1 = ? ? ? ? 0 otherwise Then, consumer 1’s currency substitution problem is
U = max[U subst , U no subst ]
s1
(4.1)
U subst = u( U no subst
(1 ? ? )y ) ? v (d) 1 + ?? y ) ? v (0) = u( 1+?
Consumer 2’s problem is analogous, but with a lower utility payo? when sub95
stituting local for domestic currency balances:
U = max[U subst , U no subst ]
s2
(4.2)
U subst = u( U no subst
(1 ? ? )y ) ? v (2d) 1 + ?? y ) ? v (0) = u( 1+?
Then, in each period consumers one and two will substitute domestic for foreign currency holdings as long as
u( and
(1 ? ? )y y ) ? v (d) > u( ) ? v (0) ? 1+? 1+?
(4.3)
u(
(1 ? ? )y y ) ? v (2d) > u( ) ? v (0) ? 1+? 1+?
(4.4)
For a given level of foreign in?ation, ? ? , these two conditions implicitly de?ne two in?ation thresholds for currency substitution:
u(
(1 ? ? )y y ) ? v (d) > u( ) ? v (0) ? 1 + ?1 1+?
(4.5)
u(
(1 ? ? )y y ) ? v (2d) > u( ) ? v (0) ? 1 + ?2 1+?
(4.6)
For simplicity, consider the case of linear utility u(c) = c, v (D) = D. Then the substitution thresholds for in?ation are
96
?1 >
y (1 + ? ? ) ?1 (1 ? ? )y ? d(1 + ? ? )
(4.7)
?2 >
y (1 + ? ? ) ?1 (1 ? ? )y ? 2d(1 + ? ? )
(4.8)
As expected, the in?ation threshold increases with the cost of accessing the money exchange services provided by the ?nancial sector, and therefore agent two, who has a longer distance to walk to the nearest money exchange point, has a greater threshold than that of agent one.
Case 3. Two exchange points available, ? = {A, B } In this case both consumers are at distance d from the nearest money exchange point, and therefore they face the same problem as consumer one in the ? = {A, B } case, with both consumers willing to substitute foreign for domestic currency when ? >= ?1 . Figure 4.2 shows the relationship between in?ation and currency substitution in the three cases ? = { }, ? = {A} or ? = {B }, and ? = {A, B }. De?ne the economy’s end of period currency substitution ratio (CSR) as the ratio between foreign currency holdings evaluated at SF and total money holdings before consumption. When there are no exchange points available, this ratio is zero for every level of in?ation. When there is one exchange point available, only one consumer substitutes domestic for foreign currency when in?ation is greater than ?1 but smaller than ?2 . Then, before consumption, this consumer holds SF M ? money
97
holdings, while the other one holds MI . Therefore, the currency substitution ratio is given by
SF M ? . SF M ? +MI
When in?ation is above ?2 , both consumers hold SF M ? , so the
2SF M ? 2SF M ?
economy’s currency substitution ratio is
= 1. ?1 and ?2 correspond to levels
of in?ation at which either one or both consumers are indi?erent between holding domestic or foreign currency and therefore also admit any convex combination of these two options. For simplicity, from now on the possibility of a convex combination between the two currencies is ruled out by assuming that consumers fully switch to the foreign currency as soon as in?ation hits an indi?erence threshold. Finally, when two money exchange points are available both consumers have the same in?ation threshold and substitute domestic for foreign currency every time that ? ? ?1 .
4.2.3
The ?nancial sector’s investment problem
Each period, the ?nancial sector’s problem consists in deciding whether to install new exchange points or not. The maximum of installed exchange points is two and each one has a real cost of installation of F ? (0, ?y ). Every time that a consumer approaches a money exchange point, the ?nancial sector charges a real fee of ?y . It is assumed that once that an exchange point has been installed, it does not depreciate. Therefore, when no exchange point is available, ? = { }, the ?nancial sector decides between not investing in any exchange points, installing one exchange point at cost F , and installing two exchange points paying a cost of 2F . When there is only one exchange point available to consumers, ? = {A} or ? = {B }, the ?nancial
98
Figure 4.2: CURRENCY SUBSTITUTION AND INFLATION
sector’s problem consists of choosing whether not to invest in a new exchange point or installing it at cost F . Finally, when ? = {A, B } the ?nancial sector has no 99
investment decision. The ?nancial sector makes its investment decision before the consumers’ currency substitution decision. Then, this corresponds to a sequential game in which the ?nancial sector moves ?rst, deciding on the number of installed exchange points. This in turn is observed by the consumers, who make their currency substitution decision taking into account the availability of money exchange services. It is easier to start by considering a one-round game in which the ?nancial sector makes its investment decision, and the game ends with the consumers’ currency substitution choice after observing the behavior of the ?nancial sector.
A one period investment problem Case 1. Initial state: no exchange points available ? = { } The ?rm designs its investment strategy by anticipating the consumers’ behavior under di?erent levels of in?ation. If in?ation is below ?1 , none of the consumers requires money exchange services and the ?nancial sector pro?ts are ? = 0 when it decides not to set up any new exchange points, ? = ?F when it installs one new exchange point, and ? = ?2F when it installs two new exchange points. Its optimal decision then is not to install any exchange points. When ?1 ? ? < ?2 , only one consumer holds foreign currency when ? = {A} or ? = {B } and both consumers hold foreign currency balances when ? = {A, B }. Then, the ?nancial sector makes pro?ts ? = 0 when it decides not to set up any new exchange points, ? = ?y ? F when it installs one exchange point, and ? = 2(?y ? F ) when it installs two new exchange points. Its optimal decision then is to install two 100
exchange points. When ? ? ?2 , both consumers hold foreign currency as long as there is at least one money exchange point available. Then, the ?nancial sector pro?ts are ? = 0 when no new exchange points are installed, ? = 2?y ? F when one new exchange point is installed, and ? = 2(?y ? F ) when two ne exchange points are installed. Then, the ?nancial sector’s optimal decision is to install only one new exchange point.
Case 2. Initial state: one exchange point available ? = {A} or ? = {B } As in the previous case, when ? < ?1 the ?nancial sector’s optimal decision is not to install the new money exchange point. When ?1 ? ? < ?2 , the ?nancial sector makes pro?ts ? = ?y when it doesn’t install the new exchange point, and ? = 2?y ? F when it decides to install it. Its optimal decision then is to install the new money exchange point. When ? ? ?2 , both consumers hold foreign currency as long as there is at least one money exchange point available. Therefore, the ?nancial sector makes ? = 2?y when the new exchange point is not installed, and ? = 2?y ? F when it is installed. Then, the ?nancial sector’s optimal decision is not to install the new exchange point. Figure 4.3 depicts the relationship between the in?ation rate and the number of existing and new money exchange points.
In?ation, availability of exchange points and currency substitution Suppose that in?ation follows a stochastic process such that p(? = ? ) is the probability
101
Figure 4.3: EXCHANGE POINTS AND THE INFLATION RATE
of in?ation taking the value ? . Table 4.1 shows the probabilities governing the transition between exchange-technology states when each state is given by the number of available money exchange points. From the matrix it can be seen that, if the one period game solved above is played repeatedly, a su?ciently high number of realizations in which ? ? ?1 will lead the economy to a point in which both agents face the lowest possible cost in order to access the ?nancial sector services (that is, both agents are located at distance d from a money exchange point) and in which both agents have the same substitution threshold for in?ation (?1 ). Let no substitution, CSR = 0, partial substitution, CSR =
SF M ? SF M ? +MI
, and
complete substitution, CSR = 1 , denote the three possible currency substitution
102
outcomes of the model. Table 4.2 shows the probability of each outcome under the di?erent states given by the number of installed money exchange points. When the dollarization capital is at its maximum, ? = {A, B }, the economy does not display any partial substitution, and currency holdings are either completely denominated in domestic currency (with probability P (? < ?1 )) or fully dollarized (with probability P (? ? ?2 )). Table 4.1: In?ation Probabilities and the State of Exchange Points
Table 4.2: In?ation Probabilities and Currency Substitution
103
A forward-looking ?nancial sector Solving the ?nancial sector’s investment problem when it takes into account that consumers live in?nitely and repeat their currency substitution problem each period is cumbersome and the di?erent equilibria depend on the stream of in?ation realizations. For simplicity here I present two cases, one when in?ation is between ?1 and ?2 in every period and one when in?ation is above ?2 in very period.
Case 1. ?t = ? h ? ?2 for every t Suppose the economy starts with ? = { }. In period 1, the ?nancial sector has three options: invest in one new exchange point, invest in two new exchange points, and not to invest. If the ?nancial sector invests in two new exchange points at t = 1, then it makes ? = 2(?y ? F ) in the ?rst period and ? = 2?y in every period after that. So the present discounted value of the ?nancial sector pro?t stream is
1 1??
2?y ? 2F ,
where ? ? (0, 1) is the ?nancial sector’s time discount factor. This value is greater than that obtained when the ?nancial sector decides not to invest at t = 1 and instead installs both exchange points in the second period,
? 1??
2?y ? ? 2F , and
greater than that obtained when no investment is made in t = {1, 2} and both exchange points are installed in the third period,
?2 1??
2?y ? ? 2 2F and so on.
If the ?nancial sector invests in only one exchange point at t=1, then it makes ? = 2?y ? F in the ?rst period and ? = 2?y every period after that, so the present discounted value of its pro?t stream is
1 1??
2?y ? F , greater than those
? 1??
obtained if the investment is made in period two,
?2 1??
2?y ? ?F , or in period 3,
2?y ? ? 2 F , and so on. 104
The ?nancial sector could also invest in the ?rst exchange point at period t = 1, and in the second one at t = 2, making present discounted pro?ts equal to
1 1??
2?y ? F ? ?F . However, postponing investing in the second exchange point
1 1??
for one period delivers a higher pro?t present discounted value,
2?y ? F ? ? 2 F .
Postponing investing in the second exchange point for two periods yields an even higher present discounted value,
1 1??
2?y ? 2F , and so on. Since in?ation is above
?2 in every period, both consumers are willing to substitute and demand money exchange services from the ?nancial sector who each period receives real fees of 2?y . This income stream is not changed by the installation of the second exchange point, so it not optimal to incur additional investment costs. After considering all possible options, the ?nancial sector’s optimal investment decision when the in?ation path is {? h , ? h , ? h , ...} is to install only one exchange point at t = 1.
Case 2. ?t = ? m , ?1 < ? m ? ?2 for every t When the ?nancial sector invests in two new exchange points at t = 1, it makes discounted pro?ts
1 1??
2?y ? 2F ,
greater than those obtained if the two exchange points are simultaneously installed at any future period. If the ?nancial sector invests in only one exchange point and does so at t = 1, the present discounted value of pro?ts is
1 1??
?y ? F , greater than
that obtained if only one exchange point is installed in any period in the future. If the ?nancial sector invests in one exchange point in period t = 1 and in another in period t = 2, the present discounted value of pro?ts is ?y +
? 1??
2?y ?
(1 + ? )F , greater than that obtained if the two exchange points are separately
105
installed at any two di?erent periods in the future. After considering all possible options, the ?nancial sector’s optimal investment decision when the in?ation path is {? m , ? m , ? m , ...} is to install two exchange points in the ?rst period.
An example of the path of in?ation and currency substitution over time After the analysis of the problems of the two consumers and the ?nancial sector it is easy to think about some possible cases in which the co-movement between currency substitution and in?ation will not be the same before and after a period of high in?ation. Think for example of a case in which before period T in?ation remains at ? l < ?1 , then it increases to ? h ? ?2 at t = T , and decreases to ? m ? [?1 , ?2 ) from t = T + 1 onwards. Assume also that there are no exchange points installed before t = T. Using the analysis described in the previous section, it can be shown that the ?nancial sector’s optimal investment decision when the in?ation path is {..., ?T ?1 = ? l , ?T = ? h , ?T +1 = ? m , ?T +2 = ? m , ...} is not to invest before t = T , invest in one exchange point at t = T and invest in the second one at t = T +1. The second panel of Figure 4.4 shows the time path of economy’s dollarization capital (the optimal number of available exchange points). The third panel of the ?gure depicts the time path of currency substitution associated with the given pattern of in?ation. Before t = T , the currency substitution ratio is zero in every period; at t = T , the ?nancial sector installs one exchange
106
Figure 4.4: PATHS OF INFLATION AND CURRENCY SUBSTITUTION
point and both consumers are willing to use its services, so all money balances in the economy are dollarized and the currency substitution ratio is 1. Finally, since a second exchange point is installed at t = T + 1, both consumers are at distance d from an exchange point, and an in?ation rate lower than ? h but greater or equal than ?1 is enough to guarantee that the currency substitution ratio remains at 1. The main message of the simple framework presented so far is that, in the 107
presence of ?xed costs associated with the investment decisions of the ?nancial sector, an episode of high in?ation may push the ?nancial sector into action in terms of expanding the economy’s dollarization capital, therefore reducing (maybe permanently) the foreign currency usage costs faced by consumers and decreasing the in?ation threshold at which households are willing to substitute domestic for foreign currency.
4.3
Conclusion
The framework presented here constitutes a step forward in developing a micro foundation for the presence of network e?ects and dollarization capital dynamics in models of currency substitution. The dollarization capital variable corresponds to physical capital used for the provision of money exchange services, and the network of foreign currency users is composed of the ?nancial sector and those consumers who have access to the ?nancial sector’s money exchange services. Whether a consumer belongs or not to the network depends on endogenously determined in?ation thresholds for currency substitution and on the endogenously determined optimal level of dollarization capital. The combination of ?xed costs associated with investment in money exchange services and consumer heterogeneity in terms of access to ?nancial services provides an environment in which the relationship between currency substitution and in?ation is not linear. Particularly, the model is able to deliver asymmetries in the relationship between in?ation and currency substitution before and after high in?a-
108
tion episodes. Starting from a level in which there are no exchange services available in the economy, a period of high in?ation followed by one of moderate in?ation will push the ?nancial sector to expand the economy’s dollarization capital, permanently reducing the consumer’s cost of using foreign currency and decreasing the in?ation thresholds at which they are willing to substitute foreign for domestic currency. A natural step for future research is to embed the mechanism explored here into a fully-speci?ed DSGE environment, providing a tool for a more comprehensive empirical analysis of the currency substitution phenomenon in Developing Countries and Transition Economies.
109
Appendix A
Appendix to Chapter 1
A.1
Calvo stickiness in regular prices
Optimal regular price and price aggregators When the regular price is sticky, ?rm j’s pricing decision problem is
?
p pr jt ,pjt ,fjt
max Et
s= t
?
? pr jt h
s?t
h h ?t+s/t {pp js h? (fjs , ss )
Psh pp js ch s +
?
ch s
? pr jt (1
+
pp js (1
? h)?
l
l
(fjs , sl s)
Psl pp js Psl ? pr jt Psl pp js Psl ? pr jt
? ?
?
cl s cl s}
?
+
1??
h
(fjs , sh s)
Psh ? pr jt
h
?
? h) 1 ? ? ch s
(fjs , sl s)
l
? mcjs Ps {h? +h 1??
h
(fjs , sh s) Psh ? pr jt
?
Psh pp js ch s
?
+ (1 ? h)?
l
(fjs , sl s)
cl s cl } A.1) s(
(fjs , sh s)
+ (1 ? h) 1 ? ?
(fjs , sl s)
Eliminating in?nite sums in the regular price optimality condition 110
? Rearranging the ?rst order condition for pr t :
? ? pr jt
(? ? 1)Et
t=s ?
hr ?s?t ?t+s/t h 1 ? ?h (fjs , sh js ) cjs
? + pr jt
(? ? 1)Et
t=s ?
lr ?s?t ?t+s/t (1 ? h) 1 ? ?l (fjs , sl js ) cjs
=
?Et
t=s ?
hr ?s?t ?t+s/t h 1 ? ?h (fjs , sh js ) cjs mcjs Ps
+ ?Et
t=s
lr ?s?t ?t+s/t (1 ? h) 1 ? ?l (fjs , sl js ) cjs mcjs Ps
(A.2)
The numerator and denominator terms in the right hand side of (A.2) have current and forward looking variables. Following Schmitt-Grohe and Uribe (2004b,2005) this expression can be rewritten in a recursive fashion by de?ning four auxiliary varib c d ables: xa t , xt , xt and xt .
Working with the four terms in (A.2) , de?ne
?
Pt x a t
=
? pr jt (?
? 1)Et
t=s
?
s? t
?t+s/t h 1 ? ?
h
(fjs , sh js )
? pr jt Psh
??
ch t
(A.3)
?
Pt x b t
=
? pr jt (?
? 1)Et
t=s
?
s? t
?t+s/t (1 ? h) 1 ? ?
l
(fjs , sl js )
? pr jt Psl
??
cl t
(A.4)
?
Pt x c t
= ?Et
t=s
?
s? t
?t+s/t h 1 ? ?
h
(fjs , sh js )
? pr jt Psh
??
ch t Ps mcs
(A.5)
?
Pt x d t
= ?Et
t=s
?
s?t
?t+s/t (1 ? h) 1 ? ?
l
(fjs , sl js )
? pr jt Psl
??
cl t Ps mcs
(A.6)
Where 111
• Pt x a t is the present discounted nominal marginal revenue of serving the HEC’s demand at regular prices until the next price change. • Pt x b t is the present discounted nominal marginal revenue of serving the LEC’s demand at regular prices until the next price change. • Pt x c t is the present discounted nominal marginal cost of serving the HEC’s demand at regular prices until the next price change. • Pt x d t is the present discounted nominal marginal cost of serving the LEC’s demand at regular prices until the next price change. After some algebra it can be shown that
xa t =
pr jt Pth
?? h h 1 ? ?h (fjt , sh jt ) ct (? ? 1)
? pr pr? Pt+1 a jt + Et ??t+1/t rt? x Pt pt+1 Pt t+1
(A.7)
xb t
=
pr jt Ptl
??
(1 ? h) 1 ? ?
h
(fjt , sh jt )
cl t (?
? pr pr? Pt+1 b jt ? 1) + Et ??t+1/t rt? x (A.8) Pt pt+1 Pt t+1
xc t =
pr jt Pth
?? h h 1 ? ?h (fjt , sh jt ) ct ?mct + Et ??t+1/t
Pt+1 c x Pt t+1
(A.9)
xd t
=
pr jt Ptl
?? l (1 ? h) 1 ? ?h (fjt , sh jt ) ct ?mct + Et ??t+1/t
Pt+1 d x Pt t+1
(A.10)
Then, (A.2) can be expressed as
d a b xc t + xt = xt + xt
(A.11)
112
Now the ?rst order condition for regular prices can be expressed in a recursive framework and the ?rm’s optimal pricing conditions are given by equations (2.18), (2.19) and (A.12) , and the expressions for Pth and Ptl are given by
d a b xc t + xt = x t + xt
(A.12)
p 1?? r? 1?? 1?? r + ? 1 ? ?h (f, sh Pth = ?h (f, sh + (1 ? ?) 1 ? ?h (f, sh t ) (pt?1 ) t )(pt ) t ) (pt )
1 1??
(A.13)
p 1?? 1?? r? 1?? r Ptl = ?l (f, sl + (1 ? ?) 1 ? ?l (f, sl + ? 1 ? ?l (f, sl t )(pt ) t ) (pt ) t ) (pt?1 )
1 1??
(A.14) where pr t is the average regular price across ?rms
1
pr t
=
0
pr t Ptl
dj
(A.15)
and can be expressed recursively as
r? r pr t = ?pt?1 + (1 ? ?)pt
Othe equilibrium conditions Since not all ?rms are able to set their price optimally every period, symmetry cannot be applied in the same fashion as in the ?exible price case, and several equations of the model need to be modi?ed.
113
The resource constraint and economy wide price equations are now expressed as
h l ez t hnt + (1 ? h)nt
hp h h h1 h = h?h (ft , sh t )cjt + h 1 ? ? (ft , st ) dt ct lp l l l1 l + (1 ? h)?l (ft , sl ct t )cjt + (1 ? h) 1 ? ? (ft , st ) dt (A.16)
Pt
hp l l lp h?h (ft , sh t )cjt + (1 ? h)? (ft , st )cjt p = pt ct h2 h 1 ? ?h (ft , sh t ) dt Pth + ct l2 (1 ? h) 1 ? ?l (ft , sl t ) dt Ptl + ct
(A.17)
where
hp h h h1 h l l lp l l l1 l ct = h?h (ft , sh t )cjt +h 1 ? ? (ft , st ) dt ct +(1?h)? (ft , st )cjt +(1?h) 1 ? ? (ft , st ) dt ct
The consumption aggregators are given by ?
? ? ?? 1
? ch t =
1
l And the sh t and st ?rst order conditions are
? cl t =
?
hp ? ? (f, sh t )ct ? h h2 ? [1 ? ?t (f, sh t )]dt h lp ? ?l (f, sl t )ct ? l l2 ? [1 ? ?t (f, sl t )]dt
? ?1
??1
(A.18)
1
? ? ?? 1
(A.19)
114
h v (1 ? nh t ? st ) =
? ??1 ?
hp h ? h ch t ?s (f, st ) c?h t
1
??1 ?
2 h ? dh t ct
??1 ?
u (ch t) (A.20)
h ?s (f, sh t)
pp chp 2 h ?h t ?h t ? dh u ( ch t ct t) Pth
l v (1 ? nl t ? st ) =
? ??1
lp l ? l cl t ?s (f, st ) c?l t
1
? ?1 ?
2 l ? dl t ct
? ?1 ?
u (ch t) (A.21)
l ? ?s (f, sl t)
pp chp l 2 l ?l t ?l t ? dl t ct u (ct ) l Pt
Where
1 dh t = 1 0 1 0 1 0 1 0 pr t h Pt pr t l Pt pr t h Pt pr t l Pt ??
dj
??
1 dl t =
dj
1??
2 dh t =
dj
1??
2 dl t =
dj
l2 l1 h2 1 And dh1, dh t , dt , dt and dt can be expressed recursively as
1 dh t
=?
1 h e?t
?? 1 dh t?1
+ (1 ? ?)
? pr t Pth
??
(A.22)
l1 dt
=?
1 l e?t
?? 1 dl t?1
+ (1 ? ?)
? pr t Ptl
??
(A.23)
2 dh t
=?
1 h e?t
1?? 2 dh t?1
+ (1 ? ?)
? pr t Pth
1??
(A.24)
115
2 dl t
=?
1 l e ?t
1?? 2 dl t?1
+ (1 ? ?)
? pr t Ptl
1??
(A.25)
In order to reduce the size of the state space, the model is solved around a
l2 l1 h2 1 zero-in?ation steady state, ignoring the evolution of dh t , dt , dt and dt .
In order to reduce the size of the state space, the model is solved around a
1 h2 l1 l2 zero-in?ation steady state, ignoring the evolution of dh t , dt , dt and dt .
A.2
Looking for f in the data
The James M. Kilts Center at the University of Chicago Booth School of Business has made available several datasets on weekly store-level transaction prices for over 100 stores operated by Dominick’s Finer Foods (DFF) for the 1989 – 1997 period. The customer count ?le includes information about in-store tra?c. The data is store speci?c and on a daily basis. The customer count data refers to the number of customers visiting the store and purchasing something. Also in the customer count ?le is a total dollar sales and total coupons redeemed ?gure, by DFF de?ned department (product category). The ?gures are compiled daily from the register/scanner receipts.1 The average fraction of time at which a good is o?ered on coupon promotions is calculated through the following steps: 1. Aggregate the coupon redemption ?gure by store and by week (all stores with less than 52 time observations were dropped).
1
The data is available athttp://research.chicagobooth.edu/marketing/databases/dominicks/ccount.aspx
116
2. Construct the following dummy variable for each product category: ? ? ? ? ? ? 1 if coupon redemption = 0 ? ? dt = ? ? ? ? 0 if coupon redemption = 0 ? ?
Then, the underlying assumption is that if a promotion is available in a given
week, then there is at least one person that takes advantage of it (alternatively, at least one coupon is redeemed ). Therefore, it is assumed that if the coupon redemption ?gure in a given week is zero (dt = 0), then no coupons were o?ered that week. 3. Compute fk =
t
dt /(number of weeks), the fraction of time that good k
was o?ered on promotion. 4. Compute f =
k
fk /(number of good categories), the average fraction of
time at which goods are o?ered on promotion. If the underlying assumption in step 2 is wrong, then f is a lower bound for f. Table A1 shows the results for all the product categories for which coupons were o?ered at least once in the sample time range. Table A2 presents the mean value across products and stores. Table A.1: Fraction of Weeks by Department
Table A3 presents the mean value across products and stores when including all product categories. 117
Table A.2: Fraction of Weeks: Sample I
Table A.3: Fraction of Weeks: Sample II
A.3
The Firm’s Problem Under Perfect Price Discrimination (PPD)
For simplicity, here I present the case of ?exible prices. If the ?rm could distinguish between consumer types, its pro?t maximization problem would be:
P D l,P P D ph,P ,pjt jt
max
P D h,P P D P D l,P P D ?maxjt = hph,P cjt + (1 ? h)pl,P cjt jt jt PD PD ? mcjt Pt {hch,P + (1 ? h)cl,P } jt jt
(A.26)
subject to
PD ch,P jt
=
PD ph,P jt
?? PD ch,P t
Pth,P P D
(A.27)
118
PD cl,P = jt
PD pl,P jt
?? PD cl,P t
Ptl,P P D
(A.28)
PD where ck,P , k = h, l are quantities consumed by consumers under perfect jt PD price discrimination and pk,P , k = h, l are the prices charged by the ?rm. jt
Solving the problem, the ?rm’s optimal price choices are:
PD ph,P t = Pt
? ??1
mct
(A.29)
PD pl,P t = Pt
? ??1
mct
(A.30)
These same optimal prices can be recovered from the ?rms problem with price
l promotions with sh t = 1 and st = 0 when the ?rm chooses ft = 1. To see this,
consider the optimality conditions from the ?rm’s problem in the model with price promotions solved in Section 2.1.2 are:
hr l l lr h 1 ? ?h (fjt , sh t ) cjt + (1 ? h) 1 ? ? (fjt , st ) cjt =
1?
Pt mct pr jt
hr l l lr h[1 ? ?h (fjt , sh t )]?cjt + (1 ? h)[1 ? ? (fjt , st )]?cjt
(A.31)
hp l l lp h?h (fjt , sh t )cjt + (1 ? h)? (fjt , st )cjt =
1?
Pt mct pp jt
hp lp l l h?h (fjt , sh t )?cjt + (1 ? h)? (fjt , st )?cjt
(A.32)
119
pp jt ? mct Pt pr jt ? mct Pt
hp l lp l h (fjt , sh h?f t )cjt + (1 ? h)?f (fjt , st )cjt h hr l l lr h?f (fjt , sh t )cjt + (1 ? h)?f (fjt , st )cjt
= (A.33)
l when sh t = 1 and st = 0, these collapse to
lr h(1 ? fjt )chr jt + (1 ? h)cjt =
1?
Pt mct pr jt
lr h(1 ? fjt )?chr jt + (1 ? h)?cjt
(A.34)
chp jt =
1?
Pt mct ?chp jt pp jt
(A.35)
hp r hr pp jt ? mct Pt hfjt cjt = pjt ? mct Pt hfjt cjt p from (A.36) pr jt > pjt and rearranging (A.35)
(A.36)
pp t = Pt
? ??1
mct =
PD ph,P t Pt
(A.37)
Finally, when the ?rm sets ft = 1 and rearranging (A.34)
pr t = Pt
? ??1
PD pl,P t mct = Pt
(A.38)
120
A.4
Monetary Model with Price Promotions: Impulse Response Functions
Real output (% deviation from steady state value) Labor time (% deviations from steady state values) Prices (% deviations from steady state values)
0.00%
0.05%
1
-0.02%
6
11
16 21output 26 31 Real
36
41
46
51
0.00%
0.04%
(% deviation from steady state value)
Labor time (% deviations from steady state values) nh
0.03% 1 6 11 16 21 26 31 36 41 46 51
0.05%
Prices price discount (% deviations from steady state values) relativel regular price
-0.04% 0.00% -0.06% -0.02% -0.08% -0.04% 0.00% -0.10% 1 -0.06% -0.02% -0.12% -0.08% -0.04% -0.14% -0.10% -0.06% -0.16% -0.12% -0.08% -0.18% -0.14% -0.10% -0.16% -0.12% -0.18% -0.14% 0.0003 -0.16% -0.18% 0.0002 0.0003 6 11 1 6 11
(% deviation from steady state value)
Real output 16 21 26 31
36
41
46
51
-0.05%
0.00%
Labor time (% deviations from steady state values) h
0.04%
n N
6
relative promotional price average price response Prices price discount 0.02% (% deviations from steady state values) relativel regular price relative promotional price price discount average price response relativel regular price 1 6 11 16 21 26 relative 31 36 41 46 51 promotional price average price response
0.03% 11 16 21 26 31 36 41 46 51 0.01% 0.04% 0.02% 0.00% 0.03% 11 16 21 26 31 36 41 46 51 0.01% -0.01% 0.02%
-0.10% 0.05% 16 21 26 31 36 41 46 51 -0.05% -0.15% 0.00%
1
nh N
1 6
-0.10% -0.20% -0.05% -0.15% -0.25% -0.10% -0.20%
nl N nl
Time spent looking for price promotions (% deviations from steady state values)
0.00% -0.02% 1 0.01% -0.01%
6
11
16
21
26
31
36
41
46
51
Real interest rate
-0.15% -0.25% -0.20% 0.08%
nl
Size of the promotion-economy and fraction of time 0.00% 1at which 6 11goods 16 are 21 offered 26 31 on 36promotion 41 46 51 -0.02% (% deviations from steady state values)
-0.01%
Real interest rate
Time spent looking for price promotions sl -0.25% 0.06% (% deviations from steady state values)
0.04% 0.08%
-0.02% at which goods are offered on promotion -0.02%
Size of the and36 fraction of time 1 promotion-economy 6 11 16 21 26 31 41 46 51 (% deviations from steady state values)
0.00%
Real interest rate
0.0002
0.02% 0.06% 0.08% 0.00% 0.04% 0.06% -0.02% 0.02%
0.04% -0.04% 0.00%
Time spent looking for price promotions l (%sdeviations from steady state values)
S
-0.04% 0.00% Size of the promotion-economy and fraction of time 6 goods 11 16 21 26 31 36 41 46 51 at 1 which are offered on promotion ?t -0.06% -0.02%(% deviations from steady state values) 0.00% -0.08% -0.04%
-0.02% -0.10% -0.06%
0.0002 0.0003 0.0001
0.0002 0.0002
1
sl S
6
11
16
21
26
31
36
41
46
51
1
6
11
16
21
26
31
36
41
46
51
?t
0.0001 0.0001 0.0002 0.0000 0.0001 0.0001 1 6 11 16 21 26 31 36 41 46 51
1 0.02% -0.06% -0.02% 0.00% -0.08% -0.04%
-0.02% -0.06%
6
sh
-0.04% -0.12% -0.08% 16 21 26 31 36 41 46 51 -0.06% -0.14% -0.10% -0.08% -0.16% -0.12%
-0.10% -0.14%
ft
?t
11
S
1 6
sh11
16
21
26
31
36
41
46
51
ft
0.0000 0.0001 1
6
11
16
Consumption
21 26
31
36
41
46
51
-0.04% -0.08% -0.06% 0.0016
sh
Real wage
-0.12% -0.16% -0.14% 0.00
ft
Real balances
0.0008 0.0000 1 0.0006 0.0004 0.0008 0.0002 0.0006 0.0000 0.0004 1 0.0008 -0.0002 0.0002 0.0006 -0.0004 0.0000 0.0004 -0.0006 -0.0002 0.0002 -0.0008 -0.0004 0.0000 -0.0010 1 -0.0006 -0.0002 -0.0008 -0.0004 -0.0010 -0.0006 -0.0008 -0.0010
6
11
Consumption 16 21 26 31
36
41
46
51
0.0014 -0.08% 0.0012 0.0016 0.0010 0.0014 0.0008
Real wage
HEC component of the reaL wage
1 -0.16% -0.20 0.00 -0.40 -0.20 -0.60 0.00 -0.40 1 -0.80 -0.20 -0.60 -1.00 -0.40 -0.80 -1.20 -0.60 -1.00 -1.40 41 46 51
-0.80 -1.20
6
11
16
Real balances
21
26
31
36
41
46
51
chp
chr
Consumption
al
1 6 11 16 21 26 31 Real balances 36 41 46 51
Real wage
HEC component of the reaL wage
chp
6 11 hr 16 c 21 26 31 36 41 46 51
0.0012 0.0016 0.0006 0.0010 0.0014 0.0004
w
HEC component of the reaL wage
al
6 11 16 21 26 31 36 41 46 51
ah al ah
chp
1 6
clr
11 chr16 21 26 31 36 41 46 51
0.0008 0.0012 0.0002
0.0006 0.0010 0.0000
clp
w
6 11 16 21 26 31 36 41 46 51 LEC component of the reaL wage
clr
6 11 16 21 26 31 36 41 46 51
0.0004 1 0.0008 -0.0002 0.0002 0.0006 -0.0004 0.0000 0.0004 1
w
6 11 16 21 26 31 36
clp clr clp
ah
-0.0002 0.0002 -0.0004 0.0000 1 -0.0002 -0.0004
LEC component of the reaL wage -1.00 -1.40 6 11 16 21 26 31 36 41 46 51 -1.20
LEC component of the reaL wage -1.40
121
Appendix B
Appendix to Chapter 2
ÔÔ Ò Ü ½ Ë È È Ê
Table B.1: Data Series Used in the Document
ËÖ × ÆÓÑ Ò Ð È ÆÓÑ Ò Ð È ÈÖ Ú Ø ÓÒ×ÙÑÔØ ÓÒ ÈÖ Ú Ø ÓÒ×ÙÑÔØ ÓÒ ÓÖ Ò ÙÖÖ Ò Ý ÔÓ× Ø× ÓÖ Ò ÙÖÖ Ò Ý ÔÓ× Ø× ÜØ ÖÒ Ð ÈÓ× Ø ÓÒ× Ó ÁË Ê ÔÓÖØ Ò ÜØ ÖÒ Ð ÈÓ× Ø ÓÒ× Ó ÁË Ê ÔÓÖØ Ò ÅÓÒ Ý Ö Ø× ÅÓÒ Ý Ö Ø× ÓÒ×ÙÑ Ö ÈÖ ÁÒ Ü ÓÒ×ÙÑ Ö ÈÖ ÁÒ Ü ÓÙÒØÖÝ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ËÓÙÖ ÆÁË Ê È ÆÁË ÁÅ ¹Á Ë Ê È ÁË ÁË Ê È Ê È ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ Ø ËÔ Ò ¼¹¾¼¼ ¹¾¼¼ ¼¹¾¼¼ ¹¾¼¼ ¼¹¾¼¼ ¹¾¼¼ ¼¹¾¼¼ ¹¾¼¼ ¼¹¾¼¼ ¹¾¼¼ ¹¾¼¼ ¹¾¼¼
Ò × ´Ð Ò × ´Ð
Ð Ø ×µ Ð Ø ×µ
ÆÁË ÓÐ Ú Ò Æ Ø ÓÒ Ð ÁÒ×Ø ØÙØ Ó ËØ Ø ×Ø × ÁË Ò Ó ÁÒØ ÖÒ Ø ÓÒ Ð Ë ØØÐ Ñ ÒØ× ÒØÖ Ð Ò Ó ÓÐ Ú Ê È ÒØÖ Ð Ê × ÖÚ Ò Ó È ÖÙ ÁÅ ¹Á Ë ÁÒØ ÖÒ Ø ÓÒ Ð ÅÓÒ Ø ÖÝ ÙÒ ¸ ÁÒØ ÖÒ Ø ÓÒ Ð Ò Ò Ð ËØ Ø ×Ø ×
122
ÔÔ Ò Ü ¾ Ë È È Ê
Table B.2: Money Aggregates
Ž
ÓÐ Ú
Ž³ ž ž³ Å¿ Å¿³
È ÖÙ
ÙÖÖ Ò Ý Ò Ö ÙÐ Ø ÓÒ ÔÐÙ× × Ø ÔÓ× Ø× ÒÓÑ Ò Ø Ò Ò Ø ÓÒ Ð ÙÖÖ Ò Ý Å½ ÔÐÙ× × Ø ÔÓ× Ø× ÒÓÑ Ò Ø Ò ÓÖ Ò ÙÖÖ Ò Ý ÔÓ× Ø× Å½ ÔÐÙ× × Ú Ò ÔÓ× Ø× ÒÓÑ Ò Ø Ò Ò Ø ÓÒ Ð ÙÖÖ Ò Ý Å½³ ÔÐÙ× × Ú Ò ÔÓ× Ø× ÒÓÑ Ò Ø Ò ÓÖ Ò ÙÖÖ Ò Ý Å¾ ÔÐÙ× Ø Ñ ÔÓ× Ø× Ò ÓØ Ö ×× Ø× ÒÓÑ Ò Ø Ò Ò Ø ÓÒ Ð ÙÖÖ Ò Ý Å¾³ ÔÐÙ× Ø Ñ ÔÓ× Ø× Ò ÓØ Ö ×× Ø× ÒÓÑ Ò Ø Ò ÓÖ Ò ÙÖÖ Ò Ý ÙÖÖ Ò Ý Ò Ö ÙÐ Ø ÓÒ ÔÐÙ× × Ø ÔÓ× Ø× ÒÓÑ Ò Ø Ò Ò Ø ÓÒ Ð ÙÖÖ Ò Ý Ë ÚÒ Ò ØÑ ÔÓ× Ø× Ò ÓØ Ö ×× Ø× ÒÓÑ Ò Ø Ò ÓÑ ×Ø ÙÖÖ Ò Ý Ë ÚÒ Ò ØÑ ÔÓ× Ø× Ò ÓØ Ö ×× Ø× ÒÓÑ Ò Ø Ò ÓÖ Ò ÙÖÖ Ò Ý
ÅÓÒ Ý ÉÙ × ÑÓÒ Ý Ò ÓÑ ×Ø ÉÙ × ÑÓÒ Ý Ò ÓÖ ÙÖÖ Ò Ý
Ò ÙÖÖ Ò Ý
ÔÔ Ò Ü ¿ Ë È È Ê
ÓÐ Ú
ÈÖ ¹ ÝÔ Ö Ò Ø ÓÒ ÀÝÔ Ö Ò Ø ÓÒ ÈÓ×ع ÝÔ Ö Ò Ø ÓÒ
Table B.3: In?ation Periods
Ö×
½ ¼¹½ ½ ½ ¾¹½ ½ ¹¾¼¼
ÒÒÙ Ð Ò Ø ÓÒ ´Ô Ö Ó Ú Ö µ
¾ ¸ ± ¾ ¿± ½½¸¿±
È ÖÙ
ÈÖ ÝÔ Ö Ò Ø ÓÒ ÀÝÔ Ö Ò Ø ÓÒ ÈÓ×Ø ÝÔ Ö Ò Ø ÓÒ
Ö×
½ ¹½ ½ ¹½ ½ ½ ¾¹¾¼¼
ÒÒÙ Ð Ò Ø ÓÒ ´Ô Ö Ó Ú Ö µ
¿¸ ± ¼ ± ½ ¸ ±
123
BIBLIOGRAPHY
[1] Albrecht, J., F. Postel-Vinay and S. Vroman (2010). ”A Search-Theoretic Model of Sales”.
[2] Altig, D., L. Christiano, M. Eichenbaum and J. Linde, 2005. ”Firm-Speci?c Capital, Nominal Rigidities and the Business Cycle”, NBER Working Paper No. 11034.
[3] Arseneau, D. and S. Chugh (2007). ”Bargaining, Fairness, and Price Rigidity in a DSGE Environment”.
[4] Aruoba, B. and F. Schorfheide (2009). ”Sticky Prices Versus Monetary Frictions: An Estimation of Policy Trade-o?s”, NBER Working Paper No. 14870.
[5] Aruoba, B. and F. Schorfheide (2011). ”Sticky Prices Versus Monetary Frictions: An Estimation of Policy Trade-o?s”, Forthcoming American Economic Journal: Macroeconomics
[6] Banks, J. and S. Moorthy (1999). ”A Model of Price Promotions With Consumer Search”, International Journal of Industrial Organization 17, 371-398. 124
[7] Bernard, A., J. Eaton, J. Bradford Jensen, and S. Kortum (2003). ”Plants and Productivity in International Trade”, American Economic Review, Vol. 93 No. 4.
[8] Bilbiie, F., F. Ghironi, and M. Melitz (2007). ”Monetary Policy and Business Cycles with Endogenous Entry and Product Variety”, NBER Working Paper No. 13199.
[9] Bils, M. and P. J. Klenow (2004). ”Some Evidence on the Importance of Sticky Prices”, Journal of Political Economy 112, 947-985.
[10] Cavallo, A. (2010). ”Scraped Data and Sticky Prices: Frequency, Hazards and Synchronization”, Harvard Job Market Paper.
[11] Chevalier, J. A., A. K. Kashyap and P. E. Rossi (2003). ”Why Don’t Prices Rise During Periods of Peak Demand? Evidence from Scanner Data”, The American Economic review. Vol. 93, No. 1, pp. 15-37.
[12] Cooley, T. and G. Hansen (1989). ”The In?ation Tax in a Real Business Cycle Model,” American Economic Review, vol. 79(4), pages 733-48, September.
[13] Cooley, T. and G. Hansen (1995). ”Money and the Business Cycle”, in Frontiers of Business Cycle Research, Thomas F. Cooley editor., Princeton University Press, pp. 175-216.
125
[14] Dhyne, E., L. J. lvarez, H. Le Bihan, G. Veronese, D. Dias, J. Ho?mann, N. Jonker, P. Lnnemann, F. Rumler and J. Vilmunen (2006). ”Price Changes in the Euro Area and the United States: Some Facts from Individual Consumer Price Data”, The Journal of Economic Perspectives, Vol. 20, No. 2, pp. 171-192.
[15] Eichenbaum, M., N. Jaimovich and S. Rebelo (2011). ”Reference Prices and Nominal Rigidities”, American Economic Review, vol. 101, issue 1, pp. 234262.
[16] Feige, E. (2003). “The Dynamics of Currency Substitution, Asset Substitution and De facto Dollarization and Euroization in Transition Countries”, Comparative Economic Studies 45, 358-383.
[17] Golosov, M. and R. Lucas Jr. (2007). ”Menu Costs and Phillips Curves,” Journal of Political Economy, University of Chicago Press, vol. 115, pages 171-199.
[18] Green, E. (2005). ”A Review of Interest and Prices: Foundations of a Theory of Monetary Policy by Michael Woodford”, Journal of Economic Literature Vol. XLIII, pp. 121-134.
[19] Guidotti, P. E., Rodriguez, C. A. (1992). ”Dollarization in Latin America Gresham law in reverse”, International Monetary Fund Sta? Papers, 39, 518544
[20] Guimaraes, B. and K. Sheedy (2008). ”Sales and Monetary Policy”, CEPR
126
discussion paper #6940.
[21] Guimaraes, B. and K. Sheedy (2011). ”Sales and Monetary Policy”, American Economic Review vol. 101(2), pp. 844-76.
[22] Hall, Robert E. (2007). ”Equilibrium Sticky Prices”.
[23] Hansen, G. (1985). ”Indivisible Labor and the Business Cycle”, Journal of Monetary Economics 16, 309-328.
Havrylyshyn, O. and Beddies, C.H. (2003). ”Dollarization in the former Soviet Union: From hysteria to hysteresis”. Comparative Economic Studies, 45, 329357.
[24] Hosken, D. and D. Rei?en (2004). ”How Retailers Determine Which Products Should Go on Sale: Evidence From Store-Level Data”, Journal of Consumer Policy, Vol. 27, No. 2, pp. 141-177.
[25] Kehoe, P. J. and V. Midrigan (2007). ”Sales and the Real E?ects of Monetary Policy”, Federal Reserve Bank of Minneapolis Working Paper 652.
[26] Kehoe, P. J. and V. Midrigan (2008). ”Temporary Price Deviations and the Real E?ects of Monetary Policy”, Federal Reserve Bank of Minneapolis Working Paper 661.
127
[27] Kehoe, P. J. and V. Midrigan (2010). ”Prices Are Sticky After All”, Federal Reserve Bank of Minneapolis Research Department Sta? Report 413.
[28] Klenow, P. and B. Malin (2010). ”Microeconomic Evidence on Price Setting”. Prepared for the Handbook of Monetary Economics (Benjamin Friedman and Michael Woodford, editors).
[29] Klenow, P. and J. Willis (2007). ”Sticky Information and Sticky Prices”, Journal of Monetary Economics 54, pp. 79-99.
[30] Klenow, P. and O. Kryvtsov (2008). ”State-Dependent or Time-Dependent Pricing: Does It Matter for Recent U.S. In?ation?”, The Quarterly Journal of Economics, MIT Press, vol. 123(3), pages 863-904, August.
[31] Kleshchelski, I. and N. Vincent (2007). ”Market Share and Price Rigidity”.
[32] Levin, A. and T. Yun (2008). ”Reconsidering the Microeconomic Foundations of Price-Setting Behavior”.
[33] Lu, Quiand and Sridhar Moorthy (2007). ”Coupons Versus Rebates”, Marketing Science Vol. 26, No. 1, pp. 67-82.
[34] Mackowiak, B. and F. Smets (2008). ”On Implications of Micro Price Data for Macro Models”, ECB Working Paper No. 960.
128
[35] Mendoza, E. (1991). “Real Business Cycles in a Small Open Economy”, The American Economic Review, Vol. 81, No. 4 797-818.
[36] Mendoza, E. and M. Uribe (1997). ”The Syndrome of Exchange-Rate-Based Stabilizations and the Uncertain Duration of Currency Pegs”, Federal Reserve Bank of Minneapolis, Institute for Empirical Macroeconomics Discussion Paper 121.
[37] Mendoza, E. and M. Uribe (1999). “The Business Cycles of Balance of Payment Crises: A Revision of a Mundellian Framework”, NBER WP 7045.
[38] Mendoza, E. and M. Uribe (2000). “Devaluation Risk and Business-Cycle Implications of Exchange-Rate Management”, Carnegie-Rochester Conference Series on Public Policy 55, 239-296.
[39] Midrigan, V. (2008), ”Menu Costs, Multi-Product Firms and Aggregate Fluctuations”.
[40] Nakamura, E. (2008). ”Pass-Through in Retail and Wholesale”, American Economic Review: Papers and Proceedings 98:2, pp. 430-437.
[41] Nakamura, E. and J. Steinsson (2008). ”Five Facts About Prices: A Reevaluation of Menu Cost Models”, Quarterly Journal of Economics, 123(4), 1415-1464.
[42] Nakamura, E. and J. Steinsson (2009). ”Price Setting in Forward-Looking Customer Markets”. 129
[43] Nelson, P., J. J. Siegfried and J. Howell. ”A Simulatneous Equations Model of Co?ee Brand Pricing and Advertising”, Review of Economics and Statistics, Vol. 74, No. 1, pp. 54-63.
[44] Reding, P. and J. A. Morales (2004). “Currency Substitution and Network Externalities”, University of Namur, mimeo.
[45] Rojas-Suarez, L. (1992). “Currency Substitution and In?ation in Peru”, Revista de Analisis Economico, Vol. 7, No. 1, 153-176.
[46] Reinhart, C. and C. Vegh (1995), “Nominal Interest Rates, Consumption Booms and Lack of Credibility: A Quantitative Examination”, Journal of Development Economics 46, 357-378.
[47] Savastano, M. (1996). ”Dollarization in Latin America: Recent Evidence and Some Policy Issues.” In The Macroeconomics of International Currencies, Paul Mizen and Eric Pentecost editors. Edward Elgar Publishing.
[48] Schmitt-Grohe, S. and M. Uribe (2004a). ”Solving Dynamic General Equilibrium Models Using a Second-order Approximation to the Policy Function,” Journal of Economic Dynamics and Control, vol. 28(4), pages 755-775, January.
[49] Schmitt-Grohe, S. and M. Uribe (2004b). ”Optimal Simple and Implementable Monetary and Fiscal Rules”. NBER Working Paper No. 10253.
130
[50] Schmitt-Grohe, S. and M. Uribe (2005). ”Optimal Fiscal and Monetary Policy in a Medium-Scale Macroeconomic Model”, in NBER Macroeconomics Annual 2005 (Mark Gertler and Kenneth Rogo?, edsitors) MIT Press. Cambridge MA, 2006, 383-425.
[51] Uribe, M. (1997), “Hysteresis in a Simple Model of Currency Substitution”, Journal of Monetary Economics 40, 185-202.
[52] Valev, N. (2007), ”The Hysteresis of Currency Substitution: Currency Risk vs Network Externalities”, Andrew Young School of Policy Studies Research Paper Series, Working Paper 07-23.
131
doc_489503664.pdf
The International Finance Corporation (IFC) is an international financial institution which offers investment, advisory, and asset management services to encourage private sector development in developing countries.
ABSTRACT
Title of dissertation:
ESSAYS IN MACROECONOMICS AND INTERNATIONAL FINANCE
Daniel Hernaiz Diez de Medina, Doctor of Philosophy, 2012
Dissertation directed by:
Professors Boragan Aruoba and John Shea Department of Economics
This document is a collection of essays in two issues of interest in macroeconomics and international ?nance. Chapter 2 introduces price promotions in a monetary DSGE model where consumers di?er in their price sensitivity and look for promotions, and where ?rms choose their regular and promotional prices as well as the frequency of promotions. In this environment, regular and promotional prices coexist, ?rm-level prices show rigidity in the form of inertial reference values from which weekly prices temporarily deviate, and promotions provide a new channel of price adjustment in the face of shocks. As a result, the economy displays near neutrality with respect to monetary shocks, with an impact response of output equal to one third of the one obtained in a model with no promotions. This result contrasts sharply with those of similar studies which, using alternative rationales for price
promotions, ?nd that price promotions do not fundamentally alter the real e?ects of monetary shocks. Chapter 3 studies the currency substitution phenomenon and develops a two-currency model that introduces ”dollarization capital” as a means to capture the economy’s accumulated experience in using the foreign currency. The model is able to generate a low-in?ation-high-substitution equilibrium consistent the data, and explains 1/6 of the gap between the observed currency substitution ratios and those generated by a model with no dollarization capital dynamics. The model, however, does not generate asymmetries in the relationship between in?ation and currency substitution before and after high in?ation episodes. Therefore, Chapter 4 presents a simple framework that creates non-linearities between in?ation and currency substitution. The model has two consumers who can di?er in their distance from money exchange points provided by the ?nancial sector, who decides whether or not to pay a ?xed cost necessary to install these exchange points. In this environment, a sequence of episodes of high and moderate in?ation may push the ?nancial sector into expanding the number of available money exchange points, therefore permanently reducing the consumers’ cost of using the foreign currency and decreasing the in?ation threshold at which households are willing to substitute foreign for domestic currency.
ESSAYS IN MACROECONOMICS AND INTERNATIONAL FINANCE
by Daniel Hernaiz Diez de Medina
Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial ful?llment of the requirements for the degree of Doctor of Philosophy 2012
Advisory Commmittee: Professor Professor Assistant Professor Professor Boragan Aruoba, Co-Chair/Advisor John Shea, Co-Chair/Advisor Professor Sanjay Chugh Pallassana Kannan Carlos Vegh
c Copyright by Daniel Hernaiz Diez de Medina 2012
ACKNOWLEDGEMENTS
Above all I want to thank the Lord Jesus Christ, my savior, for making it possible for me to earn this degree. Without Him I could do nothing. Without Him I would be lost. Jesus, I have no words to tell you how much I appreciate all you have done for me. I have had a great dissertation committee. John Shea was willing to read every piece of work that I sent to him (even when he was not at UMD and was busy working at the Treasury Department!). Boragan Aruoba has been very patient, supportive and helpful. He is a terri?c advisor, inspiring and always willing to spend time with his students. Sanjay Chugh is the person that ?rst got me interested in monetary economics. His macro course was outstanding; my discussions with him were the seed of my job market paper. Carlos Vegh has been an inspiration, a mentor and a friend (gracias!). I also thank professor P.K. Kannan from the Robert H. Smith School of Business for accepting the invitation to be the Dean’s Representative in my committee. To all of you, thank you! I wish you all the best in your professional and personal lives. I would also like to thank Carmen Reinhart for all her support during her time at Maryland. Working as a research assistant for her and Carlos Vegh was an ii
extremely rewarding experience. Also, I’d like to thank Enrique Mendoza, Anton Korinek and Pablo D’Erasmo for all the helpful discussions that we had during the time of preparation of my job market paper. I also thank Tom Powers, Gerry Caprio, Peter Montiel, Peter Pedroni, Jon Bakija and Dukes Love from the Center for Development Economics and the Department of Economics at Williams College. I thank my family (Joaquin, Maricarmen and Viviana) for their love and support, and Carlos Echazu (closest thing I have to a blood brother) for always being there. I thank Avy, Carola, Cristina, Daniela, Chris, Danny, Ethan and Zoe, my Virginian family. I’ve had some really good days during my time in Maryland, but the ones I spend with Ethan and Danny were among the best. Five years ago I met two guys looking for a roommate. Today I see them as my brothers. Cesar and Gabo, aguante el Chateau!!! I thank Juandi and Caro for being like they are: two of the best people I’ve met in my life. I thank Pablo Cuba for his friendship (he is always willing to help somebody in need). I’m glad he came to Maryland and I expect him to be one of the best macroeconomists this university has produced. Finally, I thank Tim and Maria Belen, Teresa and Greg, and Abby for being such good friends.
iii
TABLE OF CONTENTS
List of Figures List of Tables Introduction A Monetary Model With Price Promotions
2.1
vii ix 1 6
1
2
The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.1.7 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 The Government . . . . . . . . . . . . . . . . . . . . . . . . . 24 The Economy’s Resource Constraint . . . . . . . . . . . . . . 25 Characterizing the Economy-wide Price Level . . . . . . . . . 26 Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . 28 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
iv
2.1.8 2.2 2.3
Price Discrimination in General Equilibrium . . . . . . . . . . 29
Solution Method and Parameter Values . . . . . . . . . . . . . . . . . 37 The Workings of the Model . . . . . . . . . . . . . . . . . . . . . . . 41 2.3.1 2.3.2 Individual Price Setting Behavior . . . . . . . . . . . . . . . . 41 Does Micro Flexibility Translates Into Higher Neutrality at the Macro Level? . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3
A Quantitative Analysis of Currency Substitution
3.1 3.2
60
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Currency Substitution in Two Selected Economies . . . . . . . . . . . 62 3.2.1 3.2.2 Currency substitution and in?ation . . . . . . . . . . . . . . . 62 Inverse velocities of money . . . . . . . . . . . . . . . . . . . . 66
3.3
A Model of Currency Substitution . . . . . . . . . . . . . . . . . . . . 67 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . 69 Transaction Costs . . . . . . . . . . . . . . . . . . . . . . . . . 69 Dollarization Capital . . . . . . . . . . . . . . . . . . . . . . . 70 Maximization Problem and Competitive Equilibrium . . . . . 71
3.4
IV. Solving the Model . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.4.1 Parametrization and Solution Method . . . . . . . . . . . . . . 75
v
3.4.2 3.5
Transitional Dynamics from High to Low in?ation
. . . . . . 79
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4
Investment Activity in the Financial Sector and the Relationship between In?ation and Currency Substitution
4.1 4.2
85
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 A simple three-agent model . . . . . . . . . . . . . . . . . . . . . . . 91 4.2.1 4.2.2 4.2.3 The environment . . . . . . . . . . . . . . . . . . . . . . . . . 91 Consumer’s problem . . . . . . . . . . . . . . . . . . . . . . . 92 The ?nancial sector’s investment problem . . . . . . . . . . . 98
4.3
Conclusion
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A
Appendix to Chapter 1
110
A.1 Calvo stickiness in regular prices . . . . . . . . . . . . . . . . . . . . . 110 A.2 Looking for f in the data . . . . . . . . . . . . . . . . . . . . . . . . . 116 A.3 The Firm’s Problem Under Perfect Price Discrimination (PPD) . . . 118 A.4 Monetary Model with Price Promotions: Impulse Response Functions 121
B
Appendix to Chapter 2
122 124
Bibliography
vi
LIST OF FIGURES
2.1 2.2 2.3 2.4
FIRMS PRICES IN THE ABSENCE OF MACRO SHOCKS . . . . . 35 PRICE EVOLUTION IN FOUR SELECTED PRODUCTS . . . . . . 44 SIMULATED PRICE FOR AN INDIVIDUAL FIRM . . . . . . . . . 45 SIMULATED PRICE FOR AN INDIVIDUAL FIRM: THE CASE OF POSITIVE STEADY STATE INFLATION . . . . . . . . . . . . 46
2.5 2.6 2.7 2.8
OUTPUT RESPONSE TO A MONETARY POLICY SHOCK . . . . 54 IMPULSE RESPONSE ANALYSIS . . . . . . . . . . . . . . . . . . . 55 TIME ALLOCATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 56 THE RESPONSE IN THE MODEL WITH PRICE PROMOTIONS COMPARED THAT OF A CALVO MODEL CALIBRATED TO DIFFERENT TIMES BETWEEN CHANGES . . . . . . . . . . . . . 56
3.1 3.2 3.3 4.1
CURRENCY SUBSTITUTION IN BOLIVIA AND PERU . . . . . . 65 TRANSITIONAL DYNAMICS . . . . . . . . . . . . . . . . . . . . . 80 TRANSITION WITH AND WITHOUT DOLLARIZATION CAPITAL 82 MODEL ENVIRONMENT . . . . . . . . . . . . . . . . . . . . . . . . 92
vii
4.2 4.3 4.4
CURRENCY SUBSTITUTION AND INFLATION . . . . . . . . . . 99 EXCHANGE POINTS AND THE INFLATION RATE . . . . . . . . 102 PATHS OF INFLATION AND CURRENCY SUBSTITUTION . . . 107
viii
LIST OF TABLES
2.1 2.2 3.1 3.2 3.3 3.4 4.1 4.2
Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Steady State Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Model Results and Calibration Targets . . . . . . . . . . . . . . . . . 77 Currency Substitution Ratios in High-in?ation Periods . . . . . . . . 79 Currency Substitution Ratios in High-in?ation Periods . . . . . . . . 83 In?ation Probabilities and the State of Exchange Points . . . . . . . . 103 In?ation Probabilities and Currency Substitution . . . . . . . . . . . 103
A.1 Fraction of Weeks by Department . . . . . . . . . . . . . . . . . . . . 117 A.2 Fraction of Weeks: Sample I . . . . . . . . . . . . . . . . . . . . . . . 118 A.3 Fraction of Weeks: Sample II . . . . . . . . . . . . . . . . . . . . . . 118 B.1 Data Series Used in the Document . . . . . . . . . . . . . . . . . . . 122 B.2 Money Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 B.3 In?ation Periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
ix
Chapter 1
Introduction
This document is a collection of essays On two di?erent issues of interest in macroeconomics and international ?nance. The second chapter presents a study on the role of sale-induced high frequency price ?uctuations in monetary economics. The third and fourth chapters focus on the phenomenon of currency substitution observed in several developing countries and transition economies. Chapter 2 is motivated by recent microeconomic price evidence that shows that price promotions may have a signi?cant bearing on the measured frequency of price changes. This ?nding raises the question of whether micro price ?exibility caused by the presence of price promotions translates into macro neutrality to monetary shocks. The issue is addressed by introducing price promotions in a dynamic stochastic general equilibrium (DSGE) environment where agents di?er in their de-
1
gree of price sensitivity and face a time cost when looking for promotions. On the production side, ?rms optimally choose their regular and promotional prices as well as the frequency of promotions. In this framework, regular and promotional prices coexist and promotions provide a new source of ?rm-level price ?exibility. After introducing Calvo-stickiness in regular prices, individual price series behave similarly to those reported in recent empirical studies: regular prices are sticky; prices including promotions change very frequently, and realized prices show rigidity in the form of inertial reference values from which weekly prices temporarily deviate. In the aggregate, the economy displays near neutrality with respect to monetary shocks with a response of output that, on impact, is equal to one third of the one obtained from a standard Calvo model, a result that shows the importance of further exploration of ?rm-customer interactions in macroeconomic models. Chapter 2 is organized in ?ve sections. The ?rst one presents the introduction. The model is developed in the second section. The solution method, parameters and steady state values are discussed in the third section. The fourth section presents results on the model’s micro price behavior and the macroeconomic implications of price promotions, particularly on the responses to monetary shocks. The ?fth section concludes. Chapter 3 studies the phenomenon of currency substitution; that is, the use of foreign currency as a means of payment, as frequently observed in several developing countries and emerging economies. In several countries, currency substitution increases with in?ation during high in?ation periods and reaches its peak once the 2
economy has been stabilized, showing high persistence in the subsequent periods in spite of the downward trend in in?ation. The chapter focuses on two examples of this particular phenomenon: Bolivia and Peru. The chapter develops a perfect foresight two-currency model with exogenous production and transaction costs that is used to generate persistence in currency substitution. The model introduces ”dollarization capital” as a means to capture the economy’s accumulated experience in using the foreign currency. When parameters are set to replicate observed pre-hyperin?ation ratios in the two selected economies, the model is able to generate a low-in?ation-high-substitution equilibrium consistent with the post-stabilization behavior observed in various emerging markets and developing countries. The dollarization capital model explains from 1/6 of the gap between the observed currency substitution ratios and the ones generated by a model with no dollarization capital dynamics. As a result of quick and sizable changes in domestic currency real balances, the predicted post-stabilization currency substitution ratios adjust quickly in their path towards a low-in?ation equilibrium, a ?nding that suggests focusing future modeling e?orts on exploring plausible mechanisms that may introduce post-stabilization inertia in domestic currency holdings. Chapter 3 is organized in ?ve sections. After the introduction, the second section describes the pre and post high-in?ation pattern of currency substitution in Bolivia and Peru. The theoretical model is presented in the third section and solved in the fourth section. The ?fth section concludes. One of the limitations of the model analyzed in Chapter 3 is that it is not able to generate an asymmetric relationship between in?ation and currency substitution 3
before and after high in?ation episodes. This behavior is at odds with the data in several partially dollarized economies. Therefore, Chapter 4 explores a simple model that generates non-linearities in the relationship between currency substitution and in?ation. The chapter presents a simple three agent model with two consumers who can di?er in their distance, and therefore walking cost, from money exchange points provided by the third agent, the ?nancial sector, who is the only one that possesses the technology to exchange domestic for foreign currency. Money is used for transaction purposes and agents have an incentive to hold foreign currency balances for high enough levels of in?ation. The possibility of substitution, however, depends on whether or not the ?nancial sector pays a ?xed cost necessary to install money exchange points where consumers can buy currency exchange services. In this environment, a sequence of episodes of high and moderate in?ation may push the ?nancial sector into expanding the number of available money exchange points, therefore permanently reducing the consumers’ cost of using the foreign currency and decreasing the in?ation threshold at which households are willing to substitute foreign for domestic currency. From a theoretical point of view, the work presented in Chapter 4 constitutes an e?ort to provide a micro foundation for the emergence and functioning of network externality e?ects that have been explored as a possible explanation for high levels of currency substitution even after several years of low in?ation. Chapter 4 is organized in three sections. The ?rst section presents the introduction. The second section presents a simple three agent model used to study the 4
consumer’s optimal currency substitution behavior and the ?nancial sector’s optimal dollarization capital investment decision. The third section concludes.
5
Chapter 2
A Monetary Model With Price Promotions
Recent microeconomic price evidence shows that price promotions may have a signi?cant bearing on the measured frequency of price changes, a ?nding that raises the question of whether micro price ?exibility translates into macro neutrality to monetary shocks. This chapter addresses this issue by introducing price promotions in a dynamic stochastic general equilibrium (DSGE) environment where agents di?er in their degree of price sensitivity and face a time cost when looking for promotions. On the production side, ?rms optimally choose their regular and promotional prices as well as the frequency of promotions. Under this setting, regular and promotional prices coexist and promotions provide a new source of ?rm-level price ?exibility. After introducing Calvo-stickiness in regular prices, individual price series behave similarly to the ones reported in recent empirical studies: regular prices are sticky;
6
prices including promotions change very frequently, and realized prices show rigidity in the form of inertial reference values from which weekly prices temporarily deviate. In the aggregate, the economy displays near neutrality with respect to monetary shocks with a response of output that, on impact, is equal to one third of the one obtained from a standard Calvo model, a result that shows the importance of further exploration of ?rm-customer interactions in macroeconomic models. The exercise of studying price promotions in a macroeconomic context is motivated by recent empirical work showing that the treatment of price sales may have an important e?ect on the estimated frequency of individual price changes. An example of this is the in?uential work of Bils and Klenow (2004), who analyzed the frequency of price changes in di?erent components of the US Consumer Price Index (CPI), ?nding a median time between changes of 4.3 months. This estimate, which includes sale related price changes, is well below previous ones obtained using less comprehensive datasets. Given that the degree of price stickiness and, more speci?cally, the probability of price changes is an important element for the quantitative solution of New Keynesian models, the result has important implications for macroeconomic modeling. For example, when discussing Michael Woodford’s Interest and Prices, Green (2005) mentions that “at the very least [Bils and Klenow’s] study shows a need to recalibrate Woodford’s model.” Indeed, Bils and Klenow’s result has become a calibration reference used in well known DSGE studies such as Altig, Christiano, Eichenbaum and Linde (2005) and Golosov and Lucas (2007). Following Bils and Klenow’s seminal work, recent research by Nakamura and Steinsson (2008) and Klenow and Krystov (2008) uses a more detailed dataset (the 7
US CPI Research Database) and ?nds that the estimated time between price changes is sensitive to the inclusion of sale prices. Particularly, Nakamura and Steinsson ?nd median durations between 4.4 and 4.6 months when including sales, but between 8 and 11 months when excluding sales. This new evidence on price setting has been complemented by recent studies using higher frequency micro price datasets. Eichenbaum, Jaimovich and Rebelo (2011) analyze a new weekly scanner dataset for a major US retailer, ?nding that nominal rigidities take the form of inertia in reference prices with weekly prices ?uctuating around reference values that tend to remain constant over extended periods of time. Klenow and Malin (2010) ?nd that the reference price phenomenon documented by Eichenbaum et. al. (2011) extends to most items in the non-shelter CPI.1 These results suggest that promotional prices have a large impact on measures of the frequency of price changes, but also point to the need to explore the potential macroeconomic implications of price promotions.2 In the words of Klenow and
1
The shelter component of the CPI is composed of the following items: (i) Rent of primary
residence, (ii) Lodging away from home, (iii) Housing at school (excluding board), (iv) Other lodging away from home including hotels and motels, (v) Owners’ equivalent rent of primary residence and (vi) Tenants’ and household insurance.
2
This also seems to be the case outside the US. For example, Dhyne et. al. (2006) note
that the statistical treatment and report of sale prices may be an important factor in explaining the observed di?erences in the frequency of price adjustment across euro-area countries. Cavallo (2009), meanwhile, uses price scraped data for four Latin-American countries, ?nding that, in most cases, measured price durations are considerably increased by the exclusion of sales. Data scraping is the activity of extracting data from output intended for the screen or printer of a computer
8
Krystov (2008), “sales are not . . . [just] a discount from the regular price; they have a life of their own.” In relation to this point, Mackowiak and Smets’ (2008) survey paper on micro price evidence presents some interesting comments on the macromodeling implications of sales in micro price data. First, an optimizing model of sales will, in general, predict that the magnitude, frequency and duration of sales respond to macroeconomic shocks. The practice of excluding all sale-related price changes from macro models may therefore be unjusti?ed. Second, sale-related price changes in the Bureau of Labor Statistics (BLS) dataset are at least as sensitive to in?ation as are regular price changes (Klenow and Willis, 2007). Third, even if price promotions are caused by shocks orthogonal to the macroeconomy, the presence of sales may matter for the response of prices to macroeconomic shocks. The ?rst papers that incorporate sale prices into a macro model are Kehoe and Midrigan (2007, 2008). These papers modify the Golosov and Lucas (2007) menu cost model by explicitly including a motive for sales, allowing ?rms to pay for temporary price changes at a lower menu cost than that paid when changing their price permanently. The authors then use their sales model as a data generating process and evaluate the e?ects of ?tting a simple Calvo model (with no sales motive in it) in order to match the moments generated by the sales model. They consider two cases: one including temporary price changes (i.e. sales) from the price series generated by the benchmark sales model, and one excluding them. They ?nd that excluding sales overstates the real e?ects of monetary shocks by almost 70%, and including sales produces only 1/9 of the real e?ects of monetary policy in the bench(human-readable output) rather than from original ?les or databases (www.pcmag.com).
9
mark model. Kehoe and Midrigan’s exercise highlights the importance of explicitly developing a motive for temporary price changes in monetary models. More recently, Guimaraes and Sheedy (2011) and Kehoe and Midrigan (2010) focus on whether sale-related and temporary price changes translate into macroeconomic neutrality in a monetary DSGE environment. Guimaraes and Sheedy (2011) develop a framework in which sale prices are not linked to the existence of menu costs. They construct an environment with di?erentiated goods and di?erentiated brands for each good, with consumers willing to substitute between brands for some products, but not for others. Firms are not able to price discriminate between consumers, and therefore choose to o?er a regular price at some moments in time and a sale price at others. If a Calvo-type rigidity is introduced in regular prices, the model generates individual time series that behave similarly to those studied by Eichenbaum et al. (2011). When studying the e?ects of monetary shocks, the authors ?nd that output impulse responses are very similar to those of a model with no sales, implying that micro price ?exibility does not translate into macro ?exibility and, therefore, sales are essentially irrelevant for monetary analysis. This result is due to the fact that in their model, sales are strategic substitutes; that is, a ?rm’s incentive to have a sale is decreasing in the number of other ?rms having a sale. Continuing with their earlier work, Kehoe and Midrigan (2010) build an extension of the standard menu cost model adding features that make the predictions of the modi?ed environment consistent with the micro price data. In their model, prices are subject to both permanent and temporary shocks; retailers set a list price and a posted price and face two ?xed costs: one when changing the list price, and 10
another when the posted price temporarily di?ers from the listed one. In this environment, ?rms tend to change list prices in order to o?set permanent productivity shocks and monetary shocks and temporarily deviate from the list price in order to o?set transitory shocks. Given the menu cost friction on list prices, ?rms may recur to deviations from the listed price as a channel for o?setting transitory monetary shocks. However, since these deviations are temporary, this only allow ?rms to react temporarily to a monetary shock, so that economy presents a high degree of non neutrality even in the presence of frequent temporary price changes. Kehoe and Midrigan also show that this result does not arise from strategic interactions as in Guimaraes and Sheedy (2011) but solely from the special nature of temporary price changes in their model. A common characteristic of Kehoe and Midrigan (2007, 2008, 2010) and Guimaraes and Sheedy (2011) is that households have no choice over how often they look for price promotions. Sales are therefore exogenous from the consumer’s point of view. Letting consumers choose the time spent looking for price promotions creates a new intratemporal margin that has important implications for the model’s response to aggregate shocks. This is the line of work followed in this document.3
3
Two other models that can deliver sticky regular prices with frequent sales are Nakamura and
Steinsson (2009) and Albrecht et. al. (2010). Nakamura and Steinsson develop a habit persistence model where ?rms face a time inconsistency problem, having the incentive to promise low prices in the present and raise them once that households have developed a consumption habit. In this context, price stickiness can arise endogenously and optimally as a partial commitment device, with ?rms choosing a price cap and discretionally setting prices only when they are below the cap. Albrecht et. al. (2010), on the other hand, model shopping as a search process in a framework
11
The model presented here analyzes the behavior of a monopolistically competitive economy in which ?rms face di?erent market demands and maximize pro?ts by setting a regular price and a promotional strategy composed of a discount price and a promotion frequency. Following Banks and Moorthy (1999), the model allows for consumer heterogeneity by having agents with di?erent price elasticities of demand, and introduces a time cost of looking for price promotions. In this context, it is possible to make an explicit distinction between regular and promotional prices: regular prices are always available to anyone, while promotional prices are only available when o?ered and only to those who look for them. The approach here thus di?ers from previous work in the area in at least two important aspects. First, the de?nition of regular and promotional prices di?ers from previous work. Second, consumers choose optimally the time spent looking for price promotions. In this setting, heterogeneity in price sensitivity and the assumption that households must pay a time cost in order to take advantage of price promotions are enough to (i) ensure that household time choices interact with ?rm promotional strategies, creating an environment in which regular and promotional prices coexist and (ii) generate a new source of price ?exibility through movements in promotional prices.
similar to that used in the job search literature. The authors show that, in a model with a semidurable good and consumer heterogeneity, there is an equilibrium pattern in which ?rms choose to post a high price for a number of periods followed by a single period sale. The sale rationales developed in these papers have not been introduced in a more general monetary DSGE framework yet, so their macroeconomic implications remain to be explored.
12
Given this framework, the model generates a large degree of micro-level price movement even in the absence of macroeconomic shocks, with ?rm-level realized prices ?uctuating between the regular and promotional values in response to the ?rm’s optimal choice of the fraction of time at which its product will be o?ered on promotion and to consumers’ optimal choices of the time invested looking for those promotions. However, even though not every price movement is the result of a macroeconomic shock, the model’s rationale for promotions has e?ects on how the economy reacts to monetary shocks. When extended in order to allow for Calvostickiness in regular prices, the model generates individual price series that behave in a way consistent with recent empirical studies: (i) regular (non-promotional prices) are sticky; (ii) prices including promotions change very frequently; (iii) realized prices show rigidity in the form of inertia in reference prices around which weekly prices ?uctuate. When studying the e?ects of monetary shocks, the model displays output responses well below the ones obtained with a standard Calvo model calibrated to match the frequency of regular price changes. In this case, sales are important for macroeconomics since their existence creates a dynamic pricing arrangement in which the market can outsmart the Calvo fairy. More generally, this result points to the importance of further exploration on how consumer behavior and ?rm-customer interactions are designed in macroeconomic models. The remainder of the chapter is organized as follows. The model is developed in the second section. The solution method, parameters and steady state values are discussed in the third section. The fourth section presents results on the model’s 13
micro price behavior and the macroeconomic implications of price promotions, particularly on the responses to monetary shocks. The ?fth section concludes.
2.1
The Model
The model consists of households, ?rms and a government. Money is introduced as an argument of the utility function; households purchase goods for consumption, supply labor, spend time looking for price promotions and hold money and bonds, while ?rms hire labor and produce and sell a continuum of di?erentiated consumption goods produced in a monopolistically competitive market. Households di?er in the price elasticity parameter of the Dixit-Stiglitz consumption aggregator. Given this heterogeneity in consumption, each ?rm’s price setting decision includes a choice of a regular price, and a promotional strategy consisting of a promotional price and a promotion probability (the fraction of time that the good is o?ered at promotion prices).
2.1.1
Households
There is a measure one of in?nitely lived households divided in two possible types: measure h of high price elasticity consumers (HECs), and measure 1 ? h of low price elasticity consumers (LECs).
High Elasticity Consumers High elasticity households maximize the expected present discounted value of utility:
14
?
E0
t=0
? t u ch t +?
mh t Pth
h + v 1 ? nh t ? st
(2.1)
where u(.), ?(.), and v (.) are strictly increasing and strictly concave, mh are nominal balances, nh is the fraction of time spent working and sh is the fraction of time spent looking for price promotions. ch is a Dixit-Stiglitz composite consumption good de?ned as ?
? ? ?? 1
?h (ft ,sh t)
1
??1 ?
where the parameter ? > 1 governs the price elasticity of demand for individual goods, ?h (ft , sh t ) is the fraction of goods purchased at promotion prices (with
h h demanded quantities {chp jt }), and 1 ? ? (ft , st ) is the fraction of goods acquired at
? ch t = ?
(chp jt )
0
dj +
?h (ft ,sh t)
(chr jt )
??1 ?
? dj ?
(2.2)
regular prices (with demanded quantities {chr jt }). I do not consider any additional frictions between consumers and ?rms such as matching frictions, so ?h (f, sh t ) is given by ft · sh t where ft is the fraction of time that a ?rm o?ers its product at promotional prices.4 Notice that even though a ?rm can sell a good at promotional and regular prices simultaneously (this will become clear when presenting the problem of the ?rm), in each period of time a consumer can acquire a speci?c good at either the regular or promotional price, but not both. Therefore, ? in (2.2) has the same interpretation as it would in the standard Dixit-Stiglitz consumption aggregator
4
For simplicity, and anticipating a symmetric equilibrium, in the consumer’s problem I assume
fj,t = ft for every ?rm j .
15
and captures the elasticity of substitution between di?erentiated goods. The budget constraint for the household is
h h h h h h h nt + mh Pth wt t?1 + (1 + it?1 )Bt?1 + ?t + Tt = Pt ct + mt + Bt
(2.3)
h where Pth is the price of the consumption composite, wt is the real wage h received for labor services, Bt is the amount of nominal bonds, Tt is a nominal
transfer from the government, and ?t are nominal pro?ts from the di?erentiated ?rms that are assumed to be owned by the households.
hr From the ?rst order conditions for chp jt and cjt :
chp jt
=
pp jt Pth
??
ch t
(2.4)
chr jt
=
pr jt Pth
??
ch t
(2.5)
Then, the relationship between quantities of a good bought at regular and promotional prices is given by
chp jt = chr jt
pr jt pp jt
?
(2.6)
Replacing (2.4) and (2.5) in (2.2), the price index for aggregate consumption is given by ?
1 ? 1? ?
?h (f,sh t) 1?? (pp dj + jt ) 0
1
? Pth = ?
?h (f,sh t)
1?? ? ( pr dj ? jt )
(2.7)
16
Notice that using the demand equations (2.4) and (2.5) and the price aggregator (2.7) it can be shown that
?h (ft ,sh t) hp pp jt cjt dj 0
1
+
?h (ft ,sh t)
hr h h pr jt cjt dj = Pt ct
(2.8)
h h The ?rst order conditions for nh t , mt and Bt yield the standard intratemporal
and intertemporal optimality conditions:
h v (1 ? nh t ? st ) h = wt u ( ch ) t
(2.9)
t u ( ch t ) ? ? ( Ph ) t
mh
Pth
= ?Et
u (ch t+1 ) h Pt+1
(2.10)
(1 + it )u (ch u ( ch t+1 ) t) = ?E t h h Pt Pt+1
(2.11)
The introduction of a time cost in order to take advantage of price promotions, on the other hand, creates a new intratemporal optimal margin. The ?rst order condition for sh t is
h v (1 ? nh t ? st ) =
? ??1 +
hp h ? h ch t ?s (f, st ) c?h t
1
??1 ?
? chr ?h t
??1 ?
u (ch t) (2.12)
h ?s (f, sh t)
pr chr ? pp chp ?h t ?h t ?h t ?h t Pth
u (ch t)
Equation (2.12) implies that the high elasticity consumer will choose optimal sh t by equating the utility cost incurred when looking for promotions and the
17
marginal utility gain derived from spending an extra unit of time looking for promotions. The right hand side of (12) has two components. The ?rst one comes from a re-composition of the consumption bundle. From (2.6), chp ?h t
??1 ?
? chr ?h t
??1 ?
is greater
than zero, implying an increase in overall consumption coming from higher quantih (f, sh ties of additional goods (a fraction ?s t ) of them) now available at promotional
prices. The second component is negative and corresponds to the utility loss because of higher spending after increasing the consumer’s time searching for promotions. When a good previously consumed at regular prices is found at a lower price as a result of additional time looking for price promotions, the consumer increases her consumption in a quantity such that her new expenditure on that good is greater than previously. This is a direct result of the elastic demand assumption typical in monopolistic competition models (since ? is greater than one, pr chr ? pp chp is ?h t ?h t ?h t ?h t negative). Combining equations (2.9) and (2.12), we have
h wt =
? ??1 +
hp h ? h ch t ?s (f, st ) c?h t
1
??1 ?
? chr ?h t
??1 ?
h ?s (f, sh t)
pr chr ? pp chp ?h t ?h t ?h t ?h t Pth
(2.13)
The left hand side of (2.13) is the relative price of leisure in terms of forgone labor income, while the right hand side is the relative price of leisure in terms of forgone gains from additional time spent looking for price promotions. Then, in equilibrium, consumers optimally choose their labor and shopping time allocations by equating the two alternative opportunity costs of an additional unit of leisure. 18
High Elasticity Consumers Low elasticity consumers di?er from high elasticity ones only in the price elasticity parameter of their consumption aggregator. Their consumption aggregator is given by ?
? ? ?? 1
?l (ft ,sl t)
1
? ?1 ?
with ? > ? > 1.
? cl t = ?
(clp jt )
0
dj +
?l (ft ,sl t)
(clr jt )
? ?1 ?
? dj ?
(2.14)
The LEC set of optimality conditions is analogous to the HEC one but changing ”h” by ”l” superscripts and ? by ? when needed. The LEC price aggregator is given by ?
1 ? 1? ?
?l (f,sl t) 1?? (pp dj + jt ) 0
1
? Ptl = ?
?l (f,sl t)
1?? ? (pr dj ? jt )
(2.15)
2.1.2
Firms
Cost Minimization There is a measure one continuum of ?rms indexed by j . Firm j minimizes costs wt Njt , where wt is the real wage and Njt is total labor hired by the ?rm, subject to a production restriction summarizing the available technology where output, cjt , is a function of labor and a productivity shock: cjt = ezt Njt , with E (zt ) = 0. From the ?rm’s cost minimization problem, real marginal cost is given by mcjt = mct = wt /ezt .
19
Price Setting Decision Flexible Regular Prices. The ?rm’s price setting problem consists of choosing
p 5 pr jt , pjt and fjt to maximize nominal pro?ts:
h h hp r h h hr ?jt = pp jt h? (fjt , st )cjt + pjt h 1 ? ? (fjt , st ) cjt l l lp r l l lr + pp jt (1 ? h)? (fjt , st )cjt + pjt (1 ? h) 1 ? ? (fjt , st ) cjt hp h h hr ? mcjt Pt {h?h (fjt , sh t )cjt + h 1 ? ? (fjt , st ) cjt lp l l lr + (1 ? h)?l (fjt , sl t )cjt + (1 ? h) 1 ? ? (fjt , st ) cjt }
(2.16)
subject to the demand equations (2.4), (2.5), and their LEC counterparts.
p The ?rst order conditions for pr j , pj and fjt are
hr l l lr h 1 ? ?h (fjt , sh t ) cjt + (1 ? h) 1 ? ? (fjt , st ) cjt =
1?
Pt mct pr jt
hr l l lr h[1 ? ?h (fjt , sh t )]?cjt + (1 ? h)[1 ? ? (fjt , st )]?cjt
(2.17)
hp l l lp h?h (fjt , sh t )cjt + (1 ? h)? (fjt , st )cjt =
1?
5
Pt mct pp jt
lp hp l l h?h (fjt , sh t )?cjt + +(1 ? h)? (fjt , st )?cjt
(2.18)
A real world justi?cation for having ?rms choosing fjt may come from the existence of market-
ing agreements in which a producer speci?es the number of times in which a retailer can put the good on sale in a given period (i.e. 20 days in the next three months). Then, the exact moment of promotion is chosen by the retailer and the producer’s decision ends up being about the fraction of time that the good is on sale. Alternatively, the ?rm may have multiple retail outlets and may put the unit on sale at only a fraction of its stores.
20
pp jt ? mct Pt pr jt ? mct Pt
hp l lp l h (fjt , sh h?f t )cjt + (1 ? h)?f (fjt , st )cjt h hr l l lr h?f (fjt , sh t )cjt + (1 ? h)?f (fjt , st )cjt
= (2.19)
Equations (2.17) and (2.18) equate the marginal revenue obtained from a variation in demand because of a change in a speci?c price (regular or promotional), with the marginal production cost of satisfying that marginal demand. Equation (2.19), on the other hand, comes from the fact that ?rms choose the fraction of time that they put their good on promotion. The left hand side is the marginal pro?t obtained from demand at promotional prices when increasing fjt , while the right hand side is the marginal pro?t obtained from demand at regular prices when increasing fjt . Further intuition can be gained after some rearrangement in order to re-express (2.19) as
p hp p lp h r hr l r lr h?f (fjt , sh + (1 ? h)?f (fjt , sl t ) pjt cjt ? pjt cjt t ) pjt cjt ? pjt cjt lp hp h hr l lr + (1 ? h)?f (fjt , sl h?f (fjt , sh t )mct Pt cjt ? cjt t )mct Pt cjt ? cjt
= (2.20)
The two terms in the left hand side of (2.20) corresponds to the marginal revenue coming from increasing the probability with which the ?rm o?ers its good
h h l l l on promotion. ?f (fjt , sh t ) = st and ?f (fjt , st ) = st are the additional fractions
of consumers that ?nd the good at promotional prices after the ?rm increases ft ,
hp p lp r hr r lr and pp jt cjt ? pjt cjt and pjt cjt ? pjt cjt correspond to the additional revenue coming
21
from these new purchases.6 On the other hand, the two terms in the right hand side of the equation correspond to the marginal cost associated with increasing ft ,
lp hr lr with chp jt ? cjt and cjt ? cjt representing the change in production needed to satisfy
the higher demand coming from additional consumers able to acquire the good at promotional prices. Notice that the standard monopolistic competition model is nested in the model presented here. To see this, take (2.17) and let h tend to 1. The equation reduces to:
pr jt = Pt
? ??1
mcjt
(2.21)
With no consumer heterogeneity (h = 1), f = 0 and therefore ?h = 0. Regular prices then are the only ones in the economy and Pth in (2.7) is reduced to ?
1
1 ? 1? ?
With h = 1, Pt =
Pth ,
and (2.21) corresponds to the pricing optimality condi-
1?? ? Pth = ? (pr dj jt ) 0
(2.22)
tion of a model with monopolistic competition and ?exible prices. Sticky Regular Prices. For the exercises performed in the following sections, it will prove useful to amend the model by including a nominal rigidity in the regular price. For this purpose, it is assumed that regular prices are subject to Calvo staggering. There may be reasons to consider ridigity in promotional prices
6
Since ? > 1, revenue from sales of good j at promotional prices is greater than revenue from
hp p lp r hr r lr sales at regular prices, so the terms pp jt cjt ? pjt cjt and pjt cjt ? pjt cjt , are positive.
22
as well.7 However, there is evidence that sale prices are less sticky than regular ones (Klenow and Kryvtsov (2008)) and allowing for rigidities only on regular prices is a simple way of capturing this fact. Also, stickiness in regular prices su?ces to generate the type of reference price rigidity found in recent studies on micro price data like Eichenbaum et al. (2011) and Klenow and Malin (2010), and facilitates comparison with Guimaraes and Sheedy (2011) who also impose a Calvo rigidity only in regular prices and who argue that their exercise will provide an upper bound for price ?exibility in the aggregate if there is rigidity in promotional prices in reality. When the regular price is sticky, the price setting problem of the ?rm becomes
?
p pr jt ,pjt ,fjt
max Et
s= t
?
s? t
h h ?t+s/t {pp js h? (fjs , ss )
Psh pp js Psl pp js Psh ? pr jt Psl ? pr jt Psh pp js Psl pp js Psh ? pr jt Psl ? pr jt
? ?
?
ch s
?
+pp js (1 +
? pr jt h
? h)?
h
l
(fjs , sl s)
cl s
?
1??
(fjs , sh s)
ch s cl s}
?
? l l +pr jt (1 ? h) 1 ? ? (fjs , ss ) h
? mcjs Ps {h?
(fjs , sh s) (fjs , sl s)
ch s
?
+(1 ? h)? +h 1??
h
l
cl s
?
(fjs , sh s)
ch s cl s} (2.23)
+(1 ? h) 1 ? ?l (fjs , sl s)
Where ? is the probability of not being able to change the regular price in the period, and ?t+1/t is the ?rm’s stochastic discount factor for nominal payo?s.
7
For example, ?rms could be constrained in their ability to change their promotional strategy
because of contractual pricing arrangements between producers and retailers.
23
The ?rst order conditions for pp jt and fjt are the same as in the ?exible price
? scenario, and the ?rst order condition for pr jt is
? ? pr jt
(? ? 1)Et
t=s ?
hr ?s?t ?t+s/t h 1 ? ?h (fjs , sh js ) cjs
? + pr jt
(? ? 1)Et
t=s ?
lr ?s?t ?t+s/t (1 ? h) 1 ? ?l (fjs , sl js ) cjs
=
?Et
t=s ?
hr ?s?t ?t+s/t h 1 ? ?h (fjs , sh js ) cjs mcjs Ps
+ ?Et
t=s
lr ?s?t ?t+s/t (1 ? h) 1 ? ?l (fjs , sl js ) cjs mcjs Ps
(2.24)
Notice that when h = 1 (and therefore ft = 0) there is only one type of consumer in the economy and Pt = Pth . In this case this last equation collapses to
? pr jt
? Et t=s ?s?t ?t+s/t chr js Ps mcjs = ? s ? t ??1 Et t=s ? ?t+s/t chr js
?
(2.25)
Which is the standard optimal pricing equation in a model with Calvo rigidities and no capital. Further details on the solution of the sticky regular price case are provided in Appendix 1.
2.1.3
The Government
The Government Budget Constraint Each period, the government satis?es the following budget constraint:
(Bt ? Bt?1 ) + (Mt ? Mt?1 ) = Tt + it?1 Bt?1 24
(2.26)
where Tt are lump sum transfers.
Monetary Policy It is assumed that the Central Bank reacts to in?ation and output growth according to the following interest rate rule: ? ? ? ? ?
1 + it 1+i
=
e e?
?t
?1
yt yt?1
?2
1??R
1 + it?1 1+i
?R ?
e?R ?R,t
(2.27)
where ?t is the in?ation rate, yt is total output, ? and i are the steady state in?ation and interest rates, and ?R,t is a monetary policy shock. This speci?cation corresponds to the one used by Aruoba and Schorfheide (2011) with the exception that these authors also introduce a time varying in?ation target as part of the interest rate feedback rule.
2.1.4
The Economy’s Resource Constraint
The economy’s resource constraint can be recovered combining the consumers’ budget constraints, the government balanced budget equation and the expression for ?rms’ pro?ts. Pre-multiplying the HEC’s budget constraint (2.3) by h and the LEC’s budget constraint by 1 ? h and adding up we have:
h h h h h h h h Pth wt nt + mh t?1 + (1 + it?1 )Bt?1 + ?t + Tt ? Pt ct ? mt ? Bt =
(2.28)
(1 ? h)
l l Ptl wt nt
+
ml t?1
+ (1 +
l it?1 )Bt ?1
+ ?t + Tt ?
Ptl cl t
?
ml t
?
l Bt
Using equation (2.8) and its analogue for low elasticity consumers and applying symmetry yields: 25
h h h h Pth wt nt + mh t?1 + (1 + it?1 )Bt?1 + ?t + Tt p hp h h r hr h h ? h ?h (ft , sh t )pjt cjt + 1 ? ? (ft , st ) pjt cjt + mt + Bt l l l (1 ? h) Ptl wt nt + ml t?1 + (1 + it?1 )Bt?1 + ?t + Tt p lp l l r lr l l ? (1 ? h) ?l (ft , sl t )pjt cjt + 1 ? ? (ft , st ) pjt cjt + mt + Bt
=
(2.29)
De?ne the economy’s labor income in nominal terms as
h h l l l Pt wt Nt = hnh t Pt wt + (1 ? h)nt Pt wt l where Nt = Njt dj = hnh t + (1 ? h)nt . 0 1
(2.30)
Finally, plugging equations (2.26), (2.30) and the expressions for ?rms’ pro?ts and marginal costs into (2.29), we have:
h l ez t hnt + (1 ? h)nt
hp h h hr = h?h (ft , sh t )ct + h 1 ? ? (ft , st ) ct lp + (1 ? h)?l (ft , sl t )ct lr + (1 ? h) 1 ? ?l (ft , sl t ) ct
(2.31)
where (2.31) is the economy’s resource constraint.
2.1.5
Characterizing the Economy-wide Price Level
The ?nal equilibrium condition is the relationship between the economy wide price
r level, Pt , and the two types of prices faced by consumers, pp t and pt . In order to ?nd
this, de?ne the economy’s total consumption expenditure as 26
l l Pt ct = hPth ch t + (1 ? h)Pt ct
(2.32)
where
1
ct =
0
hp h h hr l l lp l l lr cjt = h?h (ft , sh t )ct + h[1 ? ? (ft , st )]ct +(1 ? h)? (ft , st )ct +(1 ? h)[1 ? ? (ft , st )]ct
Using equation (2.8) and its analogue for the LEC’s case, we have:
? P t ct = h ?
?
?h (ft ,sh t) hp pp jt cjt dj + 0
1
Assuming ?exible regular prices and applying symmetry, we have:
? + (1 ? h) ?
?
?h (ft ,sh t) ?l (ft ,sl t) lp pp jt cjt dj + 0
hr ? pr jt cjt dj ? 1
? ?
?l (ft ,sl t)
lr ? pr jt cjt dj ?
(2.33)
hp p h h hr r Pt ct = h?h (ft , sh t )ct pt + h 1 ? ? (ft , st ) ct pt lp p l l lr r + (1 ? h)?l (ft , sl t )ct pt + (1 ? h) 1 ? ? (ft , st ) ct pt
(2.34)
Rearranging, we have:
r Pt = ?t pp t + (1 ? ?t )pt
(2.35)
where
27
?t =
hp l l lp h?h (ft , sh t )ct + (1 ? h)? (ft , st )ct hp h hr l lp l lr h l l h?h (ft , sh t )ct + h 1 ? ? (ft , st ) ct + (1 ? h)? (ft , st )ct + (1 ? h) 1 ? ? (ft , st ) ct r Equation (2.35) de?nes Pt as a time-varying weighted average of pp t and pt ,
with the weights of each price given by the ratio of goods purchased at that price with respect to the total quantity of goods consumed in the economy. From (2.35) we can also write
1 = ?t mct
pp t Pt mct
+ (1 ? ?t )
pr t Pt mct
(2.36)
r where, from the ?rm’s ?rst order conditions for pp t and pt , the optimal real
markups associated with each price are given by
lp hp l l h?h (ft , sh pp t t )?ct + (1 ? h)? (ft , st )?ct = hp lp l l Pt mct h?h (ft , sh t )(? ? 1)ct + (1 ? h)? (ft , st )(? ? 1)ct
and
lr hr l l h 1 ? ?h (ft , sh pr t ) ?ct + (1 ? h) 1 ? ? (ft , st ) ?ct t = hr l lr l Pt mct h 1 ? ?h (ft , sh t ) (? ? 1)ct + (1 ? h) 1 ? ? (ft , st ) (? ? 1)ct
Then, equation (2.36) de?nes the economy-wide markup as a time-varying weighted average of the real markups associated with the two prices available in the economy.
2.1.6
Stochastic Processes
The stochastic process for productivity zt is given by 28
z zt+1 = ?z zt + ?t ;
z ?t ? i.i.d.(0, ?z )
(2.37)
Finally, it is assumed that the monetary policy shock ?R,t is serially uncorrelated with mean zero and variance one. Then, the autoregresive component in monetary shocks is given by the interest rate smoothing parameter ?R in (2.27).
2.1.7
Equilibrium
hr hp l lr An equilibrium for this economy is de?ned as a set of allocations {ch t , ct , ct , ct , ct , l h l h l h h l l h clp t , nt , nt , Nt , st , st , ft }, portfolio choices {mt , mt , Bt , Bt , Mt , Bt }, prices {Pt , Pt , Pt , p h l pr t , pt , wt , wt , wt , it }, and transfers {Tt , ?t } such that: hp h h h h i) {chr t , ct , nt , st , mt , Bt } solve the HEC utility maximization problem. lp l l l l ii) {clr t , ct , nt , st , mt , Bt } solve the LEC utility maximization problem. p iii) {pr t , pt , ft } are such that ?rms maximize pro?ts.
iv) Aggregation satis?es equations (2.2), (2.7), (2.14) , (2.15), (2.30) and (2.35). v) The government runs a balanced budget.
l h l vi) Markets clear: Nt = hnh t + (1 ? h)nt , Bt = hBt + (1 ? h)Bt , Mt = l hmh t + (1 ? h)mt .
2.1.8
Price Discrimination in General Equilibrium
As observed in the model’s equilibrium conditions, this economy has the feature that both regular and promotional prices coexist at the same time for each ?rm. The
29
key modeling element behind this result is the fact that consumers must spend time looking for price promotions. This is formally stated in the following propositions: Proposition 1: Given strictly increasing utility in consumption and leisure, in a general equilibrium with monopolistic competition (? > 1, ? > 1) and with
l consumers looking for price promotions (sh t ? (0, 1), st ? (0, 1)), ?rms always price p discriminate by setting a regular price greater than the promotional one (pr jt > pjt ). p Proof: Suppose not. That is, let pr jt ? pjt . Consider the HEC case; using the
demand equations (2.4) and (2.5), equation (2.12) can be re-expressed as:
v (1 ?
nh t
?
sh t)
=u
h h (ch t )?s (ft , st )
1 ??1
ch t
1?? 1?? pp ? pr jt jt
Pth
1??
(2.38)
p Given ? > 1 and the assumption that u(·) is strictly increasing, pr jt ? pjt
implies that the right hand side of equation (2.38) is lower or equal to zero, so (2.38) is satis?ed only when v (·) ? 0, a contradiction that violates the assumption that v (.) is strictly increasing. Proposition 2: Given strictly increasing utility in consumption and leisure, in a general equilibrium with monopolistic competition (? > 1, ? > 1) and with
l consumers looking for price promotions (sh t ? (0, 1), st ? (0, 1)), ?rms follow an
active promotional policy by making the promotional price available with a positive probability ft > 0. Proof: analogous to the one for Proposition 1. In this model, then, ?rms will always price discriminate; that is, they will set
p two di?erent prices for the same good (pr jt > pjt ), and they will always follow an
30
active promotional strategy (fjt > 0), making their promotional price available for consumers willing to spend the time needed to ?nd a promotion and take advantage of the lower price. The intuition behind this result is that there is a cost associated with ?nding a price promotion, and that cost is paid only by consumers and not by ?rms. If, in a given period, a ?rm decides not to o?er promotions (fjt = 0), it will charge only its regular price at every moment of time within that period without distinguishing between consumption demands. However, recognizing that looking for discounts is costly for consumers and that only a fraction of them will access price promotions, the ?rm can increase pro?ts by making the promotional price available with a given probability (fjt > 0) and therefore costlessly distinguishing between two di?erent types of demand: demand from consumers that ?nd the price promotion and demand from consumers that don’t.8 This follows the basic principle of using promotions for price discrimination purposes studied in the Industrial Organization and Marketing literature: when a ?rm wants to use a price promotion as a price discrimination tool, it should try to make it easy for some consumers to access the promotion, but harder for others; that is, the promotion must impose some cost on which consumers di?er, rewarding the people willing to bear that cost (see Banks and Moorthy (1999) and Lu and Moorthy (2007)).
8
The ?rm can price discriminate even if it puts its good on promotion all the time (ft = 1).
The reason for this is that since consumers do not spend all of their time looking for promotions
l h h l l (sh t < 1, st < 1), only fractions ? (ft , st ) and ? (ft , st ) of the ?rm’s good are sold at promotional
prices, with the complement transacted at the regular price.
31
The most salient real-world example of price promotions associated with consumer time costs is the use of coupons.9 Coupons are certainly an important promotional vehicle in the United States, but there are several other promotional arrangements that are associated with di?erent types of consumer costs; examples of these are mail-in rebates, cash-back o?ers, loyalty cards, reward programs and discount clubs.10
9
11
The mechanism developed here can be thought of as a reduced form
There are several types of time costs associated with the usage of coupons beyond the standard
“cut and clip” costs: (i) in order to take advantage of the promotion, the consumer may need to spend time looking for the coupon (i.e. going over mailed ?iers and newspapers, or browsing the internet); (ii) it may be necessary to prepare shopping lists so the coupon may be used in a future shopping trip before its expiration date; (iii) coupon redemption may be conditioned on some information exchange with the consumer (i.e. logging into a retailer’s web page and providing contact information, or participating in an on-line consumer survey).
10
According to NCH Marketing Services Inc., in 2009, 311 billion coupons were distributed by
consumer packaged-goods companies in the United States, 3.2 billion of these were redeemed, and the redemption value reached 3.5 billion dollars. Also, a recent consumer study by Inmar Inc. reports that 75% of the participants in a shopping habits survey conducted by the Food Marketing Institute stated that coupons had at least some in?uence on their decision to buy a product. Inmar also reports that in the ?rst half of 2009, 68% of US households participating in Nielsen’s Homescan Consumer Panel used at least one coupon.
11
An interesting fact about some of these promotional vehicles is that they are not used only by
grocery stores and supermarkets, which have received most of the attention in recent studies on the implications of micro price data for macroeconomic modeling. Mail-in rebates, for example, are widely used by home appliance providers and electronics retail stores, with o?ers ranging from small-ticket items like computer accessories to big-ticket ones like home entertainment systems. Di?erent types of cash-back options are also very common among automobile dealers. On the other hand, loyalty cards, typical in supermarkets and grocery stores, are also common among
32
capturing a broader fact with interesting implications when modeling price discrimination in monetary models: not every price promotion is realized, and whether a consumer ends up receiving a discount or not often depends endogenously on how much time, e?ort and money she is willing to invest in taking advantage of the o?ered promotion. This could be the case even for on-shelf promotions in the sense that even though there is no explicit consumer cost associated with them, a shopper may need to spend some time and attention comparing prices and brands before ?nally picking the products o?ered on discount.12 Thus, it is the fact that price promotions are costly for the consumer that ensures the coexistence of the two prices in the model economy. This will allow for a large amount of ?rm level transaction price variation over time even in the absence of shocks, a result consistent with Nakamura’s (2008) ?nding of a high amount of idiosyncratic price variation in product categories with temporary sales, suggesting that retail prices may vary largely as a consequence of dynamic pricing strategies on
book, music and electronics retailers, while service providers like banks and airlines often o?er loyalty programs associated with their products. Finally, discount clubs include warehouse clubs that sell grocery store and supermarket products, but also providers of big-ticket items like home furnishings. Also, wholesale clubs like Costco and BJ’s sell a variety of non-supermarket household goods, including TVs, books, clothes, etc.
12
Sometimes this may require shopping trips to di?erent locations in order to compare on-shelf
promotions between retailers. When the product is not o?ered at a physical location, taking advantage of price promotions may require spending time browsing the internet looking for the best available deals. Think, for example, about buying a plane ticket using kayak.com instead of visiting a speci?c airline, or ?nding discount lodging at hotwire.com instead of contacting a particular hotel.
33
the part of retailers or manufacturers. In the model, this dynamic pricing strategy consists of ?rms o?ering costly promotions and choosing the fraction of time at which they are available, but being indi?erent about the exact moment of time at which a promotion is realized. Consider for example a case with no shocks and zero in?ation in which ?rms choose to o?er their goods on promotion 50% of the time. Panel a) in Figure 2.1 shows a sample time path for the price strategy of an individual ?rm that randomly chooses when to o?er a price promotion, subject to ensuring that the the promotion is available half of the time. The regular price will be o?ered all the time, while the promotional price is o?ered only at intervals. Panel b) depicts the time series of the minimum price available, which is equal to
p pr t when no promotion is o?ered and pt when a promotion is in place.
The following sections show how this type of strategic combined pricing, with nominal rigidity in regular prices, helps in generating price behavior similar to that documented in the recent microeconomic evidence on price-setting, and how this pricing has important implications on the way real variables respond to monetary shocks. Among recent research on sale prices in monetary models, the Kehoe and Midrigan (2007, 2008, 2010) framework is an example of a model in which prices ?uctuate only in response to stochastic shocks and not to randomization decisions made for price discrimination purposes. In their setup, every period a ?rm can either pay a large ?xed cost and change their price permanently or pay a smaller cost and change their price only for one period. Kehoe and Midrigan’s models, therefore, require time varying shocks and price rigidities in order to generate temporary 34
Figure 2.1: FIRMS PRICES IN THE ABSENCE OF MACRO SHOCKS
movements away from the regular price. Closer in spirit to the model presented here is the work of Guimaraes and Sheedy (2011). They develop a model in which households consume a continuum of heterogeneous goods and a continuum of heterogeneous brands for each good. Consumers have di?erent price sensitivities with respect to di?erent sets of goods, being loyal to speci?c brands for a given measure of products (that is, they do not receive utility from consuming any alternative brand) but being bargain hunters willing to substitute between di?erent brands for the rest of the goods. Each ?rm 35
produces a brand speci?c product and faces a measure of loyal consumers and a measure of bargain hunters. Firms do not know the type of any individual consumer, and cannot practice price discrimination directly. Instead they follow the strategy of holding periodic sales in order to target the two types of consumers at di?erent moments of time. This is done by randomizing the timing of sales after choosing a fraction of time (i.e. a number of moments within a given period) at which the ?rm charges a lower price. At any one point in time, all consumers recive the same price. As in the framework presented in this document, Guimaraes and Sheedy’s (2011) setup is able to generate price ?uctuations even in the absence of the standard aggregate or idiosyncratic shocks included in DSGE models, as a result of the dynamic pricing strategy followed by ?rms that target di?erent types of customers. In contrast to Guimaraes and Sheedy, however, the model developed in this paper does feature price discrimination at many points in time as part of the ?rm’s optimal
p dynamic pricing strategy: for a fraction ft of the time, both pr t and pt coexist and
transactions are made using both prices. This paper’s framework thus allows for a distinction between price-quote and realized-price series. As I will show below, when combined with a nominal rigidity in the de?nition of regular prices, the model delivers individual price series with the type of rigidity recently found in studies on reference prices in micro price data, but with di?erent macroeconomic implications from those found by Guimaraes and Sheedy (2011).
36
2.2
Solution Method and Parameter Values
The model is solved around a zero-in?ation steady state applying Schmitt-Grohe and Uribe’s (2004a) local approximation algorithm. I assume the following functional forms:
h u(ch t ) = log (ct ) l u(cl t ) = log (ct )
t ?( P h ) = ?log t
mh
mh t h Pt ml t l Pt
?( P lt ) = ?log
t
ml
h h h v (1 ? nh t ? st ) = ?log 1 ? nt ? st l l l v (1 ? nl t ? st ) = ?log 1 ? nt ? st
There are fourteen parameters in the model: the intertemporal discount factor, ? ; the constants pre-multiplying the money and leisure utility terms, ? and ?; the measure of high elasticity consumers, h; the elasticities of substitution for HECs and LECs, ? and ? ; the probability of a ?rm not being able to change its regular price, ?; the interest rate smoothing parameter, ?R ; the in?ation and output growth weights in the Central Bank’s interest rate rule, ?1 and ?2 ; and the parameters governing the stochastic processes for productivity and monetary policy, ?z , ?z and ?R . The length of each period is one week, so the discount factor ? is set at 0.961/52 . The Calvo parameter, ?, is set at 0.974, implying that, on average, ?rms change their regular prices every 9 months (39 weeks); this time between changes is in the middle range of the estimates reported by Nakamura and Steinsson (2008). The values for the productivity stochastic process, ?z and ?z , correspond to the weekly counterparts
37
of the quarterly values used in Hansen (1985), while the parameters for the interest rate rule and the monetary policy stochastic process are taken from Aruoba and Schorfheide (2009): ?1 = 1.7, ?2 = 0.86, ?R = 0.611/13 , ?R = 0.0036/13. The values of ?, ?, ?, ? and h are chosen to match ?ve steady state calibration targets: average hours worked of 1/3, a weekly velocity of money of 0.15, a ratio of time spent looking for promotions with respect to hours worked of 1/4, a probability with which goods are o?ered on promotion of 0.7, and an average gross markup of 1.4. The target value for total hours worked, hnh + (1 ? h)nl , is standard in the literature. The value for money velocity was computed using the formula V = GDP/(52 · M 1), where M 1 is the weekly seasonally adjusted series for M1 of the Board of Governors of the Federal Reserve System, and GDP is annual nominal Gross Domestic Product. The 1975:1-2009:9 average is 0.15, close to the weekly analogue of the quarterly value calculated by Aruoba and Schorfheide (2009) using sweep-adjusted M 1 data. Time spent looking for price promotions is the only type of shopping time in the model. Therefore the target for the shopping/working time ratio is taken from US time surveys with information on daily time spent purchasing goods and services, and is close to the value used in Arseneau and Chugh (2007).13 The targeted markup is within the range of estimated values for the US and
13
The American Time Use Survey (ATUS) provides nationally representative estimates of how
and where Americans spend their time. Data ?les are available from 2003 to 2009 and can be accessed athttp://www.bls.gov/tus/.
38
close to values used in trade and macroeconomic studies such as Bernard et al. (2003) and Biblie et al (2007). The choice of the target value for f requires more elaboration. In the model, f is the fraction of time ?rms o?er their goods at promotional prices. Moreover, this is the only type of price promotion considered in the framework developed in Section 2. Given the model’s de?nition of promotional prices as only available when o?ered and only to those who look for them, the empirical counterpart of f should correspond to a type of promotion that is not always o?ered and that requires some search e?ort from the consumer in order to be realized. The James M. Kilts Center at the University of Chicago Booth School of Business provides data useful for constructing this target. The Booth School provides several publicly available datasets on weekly store-level transaction prices for over 100 stores operated by Dominick’s Finer Foods (DFF), which have been used in various macroeconomic studies such as Golosov and Lucas (2007), Midrigan (2008) and Kehoe and Midrigan (2007,2008). One of these datasets, the Customer Count Files, has information on total coupon redemption ?gures by DFF de?ned productcategory. Since sale coupons are a natural example of the type of promotion discussed in Section 2, I use this database to construct a proxy for the probability that ?rms o?er their goods at promotional prices in a given period. I proceed as follows: ?rst, for each product category I construct a dummy variable, dt , equal to 1 if at least one coupon was redeemed in a given week (that is, if the coupon redemption ?gure is di?erent from zero). Next, I compute the fraction of time at which category k was o?ered on promotion: 39
fk =
t
dt /(number of weeks).
Finally, I compute the average across product categories: f=
k
fk /(number of good categories).
The underlying assumption is that if a promotional price is available in a given week, then there is at least one person that takes advantage of it (alternatively, at least one coupon is redeemed). Therefore, I assume that if the coupon redemption ?gure in a given week is zero (dt = 0), then no coupons were o?ered that week. When considering a sample of all categories for which coupons were redeemed at least once in the sample period, the sales-weighted value for f is 0.87. When considering all product categories, the value is 0.7. Appendix 2 provides more details on these calculations. Of course, it would be ideal to perform a similar calculation for a broader range of goods and sectors. However, in spite of this limitation, and given the lack of richer data on non-shelf price promotions for other sectors and goods, the above described calculation provides an empirical benchmark consistent with the theoretical de?nition of f and with the model’s de?nition of promotional prices. Table 2.2 presents the model’s steady state under this parameterization, where pp and pr are relative prices with respect to the economy-wide price and ah and al are HEC and LEC real balances with respect to each consumer’s e?ective price index. HECs represent 9% of the economy’s population and spend a large fraction of their time working, and therefore are able to consume more than LECs: ?(f, sh )chp + 1 ? ?(f, sh ) chr = 0.84 ?(f, sl )clp + 1 ? ?(f, sl ) clr = 0.28 40
As expected, HECs spend a lower fraction of their time looking for price promotions. HECs are very price sensitive, and whey they ?nd a promotion they substitute a lot, buying very large quantities of a good when it is found on sale, so they are able to take advantage of price discounts even when spending only a very small fraction of time looking for them. LECs, on the other hand, substitute less when a good is on sale, and need to spend a higher fraction of time looking for promotions in order to take advantage of price discounts. Under the current parameterization, the ?rm sets an optimal discount of 31%, very close to the values reported by Nakamura and Steinsson (2008), 30%, and Klenow and Kryvtsov (2008), 25%. The discount price is available 70% of the time, but only 6% of total transactions are realized at promotional prices. This value is close to the expenditure-weighted fraction of price quotes that are sales reported by Nakamura and Steinsson (2008), 7.4%.
2.3
2.3.1
The Workings of the Model
Individual Price Setting Behavior
A ?rst step in evaluating the performance of the model is to assess its ability to generate individual price series similar to those reported in recent microeconomic studies of price setting. As mentioned in Section 1, a recently documented feature of the CPI data is that prices including sales tend to change roughly every quarter, while prices excluding sales tend to remain unchanged for two to three quarters
41
Table 2.1: Parameter Values
Parameter
Intertemporal discount factor Fraction of HECs Scale parameter leisure utility Scale parameter money utility HEC elasticity of substitution LEC elasticity of substitution Calvo parameter for regular prices Interest rate smoothing parameter In ation weight interest rate rule Output growth weight interest rate rule Standard deviation for monetary policy shocks Productivity autoregressive coe cient Standard deviation for productivity innovations
? h ? ? ? ?
Value
0.961/52
Comment
Length of a period = 1 week To match f
= 0.7
0.09 0.21 0.005 20.26 2.44 0.974
To match n = 1/3 To match V elocity = 0.15 To match s/n = 1/4 To match M arkup = 1.4 Implies a time between changes of 39 weeks Weekly analogue ofAruoba and Schorfheide's (2009) quarterly value From Aruoba and Schorfheide (2009)
?
?R
0.611/13
?1
1.7
?2
0.86
From Aruoba and Schorfheide (2009)
?R
0.0036/13
Weekly analogue ofAruoba and Schorfheide's (2009) quarterly value Weekly analogue of Hansen's (1985) quarterly value Weekly analogue of Hansen's (1985) quarterly value
?z
0.951/13
?z
0.007/13
(Nakamura and Steinsson, 2008; Klenow and Krystov, 2008; Klenow and Malin, 2010). Also, new evidence from high frequency scanner data has found that nominal rigidities take the form of inertia in reference (modal) prices, with weekly prices ?uctuating around a reference value that tends to remain constant over extended periods of time (see Kehoe and Midrigan (2007, 2008), and especially Eichenbaum
1
et al., (2011)). This point is illustrated in Figure 2.2, which displays the time series 42
Ì
Ä ¾ ÅÅÈÈ
Table 2.2: Steady State Values
? = ?h = ?l = 0
À
chr = 0.05 chp = 88.9 nh = 0.93 sh = 0.01 ? h (f, sh ) = 0.009
Ä
ÖÑ
pr = 1.11 pp = 0.77 discount = 0.31 f = 0.70 ? (f, s) = 0.06
clr
= 0.25
clp = 0.63 nl = 0.27 sl = 0.09 ? l (f, sl ) = 0.06
behavior of four selected DFF items. From the ?gure one can see that there seems to be an inertial reference price (i.e. the most observed price in a given time window) and prices tend to return to this reference value after having deviated from it. The model is able to replicate this type of behavior in prices, because it di?erentiates not only between regular and promotional prices, but also between pricequotes (like the ones recorded in CPI data) and realized transactions prices (like the ones recorded in scanner data). To see this, Figure 2.3 presents individual price simulations of the sticky regular price version of the model. Panel a) presents the regular and promotional price series of an individual ?rm for a simulation of 250 weeks.14 . The graph depicts the optimal regular price that the ?rm would set each period were it able to do so. However, the ?rm is subject to a Calvo friction and it is not able to adjust its regular price every period, so
14
The series is constructed by iterating forward the relative price optimal decision rules of the
linearized model for 250 periods, and then by simulating the behavior of an individual ?rm. Each period, there is a probability 1 ? ? that the ?rm will be able to set its price at the optimal price
r? r r level pr jt = pt , and a probability ? that the ?rm’s price will not change, pjt = pjt?1 .
43
Figure 2.2: PRICE EVOLUTION IN FOUR SELECTED PRODUCTS
its actual regular price, depicted by the dotted line, tends to remain unchanged for several periods, adjusting to the optimal value every time that the ?rm is allowed to change its price. Panel b) presents the evolution of the two prices available to consumers. The regular price is available in any period. The promotional price, however, is not always available, since the ?rm optimally chooses the fraction of time at which the price is o?ered. That is, in each period there is a probability ft that the lowest available price will correspond to pp jt and a probability 1 ? ft that the only available price will be pr jt . Consider the exercise of constructing a price quote series reporting the lowest available price in each period. In this case, the series will change almost every period, with frequent ?uctuations between the regular and promotional price and with occasional shifts to the regular one. The series of price quotes is presented in
44
Figure 2.3: SIMULATED PRICE FOR AN INDIVIDUAL FIRM
a) Regular Prices (optimal: solid line, realized: dashed line) and Optimal Promotional Prices (circle markers)
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.690
b) Available Prices (Regular: dashed line, Promotional: solid line)
1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.690 0.689
0.689
0.688 0.687 0.686 0.685
1 51 101 151 201
0.688
0.687 0.686
0.685
1 51 101 151 201
c) Minimum Available Price
1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999
1 51 101 151 201
d) Realized Price
1.000 1.000 1.000
1.000
1.000 1.000 1.000 0.999
1 51 101 151 201
0.690 0.690 0.689 0.689 0.688 0.688 0.687 0.687 0.686 0.686 0.685
1 51 101 151 201
0.690 0.690 0.689 0.689 0.688 0.688 0.687 0.687 0.686
1 51 101 151 201
panel (c). The price series described in panel (c), however, corresponds to quoted prices
45
Figure 2.4: SIMULATED PRICE FOR AN INDIVIDUAL FIRM: THE CASE OF POSITIVE STEADY STATE INFLATION
a) Regular Prices (optimal: solid line, realized: dashed line) and Optimal Promotional Prices (circle markers)
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1 51 101 151 201
b) Available Prices (Regular: dashed line, Promotional: solid line)
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1 51 101 151 201
c) Minimum Available Price
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1 51 101 151 201 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1 51
d) Realized Price
101
151
201
and not to the ones resulting from actual transactions. Each period, there is a probability ?t that the good will be purchased at the promotional price pp j , and a probability 1 ? ?t that it will be purchased at the ?rm’s regular price.15 The series of realized prices is presented in panel (d), showing the type of rigidity reported by Eichenbaum et. al. (2011). Realized prices show rigidity in the form of inertial reference values to which prices tend to return after having deviated from them.16
15 16 h l l ?t = h?t (fjt , sh t ) + (1 ? h)?t (fjt , st )
In terms of constructing the underlying price series from observed data, this exercise is more
consistent with the use of transaction-based datasets like supermarket scanner data than with price quotes like those recorded by BLS visitors. For example, think about a grocery store that uses loyalty cards in a way such that every week some of its products are o?ered on promotion and
46
The model with zero steady state in?ation is able to replicate the behavior of observed individual time series as long as these do not trend because of in?ation pressures. Since some individual price series seem to show an upward trend (see for example the Kellogg’s Corn Flakes example in Figure 2.2), the model was also solved around a 0.05 percent weekly steady state in?ation rate; this value corresponds to an annual cumulative in?ation rate of 3 percent (the post-Volker average in the US).17 The simulated price series are presented in panels (a) to (d) of Figure 2.4. The model, then, is able to deliver price-quote and realized-price series consistent with the microeconomic evidence. Because of the Calvo-type rigidity, the time series behavior of an individual ?rm’s regular price will be highly inertial. When including price promotions, on the other hand, prices will change very frequently. This behavior is consistent with the recent evidence on CPI price quotes that ?nds
their price tags display both the regular and promotional price. According to the BLS, a sale price must be temporarily lower than the regular price, be available to all consumers, and be usually identi?ed by a sign or statement on the price tag (Klenow and Krystov, 2008). In the speci?c case of loyalty cards, discounts are reported as only if the outlet con?rms that more than 50% of its customers use these cards (Nakamura and Steinsson, 2008). So, in this example, if the percent of customers using loyalty cards is lower to 50%, a price-quoting visitor will not even record the sales. But even if the sales were recorded, the visitor could gather data on both the regular and promotional price but she would have no information on the number of transactions closed at each price. A rich enough scanner dataset, on the other hand, would record both the regular and the promotional price as well as whether the loyalty card was used at the time of each transaction.
17
The pattern of steady state allocations when the model is solved around a positive in?ation
rate is similar to the one observed in the zero in?ation case but with a higher equilibrium discount, 0.45.
47
that the median frequency of price changes is sensitive to the inclusion or exclusion of sales (Nakamura and Steinsson, 2008; Klenow and Krystov, 2008; Klenow and Malin, 2010).
2.3.2
Does Micro Flexibility Translates Into Higher Neutrality at the Macro Level?
Figure 2.5 presents the responses of output to a monetary shock in the model with price promotions and sticky regular prices and in a standard model with no consumer heterogeneity and sticky prices. The latter model with no price promotions was calibrated to replicate the steady state hours, velocity and markup targets presented in Table 2.1 and with the same Calvo parameter used in the price promotions model. The model with price promotions presents a smaller and less persistent output response, with an impact deviation equal to one third of the one obtained with the standard Calvo model. Figure 2.6 helps in further understanding the intuition behind this result. Given the introduction of a New Keynesian interest rate rule, the model assumes that the impact of monetary policy on output operates through the real interest rate. There is thus a mapping between the time paths of output and the real interest rate. Panel (a) depicts the responses of these variables for both models. Real variables in the promotions model follow the same pattern as those of the Calvo model, but with smaller and less persistent responses. Panel (b) presents the responses of the relative regular and promotional prices,
48
p p r? r? ? pr t and pt , and the optimal promotional discount ((pt ? pt )/pt ).The graph also
shows the average price response constructed using ?t and 1 ? ?t as weights for the promotional regular price components respectively. After a shock to the interest rate, ?rms react mainly by reducing their promotional price and therefore increasing their optimal discount. Thus it is the possibility of adjusting their promotional price that provides ?rms with an alternative channel of adjustment when facing monetary shocks. Finally, panel (c) presents the responses of the probability of price promotions and the size of the promotion-economy (the share of real activity sold at promotional prices, ?t in equation 2.35) in response to a monetary policy shock. The graph shows that ?rms use the size of the promotional discount and not the frequency of promotions as a shock absorbing mechanism. Given the contraction in demand after the increase in the real interest rate, the share of the promotion economy also decreases and ?rms react by reducing the fraction of time at which they o?er price promotions.18 Why is it that ft decreases after a shock to the interest rate? To understand this, look at the two panels of Figure 2.7 which depict the time allocations of the two types of consumers. The shock a?ects consumers’ time-allocation decisions asymmetrically. HECs consumers take much more advantage from price promotions that LECs, and when they ?nd a promotion they substitute large quantities of goods at regular prices for good at promotional prices. Now that the size of the price discount has
18
The complete set of the models impulse response functions is presented in Appendix A.4.
49
increased, they do not need to spend as much time as they used to looking for price promotions (they ?nd less promotions but at larger discounts and they take full advantage of them) and they increase they labor time so they can have more resources dedicated to larger substitution of regular-price consumption for promotional-price consumption. Since LECs show a much lower degree of substitution when they ?nd a good on promotion, they have an incentive to increase the time they spent looking for price promotions (they do not substitute as much as HECs do, so they need to ?nd more promotions in order to take advantage of the increase in the price discount) and decrease their labor time. How does this a?ect the ?rms’ decisions about ft ? Since ?rms cannot distinguish between the two types of consumers, they price-discriminate by choosing a fraction of time at which they o?er their goods at promotional prices. As mentioned in previous sections, in doing so, the ?rms take advantage of that fact that promotions are costly in the sense that consumers have to spent time looking for promotions in other to take advantage of them. In a perfect price discrimination environment, the ?rms would be able to distinguish between types of consumers and charge a high price to LECs and a low price to HECs. In the model presented here, the ?rm could achieve perfect price discrimination if HECs looked for promotions all of their time (sh = 1) and HECs never looked for promotions (sl = 0). In that case, by setting ft = 1 the ?rm could completely distinguish between HECs and LECs and charge optimal perfect price discrimination prices (see Appendix A.3 for a formal treatment of this issue). A ?rm, then, has a larger incentive to discriminate (setting a higher ft ) when 50
l sh t /st increases. But, as explained in previous paragraphs, this is exactly the opposite
of what happens after a nominal shock when, given the asymmetric response of prices
l (the increase of the price discount) HECs decrease sh t and LECs increase st . Firms,
therefore have less incentive to price-discriminate and reduce ft . The ?rst panel in Figure 2.8 compares the output response of the model with price promotions presented in Figure 2.5 with several responses of the Calvo model calibrated to di?erent times between price changes. No Calvo response overlaps exactly with the one of the model with price promotions. The reason for this is that the model with price promotions combines features of both ?exible and sticky price models; the output response is small on impact but it dies out at a lower rate than those of the Calvo model. What is, then, the equivalent response in a Calvo model? The second panel of the ?gure presents two responses with the same cumulative impact on output. From the point of view of the overall e?ect of an interest rate shock on output, the model with price promotions calibrated to a time between regular price changes of nine months is equivalent to a Calvo model calibrated to a time between price changes of one month. The dynamics, however, are very di?erent; the response of the Calvo model shows a much higher initial impact but dies out almost twice as fast as the response of the model with price promotions. The near neutrality result contrasts with that obtained by Guimaraes and Sheedy (2011), who ?nd that even though their model delivers individual price paths similar to ones observed in the data, aggregate prices adjust by little in response to monetary shocks, which therefore have large e?ects on real variables. Since the 51
?exibility of prices at the micro level due to sales does not translate into ?exibility at the macro level, the authors conclude that sales are essentially irrelevant for monetary policy analysis. The key element behind Guimaraes and Sheedy’s (2011) non-neutrality result is that in their model sales are strategic substitutes; that is, a ?rm’s incentive to have a sale is decreasing in the number of other ?rms having a sale. For example, after a particular shock, an individual ?rm may have an incentive to have a sale and increase pro?ts coming from bargain hunters. However, if other ?rms follow the same strategy, targeting bargain hunters’ demand becomes a more competitive task, performed at the cost of charging a lower price to loyal customers willing to acquire the good at high prices. The ?rm then may ?nd it more pro?table to not have a sale, targeting only its demand from loyal customers. Guimaraes and Sheedy’s (2011) rationale for sales, then, implies a real rigidity constraining ?rms’ promotional strategies. As explained in an earlier version of their paper (Guimaraes and Sheedy, 2008), this strategic substitution implies that, following an expansionary monetary shock, an individual ?rm has an incentive to decrease sales, therefore increasing its average price. However, if all other ?rms pursue the same course of action, bargain hunters’ demand would be relatively neglected, increasing the returns to targeting non-loyal consumers. Then, in equilibrium, ?rms do not adjust sales by much in response to aggregate shocks, and monetary policy has large real e?ects. Guimaraes and Sheedy’s framework thus provides a well structured IO rationale for sales, consistent with micro price evidence on large amounts on price 52
variation due to idiosyncratic factors, and is able to generate realistic individual price series with inertial regular prices and frequent deviations from reference values. However, their model implies little adjustment in sales in response to aggregate shocks, which ends up being critical for their results on monetary non-neutrality. Is there any evidence on the response of ?rms’ promotional strategies to aggregate shocks? Chevalier et. al. (2003) use DFF data to study the behavior of prices in periods of high demand. They identify eight categories of products that a priori would seem susceptible to seasonal demand shifts, captured by dummy variables taking the value of 1 on determined holidays, as well as by temperature variables capturing weather-induced demand cycles. One of their exercises corresponds to evaluating the response of product advertising (price promotion) to demand peaks. The authors cite earlier evidence showing that high-demand items are more likely to be put on sale, and then regress the percentage of category revenues accounted for by items advertised by Dominick’s against the holiday and temperature high-demand variables. They ?nd that, in general, seasonally peaking items are signi?cantly more likely to be placed on sale.19 Even though Chevalier et. al. (2003) focus only on a small number of product categories (due to data limitations), their study ?nds evidence that sale promotions do respond to aggregate shocks, providing some ground for exploring alternatives
19
Chevalier et. al. argue that, if market share can be viewed as a proxy for high demand, then
the work of Nelson et. al. (1992) and Hosken and Rei?en (2001) shows a positive correlation between high-demand and the probability of being put on sale. Hosken and Rei?en (2004) also presents evidence that high-demand items are more likely to be placed on sale.
53
to Guimaraes and Sheedy’s dynamic pricing model.20 Figure 2.5: OUTPUT RESPONSE TO A MONETARY POLICY SHOCK
In the model presented in this document, ?rms have the alternative of o?ering regular and promotional prices at the same time, and randomize between moments of time in which only the regular price is available and moments of time in which both prices are available, implying a large amount of price ?uctuations even in a deterministic scenario as in Guimaraes and Sheedy (2011). Also, as in Guimaraes and
20
Working with a more comprehensive dataset (bimonthly observations of the CPI Research
Database), Klenow and Willis (2007) ?nd that sales seem to respond to macro information at least as much as regular price changes. Given the di?culty to identifying aggregate nominal shocks for the economy, the authors focus on the expected change in prices based only on current information about in?ation. For this purpose, they regress regular and sale individual prices against a measure of cumulative in?ation since the previous price change, ?nding that sales are at least as responsive to recent in?ation as are regular price changes.
54
Figure 2.6: IMPULSE RESPONSE ANALYSIS
(a) Output and Real Interest Rate Responses
0.0005 real int. rate response model with promotions real int. rate response Calvo Model 0.0000 1 -0.0005 6 11 16 21 26 31 36 41 46 51
output response model with promotions
-0.0010
-0.0015
output response Calvo model
-0.0020
(b) Relative Prices and Price Discount in the Model with Promotions (% deviations from steady state values)
0.04% price discount 0.03% 0.02% 0.01% 0.00% 1 -0.01% -0.02% 6 11 16 21 26 31 36 41 46 51
relativel regular price
relative promotional price average price response
(c) Size of the Promotion-Economy, Price Discount and Fraction of Time at Which Goods are Offered on Promotion (% deviations from steady state values)
0.06% 0.04% 0.02%
0.00% 1 6 11 16 21 26 31 36 41 46 51
price discount
-0.02% -0.04% -0.06% -0.08% -0.10% -0.12%
-0.14%
?t
ft
-0.16%
55
Figure 2.7: TIME ALLOCATIONS
HEC time allocations (% deviations from steady state values)
0.01%
LEC time allocations (% deviations from steady state values)
0.10% 0.05% 0.00% 1 -0.05% 6 11 16 21 26 31 36 41 46 51
nh
1 6 11 16 21 26 31 36 41 46 51
0.00% -0.01%
-0.02% -0.03%
sl
-0.10% -0.04% -0.15%
nl
-0.05% -0.06%
-0.07%
sh
-0.20% -0.25%
Figure 2.8: THE RESPONSE IN THE MODEL WITH PRICE PROMOTIONS COMPARED THAT OF A CALVO MODEL CALIBRATED TO DIFFERENT TIMES BETWEEN CHANGES
(a) Output Responses (Model with price promotions: solid line Standard Calvo Model: dashed line Units: % of steady state output)
1 0.00% 6 11 16 21 26 31 36 41 46 51 0.00%
-0.05%
(b) Two Equivalent Responses in Terms of Cumulative Effects (Units : % of steady state output)
1 6 11 16 21 26
-0.10% -0.10% -0.20% -0.15%
-0.20%
MPP TBRPC = 9 months half life: 6 weeks
-0.30%
CM TBPC = 1 month half life: 3 weeks
-0.25%
-0.40%
-0.30% -0.50% -0.35% -0.40%
-0.60%
Sheedy’s case, the inclusion of a nominal rigidity in regular prices allows the model to generate price series showing the type of reference price rigidity recently documented in the literature, providing also the opportunity of distinguishing between price quotes and realized prices. As regards e?ects of monetary policy, however, the type of price discrimination embedded in this paper provides a new source of price 56
?exibility that undermines the e?ect of nominal rigidities. When a monetary shock hits the economy and ?rms are not able to change their regular prices, they have the option of changing their promotional strategy (the promotional price and the fraction of time at which this is o?ered) in order to modify their average sale price. The key assumption behind this result is that the model’s rationale for sales relies on the use of price promotions for price discrimination, rather than on the assumption of customer loyalty. When consumers are given the possibility of endogenously determining the e?ort they want to invest to take advantage of price promotions, a new margin is created on the household side of the economy and, in a general equilibrium setting, ?rm’s and custumers’ choices interact, generating the coexistence of regular and promotional prices in a way such that the e?ects of nominal rigidities in regular prices are o?set by changes in promotional strategies. In this framework, sale prices end up being important for macroeconomics since their existence gives the market a way to outsmart the Calvo fairy. More generally, this result points out the importance of how consumer behavior is modelled. Indeed, since di?erent approaches to modeling ?rm-customer relationships may perform similarly in replicating features of the microeconomic data but di?er in their macro implications, further exploration of the interaction between ?rms and consumers may be a promising task for future research in macroeconomics.21
21
This line of research includes a wide range of possibilities such as modeling habit persistence
in di?erentiated goods as in Nakamura and Steinsson (2009), allowing for switching costs when consumers change sellers as in Kleshchelski and Vincent (2007), and modeling shopping as a search
57
2.4
Conclusion
This paper has introduced time looking for price promotions as part of the endogenous set of consumer choices. When price promotions are associated with a consumer time cost, the economy features the coexistence of regular and promotional prices. The exercise is relevant not only because of the recent evidence on micro price setting showing that the inclusion or exclusion of sale prices has bearing on the estimated frequency of price changes, but also because the rationale behind sale prices may a?ect the way in which real variables respond to aggregate shocks. When the model is complemented with a nominal rigidity in regular prices, individual price series behave in a way consistent with several features of the data: there is a large amount of price variation not associated with aggregate prices, price quotes rarely change when price promotions are excluded, and they change very often when price promotions are included. Moreover, the model allows a distinction between quoted and realized prices, with realized price series showing the type of rigidity recently found in studies using scanner data: there is inertia in reference prices, with frequent ?uctuations around the reference price. Regarding whether price rigidity at the ?rm level translates into monetary non-neutrality at the macro level, the results show that the type of price promotion considered in the model generates a new source of price ?exibility that o?sets the e?ect of nominal rigidity in regular prices. The economy thus features a dynamic
process as in Arsenau and Chugh (2007), Hall (2007), Levin and Yun (2008), and Albrecht et. al. (2010).
58
pricing arrangement in which the market is able to outmaneuver the Calvo fairy. This result is in contrast with the one recently obtained by Guimaraes and Sheedy (2011), showing the importance of how consumer behavior and ?rm-customer interactions are treated in macroeconomic models. Finally, the results suggest that gathering more empirical evidence on the relationship between price promotions and aggregate prices would be fruitful. How many goods in the economy are associated with price promotions? How many of these correspond to “o?-shelf” discounts? What types of customer costs are associated with accessing these promotions and how big are these costs? How much would these discounts a?ect estimates of the frequency of price changes? The answers to these questions could shed further light on the type and degree of price rigidity observed in the economy and on how this rigidity relates to aggregate ?uctuations.
59
Chapter 3
A Quantitative Analysis of Currency Substitution
3.1
Introduction
A striking feature of various emerging and developing economies is the high level of currency substitution observed even after several years of low in?ation. This paper focuses on two examples of this particular phenomenon: Bolivia and Peru. Data on the ratio of foreign currency deposits with respect to broad money, used as a proxy for total currency substitution, shows that the relationship between currency substitution and in?ation is not the same before and after high in?ation episodes. In both countries currency substitution increases with in?ation during high in?ation periods and reaches its peak once the economy has been stabilized, showing high persistence in the subsequent periods in spite of the downward trend in in?ation.
60
This persistence is also observed in other Latin American countries, as well as in many transition economies1 . Given that conventional monetary general equilibrium models cannot generate the hysteresis observed in the data, Uribe (1997) and Reding and Morales (2004) develop network externalities models that display low-in?ation - high-substitution steady states. Particularly, Uribe’s model proposes that the cost of buying goods with foreign currency is decreasing in the economy’s accumulated experience in transacting in the foreign currency. He refers to this accumulated experience as the economy’s “dollarization capital”. This chapter explores the quantitative implications of incorporating Uribe’s dollarization capital idea in a simple endowment economy model in which domestic and foreign currency balances are held because of their services in reducing transaction costs. Particularly, the model is used to generate a low in?ation-highsubstitution equilibrium and to compare the predicted currency substitution ratios to those observed in the data as well as those obtained using a model in which the dollarization capital mechanism is not present. When parameters are chosen as to replicate pre-hyperin?ation currency substitution levels, the model performs well in predicting high levels of currency substitution during high in?ation episodes, generating substitution ratios close to the ones observed in the data. The model also displays inertia in real foreign currency holdings during the transition towards a low-in?ation equilibrium and generates higher levels of currency substitution than a model with no dollarization capital dynamics. The model generates low in?ation currency substitution ratios that are be1
See Savastano (1996), Valev (2007) and Feige (2003).
61
tween 40% and 50% of those observed in post in?ation stabilization periods. Although the predicted currency substitution ratios are below the observed ones, the model is able to explain between 1/6 of the gap between the observed ratios and the ones generated by a model without dollarization capital dynamics. The fact that the predicted low-in?ation currency substitution ratios are below the ones observed in the data is a result of sizable post-stabilization impact e?ects on domestic currency holdings, a ?nding that suggests the need for future work on mechanisms that could induce inertia in domestic currency balances. Particularly, it would be interesting to study a model that displays uncertainty with respect to future in?ation, probably including a devaluation risk probability as in Mendoza and Uribe (1999, 2000). The rest of the chapter is organized as follows. The second Section describes the pre and post high-in?ation pattern of currency substitution in Bolivia and Peru. The theoretical model is presented in the third section and solved in the fourth section. The ?fth section concludes.
3.2
3.2.1
Currency Substitution in Two Selected Economies
Currency substitution and in?ation
The ?rst challenge in analyzing currency substitution in developing countries is constructing a relevant measure of the use of foreign currency in the domestic economy, often a di?cult task because of the lack of data on the amount of foreign currency
62
held by households outside the ?nancial system. Following Savastano (1996), a useful proxy for the total level of currency substitution in the economy is the ratio of foreign currency deposits (F CDs) to broad money. This measure, labeled F CD/BM ? , is represented by the dark gray areas in the left hand panels of Figure 3.1.2 The graphs also depict the behavior of the in?ation rate (in logarithmic scale for Bolivia and Peru). In the Bolivian case, this measure of currency substitution is not available for the 1981-1984 period when the central government imposed restrictions on the use of foreign currency in the ?nancial system, forcing the conversion of all bank liabilities into domestic currency. Therefore, this measure does not provide information on the behavior of currency substitution during the hyperin?ation period of the early eighties. When observing the 1985-2007 period, it is interesting to notice that the substitution ratio reached its peak in 1995 after several years of reductions in the annual in?ation rate, and decreased after that, even in the 2002-2008 period during which the in?ation rate gradually rose. Peruvian currency substitution follows a similar behavior. The substitution ratio was already high before 1988, with a 50% average for 1980-1987. The sharp decrease observed between 1984 and 1987 is related to the temporary prohibition
2
The broad money measure varies depending on the monetary aggregates classi?cation used
by each Central Bank. In the case of Bolivia the measure is constructed as the ratio of FCDs to M3’, the broadest monetary aggregate used by the Bolivian Central Bank, which includes short term and long term deposits denominated in local and foreign currency. In the cases of Peru , the measure is computed as the ratio of quasi-money denominated in foreign currency to total money and quasi-money.
63
of U.S. dollar denominated deposits (Rojas-Suarez, 1992). As in the Bolivian case, restrictions on F CDs limit the capacity of this measure to re?ect the relationship between in?ation and currency substitution during hyperin?ation episodes. During the post-restrictions period (1990 onwards) currency substitution remained high, achieving its peak in 1993 and showing a slow downward trend after that. Again following Savastano (1996), data limitations due to restrictions on FCDs in the domestic ?nancial system in Bolivia and Peru can be addressed by combining the F CD/BM ? substitution measure with information on foreign currency deposits held abroad (da). This new measure, labeled (F CD +da)/(BM ? +da), is represented by the light gray areas in the left hand panels of Figure 3.1. The measure was constructed using data on bank net foreign asset positions available at the Bank of International Settlements (BIS), taking the series of liabilities of BIS reporting banks against each country, converting them into domestic currency and adding them to the numerator and denominator of F CD/BM ? .3 The new and broader measure provides a clearer picture of the currency substitution - in?ation relationship before and after hyperin?ationary periods. In Bolivia, the broader substitution ratio was already high in 1980 (38%) and increased to 56% at the peak of the hyperin?ation episode in 1985, the same year in which F CD restrictions were eliminated. Currency substitution continued rising even after the hyperin?ation period ended, reaching a maximum of 83% in 1995. The reduction in the distance between the two substitution measures during the 1988-2008 pe3
BIS Banking Statistics. Table 6A: External positions of reporting banks vis--vis individual
countries, vis--vis all sectors.
64
Figure 3.1: CURRENCY SUBSTITUTION IN BOLIVIA AND PERU
riod shows that as in?ation was controlled and continually reduced, domestic agents changed the composition of their portfolios from assets held abroad to assets held in the domestic banking sector, but with little change in the currency composition of their monetary assets, relying heavily on F CDs. A similar pattern is observed in Peru, where both in?ation and the broader substitution measure were already high in the pre-hyperin?ation period. The broader ratio increased with in?ation in the 1987-1990 period, and reached its peak in 1993, by which time in?ation already presented a marked downward trend. As in the Bolivian case, once F CD restrictions were eliminated (1990) the portfolio composition shifted towards domestically held deposits, but with the currency composition still leaning towards U.S. dollar denominated monetary assets.
65
Thus, the left-hand side panels in Figure 3.1 summarize the ?rst main stylized fact that motivates the quantitative work presented later in the document: while dollarization increases quickly with in?ation during high-in?ation periods, it does not quickly revert once in?ation has been reduced and does not present a clear comovement with in?ation in the post-stabilization years.
3.2.2
Inverse velocities of money
This section describes the behavior of the Bolivian and Peruvian ?nancial systems by constructing di?erent inverse velocities of money as proxies of ?nancial deepness. Each of the right-hand side panels in Figure 3.1 presents in?ation (in logarithmic scale) and the inverse of three money velocity ratios: i) M/GDP , money over GDP, ii) BM/GDP , broad money over GDP, and iii) BM ? /GDP , broad money including foreign currency deposits over GDP.4 The top right panel shows a sharp decline in monetization ratios during the Bolivian hyperin?ation years (1984-1985); once that in?ation was controlled and F CD restrictions lifted, the inverse velocities of money in domestic currency remained relatively low for several years, while BM ? /GDP increased strongly until reaching a peak in 2001 (54%). The domestic currency ratios (M/GDP and BM/GDP ) increased in the 2004-2008 period, but this was not joined by a decrease in BM ? /GDP which increased from 43% in 2004 to 51% in 2007.
4
Bolivia:
M/GDP = M1/GDP, BM=M2/GDP, BM* = M3’/GDP. Peru:
M/GDP =
Money/GDP, BM = (Money + Quasimoney)/GDP, BM* = (Money + Quasimoney in domestic and foreign currency)/GDP. See Appendix 2.
66
In the case of Peru, there was a marked reduction in the three monetary ratios during the hyperin?ation period, followed by a strong increase in BM ? /GDP after in?ation was controlled and F CD restrictions eliminated. While both domestic currency inverse velocities followed an increasing trend, they remained well below BM ? /GDP which reached its historical peak of 30% in 2008. Overall, the right-hand side panels in Figure 3.1 summarize the second main stylized fact of interest in this document: if the inverse velocities of money presented in Figure 3.1 are understood as proxies of ?nancial deepness, then the graphs show that after high in?ation episodes, the ?nancial system recovery relies strongly on the use of the foreign currency. After the sharp decrease in monetization ratios, the post-hyperin?ation ?nancial sectors were rebuilt on the basis of the U.S. dollar instead of the national currency. The next section presents a simple perfect foresight model that seeks to capture the above mentioned stylized facts by introducing an accumulation externality in the use of the foreign currency.
3.3
A Model of Currency Substitution
The stylized facts analyzed in the previous section show that the relationship between currency substitution and in?ation follows di?erent patterns in pre-stabilization and post-stabilization periods, a type of asymmetry that is not captured by standard monetary general equilibrium models. Motivated by the high degree of persistence in currency substitution observed
67
in several developing countries, Uribe (1997) develops a cash in advance model in which the cost of buying goods with foreign currency is decreasing in the economy’s accumulated experience in transacting in foreign currency, a concept that Uribe calls the economy’s dollarization capital. Uribe’s framework delivers the possibility of an equilibrium in which the foreign currency circulates even in a low in?ation steady state. Building on Uribe’s work, Reding and Morales (2004) replace the exogenous dollarization capital assumption by modeling endogenous network externality e?ects in which the size of the foreign currency network increases with the number of agents whose foreign currency balances are larger than a given threshold. Their model also renders the possibility of high-substitution - low-in?ation equilibria by combining a learning e?ect (the acquisition of experience in the use of an alternative currency) with a size e?ect (the reduction in transaction costs caused by an increase in the number of agents with signi?cant foreign currency balances). Both of these works present heterogeneous agent models with complex dynamics and are not solved computationally. This section develops a simple representative agent monetary model incorporating Uribe’s (1997) dollarization capital idea; the model is then solved using numerical methods.
3.3.1
Preferences
Consider a perfect foresight endowment economy with income yt = y in every period and lifetime utility stream given by
68
?
? t u(ct )
t=0
(3.1)
where ? is the inter-temporal discount factor, u (ct ) > 0 and u (ct ) < 0.
3.3.2
Monetary Policy
The economy is open. It follows a predetermined exchange rate regime and the law of one price holds at any moment in time. That is, the nominal exchange rate
? St is given by St = pt /p? t , where pt and pt , are the domestic and international
price levels respectively. Therefore in?ation is given by ?t = ?t + ? ? where ? is the policy-determined devaluation rate and ? ? is international in?ation. Each period the government injects money in the economy through a transfer Tt = Mt+1 ? Mt , where Mt are nominal money balances. The transfer is such that it satis?es the law of one price and the model equilibrium conditions that will be derived below. The agent uses her resources either in consumption (ct ) or in acquiring domestic and foreign currency balances carried to the next period (mt , m? t ).
3.3.3
Transaction Costs
Money enters into the model because of its transaction cost reduction services. Each period the agent must cover a transaction cost given by
t ? ct , ? ( m ), ? ? pt
m? t , dt p? t m? t p? t
; ?c > 0, ?? < 0, ??? < 0
where
5
mt pt
and
are domestic and foreign real money balances respectively.5
? Notice that m? t are nominal foreign currency balances expressed in the foreign currency, mt St
69
The transaction cost reduction services provided by domestic currency real
t balances are given by ?( m ) with ? > 0, while the cost reduction services derived pt
from from holding foreign currency real balances are given by ??
m? t , dt p? t
, where dt
is the economy’s accumulated experience in using foreign currency (the dollarization
? ? capital) and ?m ? /p? > 0 , ?d > 0. t t
Under this structure, the agent’s budget constraint in period t is given by
y+
mt?1 m? mt m? 1 t + t? + ? + T = c + t t Pt Pt? Pt Pt mt + ? ct , ? , ?? Pt
m? t , dt Pt?
(3.2)
3.3.4
Dollarization Capital
I assume that the transaction cost reduction services provided by foreign currency depend not only on the amount of foreign currency real balances, but on the accumulated experience using this currency. The dollarization capital depreciates at ˜) and its accumulation is an increasing function of the current an exogenous rate (? level of currency substitution.
˜)dt + G dt+1 = (1 ? ? with G (.) > 0 and G (.) < 0.
m? t Pt
m? t ? Pt
+
mt Pt
(3.3)
are foreign currency balances expressed in domestic currency and currency balances expressed in real terms.
m? t St pt
t = pttp?t = p? are foreign t t
m? p
m?
70
3.3.5
Maximization Problem and Competitive Equilibrium
mt pt
Letting at =
and a? t =
m? t , p? t
the consumer’s problem is maximizing (3.1) subject
to (3.2) and (3.3), with ?rst order conditions given by
?
u (t + 1) u (t) = (1 + ?t+1 )[ (1 + ?? (t)? (t)) 1 + ?c (t + 1) 1 + ?c (t) a? + ?t G (t) ? t 2 ] (at + at )
(3.4)
?
u (t + 1) = 1 + ?c (t + 1)
u (t) ? (1 + ??? (t) ?a ? (t)) 1 + ?c (t) at ? ?t G (t) ? (at + at )2
? 1 + ?t +1 [
(3.5)
˜ ? ?t = ? ?t+1 1 ? ?
u (t + 1) ? ??? (t + 1) ?d (t + 1) 1 + ?c (t + 1)
(3.6)
where ?t is the multiplier on the dollarization capital accumulation equation, the expression (t) is used to denote that all the arguments of a given function are
? ? evaluated at period t, ?t = pt /pt?1 and ?t = p? t /pt?1 . Finally, when imposing market
clearing in the money market, that is Mt = mt , equation (3.2) is reduced to
m? t p? t
?
m? t?1 p? t
= y ? ct ? ? (t)
or
a? t ?
a? t?1 = y ? ct ? ? (t) ? 1 + ?t
(3.7)
71
? Notice that if the international price is normalized to one, ?t = 0 and this last
equation is reduced to
? a? t ? at?1 = [y ? ? (t)] ? ct
(3.8)
that is, an increase in real foreign currency balances held by domestic agents is ?nanced through a trade balance surplus, with the trade balance de?ned as the di?erence between output net of transaction costs, y ? ? (t), and consumption. Then, the model’s competitive equilibrium is de?ned as a list of sequences for consumption and dollarization capital {ct , dt }, portfolio choices {mt , m? t }, prices {pt , p? t }, and policy variables {Mt , ?t } such that: i) Equations (3.2), (3.3), (3.4), (3.5) and (3.6) solve the representative agent’s consumption maximization problem, ii) the monetary market clears (Mt = mt ) and iii) the Law of One Price is satis?ed in every period. The intuition behind the ?rst order conditions of the model is better understood by considering ?rst the case of a model without dollarization capital. The equilibrium conditions of such a model correspond to equations (3.4), (3.5) and (3.11), setting ?t = 0 and normalizing dt to one:
?
u (t + 1) 1 + ?c (t + 1)
1 1 + ?t+1
=
u (t) (1 + ?? (t) ? (t)) 1 + ?c (t)
(3.9)
?
u (t + 1) 1 + ?c (t + 1)
1 ? 1 + ?t +1
=
u (t) (1 + ??? (t) ?a? (t)) 1 + ?c (t)
(3.10)
72
a? t ?
a? t?1 = y ? ct ? ? (t) ? 1 + ?t
(3.11)
The left hand side of (3.9) is the marginal utility consuming one less unit of the good in period t and using those resources to increase domestic real balances at t + 1. In t + 1 these extra real balances are used for consumption, and the marginal utility of this future consumption is properly discounted by domestic in?ation and the marginal increase in transaction costs ?c (t + 1) . This expression is equated to the marginal utility of consuming the good in period t (right hand side of (3.9)), adjusted by the increase in transaction costs caused by additional consumption and by the opportunity cost of not carrying an extra unit of domestic real balances to the next period. This opportunity cost equals the marginal reduction in the transaction cost from carrying domestic real balances from period t to period t + 1 (remember that ?? (t) is negative). A similar interpretation is given to equation (3.10), where the left hand side is the marginal utility of carrying a unit of foreign currency real balances to the next period, while the right hand side is the marginal utility of consuming a unit of the good in the current period, including the increase in transaction costs caused by additional current consumption and by having one less unit of foreign real balances carried to the next period. Combining (3.9) and (3.10):
1 + ??? (t) ?a? (t) 1 + ?t+1 = ? 1 + ?? (t) ? (t) 1 + ?t +1
(3.12)
73
Equation (3.12) summarizes how the agent’s currency portfolio composition is a?ected by domestic and foreign in?ation in a model with no dollarization capital.
? When ?t = ?t , the opportunity cost (in transaction cost reduction terms) of not
carrying a unit of domestic real balances (?? (t) ? (t)) is equal, at an optimum, to the opportunity cost of not carrying a unit of foreign real balances (??? (t) ?a? (t)).
? When ?t+1 > ?t +1 ? ?1 however, 1 + ??? (t)?a? (t) > 1 + ?? (t)? (t).
Thus, in the absence of dollarization capital dynamics, discrepancies between domestic and foreign in?ation are immediately translated into changes in the current composition of the agent’s real balances portfolio. When endogenous accumulation of dollarization capital is introduced in the model, the equivalent of equation (3.12) is found by combining (3.4) and (3.5):
u (t) 1+?c (t)
at ? (1 + ??? (t) ?a ? (t)) ? ?t G (t) (a? +a )2
t t
u (t) 1+?c (t)
?t (1 + ?? (t) ? (t)) + ?t G (t) (a?a +a )2
t t
=
1 + ?t+1 ? 1 + ?t +1
(3.13)
This last expression implies new trade-o?s not present in (3.12). When ?t+1 =
? ?t +1 , (3.13) is reduced to:
u (t) ?t G (t) ? [??? (t) ?a ? (t) ? ?? (t) ? (t)] = 1 + ?c (t) a? t + at
(3.14)
where this last expression equates the marginal value of increasing the dollarization capital by holding a higher proportion of foreign real balances (right-hand side of 3.14) with the forgone marginal utility gain from reducing transaction costs by holding domestic balances over foreign ones and then spending the proceedings
? on consumption (left-hand side of 3.14, recalling that ??? (t) ?a ? (t) and ?? (t) ? (t)
74
are negative). In the absence of dollarization capital dynamics, the term in square brack? ets on the left-hand side of (3.14) would be zero when ?t+1 = ?t +1 (see equation
3.12), but now it is positive at an optimum. That is, the model with dollarization capital dynamics requires higher marginal transaction cost reduction services from holding domestic currency balances than would be required in a framework without dollarization capital (| ?? (t) ? (t) |>| ??? (t) ?a? (t) |). This framework thus introduces inertia through a substitution motive not present in the model without dollarization capital. Suppose that dollarization (the
? proportion of foreign real balances with respect to total real balances , a? t /(at + at ))
decreases. Then, for a given {?t , ct } pair, this would imply an increase in the right hand side of (3.14) because of the strict concavity of G(t). This, in turn, implies broadening the gap between | ?? (t) ? (t) | and | ??? (t) ?a? (t) | ( left hand side of (3.14) ), implying an increase in a? t and a decline in at .
3.4
3.4.1
IV. Solving the Model
Parametrization and Solution Method
The model is solved for the following functional forms: u (ct ) =
?? c1 t 1??
? (ct , ? (t) , ?? (t)) =
ct ?(t)?? (t)
?
ct ; ? > 0
? (t) = (at )? ; ? ? (0, 1)
75
1?? ?? (t) = (dt a? t)
G (t) =
a? t a? t +at mt Pt
?
; ? ? (0, 1)
m? t ?. Pt
where at =
and a? t =
The functional form for the transaction cost term is similar to that used in works like Mendoza and Uribe (1997,1999,2000) but replacing mt in the denominator
? 1?? by m? . t (dt mt )
Parameter
Table 3.1: Parameter Values Value
Bolivia Peru 0.96
Source
Calibration Target
-
Discount factor
? ? (0, 1)
0.96
Standard value in yearly models Reinhart and Vegh (95) Country Data Calibrated
c y
Risk Aversion Coe cient In ation Rate Exponential term: transaction cost function Exponential term: cost reduction services provided by the domestic currency Exponential term: Dollarization Capital accumulation function Dollariation Capital depreciation rate
C = Private Consumption
?>0
1.5
1.5
-
? ?>0
0.24 0.081
0.93 0.139
-
=
C GDP
? ? (1 2 , 1)
0.927
0.911
Calibrated
a y
=
N CSR GDP
? ? (0, 1)
0.689
0.490
Calibrated
a? y = DCSR?N CSR GDP
? ? (0, 1)
0.521
0.777
Calibrated
d=1
NCSR = Numerator in Currency Substitution Ratio (CSR) DCSR = Denominator in CSR
Given the predetermined exchange rate regime and normalizing p? to one, the in?ation rate is given by the devaluation rate, ?t = ?, taken as a policy parame76
Ì
Ä ¾ ËÈ È Ê
Table 3.2: Model Results and Calibration Targets
Ì
a/y a? /y c/y d CSR
ÅÓ Ð ¼º½ ¼º½½ ¼º ½º¼ ¼º¿
ÓÐ Ú Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
Ø ¼º½ ¼º½½ ¼º ¹ ¼º¿
Ë ØØ Ò Ô Ö Ñ Ø Ö× × ØÓ Ö ÔÐ ÅÓ Ð ¼º½ ¼º¾¼ ¼º ½º¼ ¼º ¼
Ì È ÖÙÚ Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
Ø ¼º½ ¼º¾¼ ¼º ¹ ¼º
Ø
ter that determines each steady state. The solution method consists of linearizing equations (3.3), (3.4), (3.5), (3.6) and (3.11) around alternative steady states using Schmitt-Grohe and Uribe’s (2004) perturbation algorithm. Regarding the values chosen for each parameter, y is normalized to one, while ? is set at a standard value of 0.96. ? is set at 1.5, in the middle of the range used in Mendoza’s (1991) study on real business cycles in small open economies; this value is also within the range estimated by Reinhart and Vegh (1995). Two sets of values for ?, ? , ? and ? are chosen to replicate the pre-hyperin?ation currency substitution ratio in Bolivia and Peru. The values for {?, ?, ?, ? } are jointly determined to match four calibration targets: ?rst, a consumption-output ratio (c/y ) equal to the observed consumptionGDP ratio in the pre-hyperin?ation period (1980-1981); second, a foreign real balances–output ratio (a? /y ) equal to the observed (F CD + da)/N GDP ratio in the pre-hyperin?ation period, where N GDP stands for nominal GDP, F CD stands for
¾
foreign currency deposits and da stands for deposits held abroad; third, a domestic real balances-output ratio (a/y ) equal to the observed (BM ? ? F CD)/GDP ratio in the pre-hyperin?ation period, where BM ? is the broad money measure used in
77
Section II; fourth, a dollarization capital value equal to one. By setting the above mentioned targets for a? /y and a/y , the model’s ratio of foreign monetary assets to output ( ay =
?
sm? ) py
corresponds to the ratio between
the numerator of the currency substitution measure used in Section II and nominal GDP (that is, the ratio of foreign currency monetary assets to nominal GDP), while the model’s ratio of domestic monetary assets to output ( a = y
m ) py
corresponds to
the ratio of the di?erence between the denominator and numerator terms of the currency substitution measure used in Section II to nominal GDP (that is, the ratio of domestic currency monetary assets to nominal GDP). Given these targets, the model’s ratio of foreign real monetary assets to total monetary assets (a? /(a? + a)) corresponds to the observed currency substitution measure discussed in Section II ((F CD + da)/(BM ? + da)). The target for dt is chosen to generate some similarity between the model’s pre-hyperin?ation equilibrium and that obtained in a model with no dollarization capital dynamics. In the two cases the value for ? is restricted to be greater than 1/2 in order to ensure that domestic real balances are greater than foreign currency when ?t+1 =
? ?t +1 and when there is no dollarization capital. To see this notice that under the
current functional forms equation (3.12) implies ? > 1/2 ensures at ¿a? t.
at a? t
=
? 1??
? when ?t+1 = ?t +1 , and
The four sets of parameter values are reported in Table 3.1. Table 3.2 presents the observed and model-generated values for each calibration target. Table 3.3 shows the performance of the model in matching the observed degree 78
of currency substitution during hyperin?ation episodes. Ì Ä ¿ ËÈ È Ê Table 3.3: Currency Substitution Ratios in High-in?ation Periods
Ë ØØ Ò Ô Ö Ñ Ø Ö× × ØÓ Ö ÔÐ
CSR d
ÅÓ Ð ¼º ¼ ½º ¼ ÅÓ Ð ¼º ½º½¼
Ì
ÓÐ Ú Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
Ø ½¶ ¼º ¹ Ø ½¶ ¼º ¼ ¹
Ø
Ø ¾¶¶ ¼º ¹ Ø ¾¶¶ ¼º ¹
Ì È ÖÙÚ Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
¶ ØØ Ô Ó Ø ¶¶ ÇÒ Ô Ö Ó Ø Ö Ø
CSR d
¹ Ò Ø ÓÒ Ô Ö Ó º ÝÔ Ö Ò Ø ÓÒº
The average value of Bolivian in?ation for the 1982-1985 period was 2700%. When in?ation is set at this value, the result is a 53% increase in dollarization capital and a currency substitution ratio of 70%, a little higher than the average between the ratio observed at the peak of the hyperin?ation and the one observed one period after the hyperin?ation. In the case of Peru, the average in?ation rate for the hyperin?ation period (1988-1991) was 4000%. When the model is solved for this in?ation rate, the dollarization capital level increases by 12% with respect to the pre-hyperin?ation period and the currency substitution ratio is 74%, seven to eight percentage points below the observed ratio.
3.4.2
Transitional Dynamics from High to Low in?ation
¿
As shown in Table 3.3, the model performs well in terms of generating high dollarization ratios for large values of in?ation. The model can also be used to study
79
transitional dynamics from a high-in?ation steady state to a low-in?ation one. Figure 3.2 presents impact and transitional e?ects of reducing in?ation from 2700% (the Bolivian post-hyperin?ation value) to 24% (the Bolivian pre-hyperin?ation value), and from 4000% (the Peruvian post-hyperin?ation value) to 90% (the Peruvian prehyperin?ation value). All series are expressed as percentage deviations from the original steady state. The adjustment in dollarization capital is slow, taking more than three years in every case, and the rapid adjustment in currency portfolios is mainly due to sharp changes in domestic currency balances. The much slower and less sizable adjustment in foreign currency balances is directly related to the inertia observed in dollarization capital dynamics. Currency substitution dynamics are shown in the third graph in each panel, with a high impact e?ect explained by the quick adjustment in domestic currency balances. Since money enters the model through a transaction cost function, the reduction in in?ation has a positive e?ect on consumption and therefore utility. Figure 3.2: TRANSITIONAL DYNAMICS
Dynamics from from High-Inflation Equilibrium Figure 2: Transitional Dynamics High-Inflation to to Low-Inflation Low-Inflation Equilibrium Equilibrium
a) Parameters set as to obtain the Bolivian pre-hyperinflation currency substitution ratio Money Balances Dollarization Capital, d
0.0 1 -0.1 -0.2 -0.3 -0.4 -0.5 4.0 0.0
a (-, left axis) a*(--, right axis)
6.0 0.2
0.2 0.1
Currency Substitution, a/(a+a*)
0.0 0.10
Consumption, c
0.08 0.06 0.04 0.02 0.00 1
Dollarization Capital, d
6.0 4.0
2.0
2
2
3
4
5
6
7
8
1
-0.2
2
3
4
5
6
7
8
-0.4 -0.6
-0.8
2.0 0.0 1 2
3 4 5 6 7 8
0.1 0.0
2
3
4
5
6
7
8
b) Parameters set as to obtain the pre-hyperinflation currency currency substitution substitution ratio ratio obtain the Peruvian Peruvian pre-hyperinflation Money Balances
a (-, left axis) a*(--, right axis)
0.1 0.1
0.0 0.0 8
Currency Substitution, a/(a+a*)
0.0 0.2
Consumption, c
1
-0.1 -0.2
3
4
5
6
7
1
-0.2
2
3
4
5
6
7
8 0.1
-0.3 -0.4
-0.4 -0.6
0.1 0.0 1
2
0.0
1 2
0.0 3 4 5 6 7 8
3
4
5
6
7
8
80
How does the model perform compared to one in which there is no dollarization capital? This question is answered by analyzing currency substitution transitional dynamics from the high-in?ation steady state to one in which in?ation equals the post-stabilization average. Panel a) in Figure 3.3 corresponds to a reduction in in?ation from 2700% (the Bolivian hyperin?ation average) to 11% (the Bolivian post stabilization average), while panel b) corresponds to a reduction in in?ation from 4000% (the Peruvian hyperin?ation average) to 17% (the Peruvian post stabilization average). Solid lines are used for the model with dollarization capital, while dashed lines are used for the model with no dollarization capital6 . In all cases the initial value is set at the high in?ation steady state in the model with dollarization capital. As expected, the dollarization capital model delivers higher post-stabilization ratios than those obtained with the model without dollarization capital.4. Panels a.1) to b.2) show the transition paths of domestic and foreign real balances. In the model with no dollarization capital foreign balances fall with respect to their levels in the previous equilibrium while they increase when dollarization capital is added to the model. However, as mentioned earlier, in both models the dynamics of the currency substitution ratio are not driven by the adjustment in foreign balances but by quick and very sizable variations in domestic balances. The currency substitution ratios of the model with dollarization capital are below the observed ratios, but still represent a large increase with respect to a more conventional model with no dollarization capital dynamics. The ratios generated by the dollarization capital model are between 40% and 50% of the observed ratios,
6
Dollarization capital dynamics are shut down by setting ? = 1 and ? = 0
81
Figure 3.3: TRANSITION WITH AND WITHOUT DOLLARIZATION CAPITAL
Inflation drops from 2700% (Bolivian 1982-1985 average) to 11% (Bolivian 1986-2008 average) Inflation drops from 3100% (Peruvian 1988-1991 average) to 17% (Peruvian 1992-2008 average)
a) Currency Substitution Ratio
0.80 0.70 0.60 0.80 0.70 0.60
b) Currency Substitution Ratio
a*/(a*+a)
0.40 0.30 0.20 0.10 0.00 1 2 3
a*/(a*+a)
4
5 6 7
0.50
0.50
0.40 0.30 0.20 0.10 0.00 1 2 3 4
5
6
7
a.1) a as % of st. st. value
700.00 600.00 500.00 400.00 600.00
b.1) a as % of st. st. value
500.00
400.00
300.00
300.00
200.00
100.00 0.00 1 20.00 15.00 10.00 5.00 0.00 1 -5.00 -10.00 -15.00 -20.00 -25.00 2 3 2 3
200.00
100.00
0.00
a.2) a* as % of st. st. value
10.00 5.00 0.00 1
Solid line: model with dollarization capital
explaining 1/6 of the gap between the observed currency substitution ratios and those obtained with a model with no dollarization capital. This is seen in Table 3.4, where the ?rst three columns in each panel present the post-stabilization currency substitution ratios obtained by models with and without dollarization capital, as well as the observed ratios. The fourth column presents the ratio between the di?erence in predicted currency substitution ratios with and without dollarization capital and the di?erence between the observed ratio and the 82
4 4
5 5
6 6
7 -5.00 7 -10.00
1
b.2) a* as % of st. st. value
2 2
3 3
4 4
5 5
6 6
7 7
-15.00
-20.00 -25.00
Dotted line: model with no dollarization capital
Ì
Ä
ËÈ È Ê
Ë ØØ Ò Ô Ö Ñ Ø Ö× × ØÓ Ö ÔÐ
Table 3.4: Currency Substitution Ratios in High-in?ation Periods
Ì
ÓÐ Ú Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
(iii)
Ø
(i)
(ii)
ÅÓ Ð
(dol capital) CSR
¼º¾
ÅÓ Ð ´no dol capitalµ ¼º¾½
(ii)
Ø ´ ¹¼ µ ¼º
(iii)
(i) (iii)
(i)?(ii) (iii)?(ii)
¶
¼º ¼
¼º½
Ì È ÖÙÚ Ò ÔÖ ¹ ÝÔ Ö Ò Ø ÓÒ ËÊ
(i)
ÅÓ Ð
(dol capital) CSR
¶
Ô
ØÛ Ò (ii) Ò
¼º¿
ÅÓ Ð ´no dol capitalµ ¼º¿¼
(iii)
ÜÔÐ Ò
Ý (i)
Ø ´ ¾¹¼ µ ¼º
(i) (iii)
(iii)?(ii) (i)?(ii)
¶
¼º ¼
¼º½
one generated by the model without dollarization capital. Overall, the dollarization capital framework delivers high post-stabilization substitution ratios using a very simple structure, and leaving ample room for further additions to the model dynamics. These additions could focus on generating inertia in the adjustment process for domestic currency holdings in a way consistent with the behavior of the inverse velocities of money discussed in Section II. An interesting line of work in this regard would be the introduction of uncertainty about the future value of in?ation, by assigning a policy reversal probability as part of the agent’s information set as in Mendoza and Uribe (1999,2000)7 .
7
In the predetermined exchange rate regime environment of the present document, this fea-
ture could be added to the model by introducing a post-stabilization time-dependent devaluation probability as in Mendoza and Uribe (2000), or by making this probability an endogenous variable conditioned on foreign reserves as in Mendoza and Uribe (1999).
83
3.5
Conclusion
The present document has developed a simple endowment-economy monetary model able to generate high levels of currency substitution in low in?ation environments. The introduction of a dollarization capital variable to capture the economy’s accumulated experience in the use of foreign currency generates a motive for holding foreign currency balances even when in?ation is low. When applied to high-in?ation equilibria, the model is able to generate currency substitution ratios very close to those observed during hyperin?ation episodes, and it presents inertia in foreign currency real balances during the adjustment towards a low-in?ation steady state. In terms of the model’s predicted post-hyperin?ation dollarization levels, these are still below the observed ratios but represent a sizable increase with respect to those obtained using a more standard framework with no dollarization capital. The dollarization capital model generates post-hyperin?ation currency substitution ratios that are between 40% and 50% of the observed ratios and is able to explain 1/6 of the gap between the observed substitution ratios and those generated by a model with no dollarization capital dynamics. Further model building e?orts could focus on introducing frictions that reduce the size of impact e?ects on post-stabilization domestic currency holdings. An important step in this direction may be the introduction of devaluation risk dynamics along the lines of Mendoza and Uribe (1999, 2000).
84
Chapter 4
Investment Activity in the Financial Sector and the Relationship between In?ation and Currency Substitution
4.1
Introduction
As shown in the previous chapter, the dollarization capital model generates a higher steady state currency substitution ratio than that obtained with a model with no dollarization capital in it. There are, however, three important limitations that a?ect the model’s ability to study currency substitution dynamics. First, the dollarization capital variable was introduced in an ad hoc manner as a stock variable entering the transaction cost function. Second, the model has a representative household, and
85
the dollarization capital variable is optimally chosen by the consumer taking into account an accumulation law of motion in which dollarization capital increases with the currency substitution ratio. In this environment, the consumer fully internalizes the e?ect of currency substitution on the dollarization capital variable, leaving no room for network externality e?ects like the ones developed in Uribe (1997) and Reding and Morales (2004). Third, the model is not able to generate an asymmetric relationship between in?ation and currency substitution before and after high in?ation episodes. This behavior is at odds with the data in several partially dollarized economies. This chapter presents a framework that provides a micro foundation for a quantitative model able to deal with the above mentioned limitations. Developing and solving such a model is beyond the scope of this chapter. The chapter rather focuses on exploring the theoretical elements needed to generate di?erent in?ationsubstitution patterns before and after high in?ation episodes. The main idea is that in an environment in which consumers show some heterogeneity in their ability to access the ?nancial sector’s money exchange services, a su?ciently high level of in?ation can induce the ?nancial sector to make a ?xed cost investment that decreases this heterogeneity by permanently reducing money exchange costs. More formally, this chapter presents a simple model of two consumers who use money to buy a consumption good. The consumers can hold either domestic or foreign currency, but they do not have the technology to transform domestic balances for foreign ones, so to do so they must use a money exchange point owned by the ?nancial sector. The only di?erence between consumers is that they may be located 86
at di?erent distances from the nearest exchange point, and they obtain disutility from walking that distance. The ?nancial sector provides only one service, money exchange, and decides on whether or not to construct money exchange points at a given ?xed cost. The ?nancial sector makes its optimal exchange point construction decision anticipating the consumers’ substitution decisions under di?erent levels of in?ation. For su?ciently high levels of in?ation, the ?nancial sector will construct new exchange points, changing consumers’ distance to the closest exchange point and therefore permanently reducing currency substitution costs. It could be said then that in this framework the dollarization capital variable corresponds to the number of exchange points set by the ?nancial sector. This seems like a plausible example of the type of investment decisions made by the ?nancial sector in developing countries as agents increase their usage of foreign currency. Think, for example, of a bank in a high-in?ation developing country deciding on whether to o?er money exchange services in some or all of its agencies. Provided that there are no legal restrictions, the bank may also decide to o?er foreign currency high liquidity services (i.e. checking accounts denominated in dollars), an action that may be associated with di?erent types of one-time costs, such as training personnel in the use of the foreign currency and setting up accounting and software systems that handle both currencies. For an example directly related to the concepts of distance and accessibility, think of banks investing in ATM machines and deciding whether to provide ATM services only in domestic currency or allowing them to work in foreign currency as well. The ?nancial system may be willing to pay these investment costs during periods of high in?ation (or of high in?ation expectations) with 87
the purpose of taking advantage of the increase in household’s demand for foreign currency. However, this investment permanently reduces household’s costs in terms of accessing foreign currency services and therefore induces currency substitution at lower levels of in?ation in the future. The combination of consumer heterogeneity and ?xed costs in exchange point construction generate in?ation regions with di?erent intensities in terms of investment in new exchange points. Particularly, starting from a state in which there are no exchange points in the economy, an episode of high in?ation will push the ?nancial sector into action in terms of expanding the economy’s dollarization capital, by installing one exchange point which will be more closely located to one consumer than to the other. For a su?ciently high in?ation rate, both consumers will be willing to walk to the exchange point, therefore eliminating any incentive of the ?nancial sector to invest in a second exchange point. If in subsequent periods in?ation declines to a level that is low enough to discourage the more distant consumer from walking to the exchange point, the ?nancial sector will have an incentive to invest in a second money exchange point. This decision will locate both consumers at the same distance from an exchange point, eliminating heterogeneity in terms of access to ?nancial services, and lowering the in?ation threshold at which the second consumer is willing to substitute foreign for domestic currency. Thus, the model presented here is able to generate an equilibrium in which the relationship between in?ation and currency substitution is path dependent and di?ers before and after periods of high in?ation. From a theoretical point of view, the work presented here constitutes a step 88
along the lines of Guidotti and Rodrigues (1992), Uribe (1997) and Reding and Morales (2004) in terms explaining non-linearities in the relationship between in?ation and currency substitution. Guidotti and Rodrigues (1992) present a model in which agents may choose the currency in which purchases are denominated, but they must pay a cost every time they decide to switch the currency denomination of their transactions. Switching is optimal when the in?ation rate is su?ciently high; when in?ation drops back to a low level, inaction becomes optimal, generating a low-in?ation - high-currency-substitution equilibrium. Uribe (1997) remarks that Guidotti and Rodriguez (1992) ignores the possibility that hysteresis in currency substitution is likely to involve network e?ects. Therefore, he develops a model in which the economy’s accumulated experience in using a foreign currency as a means of payment reduces the cost of buying goods with foreign currency. Chapter 3 of this dissertation studies a model similar to Uribe’s but solved computationally. Uribe models this accumulated experience in using a foreign currency as a dollarization capital variable that is strictly increasing in the degree of dollarization of the economy. Reding and Morales (2004) depart from Uribe’s approach by not relying on a dollarization capital variable with exogenous dynamics, but rather trying to model explicitly the network e?ects related to the use of foreign currency. They assume agents are heterogeneous with respect to the transaction cost they face when they wish to use foreign currency as a means of payment. In turn, this cost is decreasing in the size of a foreign currency network, comprised of all agents whose balances in dollars are higher than an exogenous threshold. 89
The framework presented here can be seen as an e?ort to provide a micro foundation for the emergence and functioning of such a foreign currency network. This is done by considering an aspect not studied in the papers described so far: the role of the ?nancial sector in developing the economy’s dollarization capital. When thinking about the experience of several partially dollarized developing countries, it seems that the emergence of a network of foreign currency users is highly a?ected by the decision of the ?nancial sector to provide services in foreign currency. As mentioned earlier, this is very likely to be associated with di?erent types of investment costs (some of them ?xed). In the model presented here, a network of foreign currency users emerges only after the ?nancial sector has made the proper sunk investment. In this context, and in contrast to Uribe (1997), the economy’s dollarization capital corresponds to actual physical capital (the number of available exchange points), and, in contrast to Reding and Morales (2004), the currency substitution network is not composed of agents that have foreign currency holdings above some exogenous level, but by the ?nancial sector and those agents that have access to money exchange services. Further, whether an agent has access to ?nancial sector services or not depends on the consumer’s endogenous in?ation threshold for currency substitution and on the ?nancial sector’s endogenous optimal investment decision. Network expansion e?ects, then, are the result of interactions between optimal decisions on the consumer side and on the ?nancial sector side. Consumers de?ne their substitution behavior based on the level of in?ation and the availability 90
of exchange points (the level of dollarization capital), and do not internalize the impact that their demand for currency exchange services may have on the ?nancial sector’s decision to expand the number of exchange points. The ?nancial sector makes its optimal investment decision based on the potential demand that it would face if consumers had access to the proper level of dollarization capital (the pro?t maximizing number of exchange points). The rest of this chapter is organized as follows. The second section presents a simple three agent model used to study the consumer’s optimal currency substitution behavior and the ?nancial sector’s optimal dollarization capital investment decision. The third section concludes.
4.2
4.2.1
A simple three-agent model
The environment
The world consists of a local economy given by a horizontal space of measure one, as depicted in the top panel of Figure 4.1, and an external economy (the rest of the world). Prices in the local economy are not necessarily the same as those of the rest of the world. There are three agents in the local economy: a ?nancial sector that provides only one service, money exchange, and two consumers that start each period located on positions one and two. If these consumers want to acquire foreign currency they need to walk to the closest money exchange point constructed by the ?nancial sector. There can be at most two exchange points, and these can only be
91
located in positions A and B. Figure 4.1: MODEL ENVIRONMENT
4.2.2
Consumer’s problem
Each period consumers derive utility from consumption and disutility from walked distance. Preferences then are given by u(c) ? v (D) Where u(·) and v (·) are strictly increasing Bernoulli utility functions, c is 92
consumption and D is walked distance. The consumer’s problem is an intratemporal one, so time subscripts are ignored for simplicity. Each period starts with an initial price level (PI ) and ?nishes with a ?nal price level (PF ). At the beginning of each period, each consumer receives a real endowment y . As mentioned above, consumers receive utility from consumption and it is assumed that they need domestic money to buy the consumption good. That is, consumers cannot directly change their endowment y for consumption, but need money in order to perform the transaction. Therefore, after receiving their real endowment, consumers change it for nominal balances; at the end of the period, these balances are used to buy the consumption good. For simplicity, it is assumed that there is no savings technology; therefore, at the end of each period all currency balances must be exchanged for the consumption good. Then, the consumer’s problem consists solely of choosing the currency denomination of the nominal balances that she holds within the period. The sequence of actions is clari?ed by the graph presented in the second panel of Figure 4.1. The consumer starts the period with a real endowment y , which is immediately exchanged for domestic money at the initial price level. If the consumer has access to the money exchange services provided by the ?nancial sector (that is, if there is a money exchange point located either at position A or B or both), the consumer decides whether to keep these domestic currency balances or change them for foreign currency. If she chooses not to substitute, then the consumer gets to the end of the period with the initial amount of domestic money holdings and uses them to ?nance consumption at the end of period price level. In this case the consumer’s 93
utility is given by u(c) ? v (0). If the consumer instead decides to hold foreign currency balances, she needs to walk to the closest available money exchange point (located at distance D = d or D = 2d). There she pays a real fee f in order to change her domestic currency balances for foreign ones that she holds until the end of the period, when these are once again changed for domestic money and used to ?nance consumption. In this case the consumer’s utility is u(c) ? v (D). Let ? be the set of positions where the ?nancial sector has built a money exchange point. Then, the consumers’ substitution decision can be analyzed under three case: no exchange points, ? = { }, one exchange point, ? = {A} or ? = {B }, and two exchange points, ? = {A, B }.
Case 1. No Exchange Points Available, ? = { } This is a trivial problem since none of the consumers has a choice on the denomination of her currency holdings. At the beginning of each period, each consumer receives the real endowment y , which she changes for money holdings MI = yPI , where PI is the beginning-ofperiod domestic price level. At the end of the period, these money holdings are used to ?nance real consumption c =
MI , PF
where PF is the end-of-period domestic price
PF PI
level. De?ne gross in?ation, 1 + ? =
. Then, real consumption in terms of the
yPI PF
original endowment will be given by c =
y the period is u( 1+ ) ? v (0). ?
=
y 1+?
and the consumer’s utility in
94
Case 2 One exchange point available, ? = {A} or ? = {B } Consider the case in which there is a money exchange point available at point A. Let’s start by considering agent one, who is closest to A. After exchanging its real endowment y for money balances MI = yPI , the agent must decide whether to substitute MI for foreign currency or not. As derived in Case 1, if she decides not
y to substitute her utility will be u( 1+ ) ? v (0). ?
If she wants to substitute MI for foreign currency, she ?rst needs to walk to the exchange point, deriving disutility v (d), and then pay a real fee ?y , ? ? (0, 1), before
?1 obtaining M ? = SI (M ? ?yPI ), where SI = PI ? PI
is the initial nominal exchange
rate and PI? is the begeining-of-period foreign price level. Then, foreign currency holdings are given by M ? = (1 ? ? )yPI? . At the end of the period M ? is changed for domestic currency at the end-of-period exchange rate and real consumption is c=
M ? SF PF
=
(1?? )y , 1+? ?
?? )y where the consumer’s utility is u( (1 ) ? v (d). 1+? ?
Let s? 1 be a variable that indicates whether the consumer substitutes or not: ? ? ? ? 1 if consumer 1 substitutes s1 = ? ? ? ? 0 otherwise Then, consumer 1’s currency substitution problem is
U = max[U subst , U no subst ]
s1
(4.1)
U subst = u( U no subst
(1 ? ? )y ) ? v (d) 1 + ?? y ) ? v (0) = u( 1+?
Consumer 2’s problem is analogous, but with a lower utility payo? when sub95
stituting local for domestic currency balances:
U = max[U subst , U no subst ]
s2
(4.2)
U subst = u( U no subst
(1 ? ? )y ) ? v (2d) 1 + ?? y ) ? v (0) = u( 1+?
Then, in each period consumers one and two will substitute domestic for foreign currency holdings as long as
u( and
(1 ? ? )y y ) ? v (d) > u( ) ? v (0) ? 1+? 1+?
(4.3)
u(
(1 ? ? )y y ) ? v (2d) > u( ) ? v (0) ? 1+? 1+?
(4.4)
For a given level of foreign in?ation, ? ? , these two conditions implicitly de?ne two in?ation thresholds for currency substitution:
u(
(1 ? ? )y y ) ? v (d) > u( ) ? v (0) ? 1 + ?1 1+?
(4.5)
u(
(1 ? ? )y y ) ? v (2d) > u( ) ? v (0) ? 1 + ?2 1+?
(4.6)
For simplicity, consider the case of linear utility u(c) = c, v (D) = D. Then the substitution thresholds for in?ation are
96
?1 >
y (1 + ? ? ) ?1 (1 ? ? )y ? d(1 + ? ? )
(4.7)
?2 >
y (1 + ? ? ) ?1 (1 ? ? )y ? 2d(1 + ? ? )
(4.8)
As expected, the in?ation threshold increases with the cost of accessing the money exchange services provided by the ?nancial sector, and therefore agent two, who has a longer distance to walk to the nearest money exchange point, has a greater threshold than that of agent one.
Case 3. Two exchange points available, ? = {A, B } In this case both consumers are at distance d from the nearest money exchange point, and therefore they face the same problem as consumer one in the ? = {A, B } case, with both consumers willing to substitute foreign for domestic currency when ? >= ?1 . Figure 4.2 shows the relationship between in?ation and currency substitution in the three cases ? = { }, ? = {A} or ? = {B }, and ? = {A, B }. De?ne the economy’s end of period currency substitution ratio (CSR) as the ratio between foreign currency holdings evaluated at SF and total money holdings before consumption. When there are no exchange points available, this ratio is zero for every level of in?ation. When there is one exchange point available, only one consumer substitutes domestic for foreign currency when in?ation is greater than ?1 but smaller than ?2 . Then, before consumption, this consumer holds SF M ? money
97
holdings, while the other one holds MI . Therefore, the currency substitution ratio is given by
SF M ? . SF M ? +MI
When in?ation is above ?2 , both consumers hold SF M ? , so the
2SF M ? 2SF M ?
economy’s currency substitution ratio is
= 1. ?1 and ?2 correspond to levels
of in?ation at which either one or both consumers are indi?erent between holding domestic or foreign currency and therefore also admit any convex combination of these two options. For simplicity, from now on the possibility of a convex combination between the two currencies is ruled out by assuming that consumers fully switch to the foreign currency as soon as in?ation hits an indi?erence threshold. Finally, when two money exchange points are available both consumers have the same in?ation threshold and substitute domestic for foreign currency every time that ? ? ?1 .
4.2.3
The ?nancial sector’s investment problem
Each period, the ?nancial sector’s problem consists in deciding whether to install new exchange points or not. The maximum of installed exchange points is two and each one has a real cost of installation of F ? (0, ?y ). Every time that a consumer approaches a money exchange point, the ?nancial sector charges a real fee of ?y . It is assumed that once that an exchange point has been installed, it does not depreciate. Therefore, when no exchange point is available, ? = { }, the ?nancial sector decides between not investing in any exchange points, installing one exchange point at cost F , and installing two exchange points paying a cost of 2F . When there is only one exchange point available to consumers, ? = {A} or ? = {B }, the ?nancial
98
Figure 4.2: CURRENCY SUBSTITUTION AND INFLATION
sector’s problem consists of choosing whether not to invest in a new exchange point or installing it at cost F . Finally, when ? = {A, B } the ?nancial sector has no 99
investment decision. The ?nancial sector makes its investment decision before the consumers’ currency substitution decision. Then, this corresponds to a sequential game in which the ?nancial sector moves ?rst, deciding on the number of installed exchange points. This in turn is observed by the consumers, who make their currency substitution decision taking into account the availability of money exchange services. It is easier to start by considering a one-round game in which the ?nancial sector makes its investment decision, and the game ends with the consumers’ currency substitution choice after observing the behavior of the ?nancial sector.
A one period investment problem Case 1. Initial state: no exchange points available ? = { } The ?rm designs its investment strategy by anticipating the consumers’ behavior under di?erent levels of in?ation. If in?ation is below ?1 , none of the consumers requires money exchange services and the ?nancial sector pro?ts are ? = 0 when it decides not to set up any new exchange points, ? = ?F when it installs one new exchange point, and ? = ?2F when it installs two new exchange points. Its optimal decision then is not to install any exchange points. When ?1 ? ? < ?2 , only one consumer holds foreign currency when ? = {A} or ? = {B } and both consumers hold foreign currency balances when ? = {A, B }. Then, the ?nancial sector makes pro?ts ? = 0 when it decides not to set up any new exchange points, ? = ?y ? F when it installs one exchange point, and ? = 2(?y ? F ) when it installs two new exchange points. Its optimal decision then is to install two 100
exchange points. When ? ? ?2 , both consumers hold foreign currency as long as there is at least one money exchange point available. Then, the ?nancial sector pro?ts are ? = 0 when no new exchange points are installed, ? = 2?y ? F when one new exchange point is installed, and ? = 2(?y ? F ) when two ne exchange points are installed. Then, the ?nancial sector’s optimal decision is to install only one new exchange point.
Case 2. Initial state: one exchange point available ? = {A} or ? = {B } As in the previous case, when ? < ?1 the ?nancial sector’s optimal decision is not to install the new money exchange point. When ?1 ? ? < ?2 , the ?nancial sector makes pro?ts ? = ?y when it doesn’t install the new exchange point, and ? = 2?y ? F when it decides to install it. Its optimal decision then is to install the new money exchange point. When ? ? ?2 , both consumers hold foreign currency as long as there is at least one money exchange point available. Therefore, the ?nancial sector makes ? = 2?y when the new exchange point is not installed, and ? = 2?y ? F when it is installed. Then, the ?nancial sector’s optimal decision is not to install the new exchange point. Figure 4.3 depicts the relationship between the in?ation rate and the number of existing and new money exchange points.
In?ation, availability of exchange points and currency substitution Suppose that in?ation follows a stochastic process such that p(? = ? ) is the probability
101
Figure 4.3: EXCHANGE POINTS AND THE INFLATION RATE
of in?ation taking the value ? . Table 4.1 shows the probabilities governing the transition between exchange-technology states when each state is given by the number of available money exchange points. From the matrix it can be seen that, if the one period game solved above is played repeatedly, a su?ciently high number of realizations in which ? ? ?1 will lead the economy to a point in which both agents face the lowest possible cost in order to access the ?nancial sector services (that is, both agents are located at distance d from a money exchange point) and in which both agents have the same substitution threshold for in?ation (?1 ). Let no substitution, CSR = 0, partial substitution, CSR =
SF M ? SF M ? +MI
, and
complete substitution, CSR = 1 , denote the three possible currency substitution
102
outcomes of the model. Table 4.2 shows the probability of each outcome under the di?erent states given by the number of installed money exchange points. When the dollarization capital is at its maximum, ? = {A, B }, the economy does not display any partial substitution, and currency holdings are either completely denominated in domestic currency (with probability P (? < ?1 )) or fully dollarized (with probability P (? ? ?2 )). Table 4.1: In?ation Probabilities and the State of Exchange Points
Table 4.2: In?ation Probabilities and Currency Substitution
103
A forward-looking ?nancial sector Solving the ?nancial sector’s investment problem when it takes into account that consumers live in?nitely and repeat their currency substitution problem each period is cumbersome and the di?erent equilibria depend on the stream of in?ation realizations. For simplicity here I present two cases, one when in?ation is between ?1 and ?2 in every period and one when in?ation is above ?2 in very period.
Case 1. ?t = ? h ? ?2 for every t Suppose the economy starts with ? = { }. In period 1, the ?nancial sector has three options: invest in one new exchange point, invest in two new exchange points, and not to invest. If the ?nancial sector invests in two new exchange points at t = 1, then it makes ? = 2(?y ? F ) in the ?rst period and ? = 2?y in every period after that. So the present discounted value of the ?nancial sector pro?t stream is
1 1??
2?y ? 2F ,
where ? ? (0, 1) is the ?nancial sector’s time discount factor. This value is greater than that obtained when the ?nancial sector decides not to invest at t = 1 and instead installs both exchange points in the second period,
? 1??
2?y ? ? 2F , and
greater than that obtained when no investment is made in t = {1, 2} and both exchange points are installed in the third period,
?2 1??
2?y ? ? 2 2F and so on.
If the ?nancial sector invests in only one exchange point at t=1, then it makes ? = 2?y ? F in the ?rst period and ? = 2?y every period after that, so the present discounted value of its pro?t stream is
1 1??
2?y ? F , greater than those
? 1??
obtained if the investment is made in period two,
?2 1??
2?y ? ?F , or in period 3,
2?y ? ? 2 F , and so on. 104
The ?nancial sector could also invest in the ?rst exchange point at period t = 1, and in the second one at t = 2, making present discounted pro?ts equal to
1 1??
2?y ? F ? ?F . However, postponing investing in the second exchange point
1 1??
for one period delivers a higher pro?t present discounted value,
2?y ? F ? ? 2 F .
Postponing investing in the second exchange point for two periods yields an even higher present discounted value,
1 1??
2?y ? 2F , and so on. Since in?ation is above
?2 in every period, both consumers are willing to substitute and demand money exchange services from the ?nancial sector who each period receives real fees of 2?y . This income stream is not changed by the installation of the second exchange point, so it not optimal to incur additional investment costs. After considering all possible options, the ?nancial sector’s optimal investment decision when the in?ation path is {? h , ? h , ? h , ...} is to install only one exchange point at t = 1.
Case 2. ?t = ? m , ?1 < ? m ? ?2 for every t When the ?nancial sector invests in two new exchange points at t = 1, it makes discounted pro?ts
1 1??
2?y ? 2F ,
greater than those obtained if the two exchange points are simultaneously installed at any future period. If the ?nancial sector invests in only one exchange point and does so at t = 1, the present discounted value of pro?ts is
1 1??
?y ? F , greater than
that obtained if only one exchange point is installed in any period in the future. If the ?nancial sector invests in one exchange point in period t = 1 and in another in period t = 2, the present discounted value of pro?ts is ?y +
? 1??
2?y ?
(1 + ? )F , greater than that obtained if the two exchange points are separately
105
installed at any two di?erent periods in the future. After considering all possible options, the ?nancial sector’s optimal investment decision when the in?ation path is {? m , ? m , ? m , ...} is to install two exchange points in the ?rst period.
An example of the path of in?ation and currency substitution over time After the analysis of the problems of the two consumers and the ?nancial sector it is easy to think about some possible cases in which the co-movement between currency substitution and in?ation will not be the same before and after a period of high in?ation. Think for example of a case in which before period T in?ation remains at ? l < ?1 , then it increases to ? h ? ?2 at t = T , and decreases to ? m ? [?1 , ?2 ) from t = T + 1 onwards. Assume also that there are no exchange points installed before t = T. Using the analysis described in the previous section, it can be shown that the ?nancial sector’s optimal investment decision when the in?ation path is {..., ?T ?1 = ? l , ?T = ? h , ?T +1 = ? m , ?T +2 = ? m , ...} is not to invest before t = T , invest in one exchange point at t = T and invest in the second one at t = T +1. The second panel of Figure 4.4 shows the time path of economy’s dollarization capital (the optimal number of available exchange points). The third panel of the ?gure depicts the time path of currency substitution associated with the given pattern of in?ation. Before t = T , the currency substitution ratio is zero in every period; at t = T , the ?nancial sector installs one exchange
106
Figure 4.4: PATHS OF INFLATION AND CURRENCY SUBSTITUTION
point and both consumers are willing to use its services, so all money balances in the economy are dollarized and the currency substitution ratio is 1. Finally, since a second exchange point is installed at t = T + 1, both consumers are at distance d from an exchange point, and an in?ation rate lower than ? h but greater or equal than ?1 is enough to guarantee that the currency substitution ratio remains at 1. The main message of the simple framework presented so far is that, in the 107
presence of ?xed costs associated with the investment decisions of the ?nancial sector, an episode of high in?ation may push the ?nancial sector into action in terms of expanding the economy’s dollarization capital, therefore reducing (maybe permanently) the foreign currency usage costs faced by consumers and decreasing the in?ation threshold at which households are willing to substitute domestic for foreign currency.
4.3
Conclusion
The framework presented here constitutes a step forward in developing a micro foundation for the presence of network e?ects and dollarization capital dynamics in models of currency substitution. The dollarization capital variable corresponds to physical capital used for the provision of money exchange services, and the network of foreign currency users is composed of the ?nancial sector and those consumers who have access to the ?nancial sector’s money exchange services. Whether a consumer belongs or not to the network depends on endogenously determined in?ation thresholds for currency substitution and on the endogenously determined optimal level of dollarization capital. The combination of ?xed costs associated with investment in money exchange services and consumer heterogeneity in terms of access to ?nancial services provides an environment in which the relationship between currency substitution and in?ation is not linear. Particularly, the model is able to deliver asymmetries in the relationship between in?ation and currency substitution before and after high in?a-
108
tion episodes. Starting from a level in which there are no exchange services available in the economy, a period of high in?ation followed by one of moderate in?ation will push the ?nancial sector to expand the economy’s dollarization capital, permanently reducing the consumer’s cost of using foreign currency and decreasing the in?ation thresholds at which they are willing to substitute foreign for domestic currency. A natural step for future research is to embed the mechanism explored here into a fully-speci?ed DSGE environment, providing a tool for a more comprehensive empirical analysis of the currency substitution phenomenon in Developing Countries and Transition Economies.
109
Appendix A
Appendix to Chapter 1
A.1
Calvo stickiness in regular prices
Optimal regular price and price aggregators When the regular price is sticky, ?rm j’s pricing decision problem is
?
p pr jt ,pjt ,fjt
max Et
s= t
?
? pr jt h
s?t
h h ?t+s/t {pp js h? (fjs , ss )
Psh pp js ch s +
?
ch s
? pr jt (1
+
pp js (1
? h)?
l
l
(fjs , sl s)
Psl pp js Psl ? pr jt Psl pp js Psl ? pr jt
? ?
?
cl s cl s}
?
+
1??
h
(fjs , sh s)
Psh ? pr jt
h
?
? h) 1 ? ? ch s
(fjs , sl s)
l
? mcjs Ps {h? +h 1??
h
(fjs , sh s) Psh ? pr jt
?
Psh pp js ch s
?
+ (1 ? h)?
l
(fjs , sl s)
cl s cl } A.1) s(
(fjs , sh s)
+ (1 ? h) 1 ? ?
(fjs , sl s)
Eliminating in?nite sums in the regular price optimality condition 110
? Rearranging the ?rst order condition for pr t :
? ? pr jt
(? ? 1)Et
t=s ?
hr ?s?t ?t+s/t h 1 ? ?h (fjs , sh js ) cjs
? + pr jt
(? ? 1)Et
t=s ?
lr ?s?t ?t+s/t (1 ? h) 1 ? ?l (fjs , sl js ) cjs
=
?Et
t=s ?
hr ?s?t ?t+s/t h 1 ? ?h (fjs , sh js ) cjs mcjs Ps
+ ?Et
t=s
lr ?s?t ?t+s/t (1 ? h) 1 ? ?l (fjs , sl js ) cjs mcjs Ps
(A.2)
The numerator and denominator terms in the right hand side of (A.2) have current and forward looking variables. Following Schmitt-Grohe and Uribe (2004b,2005) this expression can be rewritten in a recursive fashion by de?ning four auxiliary varib c d ables: xa t , xt , xt and xt .
Working with the four terms in (A.2) , de?ne
?
Pt x a t
=
? pr jt (?
? 1)Et
t=s
?
s? t
?t+s/t h 1 ? ?
h
(fjs , sh js )
? pr jt Psh
??
ch t
(A.3)
?
Pt x b t
=
? pr jt (?
? 1)Et
t=s
?
s? t
?t+s/t (1 ? h) 1 ? ?
l
(fjs , sl js )
? pr jt Psl
??
cl t
(A.4)
?
Pt x c t
= ?Et
t=s
?
s? t
?t+s/t h 1 ? ?
h
(fjs , sh js )
? pr jt Psh
??
ch t Ps mcs
(A.5)
?
Pt x d t
= ?Et
t=s
?
s?t
?t+s/t (1 ? h) 1 ? ?
l
(fjs , sl js )
? pr jt Psl
??
cl t Ps mcs
(A.6)
Where 111
• Pt x a t is the present discounted nominal marginal revenue of serving the HEC’s demand at regular prices until the next price change. • Pt x b t is the present discounted nominal marginal revenue of serving the LEC’s demand at regular prices until the next price change. • Pt x c t is the present discounted nominal marginal cost of serving the HEC’s demand at regular prices until the next price change. • Pt x d t is the present discounted nominal marginal cost of serving the LEC’s demand at regular prices until the next price change. After some algebra it can be shown that
xa t =
pr jt Pth
?? h h 1 ? ?h (fjt , sh jt ) ct (? ? 1)
? pr pr? Pt+1 a jt + Et ??t+1/t rt? x Pt pt+1 Pt t+1
(A.7)
xb t
=
pr jt Ptl
??
(1 ? h) 1 ? ?
h
(fjt , sh jt )
cl t (?
? pr pr? Pt+1 b jt ? 1) + Et ??t+1/t rt? x (A.8) Pt pt+1 Pt t+1
xc t =
pr jt Pth
?? h h 1 ? ?h (fjt , sh jt ) ct ?mct + Et ??t+1/t
Pt+1 c x Pt t+1
(A.9)
xd t
=
pr jt Ptl
?? l (1 ? h) 1 ? ?h (fjt , sh jt ) ct ?mct + Et ??t+1/t
Pt+1 d x Pt t+1
(A.10)
Then, (A.2) can be expressed as
d a b xc t + xt = xt + xt
(A.11)
112
Now the ?rst order condition for regular prices can be expressed in a recursive framework and the ?rm’s optimal pricing conditions are given by equations (2.18), (2.19) and (A.12) , and the expressions for Pth and Ptl are given by
d a b xc t + xt = x t + xt
(A.12)
p 1?? r? 1?? 1?? r + ? 1 ? ?h (f, sh Pth = ?h (f, sh + (1 ? ?) 1 ? ?h (f, sh t ) (pt?1 ) t )(pt ) t ) (pt )
1 1??
(A.13)
p 1?? 1?? r? 1?? r Ptl = ?l (f, sl + (1 ? ?) 1 ? ?l (f, sl + ? 1 ? ?l (f, sl t )(pt ) t ) (pt ) t ) (pt?1 )
1 1??
(A.14) where pr t is the average regular price across ?rms
1
pr t
=
0
pr t Ptl
dj
(A.15)
and can be expressed recursively as
r? r pr t = ?pt?1 + (1 ? ?)pt
Othe equilibrium conditions Since not all ?rms are able to set their price optimally every period, symmetry cannot be applied in the same fashion as in the ?exible price case, and several equations of the model need to be modi?ed.
113
The resource constraint and economy wide price equations are now expressed as
h l ez t hnt + (1 ? h)nt
hp h h h1 h = h?h (ft , sh t )cjt + h 1 ? ? (ft , st ) dt ct lp l l l1 l + (1 ? h)?l (ft , sl ct t )cjt + (1 ? h) 1 ? ? (ft , st ) dt (A.16)
Pt
hp l l lp h?h (ft , sh t )cjt + (1 ? h)? (ft , st )cjt p = pt ct h2 h 1 ? ?h (ft , sh t ) dt Pth + ct l2 (1 ? h) 1 ? ?l (ft , sl t ) dt Ptl + ct
(A.17)
where
hp h h h1 h l l lp l l l1 l ct = h?h (ft , sh t )cjt +h 1 ? ? (ft , st ) dt ct +(1?h)? (ft , st )cjt +(1?h) 1 ? ? (ft , st ) dt ct
The consumption aggregators are given by ?
? ? ?? 1
? ch t =
1
l And the sh t and st ?rst order conditions are
? cl t =
?
hp ? ? (f, sh t )ct ? h h2 ? [1 ? ?t (f, sh t )]dt h lp ? ?l (f, sl t )ct ? l l2 ? [1 ? ?t (f, sl t )]dt
? ?1
??1
(A.18)
1
? ? ?? 1
(A.19)
114
h v (1 ? nh t ? st ) =
? ??1 ?
hp h ? h ch t ?s (f, st ) c?h t
1
??1 ?
2 h ? dh t ct
??1 ?
u (ch t) (A.20)
h ?s (f, sh t)
pp chp 2 h ?h t ?h t ? dh u ( ch t ct t) Pth
l v (1 ? nl t ? st ) =
? ??1
lp l ? l cl t ?s (f, st ) c?l t
1
? ?1 ?
2 l ? dl t ct
? ?1 ?
u (ch t) (A.21)
l ? ?s (f, sl t)
pp chp l 2 l ?l t ?l t ? dl t ct u (ct ) l Pt
Where
1 dh t = 1 0 1 0 1 0 1 0 pr t h Pt pr t l Pt pr t h Pt pr t l Pt ??
dj
??
1 dl t =
dj
1??
2 dh t =
dj
1??
2 dl t =
dj
l2 l1 h2 1 And dh1, dh t , dt , dt and dt can be expressed recursively as
1 dh t
=?
1 h e?t
?? 1 dh t?1
+ (1 ? ?)
? pr t Pth
??
(A.22)
l1 dt
=?
1 l e?t
?? 1 dl t?1
+ (1 ? ?)
? pr t Ptl
??
(A.23)
2 dh t
=?
1 h e?t
1?? 2 dh t?1
+ (1 ? ?)
? pr t Pth
1??
(A.24)
115
2 dl t
=?
1 l e ?t
1?? 2 dl t?1
+ (1 ? ?)
? pr t Ptl
1??
(A.25)
In order to reduce the size of the state space, the model is solved around a
l2 l1 h2 1 zero-in?ation steady state, ignoring the evolution of dh t , dt , dt and dt .
In order to reduce the size of the state space, the model is solved around a
1 h2 l1 l2 zero-in?ation steady state, ignoring the evolution of dh t , dt , dt and dt .
A.2
Looking for f in the data
The James M. Kilts Center at the University of Chicago Booth School of Business has made available several datasets on weekly store-level transaction prices for over 100 stores operated by Dominick’s Finer Foods (DFF) for the 1989 – 1997 period. The customer count ?le includes information about in-store tra?c. The data is store speci?c and on a daily basis. The customer count data refers to the number of customers visiting the store and purchasing something. Also in the customer count ?le is a total dollar sales and total coupons redeemed ?gure, by DFF de?ned department (product category). The ?gures are compiled daily from the register/scanner receipts.1 The average fraction of time at which a good is o?ered on coupon promotions is calculated through the following steps: 1. Aggregate the coupon redemption ?gure by store and by week (all stores with less than 52 time observations were dropped).
1
The data is available athttp://research.chicagobooth.edu/marketing/databases/dominicks/ccount.aspx
116
2. Construct the following dummy variable for each product category: ? ? ? ? ? ? 1 if coupon redemption = 0 ? ? dt = ? ? ? ? 0 if coupon redemption = 0 ? ?
Then, the underlying assumption is that if a promotion is available in a given
week, then there is at least one person that takes advantage of it (alternatively, at least one coupon is redeemed ). Therefore, it is assumed that if the coupon redemption ?gure in a given week is zero (dt = 0), then no coupons were o?ered that week. 3. Compute fk =
t
dt /(number of weeks), the fraction of time that good k
was o?ered on promotion. 4. Compute f =
k
fk /(number of good categories), the average fraction of
time at which goods are o?ered on promotion. If the underlying assumption in step 2 is wrong, then f is a lower bound for f. Table A1 shows the results for all the product categories for which coupons were o?ered at least once in the sample time range. Table A2 presents the mean value across products and stores. Table A.1: Fraction of Weeks by Department
Table A3 presents the mean value across products and stores when including all product categories. 117
Table A.2: Fraction of Weeks: Sample I
Table A.3: Fraction of Weeks: Sample II
A.3
The Firm’s Problem Under Perfect Price Discrimination (PPD)
For simplicity, here I present the case of ?exible prices. If the ?rm could distinguish between consumer types, its pro?t maximization problem would be:
P D l,P P D ph,P ,pjt jt
max
P D h,P P D P D l,P P D ?maxjt = hph,P cjt + (1 ? h)pl,P cjt jt jt PD PD ? mcjt Pt {hch,P + (1 ? h)cl,P } jt jt
(A.26)
subject to
PD ch,P jt
=
PD ph,P jt
?? PD ch,P t
Pth,P P D
(A.27)
118
PD cl,P = jt
PD pl,P jt
?? PD cl,P t
Ptl,P P D
(A.28)
PD where ck,P , k = h, l are quantities consumed by consumers under perfect jt PD price discrimination and pk,P , k = h, l are the prices charged by the ?rm. jt
Solving the problem, the ?rm’s optimal price choices are:
PD ph,P t = Pt
? ??1
mct
(A.29)
PD pl,P t = Pt
? ??1
mct
(A.30)
These same optimal prices can be recovered from the ?rms problem with price
l promotions with sh t = 1 and st = 0 when the ?rm chooses ft = 1. To see this,
consider the optimality conditions from the ?rm’s problem in the model with price promotions solved in Section 2.1.2 are:
hr l l lr h 1 ? ?h (fjt , sh t ) cjt + (1 ? h) 1 ? ? (fjt , st ) cjt =
1?
Pt mct pr jt
hr l l lr h[1 ? ?h (fjt , sh t )]?cjt + (1 ? h)[1 ? ? (fjt , st )]?cjt
(A.31)
hp l l lp h?h (fjt , sh t )cjt + (1 ? h)? (fjt , st )cjt =
1?
Pt mct pp jt
hp lp l l h?h (fjt , sh t )?cjt + (1 ? h)? (fjt , st )?cjt
(A.32)
119
pp jt ? mct Pt pr jt ? mct Pt
hp l lp l h (fjt , sh h?f t )cjt + (1 ? h)?f (fjt , st )cjt h hr l l lr h?f (fjt , sh t )cjt + (1 ? h)?f (fjt , st )cjt
= (A.33)
l when sh t = 1 and st = 0, these collapse to
lr h(1 ? fjt )chr jt + (1 ? h)cjt =
1?
Pt mct pr jt
lr h(1 ? fjt )?chr jt + (1 ? h)?cjt
(A.34)
chp jt =
1?
Pt mct ?chp jt pp jt
(A.35)
hp r hr pp jt ? mct Pt hfjt cjt = pjt ? mct Pt hfjt cjt p from (A.36) pr jt > pjt and rearranging (A.35)
(A.36)
pp t = Pt
? ??1
mct =
PD ph,P t Pt
(A.37)
Finally, when the ?rm sets ft = 1 and rearranging (A.34)
pr t = Pt
? ??1
PD pl,P t mct = Pt
(A.38)
120
A.4
Monetary Model with Price Promotions: Impulse Response Functions
Real output (% deviation from steady state value) Labor time (% deviations from steady state values) Prices (% deviations from steady state values)
0.00%
0.05%
1
-0.02%
6
11
16 21output 26 31 Real
36
41
46
51
0.00%
0.04%
(% deviation from steady state value)
Labor time (% deviations from steady state values) nh
0.03% 1 6 11 16 21 26 31 36 41 46 51
0.05%
Prices price discount (% deviations from steady state values) relativel regular price
-0.04% 0.00% -0.06% -0.02% -0.08% -0.04% 0.00% -0.10% 1 -0.06% -0.02% -0.12% -0.08% -0.04% -0.14% -0.10% -0.06% -0.16% -0.12% -0.08% -0.18% -0.14% -0.10% -0.16% -0.12% -0.18% -0.14% 0.0003 -0.16% -0.18% 0.0002 0.0003 6 11 1 6 11
(% deviation from steady state value)
Real output 16 21 26 31
36
41
46
51
-0.05%
0.00%
Labor time (% deviations from steady state values) h
0.04%
n N
6
relative promotional price average price response Prices price discount 0.02% (% deviations from steady state values) relativel regular price relative promotional price price discount average price response relativel regular price 1 6 11 16 21 26 relative 31 36 41 46 51 promotional price average price response
0.03% 11 16 21 26 31 36 41 46 51 0.01% 0.04% 0.02% 0.00% 0.03% 11 16 21 26 31 36 41 46 51 0.01% -0.01% 0.02%
-0.10% 0.05% 16 21 26 31 36 41 46 51 -0.05% -0.15% 0.00%
1
nh N
1 6
-0.10% -0.20% -0.05% -0.15% -0.25% -0.10% -0.20%
nl N nl
Time spent looking for price promotions (% deviations from steady state values)
0.00% -0.02% 1 0.01% -0.01%
6
11
16
21
26
31
36
41
46
51
Real interest rate
-0.15% -0.25% -0.20% 0.08%
nl
Size of the promotion-economy and fraction of time 0.00% 1at which 6 11goods 16 are 21 offered 26 31 on 36promotion 41 46 51 -0.02% (% deviations from steady state values)
-0.01%
Real interest rate
Time spent looking for price promotions sl -0.25% 0.06% (% deviations from steady state values)
0.04% 0.08%
-0.02% at which goods are offered on promotion -0.02%
Size of the and36 fraction of time 1 promotion-economy 6 11 16 21 26 31 41 46 51 (% deviations from steady state values)
0.00%
Real interest rate
0.0002
0.02% 0.06% 0.08% 0.00% 0.04% 0.06% -0.02% 0.02%
0.04% -0.04% 0.00%
Time spent looking for price promotions l (%sdeviations from steady state values)
S
-0.04% 0.00% Size of the promotion-economy and fraction of time 6 goods 11 16 21 26 31 36 41 46 51 at 1 which are offered on promotion ?t -0.06% -0.02%(% deviations from steady state values) 0.00% -0.08% -0.04%
-0.02% -0.10% -0.06%
0.0002 0.0003 0.0001
0.0002 0.0002
1
sl S
6
11
16
21
26
31
36
41
46
51
1
6
11
16
21
26
31
36
41
46
51
?t
0.0001 0.0001 0.0002 0.0000 0.0001 0.0001 1 6 11 16 21 26 31 36 41 46 51
1 0.02% -0.06% -0.02% 0.00% -0.08% -0.04%
-0.02% -0.06%
6
sh
-0.04% -0.12% -0.08% 16 21 26 31 36 41 46 51 -0.06% -0.14% -0.10% -0.08% -0.16% -0.12%
-0.10% -0.14%
ft
?t
11
S
1 6
sh11
16
21
26
31
36
41
46
51
ft
0.0000 0.0001 1
6
11
16
Consumption
21 26
31
36
41
46
51
-0.04% -0.08% -0.06% 0.0016
sh
Real wage
-0.12% -0.16% -0.14% 0.00
ft
Real balances
0.0008 0.0000 1 0.0006 0.0004 0.0008 0.0002 0.0006 0.0000 0.0004 1 0.0008 -0.0002 0.0002 0.0006 -0.0004 0.0000 0.0004 -0.0006 -0.0002 0.0002 -0.0008 -0.0004 0.0000 -0.0010 1 -0.0006 -0.0002 -0.0008 -0.0004 -0.0010 -0.0006 -0.0008 -0.0010
6
11
Consumption 16 21 26 31
36
41
46
51
0.0014 -0.08% 0.0012 0.0016 0.0010 0.0014 0.0008
Real wage
HEC component of the reaL wage
1 -0.16% -0.20 0.00 -0.40 -0.20 -0.60 0.00 -0.40 1 -0.80 -0.20 -0.60 -1.00 -0.40 -0.80 -1.20 -0.60 -1.00 -1.40 41 46 51
-0.80 -1.20
6
11
16
Real balances
21
26
31
36
41
46
51
chp
chr
Consumption
al
1 6 11 16 21 26 31 Real balances 36 41 46 51
Real wage
HEC component of the reaL wage
chp
6 11 hr 16 c 21 26 31 36 41 46 51
0.0012 0.0016 0.0006 0.0010 0.0014 0.0004
w
HEC component of the reaL wage
al
6 11 16 21 26 31 36 41 46 51
ah al ah
chp
1 6
clr
11 chr16 21 26 31 36 41 46 51
0.0008 0.0012 0.0002
0.0006 0.0010 0.0000
clp
w
6 11 16 21 26 31 36 41 46 51 LEC component of the reaL wage
clr
6 11 16 21 26 31 36 41 46 51
0.0004 1 0.0008 -0.0002 0.0002 0.0006 -0.0004 0.0000 0.0004 1
w
6 11 16 21 26 31 36
clp clr clp
ah
-0.0002 0.0002 -0.0004 0.0000 1 -0.0002 -0.0004
LEC component of the reaL wage -1.00 -1.40 6 11 16 21 26 31 36 41 46 51 -1.20
LEC component of the reaL wage -1.40
121
Appendix B
Appendix to Chapter 2
ÔÔ Ò Ü ½ Ë È È Ê
Table B.1: Data Series Used in the Document
ËÖ × ÆÓÑ Ò Ð È ÆÓÑ Ò Ð È ÈÖ Ú Ø ÓÒ×ÙÑÔØ ÓÒ ÈÖ Ú Ø ÓÒ×ÙÑÔØ ÓÒ ÓÖ Ò ÙÖÖ Ò Ý ÔÓ× Ø× ÓÖ Ò ÙÖÖ Ò Ý ÔÓ× Ø× ÜØ ÖÒ Ð ÈÓ× Ø ÓÒ× Ó ÁË Ê ÔÓÖØ Ò ÜØ ÖÒ Ð ÈÓ× Ø ÓÒ× Ó ÁË Ê ÔÓÖØ Ò ÅÓÒ Ý Ö Ø× ÅÓÒ Ý Ö Ø× ÓÒ×ÙÑ Ö ÈÖ ÁÒ Ü ÓÒ×ÙÑ Ö ÈÖ ÁÒ Ü ÓÙÒØÖÝ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ÓÐ Ú È ÖÙ ËÓÙÖ ÆÁË Ê È ÆÁË ÁÅ ¹Á Ë Ê È ÁË ÁË Ê È Ê È ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ Ø ËÔ Ò ¼¹¾¼¼ ¹¾¼¼ ¼¹¾¼¼ ¹¾¼¼ ¼¹¾¼¼ ¹¾¼¼ ¼¹¾¼¼ ¹¾¼¼ ¼¹¾¼¼ ¹¾¼¼ ¹¾¼¼ ¹¾¼¼
Ò × ´Ð Ò × ´Ð
Ð Ø ×µ Ð Ø ×µ
ÆÁË ÓÐ Ú Ò Æ Ø ÓÒ Ð ÁÒ×Ø ØÙØ Ó ËØ Ø ×Ø × ÁË Ò Ó ÁÒØ ÖÒ Ø ÓÒ Ð Ë ØØÐ Ñ ÒØ× ÒØÖ Ð Ò Ó ÓÐ Ú Ê È ÒØÖ Ð Ê × ÖÚ Ò Ó È ÖÙ ÁÅ ¹Á Ë ÁÒØ ÖÒ Ø ÓÒ Ð ÅÓÒ Ø ÖÝ ÙÒ ¸ ÁÒØ ÖÒ Ø ÓÒ Ð Ò Ò Ð ËØ Ø ×Ø ×
122
ÔÔ Ò Ü ¾ Ë È È Ê
Table B.2: Money Aggregates
Ž
ÓÐ Ú
Ž³ ž ž³ Å¿ Å¿³
È ÖÙ
ÙÖÖ Ò Ý Ò Ö ÙÐ Ø ÓÒ ÔÐÙ× × Ø ÔÓ× Ø× ÒÓÑ Ò Ø Ò Ò Ø ÓÒ Ð ÙÖÖ Ò Ý Å½ ÔÐÙ× × Ø ÔÓ× Ø× ÒÓÑ Ò Ø Ò ÓÖ Ò ÙÖÖ Ò Ý ÔÓ× Ø× Å½ ÔÐÙ× × Ú Ò ÔÓ× Ø× ÒÓÑ Ò Ø Ò Ò Ø ÓÒ Ð ÙÖÖ Ò Ý Å½³ ÔÐÙ× × Ú Ò ÔÓ× Ø× ÒÓÑ Ò Ø Ò ÓÖ Ò ÙÖÖ Ò Ý Å¾ ÔÐÙ× Ø Ñ ÔÓ× Ø× Ò ÓØ Ö ×× Ø× ÒÓÑ Ò Ø Ò Ò Ø ÓÒ Ð ÙÖÖ Ò Ý Å¾³ ÔÐÙ× Ø Ñ ÔÓ× Ø× Ò ÓØ Ö ×× Ø× ÒÓÑ Ò Ø Ò ÓÖ Ò ÙÖÖ Ò Ý ÙÖÖ Ò Ý Ò Ö ÙÐ Ø ÓÒ ÔÐÙ× × Ø ÔÓ× Ø× ÒÓÑ Ò Ø Ò Ò Ø ÓÒ Ð ÙÖÖ Ò Ý Ë ÚÒ Ò ØÑ ÔÓ× Ø× Ò ÓØ Ö ×× Ø× ÒÓÑ Ò Ø Ò ÓÑ ×Ø ÙÖÖ Ò Ý Ë ÚÒ Ò ØÑ ÔÓ× Ø× Ò ÓØ Ö ×× Ø× ÒÓÑ Ò Ø Ò ÓÖ Ò ÙÖÖ Ò Ý
ÅÓÒ Ý ÉÙ × ÑÓÒ Ý Ò ÓÑ ×Ø ÉÙ × ÑÓÒ Ý Ò ÓÖ ÙÖÖ Ò Ý
Ò ÙÖÖ Ò Ý
ÔÔ Ò Ü ¿ Ë È È Ê
ÓÐ Ú
ÈÖ ¹ ÝÔ Ö Ò Ø ÓÒ ÀÝÔ Ö Ò Ø ÓÒ ÈÓ×ع ÝÔ Ö Ò Ø ÓÒ
Table B.3: In?ation Periods
Ö×
½ ¼¹½ ½ ½ ¾¹½ ½ ¹¾¼¼
ÒÒÙ Ð Ò Ø ÓÒ ´Ô Ö Ó Ú Ö µ
¾ ¸ ± ¾ ¿± ½½¸¿±
È ÖÙ
ÈÖ ÝÔ Ö Ò Ø ÓÒ ÀÝÔ Ö Ò Ø ÓÒ ÈÓ×Ø ÝÔ Ö Ò Ø ÓÒ
Ö×
½ ¹½ ½ ¹½ ½ ½ ¾¹¾¼¼
ÒÒÙ Ð Ò Ø ÓÒ ´Ô Ö Ó Ú Ö µ
¿¸ ± ¼ ± ½ ¸ ±
123
BIBLIOGRAPHY
[1] Albrecht, J., F. Postel-Vinay and S. Vroman (2010). ”A Search-Theoretic Model of Sales”.
[2] Altig, D., L. Christiano, M. Eichenbaum and J. Linde, 2005. ”Firm-Speci?c Capital, Nominal Rigidities and the Business Cycle”, NBER Working Paper No. 11034.
[3] Arseneau, D. and S. Chugh (2007). ”Bargaining, Fairness, and Price Rigidity in a DSGE Environment”.
[4] Aruoba, B. and F. Schorfheide (2009). ”Sticky Prices Versus Monetary Frictions: An Estimation of Policy Trade-o?s”, NBER Working Paper No. 14870.
[5] Aruoba, B. and F. Schorfheide (2011). ”Sticky Prices Versus Monetary Frictions: An Estimation of Policy Trade-o?s”, Forthcoming American Economic Journal: Macroeconomics
[6] Banks, J. and S. Moorthy (1999). ”A Model of Price Promotions With Consumer Search”, International Journal of Industrial Organization 17, 371-398. 124
[7] Bernard, A., J. Eaton, J. Bradford Jensen, and S. Kortum (2003). ”Plants and Productivity in International Trade”, American Economic Review, Vol. 93 No. 4.
[8] Bilbiie, F., F. Ghironi, and M. Melitz (2007). ”Monetary Policy and Business Cycles with Endogenous Entry and Product Variety”, NBER Working Paper No. 13199.
[9] Bils, M. and P. J. Klenow (2004). ”Some Evidence on the Importance of Sticky Prices”, Journal of Political Economy 112, 947-985.
[10] Cavallo, A. (2010). ”Scraped Data and Sticky Prices: Frequency, Hazards and Synchronization”, Harvard Job Market Paper.
[11] Chevalier, J. A., A. K. Kashyap and P. E. Rossi (2003). ”Why Don’t Prices Rise During Periods of Peak Demand? Evidence from Scanner Data”, The American Economic review. Vol. 93, No. 1, pp. 15-37.
[12] Cooley, T. and G. Hansen (1989). ”The In?ation Tax in a Real Business Cycle Model,” American Economic Review, vol. 79(4), pages 733-48, September.
[13] Cooley, T. and G. Hansen (1995). ”Money and the Business Cycle”, in Frontiers of Business Cycle Research, Thomas F. Cooley editor., Princeton University Press, pp. 175-216.
125
[14] Dhyne, E., L. J. lvarez, H. Le Bihan, G. Veronese, D. Dias, J. Ho?mann, N. Jonker, P. Lnnemann, F. Rumler and J. Vilmunen (2006). ”Price Changes in the Euro Area and the United States: Some Facts from Individual Consumer Price Data”, The Journal of Economic Perspectives, Vol. 20, No. 2, pp. 171-192.
[15] Eichenbaum, M., N. Jaimovich and S. Rebelo (2011). ”Reference Prices and Nominal Rigidities”, American Economic Review, vol. 101, issue 1, pp. 234262.
[16] Feige, E. (2003). “The Dynamics of Currency Substitution, Asset Substitution and De facto Dollarization and Euroization in Transition Countries”, Comparative Economic Studies 45, 358-383.
[17] Golosov, M. and R. Lucas Jr. (2007). ”Menu Costs and Phillips Curves,” Journal of Political Economy, University of Chicago Press, vol. 115, pages 171-199.
[18] Green, E. (2005). ”A Review of Interest and Prices: Foundations of a Theory of Monetary Policy by Michael Woodford”, Journal of Economic Literature Vol. XLIII, pp. 121-134.
[19] Guidotti, P. E., Rodriguez, C. A. (1992). ”Dollarization in Latin America Gresham law in reverse”, International Monetary Fund Sta? Papers, 39, 518544
[20] Guimaraes, B. and K. Sheedy (2008). ”Sales and Monetary Policy”, CEPR
126
discussion paper #6940.
[21] Guimaraes, B. and K. Sheedy (2011). ”Sales and Monetary Policy”, American Economic Review vol. 101(2), pp. 844-76.
[22] Hall, Robert E. (2007). ”Equilibrium Sticky Prices”.
[23] Hansen, G. (1985). ”Indivisible Labor and the Business Cycle”, Journal of Monetary Economics 16, 309-328.
Havrylyshyn, O. and Beddies, C.H. (2003). ”Dollarization in the former Soviet Union: From hysteria to hysteresis”. Comparative Economic Studies, 45, 329357.
[24] Hosken, D. and D. Rei?en (2004). ”How Retailers Determine Which Products Should Go on Sale: Evidence From Store-Level Data”, Journal of Consumer Policy, Vol. 27, No. 2, pp. 141-177.
[25] Kehoe, P. J. and V. Midrigan (2007). ”Sales and the Real E?ects of Monetary Policy”, Federal Reserve Bank of Minneapolis Working Paper 652.
[26] Kehoe, P. J. and V. Midrigan (2008). ”Temporary Price Deviations and the Real E?ects of Monetary Policy”, Federal Reserve Bank of Minneapolis Working Paper 661.
127
[27] Kehoe, P. J. and V. Midrigan (2010). ”Prices Are Sticky After All”, Federal Reserve Bank of Minneapolis Research Department Sta? Report 413.
[28] Klenow, P. and B. Malin (2010). ”Microeconomic Evidence on Price Setting”. Prepared for the Handbook of Monetary Economics (Benjamin Friedman and Michael Woodford, editors).
[29] Klenow, P. and J. Willis (2007). ”Sticky Information and Sticky Prices”, Journal of Monetary Economics 54, pp. 79-99.
[30] Klenow, P. and O. Kryvtsov (2008). ”State-Dependent or Time-Dependent Pricing: Does It Matter for Recent U.S. In?ation?”, The Quarterly Journal of Economics, MIT Press, vol. 123(3), pages 863-904, August.
[31] Kleshchelski, I. and N. Vincent (2007). ”Market Share and Price Rigidity”.
[32] Levin, A. and T. Yun (2008). ”Reconsidering the Microeconomic Foundations of Price-Setting Behavior”.
[33] Lu, Quiand and Sridhar Moorthy (2007). ”Coupons Versus Rebates”, Marketing Science Vol. 26, No. 1, pp. 67-82.
[34] Mackowiak, B. and F. Smets (2008). ”On Implications of Micro Price Data for Macro Models”, ECB Working Paper No. 960.
128
[35] Mendoza, E. (1991). “Real Business Cycles in a Small Open Economy”, The American Economic Review, Vol. 81, No. 4 797-818.
[36] Mendoza, E. and M. Uribe (1997). ”The Syndrome of Exchange-Rate-Based Stabilizations and the Uncertain Duration of Currency Pegs”, Federal Reserve Bank of Minneapolis, Institute for Empirical Macroeconomics Discussion Paper 121.
[37] Mendoza, E. and M. Uribe (1999). “The Business Cycles of Balance of Payment Crises: A Revision of a Mundellian Framework”, NBER WP 7045.
[38] Mendoza, E. and M. Uribe (2000). “Devaluation Risk and Business-Cycle Implications of Exchange-Rate Management”, Carnegie-Rochester Conference Series on Public Policy 55, 239-296.
[39] Midrigan, V. (2008), ”Menu Costs, Multi-Product Firms and Aggregate Fluctuations”.
[40] Nakamura, E. (2008). ”Pass-Through in Retail and Wholesale”, American Economic Review: Papers and Proceedings 98:2, pp. 430-437.
[41] Nakamura, E. and J. Steinsson (2008). ”Five Facts About Prices: A Reevaluation of Menu Cost Models”, Quarterly Journal of Economics, 123(4), 1415-1464.
[42] Nakamura, E. and J. Steinsson (2009). ”Price Setting in Forward-Looking Customer Markets”. 129
[43] Nelson, P., J. J. Siegfried and J. Howell. ”A Simulatneous Equations Model of Co?ee Brand Pricing and Advertising”, Review of Economics and Statistics, Vol. 74, No. 1, pp. 54-63.
[44] Reding, P. and J. A. Morales (2004). “Currency Substitution and Network Externalities”, University of Namur, mimeo.
[45] Rojas-Suarez, L. (1992). “Currency Substitution and In?ation in Peru”, Revista de Analisis Economico, Vol. 7, No. 1, 153-176.
[46] Reinhart, C. and C. Vegh (1995), “Nominal Interest Rates, Consumption Booms and Lack of Credibility: A Quantitative Examination”, Journal of Development Economics 46, 357-378.
[47] Savastano, M. (1996). ”Dollarization in Latin America: Recent Evidence and Some Policy Issues.” In The Macroeconomics of International Currencies, Paul Mizen and Eric Pentecost editors. Edward Elgar Publishing.
[48] Schmitt-Grohe, S. and M. Uribe (2004a). ”Solving Dynamic General Equilibrium Models Using a Second-order Approximation to the Policy Function,” Journal of Economic Dynamics and Control, vol. 28(4), pages 755-775, January.
[49] Schmitt-Grohe, S. and M. Uribe (2004b). ”Optimal Simple and Implementable Monetary and Fiscal Rules”. NBER Working Paper No. 10253.
130
[50] Schmitt-Grohe, S. and M. Uribe (2005). ”Optimal Fiscal and Monetary Policy in a Medium-Scale Macroeconomic Model”, in NBER Macroeconomics Annual 2005 (Mark Gertler and Kenneth Rogo?, edsitors) MIT Press. Cambridge MA, 2006, 383-425.
[51] Uribe, M. (1997), “Hysteresis in a Simple Model of Currency Substitution”, Journal of Monetary Economics 40, 185-202.
[52] Valev, N. (2007), ”The Hysteresis of Currency Substitution: Currency Risk vs Network Externalities”, Andrew Young School of Policy Studies Research Paper Series, Working Paper 07-23.
131
doc_489503664.pdf