Description
A workflow consists of a sequence of connected steps where each step follows without delay or gap and ends just before the subsequent step may begin. It is a depiction of a sequence of operations, declared as work of a person or group,[1] an organization of staff, or one or more simple or complex mechanisms
ABSTRACT
Title of Document:
ESSAYS ON JOB FLOWS DYNAMICS Fabiano Rodrigues Bastos, Ph.D., 2005
Directed By:
Professor John Haltiwanger, Department of Economics
Gross job flows dynamics, defined as the behavior of creation and destruction of jobs at the establishment level, has become a topic of great interest in economics during recent years and researchers have resorted to different empirical methodologies in order to tease out its causes and consequences, as well as its connections to overall economic activity. In this context, my dissertation attempts to contribute to the debate by advancing the usefulness of frequency-domain techniques. I emphasize not only the relevance of the economic questions being examined, but also the unique perspective that frequency-domain techniques can provide. There are three major questions I pursue. The first is why equilibrium search models of labor market frictions have trouble explaining the observed persistence in employment fluctuations. I implement a frequency-domain decomposition of the employment growth rate to isolate the contributions coming from the job creation spectrum, the job destruction spectrum, and the cross-spectrum between the two. Among other results, I show that the failure to generate a negative contemporaneous correlation between job creation and job destruction at business cycle frequencies is behind the
inability of the Mortensen-Pissarides (1994) canonical model to reproduce the empirical spectral shape of the employment growth series. The second question I
tackle relates to the direction of causality between aggregate employment fluctuations and gross job reallocation. Recent macroeconomic models suggest an active role for reallocation dynamics over the business cycle, and my results can be interpreted as supporting evidence that such a role indeed exists, but at a low frequency range. The basic idea is to look for different causality relationships at different time-scales by combining wavelet techniques with a standard Granger causality test. Finally, the third question I address investigates the connections between labor productivity growth and the frequency content of the job reallocation series for four-digit level US manufacturing industries. My results indicate that industries with relatively more influential low frequencies display inferior productivity growth. I relate these findings to the literature and propose a simple theoretical model to explain them.
ESSAYS ON JOB FLOWS DYNAMICS
By Fabiano Rodrigues Bastos
Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2005
Advisory Committee: Professor John Haltiwanger, Chair Associate Professor John Shea Associate Professor John Chao Associate Professor John Horowitz Assistant Professor Michael Pries
© Copyright by Fabiano Rodrigues Bastos 2005
Dedication
I dedicate this dissertation to my father Eduardo Marcos Chaves Bastos, my mother Almira Rodrigues, my wife Leatrisse Oba, and my daughter Ana Beatriz Oba Bastos.
ii
Acknowledgements
I would have never completed this dissertation in absence of the guidance and support I received throughout my academic journey. Professor John Haltiwanger, my main advisor, provided superb orientation and encouragement. By interacting with him I learned much more than economics. Inadvertently, he taught me the traits of a firstclass professional which are valid beyond academic walls. Professor John Shea has contributed enormously to my research through his astonishing ability to extricate “economic juice” from virtually any idea. Professor Mike Pries, a reliable source of advice permanently stationed at Tydings 4th floor, was essential for continuous progress.
From my former university in Brazil (UnB), I must mention the names of two professors who never let me settle for less: Joaquim Pinto de Andrade and Joao Ricardo Faria. Also from those times, Bernardo Borba de Andrade, a good friend who still patiently helps me with my statistical incursions.
Finally, my family deserves special credit for being supportive beyond the call of duty. In particular, my wife (Leatrisse) has demonstrated selfless allegiance to my academic pursuit; my daughter (Ana Beatriz) whose soothing smile reminded me what matters in life during this last stressful year; my mother (Almira) who has always been enthusiastic about my dreams despite the oppressive distance; and my father (Eduardo) who made my own happiness his highest priority until the last moment. iii
Table of Contents
Acknowledgements .....................................................................................................iii Table of Contents......................................................................................................... iv List of Tables ............................................................................................................... vi List of Figures ............................................................................................................. vii Chapter 1: Introduction ................................................................................................. 1 Chapter 2: Persistent employment fluctuations and the structure of search models: a frequency-domain perspective ...................................................................................... 3 2.1 Literature review and motivation........................................................................ 3 2.2 Mortensen-Pissarides model and employment dynamics ................................... 7 2.2.1 The environment .......................................................................................... 7 2.2.2 Basic features ............................................................................................... 9 2.3 Data and methodology ...................................................................................... 12 2.3.1 Data .............................................................................................................. 9 2.3.2 Spectral analysis........................................................................................... 9 2.3.3 Multivariate spectrum ................................................................................ 13 2.3.4 Univariate spectrum ................................................................................... 13 2.3.5 Cross spectrum .......................................................................................... 13 2.3.6 Estimation ................................................................................................. 13 2.4 Model and data spectra ..................................................................................... 20 2.4.1 Employment decomposition and comparisons among spectral densities .. 20 2.4.2 A canonical reduced-form model for levels and growth rates................... 24 2.5 Parameters and structure ................................................................................... 30 2.5.1 Can re-parameterization solve the problem? ............................................. 30 2.5.2 Spectral loss function: a new metric .......................................................... 34 2.5.3 Are there enough frictions in the Mortensen-Pissarides model ................. 37 2.6 Concluding remarks and future work ............................................................... 39 Chapter 3: Job reallocation dynamics and aggregate employment fluctuations in the US manufacturing: a Granger causality study across time-scales .............................. 41 3.1 Reallocation Intensity and Macroeconomics .................................................... 41 3.2 Empirical methodology..................................................................................... 44 3.2.1 Wavelets: an overview............................................................................... 44 3.2.2 Multi-scale decomposition......................................................................... 46 3.2.3 Granger causality tests across time-scales ................................................. 49 3.3 Reallocation and aggregate fluctuations: results............................................... 50 3.4 Extensions and concluding remarks.................................................................. 54 Chapter 4: Productivity growth and the frequency content of job reallocation: a crosssection study of US manufacturing industries. ........................................................... 56 4.1 Productivity growth and reallocation................................................................ 56 4.2 Measuring the importance of low frequencies.................................................. 58 4.2.1 Data ............................................................................................................ 58 4.2.2 Reallocation index one............................................................................... 59 iv
4.2.3 Reallocation index two .............................................................................. 62 4.2.4 Reallocation index three ............................................................................ 58 4.3 Empirical results ............................................................................................... 65 4.3.1 Productivity growth and the frequency content of reallocation................. 65 4.3.2 Synchronization: a further look into inefficiencies.................................... 68 4.4 Insigths from a simple theoretical model.......................................................... 71 4.4.1 The model .................................................................................................. 71 4.4.2 Dynamics ................................................................................................... 73 4.4.3 Simulation restuls....................................................................................... 77 4.5 Concluding remarks and extensions ................................................................. 82 Chapter 5: Concluding remarks ................................................................................. 84 Appendices.................................................................................................................. 85 Appendix I: Tables.............................................................................................. 85 Appendix II: Figures ........................................................................................... 91 Appendix III: Infrequent updating and spectral shape...................................... 106 Bibliography ............................................................................................................. 107
v
List of Tables
Table 2.1 Mortensen and Pissarides Model (10- vs 3-state Aggregate Shocks)….. Table 2.2 Cole and Rogerson versus Mortensen and Pissarides………………….. Table 3.1 Unit root tests…………………………………………………………... Table 3.2 VAR between employment and reallocation at different time-scales….. Table 3.3 VAR between employment and reallocation at different time-scales...... Table 3.4 Granger causality across time-scales…………………………………... Table 4.1 Correlation Matrix for Reallocation Indices…………………………… Table 4.2 Correlation Coefficients Reallocation Indices and Productivity Growth Table 4.3 OLS Results for Productivity Growth and Reallocation Index………... Table 4.4 OLS Results for Productivity Growth and Synchronization Index……. Table 4.5 Model Parameterization ……………………………………………….. Table 4.6 Reallocation index and productivity growth I ..……………………….. Table 4.7 Reallocation index and productivity growth II ……….……………….. 85 32 86 87 88 53 89 89 89 90 78 80 81
vi
List of Figures
Figure 2.1 Data and Model Spectra I (Mortensen and Pissarides)……………… 91 Figure 2.2 Data and Model Spectra II (Mortensen and Pissarides)…………….. 92 Figure 2.3 Levels and Growth Rates - Simulated Series……………………….. 93 Figure 2.4 Percentage of Variance of ?y Explained by BC Frequencies…….. 94 Figure 2.5 Percentage of Variance of ?y Explained by High Frequencies…… 94 Figure 2.6 Percentage of Variance of ?y Explained by Low Frequencies..…... 94 Figure 2.7 Response to Permanent bad shocks in alternative models………….. 95 Figure 2.8 Data and Model Spectra III (Cole and Rogerson)…………………... 96 Figure 2.9 Measure of fit ? (? ) ………………………………………………… 97 Figure 2.10 Data and Model Spectra IV (optimal job-finding probabilities)…... 98 Figure 2.11 Job Creation and Job Destruction Rates I………………………….. 99 Figure 2.12 Job Creation and Job Destruction Rates II………………………… 100 Figure 3.1 Symlet12 Wavelet…………………………………………………… 46 Figure 3.2 Sequential filtering and the Pyramid Algorithm…………………….. 48 Figure 3.3 Multi-scale Decomposition for Employment……………………….. 101 Figure 3.4 Multi-scale Decomposition for Reallocation………………………... 102 Figure 4.1 Reallocation Index One……………………………………………... 103 Figure 4.2 Reallocation Index One (Heterogeneous Seasonal Frequencies)…… 103 Figure 4.3 Reallocation Index two……………………………………………… 104 Figure 4.4 Reallocation Index three…………………………………………….. 104 Figure 4.5 Profit-vintage schedule..…………………………………………….. 76 Figure 4.6 Value function and scrapping ages ………………………….……… 105 Figure III.1 Updating and spectral shape ………………………………………. 106
vii
Chapter 1: Introduction
In his autobiography written on the occasion of the 2003 Nobel Prize in Economics, Clive Granger recounts how his pioneering book “Spectral Analysis in Economic Time Series” (1969) - co-authored with Michio Hatanaka - was produced. According to Granger, when he joined the “Time Series Project” led by Oscar Morgenstern at Princeton, Von Neumann (a close friend of Morgenstern) felt strongly that “economists should be using the Fourier methods with their data”. As a result, Granger and Hatanaka pursued that line of research by repeatedly interacting with Princeton statistician John Tukey, whose modus operandi was to prescribe a series of computer calculations, provide interpretation for the results, and restart the cycle by asking another batch of work. After a while, a solid body of knowledge emerged and a book was clearly warranted.1
The story as told suggests that Granger and Hatanaka’s book came to existence partly because Von Neumann had a gut feeling about the potential benefits of spectral analysis in economics. Although I cannot possibly speak to his reasons, it is fair to say that much of the appeal underlying frequency-domain analysis stems from its promise to generate new and rich insights by looking at the data from a different, and yet simple, perspective. Throughout the years, research has reaffirmed that spectral
Granger and Hatanaka told Tukey that they would wait for him to publish his own research first (which included seminal work on the cross-spectrum for a pair of series) before publishing their book. Tukey replied “he was far too busy doing new research to publish, and that they should just go ahead”.
1
1
techniques are indeed powerful and that they can be used not only as descriptive tools, but also for model analysis.
In this context, Watson (1993) articulates how modern dynamic macroeconomic models can be explicitly tested using frequency-domain concepts. More recently, papers such as Christiano and Vigfusson (1999), Otrok (2001a,b), Otrok, Ravikumar and Whiteman (2002), and Figura (2002, 2001) all relate spectral concepts to particular features of macroeconomic models to be improved, without having the development of formal statistical testing procedures as their main goal. These papers exploit the natural association between some aspects of macroeconomic theory and the frequency-domain.
My dissertation shares this same spirit and it is founded on the idea that models of job flows dynamics have inherent frequency content to be exploited. Each one of the next three chapters is a self-contained essay that pursues a different dimension of this argument. By the end of the dissertation I hope to have instilled in the reader more than a gut feeling (as Von Neumann may once have had) that the frictional nature of the adjustment process underlying job flows dynamics calls for a greater attention to frequency-domain methods.
2
Chapter 2: Persistent employment fluctuations and the structure of search models: a frequency-domain perspective
2.1 Literature review and motivation
Employment fluctuations are the result of a complex mix between exogenous shocks and the institutional/decision environment in which firms and workers trade labor services. At the aggregate level, the well-documented positive persistence observed in employment fluctuations is an important sign of how efficiently an economy makes use of its labor input over time. The way we interpret this persistence depends fundamentally on what we believe to be the cause of fluctuations. For example, if exogenous technology shocks shift the demand for labor in a persistent fashion, persistent employment dynamics may be nothing more than healthy Walrasian fluctuations. In contrast, if we believe that persistence results from matching frictions, then policies geared towards improving job finding rates may be socially desirable. So we care about persistence in employment fluctuations because it ultimately reflects deeper structural features of the economy, and the ability of our models to “get persistence right” is crucial for our understanding of labor market dynamics.
As pointed out by Cogley and Nason (1995), early dynamic stochastic general equilibrium models achieved persistent fluctuations without resorting to any internal propagation mechanisms, by simply assuming persistent (exogenous) driving forces. Despite being successful at times, this approach has been criticized for assuming what 3
should be explained. Modern macroeconomic models of employment fluctuations, however, have fully embraced a key non-Walrasian feature of labor markets: timeconsuming matching. The main idea behind these models is that escaping the unemployment pool may not be possible even if the agent is willing to accept the current wage and, even though, there are vacancies. A willing-to-work unemployed agent and a willing-to-hire employer need to overcome the problem of finding each other before production can start. Such matching frictions generally take the form of probabilistic hiring, which may be a function of economy-wide variables such as unemployment and vacancies. This friction implies that the stock of employed workers displays sluggish adjustment over time, potentially generating persistent employment dynamics.
A workhorse model in the macroeconomic literature on matching frictions is Mortensen and Pissarides (1994). This model can easily be adapted to study a host of different issues, such as the response of job flows to different labor market policies and institutions. Although the original version of the model is capable of matching important aspects of job flows behavior, recent studies have found important shortcomings in its ability to replicate a broader set of stylized facts.2 As a result, recent work has attempted to make matching models more reliable tools for policy design. While suggesting modifications and additions to the structural model is an important part of this task, equally important is to pinpoint empirically the source of misalignments present in the baseline framework. This paper does the latter using frequency-domain tools.
2
These studies include Cole and Rogerson (1999), Shimer (2005, 2003), Pries (2004) and Hall (2005).
4
The particular shortcoming we focus on here is the lack of persistent fluctuations in the employment growth rate generated by the model vis a vis those observed in the data. While the first-order auto-correlation coefficient of the employment growth rate is 0.68 for US manufacturing (calculated at a quarterly frequency for the period 1947 to 1993), the counterpart measure obtained from simulations of the Mortensen and Pissarides model is slightly negative, despite the fact that the simulations use a highly persistent driving force. In order to understand the empirical roots of this result, we propose a frequency-domain decomposition of the employment growth spectrum into the job creation spectrum, the job destruction spectrum and their cospectrum. To help us interpret the decomposition results, we suggest a canonical reduced-form model that illustrates the differences between achieving persistence in levels and in growth rates.
The fact that many models generate weak persistence in employment dynamics has been already pointed out by Hall (1995). More recently, Pries (2004) addressed this problem using a structural model in which match-learning effects induce recurring job losses and sluggish adjustment in employment. In contrast to these papers, we pursue a more descriptive route by comparing model and data spectra for the decomposition of the employment growth rate. We also consider Cole and Rogerson’s (1999) reduced-form representation of the Mortensen and Pissarides model to ascertain the limits of re-parameterization in fighting the lack of persistence.
5
Our results show that temporal decoupling between job creation and job destruction is a quantitatively important element behind the employment growth persistence observed in the data, and that the Mortensen-Pissarides model fails to capture it. Additionally, we show that generating persistence in the employment growth rate is not equivalent to generating decoupling between the creation and destruction margins, and although Cole and Rogerson’s parameterization clearly succeeds in the former, it appears to be less successful in the latter. Finally, we perform an exercise applying the Method of Simulated Moments (Gourieroux and Monfort (1996)), in which the moments to be matched are the empirical spectral densities estimated from the data. We find that the deviations between the spectrum implied by Cole and Rogerson’s reduced-form model and the data can be further reduced by assuming lower job-finding probabilities. Finally, we relate our empirical findings to a particular structural feature of the Mortensen-Pissarides model: the frictionless determination of meeting rates implied by the zero-profit condition on vacancy posting.
The chapter is organized as follows. Section 2.2 presents an outline of Mortensen and Pissarides (1994), emphasizing how employment dynamics are determined within the model. Section 2.3 describes the dataset used and provides a quick overview of concepts and spectral techniques employed in the paper. Section 2.4 proposes a decomposition of the employment growth rate in the frequency-domain and performs comparisons between the Mortensen-Pissarides model and data spectra. Section 2.5 studies the limits of re-parameterizing the Mortensen-Pissarides model using the
6
reduced-form representation proposed by Cole and Rogerson (1999). Section 2.6 concludes the paper and discusses directions for future research.
2.2 Mortensen-Pissarides model and employment dynamics
2.2.1 The environment
The Mortensen-Pissarides (1994) model features an environment populated by riskneutral entrepreneurs and risk-neutral workers. Existing jobs can either be matched to a worker or vacant, and workers can either be matched to an employee or searching for a job.3 Job creation takes place when a searching worker meets a vacant job. The meeting process is assumed to be time-consuming, and is modeled according to a matching function which depends on the aggregate levels of unemployment and vacancies. Additionally, vacancies are costly to maintain and any entrepreneur is free to post a vacancy or destroy one already posted. The match surplus generated by labor market frictions is shared via period-by-period wage renegotiations following a Nash bargaining solution. The productivity of each existing match depends on aggregate and idiosyncratic components. While all new matches are assumed to be created at the maximum idiosyncratic productivity, they experience new idiosyncratic shocks over time and can be terminated at any moment if their corresponding productivity falls below a certain threshold endogenously determined by the model (known as the reservation
The model assumes one worker per firm (entrepreneur), which is generally justified on the grounds of constant returns to scale technology.
3
7
productivity). Such terminations contribute to job destruction. A non-degenerate distribution of filled-job productivities is fully consistent with optimizing individual behavior, as matches experience idiosyncratic shocks that are below the upper limit at which they are created but above the threshold level for destruction. Essentially, labor market frictions make it optimal for firms and workers to tolerate filled jobs that are not as productive as brand new jobs.
Mortensen and Pissarides add cyclical dynamics to this setup by allowing the aggregate productivity component of a filled job to follow a three-state Markov process. As a result, the endogenous reservation productivity and matching rates will also fluctuate in response to the current aggregate state. Flows into unemployment will be given by the interaction between the actual distribution of idiosyncratic productivities and the fluctuating reservation productivity values, whereas flows out of unemployment will be given by the interaction between the level of unemployment and job-finding rates implied by the matching function. Once calibrated, the model can be used to generate series of job creation, job destruction and employment. Below we present and briefly discuss basic features of the model affecting the determination of employment dynamics in the presence of aggregate state fluctuations.4
The presentation of the main features of the model is intentionally brief and focuses only on what is relevant for our purposes. The interested reader is encouraged to refer to Mortensen and Pissarides (1994).
4
8
2.2.2 Basic features
Let L denote the total number of workers in the labor force (which is fixed in the model), u the unemployment rate (unemployed workers as a fraction of the labor force), and v the vacancy rate (total vacancies as a fraction of the labor force). The total number of matches at any point in time is given by Lm=m(Lv,Lu), in which m(.,.) is a matching function assumed to be increasing in both arguments and linearly homogenous. The rate at which vacant jobs are filled is given by q=m(v,u)/v, which can also be written as q(v/u) where q’(v/u)
A workflow consists of a sequence of connected steps where each step follows without delay or gap and ends just before the subsequent step may begin. It is a depiction of a sequence of operations, declared as work of a person or group,[1] an organization of staff, or one or more simple or complex mechanisms
ABSTRACT
Title of Document:
ESSAYS ON JOB FLOWS DYNAMICS Fabiano Rodrigues Bastos, Ph.D., 2005
Directed By:
Professor John Haltiwanger, Department of Economics
Gross job flows dynamics, defined as the behavior of creation and destruction of jobs at the establishment level, has become a topic of great interest in economics during recent years and researchers have resorted to different empirical methodologies in order to tease out its causes and consequences, as well as its connections to overall economic activity. In this context, my dissertation attempts to contribute to the debate by advancing the usefulness of frequency-domain techniques. I emphasize not only the relevance of the economic questions being examined, but also the unique perspective that frequency-domain techniques can provide. There are three major questions I pursue. The first is why equilibrium search models of labor market frictions have trouble explaining the observed persistence in employment fluctuations. I implement a frequency-domain decomposition of the employment growth rate to isolate the contributions coming from the job creation spectrum, the job destruction spectrum, and the cross-spectrum between the two. Among other results, I show that the failure to generate a negative contemporaneous correlation between job creation and job destruction at business cycle frequencies is behind the
inability of the Mortensen-Pissarides (1994) canonical model to reproduce the empirical spectral shape of the employment growth series. The second question I
tackle relates to the direction of causality between aggregate employment fluctuations and gross job reallocation. Recent macroeconomic models suggest an active role for reallocation dynamics over the business cycle, and my results can be interpreted as supporting evidence that such a role indeed exists, but at a low frequency range. The basic idea is to look for different causality relationships at different time-scales by combining wavelet techniques with a standard Granger causality test. Finally, the third question I address investigates the connections between labor productivity growth and the frequency content of the job reallocation series for four-digit level US manufacturing industries. My results indicate that industries with relatively more influential low frequencies display inferior productivity growth. I relate these findings to the literature and propose a simple theoretical model to explain them.
ESSAYS ON JOB FLOWS DYNAMICS
By Fabiano Rodrigues Bastos
Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2005
Advisory Committee: Professor John Haltiwanger, Chair Associate Professor John Shea Associate Professor John Chao Associate Professor John Horowitz Assistant Professor Michael Pries
© Copyright by Fabiano Rodrigues Bastos 2005
Dedication
I dedicate this dissertation to my father Eduardo Marcos Chaves Bastos, my mother Almira Rodrigues, my wife Leatrisse Oba, and my daughter Ana Beatriz Oba Bastos.
ii
Acknowledgements
I would have never completed this dissertation in absence of the guidance and support I received throughout my academic journey. Professor John Haltiwanger, my main advisor, provided superb orientation and encouragement. By interacting with him I learned much more than economics. Inadvertently, he taught me the traits of a firstclass professional which are valid beyond academic walls. Professor John Shea has contributed enormously to my research through his astonishing ability to extricate “economic juice” from virtually any idea. Professor Mike Pries, a reliable source of advice permanently stationed at Tydings 4th floor, was essential for continuous progress.
From my former university in Brazil (UnB), I must mention the names of two professors who never let me settle for less: Joaquim Pinto de Andrade and Joao Ricardo Faria. Also from those times, Bernardo Borba de Andrade, a good friend who still patiently helps me with my statistical incursions.
Finally, my family deserves special credit for being supportive beyond the call of duty. In particular, my wife (Leatrisse) has demonstrated selfless allegiance to my academic pursuit; my daughter (Ana Beatriz) whose soothing smile reminded me what matters in life during this last stressful year; my mother (Almira) who has always been enthusiastic about my dreams despite the oppressive distance; and my father (Eduardo) who made my own happiness his highest priority until the last moment. iii
Table of Contents
Acknowledgements .....................................................................................................iii Table of Contents......................................................................................................... iv List of Tables ............................................................................................................... vi List of Figures ............................................................................................................. vii Chapter 1: Introduction ................................................................................................. 1 Chapter 2: Persistent employment fluctuations and the structure of search models: a frequency-domain perspective ...................................................................................... 3 2.1 Literature review and motivation........................................................................ 3 2.2 Mortensen-Pissarides model and employment dynamics ................................... 7 2.2.1 The environment .......................................................................................... 7 2.2.2 Basic features ............................................................................................... 9 2.3 Data and methodology ...................................................................................... 12 2.3.1 Data .............................................................................................................. 9 2.3.2 Spectral analysis........................................................................................... 9 2.3.3 Multivariate spectrum ................................................................................ 13 2.3.4 Univariate spectrum ................................................................................... 13 2.3.5 Cross spectrum .......................................................................................... 13 2.3.6 Estimation ................................................................................................. 13 2.4 Model and data spectra ..................................................................................... 20 2.4.1 Employment decomposition and comparisons among spectral densities .. 20 2.4.2 A canonical reduced-form model for levels and growth rates................... 24 2.5 Parameters and structure ................................................................................... 30 2.5.1 Can re-parameterization solve the problem? ............................................. 30 2.5.2 Spectral loss function: a new metric .......................................................... 34 2.5.3 Are there enough frictions in the Mortensen-Pissarides model ................. 37 2.6 Concluding remarks and future work ............................................................... 39 Chapter 3: Job reallocation dynamics and aggregate employment fluctuations in the US manufacturing: a Granger causality study across time-scales .............................. 41 3.1 Reallocation Intensity and Macroeconomics .................................................... 41 3.2 Empirical methodology..................................................................................... 44 3.2.1 Wavelets: an overview............................................................................... 44 3.2.2 Multi-scale decomposition......................................................................... 46 3.2.3 Granger causality tests across time-scales ................................................. 49 3.3 Reallocation and aggregate fluctuations: results............................................... 50 3.4 Extensions and concluding remarks.................................................................. 54 Chapter 4: Productivity growth and the frequency content of job reallocation: a crosssection study of US manufacturing industries. ........................................................... 56 4.1 Productivity growth and reallocation................................................................ 56 4.2 Measuring the importance of low frequencies.................................................. 58 4.2.1 Data ............................................................................................................ 58 4.2.2 Reallocation index one............................................................................... 59 iv
4.2.3 Reallocation index two .............................................................................. 62 4.2.4 Reallocation index three ............................................................................ 58 4.3 Empirical results ............................................................................................... 65 4.3.1 Productivity growth and the frequency content of reallocation................. 65 4.3.2 Synchronization: a further look into inefficiencies.................................... 68 4.4 Insigths from a simple theoretical model.......................................................... 71 4.4.1 The model .................................................................................................. 71 4.4.2 Dynamics ................................................................................................... 73 4.4.3 Simulation restuls....................................................................................... 77 4.5 Concluding remarks and extensions ................................................................. 82 Chapter 5: Concluding remarks ................................................................................. 84 Appendices.................................................................................................................. 85 Appendix I: Tables.............................................................................................. 85 Appendix II: Figures ........................................................................................... 91 Appendix III: Infrequent updating and spectral shape...................................... 106 Bibliography ............................................................................................................. 107
v
List of Tables
Table 2.1 Mortensen and Pissarides Model (10- vs 3-state Aggregate Shocks)….. Table 2.2 Cole and Rogerson versus Mortensen and Pissarides………………….. Table 3.1 Unit root tests…………………………………………………………... Table 3.2 VAR between employment and reallocation at different time-scales….. Table 3.3 VAR between employment and reallocation at different time-scales...... Table 3.4 Granger causality across time-scales…………………………………... Table 4.1 Correlation Matrix for Reallocation Indices…………………………… Table 4.2 Correlation Coefficients Reallocation Indices and Productivity Growth Table 4.3 OLS Results for Productivity Growth and Reallocation Index………... Table 4.4 OLS Results for Productivity Growth and Synchronization Index……. Table 4.5 Model Parameterization ……………………………………………….. Table 4.6 Reallocation index and productivity growth I ..……………………….. Table 4.7 Reallocation index and productivity growth II ……….……………….. 85 32 86 87 88 53 89 89 89 90 78 80 81
vi
List of Figures
Figure 2.1 Data and Model Spectra I (Mortensen and Pissarides)……………… 91 Figure 2.2 Data and Model Spectra II (Mortensen and Pissarides)…………….. 92 Figure 2.3 Levels and Growth Rates - Simulated Series……………………….. 93 Figure 2.4 Percentage of Variance of ?y Explained by BC Frequencies…….. 94 Figure 2.5 Percentage of Variance of ?y Explained by High Frequencies…… 94 Figure 2.6 Percentage of Variance of ?y Explained by Low Frequencies..…... 94 Figure 2.7 Response to Permanent bad shocks in alternative models………….. 95 Figure 2.8 Data and Model Spectra III (Cole and Rogerson)…………………... 96 Figure 2.9 Measure of fit ? (? ) ………………………………………………… 97 Figure 2.10 Data and Model Spectra IV (optimal job-finding probabilities)…... 98 Figure 2.11 Job Creation and Job Destruction Rates I………………………….. 99 Figure 2.12 Job Creation and Job Destruction Rates II………………………… 100 Figure 3.1 Symlet12 Wavelet…………………………………………………… 46 Figure 3.2 Sequential filtering and the Pyramid Algorithm…………………….. 48 Figure 3.3 Multi-scale Decomposition for Employment……………………….. 101 Figure 3.4 Multi-scale Decomposition for Reallocation………………………... 102 Figure 4.1 Reallocation Index One……………………………………………... 103 Figure 4.2 Reallocation Index One (Heterogeneous Seasonal Frequencies)…… 103 Figure 4.3 Reallocation Index two……………………………………………… 104 Figure 4.4 Reallocation Index three…………………………………………….. 104 Figure 4.5 Profit-vintage schedule..…………………………………………….. 76 Figure 4.6 Value function and scrapping ages ………………………….……… 105 Figure III.1 Updating and spectral shape ………………………………………. 106
vii
Chapter 1: Introduction
In his autobiography written on the occasion of the 2003 Nobel Prize in Economics, Clive Granger recounts how his pioneering book “Spectral Analysis in Economic Time Series” (1969) - co-authored with Michio Hatanaka - was produced. According to Granger, when he joined the “Time Series Project” led by Oscar Morgenstern at Princeton, Von Neumann (a close friend of Morgenstern) felt strongly that “economists should be using the Fourier methods with their data”. As a result, Granger and Hatanaka pursued that line of research by repeatedly interacting with Princeton statistician John Tukey, whose modus operandi was to prescribe a series of computer calculations, provide interpretation for the results, and restart the cycle by asking another batch of work. After a while, a solid body of knowledge emerged and a book was clearly warranted.1
The story as told suggests that Granger and Hatanaka’s book came to existence partly because Von Neumann had a gut feeling about the potential benefits of spectral analysis in economics. Although I cannot possibly speak to his reasons, it is fair to say that much of the appeal underlying frequency-domain analysis stems from its promise to generate new and rich insights by looking at the data from a different, and yet simple, perspective. Throughout the years, research has reaffirmed that spectral
Granger and Hatanaka told Tukey that they would wait for him to publish his own research first (which included seminal work on the cross-spectrum for a pair of series) before publishing their book. Tukey replied “he was far too busy doing new research to publish, and that they should just go ahead”.
1
1
techniques are indeed powerful and that they can be used not only as descriptive tools, but also for model analysis.
In this context, Watson (1993) articulates how modern dynamic macroeconomic models can be explicitly tested using frequency-domain concepts. More recently, papers such as Christiano and Vigfusson (1999), Otrok (2001a,b), Otrok, Ravikumar and Whiteman (2002), and Figura (2002, 2001) all relate spectral concepts to particular features of macroeconomic models to be improved, without having the development of formal statistical testing procedures as their main goal. These papers exploit the natural association between some aspects of macroeconomic theory and the frequency-domain.
My dissertation shares this same spirit and it is founded on the idea that models of job flows dynamics have inherent frequency content to be exploited. Each one of the next three chapters is a self-contained essay that pursues a different dimension of this argument. By the end of the dissertation I hope to have instilled in the reader more than a gut feeling (as Von Neumann may once have had) that the frictional nature of the adjustment process underlying job flows dynamics calls for a greater attention to frequency-domain methods.
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Chapter 2: Persistent employment fluctuations and the structure of search models: a frequency-domain perspective
2.1 Literature review and motivation
Employment fluctuations are the result of a complex mix between exogenous shocks and the institutional/decision environment in which firms and workers trade labor services. At the aggregate level, the well-documented positive persistence observed in employment fluctuations is an important sign of how efficiently an economy makes use of its labor input over time. The way we interpret this persistence depends fundamentally on what we believe to be the cause of fluctuations. For example, if exogenous technology shocks shift the demand for labor in a persistent fashion, persistent employment dynamics may be nothing more than healthy Walrasian fluctuations. In contrast, if we believe that persistence results from matching frictions, then policies geared towards improving job finding rates may be socially desirable. So we care about persistence in employment fluctuations because it ultimately reflects deeper structural features of the economy, and the ability of our models to “get persistence right” is crucial for our understanding of labor market dynamics.
As pointed out by Cogley and Nason (1995), early dynamic stochastic general equilibrium models achieved persistent fluctuations without resorting to any internal propagation mechanisms, by simply assuming persistent (exogenous) driving forces. Despite being successful at times, this approach has been criticized for assuming what 3
should be explained. Modern macroeconomic models of employment fluctuations, however, have fully embraced a key non-Walrasian feature of labor markets: timeconsuming matching. The main idea behind these models is that escaping the unemployment pool may not be possible even if the agent is willing to accept the current wage and, even though, there are vacancies. A willing-to-work unemployed agent and a willing-to-hire employer need to overcome the problem of finding each other before production can start. Such matching frictions generally take the form of probabilistic hiring, which may be a function of economy-wide variables such as unemployment and vacancies. This friction implies that the stock of employed workers displays sluggish adjustment over time, potentially generating persistent employment dynamics.
A workhorse model in the macroeconomic literature on matching frictions is Mortensen and Pissarides (1994). This model can easily be adapted to study a host of different issues, such as the response of job flows to different labor market policies and institutions. Although the original version of the model is capable of matching important aspects of job flows behavior, recent studies have found important shortcomings in its ability to replicate a broader set of stylized facts.2 As a result, recent work has attempted to make matching models more reliable tools for policy design. While suggesting modifications and additions to the structural model is an important part of this task, equally important is to pinpoint empirically the source of misalignments present in the baseline framework. This paper does the latter using frequency-domain tools.
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These studies include Cole and Rogerson (1999), Shimer (2005, 2003), Pries (2004) and Hall (2005).
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The particular shortcoming we focus on here is the lack of persistent fluctuations in the employment growth rate generated by the model vis a vis those observed in the data. While the first-order auto-correlation coefficient of the employment growth rate is 0.68 for US manufacturing (calculated at a quarterly frequency for the period 1947 to 1993), the counterpart measure obtained from simulations of the Mortensen and Pissarides model is slightly negative, despite the fact that the simulations use a highly persistent driving force. In order to understand the empirical roots of this result, we propose a frequency-domain decomposition of the employment growth spectrum into the job creation spectrum, the job destruction spectrum and their cospectrum. To help us interpret the decomposition results, we suggest a canonical reduced-form model that illustrates the differences between achieving persistence in levels and in growth rates.
The fact that many models generate weak persistence in employment dynamics has been already pointed out by Hall (1995). More recently, Pries (2004) addressed this problem using a structural model in which match-learning effects induce recurring job losses and sluggish adjustment in employment. In contrast to these papers, we pursue a more descriptive route by comparing model and data spectra for the decomposition of the employment growth rate. We also consider Cole and Rogerson’s (1999) reduced-form representation of the Mortensen and Pissarides model to ascertain the limits of re-parameterization in fighting the lack of persistence.
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Our results show that temporal decoupling between job creation and job destruction is a quantitatively important element behind the employment growth persistence observed in the data, and that the Mortensen-Pissarides model fails to capture it. Additionally, we show that generating persistence in the employment growth rate is not equivalent to generating decoupling between the creation and destruction margins, and although Cole and Rogerson’s parameterization clearly succeeds in the former, it appears to be less successful in the latter. Finally, we perform an exercise applying the Method of Simulated Moments (Gourieroux and Monfort (1996)), in which the moments to be matched are the empirical spectral densities estimated from the data. We find that the deviations between the spectrum implied by Cole and Rogerson’s reduced-form model and the data can be further reduced by assuming lower job-finding probabilities. Finally, we relate our empirical findings to a particular structural feature of the Mortensen-Pissarides model: the frictionless determination of meeting rates implied by the zero-profit condition on vacancy posting.
The chapter is organized as follows. Section 2.2 presents an outline of Mortensen and Pissarides (1994), emphasizing how employment dynamics are determined within the model. Section 2.3 describes the dataset used and provides a quick overview of concepts and spectral techniques employed in the paper. Section 2.4 proposes a decomposition of the employment growth rate in the frequency-domain and performs comparisons between the Mortensen-Pissarides model and data spectra. Section 2.5 studies the limits of re-parameterizing the Mortensen-Pissarides model using the
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reduced-form representation proposed by Cole and Rogerson (1999). Section 2.6 concludes the paper and discusses directions for future research.
2.2 Mortensen-Pissarides model and employment dynamics
2.2.1 The environment
The Mortensen-Pissarides (1994) model features an environment populated by riskneutral entrepreneurs and risk-neutral workers. Existing jobs can either be matched to a worker or vacant, and workers can either be matched to an employee or searching for a job.3 Job creation takes place when a searching worker meets a vacant job. The meeting process is assumed to be time-consuming, and is modeled according to a matching function which depends on the aggregate levels of unemployment and vacancies. Additionally, vacancies are costly to maintain and any entrepreneur is free to post a vacancy or destroy one already posted. The match surplus generated by labor market frictions is shared via period-by-period wage renegotiations following a Nash bargaining solution. The productivity of each existing match depends on aggregate and idiosyncratic components. While all new matches are assumed to be created at the maximum idiosyncratic productivity, they experience new idiosyncratic shocks over time and can be terminated at any moment if their corresponding productivity falls below a certain threshold endogenously determined by the model (known as the reservation
The model assumes one worker per firm (entrepreneur), which is generally justified on the grounds of constant returns to scale technology.
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productivity). Such terminations contribute to job destruction. A non-degenerate distribution of filled-job productivities is fully consistent with optimizing individual behavior, as matches experience idiosyncratic shocks that are below the upper limit at which they are created but above the threshold level for destruction. Essentially, labor market frictions make it optimal for firms and workers to tolerate filled jobs that are not as productive as brand new jobs.
Mortensen and Pissarides add cyclical dynamics to this setup by allowing the aggregate productivity component of a filled job to follow a three-state Markov process. As a result, the endogenous reservation productivity and matching rates will also fluctuate in response to the current aggregate state. Flows into unemployment will be given by the interaction between the actual distribution of idiosyncratic productivities and the fluctuating reservation productivity values, whereas flows out of unemployment will be given by the interaction between the level of unemployment and job-finding rates implied by the matching function. Once calibrated, the model can be used to generate series of job creation, job destruction and employment. Below we present and briefly discuss basic features of the model affecting the determination of employment dynamics in the presence of aggregate state fluctuations.4
The presentation of the main features of the model is intentionally brief and focuses only on what is relevant for our purposes. The interested reader is encouraged to refer to Mortensen and Pissarides (1994).
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2.2.2 Basic features
Let L denote the total number of workers in the labor force (which is fixed in the model), u the unemployment rate (unemployed workers as a fraction of the labor force), and v the vacancy rate (total vacancies as a fraction of the labor force). The total number of matches at any point in time is given by Lm=m(Lv,Lu), in which m(.,.) is a matching function assumed to be increasing in both arguments and linearly homogenous. The rate at which vacant jobs are filled is given by q=m(v,u)/v, which can also be written as q(v/u) where q’(v/u)