Description
A market to be competitive, there must be more than a single buyer or seller. It has been suggested that two people may trade, but it takes at least three persons to have a market, so that there is competition in at least one of its two sides.[1] However, competitive markets, as understood in formal economic theory, rely on much larger numbers of both buyers and sellers.
ABSTRACT
Title of Document:
MARKET FORCES AND URBAN SPATIAL STRUCTURE: EVIDENCE FROM BEIJING, CHINA. Xingshuo Zhao, Doctor of Philosophy, 2010
Directed By:
Dr. Chengri Ding, Urban Studies and Planning Program
This dissertation contributes to the literature on urban spatial structure by addressing two research questions. First, it empirically examines the urban economic theory by testing the relationship between the distance elasticities of land prices and housing prices. The theory indicates that land prices are more elastic with respect to distance from the city center than housing prices; in other words, land prices decline faster than housing prices. Using data from Beijing, which include matched housing and land prices, my findings support the theory. Second, this dissertation investigates the impacts of housing services production in general and the impacts of the capital-land substitution in particular on urban spatial structure. Using a constant elasticity of substitution (CES) production function for housing services, I theoretically derive the impacts of the elasticity of capital-land substitution on urban spatial structure, which is measured in terms of the distance gradients of land prices and capital densities, the housing output per unit of
land, and the ratio of the distance elasticity of land prices to the distance elasticity of housing prices. The derived results suggest that an increase in the elasticity of capitalland substitution leads to increases in the land price, the capital density, and the housing output per unit of land at any location within the city, flattening of the land price and capital density curves, an increase in the ratio of the distance elasticity of land prices to the distance elasticity of housing prices, an expansion of the city boundary, and a growth in the population. These theoretical results are verified by numerical simulations and empirical estimations using the Beijing data. The simulations also reveal the magnitudes of these impacts: a 1% change in the elasticity of capital-land substitution leads to 15-20% changes in the total land value and housing output. The findings of this dissertation have practical implications in housing market behaviors, land value assessment for property taxation, and urban land use policy and planning.
MARKET FORCES AND UBAN SPATIAL STRUCTURE: EVIDENCE FROM BEIJING, CHINA.
By Xingshuo Zhao
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 Doctoral of Philosophy 2010
Advisory Committee: Dr. Chengri Ding, Chair Dr. James R. Cohen Dr. Marie Howland Dr. Gerrit J. Knaap Dr. Erik Lichtenberg
© Copyright by Xingshuo Zhao 2010
Dedication
To Father and Mother
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Acknowledgements
I would like to express my sincere gratitude to my advisor, Dr. Chengri Ding, for his intellectual guidance during my years at the University of Maryland. Without Dr. Ding’s thoughtful advice and encouragement I would not have completed this dissertation. I would also like to thank my committee members, James R. Cohen, Marie Howland, Gerrit J. Knaap, and Erik Lichtenberg, for their insightful comments and advice, as well as their encouragement. I would also like to acknowledge Dr. Xiaochen Meng and Liang Ma for providing the data used in this dissertation. I am grateful to all of the faculty and staff in the Urban Studies & Planning Program for their help. I owe many thanks to my fellow doctoral students and my friends for their friendship and support, especially Chao Liu, Doan Nguyen, and Jung Ho Shin. I would like to thank my friend Haipeng An for helping me in using Mathematica, Fanqing Ye for all the discussions, my roommates Junfeng Huang and Shuo Huang for their understanding and support. Special thanks should also go to Dr. Lin Yi-Jiun and Paul Miller for their help and concern. I thank Weichen Zhao and my mother for taking the photos used in this dissertation, and I appreciate Adan Martinez-Cruz and Jeffrey Tiell for proofreading the draft. I am grateful to all of my friends who are not physically around me but encourage me all the time through the Internet. Finally, I would like to thank my parents. Without their love, I would not have been able to accomplish this.
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Table of Contents
List of Tables ................................................................................................................ v List of Figures .............................................................................................................. vi Chapter 1: Introduction ............................................................................................ 1 1.1 Why Urban Spatial Structure Matters .................................................... 1 1.2 Research Questions ................................................................................ 2 1.3 Organization of the Dissertation............................................................. 5 Chapter 2: Market, Urban Spatial Structure, and Planning in China ....................... 7 2.1 Land Reform and Land Market .............................................................. 7 2.2 Housing Reform and Housing Market ................................................. 11 2.3 Spatial Structure ................................................................................... 18 2.3.1 Pre-Reform ........................................................................................... 18 2.3.2 Post-Reform.......................................................................................... 20 2.4 Urban Planning ..................................................................................... 21 Chapter 3: Literature Review ................................................................................. 24 3.1 Urban Spatial Structure and Form ........................................................ 24 3.2 Housing Services Production ............................................................... 30 Chapter 4: Housing Services Production and Urban Spatial Structure .................. 35 4.1 The CES Production Function for Housing Services ........................... 35 4.2 Impacts of Elasticity of Capital-Land Substitution .............................. 39 Chapter 5: Numerical Simulation........................................................................... 47 5.1 Impacts of Capital-Land Substitution................................................... 47 5.2 Marginal Effects of Capital-Land Substitution .................................... 50 5.2.1 Housing Price Distribution and Production Function .......................... 50 5.2.2 Marginal Impacts of Elasticity of Capital-Land Substitution .............. 53 5.2.3 Social Welfare Impacts ........................................................................ 61 Chapter 6: Empirical Evidence .............................................................................. 65 6.1 Research Area....................................................................................... 65 6.2 Data ...................................................................................................... 73 6.3 Urban Decaying Phenomenon .............................................................. 78 6.4 Ratio of the Two Distance Elasticities ................................................. 81 6.5 Elasticity of Capital-Land Substitution ................................................ 86 6.6 Impacts of Elasticity of Capital-Land Substitution .............................. 91 Chapter 7: Conclusion ............................................................................................ 93 7.1 Policy and Planning Implications ......................................................... 93 7.2 Recommendation for Future Studies .................................................... 97 Appendices.................................................................................................................. 99 Appendix I: Solutions of Impacts of Elasticity of Capital-Land Substitution ... 99 Appendix II: Simulated Impacts of Capital-Land Substitution......................... 104 Appendix III: Estimation of CES Housing Production Function ....................... 107 Appendix VI: Estimation of Two Sub-Periods .................................................. 109 Bibliography ............................................................................................................. 114
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List of Tables
Table 3-1 Table 5-1 Table 5-2 Table 5-3 Table 6-1 Table 6-2 Table 6-3 Table 6-4 Table 6-5 Table 6-6 Table 6-7 Table 6-8 Table 6-9 Table 6-10 Table 6-11
Empirical Estimation of Elasticity of Capital-land Substitution for Housing Production* ............................................................................ 32 Signs of Relevant Partial Derivatives by Simulation ........................... 49 Simulated Impacts of Elasticity of Capital-Land Substitution ............. 55 Simulated Total Impacts of Elasticity of Capital-Land Substitution in the City ................................................................................................. 62 Distribution of Population Density in Beijing ...................................... 69 Descriptive Statistics ............................................................................ 76 Numbers of Observations in Each District ........................................... 76 Numbers of Observations in Each Housing Type ................................ 77 OLS Estimations of Distance Gradients for Housing Prices, Land Prices, Capital Densities, and FARs ..................................................... 79 SUR Estimations of Distance Gradients for Housing and Land Prices 83 OLS and IV Estimations of the Ratio of the Two Distance Elasticities85 NLLS Estimations of Housing Production Function ........................... 87 NLLS Estimations of Housing Production Function ........................... 88 OLS and IV Estimations of Elasticity of Capital-land Substitution ..... 90 Comparison between Estimates for Two Sub-Periods ......................... 92
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List of Figures
Figure 2-1
Land Leasing Market in China: Numbers of Plots and Hectares of Land Area, 1994-2005 ..................................................................................... 9 Figure 2-2 Land Leasing Market in China: Transaction Values, 1994-2005 ........ 10 Figure 2-3 Land Leasing Market in China: Numbers of Land Plots by Different Approaches, 1999-2005........................................................................ 10 Figure 2-4 Land Leasing Market in China: Hectares of Land Areas by Different Approaches in China, 1999-2005 ......................................................... 11 Figure 2-5 Commodity Housing Market in China: Floor Space and Value of Sales, 1999-2005 ............................................................................................. 13 Figure 2-6 Commodity housing market in China: Share in Housing Supply, 19952005 ...................................................................................................... 14 Figure 2-7 Residential Building Evolution in Zhongguancun Area, Beijing......... 16 Figure 2-8 Residential Building Evolution in Qinchuan Neighborhood, Xi’an .... 17 Figure 2-9 Beijing’s Skyline .................................................................................. 21 Figure 2-10 Detail Plan for Block 21, Plot 22, Shunyi District, Beijing .................. 22 Figure 5-1 Estimated Housing Prices over Urban Space ....................................... 51 Figure 5-2 Simulated Land Prices over Urban Space ............................................ 53 Figure 5-3 Simulated Housing Output per Unit of Land (FAR) over Urban Space .............................................................................................................. 53 Figure 5-4 Simulated Land Prices in Three Scenarios ........................................... 58 Figure 5-5 Simulated Capital Densities in Three Scenarios .................................. 58 Figure 5-6 Simulated Housing Out Put per Unit Land (FAR) in Three Scenarios 58 Figure 5-7 Simulated Ratios of the Two Distance Elasticities in Three Scenarios 59 Figure 5-8 Simulated Shares of Land Cost in Total Property Values in Three Scenarios .............................................................................................. 60 Figure 5-9 Simulated Urban Boundaries in Three Scenarios................................. 60 Figure 6-1 Land Leasing Market in Beijing: Total Number of Leases and Total Leasing Value, 1995-2005 ................................................................... 66 Figure 6-2 Commodity Housing Market Development in Beijing: Floor Space and Value of Sales, 1990-2005 ................................................................... 67 Figure 6-3 Spatial Concentration of City Functions .............................................. 68 Figure 6-4 Housing Prices, Land Prices, and FARs in the Study Area ................. 71 Figure 6-5 Administrative Area of Beijing and Research Area ............................. 74
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Chapter 1:
Introduction
1.1
Why Urban Spatial Structure Matters
Urban spatial structure is of both academic and practical importance and has
attracted wide interest from scholars, planners, and officials for the following reasons. First, urban spatial stricture is associated with urban agglomerative effects that serve as a primary engine for cities to exist and grow. Spatial proximity facilitates intrafirm economies of scale and scope, labor pooling, and technology spillover (Anas et al. 1998, Bertaud 2003, Ding 2009). Second, urban spatial structure and form can be used to measure and indicate the efficiency of urban resources, along with the land prices and housing prices.1 Efficient urban development requires land use intensity to vary with prices as a result of an optimal combination of land and capital in housing services production. Third, urban spatial structure is an important determinant for urban transportation demand, for it links to population density. Population density in turn plays a key role in determining trip length and frequency, mode choice, and the overall travel (Crane 2000, Boarnet & Crane 2001, Ewing & Cervero 2001). Finally, urban spatial structure is directly or indirectly connected to negative externalities. For instance, spatial separation of different land uses can be helpful to minimize the nuance effects resulting from spatial clustering of incompatible land uses. Studies of urban spatial structure are proved to be difficult and complicated. On the one hand, urban spatial structure reflects cumulated decision making by all
Land and housing prices refer to unit prices in RMB (Chinese yuan) per square meter throughout this dissertation.
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kinds of actors such as developers, investors, land owners, residents, planners, and government officials in urban land development. On the other hand, there are a variety of factors that influence the location, timing, uses and intensity of land development, including the market forces, infrastructure provisions, planning regulations, tax policies, social and cultural conventions, and natural endowments (Bertaud & Malpezzi 2003). Practically, it is of great value to understand urban spatial structure, for it helps planners and policymakers dealing with problems of urban development, shaping or reshaping urban structure and form to facilitate economic development and improve the overall social welfare for businesses and residents. For example, knowledge of urban spatial structure can guide planners to direct people and activities in certain spatial nodes to foster agglomerative effects (such as Manhattan in New York City), increase public transportation ridership (Transit Oriented Development), and reduce negative environmental impacts.
1.2
Research Questions
This dissertation addresses two research questions. The first research question
is an empirical question that focuses on testing the urban economic theory, which indicates that land prices are more elastic with respect to distance from the city center than housing prices; in other words, land prices decline faster than housing prices. This prediction is derived by treating land as an input factor in housing services production and regarding the demand for land as a derived demand. Despite many empirical studies on land and housing prices, few cases in the literature have
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examined land and housing prices of the same sites. Economic reform and rapid market development in China provide a good chance to conduct an empirical study of this kind. Taking advantage of the data collected from Beijing that include both land and housing prices from the same land development projects, this dissertation carries out an empirical inquiry on the relationship between land and housing prices by estimating and testing the ratio of the distance elasticity of land prices to the distance elasticity of housing prices.2 In addition, compared with abundant empirical evidence for the pattern of land and housing prices over the urban space in developed countries, fewer studies in the developing countries have been conducted; this dissertation contributes to the literature in this regard. The second research question focuses on examining the impacts of housing services production on urban spatial structure, in particular, the impacts of capitalland substitution. This dissertation investigates this question by (1) theoretical analysis that reveals the directions of the impacts (signs of partial derivatives); (2) numerical simulations that verify the analytical directions and examine the magnitudes of the impacts on social welfare; and (3) empirical estimations that provide evidence for the derived impacts. The theoretical model, which assumes a constant elasticity of substitution (CES) production function for housing services production, yields the following results: an increase in the elasticity of capital-land substitution leads to increases in the land price, the capital density, the absolute values of distance gradients of land prices and capital densities, the housing output per unit of land (or the FAR—floor area ratio) at any location with the city, an
The ratio of the distance elasticity of land prices to the distance elasticity of housing prices is denoted by ? and it is also called the ratio of the two distance elasticities for short throughout this dissertation.
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expansion of the city’s geographical boundary and a growth in the population size.3 These theoretical results are supported by numerical simulations and empirical estimations. The second question contributes to the literature since the impacts of capitalland substitution on urban spatial structure has not been sufficiently addressed. Although the importance of elasticity of capital-land substitution to urban spatial structure has been well recognized (Muth 1964, McDonald 1981), how and to what extent the elasticity of capital-land substitution affects urban spatial structure has not been adequately investigated both theoretically and empirically. McDonald (1981) pointed out that the elasticity of capital-land substitution in land development plays an critical role in understanding urban spatial structure and concluded that it is “a determinant of the land rent gradient, the population density gradient, the factor share of land and housing capital and the elasticity of supply of housing both in the aggregate and on a particular site” (p. 190). The literature, however, lacks explicit examination on the directions and magnitudes of the impacts. This question is overlooked probably because of the slow change in housing production technology in the developed countries where the impacts of capital-land substitution are less relevant. Nevertheless, this question is perhaps more relevant in China, given the profound institutional reforms of urban land and housing systems and impressive urban expansion, particularly in cities like Beijing. Dramatic changes in a relatively short period make capital-land substitution a critical factor in determining urban
Capital density refers to non-land capital intensity in RMB per square meter, and housing output per unit of land is measured by floor space in square meter and thus it is equivalent to the FAR throughout this dissertation.
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spatial structure in China. Even more important, Chinese cities provide an opportunity to empirically examine the linkage between capital-land substitution and urban spatial structure. Based on the data from Beijing, the simulation exercises indicate that capital-land substitution has considerable impacts on urban spatial structure. The findings of this dissertation will be of great value to urban planners and government officials in addressing the problem of housing prices, assisting property value assessment for tax purposes, and evaluating urban land use policies and planning regulations.
1.3
Organization of the Dissertation
This dissertation is organized in seven chapters. After this introduction, chapter 2 reviews urban land and housing markets
development in China, urban spatial structure evolution, and urban planning’s influences on urban land use. Market forces are emerging and begin to act as important forces to shape and modify urban spatial structure in China’s cities, while urban planning remains influential on urban land development. Chapter 3 provides a literature review on urban spatial structure. Urban economic theory reveals the declining phenomena of land and housing prices, and the theory of housing services production is important to understand the formation of urban landscape. Both theoretical and empirical studies are reviewed. Chapters 4 to 6 present respectively theoretical analysis, simulation analysis, and empirical analysis to address the two research questions. By using a CES production function, chapter 4 derives analytically the impacts of capital-land
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substitution in housing services production on urban spatial structure. Chapter 5 conducts numerical simulations to verify the derived directions of the impacts and examine the magnitudes of the impacts, based on the Beijing data. Chapter 6 again uses the data from Beijing, estimates and tests the negative distance gradients of housing prices, land prices, capital densities, and the housing output per unit of land (or the FARs), estimates the ratio of the two distance elasticities and tests whether it is larger than unity, and estimates the elasticity of capital-land substation as well as its impacts. Finally, chapter 7 concludes with the findings, discusses policy and planning implications, and proposes future studies.
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Chapter 2:
Market, Urban Spatial Structure, and
Planning in China
First of all, this chapter provides a brief overview of urban land market and housing market development, and then it reviews changes of urban spatial structure during the post-reform period, in which market forces have emerged and begin to influence urban spatial development in China. It also reviews the urban planning’s influences on urban land development.
2.1
Land Reform and Land Market
The land reform launched in the late 1980s separates the land use rights from
the land ownership and introduces a land leasing market to allocate state-owned urban land.4 Prior to the reform, there was no land market, and urban land was managed and assigned to land users through an administrative process. Land was distributed to land users free of charge on the basis of need for an indefinite time period. Transactions of land between land users were prohibited. If the assigned land was not used, it was to be returned to the government and be re-assigned to other land users. Since there were no economic implications for vacant land holding, this in fact seldom happened, resulting in inefficient land uses. One of the primary objectives of the land reform is to introduce market mechanisms to improve land use efficiency and land management. The most
In China, urban land is owned by the state and managed by city government, while rural land is collectively owned by farmer collectives but is in general restricted from non-agricultural uses.
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prominent change in the reform is the introduction and establishment of the Land Use Right System (LURs). In the LURs, land use rights are separated from land ownership so that private users can access state-owned urban land. City government can lease out the land use rights of state-owned urban land to private users in a longterm period depending on land uses, and a land use right fee is involved in the transaction, paid from land users to the city government. 5 This policy innovation provides an approach to paid land use without challenging the public ownership of the land, which is the cornerstone for Communist China. As expected, land leasing markets are growing quickly and begin to play a role in shaping urban spatial structure. The rapid land market development is reflected by dramatic increases in both the number of land leasing transactions and the value of land leased. In 1987, only 5 land leasing transactions (totaling 15.7 hectare) took place in China, and this number grew to 545 in 1991 (Ding 2003). Since the middle 1990s, the number of annual land leasing transactions jumped to 10,000 and peaked at 242,763 in 2002 (figure 2-1). The area of annually leased land also increased impressively, from about 50,000 hectares in 1994 to over 200,000 hectares in 2005 (figure 2-1). The total value of annually leased land increased even more dramatically by about 15 times during 1994-2005, and it reached as high as 588.4 billion RMB in 2004 (figure 2-2).6 In particular, the beginning years of the new century witnessed accelerated land leasing transactions. For the years 2000-2003, the area of leased land increased 4 times and
The maximum time period is 70 years for residential uses, 40 years for commercial, tourist and recreational uses, and 50 years for other uses such as industrial and public uses.
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Price is not adjusted.
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the average price of land increased 2.3 times, consistent with the fast growing economy and booming commodity housing market in China in this period. Since 1998, material housing distribution was prohibited according to an important document issued by the State Council.7 Nevertheless, a slight decline in the number and area of land leases can be observed since 2002, a fact that probably is due to stringent policies on land uses.8 Despite this, the total value of land leased annually appeared not much influenced, implying an increase in the unit price of land leased.
Source: China Land Resource Statistical Yearbook 2006, China Land Yearbook 1994, 1995, 1998. Data of 1997 were not available. Figure 2-1 Land Leasing Market in China: Numbers of Plots and Hectares of Land Area, 1994-2005
The document of 1998 is entitled the Notice on Further Deepening the Urban Housing System Reform and Speeding up Housing Construction. Further discussion will be found in the following section on the housing market development. In April 2002, the Ministry of Land and Resources announced the Provisions of Tender, Auction, and Listing State-Owned Land Use Right, requiring that leasing land use rights for profitable uses such as residential and commercial uses should be conducted through open bid procedures (including tender, auction, or listing). In March 2004, the Ministry of Land and Resources and the Ministry of Supervision issued the Notice on Further Enforcement and Supervision on the Profitable Land Use Right Leasing through Tender, Auction, and Listing to strictly cut off land leasing transactions through negotiation by August 31, 2004.
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Source: China Land Resource Statistical Yearbook 2006, China Land Yearbook 1994, 1995, 1998. The data of year 1997 are not available. Figure 2-2 Land Leasing Market in China: Transaction Values, 1994-2005
The relative share of land leased in the total land provision also increased substantially. In 1999, leased land made up 25% and 34% in the numbers and the area of urban land provision, respectively; in 2001, leased land exceeded free allocation; and in 2005, leased land comprised up to 70% of total land provision (figures 2-3 and 2-4).
Source: China Land Resource Statistical Yearbook 2006 Figure 2-3 Land Leasing Market in China: Numbers of Land Plots by Different Approaches, 1999-2005
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Source: China Land Resource Statistical Yearbook 2006 Figure 2-4 Land Leasing Market in China: Hectares of Land Areas by Different Approaches in China, 1999-2005
2.2
Housing Reform and Housing Market
Accompanied with the land reform, China’s urban housing reform was
launched in the late 1980s, aiming at transforming the welfare-oriented public housing system into a market-oriented housing system (Wang & Murie 1999, Huang & Clark 2002, Li & Yi 2007). The housing reform is facilitated by the land reform, which enables private developers to obtain urban land for housing services production and enhances commercialization of housing provision. Before the reform, housing was a public welfare attached with urban employment. After the new China was built in 1949, all private houses were systematically transferred to local government and a public housing system was built in urban areas (Wang & Murie 1999). Housing was considered a welfare benefit and allocated free from the work units (danwei) to their employees. Residents did not
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need to pay rent or only paid an extremely low rent since housing was regarded as part of the wage cost (Wang & Murie 2009, Huang & Clark 2002). Housing reform was carried out in a gradual way and marked by two milestone steps that promoted housing privatization. In 1988, the State Council issued permits to sell public housing stocks and encouraged private-public co-financing of housing provision for employees. Under the co-financing scheme, employees usually paid up to one-third of total construction costs, which was a substantial amount of payment compared with what was paid under the material distribution of housing. In 1998, the material distribution of housing was formally abandoned and replaced by monetary housing distribution. As expected, this triggered remarkable development in real estate sectors. Moreover, it brought enormous market opportunities that facilitated rapid changes in housing construction technology. For example, the private housing market began to emerge in the early 1990s and has been growing rapidly since 1998. From 1991 to 2005, the area of annual commodity housing sales increased 18 times from 27.5 million to 495.9 million square meters at an annual growth rate of 23%, and the total value of annual commodity housing sale increased about 70 times from 20.8 billion RMB to 1456.4 billion at a remarkable annual growth rate of 35% (figure 2-5). The growth was particularly striking after 1998, when the country prohibited the channel of material housing distribution. Housing prices also rose dramatically, from 756 RMB per square meter floor space in 1991 to 2,937 RMB per square meter in 2005 (NBS 2007); this price increase to some degree indicates the development of commodity housing market.
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Source: China Statistic Yearbook 2006 Figure 2-5 Commodity Housing Market in China: Floor Space and Value of Sales, 19992005
Commodity housing became the major component in urban housing supply, reflecting the increasing importance of the market in housing provision. As shown in figure 2-6, the shares of commodity housing in the total housing supply increased steadily since 1998 in terms of the floor area under construction, the floor area constructed, and the total housing sale value; the numbers grew from 23% to 54%, from 11% to 33%, and from 27% to 60%, respectively (NBS 2007). Noticing that the shares of commodity housing in the sale value were always higher than those in the floor area (under construction and constructed), it suggested that the prices of commodity housing were higher than other types of housing supply (such as the government subsidized reform housing and affordable housing).
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Source: China Statistical Yearbook 2006 Figure 2-6 Commodity housing market in China: Share in Housing Supply, 1995-2005
Home ownership also increased greatly. Currently, about 74% of the city and town residents in China own a housing property (only the structural construct; land is still owned by the state) (Jia 2008). This is indeed a remarkable achievement, compared with the home ownership rate of the United States, which was 68.9% in 2005.9 With the housing market development, the urban landscape has been reshaped along with the adoption of advanced technology of construction. Both the appearance and quality of residential buildings have been improved. Perhaps the most prominent change is reflected by the growing building height. Low-rise buildings have been gradually replaced by mid-rise, mid-to-high-rise, and high-rise buildings, and since the late 1990s, high-rise buildings have become dominant in many Chinese cities.10
9
U.S. Census, http://www.census.gov/hhes/www/housing/hvs/annual05/ann05t12.html
According to the Design Code for Residential Buildings issued in 1999 by the Ministry of Construction, residential buildings that have 1-3 floors are low-rise, 4-6 floors are mid-rise, 7-9 floors are mid-to-high rise, and above 10 floors are high-rise Regarding the high-rise buildings, they are usually further divided into four kinds: 9-16 floors (less than 50 meters), 17-25 floors (less than 75 meters), 26-40 floors (less than 100 meters), and super-high-rise buildings with more than 40 floors
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Improvements in technology of construction are reflected in the ways that residential buildings are built. In the 1950s, residential buildings were basically lowrise (often fewer than three floors) brick-wood (or brick-concrete) structural buildings, copied from the Soviet Union.11 These buildings can still be found today, particularly in the neighborhoods of state-owned enterprises. Figure 2-7(a) and figure 2-8 (a) presents such examples. In the 1960s and 1970s, no obvious change in housing construction happened (figure 2-7 (b)), but a number of the makeshift houses (jianyi fang) were built to cater increasing population. The makeshift houses were often characterized by shallow foundations, thin walls, and common bathrooms and kitchens (figure 2-8(b)), reflecting the influences of turbulent economic and political situations as well as natural disasters in those years.12 At the end of the 1970s, however, higher residential buildings (7-8 floors) were developed in large cities like Beijing and Shanghai, as attempts to satisfy the increasing housing demand.13
(above 100 meters). http://baike.baidu.com/view/2683768.htm?fr=ala0_1
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http://news.dichan.sina.com.cn/2009/10/10/71722_1.html http://www.51yanxiu.com/jianzhu/ziliao/qita/jianzhu_295740.html http://news.dichan.sina.com.cn/2009/10/10/71722_1.html
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(a) 50-60s
(b) 70s
(c) 80s
(d) 90s
(f) 21st century (e) 21st century Photos were taken on March 17, 2010. The building ages were learned from local residents, about 12 kilometers to Tiananmen Square. Figure 2-7 Residential Building Evolution in Zhongguancun Area, Beijing
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(a) Late 50s
(b) 70s (Makeshift house)
(c) 80s
(d) late 90s
(f) left: 93, right: 03, back: under construction (e) 21st century (white building: 08-09, right: 80s) Photos were taken on March 20, 2010. The building ages were learned from local residents, about 6 kilometers to the city center. Figure 2-8 Residential Building Evolution in Qinchuan Neighborhood, Xi’an
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The 1980s and 1990s witnessed steady growth in building quality and height. The Ministry of Construction carried out a series of urban residential building design competitions and nationwide pilot residential projects to facilitate housing industrialization.14 Apparently, the overall building height increased, particularly in the late 1990s (figures 2-7 (c) & (d), figures 2-8 (c) & (d)). Since 1998, commodity housing development has entered a very fast growing period. With the adoption of new advanced building technologies (such as applications of steel frame, frame-shearwall structure, slab-column shearwall structure, etc), high-rise residential buildings rose dramatically in China. Twenty- to thirty- or even forty-floor residential buildings are commonly observed (figures 2-7 (e) & (f), figure 2-8 (e)), and redevelopment also occurred frequently to replace the old low-rise buildings and meet the growing housing demand (figure 2-8 (f)).
2.3
Spatial Structure
Rapid market development along with fast urbanization has brought two
fundamental changes in China’s urban landscape. One is the locational changes of land uses and the other is associated with changes in land use intensity. 2.3.1 Pre-Reform Prior to the economic reform, the urban space of China’s cities was recognized as monotonous, featured by highly mixed land uses and invariant building height and density.
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The Ministry of Construction was restructured and renamed as the Ministry of Housing and UrbanRural Development in 2008.
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The highly mixed land use pattern was mainly a result of the danwei-based spatial organization of China’s urban space. A danwei was the basic unit of working and living, usually a walled and mixed residential and industrial compound (Gaubatz 1995 & 1999). It provided not only a working place but also provided a series of public services and welfare such as housing, food distribution, education, health care, recreation, etc. (for detailed examples see Ding 2004). Therefore, each danwei formed a small self-sufficient community, with very diverse land uses inside a relatively small area. There were two major reasons for this. One was the fact that production was regarded to be the priority compared with consumption and danwei served as the basic unit of production; the other was that residents did not need to travel beyond the walls, thus, danwei minimized travel costs (Wu 1997, Gaubatz 1995 & 1999). As urban space grew, it spread through the increase of the cells of danwei. Therefore, the entire urban space featured highly mixed land uses. The invariant land development intensity, manifested by the flat building height across urban space, was due to the lack of market mechanism. Since land was of no value and assigned to each danwei for free on a basis of need, there was no incentive for danwei to economize land or substitute land with capital to improve land use efficiency. Land development intensity was irrelevant to the location. Tall buildings were developed mostly for political reasons rather than economic reasons. Therefore, the typical urban landscape in the pre-reform period was characterized by the walled danwei and similar low-rise brick buildings (Gaubatz 1995 & 1999).
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2.3.2 Post-Reform Land prices rose rapidly in the post-reform period, particularly in cities like Beijing, Shanghai, Shenzhen and many other cities in the coastal regions. Rising land prices forced industrial buildings and warehouses that were occupying the central locations to relocate to urban outskirts. For instance, manufacturing firms were forced out in Beijing in the middle 1990s, and the previously occupied land was redeveloped for residential, commercial, or mixed uses (Wu 1997, Gaubatz 1995 & 1999). Erection of skyscrapers in central locations has not only changed land use intensity but also reshaped urban landscape and created new city images. For example, development of the Chaoyang central business center (CBD) in Beijing has substantially increased the density in that area in the first decade of the 21st century. Recently, the former highest building in Beijing, Jingguang Center, which is 209 meters tall, has been overtaken by the China World Tower 3 (Guomao Sanqi), which is 330 meters tall with 88 floors, accompanied by the China Central Television building (234 meters tall) under construction and the Yintai Center (249.9 meters tall) as shown in figure 2-9.
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Overview of the CBD in Chaoyang District from Ritan Park. Source: http://www.danwei.org/architecture/beijing_new_skyline.php
Figure 2-9
Beijing’s Skyline
2.4
Urban Planning
Planning regulations affect urban spatial structure since land development is
often subject to certain requirements and limitations. Like many other cities in Western countries, urban planning affects urban spatial structure by regulating the types (residential, commercial, industrial, education, sport, public facilities, municipal utilities, road, green space, etc.) and intensity (density and FAR) of land development at given sites. It also specifies setbacks from the roads and developable land in a given lot. By combining the permitted FAR and percentage of developable land, the maximum building height and floor space can be derived. Figure 2-10 presents an example of a detail plan of one block in the Shunyi New City in Beijing. Within the boundary of the block, the attached table on the right side presents the allowable land uses, land area, FAR, floor space, building density,
21
building height, green space ratio, and the numbers of parking lots for each land plot. Land development should strictly follow these requirements in order to obtain required construction permits from the Department of Construction (or Planning).
Source: Shunyi Planning Office. http://www.guihua.bjshy.gov.cn/content.aspx?id=410 Figure 2-10 Detail Plan for Block 21, Plot 22, Shunyi District, Beijing
It should be noted that it is not unusual for developers to break these mandated requirements such as the building height caps and FAR controls to increase their profits. There are many reports that document developers’ violation of zoning requirements. However, due to lack of systematic records the total impact of the violations is hardly ever gauged. Planning regulations on land use could be beneficial if they serve to correct market failures; however, they may hinder the formation of an efficient urban spatial
22
structure. Under the market forces, developers optimize the combination of input factors as well as the output level based according to market rules. With strict regulations on land development intensity, such as building height and FAR controls, urban plans may act as constraints on housing services production, particularly on the substitution of capital and land. For example, suppose a 20-floor residential building is the best choice for the developer on a land lot given the technology of construction, land and capital prices, and other factors, but constructing a 20-floor building violates planning regulations and the developer has to reduce it by five floors. In this case, not only is the final housing output affected, but also the capital-land substitution is constrained and so the efficiency of resource utilization is harmed given that land and capital are not used in the most efficient way. Looking at the larger picture, citywide land use restrictions might divert urban land development from the economically efficient one and cause welfare loss.
23
Chapter 3:
Literature Review
This chapter reviews the theoretical understanding and empirical evidence of urban spatial structure. It starts with a review of the urban economic theory that reveals the declining phenomena of land and housing prices, and then it reviews the theory of housing services production, which is also important in understanding how urban landscape is shaped. Both theoretical framework and empirical evidence are discussed.
3.1
Urban Spatial Structure and Form
Theoretical understanding of urban spatial structure was formally developed
by Alonso (1964), Muth (1969) and Mills (1972). Based on the utility maximization for residents subject to the income constraint, housing price and housing consumption at a given location can be solved at the equilibrium when no one can improve their utility by simple relocation. Treating land as an input factor along with non-land capital in housing services production and taking the spatially variant housing prices given, land development intensity and land price are determined through profit maximization in competitive market. Therefore, urban spatial structure is characterized by declining housing and land prices and land development intensity with respect to distance from the city center (or the CBD). Following Brueckner (1987), the formal model starts with the utility theory in which residents maximize their utility by making tradeoffs between housing prices and transportation (commuting) costs, both depending on location. The model is
24
structured as follows. The city has a single CBD and residents commute to work. All residents earn identical income y and have the same strictly quasi-concave utility function v(c, q) , which depends on housing services consumption q and a numerical non-housing consumption c. Residents located at x kilometers from the CBD have to pay the transportation costs tx. By choosing q, residents maximize their utility subject to income constraint:
max v( y ? pq ? tx, q )
q
(1)
Locational equilibrium requires the first order condition of (1) and also requires that the maximized utility at all locations are identical, denoted by u. Using these two conditions housing price p and housing services consumption q can be solved as:
p = p ( x, y , t , u ) q = q ( x, y , t , u )
(2) (3)
It can be shown that p must decrease with x to balance the increasing transportation costs and q should increase with x as long as housing services are normal goods:
?p <0 ?x
(4)
?q >0 ?x
(5)
Housing services production requires land input L and non-land capital input K, and the production function is assumed to be concave and constant return, denoted by H ( K , L ) , in which the capital marginal productivity diminishes. Given the technology of constant return, the production function for each unit of land can be 25
written h( S ) ? H ( S ,1) , where S equals K / L and represents capital density, and
hS > 0 and hSS < 0 . 15 Assuming capital price n is spatially invariant, housing
producers maximize their profit per unit of land by choosing S:
max ? = ph ? nS ? r
S
(6)
In the competitive market, profit maximization requires the first order condition of (6) and also requires the maximized profit equals zero:
phS = n
(7) (8)
ph ? nS ? r = 0
Simultaneously solving (7) and (8) yields equilibrium solutions for land price
r and capital density S:
S = S ( p, n) r = r ( p, n)
(9) (10)
where p is already decided in the demand side problem by (2). By noticing that S and
r depend on x via p, it is derived from (7) and (8) that S and r both decline with x:
h ?p ?S =? S <0 ?x phSS ?x
(11)
?r ?p =h <0 ?x ?x
(12)
And the output of housing services per unit of land h also declines with distance x because of the declining S:
?S ?h = hS <0 ?x ?x
(13)
15
These conditions imply that elasticity of capital-land substitution is larger than zero.
26
Measuring housing services in terms of floor space, (13) suggests that the FAR decreases with x. Defining ? as the ratio of distance elasticity of land prices to the distance elasticity of housing prices and using (8) and (12), it yields:
?r ? = ?x ?p ?x
r ?p r h x = ?x x = ph = nS + r = 1 + nS > 1 p ?p p r r r x ?x x
(14)
This provides the theoretical relationship that will be tested in the first research question of this dissertation. Inequality (14) indicates that land prices are more elastic with respect to distance from the CBD than housing prices, or put differently, land prices decline faster than housing prices. Indeed, an alternative interpretation of ? is as the housing price elasticity of land price:
?r ? = ?x ?p ?x ?r ?p r r x = ?p ?x x = ?r ?p p p ?p ?x x x
r p
(15)
This suggests that the land price is elastic to housing price since a 1% change in housing price leads to a more than 1% change in land price. These theoretical advances in understanding urban spatial structure and form, particularly the predictions of declining land and housing prices toward the city fringe, have been supported by numerous empirical studies throughout developed and developing countries. 16 Coulson (1991) employed data from State College, a university town in Pennsylvania, which was regarded as an ideal laboratory place to
16
There are abundant evidences in the literature regarding the pattern of declining population density (such as Mills 1972 and Macauley 1985), which is also derived from the urban economic theory.
27
test the monocentric model for the city well satisfied the assumptions of the model. His estimated results reported significant and negative distance gradients of house rent, and more importantly, the price fell with distance from the CBD at a rate approximately equal to the increase in transportation costs, while holding all other attributes constant. McMillen (2002 & 2003) estimated the distance gradient of housing prices in Chicago using three different approaches (hedonic, repeat sale, and Fourier expansion) and the findings indicated significantly negative gradients and a strong return of centralization to the Chicago housing market. Mok et al. (1995) estimated Hong Kong’s sale prices of apartments using a hedonic approach and also found significant effect of distance. Alberson (1997) examined the value of land and houses in Sydney, Australia, and found that both prices declined exponentially with distance from the CBD during 1931-1968 and the curves were flattened, until 1970, when the curves became steeper again. Atack and Margo (1998) examined vacant land prices in New York City between 1835 and 1900 and found that land price per square footage declined significantly with distance from the CBD. There is also strong evidence for declining housing and land prices in developing countries. Dowall (1992) investigated the land market in Bangkok, Thailand, and found negative slopes of land prices with respect to distance from the CBD. Lewis (2007) examined the land market in Jakarta, Indonesia, using market price and the findings also suggested negative linkages between distance and land value, and the land price curve was flattened over time. In transitional countries such as Russian and Poland, the emerging market forces had reversed the urban spatial structure that was previously shaped by political reasons, and the negative-sloped
28
distance gradients began forming (Bertaud & Renaud 1997, Dale-Johnson et al. 2005). Studies in China suggested similar findings, particularly given the rapid market development since the late 1970s. Ding (2004)’s empirical estimations suggested Beijing’s urban form had been greatly modified by market forces: land prices declining from the city center at different speeds depending on land use types. It should be recognized that the literature reports a few studies showing either positive or insignificantly negative distance gradients of housing and land prices, though empirical studies that support the declining housing and land prices are overwhelming (Heikkial et al. 1989, Yiu & Tam 2004). Several reasons could account for this trend. First, the data used to estimate distance gradients did not all conform to the monocentric assumption. The trend of suburbanization and development of sub-centers, particularly after World War II, made the spatial pattern of cities more complicated. It is possible that each sub-center has its own distinctive submarket and its own distance gradients of housing and land prices, fitting well with the monocentric model, but negative distance gradients may not be found for the metropolitan area as a whole (Coulson 1991, Dubin & Sung 1987). Second, it is speculated that neighborhood effects could cause positive distance gradients in empirical studies (Richardson 1977). If the omitted neighborhood variables are positively correlated with distance, empirical tests will produce a positive distance gradient due to specification error. This may happen since neighborhood quality can hardly be fully captured due to data limitations. Finally, as one moves toward the CBD, if the overall effect of the increasing urban negative externalities (such as pollution, traffic congestions and noise) cannot be completely offset by the savings in
29
transportation costs, positive distance gradients of land and housing prices are likely to be obtained (Richardson 1977). In this case, the urban economic model should be extended to include the amenity argument, as Brueckner et al. (1999) showed in their research, household location patterns would be affected by whether there were strong presence of positive amenities in the city core and how strongly people preferred these amenities. To sum up, despite a great number of studies testing the negative distance gradients of housing and land prices, no study has examined the relationship between the distance gradients of housing prices and land prices, probably due to lack of data. By utilizing both housing and land prices from the same sites, this dissertation will contribute to the literature by empirically estimating and testing the relationship between the two declining prices.
3.2
Housing Services Production
Besides the urban economic theory, the other important aspect with regards to
the formation and evolution of urban spatial structure is housing services production (Muth 1964, Mills 1972, Koenker 1972, Sirman & Redman 1979, McDonald 1981). According to the theory of housing services production, land is an imperative input to produce housing services and land development intensity is largely determined by the relative prices of land and capital, based on the assumption that land and capital can substitute for each other to a certain degree to produce a certain level of housing services. Therefore, housing services production plays an important role in shaping the city’s capital density profile and the general urban landscape.
30
The theory of housing services production has two important implications. One is that the demand for land is viewed as a derived demand since people demand land for the purpose of producing housing services, and the other is related to the notion of capital-land substitution, which is a key element in forming urban spatial structure. As McDonald (1981) stated, the elasticity of capital-land substitution ( ? ) is “a determinant of the land rent gradient, the population density gradient, the factor share of land and housing capital and the elasticity of supply of housing both in the aggregate and on a particular site” (p. 190). The theory of housing services production is supported by numerous empirical studies that estimated ? . Muth (1964) provided the first empirical estimation using Federal Housing Administration (FHA) data of forty-seven cities in the United States and his estimates were around 0.5. After Muth’s seminal work, a substantial amount of studies followed, summarized in table 3-1. There is clearly no consensus on the value of ? . Most of the estimates ranged from 0.3 to 0.8 and were significantly smaller than unity. Only the estimates for Chicago (McDonald 1979, Clapp 1979) and for the Oregon part of Portland Metropolitan area (Thorsnes 1997) are exceptional, reporting close to or larger than unity ? . The majority of the studies employed the CES production function, while several studies employed the variable elasticity of substitution (VES) production function.
17
Comparatively, fewer studies were
conducted in developing countries and often reported lower estimates of ? . The only empirical study on capital-land substitution in China, to the author’s knowledge, was
While the CES assumes a uniform ? in housing production but does not restrict a priori to any specific value, the VES relaxes this assumption and allows ? changing with the combination of input factors. Nevertheless, there is no theory suggesting that VES is superior to CES; it is rather an empirical question of which one is better.
17
31
conducted by Ding (2004). By using data from Beijing, Ding (2004)’s estimates of ? fell between 0.3-0.4 during 1993-1995 and jumped to over 0.45 in 1996 and steadily rose since then. Ding (2004) also showed that ? varied across land use types.
Table 3-1
Studies Muth (1964 & 1971)
Empirical Estimation of Elasticity of Capital-land Substitution for Housing Production*
Estimates** 0.5-0.75 (CES) Cities/Regions 47 metropolitan areas, United States Ann Arbor, United States Brown County, United States Los Angeles, United States Chicago, United States Single-family houses from 31 metropolitan areas, United States 23 Metropolitan areas, Canada Data Collected 1966 1964-1966 1974 1972-1974 1970-1972 1969 1975-1976 1969-1971, 1970-1972 1969 1960 Sig. less than one Yes Yes Yes Yes No Yes Yes No Yes Yes
Koenker (1972) 0.71 (CES) Rydell (1976) 0.50 (CES)
Fountain (1977) 0.57 Clapp (1979) Rosen (1978) Arnott and Lewis (1979) McDonald (1979) 0.98 (CES) 0.43 (CES) 0.36 (CES)
1.13, 0.86 (CES, Chicago, United States IV) Single-family houses from 31 metropolitan area, United States
Polinsky and 0.45 (CES) Ellwood (1979) Sirmans et al (1979)
0.93-0.66 (VES) Santa Clara County, United States
0.52,0.55,0.46 Sirmans and (CES) Redman (1979) 0.55, 0.52, 0.45 (VES) Asabere et al 0.53 (CES) (1982) 0.227, 0.889, Kau and 0.455, 0.539 Sirmans (1983) (VES) Jackson et al 0.499 (1984) Dowall and 0.69 (CES) Treffeisen (1991) Ding (2004) Thorsnes (1997)
52 metropolitan areas, United States
1967, 1971, 1975
Yes
Accra, Ghana Dallas, Dayton, Louisville, and Stockton, United States Knoxville, United States Bogotá, Colombia 1966-1978 1970 1984-1989 1993-2000
Yes Yes Yes Yes Yes
0.32-0.74 (CES) Beijing, China
0.88 (CES), 0.81 Oregon part of Portland Metro, United (VES), 0.96 1985-1989 (CES, IV), 1.08 States (VES, IV) Erol and Güzel 0.078 (CES), Ankara, Turkey 2000 0.118 (VES) (2006)
No
Yes
* The table is an updated version based on McDonald (1981)’s review ** VES estimates are reported mean value
32
In theory, ? is affected by two different factors. One is technological change of construction and the other is planning regulations (such as zoning ordinance) that may impose restrictions on capital investment on a given land lot. The impacts of planning regulations depend on how rigorously they are implemented and to what extent the market forces can alter planning regulations. Empirically, there are also many studies providing evidence for the changes in ? (Simans & Redman 1979, Kau & Sirmans 1983, Jackson et al. 1984, Ding 2004, Erol & Güzel 2006). The importance of capital-land substitution in influencing urban spatial structure is well recognized (Muth 1964 & 1971, McDonald 1981, Kau & Lee 1976); in contrast, its explicit impacts on urban spatial structure have not been adequately examined. Kau and Lee (1976) derived the impacts of ? on the prices of housing services, the supply of housing services, and the demand for housing services. However, their conclusions are undetermined and depend on extra assumptions. For example, they concluded that land rent is negatively related to ? relying on the assumptions that the base year capital land ratio is unity and capital is expanding faster than land.18
18
Kau and Lee (1976) derived R (u ) = further derived the
? K (u ) 1+ ? ] r [ 1 ? ? L(u )
of
from the market equilibrium conditions, with respect to
and
partial
R(u )
?
:
? K (u ) 1+ ? ?R(u ) K (u ) =r ) , where R(u ) is the land rent at distance u , ? is the ] log( [ ?? L(u ) 1 ? ? L(u ) 1 , K and L are capital and land input, r is the capital price. By substitution parameter and ? = 1+ ? ?R (u ) K = 1 for the base year, the sign of is decided by whether land is growing faster assuming L ??
than capital. Besides the extra assumption of the initial capital-land ratio and the fast expanding speed of capital, another problem of their derivation is that it does not account for the impact of changes in
33
This dissertation will extend the understanding of impacts of housing services production on urban spatial structure by explicitly modeling housing services production function and analyzing impacts of ? . The investigation on the impacts of housing services production in general and the impacts of capital-land substitution in particular on urban spatial structure constitutes the major contribution of this dissertation to the literature. I will examine the impacts by theoretical analysis, numerical simulation, and empirical estimation.
K (u ) . In fact, if ? changes, producer’s decision on inputs combination would also L(u ) adjust and further should affect the equilibrium land price R (u ) .
? on the ratio of
34
Chapter 4:
Housing Services Production and Urban
Spatial Structure
This chapter examines the linkage between housing services production and urban spatial structure. More specifically, it analyzes the impacts of capital-land substitution. Based on a CES production function for housing services, I derive the directions of the changes of urban spatial structure measured by the distance gradients of land prices and capital densities, the housing output per unit of land, and the degree that land prices decline faster with respect to distance from the CBD than housing prices, brought by a change in capital-land substitution.
4.1
The CES Production Function for Housing Services
It is assumed that housing services are provided by a CES production function
in which land and capital constitute the two inputs.19 It is specified as:
H ( K , L) = ? [?K
??
+ (1 ? ? ) L ]
??
?
1
?
(16)
where H is the output of housing services; K is the non-land capital input; L is the land input, ? is the scale parameter called the neutral technological parameter and is positive; ? is the non-neutral distribution parameter, reflecting the intensiveness of capital use in production and should be positive and smaller than unity. ? is the
19
The CES production function was introduced by Solow (1956) and formally developed by Arrow et al. (1961).
35
substitution parameter, ranging from -1 to infinity. The elasticity of capital-land substitution ? is given by:
? =
1 1+ ?
(17)
The CES production function describes a production technology that has a constant return to scale and constant elasticity of substitution between land and capital.20 In addition, it is demonstrated that the CES production function also has a property of positive effect of capital-land substitution on housing output and this can be written: 21
H ? > 0 (or H ? < 0 )
(18)
Let h = H / L , and S = K / L , (16) yields the CES function for housing output per unit of land:
h( S ) = ? [?S
??
+ (1 ? ? )]
?
1
?
(19)
Accordingly, the following relationship holds:22
20
The CES function includes the Cobb-Douglas function, Leontief production function (perfect complements), and linear production function (perfect substitutes) as special cases. When ? ? 0 (or ? ? ? ), H ( K , L) = ? min{K , L} , it becomes the Leontief production function, which assumes no
when ? ? ? ( ? ? ?1) , H ( K , L) = ? [?K + (1 ? ? ) L] , it implies that the extent of substitution is infinite and the isoquants become straight lines.
21
substitution between the two input factors and the isoquants are right-angle shaped; when ? ? 1 (or ? ? 0 ), H ( K , L) = ?K ? L1?? , it becomes the Cobb-Douglass production function; and
in
Brown (1967, 57) had shown that all relevant limits are positive and tentatively concluded that a rise ? raises the output rate by deriving all , but his proof does not assure that H ? < 0 for all values
of variables and other parameters. This potential problem will be addressed by simulation analysis in next chapter.
22
In this dissertation, I use h? to denote the partial derivative of h with respect to
?
derived directly
from the CES function for housing production (for a given set of input factors of production), and I use
36
h? > 0 (or h? < 0 )
(20)
In theory, the value of ? can range from zero to infinity in the CES production function, but for housing services production, ? should be positive and no larger than unity. This is because of the following reasons. First, given the observed capital-land substitution in housing construction, ? should not be zero but larger than zero; in other words, the Leontief function does not fit. Second, ? should not be larger than unity, as shown in (19), when ? > 1 (or ? 1 < ? < 0 ), as S ? ? ,
h ? ? , and as S ? 0 , h ? ? (1 ? ? )
? 1
?
. This implies that on a given land lot of fixed
size, the output of housing services will become indefinitely large as capital input keeps increasing, and when the capital input approaches zero, the output will still reach a positive lower limit. This is certainly not the case for housing services production. In reality, due to technological constraints, it is impossible to produce indefinitely large housing output on a given piece of land. Also, it is unrealistic to produce housing structure only by land input without any capital input. On the contrary, when ? < 1 , using the CES production function to describe housing services production makes sense, as shown in (19), when ? < 1 (or ? > 0 ), as S ? ? , h ? ? (1 ? ? )
? 1
?
, and as S ? 0 , h ? 0 (Arrow et al. 1961). This implies
that when a large amount of capital is invested on a fixed piece of land, the output of housing services will reach an upper limit, and when no capital is invested, no
?h to denote the partial derivative of h with respect to ? derived from the equilibrium solution of h ?? ?h ?S (after input factors adjust to ? ); in fact = hS + h? . ?? ??
37
housing structure will be produced. This is intuitively true given the fact that one can neither build indefinitely tall buildings nor build houses without capital but only with land. Brown (1967) provided an insightful interpretation of these behaviors of the CES production function from a technological point of view. According to Brown,
? > 1 indicates a technology that treats the input factors as resembling each other.
When holding one input constant and increasing the other one indefinitely, the technology allows the expanding factor to easily substitute for the constant factor, and so that both factors seem to be increasing indefinitely and the output increases also indefinitely. On the other side, ? < 1 indicates a technology that views the factors as dissimilar to each other and difficult to substitute one for another, and so the output reaches an upper limit even though one input expands indefinitely. In housing services production, capital and land are dissimilar since houses are build on land with capital, and the output of housing services is to a certain degree constrained by land. The argument of 0 < ? < 1 in housing services production is also supported by empirical evidence (see chapter 3). Therefore, this dissertation examines the impacts of ? only when 0 < ? < 1 is in the simulation analysis and tests the estimates of ? in the empirical analysis.
38
4.2
Impacts of Elasticity of Capital-Land Substitution
This section examines analytically the impacts of ? on urban spatial structure
under the competitive market in the open city case.23 First of all, I obtain the explicit solutions for S, r, h, and ? at the market equilibrium. Substituting the housing production function per unit of land by (19) for (6) and solving the profit maximization problem by using the two conditions (7) and (8) yield land price r and capital density S as:
n ?(1?? ) ?? ? ) p?? ]1?? S =[ 1? ? (
n ?(1?? ) n ?(1?? ) ?? ?? ? ) ( ) ? ? p?? p?? ?1 1?? ? n[ r = p? [(? [ ] + (1 ? ? )] ]1?? 1? ? 1? ? (
(21)
(22)
where p is the housing price already decided in the housing demand side question, and n is the spatially invariant capital price. Replacing S in (19) by (21), the housing output per unit of land h at equilibrium is known:
? ? ? ? 1?? ? h=?? ?1 ? ? ( n )1?? ? ? ? p?? ? ?
? 1??
?
(23)
Replacing S and r in (14) by (21) and (22), ? can be solved:
23
The author would like to argue that the open city case (which assumes free migration) approximates better the reality compared with the closed city case (which assumes no migration at all), since modern cities are hardly closed given the advances in transportation and communication. In particular, China is currently experiencing fast urbanization and witnessing mass migration among cities and from rural to urban areas. It is estimated that there are 150-200 million internal migrants in China (Ding and Zhao, forthcoming). Therefore, this dissertation focuses on the impacts of ? in the open city case.
39
? =1+
1 p? p?? ? ( ) ?1 n n
1
(24)
More generally, using the relationship between ? and ? by (17), (21)-(24) can be rewritten as:
S = S ( p , n, ? , ? , ? )
r = r ( p , n, ? , ? , ? )
(25) (26) (27) (28)
h = h( S ( p, n, ? , ? , ? ), ? , ? , ? )
? = ? ( S ( p, n, ? , ? , ? ), r ( p, n, ? , ? , ? ), n)
In the open city case, which assumes exogenous utility level u, the housing price p and housing consumption q are not affected by changes in ? (or ? ). But equations (25)-(28) reveal that a change in ? will affect capital density, land price, the housing output per unit of land, and the ratio of the two distance elasticities.24 Following the approach of total differentiation used by Brueckner (1987), I derive the directions of impacts of ? on r, S, and h in a way that does not require using the complicated solutions by (21), (22), and (23). Replacing h in (8) with (19) and totally differentiating (8) with respect to ? yields:
p[hS
24
?S ?S ?r + h? ] ? n ? =0 ?? ?? ??
(29)
It should be noted that there are differences between ? and ? . As a production parameter, ? describes a production technology together with other parameters and the specified function form, and thus ? will only change if technology changes. ? is defined as the proportional change of input factors to the proportional change of relative prices of input factors, reflecting the substitutability between input factors. Therefore, besides technology improvement, policies and regulations on land use could also affect the value of ? . Despite these differences, analytical analysis in this dissertation examines the impacts of
? by employing the relationship of ? =
1 by (17). 1+ ?
40
As observed in (29), ? affects h both as a parameter of the production function ( h? ) and by affecting S ( hS ?S ). Since phS ? n = 0 by (7), (29) yields: ?? (30)
?r = ph? > 0 ??
Inequality (30) holds because h? > 0 by (20) and it implies that an increase in
? leads to increase in r at each location.
Due to capital-land substitution in housing services production, developers tend to use more capital to substitute for land when land becomes more expensive. So, an increase in land price leads to an increase in capital density. This indicates a positive relationship between ? and S, formally expressed as:
?S ?r =? >0 ?? ??
(31)
where ? represents the impact of change in land price on capital input, a substitution
?1 effect between capital and land. In fact, ? = (?MRTS ?S |? =0 )
1 , where MRTS is the n
marginal rate of technology substitution, and MRTS ?
H L 25 . Since it is assumed that HK
hS > 0 and hSS < 0 , and MRTS ?
H L h ? ShS , it is easy to have ?MRTS ?S > 0 . = HK hSS
Thus ? is intrinsically a positive number. Replacing h in (12) with (19) and totally differentiating (12) with respect to ? yields:
25
?1 ? = (?MRTS ?S |? =0 )
? (h hS ) 1 1 1 ? 1 ?1 =[ ? 1] |? = S ? ? |? =0 > 0 =0 n ?S n n 1+ ? 1+ ?
41
? 2r ?h ?p ?S ?p = = (hS + h? ) <0 ?x?? ?? ?x ?? ?x
(32)
Inequality (32) holds because
?p < 0 by (4), hS > 0 as assumed property of ?x
the production function,
?S > 0 by (31), and h? > 0 by (20). Inequality (32) ??
indicates that an increase in ? leads to a steeper land price curve. It is also shown that ? affects the distance gradient of land prices by affecting the housing output per unit of land (
?h ). ??
For the impact of ? on distance gradient of capital density, totally differentiating (31) with respect to x yields:
?2S ? 2r =? <0 ?x?? ?x??
(33)
Inequality (33) indicates that an increase in ? also leads to a steeper capital density curve. As mentioned above, the impact of ? on h is composed of two parts, since ? affects h as a parameter in producing housing services and by affecting S:
?h ?S = hS + h? > 0 ?? ??
(34)
Inequality (34) holds because hS > 0 as assumed property of the housing production function,
?S > 0 by (31), and h? > 0 by (30). Inequality (34) indicates ??
that as ? increases, the housing output per unit of land increases at any location within the urban area.
42
Intuitively, since ? positively affects land prices and the distance gradient of land prices but does not affect housing prices in the open city case, an increase in ? leads to steeper land price curve and thus positively affects ? , the degree that land prices are more elastic with respect to distance from the CBD than housing prices. Here is the proof. In the solution of ? by (24), if
p?? > 1 , it is easy to have:26 n
(35)
?? >0 ??
In the open city case, the capital-land substitution also affects the city size in terms of territory (denoted by x as the city boundary) and population (denoted by N). Following Brueckner (1987), the spatial equilibrium of the urban space requires two conditions. One is that at the city boundary x , the urban land price equals to agricultural land price ra ; and the other is that all of the residents N fit exactly into the urban boundary with their housing demand met by housing provision. By specifying the housing production function in the CES form, these two conditions are written as follows:
r ( p ( x , y, t , u ), n, ? , ? , ? ) = ra
(36) (37)
?
x
0
h( S ( p( x, y, t , u ), n, ? , ? , ? ), ? , ? , ? ) ?xdx = N q ( x, y , t , u )
where D( x, y, t , u, n, ? , ? , ? ) =
h( S ( p( x, y, t , u ), n, ? , ? , ? ), ? , ? , ? ) is the population q ( x, y , t , u )
density, ? is a constant parameter of radius of land that are available for housing services production.
26
Since usually p>>n, so
p?? > 1 is easy to hold. n
43
The utility level u and agricultural land price ra are exogenously determined. Assuming all other parameters are constant (including y, t, u, n, ? , ? ), keeping only the interested variables and parameters, (36) and (37) can be simplified as:
r ( x , ? ) = ra
(38) (39)
?
x
0
h( S ( x, ? ), ? ) ?xdx = N q( x)
Recursively solving (38) and (39) yields the solutions for x and N, respectively. To investigate the impact of ? on x , totally differentiating (38) with respect to ? yields:
?r ?x ?r + =0 ?x ?? ??
Given that
(40)
?r ?r > 0 by (30) and < 0 by (12), and x is only affected by ? ?? ?x
in (38) as all other parameters are constant, so it can be inferred from (40) that:
dx >0 d?
(41)
Totally differentiating (39) with respect to ? yields:
x ?x ?S h( S ( x, ? ), ? ) ?x dN ?x +? (hS + h? )dx = 0 q ( x) q( x) d? ?? ??
(42)
Given that
?x > 0 by (41), hS > 0 as assumed property of housing ??
production function, that: dN >0 d?
?S > 0 by (31) and h? > 0 by (20), it can be inferred from (42) ??
(43)
44
Therefore, inequalities (41) and (43) indicate that an increase in ? leads to increases in both the city’s geographical size x and its population N. To sum up, under the competitive market in the open city case, the elasticity of capital-land substitution does not affect housing price and housing consumption, but positively affects the land price (
?r ?S > 0 ) and capital density ( > 0 ) at any ?? ??
location within the urban area, negatively affects distance gradients of land prices and capital densities (
? 2r ?2S < 0 and < 0 ), positively affects the housing output per ?x?? ?x??
unit of land (
?h > 0 ), positively affects the ratio of the two distance elasticities ??
(
?? > 0 ), and positively affects the city’s geographical size and population size ??
(
dN dx > 0 ). > 0 and d? d?
These impacts of a change in the elasticity of capital-land substitution can be
intuitively interpreted as follows. As ? increases, it eases substitution between land and capital and raises housing output at each location. Increases in output in turn raise the residual land prices under the competitive market. Moreover, since housing prices (output prices) decline with distance from the CBD, increases in the residual land prices are higher at locations closer to the CBD as compared with in suburbs, and so the land price curve becomes steeper. Further, as land becomes more expensive, capital investment rises to substitute for land, and relatively more capital is invested at central locations where land prices increase more, and so the capital density curve also rises and becomes steeper. The gaps between the declining housing and land
45
prices also increase, for the land price curve becomes steeper with the housing price curve held unchanged. The urban boundary expands, as a consequence of the higher urban land price curve, and the population increases (migrant from other cities or rural areas) to fill in the surplus of housing output so as to maintain the utility level.
46
Chapter 5:
Numerical Simulation
The purpose of numerical simulations is twofold. First, it verifies the predicted impacts of housing services production on urban spatial structure, particularly the derived impacts of capital-land substitution. Second, it examines the magnitudes of these impacts by a series of estimations and simulations. I estimate the housing production function (elasticity of capital-land substitution and other production parameters), spatial distributions of housing prices, land prices, capital densities, and the housing output per unit of land, and then I calculate the marginal impacts of capital-land substitution. The estimated impacts of a 1% change of the elasticity of capital-land substitution include effects on land prices, capital densities, the housing output per unit of land (or the FARs), the ratio of the two distance elasticities , the share of land cost in total property value, and the welfare implications in terms of aggregated values of land and housing output.
5.1
Impacts of Capital-Land Substitution
The impacts of ? on land price, capital density, housing output per unit of
land (or the FAR), and the ratio of the two distance elasticities, implied by the partial derivatives of
?r ?S ?h ?? , , , and , respectively, can be solved as explicit ?? ?? ?? ??
functions of p, n, ? , ? , and ? directly from the equilibrium solutions of S, r, h, and
? by (21), (22), (23), and (24) .
47
The impacts of ? on distance gradients of land prices and capital densities (
?2S ? 2r ?2S ? 2r ) are examined by verifying signs of and < 0 and <0. ?x?? ?p?? ?p?? ?x??
This is based on the fact that r and S are linked to distance only through p by (11) and
?2S ? 2r and can be written as: (12), and ?x?? ?x??
? 2r ? 2 r ?p = × <0 ?x?? ?p?? ?x ?2S ? 2 S ?p = × <0 ?x?? ?p?? ?x
The solutions for
(44)
(45)
?r ?h ?S ?? ?2S ? 2r , , , , and are very ?? ?? ?? ?? ?p?? ?p??
complicated (see Appendix I) and Mathematica is used to determine their signs with different combinations of parameters of p, n, ? , ? , ? . The value of p is chosen to change from 1,000 to 30,000, based on observations of housing prices from the Beijing data, in which the lowest housing price was 2,034 RMB per square meter, the highest was 19,478 RMB per square meter, and the mean was 6,888 RMB per square meter (see table 6-2). Capital price n is normalized to unity. Value ranges of the three production parameters ? , ? , ? are determined based on their theoretical values. Since ? is a positive scale parameter, its value should be irrelevant to the impacts of ? , and so the range of ? is taken from 0.1 to 3.0 for convenience without loss of generality. ? is a positive number less than unity in the CES function and so its range is taken from 0.01 to 0.99, and the value
48
range of ? is also taken from 0.01 to 0.99 (correspondingly ? varies from 0.01 to 99) (see Chapter 4). There are constraints on values of p, n, ? , ? , ? that can be chosen implied in (21) and (22). These constraints ensure that S is a positive and r is not negative and they are: ( n ?(1?? ) ) ?? > 0 p??
(
(46)
n ?(1?? ) n ?(1?? ) ) ?? ( ) ?? ? ? ? p?? p?? ]?1 + (1 ? ? )] 1?? ? n[ ]1?? ? 0 r = p? [(? [ 1? ? 1? ?
(47)
Table 5-1 reports the summary of the simulated results. These results are as expected and consistent with what the theory predicts (see Chapter 4).
Table 5-1 Signs of Relevant Partial Derivatives by Simulation
?S ??
p =1000,2000,3000,…,28000,29000,30000 n =1 ? =0.1, 0.2,0.3,…,2.9,3.0 ?=0.01,0.02,0.03,…,0.99 ?=0.01,0.02,0.03,…,0.99
?r ??
? 2S ?p??
? 2r ?p??
?? ??
?h ??
>0
>0
>0
>0
>0
>0
A close examination of these simulated results reveals a non-linear relationship between ? and urban spatial structure variables such as S, r, and ? (Appendix II). For instance, for the chosen ranges of p, n, ? , ? , ? , these partial derivatives increase exponentially along with ? when p, ? , ? are large. Holding ? , ? and ? unchanged and increasing p, impacts of ? on S and r also increase accordingly, and this is consistent with the positive signs of the secondary partial
49
derivatives (
? 2r ?2S > 0 and > 0 ). However, holding ? , ? and ? unchanged ?p?? ?p??
and increasing p, the impact of ? on ? decreases, and this is consistent with the theoretical result that as moving toward the city center ? decreases with p.
5.2
Marginal Effects of Capital-Land Substitution
The above simulated results reveal that the marginal effects of capital-land
substitution on urban spatial structure can be substantial. This section will estimate these marginal effects based on the Beijing data. This is carried out by estimating the housing production function (elasticity of capital-land substitution and other production parameters), spatial distributions of housing prices, land prices, capital densities, and the housing output per unit of land, calculating the marginal impacts of the elasticity of capital-land substitution, and finally determining the welfare implication by estimating aggregated values of land and housing output.
5.2.1 Housing Price Distribution and Production Function
Using data from Beijing (see chapter 6 for detailed data description), housing prices are estimated as an exponential function of distance from the city center— Tiananmen Square.
p = exp(9.234732 ? 0.0400622 x )
(48)
(36.94)
(-13.00)
R-sq=0.3904, Obs.=266.
50
where p is the housing price per square meter floor space in RMB and x is the distance from Tiananmen Square in kilometers. Figure 5-1 illustrates this estimated housing price curve as compared to observations from the sample. The estimated housing price is 10,247 RMB per square meter at the city center and drops gradually with distance from the city center.
Figure 5-1
Estimated Housing Prices over Urban Space
To determine the CES housing production function, three parameters need to be determined. Among them, ? is the key parameter and is estimated by several approaches. The estimates suggest robust results ranging from 0.37 to 0.65 (see chapter 6 for more details). Based on these estimates, 0.5 is chosen for ? in the baseline scenario. With ? determined, the other two parameters ? and ? are then estimated by multiple approaches as well, and their estimates fall into the interval of 0.000316-0.000953 and 0.99975-0.99996 (see Appendix III for more details). Based on these estimates, ? and ? are taken 0.0005 and 0.99995, respectively, with consideration on the fitness of the simulated land prices and housing output per unit
51
of land to the real observations.27 It should be noted that land prices and housing output per unit of land generated by this simulation are respectively overestimated and underestimated to certain degrees when compared with real observations (figure 5-2 and figure 5-3). This is due to the gaps between the reality and the theoretical model. Nevertheless, these errors are regarded as acceptable, for this simulation focuses on demonstration of relative changes caused by 1% change in the elasticity of capital-land substitution rather than the absolute changes. Estimations are carried out under the assumption that there is a 30% marginal profit in land development. This number makes the estimations fit better the data than a zero profit assumption. This assumption makes sense because of two reasons. First, although markets are emerging at a fast rate in China, specifically in Beijing, they are far from the competitive markets. Second, there is evidence suggesting that a substantial level of profits can be made from land development.28
Ideally, the simulated land price and housing output per unit of land would both fit the real observations with the estimated housing prices and production parameters, if the analytical model can perfectly explain the reality. However, models are simplifications of the real world and rely on certain assumptions, and the analytical model used in this study is not exceptional. Therefore, simulations based on the analytical model cannot fully fit real data. In this case, many of the model assumptions may be not satisfied in Beijing, such as the competitive market, market equilibrium conditions, zero profit condition, unity capital price, constant return to scale, and market equilibrium. Due to the gaps between the reality and theoretical model, it is hard to find a pair of ? and ? to generate simulated land price and housing output per unit of land that both fit the data well. So the strategy used here is to pick up a pair of ? and ? from the ranges of estimates of these two parameters (see Appendix III) that generate acceptable simulated land price and housing output per unit of land.
28
27
The 30% average profit ratio of sales is based on a survey of real estate profit done in China by the Ministry of Finance in 2005, which reported 26.79% profit ratio of sales of 39 real estate developers. Retrieved on July 13, 2010, from http://finance.sina.com.cn/g/20061108/14573060647.shtml
52
Figure 5-2
Simulated Land Prices over Urban Space
Figure 5-3
Simulated Housing Output per Unit of Land (FAR) over Urban Space
5.2.2 Marginal Impacts of Elasticity of Capital-Land Substitution
The baseline for estimating marginal effects of capital-land substitution is chosen as ? 0 = 0.5 and marginal effects are calculated by both a 1% increase and a
53
1% decrease in ? , respectively. That is, there is one baseline scenario and two simulated scenarios ( ? 1 = 0.505 and ? 2 = 0.495 ).29 Table 5-2 reports simulations of variables of interest in the three scenarios at selected locations. Besides r, S, h, and ? that can be computed directly by (21), (22), (23), and (24), the share of land cost in total property value (includes both land and land improvements), denoted by ? L , and the city’s geographical size x are also concerned. In the baseline scenario, r drops from 15,978 RMB in the city center to 150 RMB per square meter at the city boundary x0 =27.73, where the urban land price intercepts the agricultural land price of 150 RMB per square meter (figure 5-4).30 This simulated result of city size is reasonable, given that currently urban development in Beijing is expanding from the fifth ring road to the sixth ring road.31 S drops from 17,876 RMB per square meter to 989 RMB per square meter and h (or the FAR) decreases from 4.72 to 0.47, from the city center to the urban fringe (figure 5-5 and figure 5-6). Compared with observations in the sample, capital density and the FAR are both underestimated to certain extents in this simulation.
In reality, it is unlikely that only ? changes with the other two parameters held. For example, advances in technology facilitate capital-land substitution as well as affect the other two production parameters ? and ? . This is why in this simulation analysis, a small change (one percent) in ? is manipulated. The production function will no longer generate reasonable results if ? changes too much.
29 30
The agricultural land price is based on estimation of land acquisition projects in 2004 in Beijing provided by the Land & Resource Bureau and related policy documents on the minimum compensation. The land acquisition price was about 1.52 million per hectare (Zhao 2003, Thesis of Master degree). Beijing has five ring roads: while the second ring road is basically built on the ruins of the old city wall at about 3-5 kilometers from the city center, the other four rings are located respectively about 3-5 kilometers, 6-10 kilometers, 10-15 kilometers, 20-25 kilometers, 30-35 kilometers away from Tiananmen Square (as shown in figures 6-3 and 6-5).
31
54
Table 5-2
Simulated Impacts of Elasticity of Capital-land Substitution
land price r (RMB per square meter) capital density S (RMB per square meter) S0 S1 % change S2 % change S0 S1 % change S2 % change 0 km 15978 18946 18.6 13518 -15.4 17876 21486 20.2 14921 -16.5 5 km 10177 12027 18.2 8638 -15.1 14266 17080 19.7 11954 -16.2 10 km 6051 7122 17.7 5157 -14.8 11001 13109 19.2 9260 -15.8 15 km 3237 3790 17.1 2773 -14.3 8046 9533 18.5 6812 -15.3 20 km 1444 1679 16.3 1245 -13.8 5373 6318 17.6 4583 -14.7 25 km 437 502 15.0 381 -12.8 2955 3435 16.2 2549 -13.7 30 km 29 33 12.0 26 -10.6 768 869 13.2 680 -11.5 lamda (?) housing output per unit of land h (FAR) S0 S1 % change S2 % change S0 S1 % change S2 % change 0 km 4.72 5.64 19.4 3.96 -16.0 2.12 2.13 0.7 2.10 -0.7 5 km 4.16 4.96 19.1 3.51 -15.8 2.40 2.42 0.8 2.38 -0.7 10 km 3.55 4.21 18.6 3.00 -15.5 2.82 2.84 0.8 2.80 -0.8 15 km 2.87 3.39 18.1 2.44 -15.1 3.49 3.52 0.8 3.46 -0.8 20 km 2.12 2.48 17.3 1.81 -14.5 4.72 4.76 0.9 4.68 -0.9 25 km 1.29 1.49 16.1 1.11 -13.6 7.77 7.84 0.9 7.70 -0.9 30 km 0.37 0.42 13.1 0.33 -11.4 27.05 27.32 1.0 26.79 -1.0 share of land cost ( ? L) x (km) S0 S1 % change S2 % change S0 S1 % change S2 % change 0 km 0.33 0.33 -0.7 0.33 0.7 5 km 0.29 0.29 -0.8 0.29 0.8 10 km 0.25 0.25 -0.8 0.25 0.8 27.73 27.98 0.9 27.47 -0.9 15 km 0.20 0.20 -0.8 0.20 0.8 20 km 0.15 0.15 -0.9 0.15 0.9 25 km 0.09 0.09 -0.9 0.09 0.9 30 km 0.03 0.03 -1.0 0.03 1.0 Note: S0, S1, and S2 are respectively the scenarios with sigma=0.5, 0.505, and 0.495.
As expected, the simulated ? is larger than unity at any location, consistent with the analytical result and indicating that land prices decline faster than housing prices. Moreover, this simulation also indicates that ? increases with x (figure 5-7). The positive relationship between ? and x can be easily derived from the solution of
? by (23), noting that p is in the denominator and p decreases as x increases by (3).
55
The fact that ? is smaller than unity leads to a decreasing share of land cost in total property value towards the city edges.32 This expected phenomenon is also supported by the simulated results (figure 5-8 and table 5-2). The simulated results show that the spatial variation of the share of land cost is remarkable. For example, land cost accounts for 33% of the total property value at the city center, but the number drops to 3% at the location 30 kilometers away (figure 5-8 and table 5-2). This implies profound policy implications, particularly for property taxation and assessment. In a two-rate property tax system in which land and improvements are imposed by different tax rates, the conventional method to determine land value often assumes a fixed share of land value in the total property (such as 20%) for all properties across the urban space. According to the above simulation, it has been demonstrated that a fixed portion of land value causes inaccurate assessment of land value and leads to efficiency loss. The declining share of land cost in total property value ( ? L ) with distance from the CBD can be intuitively understood as the consequence of two different effects. One is the price effect and the other is the substitution effect. The price effect is related to the fact that land prices decline faster than housing prices with respect to distance and the substitution effect refers to the increasing intensity of land use as moving toward city edges due to the dropping land prices. Theory suggests that when
? < 1 the price effect overwhelms the substitution effect, and the simulation reveals
consistent results.
32
?L
can be derived to be
?L = 1?
n p?? ? ?? L ( ) and it is easy to derive that < 0 when p? n ?x
? < 1.
56
Now, look at the impacts caused by 1% change in ? by comparing the two simulated scenarios to the baseline scenario. First of all, results of the simulation suggest that land prices and capital densities are very sensitive to ? , particularly at the central locations. As ? increases (or decreases), both land price curve and capital density curve rise (or lower) and rotate clockwise (or counterclockwise), in accordance with the analytical results that ? positively affects land prices and capital densities and negatively affects their distance gradients (figure 5-4 and figure 5-5). At the city center, a 1% increase in ? leads to 18.6% increase (or 15.4% decrease) in land price and 20.2% increase (or 16.5% decrease) in capital density, at locations 30 kilometers away, the impacts of a 1% change in ? diminish to 10-13% change in land price and capital density (figure 5-4, figure 5-5, and table 5-2). Second, housing output per unit of land (or the FAR) is also highly responsive to ? , particularly in the central locations, as illustrated by figure 5-6. A 1% change in
? leads to 19.4% increase or 16.0% decrease in the FAR at the city center, and the
impacts decrease to 13.1% increase or 11.4% decrease at locations 30 kilometers away. This indicates that ? has considerable impacts on the urban housing structure at any location and it can be inferred ? must have large impact on the aggregated total housing output in the city.
57
RMB per square meter
Land price (r)
17500 15000 12500 10000 7500 5000 2500 5 10 15 20 25 30 distanceHkmL
Sigma=0.505 Sigma=0.500 Sigma=0.495
Figure 5-4
Simulated Land Prices in Three Scenarios
RMB per square meter
Capital Density (S)
20000 15000 10000 5000 distanceHkmL
Sigma=0.505 Sigma=0.500 Sigma=0.495
5
10
15
20
25
30
Figure 5-5
Simulated Capital Densities in Three Scenarios
Figure 5-6
Simulated Housing Out Put per Unit Land (FAR) in Three Scenarios
58
Comparatively, ? , ? L , and x are less sensitive to ? . A 1% change in ? in general leads to less than 1% change in these three variables. The small impact of ? on x is easy to understand given the diminishing impacts of ? on urban land prices when moving towards the urban edges. The small impact of ? on ? is probably because ? is a ratio of the marginal changes already. Nevertheless, the directions of changes confirm the analytical results that ? positively affects ? and x (figure 5-7, figure 5-9 and table 5-2). In contrast, ? L is negatively affected by ? (figure 5-8 and table 5-2). To understand this intuitively, note that the larger ? implies the larger degree that land is substituted with capital, thus as ? increases, more capital is used and the share of land value decreases.
lamda 17.5 15 12.5 10 7.5 5 2.5 5 10
Lamda (?) Sigma=0.505 Sigma=0.500 Sigma=0.495
1
15 20 25 30
distance HkmL
Figure 5-7
Simulated Ratios of the Two Distance Elasticities in Three Scenarios
59
Figure 5-8
Simulated Shares of Land Cost in Total Property Values in Three Scenarios
RMB per square meter 500 400 300 200 100
Land Price (r)
Sigma=0.505 Sigma=0.500 Sigma=0.495
ra
distanceHkmL
26
27
28
29
30
x2 x0 x1
Figure 5-9 Simulated Urban Boundaries in Three Scenarios
To sum up, results of the simulated three scenarios suggest that ? has substantial impacts on land prices, capital densities, and the housing output per unit of land (a 1% change in ? leads to 10-20% change in r, S, and h). These impacts are larger at central locations and diminish with distance. Comparatively, ? has smaller impacts on the ratio of the two distance elasticities, the share of land cost in total property value, and the city size. 60
5.2.3
Social Welfare Impacts
Shift and rotation of the land price curve caused by a change in capital-land substitution have social welfare implications. Land is one of the important sources for local government to obtain revenue in China through collecting land leasing fees and in the United States through levying property (land) tax (Oates 2001, Ding & Lichtenberg 2010). The welfare impacts of capital-land substitution are also reflected in the overall changes in the aggregated housing output, housing value, and population scale. The total impacts caused by 1% changes in ? , on the total land value, total housing output, total housing value, and total population capacity at the equilibrium of urban space are determined by the following equations, respectively:
TotalLandValue = ? r ( p ( x), n, ? , ? , ? )2?x? * 1,000,000dx
0 x
(49) (50)
TotalFloorSpace = ? h( S ( p ( x); n, ? , ? , ? ); ? , ? , ? )2?x? * 1,000,000dx
0
X
x
TotalHou s eValue = ? p( x)h( S ( p( x); n, ? , ? , ? ); ? , ? , ? )2?x? *1,000,000dx (51)
0
TotalPopCa pacity = ? h( S ( p ( x); n, ? , ? , ? ); ? , ? , ? )2?x? * 1,000,000 / ?dx (52)
0
x
where ? denotes the percentage of land that can be used for residential uses and is taken to be 0.3;33 ? is the average personal occupied floor space, and is assumed to be 30 square meters per person; 34 and 1,000,000 is used to adjust the unit of area.
33
According to the Urban Land Use Classification and Land for Construction Standards by the Ministry of Housing and Urban-Rural Development of the China (previously the Ministry of Construction) in 1990, the share of urban constructive land for residential should be 20-32%. http://www.law110.com/lawserve/guihua/1800004.htm
34
In fact, more strictly, housing consumption should be determined from the housing demand side problem and varies in urban space; however, for convenience here a constant consumption of housing
61
Table 5-3 presents the results. The total residential land value is estimated to be 1.94 trillion RMB, 2.28 trillion RMB, and 1.66 trillion RMB in the three scenarios, respectively. A 1% change in ? leads to 17.5% increase or 14.66% decrease in the total land value. These are remarkable impacts, as compared with the 0.2 trillion RMB total government revenue of Beijing in 2009.35 Moreover, by integrating the land values for each annulus, it suggests that the central annulus witness larger impacts on land value brought by 1% change in ? .
Table 5-3 Simulated Total Impacts of Elasticity of Capital-land Substitution in the City
0-5 km 5-10 km 10-15 km 15-20 km 20-x bar total
S0 281.68 548.64 524.76 366.71 220.99 1942.77
land value (billion RMB) S1 % change S2 333.30 18.3 238.80 647.06 17.9 466.62 616.16 17.4 448.25 428.09 16.7 315.04 257.49 16.5 189.79 2282.10 17.5 1658.50
% change -15.2 -14.9 -14.6 -14.1 -14.1 -14.6
S0 102.58 270.52 376.03 409.33 500.63 1659.08
housing output (million sq meter) S1 % change S2 % change 122.28 19.2 86.33 -15.8 321.51 18.9 228.33 -15.6 445.10 18.4 318.66 -15.3 481.87 17.7 348.75 -14.8 594.51 18.8 421.33 -15.8 1965.26 18.5 1403.40 -15.4
housing value (billion RMB) population capacity (million people) S0 S1 % change S2 % change S0 S1 % change S2 % change 0-5 km 2987.79 3560.75 19.2 2515.13 -15.8 3.42 4.08 19.2 2.88 -15.8 5-10 km 15556.84 18487.06 18.8 13132.58 -15.6 9.02 10.72 18.9 7.61 -15.6 10-15 km 29137.69 34487.13 18.4 24693.95 -15.3 12.53 14.84 18.4 10.62 -15.3 15-20 km 36294.56 42724.14 17.7 30924.10 -14.8 13.64 16.06 17.7 11.62 -14.8 20-x bar 46822.00 55600.65 18.7 39406.14 -15.8 16.69 19.82 18.8 14.04 -15.8 total 130798.87 154859.73 18.4 110671.90 -15.4 55.30 65.51 18.5 46.78 -15.4 Note: Assume 30 percent land for residential use, and 30 square meters housing consumption per person. S0, S1, and S2 are respectively the scenarios with sigma=0.5, 0.505, and 0.495.
The impacts ? on the total housing output are also remarkable. This is as expected since the FAR is very responsive to ? (figure 5-6). One percent change in
? leads to 18.5% increase or 15.4% decrease in the total housing output of the city.
over the urban space is assumed to calculate population capacity. The 30-square-meter living space per person is targeted by the government of Beijing City’s target by 2010: http://news.sina.com.cn/c/2010-03-12/092419848868.shtml.
35
ChinaNews: http://www.chinanews.com.cn/cj/cj-gncj/news/2010/01-02/2050451.shtml
62
Also, the central locations experience larger impact when compared with the periphery areas. Although housing price is unaffected by ? in the open city case, the total housing value changes with ? due to changes in housing output. The total housing value is simulated to be 131 trillion RMB, 155 trillion RMB, and 111 trillion RMB in the three scenarios, respectively. It suggests that a 1% change in ? leads to 18.4% increase or 15.4% decrease in the total housing value. In other words, a 1% change in
? could mean about 20 trillion RMB, which is a huge impact in the city’s wealth.
The total population capacity of the city is estimated to be 55.3 million, 65.5 million and 46.8 million population in the three scenarios, respectively, by assuming an average floor space consumption of 30 square meters per person. These simulated numbers appear overestimated, given that currently 15.81 million permanent populations live in Beijing in 2006 within the administrative area of 16,400 square kilometers (BSB 2007).36 However, considering that the Tokyo Metropolitan Area in Japan housed 33.4 million population in 2000 while occupying about 13,556 square kilometer land (about 65 kilometers radius), and China is experiencing rapid urbanization and massive rural-urban migration, some 50 million population might be a possible future if Beijing continues to grow. To sum up, 1% changes in ? leads to 14-18% changes in the total land value, 15-19% changes in the total housing output, the total housing value, and the total population of the city. These numbers suggest that the total social welfare impacts caused by changes in capital-land substitution in housing services production are
36
Permanent populations include migrants from other provinces that have stayed longer than six months but exclude temperate migrants staying less than six months.
63
substantial. These findings indicate that the opportunity cost of land development restrictions such as the building height caps and the FAR controls may be very high. Thus, policies and regulations that might constrain land development should be carefully examined before implementation.
64
Chapter 6:
Empirical Evidence
By using land development data from Beijing City, this chapter empirically examines the two research questions of this dissertation. After a brief introduction of the research area and data, I first test the classical predictions of the negative distance gradients of housing prices, land prices, capital densities, and the FARs. Then I examine the relationship between the distance elasticities of land prices and housing prices. Finally, I estimate the elasticity of capital-land substitution and examine its impacts by dividing the data into two sub-periods and comparing the changes of the estimated elasticity of capital-land substitution, distance gradients of land prices and capital densities, and the ratio of the two distance elasticities.
6.1
Research Area
Beijing is selected as a typical example of a prosperous city where land and
housing markets have developed rapidly since the late 1980s. In 1995 there were only 419 land leasing transactions (1,219 hectares and 3.7 billion RMB in total), compared to 3147 free land assignments (5,006 hectares) (MLR 1996). However, the land leasing market grew quickly and began to play the dominant role in distributing urban land resources. In 2004, the number of land leasing transactions climbed to 2,073 (6225 hectares and 63.1 billion RMB in total), compared to only 89 cases of land grant for free (453 hectares) (figure 6-1) (MLR 2005). 37 The housing market in
The sharp drop of land leasing transactions in 2005 (shown in figure 6-1) is due to a series of stringent policies on urban land supply to suppress the overheated real estate development and the
37
65
Beijing also developed rapidly, particularly after the year of 1998 when material housing distribution was formally prohibited. The annual sale of commodity housing rose from 1.42 million square meters in 1990 to 4.09 million square meters in 1998 and jumped to 28.03 million square meters in 2005, increasing at an annual growth rate of 14.1% during 1990-1998 and 31.6% during 1998-2005. Accordingly, the total value of annual sale shot up from 2 billion RMB to 176 billion RMB during this fifteen-year period at an impressive annual growth rate of 34.6% (BSB 2006) (figure 6-2).
Source: MLR 1996-2006, data of 1997 are unavailable Figure 6-1 Land Leasing Market in Beijing: Total Number of Leases and Total Leasing Value, 1995-2005
fever of special economic zones and industrial parks. The land leasing market in Beijing had been “frozen” during the second half of 2004 and the first half of 2005.
66
Source: BSB, Statistical Year Book of Beijing Figure 6-2 Commodity Housing Market Development in Beijing: Floor Space and Value of Sales, 1990-2005
Combining with the advances in technology of construction, the emerging urban land and housing markets are reshaping Beijing’s urban landscape. Before, Beijing was characterized with a flat skyline, resulting from the danwei-based urban landscape, lack of incentives to economize land, and strict planning regulations. After, one of the most salient changes in the urban landscape was the emergence of taller and taller buildings (figures 2-7, 2-8, and 2-9). Also, the spatial distribution of land uses evolved, manifested by the relocation of industries from the central locations to the suburbs and the concentration of business and commercial activities in the central region of Beijing. Driven by the market forces, Beijing’s urban landscape presents many similarities to Western cities. Figure 6-3 illustrates the spatial concentration of the functions in Beijing. Despite the preserved Forbidden City lying in the center of the
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city, the central locations are favored by various activities including business, commerce, administration, education and research, etc. For example, within the third ring road are located the three commercial centers and one commercial street (Xidan, Wangfujing, Qianmen, and Jinrongjie), offices for more than 20 central government departments, hundreds of city departments and about 250 government agencies (Ding et al. 2005).
Hotels, embassies, convention centers, and foreign banks
Office buildings
2nd 3rd Facilities for culture uses, sports, and hospitals 4th 5th
Central and Beijing government agencies
Liaison office of other provinces
Universities and Colleges
Research institutes
Source: China Academe of Urban Planning & Design, Beijing Urban Spatial Development Research. 2003. Figure 6-3 Spatial Concentration of City Functions
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Population density declines with distance from the city center in Beijing. If dividing the city by its five ring roads, within the second ring road, population density was about 27,400 people per square kilometer in 2004, even higher compared with the central 23 wards in Tokyo, Japan;38 within the third ring, population density was 24,000 people per square kilometer; and it decreased to 19,700, 12,600, 4,400, 2,000 and 840 for within the fourth ring, fifth ring, sixth ring, Beijing Bay, and the entire administrative area of Beijing, respectively (table 6-1).
Table 6-1 Distribution of Population Density in Beijing
Current population density 2 (10,000 pop/km ) 2.740 2.400 1.970 1.260 0.440 0.200 0.084 Planned Population Capacity for 2020 (10,000 pop) 124 350 565 915 1235 1650 1750
Within 2 ring rd Within 3 ring th Within 4 ring th Within 5 ring th Within 6 ring Beijing Bay (exclude west and north mountainous area ) Beijing
nd
Source: Beijing Municipal Institute of City Planning & Design, From Olympic Games to Future, 2004.
Empirical studies have also provided evidence for the distance decay phenomena of land and housing prices in Beijing. For example, Ding (2004) examined the revolution of urban spatial structure in Beijing using the land leasing data from 1993 to 2000. By comparing the land prices in different rings of the city by different land uses and estimating the price gradients and their changes, Ding’s findings indicated that the distant gradients were all significantly negative and were dependent on land uses.
38
The population density of the 23 wards in Tokyo was estimated to be 13,660 people per square kilometer Tokyo Statistic Yearbook 2005: http://www.toukei.metro.tokyo.jp/tnenkan/2005/tn05qyte0510b.htm
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The data set used in this dissertation also depicts a clear picture of spatial patterns of Beijing. By using the GIS software ArcScene, figure 6-4 presents the spatial distribution of the housing prices, land prices, and the FARs. Nevertheless, it should be noted that despite growing markets, policies and planning regulations do play important roles in influencing the urban spatial structure of Beijing. For example, in 1989 the government of Beijing issued a policy—the Decision on the Strict Control of High-rise Residential Building Provision (Beijing [1989]42)—to control high-rise buildings, and this policy effectively curbed construction of high-rise buildings. The share of annually completed floor space of 10-and-above-floor buildings decreased from 40% in the late 1980s to less than 25% by 1992. This policy was later revised in 1994 and finally abolished in 2003. Afterward, the share of the 10-and-above-floor buildings rose again and currently reaches more than 40%. 39 It is true that developers often break land development requirements as subscribed to in urban plan and land leasing contracts (mostly the building height caps and the FAR controls) through bribing officials or even at the expense of paying the fines. However, this example illustrates that rigorous policy and plan implementation could serve as strict constraints on urban land development and significantly influence urban spatial structure, when stimulated by special incidences.
39
High-rise Building Development in Beijing (in Chinese), retrieved on May 2010, from http://www.chinajsb.cn/gb/content/2005-01/06/content_120207.htm
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Housing price
Land price
FAR
Figure 6-4 Housing Prices, Land Prices, and FARs in the Study Area
71
During the research period of 1999-2003, it is observed that stricter policy and planning implementation were introduced around the year 2002, partly for preparing for the 2008 Olympic Games and partly for controlling the overheated land development.40 On the one hand, it was mandated that all state-owned urban land for profitable uses must be leased through open bid approaches (such as tender, auction, and listing) and no project should violate the plan, otherwise monetary penalty and even some jail time would be imposed. On the other hand, rigorous plan implementation was carried out and a great amount of illegal building structures were demolished.41 The stringent policies could have probably constrained the market in allocating land and capital resources and limited the capital-land substitution in housing services production. The following estimations should take this into consideration.
40
The year 2002 was the first year that the Olympic Games Plan implementation was started. In tracking the policy documents issued in that year, several of them are important and deserve a note. On April 2002, the Ministry of Land and Resources announced the Provisions of Tender, Auction, and Listing State-Owned Land Use Right, requiring that urban land use rights for profitable uses (including commodity housing development and commercial and office real estate development) must be leased to private users through open bid approaches (tender, auction, or listing). Following this national document, the Beijing government issued Provisions of Stop State-Owned Land Use Right Leasing to Profit Making Projects by Negotiation on July 2002. At the same time, the Beijing government also issued Measures on Violation of the Provisions of Land Management Administrative Responsibility. In December of the same year, the Beijing government issued the Notice of Adjusting State-Owned Land Use Right Benchmark Price. These formally issued documents play important roles to tighten the urban land use management.
Besides the tightening of land use policies and regulations, the citywide inspection of land use started in 2003 helped to reduce the number of cases of building permit violations. Furthermore, the successful bidding to the 2008 Olympic Games in 2001 triggered large-scale demolition of constructions that violated planning regulations zoning ordinances in the years after. For instance, a total 4.5 million square meters of building space were demolished in 2006. Source (In Chinese): http://www.landscapecn.com/news/html/news/detail.asp?id=8074. http://www.515home.com/commom/news_content.asp?id=32098. http://huaxianews.cn/news/2006-3/27/2006327135600.htm.
41
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6.2
Data
The data used in the empirical analysis of this dissertation include land price
per square meter, housing price per square meter, total square meters of land lot, total square meters of floor space, the FAR, location information, and so on, for each observation of housing project. Both housings price and land prices are needed for the same land lots so as to estimate ? and ? , test the relationship of ? > 1 , and examine the impacts of ? . Housing price data were collected from the largest online housing information website (http://www.soufun.com) in China on March 2007. The housing data provided information of project name, starting date of sale, location, the average housing prices per square meter floor space, housing type, and if furnished or not. The housing data were then matched to the land leasing transaction data, which were obtained from the Beijing Land Resource and Management Bureau, by project name and location information. The land leasing data provided information on project name, land leasing date, location, total square meters of land lot, total planned square meters of floor space, and land price per square meter. Matching these records from both sources greatly reduced the number of usable observations. After excluding government-subsided affordable housing (jingji shiyong fang) projects, single detached dwellings, and observations located more than 30 kilometers from the city center as well as the very few observations in the remote suburban districts that were considered as outliers, a total of 266 observations were obtained. Figure 6-5 presents the spatial distribution of these observations.
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Note: land for construction includes the urban & town land, single sites for industry, sites of special use, but excludes the sites for rural villages. Source: Beijing Current Land Use Map of 2004, Beijing Land Resource and Management Bureau.
Figure 6-5
Administrative Area of Beijing and Research Area
Table 6-2 provides the descriptive statistics of the variables used in the following empirical analysis. The average land price per square meter was 2,211 RMB, which was about one-third of the average per square meter housing price. The housing structure floor space per unit of land or the FAR varied remarkably from 0.44 to 20.63, with the mean of 4.55. The capital density was estimated by
S = ( pH * 0.7 ? rL) / n , based on the assumption that there was an average profit ratio
of housing sales of 30% in urban housing market (as in the simulation analysis). The average capital density was 20,550 RMB per square meter of land in the sample. The mean location of observations was 11.4 kilometers away from the city center—
74
Tiananmen Square.42 The years of land purchase varied from 1999 to 2003, and the starting years of housing sales varied from 1999 to 2007. There were time gaps between land purchases and housing sales, ranging from one year to seven years, which could be related to project scales. Usually it takes less time to finish smaller land development projects than larger ones. On average, the time lag was a bit more than one year. The total land area and total housing floor space varied dramatically among the observations, indicating the project scale had a large variance. About 38% of the housing projects had furnished the rooms. Tables 6-3 and 6-4 also provide information of the numbers of observations by district and housing type. This data set has several advantages. First, each observation has matched housing and land prices that were directly observed from transactions. This is helpful to obtain better estimates, because measurement errors that are associated with systematically biased estimation of land prices are less likely to occur in this data set (McDonald 1981, Thorsnes 1997). Second, all of the observations were newly developed commodity housing projects, and thus this data set is not associated with the problem that old dwellings fail to continuously adjust land and capital input according to prices (Jackson et al. 1984). Moreover, rapid urban expansion and housing project development in Beijing offers spatially widely scattered observations, from the city center to the urban edges, as compared with the fact that in the developed countries new housing development are mostly clustered only in the suburbs.
42
Despite the Forbidden City, which only occupies 0.72-kilometer squares, the central areas of Beijing remain attractive to business, commercial, and administrative activities. In this study, Tiananmen Square is regarded as the city center, which is itself not an employment center but rather symbolic for the highly concentrated economic activities in Beijing.
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Table 6-2
Descriptive Statistics
Mean 6887.7 2211.0 8.78 7.26 4.55 1.35 Std. Dev. 2481.0 1939.1 0.35 1.12 2.69 0.58 Min 2034.4 30.8 7.62 3.43 0.44 -0.82 Max 19477.9 14940.4 9.88 9.61 20.63 3.03
p r ln(p) ln(r ) h (or the FAR) ln(h)
S ln(S) x LY HY DIFF FA LA FUR DT TP
Variable Obs unit housing price per square 266 meter structure space in RMB unit land price per square meter 266 land in RMB Logarithm of housing price 266 Logarithm of land price 266 floor area ratio, measuring the 254 housing output per unit land Logarithm of housing output per 254 unit of land capita density, estimated by subtracting total housing sale value 254 with total land cost and divided by total land area logarithmic capital density 254 distance from Tiananmen Square 266 in kilometer land leasing year 266 housing sale year 266 Year difference between land 266 purchase and housing sale total floor area of structure space 254 for each observation in square meter total land area for each observation 266 in square meter dummy variable: Furnish=1 if 253 housing is furnished; otherwise Furnish=0 dummy variables: districts 256 dummy variables: housing types 266
20549.9 9.70 11.42 2001.05 2002.1 1.02 61594.0 17309.3 0.38
15859.3 0.71 5.46
1348.7 7.21 2.26
157992.0 11.97 25.60 2003.00 2007.0 7.00 1433262.0 427283.0 1.00
1.40 1999.00 2.0 1999.0 1.20 101142.4 31209.4 0.49 0.00 676.0 248.0 0.00
Table 6-3
Districts 1 2 3 4 5 6 7 Total
Numbers of Observations in Each District
Dongcheng Xicheng Xuanwu Chaoyang Haidian Shijingshan Tongzhou Freq. 10 7 12 109 81 21 26 266 Percent 3.76 2.63 4.51 40.98 30.45 7.89 9.77 100
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Table 6-4
Housing types 1 2 3 4 5 6 7 Total
Numbers of Observations in Each Housing Type
Freq. 10 7 12 109 81 21 26 266 Percent 3.76 2.63 4.51 40.98 30.45 7.89 9.77 100
Slab Tower & Slab Tower Mid-rise High-rise Mid-to-high-rise Slab & Mid-to-high-rise
Note: these types are provided by the developers on the website, and they are not strictly exclusive to each other.
The data also bear several shortcomings. First, the observations were housing projects rather than single dwellings and the housing prices were the average prices of housing project. Compared with the prevalence of single-house dwellings in the developed countries, China’s residential development is mostly high-rise compound buildings, each providing dozens to hundreds of apartment flats. The average housing price cannot reflect the structural differences (such as the floor number, number of bedrooms and bathrooms, layout, window directions) among housing apartment flats within one project. Second, the total structural space of each housing project and the FAR were from land leasing records, which were planned rather than completed. Therefore, they might be biased if the final housing output exceeded the planned structural space subscribed on the land leases. Finally, land prices were determined through the approach of negotiation, which is the most used approach but is often regarded as being associated with non-market factors. 43 Nevertheless, the way in which land prices are determined by negotiation is similar to that in the market, since
43
During 1999-2003, there are totally 8,865 land leasing cases in Beijing, 8,738 of them were through negotiation, and the others were through tender, auction, and listing (MLR 2000-2004).
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the final land leasing price is agreed to by both the city government and the developers and dependent on land use type, location, neighborhood characteristics, etc.
6.3
Urban Decaying Phenomenon
The first empirical question is to test the spatial decay functions. According to
(4), (11), (12), (13), housing prices, land prices, capital intensities, and the housing output per unit of land (or the FARs) decline with distance from the city center. To estimate and test these negative distance gradients, the estimating equation is specified as:
ln(O ) = ? 0 + ?1 x + ? ? j A j + ?
j =2
(53)
where O denotes the housing price p, land price r, capital density S, or housing output per unit land h (or the FAR); x denotes the distance from the city center; A j denotes control variables, which vary with dependent variables; ?0 is the intercept; ?1 is the distance gradient, which is expected to be significantly negative; ? j are coefficients of control variables; and ? is the error term. Table 6-5 reports estimated results by ordinary least square (OLS). 44 The models present a moderate goodness-to-fit, with the R-squared ranging from 0.3 to 0.6. All of the distance gradients of housing prices, land prices, capital intensities and the FARs are significantly negative numbers, consistent with the model predictions of the urban decaying phenomenon.
44
Stata is used in all estimations.
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Table 6-5
OLS Estimations of Distance Gradients for Housing Prices, Land Prices, Capital Densities, and FARs
ln(p) ln(r ) ln(S) ln(FAR) obs=242,R-sq=0.5115 obs=266, R-sq=0.615 obs=242, R-sq=0.4047 obs=254, R-sq=0.3098 Coef. t sig. Coef. t sig. Coef. t sig. Coef. t sig. distance -0.0383 -6.30 **** -0.0943 -5.55 **** -0.05986 -4.37 **** -0.0272 -2.28 ** district_2 -0.0359 -0.30 -0.0475 -0.13 -0.17693 -0.64 -0.1344 -0.54 district_3 -0.2709 -2.46 ** -0.1809 -0.59 -0.09603 -0.37 0.0617 0.29 district_4 -0.2263 -2.64 *** -0.0994 -0.40 -0.34127 -1.73 * -0.0971 -0.56 district_5 -0.1254 -1.41 -0.2025 -0.78 -0.31262 -1.53 -0.1772 -0.98 district_6 -0.2738 -2.24 ** -0.0534 -0.15 -0.40446 -1.45 -0.0818 -0.34 district_7 -0.2380 -1.61 -1.5336 -3.76 **** -0.70436 -2.08 ** -0.4784 -1.61 type_2 0.0144 0.33 0.253581 2.54 ** 0.2042 2.33 ** type_3 -0.0620 -1.52 0.205752 2.22 ** 0.3346 4.17 **** type_4 -0.0506 -0.40 -0.61001 -2.11 ** -0.4413 -2.10 ** type_5 -0.1939 -2.14 ** 0.188219 0.92 0.4569 2.97 *** type_6 0.0290 0.28 0.021759 0.09 -0.1373 -0.74 type_7 -0.0219 -0.24 -0.18304 -0.88 -0.1111 -0.60 FUR 0.0179 0.53 0.073118 0.95 FA 0.0000 1.57 HY_2000 -0.0037 -0.05 HY_2001 -0.0624 -0.93 HY_2003 0.0569 0.83 HY_2004 0.1425 2.05 ** HY_2005 0.2597 3.09 *** HY_2006 0.2981 2.56 ** HY_2007 0.4307 2.39 ** LA 0.0000 -0.32 LY_2000 -0.0248 -0.17 LY_2001 -0.2229 -1.38 LY_2002 0.1540 0.96 LY_2003 0.0508 0.33 DIFF 0.040743 1.30 CONST 9.3609 88.68 **** 8.6690 32.47 **** 10.51319 53.26 **** 1.6430 9.46 **** ****99.9%, ***99%, **95%, * 90%
Calculating at the mean distance (11.4 kilometers), the distance elasticities of housing prices, land prices, capital densities, and the FARs were -0.44, -1.08, -0.68, and -0.31, respectively, suggesting that a 1% increase in the distance from the city center would decrease housing prices by 0.44%, land prices by 1.08%, capital densities by 0.68%, and the FARs by 0.31%, respectively. These results suggest that land prices behaved in a more elastic way with respect to distance, when compared to
79
housing prices. To better understand the speeds of these declines, supposing that a one-kilometer move is made at the mean distance away from the city center in Chaoyang district, the housing type is slab and it is not furnished, the total floor space and land areas are taken by the means of the sample, and the land purchase year is 2001 and housing sale year is 2003, this move will make the housing price drop by 288 RMB per square meter, land prices drop by 142 RMB per square meter, capital densities drop by 637 RMB per square meter, and the FARs drop by 0.066. Coefficients of the control variables suggest some interesting findings. First, effects of the district dummy variables are mixed compared with the expectation. Housing prices would be higher if it was located in Chaoyang, Xuanwu, and Shijingshan. This is reasonable given the development of Chaoyang CBD and the closeness to the city center of Xuanwu and Shijingshan. It is unexpected that Haidian did not have a positive influence on housing prices given the concentration of hightech business and universities in Haidian district especially in its Zhongguancun area. A possible explanation is that Haidian is a large district and includes also less urbanized areas that offset its attractiveness. Tongzhou was the only district dummy variable that had significant and negative influence on land prices, probably due to the newly government-facilitated and to a certain degree subsidized land development (Tongzhou is among three of the key new cities in the 2004 master plan). Capital density was significantly higher in Chaoyang and lower in Tongzhou, suggesting difference in quality of residential development. No district dummy variable was significant for the FAR. Second, high-rise and tower housing buildings in general were associated with higher housing prices, capital intensities, and FARs, but not
80
associated with land price. Third, the effects housing project scale and land development scale on housing prices and land prices were as expected but not significant.45 Fourth, housing prices and land prices appeared to increase with time, consistent with economic growth, but the time effect on land prices was not significant. Finally, the time lag had a positive sign on capital density as expected but was not significant.
6.4
Ratio of the Two Distance Elasticities
According to (14), land prices are more elastic with respect to distance from
the city center: ? > 1 . To estimate ? , I employ two different approaches. The first approach is to estimate ? by computing the ratio directly from the estimated distance gradients of land prices and housing prices. According to the definition of ? by (14):
?r ? = ?x ?p ?x
? ln r r ?r r ? x = ?x = ?x = 1r p ?p ? ln p ?1 p p ?x x ?x
(54)
where ?1r and ?1 p are respectively the estimated distance gradients of land prices and housing prices by (53). According to the OLS results shown in table 6-5,
?=
? 0.0943 = 2.46 > 1 . ? 0.0383
45
Large housing projects are expected to positively affect housing prices for they provided better services and facilities. Larger land lots, however, are expected to negatively affect land prices because fewer developers were able to bid for large scale land development and thus they had more power to bargain with the government.
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However, this simple computation from the independent OLS estimations cannot tell whether ? is statistically significant larger than unity. For the purpose of testing ? > 1 , I also employ the seemingly unrelated regression (SUR) estimation. The SUR estimation jointly estimates the housing prices function and land prices function and yields more efficient estimates, for it takes into account the potential correlations between the error terms of the two equations. The SUR estimation makes sense in this case because both housing prices and land prices came from the same data set, and therefore the error terms of the two equations are likely to be correlated. More important, it can be tested whether the distance gradients from the two equations are significantly different from each other by conducting a cross-equation
? 2 test.
Table 6-6 reports the results of the SUR estimations. The estimated distance gradients are similar to those of the OLS, and both are significantly negative. Using these estimates, ? =
? 0.0892 = 2.34 > 1 . The ? 2 test reports that the null hypothesis ? 0.0382
of ?1r = ?1 p is rejected at a 99% level in favor of the alternative hypothesis that the two distance gradients are significantly different from each other, and this provides statistical evidence for ? > 1 .46
46
Chi2(1)=9.26, Prob>chi2=0.0023.
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Table 6-6
SUR Estimations of Distance Gradients for Housing and Land Prices
ln(p) obs. 242, R-sq=0.5115 coef. z sig. -0.0381691 -6.61 **** -0.0345822 -0.30 -0.2708801 -2.59 *** -0.2271482 -2.79 ** -0.1255459 -1.48 -0.2753058 -2.37 ** -0.2389175 -1.70 * 0.0156686 0.37 -0.0596148 -1.54 -0.0537071 -0.45 -0.1897537 -2.20 ** 0.0300463 0.30 -0.0230342 -0.26 0.0177716 0.56 2.57E-07 1.70 * -0.0041231 -0.06 -0.0624409 -0.98 0.0569865 0.88 0.1412889 2.13 ** 0.2587748 3.23 **** 0.294404 2.66 *** 0.4375647 2.55 ** ln(r ) obs. 242, R-sq=0.4621 coef. z sig. -0.0891899 -5.70 **** -0.0230039 -0.07 -0.0311796 -0.10 -0.1085817 -0.48 -0.2247626 -0.95 -0.0054501 -0.02 -0.8121863 -2.09 **
distance district_2 district_3 district_4 district_5 district_6 district_7 type_2 type_3 type_4 type_5 type_6 type_7 FUR FA HY_2000 HY_2001 HY_2003 HY_2004 HY_2005 HY_2006 HY_2007 LA LY_2000 LY_2001 LY_2002 LY_2003 CONST 9.359147 93.21 **** ****99.9%, ***99%, **95%, * 90%
-2.44E-06 0.017005 -0.1911381 0.079664 0.0064016 8.636603
-1.77 * 0.12 -1.22 0.50 0.04 34.87 ****
The second approach is to estimate ? based on its alternative representation as the housing price elasticity of land price. According to (15) and (26), ? can be estimated by the following equation:
ln(r ) = ? 0 + ? ln( p) + ?
(55)
where r and p denote per square meter land price and housing price, respectively; and
? 0 is the intercept. I use both OLS and instrumental variable (IV) estimations to
estimate ? . The reason for using the IV estimation is that housing price is probably
83
correlated with the error term, due to the uncontrolled factors that affect both housing and land prices such as the neighborhood effects. I choose the housing type (TP), housing sale year (HY), and whether the rooms are furnished (FUR) as instrumental variables since they are correlated with housing prices but are not apparently associated with land prices. I also include land leasing year (LY), land area (LA) and square of land area (LA_square) in the major function as control variables. Table 6-7 reports the results of both the OLS and two stage least square (2sls) IV estimations. The OLS estimation yields ? = 1.69 with the T-statistics suggesting that ? is significantly larger than unity, and the IV-2sls estimation yields ? = 2.75 , which is also significantly larger than unity. 47 It should be noted that although theoretically the IV estimation improves the estimation by correcting the endogenous problem, it is also associated with the problem of “weak” IV that impairs the precision of the estimates, especially in this case that the R-squared and the Fstatistics of the first stage estimation that are quite small. In conclusion, by using the Beijing data, different approaches and estimation methods yield considerably robust estimates of ? ranging from 1.69 to 2.75, and the statistical tests indicate that ? is significantly larger than unity, consistent with the theory that land prices are more elastic with respect to distance from the city center than housing prices.
The T-statistics for ? > 1 is 4.28 for the OLS estimation, and 3.44 for the IV estimation, all significant at a 99.9% level.
47
84
Table 6-7
OLS and IV Estimations of the Ratio of the Two Distance Elasticities OLS obs=266, R-sq=0.3878, lamda sig.>1**** t sig. 1.689699 10.49 **** -0.0000259 -6.55 **** 6.38E-11 5.95 **** -0.121649 -0.69 -0.2867924 -1.45 0.7089738 3.56 **** 0.2098351 1.11 -6.950496 -4.95 **** IV-2SLS First stage regression obs=242, R-sq = 0.1709, F(21,220)=2.16 t sig. -5.81E-06 -2.75 ** -8.31E-12 -1.87 * 0.14141 1.34 0.1707963 1.37 0.2860518 2.16 * 0.2187656 1.68 * -0.0379462 -0.65 -0.0797368 -1.50 0.0506728 0.31 -0.1342184 -1.17 -0.1811546 -1.35 -0.0388464 -0.33 0.0520186 1.21 -0.047188 -0.40 -0.1908059 -1.40 -0.1618301 -1.10 -0.1428123 -0.96 -0.0555139 -0.35 0.0678337 0.34 0.2445954 0.95 2.75E-06 3.93 **** 8.722184 102.07 **** Instrumental variables (2SLS) regression obs=242, R-sq=0.4114, lamda sig.>1 **** t sig. 2.753689 5.40 **** -0.0000313 -7.68 **** 7.46E-11 6.81 **** -0.1783376 -0.90 -0.2345336 -1.08 0.6820098 2.89 ** 0.431023 1.97 * -16.07865 -3.61 ****
Dependent: ln( r) ln(p) LA LA_square LY_2000 LY_2001 LY_2002 LY_2003 CONST
coef.
Dependent: ln(p) LA LA_square LY_2000 LY_2001 LY_2002 LY_2003 type_2 type_3 type_4 type_5 type_6 type_7 FUR HY_2000 HY_2001 HY_2003 HY_2004 HY_2005 HY_2006 HY_2007 FA CONST
Coef.
Dependent: ln(r) ln (p) LA LA_square LY_2000 LY_2001 LY_2002 LY_2003 CONST
Coef.
****99.9%, ***99%, **95%, * 90%
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6.5
Elasticity of Capital-Land Substitution
The elasticity of capital-land substitution is defined as the elasticity of the
ratio of the factors with respect to the marginal rate of technical substitution between them, reflecting how sensitive the cost-minimizing factor input proportions is to changes in relative factor prices (McFadden 1978). Mathematically it is presented:
?=
d ln( K / L) d ln(r / n)
(56)
where ? is the elasticity of capital-land substitution, K is the capital input (non-land input), L is the land input, r is the land price, and n is the capital price. I employ three approaches to estimate ? . The first approach is to estimate ? directly from the CES function by (19). Given the non-linearity of the CES function, the non-linear least square (NLLS) estimation is employed and the estimating functions are:
h = ? [?S
??
+ (1 ? ? )]
1
?
1
?
+?
(57) (58)
ln(h) = ln(? ) ?
?
ln(?S ?? + (1 ? ? )) + ?
where h is the housing output per unit of land (or the FAR), S is the capital density,
? , ? , ? are production parameters, and ? =
1 by (17). This approach is ? +1
straightforward, and it yields estimates not only for ? but also for ? and ? . However, it should be noted that there are several drawbacks of this approach. First, direct estimation of the CES function is associated with the problem of multicollinearity between the inputs and the problem of simultaneous equation bias
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(Caddy 1976). Second, since S is not observed but estimated by subtracting land cost and an average proportion of profit from the housing sale value, S tends to be correlated with the error terms. And finally, the NLLS estimation by Stata may not obtain the global best estimates but can only assure the local optimal estimates, for it starts with arbitrarily decided initials and iteratively solves the estimates to minimize the summation of squared residuals. Table 6-8 reports the estimated results. While ? and ? from the logarithmic equation by (58) are not significant, ? , ? , and ? are all significant from the original form by (57) and ? is computed from ? to be 0.49.
Table 6-8 NLLS Estimations of Housing Production Function
ln(h) R-sq=0.7691, Obs=254 parameter t sig. 0.0019933 0.62 0.8376112 2.87 ** 0.0731662 0.33 0.9318
?
h R-sq=0.9187, Obs=254 parameter t sig. ? 0.000307 6.62 **** 0.9999906 23676.29 **** ? ? 1.043628 2.38 ** ? 0.4893 is calculated from the estimated ? .
The second approach is to estimate ? from the equilibrium solution of h by (23), which describes also a non-linear relationship and NLLS is used. Assuming the 30% profit of housing sales, the estimating functions are:
? ? 1?? h( p) = ? ? ? ? n 1+ ? ?1 ? ? ( ) 0.7 p?? ? ?
? ? ? ? ? ? ?
?
1
?
+?
(59)
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? ? 1 ? 1?? ln(h) = ln(? ) ? ln ? ? ? n 1+ ? ?1 ? ? ( ) 0.7 p?? ? ?
? ? ? +? ? ? ? ?
(60)
The advantage of this approach is to avoid the endogenous problem as in the first approach; however, the function form is further complicated, which might impair the precision of the estimation. Table 6-9 reports the estimated results. Only the logarithmic equation by (60) yields significant estimate of ? , and correspondingly ? is computed to be 0.37.
Table 6-9 NLLS Estimations of Housing Production Function
ln(h) R-sq=0.0427, obs=254 paremeter 0.0008514 0.9999996 1.674321 0.374 t 2.22 6.40E+05 1.79 sig. ** **** *
h R-sq=0.7448, obs=254 parameter t 0.0007836 1.87 0.9999995 4.90E+05 1.597259 1.4 0.385 is calculated from the estimated ? .
?
? ? ? ?
sig. * ****
The third approach is to employ the market equilibrium conditions that the marginal factor output equals to the ratio of the factor price over the product price.
? H n ?H = ? ( )1+ ? = p ?K ? K
?H 1 ? ? H 1+ ? r = ? ( ) = ? L p ?L (61) and (62) yields:
(61)
(62)
K n ( ) ?? ?1 = 1? ? L r
Taking the logarithm on both sides:
?
(63)
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K r ? 1 1 ln( ) = ln( )+ ln( ) L ? +1 1?? ? +1 n
(64)
Replace S =
K and suppose the capital price n is spatially invariant constant, L
then ? can be estimated the follow equation:
ln(S ) = a + ? ln(r ) + ?
(65)
where S is the capital density and r the land price. Compared with the above two approaches, the third approach is simple in equation form, and ? is a first-order parameter in the estimating function, increasing the possibility that ? is estimated with precision (Caddy 1976). Nevertheless, this approach is also associated with the endogenous problem since S is estimated from h, p and r and there might be uncontrolled factors that both affect r and S. Therefore, besides using the OLS estimation, the IV method is also employed. I choose the land area (LA), the square of land area (LA_square), and the land leasing years (LY) as the instrumental variables, and I include the housing type (TP) and the time lag between land purchase and housing sale (DIFF) as control variables in the major equation. Table 6-10 reports the results of OLS and IV-2sls estimations. The estimates of ? are 0.65 and 0.46 from the OLS and IV estimations, respectively, both significantly larger than zero and smaller than unity according to the T-tests, consistent with the theoretical analysis.48 To sum up, different approaches and estimation methods generate in general robust estimates of ? , ranging from 0.37 to 0.65. These values fall in the middle
The T-statistics for ? < 1 are 11.49 and 7.87 in the OLS and IV estimations, respectively, both significant at a 99.9 % level.
48
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range of results reviewed by McDonald (1981). These values are also in accordance with Ding (2004)’s estimation of 0.32-0.74 in 1993-2000 by using also Beijing data.
Table 6-10 OLS and IV Estimations of Elasticity of Capital-land Substitution OLS obs=254, R-sq=0.6877, sigma sig.<1**** t sig. 0.6468159 21.04 **** 0.1101075 1.56 -0.0118449 -0.18 -0.3490511 -2.03 ** -0.1441138 -1.16 -0.2347224 -1.58 -0.0687507 -0.46 0.0519092 2.32 ** 4.861718 21.34 **** IV-2SLS
Dependent: ln(S) ln(r) type_2 type_3 type_4 type_5 type_6 type_7 DIFF CONST
coef.
Dependent: ln(r ) LA LA_square LY_2000 LY_2001 LY_2002 LY_2003 type_2 type_3 type_4 type_5 type_6 type_7 DIFF CONST
Dependent: ln(S) ln (r) type_2 type_3 type_4 type_5 type_6 type_7 DIFF CONST
First stage regression obs=254, R-sq = 0.3465, F(13,240)=9.79 Coef. t sig. -0.0000274 -8.00 **** 6.49E-11 7.11 **** 0.1382444 0.88 0.0299359 0.17 0.0125844 0.07 0.1825713 1.08 0.3615043 2.78 ** 0.3553335 2.93 ** -0.4070911 -1.27 0.706637 3.00 ** -0.3522217 -1.29 -0.1189245 -0.42 -0.0342514 -0.80 7.561267 47.33 **** Instrumental variables (2SLS) regression obs=254, R-sq=0.6403, sigma sig.<1 **** Coef. t sig. 0.4594759 6.69 **** 0.174936 2.23 ** 0.0890905 1.15 -0.4468925 -2.39 ** 0.033356 0.23 -0.3020863 -1.88 * -0.0864005 -0.54 0.0367899 1.50 6.217255 12.44 ****
****99.9%, ***99%, **95%, * 90%
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6.6
Impacts of Elasticity of Capital-Land Substitution
To examine the impacts of the elasticity of capital-land substitution on urban
spatial structure, it first requires examining whether ? has changed. I expect a decrease in ? in the research period of 1999-2003, because of the stringent policies on urban land use around the year 2002. Technology of construction is regarded unlikely to have changed during this short period. Further, if ? decreases, the land price and capital density curves will become flatter and ? will also decrease, according to the theoretical results by (31), (32), and (34), if the housing prices are held. Therefore, by dividing the data into two sub-samples: 1999-2001, and 20022003, I examine the impacts of ? by comparing the changes in ? and the changes in distance gradients of land prices and capital densities as well as ? . If the changes are consistent with the theoretical results, it would provide certain evidence. Table 6-11 reports the summary of the estimated results (for more details see Appendix IV). The findings in general provide consistent evidence to the theoretical results. The estimates of ? did decline during the research period: estimates from the OLS estimation were 0.71 and 0.62 for the first and the second sub-periods, respectively; estimates from the IV estimation were 0.56 and 0.44 for the two subperiods, respectively. This is consistent to the expectation that the stringent policies on urban land use around 2002 suppressed capital-land substitution. The absolute values of distance gradients of land prices and capital densities both decreased (from 0.095 to -0.067 and from -0.066 to -0.059, respectively), indicating that both the two curves were flattened. The estimated ? also decreased according to the results from
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multiple approaches, indicating the gap between the decaying land and housing prices became smaller.
Table 6-11 Comparison between Estimates for Two Sub-Periods
1999-2001 2002-2003 change sig. OLS 0.70 0.62 decrease * sigma IV 0.56 0.44 decrease **** land price gradient OLS -0.095 -0.067 flatter * capital density gradient OLS -0.066 -0.059 flatter *** OLS 1.89 1.52 decrease not tested lamda SUR 2.40 1.58 decrease IV 3.25 2.07 decrease **** ****99.9%, ***99%, **95%, * 90% Note: F-statistics are calculated to test the changes of the estimates in the two sub-periods
It should be noted that the above analysis is based on the assumption that housing price stayed unchanged. Estimated results suggest that the housing price curve became steeper during the research period (the estimated distance gradients of housing price were -0.035 to -0.039, respectively). However, this change is not statistically significant. So there must exist some forces that drove the land price and capital density curves to become flatter; and the decrease in ? was probably one of the reasons.
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Chapter 7:
Conclusion
The contribution of this dissertation to the literature is twofold. First, it investigates empirically the relationship between the distance elasticities of land prices and housing prices, and it provides evidence for what the urban economic theory predicts: as derived demand for land, land prices drop faster than housing prices towards the urban edges. Second, it investigates the impacts of the capital-land substitution, one of the most important properties of housing services production, on urban spatial structure through analytical exercise, numerical simulation, and empirical estimation. The findings suggest that an increase in the elasticity of capitalland substitution leads to increases in the land price, the capital density, and the housing output per unit of land at any location within the city, flattening of the land price and capital density curves, an increase in the ratio of the distance elasticity of land prices to the distance elasticity of housing prices, an expansion of the city boundary, and a growth in the population.
7.1
Policy and Planning Implications
The findings of this dissertation have three policy and planning implications.
The first one links to the skyrocketing housing prices in Beijing and a few other cities in China. The climbing housing prices in cities, such as Beijing, are attributable to many sources; including the rapid urbanization, the historical shortages of housing stocks, the increase in income, the housing pre-sale system, and the rise in land
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prices. 49 Many developers and investors put the blame on the government for not controlling land prices and they claim the rising land prices are the primary reason for soaring housing prices. 50 However, the findings of this dissertation suggest an alternative explanation. By examining the spatial patterns of land and housing prices and revealing their relationships, this dissertation provides empirical evidence for the theory that land is an input factor in housing services production and the demand for land is a derived demand. Under the land use right system in China, it is mandated that land use rights of the state-owned urban land should be transferred to private developers through open bid process (such as an auction). Thus the final bid land price is determined by the expected housing prices in the future and other market conditions. Given that land is an input to produce housing services, developers who aim to maximize profit will hardly set housing prices lower than market prices, even if the governments reduce land prices. Therefore, based on the theory of housing services production and empirical findings, there is evidence to conclude that it is unlikely that the pace of housing prices increase in Beijing will be slowed down by controlling land prices in land markets, or the impact of land price declines on housing prices will be trivial if there will be any. The policy implication is that the problem of skyrocketing housing prices should be addressed through other approaches, for instance, improvement on the housing financing mechanism, taxes on
49
In the housing pre-sale system, developers sell housing properties to residents before buildings are constructed. This pre-sale system was adopted to boost China’s urban housing market and solve the problem of lack of startup capital. However, this system favors sellers and push forward housing prices. It has been a hot topic in recent years whether or not to cancel the housing pre-sale system in China.
Some examples (in Chinese) can be found from (retrieved on May, 2010) http://www.sohochina.com/news/soho_news.aspx?id=13386 http://www.ln.xinhuanet.com/fcpd/2006-05/26/content_7104149.htm http://lianghui.china.com.cn/zhibo/2009lh/2009-03/06/content_17384784.htm?show=t
50
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vacant housing properties, taxes on income from speculative housing purchases, and provision of affordable public housing services for low-income households. Second, the findings of this dissertation reveal that the share of land cost in the total value of the property declines with distance from the CBD to the urban fringes and this has important implication on land value assessment. Land tax is regarded as the best tax that does not distort resource allocation in markets. Land tax is also important as a widely used approach to improve social welfare by redistributing income and reducing poverty, according to Henry George (1879). The moral basis for levying tax on land is to collect the value increments of land that are not due to landowner actions, but due to the population growth of the city and the improvement of infrastructure by public expenditure (Nicholson 1998, Nechyba 1988). In comparison, a tax on land improvements is not as desirable, since it depresses investment and development. Therefore, economists favor the split-rate property tax, and argue that a switch from a single-rate property tax to a split-rate property tax would increase land use efficiency, minimize excess burden, stimulate economic development, preserve environment, reduce urban sprawl, and improve quality of life (Dye & England 2009, Cohen & Coughlin 2005). In the split-rate tax system, different tax rates are set for land and improvements and often, that for land is higher than improvements. Given the theoretical advantages of land tax over a general property tax, many local jurisdictions (such as two counties in Hawaii and sixteen Pennsylvania municipalities) apply split-rate property tax in order to improve efficiency and facilitate development (Kwak et al. 2009).
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Currently, one of the greatest concerns of the split-rate property tax system lies in the property assessment. Without observed land value, land is typically assessed as a certain percentage of the total property value (such as 20%) regardless the location and land use intensity, and this leads to inaccurate land valuation. This dissertation finds that the share of land cost over the total housing property in the city of Beijing can be high as one-third at the central locations and drop to only 3% at 30 kilometers away from the city center. The findings of this dissertation can improve the accuracy of land value assessments and improve the efficiency of the split-rate property tax system, by adopting variant land value shares depending on locations instead of the fixed share of land value that is used currently in many local municipalities. Certainly, empirical and/or simulation studies are needed for specific cities to obtain more accurate and fitting parameters. The third implication is associated with zoning ordinances and planning regulations on land use and land development. Given a certain level of technology, efficient land development requires capital-land substitution in housing services production. Regulative restrictions on building height and density not only affect housing output, but more important, they restrict capital-land substitution and thus affect the overall land value, which in turn influences the social welfare. The simulated results based on the Beijing data illustrate that a 1% change in the elasticity of capital-land substitution leads to 14-18% changes in the total land value and 1519% changes in the total housing output. These numbers suggest remarkable opportunity cost and social welfare impacts that may be caused by planning regulations on land use and development intensity. Therefore, careful examination on
96
the potential impacts is indeed needed before imposing any restriction on land development for environment justice and land use externalities.
7.2
Recommendation for Future Studies
One direction to extend this dissertation is to build longer period data for
housing and land development data to document changes in urban spatial structure and capital-land substitution over time. Empirical studies can also be improved by collecting more detailed data including housing units’ characteristics and neighborhood features to better control the estimation of spatial variant housing prices. Also, this dissertation can be extended to study locational differences of the marginal effects brought by policies and planning regulations. As demonstrated in this dissertation, numerical simulations suggest that the impacts of changes in capitalland substitution differ considerably across locations, suggesting that constraints on land use will cause different opportunity costs and social welfare impacts at different places. Therefore, examination of the locational variant influences of the same policy or regulation will have practical significance for policy assessment. Third, a formal model can be developed as an extension of this dissertation to investigate the impacts of the expected growth of housing prices on land prices over the urban space. This will be helpful in understanding land market behaviors and developing land use policies and planning regulations. Finally, the research can be extended to introduce a VES housing services production function, in which the elasticity of capital-land substitution depends on the
97
ratio of land and capital inputs and varies with location. Numerical simulations and empirical studies can be conducted to link the variant elasticity of capital-land substitution to urban land development and urban spatial structure.
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Appendices
Appendix I: Solutions of Impacts of Elasticity of Capital-Land Substitution
?S ??
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1
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2 I? 1 + 1 M
?
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?
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y z z z z z z z z z {
i j j j j j j j j j j j j j j j j j j j j j 1 j j ? jp ? 2 H? 1 + ? L j j j j j j j j j j j j j j j j j j j j j k
?1+? ? i y ?1+? ?1+? ? j z i 1?? y j z j z i ??y J n N j z z j z j j z z j z j p ? ? j z z j z j j z z j z j 1 ? ? + ? j z z j z j j z z j z j j z 1?? z j z j j z j z j z j z { k k { k { ?
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?1+? ?1+??? y 1? y ? N z ?? z z
z z z {
z z z z {
?1+??? ? J n N i y j z y 1?? i J n N?1+??? z j z j ? LogB p ? ? F z j p?? j z z j z 1?? z j F +LogBj j z z j z j j z ?1+? 1?? z j j z z j i y j z j z j z 1 n n { k j z z ? I? 1 + M j + ? 1 + Log B F j z j ? j z 2 n j z ? j ? p?? z n ? p ? J N z j z p?? k { j z j z j z j z j z k { + ? 1 +? ii J n N?1+??? y 1? y ? ?? j z z jj z p?? z z 1? ?+ j ? z jj z j z j z 1?? jj z { k k {
j LogB1 ? ? + j j jj j
i j i jj j kk
y y z z z z z z z zz z z z z z z z z z z z ?1+? z ? zz z ? 1 +? n y ? z z ?? z J N y 1?? z z z z z p?? z z zz z ?F z z z z z z z z 1?? z z zz z { z z { z z z zz z z z 2 ? z z z zz z z z z z z zz z z z z z z z z zz z z z z z z zz z z z z z z zz z {{
99
i j j j j j j j j j j j j j j j j j j j j j 1 j j ? j? 2 H? 1 + ?L j j j j j j j j j j j j j j j j j j j j j k
?h ??
? i j ? i j j z y 1?? y i J n N?1+? ? ? z j j z j j j z z j p ? ? j j z z j j j z z j 1 ? ? + j j z z j j j z z j j 1? ? j z z j jj z j j { k k { k
?1+?
y ?1+? z z z z z 2 z ?z ? z z z z z {
?
?1+??? ? J n N i y i j z ?1+??? y j i j z j J n N j z 1?? ? LogB p ? ? F j z j z j j z p?? j z ?1+? j 1?? j z j z ? Log B F + j j z j j z z j ? 1 +? n y ? ? 1 +? 1 ?? i j z j z j j z ?? z y 1?? z i y i Jp??N j jj z j j j z j z j 1M j n n Fz z k z { jj j j z z j ? I ? 1 + + ? 1 + Log B z z j j z j z j ?z z z j j 2 n j j z j 1 ?? ? ? p ? ? z j n ? p ? J N j z j j z j p ? ? { k { k j z j { k j z j j z j j z j j z j j j k { + j j j j ? 1 +? j j ii J n N?1+??? y 1? y ? j ?? j z j z jj z j z j z j 1? ? + j ? z j j p?? z j z j z j 1?? jj z j j { k j k { j j j j j j j j j k
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y y z z z z z z z zz z z z z zz z z z z z ?1+? z ? zz z ?1+??? y 1?? y ? z z J n N z z z z z z z p?? z z z ?F z z z zz z z z z 1?? z z z z { zz z { z z z z z zz z ?2 z z z zz z z z z z z zz z z z z z z z z zz z z z z z z zz z z z z z z zz z {{
100
i j j j j j j j np? j j j j j j k
?? ??
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?1+? ? zy z ?1+? y ? y z 1?? z y zz z z z z z z z z z z z z z z z z z z z z z z z z z z z z z zz z { { {{ ?
ii J n N?1+? ? ? j j jj j p?? n i n z i i n z z jj j j z H? 1 + ?L ? LogB jn ? p ? j j z z LogB1 ? ? + j p? j F +j j j j j p? ? 1? ? j k p? ? { k k p? ? { { jj kk y?y y 1?? i Jn ? p ? J n N N ? z j z j p?? z z j nj z j z j z j n H? 1 + ?L { k
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101
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p??
?j n? J n N j j j p??
i Jn?p ? J n k
p?? n H?1+?L
N N?
?
?1+??? y y ?1+ 1 j i J n N z ? ? z p?? n z ? ?j F + p ? J n N H1 ? 3 ? + 2 ?2L LogB n Fz z j z jJn ? p ? J p ? ? N N LogB z 1?? p?? p?? z { ? { k ? 2 Jn ? p ? J n N N H? 1 + ?L2
1
p??
i 1 j ? j i j ji j Jn ? p ? J n N N ? y ?1+ 1 z j ? j j j z n y j p?? ? j 2i j z j j j z j z j j z p ? ? j j z j j j ? 2 z j j n H? 1 + ?L z j k p? ? { j jj Jn ? p ? J n N N H? 1 + ?L2 j j { p?? j kk k
1
? y z z z z z z z z z {
?1+?
i i ? j j i j j j i Jn ? p ? J n N N ? j j j j j j j j p?? j j j j j j j j 1 + ? ? 1 + j j j j j j j j j j n H?1 + ?L j j j jj j j j j kk k k
y ?1+ 1 z z ? z z z z z {
1
yz y ?1+? ? z y zz z z z z z z z z z z z z z ? z z z z z z z z z z z z z zz z { {{
?1+?
1
i j j j j j y j z ?1+? j z n j z i y J N ?? j z j z ? ? j z j z n n n 1 i y z y p?? i y i j z 2 j z j z j z j z j j z F+ p? j Fzz ? z z LogB z H1 ? 3 ? + 2 ? L LogB jn ? p ? j j j j? z j z ? 1 +? z 1? ? p ? ? zz n N 1 M ?2 j jk k p? ? { { k p? ? { j JJ ? ? N I ? 1 + j z j p?? ? k {z j z j j { j j j k i j j j j j j ?1+? j n j i ?? j j J p?? N j j j jLogBj j H?1 + ?L j j j j j 1 ? ? j j j j k j j j j j j k
?1+? ii j ?? J n N j j j j j j p?? j jj j j j j 1?? j jj kk
y ?1+ 1 z z ? z z z z z {
1
y ? z z z z z z z z z z {
?1+?
i j j ?1+? j j n y i j j z j j z ?j 1? ? + j j j j j j j j j p ? ? j k { j j jk j j k k
?1+? 1 ?1+? ii y ? j z ??y J n N ?1+ 1 z j z jj z z j ? p ? ? j z z j
1? ?
z z z z {
z z z z z z {
z z z z z ?z z z z z z {
1 y ?1+? z
?1+??? i y J n N y j zy z z j z z H?1+?L LogB n F z LogB p ? ? F j z z p?? z j z z z 1 ?? j z z z + ?j 1 z z z 2 1 ?? n ? j z z z ?N ? z J?1+J N j z z 1 y j z z z ? 1 + p ? ? z z z ? z z z k { zz z? z F ? z z z z z z 2 1 z z zz z I?1 + M z z ? z z { z zz z z z z z z zz z {{
102
i j j j j j j j j j j j j j j j j j j j j j j j j j 1 j j j ? j ? 1 +? j JJ n N ? ?N I?1 + 1 M j j p?? ? j j j j j j j j j j j j j j j j j j j j j j k
1 ?1+? ii j y ?1+ 1 J n N ??z j j j j z ? p?? j j z j j z jj j z j z j z 1? ? j jj k { k
y ? z z z z z z z z z z {
?1+?
i n z j j z k p? ? {
y?1+?
i j ?1+? ii n j j ?? j j j J p?? N j j j jj j j j ?j 1?? + j j j j j j j jj 1? ? j j j j j kk k
y ?1+ 1 z z ? z z z z z {
1
?1+? y z ?1+? y ? z z z z z z z z z z ?z H? 1 + ?L z z z z z z z z z z { {
1
i j j j j j j j j ii J n N?1+??? y 1 1 j j j j z ?1+ j j j p?? z jj ? jj j z j j z j j 1?? j jk j { j k j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j k
?1+? y ? z
z z z z z z {
?1+??? y i y z j i y J n N zy j z j z z p?? j z j z 1 H?1+?L LogB n F z zz j F z j z z j i J n N?1+??? z y p?? z z j LogB z z j z 1?? j z z j z z H?1+?L j + j z z j ?1+ 1 z j z z j z p?? z j 2 1 ?? j z n z j z j z z ? ? Log B F j z j ?N ? z J?1+J N z j z z j z z j 1 ?? z j z j z z z j p ? ? j z zz j z j z z j z z {z k { k z z j ?j + z z z z j z z 2 ?2 ?1+? z j z z J?1+ 1 N ? 1 z j z z ? z j z z ii J n N?1+??? y y ? z j z z j z z j z z j j z ?1+ 1 z p ? ? z j z z j z j z ?z z j z j z LogB1 ? ? + j ?F z z j z j z j z z j z zz j z 1?? j z jk z z z z z { z z k { ? k { z z z z ? z z ?1+? y z z H ?1 + ?L2 z z i 1 z z j z ii J n N?1+??? y y ? z z j z j z z z j z j z ?1+ 1 z j z z j z p ? ? j z z j z z j1 ? ? + j ? z jj z ?z H?1 + ?L j z z j z z z z z j z 1?? j z z z j z jk z z z j z { z z k { z z z z k { z z z z z z zz z z z z z z zz z z z z zz {{
i j j j j j j j j j j j j j j j j j j j j j j j j j 1 j j j? 2j 1 j I? 1 + M j j j ? j j j j j j j j j j j j j j j j j j j j j k
i j ?1+? i j j i j J n N ?? j j j j j j p?? j j j j j j 1 ? ? + j j j j j j j j 1 ? ? j j j j j kk k
y ?1+ 1 z z ? z z z z z {
1
?1+? y ?1+? z ? y z z z z z z z z z z z ? z z z z z z z z z z { { ?
i j j j j j j j j i J n N?1+??? y 1 1 j j j ji j z ?1+ j j p?? z j ? j z jj jj z j j 1?? j jj j { j j kk j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j k
?1+? y ? z
z z z z z z {
i j j 1 j n ?1+??? y i j j z j j Jp? ?N z ?1+ 1 j z j z j ? LogBj j z j j z 1?? j j z j z j j k { ? I? 1 + 1 M j j 2 ? j ? j j j j j j j j j j k j j 1? ? + j jj j
F
+
?1+??? y i J n N z j z j p?? j H?1+?L LogB n F z z j F j p?? z z j LogB 1?? z H?1+?L j + j z j 1?? ?N ? z z j ?2 z j J?1+J n N z j z j p?? z j { k
J?1+ 1 N ?
2
?
1 i ?1+??? y j i J pn N jj z ?1+ 1 ?? z ? z z j 1 ?? jk { k
y ? z z z z ? z z z {
?1+?
y z z z z z z z z z z z z z z z 1 z z i ?1+? z j i Jpn ?? z N y ?1+ 1 z jj ?? z j z ? z j j z LogB1 ? ? + j z j j z z j 1 ?? z jk { { + k ?2
y yz z z z z z z z zz z z z z z z zz z z z z z z zz z z ?1+? z z z z z y ? z zz z z z z z z z z z ? F z zz z z z z z z z z z zz { z z z z zz z z z z z z zz z z z z z z zz z z z z z z z z zz z z z z z z zz z z z z z z zz z z z z z zz z {{
103
Appendix II:
Simulated Impacts of Capital-Land Substitution
(Selected parameter values)
p
n ? ? ?
?S ??
3.0702 8.5754 27.0033 7.56249 80.0829 5897.16 14.7907 1102.53 2.52334 × 109 6.03828 32.6895 227.374 11.9472 244.529 72215.5 21.273 3021.69 6.83001 × 1010 9.32596 88.2102 1194.21 16.7242 591.682 508607. 28.245 6834.28 7.70159 × 1011
?2S ?p??
0.00160289 0.00807346 0.0388654 0.00239554 0.0593352 9.80324 0.00357154 0.726286 5.73211 × 106 0.00210748 0.0246564 0.282051 0.00308436 0.160731 105.932 0.00452759 1.81863 1.27341 × 108 0.00265411 0.0604291 1.38486 0.00383249 0.367349 689.408 0.00556523 3.94992 1.26678 × 109
?r ??
8.16207 14.8503 30.7643 82.0227 325.38 6660.91 348.17 6446.27 1.66521 × 109 57.242 136.194 446.451 446.524 2141.31 112069. 1809.16 38950. 6.41848 × 1010 250.727 695.819 3248.49 1827.25 9635.46 993658. 7308.21 168606. 9.3813 × 1011
? 2r ?p??
0.0112323 0.0234257 0.0577676 0.0895852 0.405463 12.5581 0.362961 7.54881 4.18856 × 106 0.0632802 0.168884 0.673825 0.458471 2.38584 184.284 1.83043 41.9717 1.32485 × 108 0.260053 0.784029 4.4427 1.84397 10.2271 1502.26 7.33645 175.44 1.70829 × 109
?? ??
0.0297317 1 0.0776473 0.215826 0.059599 0.32032 3.01938 0.0728364 0.521065 14.2214 0.0116386 1 0.056923 0.304314 0.0193153 0.186194 3.13397 0.0226749 0.28267 11.4111 0.00450764 0.0380003 0.352157 0.00690516 0.112759 3.08228 0.0079473 0.165971 9.65307
?h ??
0.00407306 0.00756336 0.0130116 0.354941 2.38584 184.284 1.20111 41.9717 1.32485 × 108 0.00407306 0.00756336 0.0130116 0.354941 2.38584 184.284 1.20111 41.9717 1.32485 × 108 0.0194279 0.0494516 0.122496 1.4232 10.2271 1502.26 4.808 175.44 1.70829 × 109
1000 1 0.1 0.1 0.1 1000 1 0.1 0.1 0.5 1000 1 0.1 0.1 0.9 1000 1 0.1 0.5 0.1 1000 1 0.1 0.5 0.5 1000 1 0.1 0.5 0.9 1000 1 0.1 0.9 0.1 1000 1 0.1 0.9 0.5 1000 1 0.1 0.9 0.9 1000 1 0.5 0.1 0.1 1000 1 0.5 0.1 0.5 1000 1 0.5 0.1 0.9 1000 1 0.5 0.5 0.1 1000 1 0.5 0.5 0.5 1000 1 0.5 0.5 0.9 1000 1 0.5 0.9 0.1 1000 1 0.5 0.9 0.5 1000 1 0.5 0.9 0.9 1000 1 2 0.1 0.1 1000 1 2 0.1 0.5 1000 1 2 0.1 0.9 1000 1 2 0.5 0.1 1000 1 2 0.5 0.5 1000 1 2 0.5 0.9 1000 1 2 0.9 0.1 1000 1 2 0.9 0.5 1000 1 2 0.9 0.9
104
p
n ? ? ?
?S ??
7.58745 54.3388 528.367 14.2061 382.763 195371. 24.5793 4563.03 2.38207 × 1011 11.9488 163.003 3397.2 20.4967 1037.26 1.71458 × 106 33.7053 11551.2 3.30391 × 10 16.7265 396.454 15675. 27.308 2371.4 9.87896 × 10 43.4907 25207.4 2.54366 × 1013
6 12
?2S ?p??
0.000236694 0.00388134 0.0631233 0.000343962 0.0243658 27.4798 0.000502068 0.268363 4.15457 × 107 0.000307995 0.0107059 0.381827 0.000441408 0.0627822 222.702 0.000636975 0.656336 5.08062 × 10 0.000383686 0.0248785 1.69975 0.000544475 0.139629 1215.71 0.000779114 1.40748 3.59465 × 109
8
?r ??
121.193 313.857 1233.88 905.975 4583.62 341423. 3641.02 81554.7 2.55898 × 1011 642.429 1914.31 11049.3 4595.55 25231. 3.84798 × 106 18316.3 434479. 4.70361 × 10 2610.87 8371.75 64539.5 18451.3 105338. 2.69567 × 10 73377.1 1.78601 × 10
6 7 12
? 2r ?p??
0.0128781 0.0368196 0.176225 0.0920181 0.496639 53.6794 0.36656 8.61178 4.94105 × 107 0.0654378 0.207731 1.44465 0.461604 2.62682 556.256 1.835 44.6031 8.00752 × 10 0.26276 0.876821 8.02144 1.84786 10.7709 3683.56 7.34206 181.122 7.04957 × 10
9 8
?? ??
0.00732189 1 0.0469867 0.331021 0.0116126 0.145392 3.11999 0.0134835 0.21689 10.4722 0.0023156 1 0.0280428 0.372798 0.0034248 0.0798291 3.00682 0.00390521 0.115947 8.71811 0.000812889 0.0170724 0.391165 0.00115706 0.0465157 2.85785 0.00130544 0.0666186 7.54982
?h ??
0.00476872 0.0115105 0.0265717 0.355702 2.52874 328.137 1.2019 43.557 3.43121 × 108 0.00476872 0.0115105 0.0265717 0.355702 2.52874 328.137 1.2019 43.557 3.43121 × 108 0.0201421 0.0600061 0.190667 1.42398 10.5514 2391.24 4.80882 178.872 3.58966 × 109
10000 1 0.1 0.1 0.1 10000 1 0.1 0.1 0.5 10000 1 0.1 0.1 0.9 10000 1 0.1 0.5 0.1 10000 1 0.1 0.5 0.5 10000 1 0.1 0.5 0.9 10000 1 0.1 0.9 0.1 10000 1 0.1 0.9 0.5 10000 1 0.1 0.9 0.9 10000 1 0.5 0.1 0.1 10000 1 0.5 0.1 0.5 10000 1 0.5 0.1 0.9 10000 1 0.5 0.5 0.1 10000 1 0.5 0.5 0.5 10000 1 0.5 0.5 0.9 10000 1 0.5 0.9 0.1 10000 1 0.5 0.9 0.5 10000 1 0.5 0.9 0.9 10000 1 2 0.1 0.1 10000 1 2 0.1 0.5 10000 1 2 0.1 0.9 10000 1 2 0.5 0.1 10000 1 2 0.5 0.5 10000 1 2 0.5 0.9 10000 1 2 0.9 0.1 10000 1 2 0.9 0.5 10000 1 2 0.9 0.9
4.50591 × 1013
105
p
n ? ? ?
?S ??
10.4386 116.123 1904.38 18.328 759.87 876420. 30.5706 8630.52 1.48495 × 1012 15.6472 330.731 11462.6 25.7749 2001.07 6.92104 × 106 41.2952 21461.6 1.68843 × 1013 21.3223 782.583 50904.6 33.8065 4504.19 3.7259 × 10 52.761 46409.7 1.15054 × 10
14 7
?2S ?p??
0.0000945261 0.00259874 0.072533 0.000136026 0.0155356 38.8278 0.000196963 0.164904 7.89247 × 107 0.000122257 0.00697447 0.417058 0.000173824 0.0394679 286.844 0.000249145 0.400654 8.08228 × 108 0.000151579 0.0159449 1.80008 0.000213637 0.0870066 1474.73 0.000303897 0.855602 5.12785 × 10
9
?r ??
381.01 1094.05 5622.17 2749.6 14786.6 1.8226 × 106 10977. 256728. 1.94056 × 1012 1954.11 6188.55 45064.4 13831.8 78460.1 1.81564 × 107 55022.3 1.33371 × 106 2.86252 × 1013 7869.71 26184.5 247499. 55413.5 322291. 1.17601 × 10 220226. 5.42379 × 10 2.39564 × 10
6 14 8
?2r ?p??
0.0130483 0.040339 0.250885 0.0922644 0.518215 89.9672 0.366918 8.84528 1.14184 × 108 0.0656587 0.217309 1.88423 0.46192 2.68204 835.914 1.83545 45.1723 1.51698 × 109 0.263034 0.898903 9.94679 1.84824 10.8932 5162.01 7.34262 182.34 1.18206 × 10
10
?? ??
0.00336718 0.0333144 0.362239 0.00507222 0.096899 3.0519 0.00581214 0.141716 9.22063 0.00101332 0.0189805 0.388456 0.00145228 0.052115 2.89118 0.0016417 0.0748222 7.77177 0.000346094 0.0112601 0.39706 0.000481744 0.0299319 2.72328 0.000540042 0.0425317 6.78348
1 1
?h ??
0.00509018 0.0165721 0.0634334 0.356054 2.68204 835.914 1.20227 45.1723 1.51698 × 109 0.00509018 0.0165721 0.0634334 0.356054 2.68204 835.914 1.20227 45.1723 1.51698 × 109 0.0204723 0.0726075 0.356777 1.42434 10.8932 5162.01 4.80919 182.34 1.18206 × 1010
30000 1 0.1 0.1 0.1 30000 1 0.1 0.1 0.5 30000 1 0.1 0.1 0.9 30000 1 0.1 0.5 0.1 30000 1 0.1 0.5 0.5 30000 1 0.1 0.5 0.9 30000 1 0.1 0.9 0.1 30000 1 0.1 0.9 0.5 30000 1 0.1 0.9 0.9 30000 1 0.5 0.1 0.1 30000 1 0.5 0.1 0.5 30000 1 0.5 0.1 0.9 30000 1 0.5 0.5 0.1 30000 1 0.5 0.5 0.5 30000 1 0.5 0.5 0.9 30000 1 0.5 0.9 0.1 30000 1 0.5 0.9 0.5 30000 1 0.5 0.9 0.9 30000 1 2 0.1 0.1 30000 1 2 0.1 0.5 30000 1 2 0.1 0.9 30000 1 2 0.5 0.1 30000 1 2 0.5 0.5 30000 1 2 0.5 0.9 30000 1 2 0.9 0.1 30000 1 2 0.9 0.5 30000 1 2 0.9 0.9
106
Appendix III:
Estimation of CES Housing Production Function
Supposing it is already known that ? = 0.5 , the other two parameters ? and
? of the CES housing production function can be estimated by the following
approaches. The first approach is to substitute ? = 0.5 in the production function by (19) and it can be written:
h ?1 = ? ?1?S ?1 + ? ?1 (1 ? ? )
(66)
where h is the housing output per unit of land and S is the capital intensity per unit of land. Thus ? and ? can be estimated by the following linear function:
h ?1 = b1S ?1 + b2 + ?
(67)
where b1 = ? ?1? , b2 = ? ?1 (1 ? ? ) , and ? is the disturbance term. h is measured by the floor space in square meters; S is the capital density, estimated by
S = ( ph * 0.7 ? r ) / n where n is assumed to be unity and 0.7 comes from the
assumption of the 30% average profit ratio of sales. Once b1 and b2 are estimated, ? and ? can be easily to be calculated. Table III-1 reports the estimated results and the estimated ? and ? are respectively 0.000315719 and 0.999957485. Table III-1
h ?1
Obs=254, R-sq=0.573 b1 b2 Coef. 3167.237 0.1346622 t 18.39 10.22 Sig. **** ****
delta 0.999957485 gama 0.000315719 ****99.9%, ***99%, **95%, * 90%
107
The second approach is to substitute ? = 0.5 in (57) or (58) and apply the non-linear least square method, where ? and ? can be estimated by treating h as the dependent variable and p as the independent variable. Table III-2 reports the estimated results and the estimated ? and ? are 0.0016509 and 0.9997479, 0.0009533 and 0.999854, respectively. Table III-2
h Obs=254, R-sq=0.7456 Coef. t Sig. gama 0.0016509 1.42 delta 0.9997479 4631.85 **** ****99.9%, ***99%, **95%, * 90% ln(h) Obs=254, R-sq=0.8513 Coef. t Sig. 0.0009533 3.29 **** 0.999854 16649.77 ****
Based on the above estimation, ? and ? should fall into the intervals of 0.99975-0.99996 and 0.000316-0.000953, respectively.
108
Appendix VI:
Sigma:
Estimation of Two Sub-Periods
1999-2001 obs=151, R-sq=0.7265 Dependent=ln(S) coef. t ln(r) 0.7022315 17.49 type_2 0.0428595 0.42 type_3 0.008564 0.11 type_4 -0.2547021 -1.52 type_5 -0.1526961 -1.18 type_6 -0.1404384 -0.78 type_7 0.0267254 0.18 DIFF 0.0137849 0.54 CONST 4.402439 14.74 ****99.9%, ***99%, **95%, * 90%
OLS: 0.70?0.62
sig. ****
****
2002-2003 obs=254, R-sq=0.6877 coef. t 0.6178752 13.34 0.0970794 1.02 0.0141701 0.12 (dropped) 0.1513824 0.36 -0.4004511 -1.63 (dropped) 0 0.1116875 2.7 5.092465 14.73
sig. ****
** ****
1999-2001 First stage regression obs=151, R-sq = 0.3912, F(11,139)=8.12 Dependent: ln (r) Coef. t sig. LA -0.0000445 -2.74 ** LA_square 1.97E-10 0.58 LY_2000 0.0613893 0.41 LY_2001 0.0387226 0.23 LY_2002 (dropped) LY_2003 (dropped) type_2 0.5002565 2.7 ** type_3 0.2794933 1.97 * type_4 -0.3259073 -1.07 type_5 0.5889165 2.47 ** type_6 -0.3797841 -1.17 type_7 -0.074253 -0.28 DIFF -0.009061 -0.19 CONST 7.761807 39.56 **** Instrumental variables (2SLS) regression obs=151, R-sq=0.7008 Dependent: ln(S) Coef. t sig. ln (r) 0.5556762 6.87 **** type_2 0.1054098 0.95 type_3 0.0720154 0.81 type_4 -0.3374698 -1.88 * type_5 -0.0225876 -0.15 type_6 -0.1892699 -1 type_7 0.0022114 0.01 DIFF 0.009637 0.36 CONST 5.467817 9.24 **** ****99.9%, ***99%, **95%, * 90%
IV: 0.56?0.44
2002-2003 First stage regression obs=103, R-sq = 0.3227, F(8,94)=5.6 Coef. t sig. -0.0000217 -4.82 **** 5.28E-11 4.59 **** (dropped) (dropped) -0.1150343 -0.63 (dropped) 0.308107 1.62 0.5283118 2.34 ** (dropped) 0.9566668 1.16 -0.2855733 -0.58 (dropped) -0.1078504 -1.18 7.685078 43.32 **** Instrumental variables (2SLS) regression obs=254, R-sq=0.6403 Coef. t sig. 0.4415493 3.97 **** 0.1596857 1.48 0.144792 1 (dropped) 0.3480703 0.76 -0.4563119 -1.72 * (dropped) 0.0781371 1.62 6.375571 7.84 ****
109
Distance gradients:
Land price gradient:
1999-2001 Dependent: ln(r ) obs=159, R-sq=0.6479 Coef. t sig. distance -0.095465 -4.11 **** district_2 -0.4776704 -1.02 district_3 -0.1774067 -0.52 district_4 -0.0023648 -0.01 district_5 -0.0365615 -0.12 district_6 0.055358 0.13 district_7 -1.490193 -2.86 *** LA -0.0000163 -3 **** LY_2000 -0.0930291 -0.68 LY_2001 -0.1248155 -0.81 LY_2002 (dropped) LY_2003 (dropped) CONST 8.78168 29.21 **** ****99.9%, ***99%, **95%, * 90%
OLS: -0.095?-0.067
2002-2003 obs=107, R-sq=0.6186 Coef. t sig. -0.0667709 -2.56 *** 0.1628664 0.28 -0.2120427 -0.35 -0.4940625 -1.05 -0.6162681 -1.25 -0.6907258 -1.13 -2.125974 -3.09 **** 5.92E-07 0.36 (dropped) (dropped) 0.1782791 1.16 (dropped) 8.737746 19.27 ****
Capital density gradient:
1999-2001 Dependent: ln(S ) obs=139, R-sq=0.3935 Coef. t sig. distance -0.0661747 -3.3 *** district_2 -0.607306 -1.5 district_3 0.0048936 0.02 district_4 -0.2657346 -1.08 district_5 -0.2230217 -0.88 district_6 -0.1732663 -0.46 district_7 -0.7576845 -1.51 0.2532012 1.6 type_2 0.2213518 1.82 * type_3 type_4 -0.4055043 -1.31 type_5 0.2127154 0.92 0.1092993 0.31 type_6 -0.0641873 -0.29 type_7 FUR 0.0996064 1.01 DIFF 0.0114207 0.29 CONST 10.40865 41.45 **** ****99.9%, ***99%, **95%, * 90%
OLS: -0.066?-0.059
2002-2003 obs=103, R-sq=0.5141 Coef. t sig. -0.0588481 -2.99 ** -0.0312926 -0.08 -0.2796232 -0.63 -0.5325892 -1.54 -0.5377934 -1.49 -0.748735 -1.67 -0.8589035 -1.66 * 0.2199796 1.66 * 0.3006749 1.99 ** (dropped) 0.3718363 0.67 -0.169886 -0.51 (dropped) 0.0757755 0.58 0.0970926 1.72 * 10.73471 32.47 ****
110
Housing price gradient:
1999-2001 Dependent: ln(p ) obs=139,R-sq=0.5937 Coef. t sig. distance -0.0350837 -4.6 **** district_2 -0.1205275 -0.79 district_3 -0.3313874 -2.83 *** district_4 -0.280393 -3.05 **** district_5 -0.184606 -1.95 * district_6 -0.303356 -2.14 *** district_7 -0.5480769 -2.91 *** type_2 0.0006714 0.01 type_3 -0.059781 -1.32 type_4 -0.0487966 -0.42 type_5 -0.2066416 -2.36 *** -0.0311322 -0.23 type_6 type_7 -0.0033267 -0.04 FUR -0.0042606 -0.11 FA 8.71E-07 1.53 HY_2000 -0.006265 -0.1 HY_2001 -0.0789065 -1.33 HY_2003 -0.0052702 -0.07 HY_2004 -0.0170736 -0.19 HY_2005 -0.1262459 -0.79 HY_2006 0.0686494 1.25 HY_2007 0.2157619 0.98 CONST 9.385247 85.25 **** ****99.9%, ***99%, **95%, * 90%
OLS: -0.035?-0.039
2002-2003 obs=103,R-sq=47660.5115 Coef. t sig. -0.0386754 -3.83 **** 0.1353335 0.65 -0.1954402 -0.87 -0.0955313 -0.54 0.0069479 0.04 -0.1573831 -0.69 0.00145 0.01 -0.0159167 -0.23 -0.0875994 -1.13 (dropped) -0.1974976 -0.69 0.0200667 0.12 (dropped) 0.0942277 1.38 1.40E-07 0.72 (dropped) (dropped) -0.216687 -1.71 * -0.1243462 -1.02 0.0120849 0.09 0.0638622 1.13 0.2450864 0.8 9.523182 45.29 ****
111
Lamda: OLS: 1.886?1.519 (according to above OLS estimates)
SUR 1999-2001 Dependent: ln (p ) obs=139, R-sq=0.5937 coef. t sig. -0.035033 -5 **** -0.120029 -0.86 -0.331745 -3.09 *** -0.280464 -3.33 **** -0.184784 -2.13 *** -0.303437 -2.33 *** -0.548974 -3.17 *** 0.0011134 0.02 -0.059166 -1.42 -0.049894 -0.47 -0.205077 -2.56 ** -0.032229 -0.26 -0.003806 -0.05 -0.004111 -0.12 8.97E-07 1.71 * -0.006195 -0.11 -0.079076 -1.45 -0.005365 -0.07 -0.01825 -0.22 -0.127976 -0.87 0.08542 1.21 0.2184223 1.08
SUR: 2.400?1.584
distance district_2 district_3 district_4 district_5 district_6 district_7 type_2 type_3 type_4 type_5 type_6 type_7 FUR FA HY_2000 HY_2001 HY_2003 HY_2004 HY_2005 HY_2006 HY_2007 LA LY_2000 LY_2001 LY_2002 LY_2003 CONST
ln (r ) obs=139, R-sq=0.5370 coef. t sig. -0.0839871 -4.27 **** -0.4213375 -1.09 0.0348868 0.11 -0.0601065 -0.25 -0.0346842 -0.14 0.1701211 0.46 -0.3674741 -0.77
9.383475
92.91 ****
-0.0000283 -0.0714568 -0.038906 (dropped) (dropped) 8.801487
-5.88 **** -0.57 -0.28
34.85 ****
SUR 2002-2003 ln (p ) ln (r ) obs=103, R-sq=0.4761 obs=103, R-sq=0.5158 coef. t sig. coef. t sig. -0.038257 -4.18 **** -0.060597 -2.62 *** 0.1403827 0.74 0.1666664 0.33 -0.195436 -0.95 -0.158523 -0.29 -0.098352 -0.62 -0.501811 -1.21 0.0066776 0.04 -0.664141 -1.53 -0.163482 -0.79 -0.811953 -1.51 -0.00042 0 -1.654584 -2.7 *** -0.008698 -0.14 -0.071213 -1.01 (dropped) -0.174516 -0.67 0.0303399 0.2 (dropped) 0.0921512 1.49 1.57E-07 0.89 (dropped) (dropped) -0.199691 -1.74 * -0.111332 -1 0.0288473 0.24 0.058776 0.98 0.2981786 1.07 -8.28E-07 -0.56 (dropped) (dropped) 8.638426 21.54 **** (dropped) 9.49856 49.78 **** 8.673336 21.76 ****
****99.9%, ***99%, **95%, * 90%
112
Dependent: ln(p ) LY_2000 LY_2001 LY_2002 LY_2003 LA LA_square type_2 type_3 type_4 type_5 type_6 type_7 FUR HY_2000 HY_2001 HY_2003 HY_2004 HY_2005 HY_2006 HY_2007 FA CONST
dependent: ln(r) ln (p ) LY_2000 LY_2001 LY_2002 LY_2003 LA LA_square CONST
1999-2001 first stage regression obs=139, R-sq=0.1559, F(18,120)=1.23 coef. P>t sig. 0.1059809 1.01 0.1297779 1.02 (dropped) (dropped) -5.46E-06 -0.62 -9.22E-11 -0.58 0.0089699 0.1 -0.0694731 -1.09 0.0712955 0.45 -0.1391959 -1.15 -0.2103704 -1.15 0.0006209 0.01 0.0122603 0.23 -0.020139 -0.18 -0.1603289 -1.2 -0.0610789 -0.39 -0.1647709 -0.99 -0.1216464 -0.52 (dropped) 0.0195644 0.06 3.17E-06 2.56 ** 8.731107 87.21 **** Instrumental variable (2SLS) regression obs=139, R-sq=0.1765, lamda>1 *** coef. t sig. 3.252312 4.44 **** -0.2689838 -1.29 -0.2278908 -1 (dropped) (dropped) -0.0000871 -3.85 **** 1.18E-09 2.39 ** -20.02213 -3.15 **
IV: 3.25?2.07
2002-2003 first stage regression obs=103, R_sq=0.1673, F(13,89)=1.38 Coef. t sig. (dropped) (dropped) 0.0615543 0.85 (dropped) -3.47E-06 -1.21 -9.20E-12 -1.63 -0.0736675 -0.86 -0.0870994 -0.89 (dropped) -0.1035485 -0.3 -0.1406371 -0.68 (dropped) 0.1480448 1.87 * (dropped) (dropped) -0.2219412 -1.35 -0.1604551 -1.04 -0.06413 -0.37 (dropped) 0.3192789 0.83 2.12E-06 2.17 ** 8.954684 52.39 **** Instrumental variable (2SLS) regression obs=103, R_sq=2193, lamda>1 * coef. t sig. 2.070356 3.35 *** (dropped) (dropped) -0.2373032 -1.37 (dropped) -0.0000271 -5.92 **** 6.48E-11 5.46 **** -10.51844 -1.92 **
****99.9%, ***99%, **95%, * 90%
113
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doc_907434215.pdf
A market to be competitive, there must be more than a single buyer or seller. It has been suggested that two people may trade, but it takes at least three persons to have a market, so that there is competition in at least one of its two sides.[1] However, competitive markets, as understood in formal economic theory, rely on much larger numbers of both buyers and sellers.
ABSTRACT
Title of Document:
MARKET FORCES AND URBAN SPATIAL STRUCTURE: EVIDENCE FROM BEIJING, CHINA. Xingshuo Zhao, Doctor of Philosophy, 2010
Directed By:
Dr. Chengri Ding, Urban Studies and Planning Program
This dissertation contributes to the literature on urban spatial structure by addressing two research questions. First, it empirically examines the urban economic theory by testing the relationship between the distance elasticities of land prices and housing prices. The theory indicates that land prices are more elastic with respect to distance from the city center than housing prices; in other words, land prices decline faster than housing prices. Using data from Beijing, which include matched housing and land prices, my findings support the theory. Second, this dissertation investigates the impacts of housing services production in general and the impacts of the capital-land substitution in particular on urban spatial structure. Using a constant elasticity of substitution (CES) production function for housing services, I theoretically derive the impacts of the elasticity of capital-land substitution on urban spatial structure, which is measured in terms of the distance gradients of land prices and capital densities, the housing output per unit of
land, and the ratio of the distance elasticity of land prices to the distance elasticity of housing prices. The derived results suggest that an increase in the elasticity of capitalland substitution leads to increases in the land price, the capital density, and the housing output per unit of land at any location within the city, flattening of the land price and capital density curves, an increase in the ratio of the distance elasticity of land prices to the distance elasticity of housing prices, an expansion of the city boundary, and a growth in the population. These theoretical results are verified by numerical simulations and empirical estimations using the Beijing data. The simulations also reveal the magnitudes of these impacts: a 1% change in the elasticity of capital-land substitution leads to 15-20% changes in the total land value and housing output. The findings of this dissertation have practical implications in housing market behaviors, land value assessment for property taxation, and urban land use policy and planning.
MARKET FORCES AND UBAN SPATIAL STRUCTURE: EVIDENCE FROM BEIJING, CHINA.
By Xingshuo Zhao
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 Doctoral of Philosophy 2010
Advisory Committee: Dr. Chengri Ding, Chair Dr. James R. Cohen Dr. Marie Howland Dr. Gerrit J. Knaap Dr. Erik Lichtenberg
© Copyright by Xingshuo Zhao 2010
Dedication
To Father and Mother
ii
Acknowledgements
I would like to express my sincere gratitude to my advisor, Dr. Chengri Ding, for his intellectual guidance during my years at the University of Maryland. Without Dr. Ding’s thoughtful advice and encouragement I would not have completed this dissertation. I would also like to thank my committee members, James R. Cohen, Marie Howland, Gerrit J. Knaap, and Erik Lichtenberg, for their insightful comments and advice, as well as their encouragement. I would also like to acknowledge Dr. Xiaochen Meng and Liang Ma for providing the data used in this dissertation. I am grateful to all of the faculty and staff in the Urban Studies & Planning Program for their help. I owe many thanks to my fellow doctoral students and my friends for their friendship and support, especially Chao Liu, Doan Nguyen, and Jung Ho Shin. I would like to thank my friend Haipeng An for helping me in using Mathematica, Fanqing Ye for all the discussions, my roommates Junfeng Huang and Shuo Huang for their understanding and support. Special thanks should also go to Dr. Lin Yi-Jiun and Paul Miller for their help and concern. I thank Weichen Zhao and my mother for taking the photos used in this dissertation, and I appreciate Adan Martinez-Cruz and Jeffrey Tiell for proofreading the draft. I am grateful to all of my friends who are not physically around me but encourage me all the time through the Internet. Finally, I would like to thank my parents. Without their love, I would not have been able to accomplish this.
iii
Table of Contents
List of Tables ................................................................................................................ v List of Figures .............................................................................................................. vi Chapter 1: Introduction ............................................................................................ 1 1.1 Why Urban Spatial Structure Matters .................................................... 1 1.2 Research Questions ................................................................................ 2 1.3 Organization of the Dissertation............................................................. 5 Chapter 2: Market, Urban Spatial Structure, and Planning in China ....................... 7 2.1 Land Reform and Land Market .............................................................. 7 2.2 Housing Reform and Housing Market ................................................. 11 2.3 Spatial Structure ................................................................................... 18 2.3.1 Pre-Reform ........................................................................................... 18 2.3.2 Post-Reform.......................................................................................... 20 2.4 Urban Planning ..................................................................................... 21 Chapter 3: Literature Review ................................................................................. 24 3.1 Urban Spatial Structure and Form ........................................................ 24 3.2 Housing Services Production ............................................................... 30 Chapter 4: Housing Services Production and Urban Spatial Structure .................. 35 4.1 The CES Production Function for Housing Services ........................... 35 4.2 Impacts of Elasticity of Capital-Land Substitution .............................. 39 Chapter 5: Numerical Simulation........................................................................... 47 5.1 Impacts of Capital-Land Substitution................................................... 47 5.2 Marginal Effects of Capital-Land Substitution .................................... 50 5.2.1 Housing Price Distribution and Production Function .......................... 50 5.2.2 Marginal Impacts of Elasticity of Capital-Land Substitution .............. 53 5.2.3 Social Welfare Impacts ........................................................................ 61 Chapter 6: Empirical Evidence .............................................................................. 65 6.1 Research Area....................................................................................... 65 6.2 Data ...................................................................................................... 73 6.3 Urban Decaying Phenomenon .............................................................. 78 6.4 Ratio of the Two Distance Elasticities ................................................. 81 6.5 Elasticity of Capital-Land Substitution ................................................ 86 6.6 Impacts of Elasticity of Capital-Land Substitution .............................. 91 Chapter 7: Conclusion ............................................................................................ 93 7.1 Policy and Planning Implications ......................................................... 93 7.2 Recommendation for Future Studies .................................................... 97 Appendices.................................................................................................................. 99 Appendix I: Solutions of Impacts of Elasticity of Capital-Land Substitution ... 99 Appendix II: Simulated Impacts of Capital-Land Substitution......................... 104 Appendix III: Estimation of CES Housing Production Function ....................... 107 Appendix VI: Estimation of Two Sub-Periods .................................................. 109 Bibliography ............................................................................................................. 114
iv
List of Tables
Table 3-1 Table 5-1 Table 5-2 Table 5-3 Table 6-1 Table 6-2 Table 6-3 Table 6-4 Table 6-5 Table 6-6 Table 6-7 Table 6-8 Table 6-9 Table 6-10 Table 6-11
Empirical Estimation of Elasticity of Capital-land Substitution for Housing Production* ............................................................................ 32 Signs of Relevant Partial Derivatives by Simulation ........................... 49 Simulated Impacts of Elasticity of Capital-Land Substitution ............. 55 Simulated Total Impacts of Elasticity of Capital-Land Substitution in the City ................................................................................................. 62 Distribution of Population Density in Beijing ...................................... 69 Descriptive Statistics ............................................................................ 76 Numbers of Observations in Each District ........................................... 76 Numbers of Observations in Each Housing Type ................................ 77 OLS Estimations of Distance Gradients for Housing Prices, Land Prices, Capital Densities, and FARs ..................................................... 79 SUR Estimations of Distance Gradients for Housing and Land Prices 83 OLS and IV Estimations of the Ratio of the Two Distance Elasticities85 NLLS Estimations of Housing Production Function ........................... 87 NLLS Estimations of Housing Production Function ........................... 88 OLS and IV Estimations of Elasticity of Capital-land Substitution ..... 90 Comparison between Estimates for Two Sub-Periods ......................... 92
v
List of Figures
Figure 2-1
Land Leasing Market in China: Numbers of Plots and Hectares of Land Area, 1994-2005 ..................................................................................... 9 Figure 2-2 Land Leasing Market in China: Transaction Values, 1994-2005 ........ 10 Figure 2-3 Land Leasing Market in China: Numbers of Land Plots by Different Approaches, 1999-2005........................................................................ 10 Figure 2-4 Land Leasing Market in China: Hectares of Land Areas by Different Approaches in China, 1999-2005 ......................................................... 11 Figure 2-5 Commodity Housing Market in China: Floor Space and Value of Sales, 1999-2005 ............................................................................................. 13 Figure 2-6 Commodity housing market in China: Share in Housing Supply, 19952005 ...................................................................................................... 14 Figure 2-7 Residential Building Evolution in Zhongguancun Area, Beijing......... 16 Figure 2-8 Residential Building Evolution in Qinchuan Neighborhood, Xi’an .... 17 Figure 2-9 Beijing’s Skyline .................................................................................. 21 Figure 2-10 Detail Plan for Block 21, Plot 22, Shunyi District, Beijing .................. 22 Figure 5-1 Estimated Housing Prices over Urban Space ....................................... 51 Figure 5-2 Simulated Land Prices over Urban Space ............................................ 53 Figure 5-3 Simulated Housing Output per Unit of Land (FAR) over Urban Space .............................................................................................................. 53 Figure 5-4 Simulated Land Prices in Three Scenarios ........................................... 58 Figure 5-5 Simulated Capital Densities in Three Scenarios .................................. 58 Figure 5-6 Simulated Housing Out Put per Unit Land (FAR) in Three Scenarios 58 Figure 5-7 Simulated Ratios of the Two Distance Elasticities in Three Scenarios 59 Figure 5-8 Simulated Shares of Land Cost in Total Property Values in Three Scenarios .............................................................................................. 60 Figure 5-9 Simulated Urban Boundaries in Three Scenarios................................. 60 Figure 6-1 Land Leasing Market in Beijing: Total Number of Leases and Total Leasing Value, 1995-2005 ................................................................... 66 Figure 6-2 Commodity Housing Market Development in Beijing: Floor Space and Value of Sales, 1990-2005 ................................................................... 67 Figure 6-3 Spatial Concentration of City Functions .............................................. 68 Figure 6-4 Housing Prices, Land Prices, and FARs in the Study Area ................. 71 Figure 6-5 Administrative Area of Beijing and Research Area ............................. 74
vi
Chapter 1:
Introduction
1.1
Why Urban Spatial Structure Matters
Urban spatial structure is of both academic and practical importance and has
attracted wide interest from scholars, planners, and officials for the following reasons. First, urban spatial stricture is associated with urban agglomerative effects that serve as a primary engine for cities to exist and grow. Spatial proximity facilitates intrafirm economies of scale and scope, labor pooling, and technology spillover (Anas et al. 1998, Bertaud 2003, Ding 2009). Second, urban spatial structure and form can be used to measure and indicate the efficiency of urban resources, along with the land prices and housing prices.1 Efficient urban development requires land use intensity to vary with prices as a result of an optimal combination of land and capital in housing services production. Third, urban spatial structure is an important determinant for urban transportation demand, for it links to population density. Population density in turn plays a key role in determining trip length and frequency, mode choice, and the overall travel (Crane 2000, Boarnet & Crane 2001, Ewing & Cervero 2001). Finally, urban spatial structure is directly or indirectly connected to negative externalities. For instance, spatial separation of different land uses can be helpful to minimize the nuance effects resulting from spatial clustering of incompatible land uses. Studies of urban spatial structure are proved to be difficult and complicated. On the one hand, urban spatial structure reflects cumulated decision making by all
Land and housing prices refer to unit prices in RMB (Chinese yuan) per square meter throughout this dissertation.
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kinds of actors such as developers, investors, land owners, residents, planners, and government officials in urban land development. On the other hand, there are a variety of factors that influence the location, timing, uses and intensity of land development, including the market forces, infrastructure provisions, planning regulations, tax policies, social and cultural conventions, and natural endowments (Bertaud & Malpezzi 2003). Practically, it is of great value to understand urban spatial structure, for it helps planners and policymakers dealing with problems of urban development, shaping or reshaping urban structure and form to facilitate economic development and improve the overall social welfare for businesses and residents. For example, knowledge of urban spatial structure can guide planners to direct people and activities in certain spatial nodes to foster agglomerative effects (such as Manhattan in New York City), increase public transportation ridership (Transit Oriented Development), and reduce negative environmental impacts.
1.2
Research Questions
This dissertation addresses two research questions. The first research question
is an empirical question that focuses on testing the urban economic theory, which indicates that land prices are more elastic with respect to distance from the city center than housing prices; in other words, land prices decline faster than housing prices. This prediction is derived by treating land as an input factor in housing services production and regarding the demand for land as a derived demand. Despite many empirical studies on land and housing prices, few cases in the literature have
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examined land and housing prices of the same sites. Economic reform and rapid market development in China provide a good chance to conduct an empirical study of this kind. Taking advantage of the data collected from Beijing that include both land and housing prices from the same land development projects, this dissertation carries out an empirical inquiry on the relationship between land and housing prices by estimating and testing the ratio of the distance elasticity of land prices to the distance elasticity of housing prices.2 In addition, compared with abundant empirical evidence for the pattern of land and housing prices over the urban space in developed countries, fewer studies in the developing countries have been conducted; this dissertation contributes to the literature in this regard. The second research question focuses on examining the impacts of housing services production on urban spatial structure, in particular, the impacts of capitalland substitution. This dissertation investigates this question by (1) theoretical analysis that reveals the directions of the impacts (signs of partial derivatives); (2) numerical simulations that verify the analytical directions and examine the magnitudes of the impacts on social welfare; and (3) empirical estimations that provide evidence for the derived impacts. The theoretical model, which assumes a constant elasticity of substitution (CES) production function for housing services production, yields the following results: an increase in the elasticity of capital-land substitution leads to increases in the land price, the capital density, the absolute values of distance gradients of land prices and capital densities, the housing output per unit of land (or the FAR—floor area ratio) at any location with the city, an
The ratio of the distance elasticity of land prices to the distance elasticity of housing prices is denoted by ? and it is also called the ratio of the two distance elasticities for short throughout this dissertation.
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expansion of the city’s geographical boundary and a growth in the population size.3 These theoretical results are supported by numerical simulations and empirical estimations. The second question contributes to the literature since the impacts of capitalland substitution on urban spatial structure has not been sufficiently addressed. Although the importance of elasticity of capital-land substitution to urban spatial structure has been well recognized (Muth 1964, McDonald 1981), how and to what extent the elasticity of capital-land substitution affects urban spatial structure has not been adequately investigated both theoretically and empirically. McDonald (1981) pointed out that the elasticity of capital-land substitution in land development plays an critical role in understanding urban spatial structure and concluded that it is “a determinant of the land rent gradient, the population density gradient, the factor share of land and housing capital and the elasticity of supply of housing both in the aggregate and on a particular site” (p. 190). The literature, however, lacks explicit examination on the directions and magnitudes of the impacts. This question is overlooked probably because of the slow change in housing production technology in the developed countries where the impacts of capital-land substitution are less relevant. Nevertheless, this question is perhaps more relevant in China, given the profound institutional reforms of urban land and housing systems and impressive urban expansion, particularly in cities like Beijing. Dramatic changes in a relatively short period make capital-land substitution a critical factor in determining urban
Capital density refers to non-land capital intensity in RMB per square meter, and housing output per unit of land is measured by floor space in square meter and thus it is equivalent to the FAR throughout this dissertation.
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spatial structure in China. Even more important, Chinese cities provide an opportunity to empirically examine the linkage between capital-land substitution and urban spatial structure. Based on the data from Beijing, the simulation exercises indicate that capital-land substitution has considerable impacts on urban spatial structure. The findings of this dissertation will be of great value to urban planners and government officials in addressing the problem of housing prices, assisting property value assessment for tax purposes, and evaluating urban land use policies and planning regulations.
1.3
Organization of the Dissertation
This dissertation is organized in seven chapters. After this introduction, chapter 2 reviews urban land and housing markets
development in China, urban spatial structure evolution, and urban planning’s influences on urban land use. Market forces are emerging and begin to act as important forces to shape and modify urban spatial structure in China’s cities, while urban planning remains influential on urban land development. Chapter 3 provides a literature review on urban spatial structure. Urban economic theory reveals the declining phenomena of land and housing prices, and the theory of housing services production is important to understand the formation of urban landscape. Both theoretical and empirical studies are reviewed. Chapters 4 to 6 present respectively theoretical analysis, simulation analysis, and empirical analysis to address the two research questions. By using a CES production function, chapter 4 derives analytically the impacts of capital-land
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substitution in housing services production on urban spatial structure. Chapter 5 conducts numerical simulations to verify the derived directions of the impacts and examine the magnitudes of the impacts, based on the Beijing data. Chapter 6 again uses the data from Beijing, estimates and tests the negative distance gradients of housing prices, land prices, capital densities, and the housing output per unit of land (or the FARs), estimates the ratio of the two distance elasticities and tests whether it is larger than unity, and estimates the elasticity of capital-land substation as well as its impacts. Finally, chapter 7 concludes with the findings, discusses policy and planning implications, and proposes future studies.
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Chapter 2:
Market, Urban Spatial Structure, and
Planning in China
First of all, this chapter provides a brief overview of urban land market and housing market development, and then it reviews changes of urban spatial structure during the post-reform period, in which market forces have emerged and begin to influence urban spatial development in China. It also reviews the urban planning’s influences on urban land development.
2.1
Land Reform and Land Market
The land reform launched in the late 1980s separates the land use rights from
the land ownership and introduces a land leasing market to allocate state-owned urban land.4 Prior to the reform, there was no land market, and urban land was managed and assigned to land users through an administrative process. Land was distributed to land users free of charge on the basis of need for an indefinite time period. Transactions of land between land users were prohibited. If the assigned land was not used, it was to be returned to the government and be re-assigned to other land users. Since there were no economic implications for vacant land holding, this in fact seldom happened, resulting in inefficient land uses. One of the primary objectives of the land reform is to introduce market mechanisms to improve land use efficiency and land management. The most
In China, urban land is owned by the state and managed by city government, while rural land is collectively owned by farmer collectives but is in general restricted from non-agricultural uses.
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prominent change in the reform is the introduction and establishment of the Land Use Right System (LURs). In the LURs, land use rights are separated from land ownership so that private users can access state-owned urban land. City government can lease out the land use rights of state-owned urban land to private users in a longterm period depending on land uses, and a land use right fee is involved in the transaction, paid from land users to the city government. 5 This policy innovation provides an approach to paid land use without challenging the public ownership of the land, which is the cornerstone for Communist China. As expected, land leasing markets are growing quickly and begin to play a role in shaping urban spatial structure. The rapid land market development is reflected by dramatic increases in both the number of land leasing transactions and the value of land leased. In 1987, only 5 land leasing transactions (totaling 15.7 hectare) took place in China, and this number grew to 545 in 1991 (Ding 2003). Since the middle 1990s, the number of annual land leasing transactions jumped to 10,000 and peaked at 242,763 in 2002 (figure 2-1). The area of annually leased land also increased impressively, from about 50,000 hectares in 1994 to over 200,000 hectares in 2005 (figure 2-1). The total value of annually leased land increased even more dramatically by about 15 times during 1994-2005, and it reached as high as 588.4 billion RMB in 2004 (figure 2-2).6 In particular, the beginning years of the new century witnessed accelerated land leasing transactions. For the years 2000-2003, the area of leased land increased 4 times and
The maximum time period is 70 years for residential uses, 40 years for commercial, tourist and recreational uses, and 50 years for other uses such as industrial and public uses.
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Price is not adjusted.
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the average price of land increased 2.3 times, consistent with the fast growing economy and booming commodity housing market in China in this period. Since 1998, material housing distribution was prohibited according to an important document issued by the State Council.7 Nevertheless, a slight decline in the number and area of land leases can be observed since 2002, a fact that probably is due to stringent policies on land uses.8 Despite this, the total value of land leased annually appeared not much influenced, implying an increase in the unit price of land leased.
Source: China Land Resource Statistical Yearbook 2006, China Land Yearbook 1994, 1995, 1998. Data of 1997 were not available. Figure 2-1 Land Leasing Market in China: Numbers of Plots and Hectares of Land Area, 1994-2005
The document of 1998 is entitled the Notice on Further Deepening the Urban Housing System Reform and Speeding up Housing Construction. Further discussion will be found in the following section on the housing market development. In April 2002, the Ministry of Land and Resources announced the Provisions of Tender, Auction, and Listing State-Owned Land Use Right, requiring that leasing land use rights for profitable uses such as residential and commercial uses should be conducted through open bid procedures (including tender, auction, or listing). In March 2004, the Ministry of Land and Resources and the Ministry of Supervision issued the Notice on Further Enforcement and Supervision on the Profitable Land Use Right Leasing through Tender, Auction, and Listing to strictly cut off land leasing transactions through negotiation by August 31, 2004.
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Source: China Land Resource Statistical Yearbook 2006, China Land Yearbook 1994, 1995, 1998. The data of year 1997 are not available. Figure 2-2 Land Leasing Market in China: Transaction Values, 1994-2005
The relative share of land leased in the total land provision also increased substantially. In 1999, leased land made up 25% and 34% in the numbers and the area of urban land provision, respectively; in 2001, leased land exceeded free allocation; and in 2005, leased land comprised up to 70% of total land provision (figures 2-3 and 2-4).
Source: China Land Resource Statistical Yearbook 2006 Figure 2-3 Land Leasing Market in China: Numbers of Land Plots by Different Approaches, 1999-2005
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Source: China Land Resource Statistical Yearbook 2006 Figure 2-4 Land Leasing Market in China: Hectares of Land Areas by Different Approaches in China, 1999-2005
2.2
Housing Reform and Housing Market
Accompanied with the land reform, China’s urban housing reform was
launched in the late 1980s, aiming at transforming the welfare-oriented public housing system into a market-oriented housing system (Wang & Murie 1999, Huang & Clark 2002, Li & Yi 2007). The housing reform is facilitated by the land reform, which enables private developers to obtain urban land for housing services production and enhances commercialization of housing provision. Before the reform, housing was a public welfare attached with urban employment. After the new China was built in 1949, all private houses were systematically transferred to local government and a public housing system was built in urban areas (Wang & Murie 1999). Housing was considered a welfare benefit and allocated free from the work units (danwei) to their employees. Residents did not
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need to pay rent or only paid an extremely low rent since housing was regarded as part of the wage cost (Wang & Murie 2009, Huang & Clark 2002). Housing reform was carried out in a gradual way and marked by two milestone steps that promoted housing privatization. In 1988, the State Council issued permits to sell public housing stocks and encouraged private-public co-financing of housing provision for employees. Under the co-financing scheme, employees usually paid up to one-third of total construction costs, which was a substantial amount of payment compared with what was paid under the material distribution of housing. In 1998, the material distribution of housing was formally abandoned and replaced by monetary housing distribution. As expected, this triggered remarkable development in real estate sectors. Moreover, it brought enormous market opportunities that facilitated rapid changes in housing construction technology. For example, the private housing market began to emerge in the early 1990s and has been growing rapidly since 1998. From 1991 to 2005, the area of annual commodity housing sales increased 18 times from 27.5 million to 495.9 million square meters at an annual growth rate of 23%, and the total value of annual commodity housing sale increased about 70 times from 20.8 billion RMB to 1456.4 billion at a remarkable annual growth rate of 35% (figure 2-5). The growth was particularly striking after 1998, when the country prohibited the channel of material housing distribution. Housing prices also rose dramatically, from 756 RMB per square meter floor space in 1991 to 2,937 RMB per square meter in 2005 (NBS 2007); this price increase to some degree indicates the development of commodity housing market.
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Source: China Statistic Yearbook 2006 Figure 2-5 Commodity Housing Market in China: Floor Space and Value of Sales, 19992005
Commodity housing became the major component in urban housing supply, reflecting the increasing importance of the market in housing provision. As shown in figure 2-6, the shares of commodity housing in the total housing supply increased steadily since 1998 in terms of the floor area under construction, the floor area constructed, and the total housing sale value; the numbers grew from 23% to 54%, from 11% to 33%, and from 27% to 60%, respectively (NBS 2007). Noticing that the shares of commodity housing in the sale value were always higher than those in the floor area (under construction and constructed), it suggested that the prices of commodity housing were higher than other types of housing supply (such as the government subsidized reform housing and affordable housing).
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Source: China Statistical Yearbook 2006 Figure 2-6 Commodity housing market in China: Share in Housing Supply, 1995-2005
Home ownership also increased greatly. Currently, about 74% of the city and town residents in China own a housing property (only the structural construct; land is still owned by the state) (Jia 2008). This is indeed a remarkable achievement, compared with the home ownership rate of the United States, which was 68.9% in 2005.9 With the housing market development, the urban landscape has been reshaped along with the adoption of advanced technology of construction. Both the appearance and quality of residential buildings have been improved. Perhaps the most prominent change is reflected by the growing building height. Low-rise buildings have been gradually replaced by mid-rise, mid-to-high-rise, and high-rise buildings, and since the late 1990s, high-rise buildings have become dominant in many Chinese cities.10
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U.S. Census, http://www.census.gov/hhes/www/housing/hvs/annual05/ann05t12.html
According to the Design Code for Residential Buildings issued in 1999 by the Ministry of Construction, residential buildings that have 1-3 floors are low-rise, 4-6 floors are mid-rise, 7-9 floors are mid-to-high rise, and above 10 floors are high-rise Regarding the high-rise buildings, they are usually further divided into four kinds: 9-16 floors (less than 50 meters), 17-25 floors (less than 75 meters), 26-40 floors (less than 100 meters), and super-high-rise buildings with more than 40 floors
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Improvements in technology of construction are reflected in the ways that residential buildings are built. In the 1950s, residential buildings were basically lowrise (often fewer than three floors) brick-wood (or brick-concrete) structural buildings, copied from the Soviet Union.11 These buildings can still be found today, particularly in the neighborhoods of state-owned enterprises. Figure 2-7(a) and figure 2-8 (a) presents such examples. In the 1960s and 1970s, no obvious change in housing construction happened (figure 2-7 (b)), but a number of the makeshift houses (jianyi fang) were built to cater increasing population. The makeshift houses were often characterized by shallow foundations, thin walls, and common bathrooms and kitchens (figure 2-8(b)), reflecting the influences of turbulent economic and political situations as well as natural disasters in those years.12 At the end of the 1970s, however, higher residential buildings (7-8 floors) were developed in large cities like Beijing and Shanghai, as attempts to satisfy the increasing housing demand.13
(above 100 meters). http://baike.baidu.com/view/2683768.htm?fr=ala0_1
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http://news.dichan.sina.com.cn/2009/10/10/71722_1.html http://www.51yanxiu.com/jianzhu/ziliao/qita/jianzhu_295740.html http://news.dichan.sina.com.cn/2009/10/10/71722_1.html
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(a) 50-60s
(b) 70s
(c) 80s
(d) 90s
(f) 21st century (e) 21st century Photos were taken on March 17, 2010. The building ages were learned from local residents, about 12 kilometers to Tiananmen Square. Figure 2-7 Residential Building Evolution in Zhongguancun Area, Beijing
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(a) Late 50s
(b) 70s (Makeshift house)
(c) 80s
(d) late 90s
(f) left: 93, right: 03, back: under construction (e) 21st century (white building: 08-09, right: 80s) Photos were taken on March 20, 2010. The building ages were learned from local residents, about 6 kilometers to the city center. Figure 2-8 Residential Building Evolution in Qinchuan Neighborhood, Xi’an
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The 1980s and 1990s witnessed steady growth in building quality and height. The Ministry of Construction carried out a series of urban residential building design competitions and nationwide pilot residential projects to facilitate housing industrialization.14 Apparently, the overall building height increased, particularly in the late 1990s (figures 2-7 (c) & (d), figures 2-8 (c) & (d)). Since 1998, commodity housing development has entered a very fast growing period. With the adoption of new advanced building technologies (such as applications of steel frame, frame-shearwall structure, slab-column shearwall structure, etc), high-rise residential buildings rose dramatically in China. Twenty- to thirty- or even forty-floor residential buildings are commonly observed (figures 2-7 (e) & (f), figure 2-8 (e)), and redevelopment also occurred frequently to replace the old low-rise buildings and meet the growing housing demand (figure 2-8 (f)).
2.3
Spatial Structure
Rapid market development along with fast urbanization has brought two
fundamental changes in China’s urban landscape. One is the locational changes of land uses and the other is associated with changes in land use intensity. 2.3.1 Pre-Reform Prior to the economic reform, the urban space of China’s cities was recognized as monotonous, featured by highly mixed land uses and invariant building height and density.
14
The Ministry of Construction was restructured and renamed as the Ministry of Housing and UrbanRural Development in 2008.
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The highly mixed land use pattern was mainly a result of the danwei-based spatial organization of China’s urban space. A danwei was the basic unit of working and living, usually a walled and mixed residential and industrial compound (Gaubatz 1995 & 1999). It provided not only a working place but also provided a series of public services and welfare such as housing, food distribution, education, health care, recreation, etc. (for detailed examples see Ding 2004). Therefore, each danwei formed a small self-sufficient community, with very diverse land uses inside a relatively small area. There were two major reasons for this. One was the fact that production was regarded to be the priority compared with consumption and danwei served as the basic unit of production; the other was that residents did not need to travel beyond the walls, thus, danwei minimized travel costs (Wu 1997, Gaubatz 1995 & 1999). As urban space grew, it spread through the increase of the cells of danwei. Therefore, the entire urban space featured highly mixed land uses. The invariant land development intensity, manifested by the flat building height across urban space, was due to the lack of market mechanism. Since land was of no value and assigned to each danwei for free on a basis of need, there was no incentive for danwei to economize land or substitute land with capital to improve land use efficiency. Land development intensity was irrelevant to the location. Tall buildings were developed mostly for political reasons rather than economic reasons. Therefore, the typical urban landscape in the pre-reform period was characterized by the walled danwei and similar low-rise brick buildings (Gaubatz 1995 & 1999).
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2.3.2 Post-Reform Land prices rose rapidly in the post-reform period, particularly in cities like Beijing, Shanghai, Shenzhen and many other cities in the coastal regions. Rising land prices forced industrial buildings and warehouses that were occupying the central locations to relocate to urban outskirts. For instance, manufacturing firms were forced out in Beijing in the middle 1990s, and the previously occupied land was redeveloped for residential, commercial, or mixed uses (Wu 1997, Gaubatz 1995 & 1999). Erection of skyscrapers in central locations has not only changed land use intensity but also reshaped urban landscape and created new city images. For example, development of the Chaoyang central business center (CBD) in Beijing has substantially increased the density in that area in the first decade of the 21st century. Recently, the former highest building in Beijing, Jingguang Center, which is 209 meters tall, has been overtaken by the China World Tower 3 (Guomao Sanqi), which is 330 meters tall with 88 floors, accompanied by the China Central Television building (234 meters tall) under construction and the Yintai Center (249.9 meters tall) as shown in figure 2-9.
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Overview of the CBD in Chaoyang District from Ritan Park. Source: http://www.danwei.org/architecture/beijing_new_skyline.php
Figure 2-9
Beijing’s Skyline
2.4
Urban Planning
Planning regulations affect urban spatial structure since land development is
often subject to certain requirements and limitations. Like many other cities in Western countries, urban planning affects urban spatial structure by regulating the types (residential, commercial, industrial, education, sport, public facilities, municipal utilities, road, green space, etc.) and intensity (density and FAR) of land development at given sites. It also specifies setbacks from the roads and developable land in a given lot. By combining the permitted FAR and percentage of developable land, the maximum building height and floor space can be derived. Figure 2-10 presents an example of a detail plan of one block in the Shunyi New City in Beijing. Within the boundary of the block, the attached table on the right side presents the allowable land uses, land area, FAR, floor space, building density,
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building height, green space ratio, and the numbers of parking lots for each land plot. Land development should strictly follow these requirements in order to obtain required construction permits from the Department of Construction (or Planning).
Source: Shunyi Planning Office. http://www.guihua.bjshy.gov.cn/content.aspx?id=410 Figure 2-10 Detail Plan for Block 21, Plot 22, Shunyi District, Beijing
It should be noted that it is not unusual for developers to break these mandated requirements such as the building height caps and FAR controls to increase their profits. There are many reports that document developers’ violation of zoning requirements. However, due to lack of systematic records the total impact of the violations is hardly ever gauged. Planning regulations on land use could be beneficial if they serve to correct market failures; however, they may hinder the formation of an efficient urban spatial
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structure. Under the market forces, developers optimize the combination of input factors as well as the output level based according to market rules. With strict regulations on land development intensity, such as building height and FAR controls, urban plans may act as constraints on housing services production, particularly on the substitution of capital and land. For example, suppose a 20-floor residential building is the best choice for the developer on a land lot given the technology of construction, land and capital prices, and other factors, but constructing a 20-floor building violates planning regulations and the developer has to reduce it by five floors. In this case, not only is the final housing output affected, but also the capital-land substitution is constrained and so the efficiency of resource utilization is harmed given that land and capital are not used in the most efficient way. Looking at the larger picture, citywide land use restrictions might divert urban land development from the economically efficient one and cause welfare loss.
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Chapter 3:
Literature Review
This chapter reviews the theoretical understanding and empirical evidence of urban spatial structure. It starts with a review of the urban economic theory that reveals the declining phenomena of land and housing prices, and then it reviews the theory of housing services production, which is also important in understanding how urban landscape is shaped. Both theoretical framework and empirical evidence are discussed.
3.1
Urban Spatial Structure and Form
Theoretical understanding of urban spatial structure was formally developed
by Alonso (1964), Muth (1969) and Mills (1972). Based on the utility maximization for residents subject to the income constraint, housing price and housing consumption at a given location can be solved at the equilibrium when no one can improve their utility by simple relocation. Treating land as an input factor along with non-land capital in housing services production and taking the spatially variant housing prices given, land development intensity and land price are determined through profit maximization in competitive market. Therefore, urban spatial structure is characterized by declining housing and land prices and land development intensity with respect to distance from the city center (or the CBD). Following Brueckner (1987), the formal model starts with the utility theory in which residents maximize their utility by making tradeoffs between housing prices and transportation (commuting) costs, both depending on location. The model is
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structured as follows. The city has a single CBD and residents commute to work. All residents earn identical income y and have the same strictly quasi-concave utility function v(c, q) , which depends on housing services consumption q and a numerical non-housing consumption c. Residents located at x kilometers from the CBD have to pay the transportation costs tx. By choosing q, residents maximize their utility subject to income constraint:
max v( y ? pq ? tx, q )
q
(1)
Locational equilibrium requires the first order condition of (1) and also requires that the maximized utility at all locations are identical, denoted by u. Using these two conditions housing price p and housing services consumption q can be solved as:
p = p ( x, y , t , u ) q = q ( x, y , t , u )
(2) (3)
It can be shown that p must decrease with x to balance the increasing transportation costs and q should increase with x as long as housing services are normal goods:
?p <0 ?x
(4)
?q >0 ?x
(5)
Housing services production requires land input L and non-land capital input K, and the production function is assumed to be concave and constant return, denoted by H ( K , L ) , in which the capital marginal productivity diminishes. Given the technology of constant return, the production function for each unit of land can be 25
written h( S ) ? H ( S ,1) , where S equals K / L and represents capital density, and
hS > 0 and hSS < 0 . 15 Assuming capital price n is spatially invariant, housing
producers maximize their profit per unit of land by choosing S:
max ? = ph ? nS ? r
S
(6)
In the competitive market, profit maximization requires the first order condition of (6) and also requires the maximized profit equals zero:
phS = n
(7) (8)
ph ? nS ? r = 0
Simultaneously solving (7) and (8) yields equilibrium solutions for land price
r and capital density S:
S = S ( p, n) r = r ( p, n)
(9) (10)
where p is already decided in the demand side problem by (2). By noticing that S and
r depend on x via p, it is derived from (7) and (8) that S and r both decline with x:
h ?p ?S =? S <0 ?x phSS ?x
(11)
?r ?p =h <0 ?x ?x
(12)
And the output of housing services per unit of land h also declines with distance x because of the declining S:
?S ?h = hS <0 ?x ?x
(13)
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These conditions imply that elasticity of capital-land substitution is larger than zero.
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Measuring housing services in terms of floor space, (13) suggests that the FAR decreases with x. Defining ? as the ratio of distance elasticity of land prices to the distance elasticity of housing prices and using (8) and (12), it yields:
?r ? = ?x ?p ?x
r ?p r h x = ?x x = ph = nS + r = 1 + nS > 1 p ?p p r r r x ?x x
(14)
This provides the theoretical relationship that will be tested in the first research question of this dissertation. Inequality (14) indicates that land prices are more elastic with respect to distance from the CBD than housing prices, or put differently, land prices decline faster than housing prices. Indeed, an alternative interpretation of ? is as the housing price elasticity of land price:
?r ? = ?x ?p ?x ?r ?p r r x = ?p ?x x = ?r ?p p p ?p ?x x x
r p
(15)
This suggests that the land price is elastic to housing price since a 1% change in housing price leads to a more than 1% change in land price. These theoretical advances in understanding urban spatial structure and form, particularly the predictions of declining land and housing prices toward the city fringe, have been supported by numerous empirical studies throughout developed and developing countries. 16 Coulson (1991) employed data from State College, a university town in Pennsylvania, which was regarded as an ideal laboratory place to
16
There are abundant evidences in the literature regarding the pattern of declining population density (such as Mills 1972 and Macauley 1985), which is also derived from the urban economic theory.
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test the monocentric model for the city well satisfied the assumptions of the model. His estimated results reported significant and negative distance gradients of house rent, and more importantly, the price fell with distance from the CBD at a rate approximately equal to the increase in transportation costs, while holding all other attributes constant. McMillen (2002 & 2003) estimated the distance gradient of housing prices in Chicago using three different approaches (hedonic, repeat sale, and Fourier expansion) and the findings indicated significantly negative gradients and a strong return of centralization to the Chicago housing market. Mok et al. (1995) estimated Hong Kong’s sale prices of apartments using a hedonic approach and also found significant effect of distance. Alberson (1997) examined the value of land and houses in Sydney, Australia, and found that both prices declined exponentially with distance from the CBD during 1931-1968 and the curves were flattened, until 1970, when the curves became steeper again. Atack and Margo (1998) examined vacant land prices in New York City between 1835 and 1900 and found that land price per square footage declined significantly with distance from the CBD. There is also strong evidence for declining housing and land prices in developing countries. Dowall (1992) investigated the land market in Bangkok, Thailand, and found negative slopes of land prices with respect to distance from the CBD. Lewis (2007) examined the land market in Jakarta, Indonesia, using market price and the findings also suggested negative linkages between distance and land value, and the land price curve was flattened over time. In transitional countries such as Russian and Poland, the emerging market forces had reversed the urban spatial structure that was previously shaped by political reasons, and the negative-sloped
28
distance gradients began forming (Bertaud & Renaud 1997, Dale-Johnson et al. 2005). Studies in China suggested similar findings, particularly given the rapid market development since the late 1970s. Ding (2004)’s empirical estimations suggested Beijing’s urban form had been greatly modified by market forces: land prices declining from the city center at different speeds depending on land use types. It should be recognized that the literature reports a few studies showing either positive or insignificantly negative distance gradients of housing and land prices, though empirical studies that support the declining housing and land prices are overwhelming (Heikkial et al. 1989, Yiu & Tam 2004). Several reasons could account for this trend. First, the data used to estimate distance gradients did not all conform to the monocentric assumption. The trend of suburbanization and development of sub-centers, particularly after World War II, made the spatial pattern of cities more complicated. It is possible that each sub-center has its own distinctive submarket and its own distance gradients of housing and land prices, fitting well with the monocentric model, but negative distance gradients may not be found for the metropolitan area as a whole (Coulson 1991, Dubin & Sung 1987). Second, it is speculated that neighborhood effects could cause positive distance gradients in empirical studies (Richardson 1977). If the omitted neighborhood variables are positively correlated with distance, empirical tests will produce a positive distance gradient due to specification error. This may happen since neighborhood quality can hardly be fully captured due to data limitations. Finally, as one moves toward the CBD, if the overall effect of the increasing urban negative externalities (such as pollution, traffic congestions and noise) cannot be completely offset by the savings in
29
transportation costs, positive distance gradients of land and housing prices are likely to be obtained (Richardson 1977). In this case, the urban economic model should be extended to include the amenity argument, as Brueckner et al. (1999) showed in their research, household location patterns would be affected by whether there were strong presence of positive amenities in the city core and how strongly people preferred these amenities. To sum up, despite a great number of studies testing the negative distance gradients of housing and land prices, no study has examined the relationship between the distance gradients of housing prices and land prices, probably due to lack of data. By utilizing both housing and land prices from the same sites, this dissertation will contribute to the literature by empirically estimating and testing the relationship between the two declining prices.
3.2
Housing Services Production
Besides the urban economic theory, the other important aspect with regards to
the formation and evolution of urban spatial structure is housing services production (Muth 1964, Mills 1972, Koenker 1972, Sirman & Redman 1979, McDonald 1981). According to the theory of housing services production, land is an imperative input to produce housing services and land development intensity is largely determined by the relative prices of land and capital, based on the assumption that land and capital can substitute for each other to a certain degree to produce a certain level of housing services. Therefore, housing services production plays an important role in shaping the city’s capital density profile and the general urban landscape.
30
The theory of housing services production has two important implications. One is that the demand for land is viewed as a derived demand since people demand land for the purpose of producing housing services, and the other is related to the notion of capital-land substitution, which is a key element in forming urban spatial structure. As McDonald (1981) stated, the elasticity of capital-land substitution ( ? ) is “a determinant of the land rent gradient, the population density gradient, the factor share of land and housing capital and the elasticity of supply of housing both in the aggregate and on a particular site” (p. 190). The theory of housing services production is supported by numerous empirical studies that estimated ? . Muth (1964) provided the first empirical estimation using Federal Housing Administration (FHA) data of forty-seven cities in the United States and his estimates were around 0.5. After Muth’s seminal work, a substantial amount of studies followed, summarized in table 3-1. There is clearly no consensus on the value of ? . Most of the estimates ranged from 0.3 to 0.8 and were significantly smaller than unity. Only the estimates for Chicago (McDonald 1979, Clapp 1979) and for the Oregon part of Portland Metropolitan area (Thorsnes 1997) are exceptional, reporting close to or larger than unity ? . The majority of the studies employed the CES production function, while several studies employed the variable elasticity of substitution (VES) production function.
17
Comparatively, fewer studies were
conducted in developing countries and often reported lower estimates of ? . The only empirical study on capital-land substitution in China, to the author’s knowledge, was
While the CES assumes a uniform ? in housing production but does not restrict a priori to any specific value, the VES relaxes this assumption and allows ? changing with the combination of input factors. Nevertheless, there is no theory suggesting that VES is superior to CES; it is rather an empirical question of which one is better.
17
31
conducted by Ding (2004). By using data from Beijing, Ding (2004)’s estimates of ? fell between 0.3-0.4 during 1993-1995 and jumped to over 0.45 in 1996 and steadily rose since then. Ding (2004) also showed that ? varied across land use types.
Table 3-1
Studies Muth (1964 & 1971)
Empirical Estimation of Elasticity of Capital-land Substitution for Housing Production*
Estimates** 0.5-0.75 (CES) Cities/Regions 47 metropolitan areas, United States Ann Arbor, United States Brown County, United States Los Angeles, United States Chicago, United States Single-family houses from 31 metropolitan areas, United States 23 Metropolitan areas, Canada Data Collected 1966 1964-1966 1974 1972-1974 1970-1972 1969 1975-1976 1969-1971, 1970-1972 1969 1960 Sig. less than one Yes Yes Yes Yes No Yes Yes No Yes Yes
Koenker (1972) 0.71 (CES) Rydell (1976) 0.50 (CES)
Fountain (1977) 0.57 Clapp (1979) Rosen (1978) Arnott and Lewis (1979) McDonald (1979) 0.98 (CES) 0.43 (CES) 0.36 (CES)
1.13, 0.86 (CES, Chicago, United States IV) Single-family houses from 31 metropolitan area, United States
Polinsky and 0.45 (CES) Ellwood (1979) Sirmans et al (1979)
0.93-0.66 (VES) Santa Clara County, United States
0.52,0.55,0.46 Sirmans and (CES) Redman (1979) 0.55, 0.52, 0.45 (VES) Asabere et al 0.53 (CES) (1982) 0.227, 0.889, Kau and 0.455, 0.539 Sirmans (1983) (VES) Jackson et al 0.499 (1984) Dowall and 0.69 (CES) Treffeisen (1991) Ding (2004) Thorsnes (1997)
52 metropolitan areas, United States
1967, 1971, 1975
Yes
Accra, Ghana Dallas, Dayton, Louisville, and Stockton, United States Knoxville, United States Bogotá, Colombia 1966-1978 1970 1984-1989 1993-2000
Yes Yes Yes Yes Yes
0.32-0.74 (CES) Beijing, China
0.88 (CES), 0.81 Oregon part of Portland Metro, United (VES), 0.96 1985-1989 (CES, IV), 1.08 States (VES, IV) Erol and Güzel 0.078 (CES), Ankara, Turkey 2000 0.118 (VES) (2006)
No
Yes
* The table is an updated version based on McDonald (1981)’s review ** VES estimates are reported mean value
32
In theory, ? is affected by two different factors. One is technological change of construction and the other is planning regulations (such as zoning ordinance) that may impose restrictions on capital investment on a given land lot. The impacts of planning regulations depend on how rigorously they are implemented and to what extent the market forces can alter planning regulations. Empirically, there are also many studies providing evidence for the changes in ? (Simans & Redman 1979, Kau & Sirmans 1983, Jackson et al. 1984, Ding 2004, Erol & Güzel 2006). The importance of capital-land substitution in influencing urban spatial structure is well recognized (Muth 1964 & 1971, McDonald 1981, Kau & Lee 1976); in contrast, its explicit impacts on urban spatial structure have not been adequately examined. Kau and Lee (1976) derived the impacts of ? on the prices of housing services, the supply of housing services, and the demand for housing services. However, their conclusions are undetermined and depend on extra assumptions. For example, they concluded that land rent is negatively related to ? relying on the assumptions that the base year capital land ratio is unity and capital is expanding faster than land.18
18
Kau and Lee (1976) derived R (u ) = further derived the
? K (u ) 1+ ? ] r [ 1 ? ? L(u )
of
from the market equilibrium conditions, with respect to
and
partial
R(u )
?
:
? K (u ) 1+ ? ?R(u ) K (u ) =r ) , where R(u ) is the land rent at distance u , ? is the ] log( [ ?? L(u ) 1 ? ? L(u ) 1 , K and L are capital and land input, r is the capital price. By substitution parameter and ? = 1+ ? ?R (u ) K = 1 for the base year, the sign of is decided by whether land is growing faster assuming L ??
than capital. Besides the extra assumption of the initial capital-land ratio and the fast expanding speed of capital, another problem of their derivation is that it does not account for the impact of changes in
33
This dissertation will extend the understanding of impacts of housing services production on urban spatial structure by explicitly modeling housing services production function and analyzing impacts of ? . The investigation on the impacts of housing services production in general and the impacts of capital-land substitution in particular on urban spatial structure constitutes the major contribution of this dissertation to the literature. I will examine the impacts by theoretical analysis, numerical simulation, and empirical estimation.
K (u ) . In fact, if ? changes, producer’s decision on inputs combination would also L(u ) adjust and further should affect the equilibrium land price R (u ) .
? on the ratio of
34
Chapter 4:
Housing Services Production and Urban
Spatial Structure
This chapter examines the linkage between housing services production and urban spatial structure. More specifically, it analyzes the impacts of capital-land substitution. Based on a CES production function for housing services, I derive the directions of the changes of urban spatial structure measured by the distance gradients of land prices and capital densities, the housing output per unit of land, and the degree that land prices decline faster with respect to distance from the CBD than housing prices, brought by a change in capital-land substitution.
4.1
The CES Production Function for Housing Services
It is assumed that housing services are provided by a CES production function
in which land and capital constitute the two inputs.19 It is specified as:
H ( K , L) = ? [?K
??
+ (1 ? ? ) L ]
??
?
1
?
(16)
where H is the output of housing services; K is the non-land capital input; L is the land input, ? is the scale parameter called the neutral technological parameter and is positive; ? is the non-neutral distribution parameter, reflecting the intensiveness of capital use in production and should be positive and smaller than unity. ? is the
19
The CES production function was introduced by Solow (1956) and formally developed by Arrow et al. (1961).
35
substitution parameter, ranging from -1 to infinity. The elasticity of capital-land substitution ? is given by:
? =
1 1+ ?
(17)
The CES production function describes a production technology that has a constant return to scale and constant elasticity of substitution between land and capital.20 In addition, it is demonstrated that the CES production function also has a property of positive effect of capital-land substitution on housing output and this can be written: 21
H ? > 0 (or H ? < 0 )
(18)
Let h = H / L , and S = K / L , (16) yields the CES function for housing output per unit of land:
h( S ) = ? [?S
??
+ (1 ? ? )]
?
1
?
(19)
Accordingly, the following relationship holds:22
20
The CES function includes the Cobb-Douglas function, Leontief production function (perfect complements), and linear production function (perfect substitutes) as special cases. When ? ? 0 (or ? ? ? ), H ( K , L) = ? min{K , L} , it becomes the Leontief production function, which assumes no
when ? ? ? ( ? ? ?1) , H ( K , L) = ? [?K + (1 ? ? ) L] , it implies that the extent of substitution is infinite and the isoquants become straight lines.
21
substitution between the two input factors and the isoquants are right-angle shaped; when ? ? 1 (or ? ? 0 ), H ( K , L) = ?K ? L1?? , it becomes the Cobb-Douglass production function; and
in
Brown (1967, 57) had shown that all relevant limits are positive and tentatively concluded that a rise ? raises the output rate by deriving all , but his proof does not assure that H ? < 0 for all values
of variables and other parameters. This potential problem will be addressed by simulation analysis in next chapter.
22
In this dissertation, I use h? to denote the partial derivative of h with respect to
?
derived directly
from the CES function for housing production (for a given set of input factors of production), and I use
36
h? > 0 (or h? < 0 )
(20)
In theory, the value of ? can range from zero to infinity in the CES production function, but for housing services production, ? should be positive and no larger than unity. This is because of the following reasons. First, given the observed capital-land substitution in housing construction, ? should not be zero but larger than zero; in other words, the Leontief function does not fit. Second, ? should not be larger than unity, as shown in (19), when ? > 1 (or ? 1 < ? < 0 ), as S ? ? ,
h ? ? , and as S ? 0 , h ? ? (1 ? ? )
? 1
?
. This implies that on a given land lot of fixed
size, the output of housing services will become indefinitely large as capital input keeps increasing, and when the capital input approaches zero, the output will still reach a positive lower limit. This is certainly not the case for housing services production. In reality, due to technological constraints, it is impossible to produce indefinitely large housing output on a given piece of land. Also, it is unrealistic to produce housing structure only by land input without any capital input. On the contrary, when ? < 1 , using the CES production function to describe housing services production makes sense, as shown in (19), when ? < 1 (or ? > 0 ), as S ? ? , h ? ? (1 ? ? )
? 1
?
, and as S ? 0 , h ? 0 (Arrow et al. 1961). This implies
that when a large amount of capital is invested on a fixed piece of land, the output of housing services will reach an upper limit, and when no capital is invested, no
?h to denote the partial derivative of h with respect to ? derived from the equilibrium solution of h ?? ?h ?S (after input factors adjust to ? ); in fact = hS + h? . ?? ??
37
housing structure will be produced. This is intuitively true given the fact that one can neither build indefinitely tall buildings nor build houses without capital but only with land. Brown (1967) provided an insightful interpretation of these behaviors of the CES production function from a technological point of view. According to Brown,
? > 1 indicates a technology that treats the input factors as resembling each other.
When holding one input constant and increasing the other one indefinitely, the technology allows the expanding factor to easily substitute for the constant factor, and so that both factors seem to be increasing indefinitely and the output increases also indefinitely. On the other side, ? < 1 indicates a technology that views the factors as dissimilar to each other and difficult to substitute one for another, and so the output reaches an upper limit even though one input expands indefinitely. In housing services production, capital and land are dissimilar since houses are build on land with capital, and the output of housing services is to a certain degree constrained by land. The argument of 0 < ? < 1 in housing services production is also supported by empirical evidence (see chapter 3). Therefore, this dissertation examines the impacts of ? only when 0 < ? < 1 is in the simulation analysis and tests the estimates of ? in the empirical analysis.
38
4.2
Impacts of Elasticity of Capital-Land Substitution
This section examines analytically the impacts of ? on urban spatial structure
under the competitive market in the open city case.23 First of all, I obtain the explicit solutions for S, r, h, and ? at the market equilibrium. Substituting the housing production function per unit of land by (19) for (6) and solving the profit maximization problem by using the two conditions (7) and (8) yield land price r and capital density S as:
n ?(1?? ) ?? ? ) p?? ]1?? S =[ 1? ? (
n ?(1?? ) n ?(1?? ) ?? ?? ? ) ( ) ? ? p?? p?? ?1 1?? ? n[ r = p? [(? [ ] + (1 ? ? )] ]1?? 1? ? 1? ? (
(21)
(22)
where p is the housing price already decided in the housing demand side question, and n is the spatially invariant capital price. Replacing S in (19) by (21), the housing output per unit of land h at equilibrium is known:
? ? ? ? 1?? ? h=?? ?1 ? ? ( n )1?? ? ? ? p?? ? ?
? 1??
?
(23)
Replacing S and r in (14) by (21) and (22), ? can be solved:
23
The author would like to argue that the open city case (which assumes free migration) approximates better the reality compared with the closed city case (which assumes no migration at all), since modern cities are hardly closed given the advances in transportation and communication. In particular, China is currently experiencing fast urbanization and witnessing mass migration among cities and from rural to urban areas. It is estimated that there are 150-200 million internal migrants in China (Ding and Zhao, forthcoming). Therefore, this dissertation focuses on the impacts of ? in the open city case.
39
? =1+
1 p? p?? ? ( ) ?1 n n
1
(24)
More generally, using the relationship between ? and ? by (17), (21)-(24) can be rewritten as:
S = S ( p , n, ? , ? , ? )
r = r ( p , n, ? , ? , ? )
(25) (26) (27) (28)
h = h( S ( p, n, ? , ? , ? ), ? , ? , ? )
? = ? ( S ( p, n, ? , ? , ? ), r ( p, n, ? , ? , ? ), n)
In the open city case, which assumes exogenous utility level u, the housing price p and housing consumption q are not affected by changes in ? (or ? ). But equations (25)-(28) reveal that a change in ? will affect capital density, land price, the housing output per unit of land, and the ratio of the two distance elasticities.24 Following the approach of total differentiation used by Brueckner (1987), I derive the directions of impacts of ? on r, S, and h in a way that does not require using the complicated solutions by (21), (22), and (23). Replacing h in (8) with (19) and totally differentiating (8) with respect to ? yields:
p[hS
24
?S ?S ?r + h? ] ? n ? =0 ?? ?? ??
(29)
It should be noted that there are differences between ? and ? . As a production parameter, ? describes a production technology together with other parameters and the specified function form, and thus ? will only change if technology changes. ? is defined as the proportional change of input factors to the proportional change of relative prices of input factors, reflecting the substitutability between input factors. Therefore, besides technology improvement, policies and regulations on land use could also affect the value of ? . Despite these differences, analytical analysis in this dissertation examines the impacts of
? by employing the relationship of ? =
1 by (17). 1+ ?
40
As observed in (29), ? affects h both as a parameter of the production function ( h? ) and by affecting S ( hS ?S ). Since phS ? n = 0 by (7), (29) yields: ?? (30)
?r = ph? > 0 ??
Inequality (30) holds because h? > 0 by (20) and it implies that an increase in
? leads to increase in r at each location.
Due to capital-land substitution in housing services production, developers tend to use more capital to substitute for land when land becomes more expensive. So, an increase in land price leads to an increase in capital density. This indicates a positive relationship between ? and S, formally expressed as:
?S ?r =? >0 ?? ??
(31)
where ? represents the impact of change in land price on capital input, a substitution
?1 effect between capital and land. In fact, ? = (?MRTS ?S |? =0 )
1 , where MRTS is the n
marginal rate of technology substitution, and MRTS ?
H L 25 . Since it is assumed that HK
hS > 0 and hSS < 0 , and MRTS ?
H L h ? ShS , it is easy to have ?MRTS ?S > 0 . = HK hSS
Thus ? is intrinsically a positive number. Replacing h in (12) with (19) and totally differentiating (12) with respect to ? yields:
25
?1 ? = (?MRTS ?S |? =0 )
? (h hS ) 1 1 1 ? 1 ?1 =[ ? 1] |? = S ? ? |? =0 > 0 =0 n ?S n n 1+ ? 1+ ?
41
? 2r ?h ?p ?S ?p = = (hS + h? ) <0 ?x?? ?? ?x ?? ?x
(32)
Inequality (32) holds because
?p < 0 by (4), hS > 0 as assumed property of ?x
the production function,
?S > 0 by (31), and h? > 0 by (20). Inequality (32) ??
indicates that an increase in ? leads to a steeper land price curve. It is also shown that ? affects the distance gradient of land prices by affecting the housing output per unit of land (
?h ). ??
For the impact of ? on distance gradient of capital density, totally differentiating (31) with respect to x yields:
?2S ? 2r =? <0 ?x?? ?x??
(33)
Inequality (33) indicates that an increase in ? also leads to a steeper capital density curve. As mentioned above, the impact of ? on h is composed of two parts, since ? affects h as a parameter in producing housing services and by affecting S:
?h ?S = hS + h? > 0 ?? ??
(34)
Inequality (34) holds because hS > 0 as assumed property of the housing production function,
?S > 0 by (31), and h? > 0 by (30). Inequality (34) indicates ??
that as ? increases, the housing output per unit of land increases at any location within the urban area.
42
Intuitively, since ? positively affects land prices and the distance gradient of land prices but does not affect housing prices in the open city case, an increase in ? leads to steeper land price curve and thus positively affects ? , the degree that land prices are more elastic with respect to distance from the CBD than housing prices. Here is the proof. In the solution of ? by (24), if
p?? > 1 , it is easy to have:26 n
(35)
?? >0 ??
In the open city case, the capital-land substitution also affects the city size in terms of territory (denoted by x as the city boundary) and population (denoted by N). Following Brueckner (1987), the spatial equilibrium of the urban space requires two conditions. One is that at the city boundary x , the urban land price equals to agricultural land price ra ; and the other is that all of the residents N fit exactly into the urban boundary with their housing demand met by housing provision. By specifying the housing production function in the CES form, these two conditions are written as follows:
r ( p ( x , y, t , u ), n, ? , ? , ? ) = ra
(36) (37)
?
x
0
h( S ( p( x, y, t , u ), n, ? , ? , ? ), ? , ? , ? ) ?xdx = N q ( x, y , t , u )
where D( x, y, t , u, n, ? , ? , ? ) =
h( S ( p( x, y, t , u ), n, ? , ? , ? ), ? , ? , ? ) is the population q ( x, y , t , u )
density, ? is a constant parameter of radius of land that are available for housing services production.
26
Since usually p>>n, so
p?? > 1 is easy to hold. n
43
The utility level u and agricultural land price ra are exogenously determined. Assuming all other parameters are constant (including y, t, u, n, ? , ? ), keeping only the interested variables and parameters, (36) and (37) can be simplified as:
r ( x , ? ) = ra
(38) (39)
?
x
0
h( S ( x, ? ), ? ) ?xdx = N q( x)
Recursively solving (38) and (39) yields the solutions for x and N, respectively. To investigate the impact of ? on x , totally differentiating (38) with respect to ? yields:
?r ?x ?r + =0 ?x ?? ??
Given that
(40)
?r ?r > 0 by (30) and < 0 by (12), and x is only affected by ? ?? ?x
in (38) as all other parameters are constant, so it can be inferred from (40) that:
dx >0 d?
(41)
Totally differentiating (39) with respect to ? yields:
x ?x ?S h( S ( x, ? ), ? ) ?x dN ?x +? (hS + h? )dx = 0 q ( x) q( x) d? ?? ??
(42)
Given that
?x > 0 by (41), hS > 0 as assumed property of housing ??
production function, that: dN >0 d?
?S > 0 by (31) and h? > 0 by (20), it can be inferred from (42) ??
(43)
44
Therefore, inequalities (41) and (43) indicate that an increase in ? leads to increases in both the city’s geographical size x and its population N. To sum up, under the competitive market in the open city case, the elasticity of capital-land substitution does not affect housing price and housing consumption, but positively affects the land price (
?r ?S > 0 ) and capital density ( > 0 ) at any ?? ??
location within the urban area, negatively affects distance gradients of land prices and capital densities (
? 2r ?2S < 0 and < 0 ), positively affects the housing output per ?x?? ?x??
unit of land (
?h > 0 ), positively affects the ratio of the two distance elasticities ??
(
?? > 0 ), and positively affects the city’s geographical size and population size ??
(
dN dx > 0 ). > 0 and d? d?
These impacts of a change in the elasticity of capital-land substitution can be
intuitively interpreted as follows. As ? increases, it eases substitution between land and capital and raises housing output at each location. Increases in output in turn raise the residual land prices under the competitive market. Moreover, since housing prices (output prices) decline with distance from the CBD, increases in the residual land prices are higher at locations closer to the CBD as compared with in suburbs, and so the land price curve becomes steeper. Further, as land becomes more expensive, capital investment rises to substitute for land, and relatively more capital is invested at central locations where land prices increase more, and so the capital density curve also rises and becomes steeper. The gaps between the declining housing and land
45
prices also increase, for the land price curve becomes steeper with the housing price curve held unchanged. The urban boundary expands, as a consequence of the higher urban land price curve, and the population increases (migrant from other cities or rural areas) to fill in the surplus of housing output so as to maintain the utility level.
46
Chapter 5:
Numerical Simulation
The purpose of numerical simulations is twofold. First, it verifies the predicted impacts of housing services production on urban spatial structure, particularly the derived impacts of capital-land substitution. Second, it examines the magnitudes of these impacts by a series of estimations and simulations. I estimate the housing production function (elasticity of capital-land substitution and other production parameters), spatial distributions of housing prices, land prices, capital densities, and the housing output per unit of land, and then I calculate the marginal impacts of capital-land substitution. The estimated impacts of a 1% change of the elasticity of capital-land substitution include effects on land prices, capital densities, the housing output per unit of land (or the FARs), the ratio of the two distance elasticities , the share of land cost in total property value, and the welfare implications in terms of aggregated values of land and housing output.
5.1
Impacts of Capital-Land Substitution
The impacts of ? on land price, capital density, housing output per unit of
land (or the FAR), and the ratio of the two distance elasticities, implied by the partial derivatives of
?r ?S ?h ?? , , , and , respectively, can be solved as explicit ?? ?? ?? ??
functions of p, n, ? , ? , and ? directly from the equilibrium solutions of S, r, h, and
? by (21), (22), (23), and (24) .
47
The impacts of ? on distance gradients of land prices and capital densities (
?2S ? 2r ?2S ? 2r ) are examined by verifying signs of and < 0 and <0. ?x?? ?p?? ?p?? ?x??
This is based on the fact that r and S are linked to distance only through p by (11) and
?2S ? 2r and can be written as: (12), and ?x?? ?x??
? 2r ? 2 r ?p = × <0 ?x?? ?p?? ?x ?2S ? 2 S ?p = × <0 ?x?? ?p?? ?x
The solutions for
(44)
(45)
?r ?h ?S ?? ?2S ? 2r , , , , and are very ?? ?? ?? ?? ?p?? ?p??
complicated (see Appendix I) and Mathematica is used to determine their signs with different combinations of parameters of p, n, ? , ? , ? . The value of p is chosen to change from 1,000 to 30,000, based on observations of housing prices from the Beijing data, in which the lowest housing price was 2,034 RMB per square meter, the highest was 19,478 RMB per square meter, and the mean was 6,888 RMB per square meter (see table 6-2). Capital price n is normalized to unity. Value ranges of the three production parameters ? , ? , ? are determined based on their theoretical values. Since ? is a positive scale parameter, its value should be irrelevant to the impacts of ? , and so the range of ? is taken from 0.1 to 3.0 for convenience without loss of generality. ? is a positive number less than unity in the CES function and so its range is taken from 0.01 to 0.99, and the value
48
range of ? is also taken from 0.01 to 0.99 (correspondingly ? varies from 0.01 to 99) (see Chapter 4). There are constraints on values of p, n, ? , ? , ? that can be chosen implied in (21) and (22). These constraints ensure that S is a positive and r is not negative and they are: ( n ?(1?? ) ) ?? > 0 p??
(
(46)
n ?(1?? ) n ?(1?? ) ) ?? ( ) ?? ? ? ? p?? p?? ]?1 + (1 ? ? )] 1?? ? n[ ]1?? ? 0 r = p? [(? [ 1? ? 1? ?
(47)
Table 5-1 reports the summary of the simulated results. These results are as expected and consistent with what the theory predicts (see Chapter 4).
Table 5-1 Signs of Relevant Partial Derivatives by Simulation
?S ??
p =1000,2000,3000,…,28000,29000,30000 n =1 ? =0.1, 0.2,0.3,…,2.9,3.0 ?=0.01,0.02,0.03,…,0.99 ?=0.01,0.02,0.03,…,0.99
?r ??
? 2S ?p??
? 2r ?p??
?? ??
?h ??
>0
>0
>0
>0
>0
>0
A close examination of these simulated results reveals a non-linear relationship between ? and urban spatial structure variables such as S, r, and ? (Appendix II). For instance, for the chosen ranges of p, n, ? , ? , ? , these partial derivatives increase exponentially along with ? when p, ? , ? are large. Holding ? , ? and ? unchanged and increasing p, impacts of ? on S and r also increase accordingly, and this is consistent with the positive signs of the secondary partial
49
derivatives (
? 2r ?2S > 0 and > 0 ). However, holding ? , ? and ? unchanged ?p?? ?p??
and increasing p, the impact of ? on ? decreases, and this is consistent with the theoretical result that as moving toward the city center ? decreases with p.
5.2
Marginal Effects of Capital-Land Substitution
The above simulated results reveal that the marginal effects of capital-land
substitution on urban spatial structure can be substantial. This section will estimate these marginal effects based on the Beijing data. This is carried out by estimating the housing production function (elasticity of capital-land substitution and other production parameters), spatial distributions of housing prices, land prices, capital densities, and the housing output per unit of land, calculating the marginal impacts of the elasticity of capital-land substitution, and finally determining the welfare implication by estimating aggregated values of land and housing output.
5.2.1 Housing Price Distribution and Production Function
Using data from Beijing (see chapter 6 for detailed data description), housing prices are estimated as an exponential function of distance from the city center— Tiananmen Square.
p = exp(9.234732 ? 0.0400622 x )
(48)
(36.94)
(-13.00)
R-sq=0.3904, Obs.=266.
50
where p is the housing price per square meter floor space in RMB and x is the distance from Tiananmen Square in kilometers. Figure 5-1 illustrates this estimated housing price curve as compared to observations from the sample. The estimated housing price is 10,247 RMB per square meter at the city center and drops gradually with distance from the city center.
Figure 5-1
Estimated Housing Prices over Urban Space
To determine the CES housing production function, three parameters need to be determined. Among them, ? is the key parameter and is estimated by several approaches. The estimates suggest robust results ranging from 0.37 to 0.65 (see chapter 6 for more details). Based on these estimates, 0.5 is chosen for ? in the baseline scenario. With ? determined, the other two parameters ? and ? are then estimated by multiple approaches as well, and their estimates fall into the interval of 0.000316-0.000953 and 0.99975-0.99996 (see Appendix III for more details). Based on these estimates, ? and ? are taken 0.0005 and 0.99995, respectively, with consideration on the fitness of the simulated land prices and housing output per unit
51
of land to the real observations.27 It should be noted that land prices and housing output per unit of land generated by this simulation are respectively overestimated and underestimated to certain degrees when compared with real observations (figure 5-2 and figure 5-3). This is due to the gaps between the reality and the theoretical model. Nevertheless, these errors are regarded as acceptable, for this simulation focuses on demonstration of relative changes caused by 1% change in the elasticity of capital-land substitution rather than the absolute changes. Estimations are carried out under the assumption that there is a 30% marginal profit in land development. This number makes the estimations fit better the data than a zero profit assumption. This assumption makes sense because of two reasons. First, although markets are emerging at a fast rate in China, specifically in Beijing, they are far from the competitive markets. Second, there is evidence suggesting that a substantial level of profits can be made from land development.28
Ideally, the simulated land price and housing output per unit of land would both fit the real observations with the estimated housing prices and production parameters, if the analytical model can perfectly explain the reality. However, models are simplifications of the real world and rely on certain assumptions, and the analytical model used in this study is not exceptional. Therefore, simulations based on the analytical model cannot fully fit real data. In this case, many of the model assumptions may be not satisfied in Beijing, such as the competitive market, market equilibrium conditions, zero profit condition, unity capital price, constant return to scale, and market equilibrium. Due to the gaps between the reality and theoretical model, it is hard to find a pair of ? and ? to generate simulated land price and housing output per unit of land that both fit the data well. So the strategy used here is to pick up a pair of ? and ? from the ranges of estimates of these two parameters (see Appendix III) that generate acceptable simulated land price and housing output per unit of land.
28
27
The 30% average profit ratio of sales is based on a survey of real estate profit done in China by the Ministry of Finance in 2005, which reported 26.79% profit ratio of sales of 39 real estate developers. Retrieved on July 13, 2010, from http://finance.sina.com.cn/g/20061108/14573060647.shtml
52
Figure 5-2
Simulated Land Prices over Urban Space
Figure 5-3
Simulated Housing Output per Unit of Land (FAR) over Urban Space
5.2.2 Marginal Impacts of Elasticity of Capital-Land Substitution
The baseline for estimating marginal effects of capital-land substitution is chosen as ? 0 = 0.5 and marginal effects are calculated by both a 1% increase and a
53
1% decrease in ? , respectively. That is, there is one baseline scenario and two simulated scenarios ( ? 1 = 0.505 and ? 2 = 0.495 ).29 Table 5-2 reports simulations of variables of interest in the three scenarios at selected locations. Besides r, S, h, and ? that can be computed directly by (21), (22), (23), and (24), the share of land cost in total property value (includes both land and land improvements), denoted by ? L , and the city’s geographical size x are also concerned. In the baseline scenario, r drops from 15,978 RMB in the city center to 150 RMB per square meter at the city boundary x0 =27.73, where the urban land price intercepts the agricultural land price of 150 RMB per square meter (figure 5-4).30 This simulated result of city size is reasonable, given that currently urban development in Beijing is expanding from the fifth ring road to the sixth ring road.31 S drops from 17,876 RMB per square meter to 989 RMB per square meter and h (or the FAR) decreases from 4.72 to 0.47, from the city center to the urban fringe (figure 5-5 and figure 5-6). Compared with observations in the sample, capital density and the FAR are both underestimated to certain extents in this simulation.
In reality, it is unlikely that only ? changes with the other two parameters held. For example, advances in technology facilitate capital-land substitution as well as affect the other two production parameters ? and ? . This is why in this simulation analysis, a small change (one percent) in ? is manipulated. The production function will no longer generate reasonable results if ? changes too much.
29 30
The agricultural land price is based on estimation of land acquisition projects in 2004 in Beijing provided by the Land & Resource Bureau and related policy documents on the minimum compensation. The land acquisition price was about 1.52 million per hectare (Zhao 2003, Thesis of Master degree). Beijing has five ring roads: while the second ring road is basically built on the ruins of the old city wall at about 3-5 kilometers from the city center, the other four rings are located respectively about 3-5 kilometers, 6-10 kilometers, 10-15 kilometers, 20-25 kilometers, 30-35 kilometers away from Tiananmen Square (as shown in figures 6-3 and 6-5).
31
54
Table 5-2
Simulated Impacts of Elasticity of Capital-land Substitution
land price r (RMB per square meter) capital density S (RMB per square meter) S0 S1 % change S2 % change S0 S1 % change S2 % change 0 km 15978 18946 18.6 13518 -15.4 17876 21486 20.2 14921 -16.5 5 km 10177 12027 18.2 8638 -15.1 14266 17080 19.7 11954 -16.2 10 km 6051 7122 17.7 5157 -14.8 11001 13109 19.2 9260 -15.8 15 km 3237 3790 17.1 2773 -14.3 8046 9533 18.5 6812 -15.3 20 km 1444 1679 16.3 1245 -13.8 5373 6318 17.6 4583 -14.7 25 km 437 502 15.0 381 -12.8 2955 3435 16.2 2549 -13.7 30 km 29 33 12.0 26 -10.6 768 869 13.2 680 -11.5 lamda (?) housing output per unit of land h (FAR) S0 S1 % change S2 % change S0 S1 % change S2 % change 0 km 4.72 5.64 19.4 3.96 -16.0 2.12 2.13 0.7 2.10 -0.7 5 km 4.16 4.96 19.1 3.51 -15.8 2.40 2.42 0.8 2.38 -0.7 10 km 3.55 4.21 18.6 3.00 -15.5 2.82 2.84 0.8 2.80 -0.8 15 km 2.87 3.39 18.1 2.44 -15.1 3.49 3.52 0.8 3.46 -0.8 20 km 2.12 2.48 17.3 1.81 -14.5 4.72 4.76 0.9 4.68 -0.9 25 km 1.29 1.49 16.1 1.11 -13.6 7.77 7.84 0.9 7.70 -0.9 30 km 0.37 0.42 13.1 0.33 -11.4 27.05 27.32 1.0 26.79 -1.0 share of land cost ( ? L) x (km) S0 S1 % change S2 % change S0 S1 % change S2 % change 0 km 0.33 0.33 -0.7 0.33 0.7 5 km 0.29 0.29 -0.8 0.29 0.8 10 km 0.25 0.25 -0.8 0.25 0.8 27.73 27.98 0.9 27.47 -0.9 15 km 0.20 0.20 -0.8 0.20 0.8 20 km 0.15 0.15 -0.9 0.15 0.9 25 km 0.09 0.09 -0.9 0.09 0.9 30 km 0.03 0.03 -1.0 0.03 1.0 Note: S0, S1, and S2 are respectively the scenarios with sigma=0.5, 0.505, and 0.495.
As expected, the simulated ? is larger than unity at any location, consistent with the analytical result and indicating that land prices decline faster than housing prices. Moreover, this simulation also indicates that ? increases with x (figure 5-7). The positive relationship between ? and x can be easily derived from the solution of
? by (23), noting that p is in the denominator and p decreases as x increases by (3).
55
The fact that ? is smaller than unity leads to a decreasing share of land cost in total property value towards the city edges.32 This expected phenomenon is also supported by the simulated results (figure 5-8 and table 5-2). The simulated results show that the spatial variation of the share of land cost is remarkable. For example, land cost accounts for 33% of the total property value at the city center, but the number drops to 3% at the location 30 kilometers away (figure 5-8 and table 5-2). This implies profound policy implications, particularly for property taxation and assessment. In a two-rate property tax system in which land and improvements are imposed by different tax rates, the conventional method to determine land value often assumes a fixed share of land value in the total property (such as 20%) for all properties across the urban space. According to the above simulation, it has been demonstrated that a fixed portion of land value causes inaccurate assessment of land value and leads to efficiency loss. The declining share of land cost in total property value ( ? L ) with distance from the CBD can be intuitively understood as the consequence of two different effects. One is the price effect and the other is the substitution effect. The price effect is related to the fact that land prices decline faster than housing prices with respect to distance and the substitution effect refers to the increasing intensity of land use as moving toward city edges due to the dropping land prices. Theory suggests that when
? < 1 the price effect overwhelms the substitution effect, and the simulation reveals
consistent results.
32
?L
can be derived to be
?L = 1?
n p?? ? ?? L ( ) and it is easy to derive that < 0 when p? n ?x
? < 1.
56
Now, look at the impacts caused by 1% change in ? by comparing the two simulated scenarios to the baseline scenario. First of all, results of the simulation suggest that land prices and capital densities are very sensitive to ? , particularly at the central locations. As ? increases (or decreases), both land price curve and capital density curve rise (or lower) and rotate clockwise (or counterclockwise), in accordance with the analytical results that ? positively affects land prices and capital densities and negatively affects their distance gradients (figure 5-4 and figure 5-5). At the city center, a 1% increase in ? leads to 18.6% increase (or 15.4% decrease) in land price and 20.2% increase (or 16.5% decrease) in capital density, at locations 30 kilometers away, the impacts of a 1% change in ? diminish to 10-13% change in land price and capital density (figure 5-4, figure 5-5, and table 5-2). Second, housing output per unit of land (or the FAR) is also highly responsive to ? , particularly in the central locations, as illustrated by figure 5-6. A 1% change in
? leads to 19.4% increase or 16.0% decrease in the FAR at the city center, and the
impacts decrease to 13.1% increase or 11.4% decrease at locations 30 kilometers away. This indicates that ? has considerable impacts on the urban housing structure at any location and it can be inferred ? must have large impact on the aggregated total housing output in the city.
57
RMB per square meter
Land price (r)
17500 15000 12500 10000 7500 5000 2500 5 10 15 20 25 30 distanceHkmL
Sigma=0.505 Sigma=0.500 Sigma=0.495
Figure 5-4
Simulated Land Prices in Three Scenarios
RMB per square meter
Capital Density (S)
20000 15000 10000 5000 distanceHkmL
Sigma=0.505 Sigma=0.500 Sigma=0.495
5
10
15
20
25
30
Figure 5-5
Simulated Capital Densities in Three Scenarios
Figure 5-6
Simulated Housing Out Put per Unit Land (FAR) in Three Scenarios
58
Comparatively, ? , ? L , and x are less sensitive to ? . A 1% change in ? in general leads to less than 1% change in these three variables. The small impact of ? on x is easy to understand given the diminishing impacts of ? on urban land prices when moving towards the urban edges. The small impact of ? on ? is probably because ? is a ratio of the marginal changes already. Nevertheless, the directions of changes confirm the analytical results that ? positively affects ? and x (figure 5-7, figure 5-9 and table 5-2). In contrast, ? L is negatively affected by ? (figure 5-8 and table 5-2). To understand this intuitively, note that the larger ? implies the larger degree that land is substituted with capital, thus as ? increases, more capital is used and the share of land value decreases.
lamda 17.5 15 12.5 10 7.5 5 2.5 5 10
Lamda (?) Sigma=0.505 Sigma=0.500 Sigma=0.495
1
15 20 25 30
distance HkmL
Figure 5-7
Simulated Ratios of the Two Distance Elasticities in Three Scenarios
59
Figure 5-8
Simulated Shares of Land Cost in Total Property Values in Three Scenarios
RMB per square meter 500 400 300 200 100
Land Price (r)
Sigma=0.505 Sigma=0.500 Sigma=0.495
ra
distanceHkmL
26
27
28
29
30
x2 x0 x1
Figure 5-9 Simulated Urban Boundaries in Three Scenarios
To sum up, results of the simulated three scenarios suggest that ? has substantial impacts on land prices, capital densities, and the housing output per unit of land (a 1% change in ? leads to 10-20% change in r, S, and h). These impacts are larger at central locations and diminish with distance. Comparatively, ? has smaller impacts on the ratio of the two distance elasticities, the share of land cost in total property value, and the city size. 60
5.2.3
Social Welfare Impacts
Shift and rotation of the land price curve caused by a change in capital-land substitution have social welfare implications. Land is one of the important sources for local government to obtain revenue in China through collecting land leasing fees and in the United States through levying property (land) tax (Oates 2001, Ding & Lichtenberg 2010). The welfare impacts of capital-land substitution are also reflected in the overall changes in the aggregated housing output, housing value, and population scale. The total impacts caused by 1% changes in ? , on the total land value, total housing output, total housing value, and total population capacity at the equilibrium of urban space are determined by the following equations, respectively:
TotalLandValue = ? r ( p ( x), n, ? , ? , ? )2?x? * 1,000,000dx
0 x
(49) (50)
TotalFloorSpace = ? h( S ( p ( x); n, ? , ? , ? ); ? , ? , ? )2?x? * 1,000,000dx
0
X
x
TotalHou s eValue = ? p( x)h( S ( p( x); n, ? , ? , ? ); ? , ? , ? )2?x? *1,000,000dx (51)
0
TotalPopCa pacity = ? h( S ( p ( x); n, ? , ? , ? ); ? , ? , ? )2?x? * 1,000,000 / ?dx (52)
0
x
where ? denotes the percentage of land that can be used for residential uses and is taken to be 0.3;33 ? is the average personal occupied floor space, and is assumed to be 30 square meters per person; 34 and 1,000,000 is used to adjust the unit of area.
33
According to the Urban Land Use Classification and Land for Construction Standards by the Ministry of Housing and Urban-Rural Development of the China (previously the Ministry of Construction) in 1990, the share of urban constructive land for residential should be 20-32%. http://www.law110.com/lawserve/guihua/1800004.htm
34
In fact, more strictly, housing consumption should be determined from the housing demand side problem and varies in urban space; however, for convenience here a constant consumption of housing
61
Table 5-3 presents the results. The total residential land value is estimated to be 1.94 trillion RMB, 2.28 trillion RMB, and 1.66 trillion RMB in the three scenarios, respectively. A 1% change in ? leads to 17.5% increase or 14.66% decrease in the total land value. These are remarkable impacts, as compared with the 0.2 trillion RMB total government revenue of Beijing in 2009.35 Moreover, by integrating the land values for each annulus, it suggests that the central annulus witness larger impacts on land value brought by 1% change in ? .
Table 5-3 Simulated Total Impacts of Elasticity of Capital-land Substitution in the City
0-5 km 5-10 km 10-15 km 15-20 km 20-x bar total
S0 281.68 548.64 524.76 366.71 220.99 1942.77
land value (billion RMB) S1 % change S2 333.30 18.3 238.80 647.06 17.9 466.62 616.16 17.4 448.25 428.09 16.7 315.04 257.49 16.5 189.79 2282.10 17.5 1658.50
% change -15.2 -14.9 -14.6 -14.1 -14.1 -14.6
S0 102.58 270.52 376.03 409.33 500.63 1659.08
housing output (million sq meter) S1 % change S2 % change 122.28 19.2 86.33 -15.8 321.51 18.9 228.33 -15.6 445.10 18.4 318.66 -15.3 481.87 17.7 348.75 -14.8 594.51 18.8 421.33 -15.8 1965.26 18.5 1403.40 -15.4
housing value (billion RMB) population capacity (million people) S0 S1 % change S2 % change S0 S1 % change S2 % change 0-5 km 2987.79 3560.75 19.2 2515.13 -15.8 3.42 4.08 19.2 2.88 -15.8 5-10 km 15556.84 18487.06 18.8 13132.58 -15.6 9.02 10.72 18.9 7.61 -15.6 10-15 km 29137.69 34487.13 18.4 24693.95 -15.3 12.53 14.84 18.4 10.62 -15.3 15-20 km 36294.56 42724.14 17.7 30924.10 -14.8 13.64 16.06 17.7 11.62 -14.8 20-x bar 46822.00 55600.65 18.7 39406.14 -15.8 16.69 19.82 18.8 14.04 -15.8 total 130798.87 154859.73 18.4 110671.90 -15.4 55.30 65.51 18.5 46.78 -15.4 Note: Assume 30 percent land for residential use, and 30 square meters housing consumption per person. S0, S1, and S2 are respectively the scenarios with sigma=0.5, 0.505, and 0.495.
The impacts ? on the total housing output are also remarkable. This is as expected since the FAR is very responsive to ? (figure 5-6). One percent change in
? leads to 18.5% increase or 15.4% decrease in the total housing output of the city.
over the urban space is assumed to calculate population capacity. The 30-square-meter living space per person is targeted by the government of Beijing City’s target by 2010: http://news.sina.com.cn/c/2010-03-12/092419848868.shtml.
35
ChinaNews: http://www.chinanews.com.cn/cj/cj-gncj/news/2010/01-02/2050451.shtml
62
Also, the central locations experience larger impact when compared with the periphery areas. Although housing price is unaffected by ? in the open city case, the total housing value changes with ? due to changes in housing output. The total housing value is simulated to be 131 trillion RMB, 155 trillion RMB, and 111 trillion RMB in the three scenarios, respectively. It suggests that a 1% change in ? leads to 18.4% increase or 15.4% decrease in the total housing value. In other words, a 1% change in
? could mean about 20 trillion RMB, which is a huge impact in the city’s wealth.
The total population capacity of the city is estimated to be 55.3 million, 65.5 million and 46.8 million population in the three scenarios, respectively, by assuming an average floor space consumption of 30 square meters per person. These simulated numbers appear overestimated, given that currently 15.81 million permanent populations live in Beijing in 2006 within the administrative area of 16,400 square kilometers (BSB 2007).36 However, considering that the Tokyo Metropolitan Area in Japan housed 33.4 million population in 2000 while occupying about 13,556 square kilometer land (about 65 kilometers radius), and China is experiencing rapid urbanization and massive rural-urban migration, some 50 million population might be a possible future if Beijing continues to grow. To sum up, 1% changes in ? leads to 14-18% changes in the total land value, 15-19% changes in the total housing output, the total housing value, and the total population of the city. These numbers suggest that the total social welfare impacts caused by changes in capital-land substitution in housing services production are
36
Permanent populations include migrants from other provinces that have stayed longer than six months but exclude temperate migrants staying less than six months.
63
substantial. These findings indicate that the opportunity cost of land development restrictions such as the building height caps and the FAR controls may be very high. Thus, policies and regulations that might constrain land development should be carefully examined before implementation.
64
Chapter 6:
Empirical Evidence
By using land development data from Beijing City, this chapter empirically examines the two research questions of this dissertation. After a brief introduction of the research area and data, I first test the classical predictions of the negative distance gradients of housing prices, land prices, capital densities, and the FARs. Then I examine the relationship between the distance elasticities of land prices and housing prices. Finally, I estimate the elasticity of capital-land substitution and examine its impacts by dividing the data into two sub-periods and comparing the changes of the estimated elasticity of capital-land substitution, distance gradients of land prices and capital densities, and the ratio of the two distance elasticities.
6.1
Research Area
Beijing is selected as a typical example of a prosperous city where land and
housing markets have developed rapidly since the late 1980s. In 1995 there were only 419 land leasing transactions (1,219 hectares and 3.7 billion RMB in total), compared to 3147 free land assignments (5,006 hectares) (MLR 1996). However, the land leasing market grew quickly and began to play the dominant role in distributing urban land resources. In 2004, the number of land leasing transactions climbed to 2,073 (6225 hectares and 63.1 billion RMB in total), compared to only 89 cases of land grant for free (453 hectares) (figure 6-1) (MLR 2005). 37 The housing market in
The sharp drop of land leasing transactions in 2005 (shown in figure 6-1) is due to a series of stringent policies on urban land supply to suppress the overheated real estate development and the
37
65
Beijing also developed rapidly, particularly after the year of 1998 when material housing distribution was formally prohibited. The annual sale of commodity housing rose from 1.42 million square meters in 1990 to 4.09 million square meters in 1998 and jumped to 28.03 million square meters in 2005, increasing at an annual growth rate of 14.1% during 1990-1998 and 31.6% during 1998-2005. Accordingly, the total value of annual sale shot up from 2 billion RMB to 176 billion RMB during this fifteen-year period at an impressive annual growth rate of 34.6% (BSB 2006) (figure 6-2).
Source: MLR 1996-2006, data of 1997 are unavailable Figure 6-1 Land Leasing Market in Beijing: Total Number of Leases and Total Leasing Value, 1995-2005
fever of special economic zones and industrial parks. The land leasing market in Beijing had been “frozen” during the second half of 2004 and the first half of 2005.
66
Source: BSB, Statistical Year Book of Beijing Figure 6-2 Commodity Housing Market Development in Beijing: Floor Space and Value of Sales, 1990-2005
Combining with the advances in technology of construction, the emerging urban land and housing markets are reshaping Beijing’s urban landscape. Before, Beijing was characterized with a flat skyline, resulting from the danwei-based urban landscape, lack of incentives to economize land, and strict planning regulations. After, one of the most salient changes in the urban landscape was the emergence of taller and taller buildings (figures 2-7, 2-8, and 2-9). Also, the spatial distribution of land uses evolved, manifested by the relocation of industries from the central locations to the suburbs and the concentration of business and commercial activities in the central region of Beijing. Driven by the market forces, Beijing’s urban landscape presents many similarities to Western cities. Figure 6-3 illustrates the spatial concentration of the functions in Beijing. Despite the preserved Forbidden City lying in the center of the
67
city, the central locations are favored by various activities including business, commerce, administration, education and research, etc. For example, within the third ring road are located the three commercial centers and one commercial street (Xidan, Wangfujing, Qianmen, and Jinrongjie), offices for more than 20 central government departments, hundreds of city departments and about 250 government agencies (Ding et al. 2005).
Hotels, embassies, convention centers, and foreign banks
Office buildings
2nd 3rd Facilities for culture uses, sports, and hospitals 4th 5th
Central and Beijing government agencies
Liaison office of other provinces
Universities and Colleges
Research institutes
Source: China Academe of Urban Planning & Design, Beijing Urban Spatial Development Research. 2003. Figure 6-3 Spatial Concentration of City Functions
68
Population density declines with distance from the city center in Beijing. If dividing the city by its five ring roads, within the second ring road, population density was about 27,400 people per square kilometer in 2004, even higher compared with the central 23 wards in Tokyo, Japan;38 within the third ring, population density was 24,000 people per square kilometer; and it decreased to 19,700, 12,600, 4,400, 2,000 and 840 for within the fourth ring, fifth ring, sixth ring, Beijing Bay, and the entire administrative area of Beijing, respectively (table 6-1).
Table 6-1 Distribution of Population Density in Beijing
Current population density 2 (10,000 pop/km ) 2.740 2.400 1.970 1.260 0.440 0.200 0.084 Planned Population Capacity for 2020 (10,000 pop) 124 350 565 915 1235 1650 1750
Within 2 ring rd Within 3 ring th Within 4 ring th Within 5 ring th Within 6 ring Beijing Bay (exclude west and north mountainous area ) Beijing
nd
Source: Beijing Municipal Institute of City Planning & Design, From Olympic Games to Future, 2004.
Empirical studies have also provided evidence for the distance decay phenomena of land and housing prices in Beijing. For example, Ding (2004) examined the revolution of urban spatial structure in Beijing using the land leasing data from 1993 to 2000. By comparing the land prices in different rings of the city by different land uses and estimating the price gradients and their changes, Ding’s findings indicated that the distant gradients were all significantly negative and were dependent on land uses.
38
The population density of the 23 wards in Tokyo was estimated to be 13,660 people per square kilometer Tokyo Statistic Yearbook 2005: http://www.toukei.metro.tokyo.jp/tnenkan/2005/tn05qyte0510b.htm
69
The data set used in this dissertation also depicts a clear picture of spatial patterns of Beijing. By using the GIS software ArcScene, figure 6-4 presents the spatial distribution of the housing prices, land prices, and the FARs. Nevertheless, it should be noted that despite growing markets, policies and planning regulations do play important roles in influencing the urban spatial structure of Beijing. For example, in 1989 the government of Beijing issued a policy—the Decision on the Strict Control of High-rise Residential Building Provision (Beijing [1989]42)—to control high-rise buildings, and this policy effectively curbed construction of high-rise buildings. The share of annually completed floor space of 10-and-above-floor buildings decreased from 40% in the late 1980s to less than 25% by 1992. This policy was later revised in 1994 and finally abolished in 2003. Afterward, the share of the 10-and-above-floor buildings rose again and currently reaches more than 40%. 39 It is true that developers often break land development requirements as subscribed to in urban plan and land leasing contracts (mostly the building height caps and the FAR controls) through bribing officials or even at the expense of paying the fines. However, this example illustrates that rigorous policy and plan implementation could serve as strict constraints on urban land development and significantly influence urban spatial structure, when stimulated by special incidences.
39
High-rise Building Development in Beijing (in Chinese), retrieved on May 2010, from http://www.chinajsb.cn/gb/content/2005-01/06/content_120207.htm
70
Housing price
Land price
FAR
Figure 6-4 Housing Prices, Land Prices, and FARs in the Study Area
71
During the research period of 1999-2003, it is observed that stricter policy and planning implementation were introduced around the year 2002, partly for preparing for the 2008 Olympic Games and partly for controlling the overheated land development.40 On the one hand, it was mandated that all state-owned urban land for profitable uses must be leased through open bid approaches (such as tender, auction, and listing) and no project should violate the plan, otherwise monetary penalty and even some jail time would be imposed. On the other hand, rigorous plan implementation was carried out and a great amount of illegal building structures were demolished.41 The stringent policies could have probably constrained the market in allocating land and capital resources and limited the capital-land substitution in housing services production. The following estimations should take this into consideration.
40
The year 2002 was the first year that the Olympic Games Plan implementation was started. In tracking the policy documents issued in that year, several of them are important and deserve a note. On April 2002, the Ministry of Land and Resources announced the Provisions of Tender, Auction, and Listing State-Owned Land Use Right, requiring that urban land use rights for profitable uses (including commodity housing development and commercial and office real estate development) must be leased to private users through open bid approaches (tender, auction, or listing). Following this national document, the Beijing government issued Provisions of Stop State-Owned Land Use Right Leasing to Profit Making Projects by Negotiation on July 2002. At the same time, the Beijing government also issued Measures on Violation of the Provisions of Land Management Administrative Responsibility. In December of the same year, the Beijing government issued the Notice of Adjusting State-Owned Land Use Right Benchmark Price. These formally issued documents play important roles to tighten the urban land use management.
Besides the tightening of land use policies and regulations, the citywide inspection of land use started in 2003 helped to reduce the number of cases of building permit violations. Furthermore, the successful bidding to the 2008 Olympic Games in 2001 triggered large-scale demolition of constructions that violated planning regulations zoning ordinances in the years after. For instance, a total 4.5 million square meters of building space were demolished in 2006. Source (In Chinese): http://www.landscapecn.com/news/html/news/detail.asp?id=8074. http://www.515home.com/commom/news_content.asp?id=32098. http://huaxianews.cn/news/2006-3/27/2006327135600.htm.
41
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6.2
Data
The data used in the empirical analysis of this dissertation include land price
per square meter, housing price per square meter, total square meters of land lot, total square meters of floor space, the FAR, location information, and so on, for each observation of housing project. Both housings price and land prices are needed for the same land lots so as to estimate ? and ? , test the relationship of ? > 1 , and examine the impacts of ? . Housing price data were collected from the largest online housing information website (http://www.soufun.com) in China on March 2007. The housing data provided information of project name, starting date of sale, location, the average housing prices per square meter floor space, housing type, and if furnished or not. The housing data were then matched to the land leasing transaction data, which were obtained from the Beijing Land Resource and Management Bureau, by project name and location information. The land leasing data provided information on project name, land leasing date, location, total square meters of land lot, total planned square meters of floor space, and land price per square meter. Matching these records from both sources greatly reduced the number of usable observations. After excluding government-subsided affordable housing (jingji shiyong fang) projects, single detached dwellings, and observations located more than 30 kilometers from the city center as well as the very few observations in the remote suburban districts that were considered as outliers, a total of 266 observations were obtained. Figure 6-5 presents the spatial distribution of these observations.
73
Note: land for construction includes the urban & town land, single sites for industry, sites of special use, but excludes the sites for rural villages. Source: Beijing Current Land Use Map of 2004, Beijing Land Resource and Management Bureau.
Figure 6-5
Administrative Area of Beijing and Research Area
Table 6-2 provides the descriptive statistics of the variables used in the following empirical analysis. The average land price per square meter was 2,211 RMB, which was about one-third of the average per square meter housing price. The housing structure floor space per unit of land or the FAR varied remarkably from 0.44 to 20.63, with the mean of 4.55. The capital density was estimated by
S = ( pH * 0.7 ? rL) / n , based on the assumption that there was an average profit ratio
of housing sales of 30% in urban housing market (as in the simulation analysis). The average capital density was 20,550 RMB per square meter of land in the sample. The mean location of observations was 11.4 kilometers away from the city center—
74
Tiananmen Square.42 The years of land purchase varied from 1999 to 2003, and the starting years of housing sales varied from 1999 to 2007. There were time gaps between land purchases and housing sales, ranging from one year to seven years, which could be related to project scales. Usually it takes less time to finish smaller land development projects than larger ones. On average, the time lag was a bit more than one year. The total land area and total housing floor space varied dramatically among the observations, indicating the project scale had a large variance. About 38% of the housing projects had furnished the rooms. Tables 6-3 and 6-4 also provide information of the numbers of observations by district and housing type. This data set has several advantages. First, each observation has matched housing and land prices that were directly observed from transactions. This is helpful to obtain better estimates, because measurement errors that are associated with systematically biased estimation of land prices are less likely to occur in this data set (McDonald 1981, Thorsnes 1997). Second, all of the observations were newly developed commodity housing projects, and thus this data set is not associated with the problem that old dwellings fail to continuously adjust land and capital input according to prices (Jackson et al. 1984). Moreover, rapid urban expansion and housing project development in Beijing offers spatially widely scattered observations, from the city center to the urban edges, as compared with the fact that in the developed countries new housing development are mostly clustered only in the suburbs.
42
Despite the Forbidden City, which only occupies 0.72-kilometer squares, the central areas of Beijing remain attractive to business, commercial, and administrative activities. In this study, Tiananmen Square is regarded as the city center, which is itself not an employment center but rather symbolic for the highly concentrated economic activities in Beijing.
75
Table 6-2
Descriptive Statistics
Mean 6887.7 2211.0 8.78 7.26 4.55 1.35 Std. Dev. 2481.0 1939.1 0.35 1.12 2.69 0.58 Min 2034.4 30.8 7.62 3.43 0.44 -0.82 Max 19477.9 14940.4 9.88 9.61 20.63 3.03
p r ln(p) ln(r ) h (or the FAR) ln(h)
S ln(S) x LY HY DIFF FA LA FUR DT TP
Variable Obs unit housing price per square 266 meter structure space in RMB unit land price per square meter 266 land in RMB Logarithm of housing price 266 Logarithm of land price 266 floor area ratio, measuring the 254 housing output per unit land Logarithm of housing output per 254 unit of land capita density, estimated by subtracting total housing sale value 254 with total land cost and divided by total land area logarithmic capital density 254 distance from Tiananmen Square 266 in kilometer land leasing year 266 housing sale year 266 Year difference between land 266 purchase and housing sale total floor area of structure space 254 for each observation in square meter total land area for each observation 266 in square meter dummy variable: Furnish=1 if 253 housing is furnished; otherwise Furnish=0 dummy variables: districts 256 dummy variables: housing types 266
20549.9 9.70 11.42 2001.05 2002.1 1.02 61594.0 17309.3 0.38
15859.3 0.71 5.46
1348.7 7.21 2.26
157992.0 11.97 25.60 2003.00 2007.0 7.00 1433262.0 427283.0 1.00
1.40 1999.00 2.0 1999.0 1.20 101142.4 31209.4 0.49 0.00 676.0 248.0 0.00
Table 6-3
Districts 1 2 3 4 5 6 7 Total
Numbers of Observations in Each District
Dongcheng Xicheng Xuanwu Chaoyang Haidian Shijingshan Tongzhou Freq. 10 7 12 109 81 21 26 266 Percent 3.76 2.63 4.51 40.98 30.45 7.89 9.77 100
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Table 6-4
Housing types 1 2 3 4 5 6 7 Total
Numbers of Observations in Each Housing Type
Freq. 10 7 12 109 81 21 26 266 Percent 3.76 2.63 4.51 40.98 30.45 7.89 9.77 100
Slab Tower & Slab Tower Mid-rise High-rise Mid-to-high-rise Slab & Mid-to-high-rise
Note: these types are provided by the developers on the website, and they are not strictly exclusive to each other.
The data also bear several shortcomings. First, the observations were housing projects rather than single dwellings and the housing prices were the average prices of housing project. Compared with the prevalence of single-house dwellings in the developed countries, China’s residential development is mostly high-rise compound buildings, each providing dozens to hundreds of apartment flats. The average housing price cannot reflect the structural differences (such as the floor number, number of bedrooms and bathrooms, layout, window directions) among housing apartment flats within one project. Second, the total structural space of each housing project and the FAR were from land leasing records, which were planned rather than completed. Therefore, they might be biased if the final housing output exceeded the planned structural space subscribed on the land leases. Finally, land prices were determined through the approach of negotiation, which is the most used approach but is often regarded as being associated with non-market factors. 43 Nevertheless, the way in which land prices are determined by negotiation is similar to that in the market, since
43
During 1999-2003, there are totally 8,865 land leasing cases in Beijing, 8,738 of them were through negotiation, and the others were through tender, auction, and listing (MLR 2000-2004).
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the final land leasing price is agreed to by both the city government and the developers and dependent on land use type, location, neighborhood characteristics, etc.
6.3
Urban Decaying Phenomenon
The first empirical question is to test the spatial decay functions. According to
(4), (11), (12), (13), housing prices, land prices, capital intensities, and the housing output per unit of land (or the FARs) decline with distance from the city center. To estimate and test these negative distance gradients, the estimating equation is specified as:
ln(O ) = ? 0 + ?1 x + ? ? j A j + ?
j =2
(53)
where O denotes the housing price p, land price r, capital density S, or housing output per unit land h (or the FAR); x denotes the distance from the city center; A j denotes control variables, which vary with dependent variables; ?0 is the intercept; ?1 is the distance gradient, which is expected to be significantly negative; ? j are coefficients of control variables; and ? is the error term. Table 6-5 reports estimated results by ordinary least square (OLS). 44 The models present a moderate goodness-to-fit, with the R-squared ranging from 0.3 to 0.6. All of the distance gradients of housing prices, land prices, capital intensities and the FARs are significantly negative numbers, consistent with the model predictions of the urban decaying phenomenon.
44
Stata is used in all estimations.
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Table 6-5
OLS Estimations of Distance Gradients for Housing Prices, Land Prices, Capital Densities, and FARs
ln(p) ln(r ) ln(S) ln(FAR) obs=242,R-sq=0.5115 obs=266, R-sq=0.615 obs=242, R-sq=0.4047 obs=254, R-sq=0.3098 Coef. t sig. Coef. t sig. Coef. t sig. Coef. t sig. distance -0.0383 -6.30 **** -0.0943 -5.55 **** -0.05986 -4.37 **** -0.0272 -2.28 ** district_2 -0.0359 -0.30 -0.0475 -0.13 -0.17693 -0.64 -0.1344 -0.54 district_3 -0.2709 -2.46 ** -0.1809 -0.59 -0.09603 -0.37 0.0617 0.29 district_4 -0.2263 -2.64 *** -0.0994 -0.40 -0.34127 -1.73 * -0.0971 -0.56 district_5 -0.1254 -1.41 -0.2025 -0.78 -0.31262 -1.53 -0.1772 -0.98 district_6 -0.2738 -2.24 ** -0.0534 -0.15 -0.40446 -1.45 -0.0818 -0.34 district_7 -0.2380 -1.61 -1.5336 -3.76 **** -0.70436 -2.08 ** -0.4784 -1.61 type_2 0.0144 0.33 0.253581 2.54 ** 0.2042 2.33 ** type_3 -0.0620 -1.52 0.205752 2.22 ** 0.3346 4.17 **** type_4 -0.0506 -0.40 -0.61001 -2.11 ** -0.4413 -2.10 ** type_5 -0.1939 -2.14 ** 0.188219 0.92 0.4569 2.97 *** type_6 0.0290 0.28 0.021759 0.09 -0.1373 -0.74 type_7 -0.0219 -0.24 -0.18304 -0.88 -0.1111 -0.60 FUR 0.0179 0.53 0.073118 0.95 FA 0.0000 1.57 HY_2000 -0.0037 -0.05 HY_2001 -0.0624 -0.93 HY_2003 0.0569 0.83 HY_2004 0.1425 2.05 ** HY_2005 0.2597 3.09 *** HY_2006 0.2981 2.56 ** HY_2007 0.4307 2.39 ** LA 0.0000 -0.32 LY_2000 -0.0248 -0.17 LY_2001 -0.2229 -1.38 LY_2002 0.1540 0.96 LY_2003 0.0508 0.33 DIFF 0.040743 1.30 CONST 9.3609 88.68 **** 8.6690 32.47 **** 10.51319 53.26 **** 1.6430 9.46 **** ****99.9%, ***99%, **95%, * 90%
Calculating at the mean distance (11.4 kilometers), the distance elasticities of housing prices, land prices, capital densities, and the FARs were -0.44, -1.08, -0.68, and -0.31, respectively, suggesting that a 1% increase in the distance from the city center would decrease housing prices by 0.44%, land prices by 1.08%, capital densities by 0.68%, and the FARs by 0.31%, respectively. These results suggest that land prices behaved in a more elastic way with respect to distance, when compared to
79
housing prices. To better understand the speeds of these declines, supposing that a one-kilometer move is made at the mean distance away from the city center in Chaoyang district, the housing type is slab and it is not furnished, the total floor space and land areas are taken by the means of the sample, and the land purchase year is 2001 and housing sale year is 2003, this move will make the housing price drop by 288 RMB per square meter, land prices drop by 142 RMB per square meter, capital densities drop by 637 RMB per square meter, and the FARs drop by 0.066. Coefficients of the control variables suggest some interesting findings. First, effects of the district dummy variables are mixed compared with the expectation. Housing prices would be higher if it was located in Chaoyang, Xuanwu, and Shijingshan. This is reasonable given the development of Chaoyang CBD and the closeness to the city center of Xuanwu and Shijingshan. It is unexpected that Haidian did not have a positive influence on housing prices given the concentration of hightech business and universities in Haidian district especially in its Zhongguancun area. A possible explanation is that Haidian is a large district and includes also less urbanized areas that offset its attractiveness. Tongzhou was the only district dummy variable that had significant and negative influence on land prices, probably due to the newly government-facilitated and to a certain degree subsidized land development (Tongzhou is among three of the key new cities in the 2004 master plan). Capital density was significantly higher in Chaoyang and lower in Tongzhou, suggesting difference in quality of residential development. No district dummy variable was significant for the FAR. Second, high-rise and tower housing buildings in general were associated with higher housing prices, capital intensities, and FARs, but not
80
associated with land price. Third, the effects housing project scale and land development scale on housing prices and land prices were as expected but not significant.45 Fourth, housing prices and land prices appeared to increase with time, consistent with economic growth, but the time effect on land prices was not significant. Finally, the time lag had a positive sign on capital density as expected but was not significant.
6.4
Ratio of the Two Distance Elasticities
According to (14), land prices are more elastic with respect to distance from
the city center: ? > 1 . To estimate ? , I employ two different approaches. The first approach is to estimate ? by computing the ratio directly from the estimated distance gradients of land prices and housing prices. According to the definition of ? by (14):
?r ? = ?x ?p ?x
? ln r r ?r r ? x = ?x = ?x = 1r p ?p ? ln p ?1 p p ?x x ?x
(54)
where ?1r and ?1 p are respectively the estimated distance gradients of land prices and housing prices by (53). According to the OLS results shown in table 6-5,
?=
? 0.0943 = 2.46 > 1 . ? 0.0383
45
Large housing projects are expected to positively affect housing prices for they provided better services and facilities. Larger land lots, however, are expected to negatively affect land prices because fewer developers were able to bid for large scale land development and thus they had more power to bargain with the government.
81
However, this simple computation from the independent OLS estimations cannot tell whether ? is statistically significant larger than unity. For the purpose of testing ? > 1 , I also employ the seemingly unrelated regression (SUR) estimation. The SUR estimation jointly estimates the housing prices function and land prices function and yields more efficient estimates, for it takes into account the potential correlations between the error terms of the two equations. The SUR estimation makes sense in this case because both housing prices and land prices came from the same data set, and therefore the error terms of the two equations are likely to be correlated. More important, it can be tested whether the distance gradients from the two equations are significantly different from each other by conducting a cross-equation
? 2 test.
Table 6-6 reports the results of the SUR estimations. The estimated distance gradients are similar to those of the OLS, and both are significantly negative. Using these estimates, ? =
? 0.0892 = 2.34 > 1 . The ? 2 test reports that the null hypothesis ? 0.0382
of ?1r = ?1 p is rejected at a 99% level in favor of the alternative hypothesis that the two distance gradients are significantly different from each other, and this provides statistical evidence for ? > 1 .46
46
Chi2(1)=9.26, Prob>chi2=0.0023.
82
Table 6-6
SUR Estimations of Distance Gradients for Housing and Land Prices
ln(p) obs. 242, R-sq=0.5115 coef. z sig. -0.0381691 -6.61 **** -0.0345822 -0.30 -0.2708801 -2.59 *** -0.2271482 -2.79 ** -0.1255459 -1.48 -0.2753058 -2.37 ** -0.2389175 -1.70 * 0.0156686 0.37 -0.0596148 -1.54 -0.0537071 -0.45 -0.1897537 -2.20 ** 0.0300463 0.30 -0.0230342 -0.26 0.0177716 0.56 2.57E-07 1.70 * -0.0041231 -0.06 -0.0624409 -0.98 0.0569865 0.88 0.1412889 2.13 ** 0.2587748 3.23 **** 0.294404 2.66 *** 0.4375647 2.55 ** ln(r ) obs. 242, R-sq=0.4621 coef. z sig. -0.0891899 -5.70 **** -0.0230039 -0.07 -0.0311796 -0.10 -0.1085817 -0.48 -0.2247626 -0.95 -0.0054501 -0.02 -0.8121863 -2.09 **
distance district_2 district_3 district_4 district_5 district_6 district_7 type_2 type_3 type_4 type_5 type_6 type_7 FUR FA HY_2000 HY_2001 HY_2003 HY_2004 HY_2005 HY_2006 HY_2007 LA LY_2000 LY_2001 LY_2002 LY_2003 CONST 9.359147 93.21 **** ****99.9%, ***99%, **95%, * 90%
-2.44E-06 0.017005 -0.1911381 0.079664 0.0064016 8.636603
-1.77 * 0.12 -1.22 0.50 0.04 34.87 ****
The second approach is to estimate ? based on its alternative representation as the housing price elasticity of land price. According to (15) and (26), ? can be estimated by the following equation:
ln(r ) = ? 0 + ? ln( p) + ?
(55)
where r and p denote per square meter land price and housing price, respectively; and
? 0 is the intercept. I use both OLS and instrumental variable (IV) estimations to
estimate ? . The reason for using the IV estimation is that housing price is probably
83
correlated with the error term, due to the uncontrolled factors that affect both housing and land prices such as the neighborhood effects. I choose the housing type (TP), housing sale year (HY), and whether the rooms are furnished (FUR) as instrumental variables since they are correlated with housing prices but are not apparently associated with land prices. I also include land leasing year (LY), land area (LA) and square of land area (LA_square) in the major function as control variables. Table 6-7 reports the results of both the OLS and two stage least square (2sls) IV estimations. The OLS estimation yields ? = 1.69 with the T-statistics suggesting that ? is significantly larger than unity, and the IV-2sls estimation yields ? = 2.75 , which is also significantly larger than unity. 47 It should be noted that although theoretically the IV estimation improves the estimation by correcting the endogenous problem, it is also associated with the problem of “weak” IV that impairs the precision of the estimates, especially in this case that the R-squared and the Fstatistics of the first stage estimation that are quite small. In conclusion, by using the Beijing data, different approaches and estimation methods yield considerably robust estimates of ? ranging from 1.69 to 2.75, and the statistical tests indicate that ? is significantly larger than unity, consistent with the theory that land prices are more elastic with respect to distance from the city center than housing prices.
The T-statistics for ? > 1 is 4.28 for the OLS estimation, and 3.44 for the IV estimation, all significant at a 99.9% level.
47
84
Table 6-7
OLS and IV Estimations of the Ratio of the Two Distance Elasticities OLS obs=266, R-sq=0.3878, lamda sig.>1**** t sig. 1.689699 10.49 **** -0.0000259 -6.55 **** 6.38E-11 5.95 **** -0.121649 -0.69 -0.2867924 -1.45 0.7089738 3.56 **** 0.2098351 1.11 -6.950496 -4.95 **** IV-2SLS First stage regression obs=242, R-sq = 0.1709, F(21,220)=2.16 t sig. -5.81E-06 -2.75 ** -8.31E-12 -1.87 * 0.14141 1.34 0.1707963 1.37 0.2860518 2.16 * 0.2187656 1.68 * -0.0379462 -0.65 -0.0797368 -1.50 0.0506728 0.31 -0.1342184 -1.17 -0.1811546 -1.35 -0.0388464 -0.33 0.0520186 1.21 -0.047188 -0.40 -0.1908059 -1.40 -0.1618301 -1.10 -0.1428123 -0.96 -0.0555139 -0.35 0.0678337 0.34 0.2445954 0.95 2.75E-06 3.93 **** 8.722184 102.07 **** Instrumental variables (2SLS) regression obs=242, R-sq=0.4114, lamda sig.>1 **** t sig. 2.753689 5.40 **** -0.0000313 -7.68 **** 7.46E-11 6.81 **** -0.1783376 -0.90 -0.2345336 -1.08 0.6820098 2.89 ** 0.431023 1.97 * -16.07865 -3.61 ****
Dependent: ln( r) ln(p) LA LA_square LY_2000 LY_2001 LY_2002 LY_2003 CONST
coef.
Dependent: ln(p) LA LA_square LY_2000 LY_2001 LY_2002 LY_2003 type_2 type_3 type_4 type_5 type_6 type_7 FUR HY_2000 HY_2001 HY_2003 HY_2004 HY_2005 HY_2006 HY_2007 FA CONST
Coef.
Dependent: ln(r) ln (p) LA LA_square LY_2000 LY_2001 LY_2002 LY_2003 CONST
Coef.
****99.9%, ***99%, **95%, * 90%
85
6.5
Elasticity of Capital-Land Substitution
The elasticity of capital-land substitution is defined as the elasticity of the
ratio of the factors with respect to the marginal rate of technical substitution between them, reflecting how sensitive the cost-minimizing factor input proportions is to changes in relative factor prices (McFadden 1978). Mathematically it is presented:
?=
d ln( K / L) d ln(r / n)
(56)
where ? is the elasticity of capital-land substitution, K is the capital input (non-land input), L is the land input, r is the land price, and n is the capital price. I employ three approaches to estimate ? . The first approach is to estimate ? directly from the CES function by (19). Given the non-linearity of the CES function, the non-linear least square (NLLS) estimation is employed and the estimating functions are:
h = ? [?S
??
+ (1 ? ? )]
1
?
1
?
+?
(57) (58)
ln(h) = ln(? ) ?
?
ln(?S ?? + (1 ? ? )) + ?
where h is the housing output per unit of land (or the FAR), S is the capital density,
? , ? , ? are production parameters, and ? =
1 by (17). This approach is ? +1
straightforward, and it yields estimates not only for ? but also for ? and ? . However, it should be noted that there are several drawbacks of this approach. First, direct estimation of the CES function is associated with the problem of multicollinearity between the inputs and the problem of simultaneous equation bias
86
(Caddy 1976). Second, since S is not observed but estimated by subtracting land cost and an average proportion of profit from the housing sale value, S tends to be correlated with the error terms. And finally, the NLLS estimation by Stata may not obtain the global best estimates but can only assure the local optimal estimates, for it starts with arbitrarily decided initials and iteratively solves the estimates to minimize the summation of squared residuals. Table 6-8 reports the estimated results. While ? and ? from the logarithmic equation by (58) are not significant, ? , ? , and ? are all significant from the original form by (57) and ? is computed from ? to be 0.49.
Table 6-8 NLLS Estimations of Housing Production Function
ln(h) R-sq=0.7691, Obs=254 parameter t sig. 0.0019933 0.62 0.8376112 2.87 ** 0.0731662 0.33 0.9318
?
h R-sq=0.9187, Obs=254 parameter t sig. ? 0.000307 6.62 **** 0.9999906 23676.29 **** ? ? 1.043628 2.38 ** ? 0.4893 is calculated from the estimated ? .
The second approach is to estimate ? from the equilibrium solution of h by (23), which describes also a non-linear relationship and NLLS is used. Assuming the 30% profit of housing sales, the estimating functions are:
? ? 1?? h( p) = ? ? ? ? n 1+ ? ?1 ? ? ( ) 0.7 p?? ? ?
? ? ? ? ? ? ?
?
1
?
+?
(59)
87
? ? 1 ? 1?? ln(h) = ln(? ) ? ln ? ? ? n 1+ ? ?1 ? ? ( ) 0.7 p?? ? ?
? ? ? +? ? ? ? ?
(60)
The advantage of this approach is to avoid the endogenous problem as in the first approach; however, the function form is further complicated, which might impair the precision of the estimation. Table 6-9 reports the estimated results. Only the logarithmic equation by (60) yields significant estimate of ? , and correspondingly ? is computed to be 0.37.
Table 6-9 NLLS Estimations of Housing Production Function
ln(h) R-sq=0.0427, obs=254 paremeter 0.0008514 0.9999996 1.674321 0.374 t 2.22 6.40E+05 1.79 sig. ** **** *
h R-sq=0.7448, obs=254 parameter t 0.0007836 1.87 0.9999995 4.90E+05 1.597259 1.4 0.385 is calculated from the estimated ? .
?
? ? ? ?
sig. * ****
The third approach is to employ the market equilibrium conditions that the marginal factor output equals to the ratio of the factor price over the product price.
? H n ?H = ? ( )1+ ? = p ?K ? K
?H 1 ? ? H 1+ ? r = ? ( ) = ? L p ?L (61) and (62) yields:
(61)
(62)
K n ( ) ?? ?1 = 1? ? L r
Taking the logarithm on both sides:
?
(63)
88
K r ? 1 1 ln( ) = ln( )+ ln( ) L ? +1 1?? ? +1 n
(64)
Replace S =
K and suppose the capital price n is spatially invariant constant, L
then ? can be estimated the follow equation:
ln(S ) = a + ? ln(r ) + ?
(65)
where S is the capital density and r the land price. Compared with the above two approaches, the third approach is simple in equation form, and ? is a first-order parameter in the estimating function, increasing the possibility that ? is estimated with precision (Caddy 1976). Nevertheless, this approach is also associated with the endogenous problem since S is estimated from h, p and r and there might be uncontrolled factors that both affect r and S. Therefore, besides using the OLS estimation, the IV method is also employed. I choose the land area (LA), the square of land area (LA_square), and the land leasing years (LY) as the instrumental variables, and I include the housing type (TP) and the time lag between land purchase and housing sale (DIFF) as control variables in the major equation. Table 6-10 reports the results of OLS and IV-2sls estimations. The estimates of ? are 0.65 and 0.46 from the OLS and IV estimations, respectively, both significantly larger than zero and smaller than unity according to the T-tests, consistent with the theoretical analysis.48 To sum up, different approaches and estimation methods generate in general robust estimates of ? , ranging from 0.37 to 0.65. These values fall in the middle
The T-statistics for ? < 1 are 11.49 and 7.87 in the OLS and IV estimations, respectively, both significant at a 99.9 % level.
48
89
range of results reviewed by McDonald (1981). These values are also in accordance with Ding (2004)’s estimation of 0.32-0.74 in 1993-2000 by using also Beijing data.
Table 6-10 OLS and IV Estimations of Elasticity of Capital-land Substitution OLS obs=254, R-sq=0.6877, sigma sig.<1**** t sig. 0.6468159 21.04 **** 0.1101075 1.56 -0.0118449 -0.18 -0.3490511 -2.03 ** -0.1441138 -1.16 -0.2347224 -1.58 -0.0687507 -0.46 0.0519092 2.32 ** 4.861718 21.34 **** IV-2SLS
Dependent: ln(S) ln(r) type_2 type_3 type_4 type_5 type_6 type_7 DIFF CONST
coef.
Dependent: ln(r ) LA LA_square LY_2000 LY_2001 LY_2002 LY_2003 type_2 type_3 type_4 type_5 type_6 type_7 DIFF CONST
Dependent: ln(S) ln (r) type_2 type_3 type_4 type_5 type_6 type_7 DIFF CONST
First stage regression obs=254, R-sq = 0.3465, F(13,240)=9.79 Coef. t sig. -0.0000274 -8.00 **** 6.49E-11 7.11 **** 0.1382444 0.88 0.0299359 0.17 0.0125844 0.07 0.1825713 1.08 0.3615043 2.78 ** 0.3553335 2.93 ** -0.4070911 -1.27 0.706637 3.00 ** -0.3522217 -1.29 -0.1189245 -0.42 -0.0342514 -0.80 7.561267 47.33 **** Instrumental variables (2SLS) regression obs=254, R-sq=0.6403, sigma sig.<1 **** Coef. t sig. 0.4594759 6.69 **** 0.174936 2.23 ** 0.0890905 1.15 -0.4468925 -2.39 ** 0.033356 0.23 -0.3020863 -1.88 * -0.0864005 -0.54 0.0367899 1.50 6.217255 12.44 ****
****99.9%, ***99%, **95%, * 90%
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6.6
Impacts of Elasticity of Capital-Land Substitution
To examine the impacts of the elasticity of capital-land substitution on urban
spatial structure, it first requires examining whether ? has changed. I expect a decrease in ? in the research period of 1999-2003, because of the stringent policies on urban land use around the year 2002. Technology of construction is regarded unlikely to have changed during this short period. Further, if ? decreases, the land price and capital density curves will become flatter and ? will also decrease, according to the theoretical results by (31), (32), and (34), if the housing prices are held. Therefore, by dividing the data into two sub-samples: 1999-2001, and 20022003, I examine the impacts of ? by comparing the changes in ? and the changes in distance gradients of land prices and capital densities as well as ? . If the changes are consistent with the theoretical results, it would provide certain evidence. Table 6-11 reports the summary of the estimated results (for more details see Appendix IV). The findings in general provide consistent evidence to the theoretical results. The estimates of ? did decline during the research period: estimates from the OLS estimation were 0.71 and 0.62 for the first and the second sub-periods, respectively; estimates from the IV estimation were 0.56 and 0.44 for the two subperiods, respectively. This is consistent to the expectation that the stringent policies on urban land use around 2002 suppressed capital-land substitution. The absolute values of distance gradients of land prices and capital densities both decreased (from 0.095 to -0.067 and from -0.066 to -0.059, respectively), indicating that both the two curves were flattened. The estimated ? also decreased according to the results from
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multiple approaches, indicating the gap between the decaying land and housing prices became smaller.
Table 6-11 Comparison between Estimates for Two Sub-Periods
1999-2001 2002-2003 change sig. OLS 0.70 0.62 decrease * sigma IV 0.56 0.44 decrease **** land price gradient OLS -0.095 -0.067 flatter * capital density gradient OLS -0.066 -0.059 flatter *** OLS 1.89 1.52 decrease not tested lamda SUR 2.40 1.58 decrease IV 3.25 2.07 decrease **** ****99.9%, ***99%, **95%, * 90% Note: F-statistics are calculated to test the changes of the estimates in the two sub-periods
It should be noted that the above analysis is based on the assumption that housing price stayed unchanged. Estimated results suggest that the housing price curve became steeper during the research period (the estimated distance gradients of housing price were -0.035 to -0.039, respectively). However, this change is not statistically significant. So there must exist some forces that drove the land price and capital density curves to become flatter; and the decrease in ? was probably one of the reasons.
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Chapter 7:
Conclusion
The contribution of this dissertation to the literature is twofold. First, it investigates empirically the relationship between the distance elasticities of land prices and housing prices, and it provides evidence for what the urban economic theory predicts: as derived demand for land, land prices drop faster than housing prices towards the urban edges. Second, it investigates the impacts of the capital-land substitution, one of the most important properties of housing services production, on urban spatial structure through analytical exercise, numerical simulation, and empirical estimation. The findings suggest that an increase in the elasticity of capitalland substitution leads to increases in the land price, the capital density, and the housing output per unit of land at any location within the city, flattening of the land price and capital density curves, an increase in the ratio of the distance elasticity of land prices to the distance elasticity of housing prices, an expansion of the city boundary, and a growth in the population.
7.1
Policy and Planning Implications
The findings of this dissertation have three policy and planning implications.
The first one links to the skyrocketing housing prices in Beijing and a few other cities in China. The climbing housing prices in cities, such as Beijing, are attributable to many sources; including the rapid urbanization, the historical shortages of housing stocks, the increase in income, the housing pre-sale system, and the rise in land
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prices. 49 Many developers and investors put the blame on the government for not controlling land prices and they claim the rising land prices are the primary reason for soaring housing prices. 50 However, the findings of this dissertation suggest an alternative explanation. By examining the spatial patterns of land and housing prices and revealing their relationships, this dissertation provides empirical evidence for the theory that land is an input factor in housing services production and the demand for land is a derived demand. Under the land use right system in China, it is mandated that land use rights of the state-owned urban land should be transferred to private developers through open bid process (such as an auction). Thus the final bid land price is determined by the expected housing prices in the future and other market conditions. Given that land is an input to produce housing services, developers who aim to maximize profit will hardly set housing prices lower than market prices, even if the governments reduce land prices. Therefore, based on the theory of housing services production and empirical findings, there is evidence to conclude that it is unlikely that the pace of housing prices increase in Beijing will be slowed down by controlling land prices in land markets, or the impact of land price declines on housing prices will be trivial if there will be any. The policy implication is that the problem of skyrocketing housing prices should be addressed through other approaches, for instance, improvement on the housing financing mechanism, taxes on
49
In the housing pre-sale system, developers sell housing properties to residents before buildings are constructed. This pre-sale system was adopted to boost China’s urban housing market and solve the problem of lack of startup capital. However, this system favors sellers and push forward housing prices. It has been a hot topic in recent years whether or not to cancel the housing pre-sale system in China.
Some examples (in Chinese) can be found from (retrieved on May, 2010) http://www.sohochina.com/news/soho_news.aspx?id=13386 http://www.ln.xinhuanet.com/fcpd/2006-05/26/content_7104149.htm http://lianghui.china.com.cn/zhibo/2009lh/2009-03/06/content_17384784.htm?show=t
50
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vacant housing properties, taxes on income from speculative housing purchases, and provision of affordable public housing services for low-income households. Second, the findings of this dissertation reveal that the share of land cost in the total value of the property declines with distance from the CBD to the urban fringes and this has important implication on land value assessment. Land tax is regarded as the best tax that does not distort resource allocation in markets. Land tax is also important as a widely used approach to improve social welfare by redistributing income and reducing poverty, according to Henry George (1879). The moral basis for levying tax on land is to collect the value increments of land that are not due to landowner actions, but due to the population growth of the city and the improvement of infrastructure by public expenditure (Nicholson 1998, Nechyba 1988). In comparison, a tax on land improvements is not as desirable, since it depresses investment and development. Therefore, economists favor the split-rate property tax, and argue that a switch from a single-rate property tax to a split-rate property tax would increase land use efficiency, minimize excess burden, stimulate economic development, preserve environment, reduce urban sprawl, and improve quality of life (Dye & England 2009, Cohen & Coughlin 2005). In the split-rate tax system, different tax rates are set for land and improvements and often, that for land is higher than improvements. Given the theoretical advantages of land tax over a general property tax, many local jurisdictions (such as two counties in Hawaii and sixteen Pennsylvania municipalities) apply split-rate property tax in order to improve efficiency and facilitate development (Kwak et al. 2009).
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Currently, one of the greatest concerns of the split-rate property tax system lies in the property assessment. Without observed land value, land is typically assessed as a certain percentage of the total property value (such as 20%) regardless the location and land use intensity, and this leads to inaccurate land valuation. This dissertation finds that the share of land cost over the total housing property in the city of Beijing can be high as one-third at the central locations and drop to only 3% at 30 kilometers away from the city center. The findings of this dissertation can improve the accuracy of land value assessments and improve the efficiency of the split-rate property tax system, by adopting variant land value shares depending on locations instead of the fixed share of land value that is used currently in many local municipalities. Certainly, empirical and/or simulation studies are needed for specific cities to obtain more accurate and fitting parameters. The third implication is associated with zoning ordinances and planning regulations on land use and land development. Given a certain level of technology, efficient land development requires capital-land substitution in housing services production. Regulative restrictions on building height and density not only affect housing output, but more important, they restrict capital-land substitution and thus affect the overall land value, which in turn influences the social welfare. The simulated results based on the Beijing data illustrate that a 1% change in the elasticity of capital-land substitution leads to 14-18% changes in the total land value and 1519% changes in the total housing output. These numbers suggest remarkable opportunity cost and social welfare impacts that may be caused by planning regulations on land use and development intensity. Therefore, careful examination on
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the potential impacts is indeed needed before imposing any restriction on land development for environment justice and land use externalities.
7.2
Recommendation for Future Studies
One direction to extend this dissertation is to build longer period data for
housing and land development data to document changes in urban spatial structure and capital-land substitution over time. Empirical studies can also be improved by collecting more detailed data including housing units’ characteristics and neighborhood features to better control the estimation of spatial variant housing prices. Also, this dissertation can be extended to study locational differences of the marginal effects brought by policies and planning regulations. As demonstrated in this dissertation, numerical simulations suggest that the impacts of changes in capitalland substitution differ considerably across locations, suggesting that constraints on land use will cause different opportunity costs and social welfare impacts at different places. Therefore, examination of the locational variant influences of the same policy or regulation will have practical significance for policy assessment. Third, a formal model can be developed as an extension of this dissertation to investigate the impacts of the expected growth of housing prices on land prices over the urban space. This will be helpful in understanding land market behaviors and developing land use policies and planning regulations. Finally, the research can be extended to introduce a VES housing services production function, in which the elasticity of capital-land substitution depends on the
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ratio of land and capital inputs and varies with location. Numerical simulations and empirical studies can be conducted to link the variant elasticity of capital-land substitution to urban land development and urban spatial structure.
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Appendices
Appendix I: Solutions of Impacts of Elasticity of Capital-Land Substitution
?S ??
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99
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102
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?1+? y ? z
z z z z z z {
?1+??? y i y z j i y J n N zy j z j z z p?? j z j z 1 H?1+?L LogB n F z zz j F z j z z j i J n N?1+??? z y p?? z z j LogB z z j z 1?? j z z j z z H?1+?L j + j z z j ?1+ 1 z j z z j z p?? z j 2 1 ?? j z n z j z j z z ? ? Log B F j z j ?N ? z J?1+J N z j z z j z z j 1 ?? z j z j z z z j p ? ? j z zz j z j z z j z z {z k { k z z j ?j + z z z z j z z 2 ?2 ?1+? z j z z J?1+ 1 N ? 1 z j z z ? z j z z ii J n N?1+??? y y ? z j z z j z z j z z j j z ?1+ 1 z p ? ? z j z z j z j z ?z z j z j z LogB1 ? ? + j ?F z z j z j z j z z j z zz j z 1?? j z jk z z z z z { z z k { ? k { z z z z ? z z ?1+? y z z H ?1 + ?L2 z z i 1 z z j z ii J n N?1+??? y y ? z z j z j z z z j z j z ?1+ 1 z j z z j z p ? ? j z z j z z j1 ? ? + j ? z jj z ?z H?1 + ?L j z z j z z z z z j z 1?? j z z z j z jk z z z j z { z z k { z z z z k { z z z z z z zz z z z z z z zz z z z z zz {{
i j j j j j j j j j j j j j j j j j j j j j j j j j 1 j j j? 2j 1 j I? 1 + M j j j ? j j j j j j j j j j j j j j j j j j j j j k
i j ?1+? i j j i j J n N ?? j j j j j j p?? j j j j j j 1 ? ? + j j j j j j j j 1 ? ? j j j j j kk k
y ?1+ 1 z z ? z z z z z {
1
?1+? y ?1+? z ? y z z z z z z z z z z z ? z z z z z z z z z z { { ?
i j j j j j j j j i J n N?1+??? y 1 1 j j j ji j z ?1+ j j p?? z j ? j z jj jj z j j 1?? j jj j { j j kk j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j j k
?1+? y ? z
z z z z z z {
i j j 1 j n ?1+??? y i j j z j j Jp? ?N z ?1+ 1 j z j z j ? LogBj j z j j z 1?? j j z j z j j k { ? I? 1 + 1 M j j 2 ? j ? j j j j j j j j j j k j j 1? ? + j jj j
F
+
?1+??? y i J n N z j z j p?? j H?1+?L LogB n F z z j F j p?? z z j LogB 1?? z H?1+?L j + j z j 1?? ?N ? z z j ?2 z j J?1+J n N z j z j p?? z j { k
J?1+ 1 N ?
2
?
1 i ?1+??? y j i J pn N jj z ?1+ 1 ?? z ? z z j 1 ?? jk { k
y ? z z z z ? z z z {
?1+?
y z z z z z z z z z z z z z z z 1 z z i ?1+? z j i Jpn ?? z N y ?1+ 1 z jj ?? z j z ? z j j z LogB1 ? ? + j z j j z z j 1 ?? z jk { { + k ?2
y yz z z z z z z z zz z z z z z z zz z z z z z z zz z z ?1+? z z z z z y ? z zz z z z z z z z z z ? F z zz z z z z z z z z z zz { z z z z zz z z z z z z zz z z z z z z zz z z z z z z z z zz z z z z z z zz z z z z z z zz z z z z z zz z {{
103
Appendix II:
Simulated Impacts of Capital-Land Substitution
(Selected parameter values)
p
n ? ? ?
?S ??
3.0702 8.5754 27.0033 7.56249 80.0829 5897.16 14.7907 1102.53 2.52334 × 109 6.03828 32.6895 227.374 11.9472 244.529 72215.5 21.273 3021.69 6.83001 × 1010 9.32596 88.2102 1194.21 16.7242 591.682 508607. 28.245 6834.28 7.70159 × 1011
?2S ?p??
0.00160289 0.00807346 0.0388654 0.00239554 0.0593352 9.80324 0.00357154 0.726286 5.73211 × 106 0.00210748 0.0246564 0.282051 0.00308436 0.160731 105.932 0.00452759 1.81863 1.27341 × 108 0.00265411 0.0604291 1.38486 0.00383249 0.367349 689.408 0.00556523 3.94992 1.26678 × 109
?r ??
8.16207 14.8503 30.7643 82.0227 325.38 6660.91 348.17 6446.27 1.66521 × 109 57.242 136.194 446.451 446.524 2141.31 112069. 1809.16 38950. 6.41848 × 1010 250.727 695.819 3248.49 1827.25 9635.46 993658. 7308.21 168606. 9.3813 × 1011
? 2r ?p??
0.0112323 0.0234257 0.0577676 0.0895852 0.405463 12.5581 0.362961 7.54881 4.18856 × 106 0.0632802 0.168884 0.673825 0.458471 2.38584 184.284 1.83043 41.9717 1.32485 × 108 0.260053 0.784029 4.4427 1.84397 10.2271 1502.26 7.33645 175.44 1.70829 × 109
?? ??
0.0297317 1 0.0776473 0.215826 0.059599 0.32032 3.01938 0.0728364 0.521065 14.2214 0.0116386 1 0.056923 0.304314 0.0193153 0.186194 3.13397 0.0226749 0.28267 11.4111 0.00450764 0.0380003 0.352157 0.00690516 0.112759 3.08228 0.0079473 0.165971 9.65307
?h ??
0.00407306 0.00756336 0.0130116 0.354941 2.38584 184.284 1.20111 41.9717 1.32485 × 108 0.00407306 0.00756336 0.0130116 0.354941 2.38584 184.284 1.20111 41.9717 1.32485 × 108 0.0194279 0.0494516 0.122496 1.4232 10.2271 1502.26 4.808 175.44 1.70829 × 109
1000 1 0.1 0.1 0.1 1000 1 0.1 0.1 0.5 1000 1 0.1 0.1 0.9 1000 1 0.1 0.5 0.1 1000 1 0.1 0.5 0.5 1000 1 0.1 0.5 0.9 1000 1 0.1 0.9 0.1 1000 1 0.1 0.9 0.5 1000 1 0.1 0.9 0.9 1000 1 0.5 0.1 0.1 1000 1 0.5 0.1 0.5 1000 1 0.5 0.1 0.9 1000 1 0.5 0.5 0.1 1000 1 0.5 0.5 0.5 1000 1 0.5 0.5 0.9 1000 1 0.5 0.9 0.1 1000 1 0.5 0.9 0.5 1000 1 0.5 0.9 0.9 1000 1 2 0.1 0.1 1000 1 2 0.1 0.5 1000 1 2 0.1 0.9 1000 1 2 0.5 0.1 1000 1 2 0.5 0.5 1000 1 2 0.5 0.9 1000 1 2 0.9 0.1 1000 1 2 0.9 0.5 1000 1 2 0.9 0.9
104
p
n ? ? ?
?S ??
7.58745 54.3388 528.367 14.2061 382.763 195371. 24.5793 4563.03 2.38207 × 1011 11.9488 163.003 3397.2 20.4967 1037.26 1.71458 × 106 33.7053 11551.2 3.30391 × 10 16.7265 396.454 15675. 27.308 2371.4 9.87896 × 10 43.4907 25207.4 2.54366 × 1013
6 12
?2S ?p??
0.000236694 0.00388134 0.0631233 0.000343962 0.0243658 27.4798 0.000502068 0.268363 4.15457 × 107 0.000307995 0.0107059 0.381827 0.000441408 0.0627822 222.702 0.000636975 0.656336 5.08062 × 10 0.000383686 0.0248785 1.69975 0.000544475 0.139629 1215.71 0.000779114 1.40748 3.59465 × 109
8
?r ??
121.193 313.857 1233.88 905.975 4583.62 341423. 3641.02 81554.7 2.55898 × 1011 642.429 1914.31 11049.3 4595.55 25231. 3.84798 × 106 18316.3 434479. 4.70361 × 10 2610.87 8371.75 64539.5 18451.3 105338. 2.69567 × 10 73377.1 1.78601 × 10
6 7 12
? 2r ?p??
0.0128781 0.0368196 0.176225 0.0920181 0.496639 53.6794 0.36656 8.61178 4.94105 × 107 0.0654378 0.207731 1.44465 0.461604 2.62682 556.256 1.835 44.6031 8.00752 × 10 0.26276 0.876821 8.02144 1.84786 10.7709 3683.56 7.34206 181.122 7.04957 × 10
9 8
?? ??
0.00732189 1 0.0469867 0.331021 0.0116126 0.145392 3.11999 0.0134835 0.21689 10.4722 0.0023156 1 0.0280428 0.372798 0.0034248 0.0798291 3.00682 0.00390521 0.115947 8.71811 0.000812889 0.0170724 0.391165 0.00115706 0.0465157 2.85785 0.00130544 0.0666186 7.54982
?h ??
0.00476872 0.0115105 0.0265717 0.355702 2.52874 328.137 1.2019 43.557 3.43121 × 108 0.00476872 0.0115105 0.0265717 0.355702 2.52874 328.137 1.2019 43.557 3.43121 × 108 0.0201421 0.0600061 0.190667 1.42398 10.5514 2391.24 4.80882 178.872 3.58966 × 109
10000 1 0.1 0.1 0.1 10000 1 0.1 0.1 0.5 10000 1 0.1 0.1 0.9 10000 1 0.1 0.5 0.1 10000 1 0.1 0.5 0.5 10000 1 0.1 0.5 0.9 10000 1 0.1 0.9 0.1 10000 1 0.1 0.9 0.5 10000 1 0.1 0.9 0.9 10000 1 0.5 0.1 0.1 10000 1 0.5 0.1 0.5 10000 1 0.5 0.1 0.9 10000 1 0.5 0.5 0.1 10000 1 0.5 0.5 0.5 10000 1 0.5 0.5 0.9 10000 1 0.5 0.9 0.1 10000 1 0.5 0.9 0.5 10000 1 0.5 0.9 0.9 10000 1 2 0.1 0.1 10000 1 2 0.1 0.5 10000 1 2 0.1 0.9 10000 1 2 0.5 0.1 10000 1 2 0.5 0.5 10000 1 2 0.5 0.9 10000 1 2 0.9 0.1 10000 1 2 0.9 0.5 10000 1 2 0.9 0.9
4.50591 × 1013
105
p
n ? ? ?
?S ??
10.4386 116.123 1904.38 18.328 759.87 876420. 30.5706 8630.52 1.48495 × 1012 15.6472 330.731 11462.6 25.7749 2001.07 6.92104 × 106 41.2952 21461.6 1.68843 × 1013 21.3223 782.583 50904.6 33.8065 4504.19 3.7259 × 10 52.761 46409.7 1.15054 × 10
14 7
?2S ?p??
0.0000945261 0.00259874 0.072533 0.000136026 0.0155356 38.8278 0.000196963 0.164904 7.89247 × 107 0.000122257 0.00697447 0.417058 0.000173824 0.0394679 286.844 0.000249145 0.400654 8.08228 × 108 0.000151579 0.0159449 1.80008 0.000213637 0.0870066 1474.73 0.000303897 0.855602 5.12785 × 10
9
?r ??
381.01 1094.05 5622.17 2749.6 14786.6 1.8226 × 106 10977. 256728. 1.94056 × 1012 1954.11 6188.55 45064.4 13831.8 78460.1 1.81564 × 107 55022.3 1.33371 × 106 2.86252 × 1013 7869.71 26184.5 247499. 55413.5 322291. 1.17601 × 10 220226. 5.42379 × 10 2.39564 × 10
6 14 8
?2r ?p??
0.0130483 0.040339 0.250885 0.0922644 0.518215 89.9672 0.366918 8.84528 1.14184 × 108 0.0656587 0.217309 1.88423 0.46192 2.68204 835.914 1.83545 45.1723 1.51698 × 109 0.263034 0.898903 9.94679 1.84824 10.8932 5162.01 7.34262 182.34 1.18206 × 10
10
?? ??
0.00336718 0.0333144 0.362239 0.00507222 0.096899 3.0519 0.00581214 0.141716 9.22063 0.00101332 0.0189805 0.388456 0.00145228 0.052115 2.89118 0.0016417 0.0748222 7.77177 0.000346094 0.0112601 0.39706 0.000481744 0.0299319 2.72328 0.000540042 0.0425317 6.78348
1 1
?h ??
0.00509018 0.0165721 0.0634334 0.356054 2.68204 835.914 1.20227 45.1723 1.51698 × 109 0.00509018 0.0165721 0.0634334 0.356054 2.68204 835.914 1.20227 45.1723 1.51698 × 109 0.0204723 0.0726075 0.356777 1.42434 10.8932 5162.01 4.80919 182.34 1.18206 × 1010
30000 1 0.1 0.1 0.1 30000 1 0.1 0.1 0.5 30000 1 0.1 0.1 0.9 30000 1 0.1 0.5 0.1 30000 1 0.1 0.5 0.5 30000 1 0.1 0.5 0.9 30000 1 0.1 0.9 0.1 30000 1 0.1 0.9 0.5 30000 1 0.1 0.9 0.9 30000 1 0.5 0.1 0.1 30000 1 0.5 0.1 0.5 30000 1 0.5 0.1 0.9 30000 1 0.5 0.5 0.1 30000 1 0.5 0.5 0.5 30000 1 0.5 0.5 0.9 30000 1 0.5 0.9 0.1 30000 1 0.5 0.9 0.5 30000 1 0.5 0.9 0.9 30000 1 2 0.1 0.1 30000 1 2 0.1 0.5 30000 1 2 0.1 0.9 30000 1 2 0.5 0.1 30000 1 2 0.5 0.5 30000 1 2 0.5 0.9 30000 1 2 0.9 0.1 30000 1 2 0.9 0.5 30000 1 2 0.9 0.9
106
Appendix III:
Estimation of CES Housing Production Function
Supposing it is already known that ? = 0.5 , the other two parameters ? and
? of the CES housing production function can be estimated by the following
approaches. The first approach is to substitute ? = 0.5 in the production function by (19) and it can be written:
h ?1 = ? ?1?S ?1 + ? ?1 (1 ? ? )
(66)
where h is the housing output per unit of land and S is the capital intensity per unit of land. Thus ? and ? can be estimated by the following linear function:
h ?1 = b1S ?1 + b2 + ?
(67)
where b1 = ? ?1? , b2 = ? ?1 (1 ? ? ) , and ? is the disturbance term. h is measured by the floor space in square meters; S is the capital density, estimated by
S = ( ph * 0.7 ? r ) / n where n is assumed to be unity and 0.7 comes from the
assumption of the 30% average profit ratio of sales. Once b1 and b2 are estimated, ? and ? can be easily to be calculated. Table III-1 reports the estimated results and the estimated ? and ? are respectively 0.000315719 and 0.999957485. Table III-1
h ?1
Obs=254, R-sq=0.573 b1 b2 Coef. 3167.237 0.1346622 t 18.39 10.22 Sig. **** ****
delta 0.999957485 gama 0.000315719 ****99.9%, ***99%, **95%, * 90%
107
The second approach is to substitute ? = 0.5 in (57) or (58) and apply the non-linear least square method, where ? and ? can be estimated by treating h as the dependent variable and p as the independent variable. Table III-2 reports the estimated results and the estimated ? and ? are 0.0016509 and 0.9997479, 0.0009533 and 0.999854, respectively. Table III-2
h Obs=254, R-sq=0.7456 Coef. t Sig. gama 0.0016509 1.42 delta 0.9997479 4631.85 **** ****99.9%, ***99%, **95%, * 90% ln(h) Obs=254, R-sq=0.8513 Coef. t Sig. 0.0009533 3.29 **** 0.999854 16649.77 ****
Based on the above estimation, ? and ? should fall into the intervals of 0.99975-0.99996 and 0.000316-0.000953, respectively.
108
Appendix VI:
Sigma:
Estimation of Two Sub-Periods
1999-2001 obs=151, R-sq=0.7265 Dependent=ln(S) coef. t ln(r) 0.7022315 17.49 type_2 0.0428595 0.42 type_3 0.008564 0.11 type_4 -0.2547021 -1.52 type_5 -0.1526961 -1.18 type_6 -0.1404384 -0.78 type_7 0.0267254 0.18 DIFF 0.0137849 0.54 CONST 4.402439 14.74 ****99.9%, ***99%, **95%, * 90%
OLS: 0.70?0.62
sig. ****
****
2002-2003 obs=254, R-sq=0.6877 coef. t 0.6178752 13.34 0.0970794 1.02 0.0141701 0.12 (dropped) 0.1513824 0.36 -0.4004511 -1.63 (dropped) 0 0.1116875 2.7 5.092465 14.73
sig. ****
** ****
1999-2001 First stage regression obs=151, R-sq = 0.3912, F(11,139)=8.12 Dependent: ln (r) Coef. t sig. LA -0.0000445 -2.74 ** LA_square 1.97E-10 0.58 LY_2000 0.0613893 0.41 LY_2001 0.0387226 0.23 LY_2002 (dropped) LY_2003 (dropped) type_2 0.5002565 2.7 ** type_3 0.2794933 1.97 * type_4 -0.3259073 -1.07 type_5 0.5889165 2.47 ** type_6 -0.3797841 -1.17 type_7 -0.074253 -0.28 DIFF -0.009061 -0.19 CONST 7.761807 39.56 **** Instrumental variables (2SLS) regression obs=151, R-sq=0.7008 Dependent: ln(S) Coef. t sig. ln (r) 0.5556762 6.87 **** type_2 0.1054098 0.95 type_3 0.0720154 0.81 type_4 -0.3374698 -1.88 * type_5 -0.0225876 -0.15 type_6 -0.1892699 -1 type_7 0.0022114 0.01 DIFF 0.009637 0.36 CONST 5.467817 9.24 **** ****99.9%, ***99%, **95%, * 90%
IV: 0.56?0.44
2002-2003 First stage regression obs=103, R-sq = 0.3227, F(8,94)=5.6 Coef. t sig. -0.0000217 -4.82 **** 5.28E-11 4.59 **** (dropped) (dropped) -0.1150343 -0.63 (dropped) 0.308107 1.62 0.5283118 2.34 ** (dropped) 0.9566668 1.16 -0.2855733 -0.58 (dropped) -0.1078504 -1.18 7.685078 43.32 **** Instrumental variables (2SLS) regression obs=254, R-sq=0.6403 Coef. t sig. 0.4415493 3.97 **** 0.1596857 1.48 0.144792 1 (dropped) 0.3480703 0.76 -0.4563119 -1.72 * (dropped) 0.0781371 1.62 6.375571 7.84 ****
109
Distance gradients:
Land price gradient:
1999-2001 Dependent: ln(r ) obs=159, R-sq=0.6479 Coef. t sig. distance -0.095465 -4.11 **** district_2 -0.4776704 -1.02 district_3 -0.1774067 -0.52 district_4 -0.0023648 -0.01 district_5 -0.0365615 -0.12 district_6 0.055358 0.13 district_7 -1.490193 -2.86 *** LA -0.0000163 -3 **** LY_2000 -0.0930291 -0.68 LY_2001 -0.1248155 -0.81 LY_2002 (dropped) LY_2003 (dropped) CONST 8.78168 29.21 **** ****99.9%, ***99%, **95%, * 90%
OLS: -0.095?-0.067
2002-2003 obs=107, R-sq=0.6186 Coef. t sig. -0.0667709 -2.56 *** 0.1628664 0.28 -0.2120427 -0.35 -0.4940625 -1.05 -0.6162681 -1.25 -0.6907258 -1.13 -2.125974 -3.09 **** 5.92E-07 0.36 (dropped) (dropped) 0.1782791 1.16 (dropped) 8.737746 19.27 ****
Capital density gradient:
1999-2001 Dependent: ln(S ) obs=139, R-sq=0.3935 Coef. t sig. distance -0.0661747 -3.3 *** district_2 -0.607306 -1.5 district_3 0.0048936 0.02 district_4 -0.2657346 -1.08 district_5 -0.2230217 -0.88 district_6 -0.1732663 -0.46 district_7 -0.7576845 -1.51 0.2532012 1.6 type_2 0.2213518 1.82 * type_3 type_4 -0.4055043 -1.31 type_5 0.2127154 0.92 0.1092993 0.31 type_6 -0.0641873 -0.29 type_7 FUR 0.0996064 1.01 DIFF 0.0114207 0.29 CONST 10.40865 41.45 **** ****99.9%, ***99%, **95%, * 90%
OLS: -0.066?-0.059
2002-2003 obs=103, R-sq=0.5141 Coef. t sig. -0.0588481 -2.99 ** -0.0312926 -0.08 -0.2796232 -0.63 -0.5325892 -1.54 -0.5377934 -1.49 -0.748735 -1.67 -0.8589035 -1.66 * 0.2199796 1.66 * 0.3006749 1.99 ** (dropped) 0.3718363 0.67 -0.169886 -0.51 (dropped) 0.0757755 0.58 0.0970926 1.72 * 10.73471 32.47 ****
110
Housing price gradient:
1999-2001 Dependent: ln(p ) obs=139,R-sq=0.5937 Coef. t sig. distance -0.0350837 -4.6 **** district_2 -0.1205275 -0.79 district_3 -0.3313874 -2.83 *** district_4 -0.280393 -3.05 **** district_5 -0.184606 -1.95 * district_6 -0.303356 -2.14 *** district_7 -0.5480769 -2.91 *** type_2 0.0006714 0.01 type_3 -0.059781 -1.32 type_4 -0.0487966 -0.42 type_5 -0.2066416 -2.36 *** -0.0311322 -0.23 type_6 type_7 -0.0033267 -0.04 FUR -0.0042606 -0.11 FA 8.71E-07 1.53 HY_2000 -0.006265 -0.1 HY_2001 -0.0789065 -1.33 HY_2003 -0.0052702 -0.07 HY_2004 -0.0170736 -0.19 HY_2005 -0.1262459 -0.79 HY_2006 0.0686494 1.25 HY_2007 0.2157619 0.98 CONST 9.385247 85.25 **** ****99.9%, ***99%, **95%, * 90%
OLS: -0.035?-0.039
2002-2003 obs=103,R-sq=47660.5115 Coef. t sig. -0.0386754 -3.83 **** 0.1353335 0.65 -0.1954402 -0.87 -0.0955313 -0.54 0.0069479 0.04 -0.1573831 -0.69 0.00145 0.01 -0.0159167 -0.23 -0.0875994 -1.13 (dropped) -0.1974976 -0.69 0.0200667 0.12 (dropped) 0.0942277 1.38 1.40E-07 0.72 (dropped) (dropped) -0.216687 -1.71 * -0.1243462 -1.02 0.0120849 0.09 0.0638622 1.13 0.2450864 0.8 9.523182 45.29 ****
111
Lamda: OLS: 1.886?1.519 (according to above OLS estimates)
SUR 1999-2001 Dependent: ln (p ) obs=139, R-sq=0.5937 coef. t sig. -0.035033 -5 **** -0.120029 -0.86 -0.331745 -3.09 *** -0.280464 -3.33 **** -0.184784 -2.13 *** -0.303437 -2.33 *** -0.548974 -3.17 *** 0.0011134 0.02 -0.059166 -1.42 -0.049894 -0.47 -0.205077 -2.56 ** -0.032229 -0.26 -0.003806 -0.05 -0.004111 -0.12 8.97E-07 1.71 * -0.006195 -0.11 -0.079076 -1.45 -0.005365 -0.07 -0.01825 -0.22 -0.127976 -0.87 0.08542 1.21 0.2184223 1.08
SUR: 2.400?1.584
distance district_2 district_3 district_4 district_5 district_6 district_7 type_2 type_3 type_4 type_5 type_6 type_7 FUR FA HY_2000 HY_2001 HY_2003 HY_2004 HY_2005 HY_2006 HY_2007 LA LY_2000 LY_2001 LY_2002 LY_2003 CONST
ln (r ) obs=139, R-sq=0.5370 coef. t sig. -0.0839871 -4.27 **** -0.4213375 -1.09 0.0348868 0.11 -0.0601065 -0.25 -0.0346842 -0.14 0.1701211 0.46 -0.3674741 -0.77
9.383475
92.91 ****
-0.0000283 -0.0714568 -0.038906 (dropped) (dropped) 8.801487
-5.88 **** -0.57 -0.28
34.85 ****
SUR 2002-2003 ln (p ) ln (r ) obs=103, R-sq=0.4761 obs=103, R-sq=0.5158 coef. t sig. coef. t sig. -0.038257 -4.18 **** -0.060597 -2.62 *** 0.1403827 0.74 0.1666664 0.33 -0.195436 -0.95 -0.158523 -0.29 -0.098352 -0.62 -0.501811 -1.21 0.0066776 0.04 -0.664141 -1.53 -0.163482 -0.79 -0.811953 -1.51 -0.00042 0 -1.654584 -2.7 *** -0.008698 -0.14 -0.071213 -1.01 (dropped) -0.174516 -0.67 0.0303399 0.2 (dropped) 0.0921512 1.49 1.57E-07 0.89 (dropped) (dropped) -0.199691 -1.74 * -0.111332 -1 0.0288473 0.24 0.058776 0.98 0.2981786 1.07 -8.28E-07 -0.56 (dropped) (dropped) 8.638426 21.54 **** (dropped) 9.49856 49.78 **** 8.673336 21.76 ****
****99.9%, ***99%, **95%, * 90%
112
Dependent: ln(p ) LY_2000 LY_2001 LY_2002 LY_2003 LA LA_square type_2 type_3 type_4 type_5 type_6 type_7 FUR HY_2000 HY_2001 HY_2003 HY_2004 HY_2005 HY_2006 HY_2007 FA CONST
dependent: ln(r) ln (p ) LY_2000 LY_2001 LY_2002 LY_2003 LA LA_square CONST
1999-2001 first stage regression obs=139, R-sq=0.1559, F(18,120)=1.23 coef. P>t sig. 0.1059809 1.01 0.1297779 1.02 (dropped) (dropped) -5.46E-06 -0.62 -9.22E-11 -0.58 0.0089699 0.1 -0.0694731 -1.09 0.0712955 0.45 -0.1391959 -1.15 -0.2103704 -1.15 0.0006209 0.01 0.0122603 0.23 -0.020139 -0.18 -0.1603289 -1.2 -0.0610789 -0.39 -0.1647709 -0.99 -0.1216464 -0.52 (dropped) 0.0195644 0.06 3.17E-06 2.56 ** 8.731107 87.21 **** Instrumental variable (2SLS) regression obs=139, R-sq=0.1765, lamda>1 *** coef. t sig. 3.252312 4.44 **** -0.2689838 -1.29 -0.2278908 -1 (dropped) (dropped) -0.0000871 -3.85 **** 1.18E-09 2.39 ** -20.02213 -3.15 **
IV: 3.25?2.07
2002-2003 first stage regression obs=103, R_sq=0.1673, F(13,89)=1.38 Coef. t sig. (dropped) (dropped) 0.0615543 0.85 (dropped) -3.47E-06 -1.21 -9.20E-12 -1.63 -0.0736675 -0.86 -0.0870994 -0.89 (dropped) -0.1035485 -0.3 -0.1406371 -0.68 (dropped) 0.1480448 1.87 * (dropped) (dropped) -0.2219412 -1.35 -0.1604551 -1.04 -0.06413 -0.37 (dropped) 0.3192789 0.83 2.12E-06 2.17 ** 8.954684 52.39 **** Instrumental variable (2SLS) regression obs=103, R_sq=2193, lamda>1 * coef. t sig. 2.070356 3.35 *** (dropped) (dropped) -0.2373032 -1.37 (dropped) -0.0000271 -5.92 **** 6.48E-11 5.46 **** -10.51844 -1.92 **
****99.9%, ***99%, **95%, * 90%
113
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