Site Density Restrictions: Measurement and Empirical Analysis

Journal of Urban Economics 49, 404᎐423 Ž2001. doi:10.1006rjuec.2000.2200, available online at http:rrwww.idealibrary.com on

Site Density Restrictions: Measurement and Empirical Analysis1 Yuming Fu Department of Real Estate and Urban Land Economics, University of Wisconsin, 975 University Avenue, Madison, Wisconsin 53706 E-mail: [email protected]

and C. Tsuriel Somerville Faculty of Commerce, University of British Columbia, 2053 Main Mall, Vancouver, British Columbia V6T 1Z2, Canada E-mail: [email protected] Received September 29, 1999; revised September 14, 2000; published online January 30, 2001 Restrictions on the density at which development can occur are a central tool of land use regulation. Yet, they are understudied in the empirical literature. In this paper, we present a methodology to identify how much restrictions on the ratio of building space to lot area constrain developers. Our approach generates a measure of the distortion from the private optimum caused by restrictions as a function of land prices and the maximum allowed ratio of floor space to lot area. We use this methodology to examine how the set of incentives facing different levels of local government in Shanghai, China, affects density constraints on redevelopment sites in the city’s emerging real estate market. 䊚 2000 Academic Press

I. INTRODUCTION Virtually every zoning law includes a limitation on the structural density, the ratio of building space to lot area, to which a parcel of land can be developed. Yet, the determinants and impacts of these density restrictions are poorly 1 The authors thank Jan Brueckner, Richard Green, Dan McMillen, Stephen Malpezzi, Will Strange, Kerry Vandell, two anonymous referees, and especially Bob Helsley for helpful comments and advice. Oli Helm, Lei Zhang, Maud Catherine-Rivard, and Hossein Sepasi provided excellent research assistance. Special thanks are due to Mr. Wilson Wong, Mr. Qin Xiaofu, Mr. Tang Bei, and Professors Huang Tongcheng and Gu Mengdi of the Shanghai Jiaotong University Management School for invaluable help in arranging interviews with developers and officials in Hong Kong and Shanghai. We thank the Canadian International Development Agency ŽCIDA. and the Real Estate Foundation of British Columbia for financial support. All errors are the responsibility of the authors.

404 0094-1190r00 $35.00 Copyright 䊚 2000 by Academic Press All rights of reproduction in any form reserved.

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understood.2 Empirical studies of land use regulation tend to focus instead on externalities arising from conflicting land uses and on the impact of restrictions on the uses to which land may be put. This paper helps to bridge the gap in our knowledge of the economics of land use regulation. We construct a methodology for measuring the impact of density restrictions on land development. We then use this methodology to examine the determinants of the variation across sites in the impact of these density restrictions using data from the emerging land and real estate markets in Shanghai, China. Our analytical approach characterizes the intensity of restrictions on development density at a site in a form that is suitable for empirical analysis. The approach is based on the standard result that land values are maximized when the ratio of land to capital prices is equal to the rate of technical substitution ŽRTS.. Under certain conditions, the RTS can be expressed as a function of the observable floor-to-area ratio ŽFAR. alone. Government regulations that restrict density drive a wedge between the RTS and land:capital price ratio. This wedge describes the increase in profit that would accrue to the landowner from a relaxation of the density restrictions. If density restrictions vary with location, then along with the FAR, location attributes will explain the variation in land prices across urban sites. In contrast, when redevelopment is unrestricted location attributes other than the site-specific FAR have no effect on land prices. In the unconstrained case, these other variables should have no effect on land prices. This is not immediately obvious since we expect location specific variables to affect land prices. However, we show analytically that these effects should all be embodied in the FAR itself. The other site characteristic variables will only matter when they are determinants of the restrictions on density. This dichotomy forms the basis for our empirical analysis. We regress land prices per buildable square meter Žm2 . on FAR and a set of variables that describe the impetus for different levels of local government to tighten or loosen density restrictions. The paper is structured as follows. Section II surveys the relevant land use regulation literature. In Section III, we present the methodology for estimating the effects of site-specific density restrictions and for testing the determinants of density regulations. Section IV motivates the empirical application of the model by examining the tradeoffs faced by municipal and district governments in Shanghai. We describe the data and present the empirical specification and results in Section V. Section VI offers suggestions for future research.

2 See Helsley and Rosenthal w15x and Wheaton w30x for a discussion of the importance of these densities for the redevelopment of urban sites.

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II. THE EXISTING LITERATURE This paper is part of an extensive theoretical and empirical literature on local government regulation of land use.3 The theoretical zoning literature includes a number of papers that look at the effects of zoning regulations that restrict development density, measured by the capital-to-land ratio, on outcomes and welfare. Absent from this literature is a methodology for easily identifying the intensity of these regulations. The empirical literature tests for the effects of broad classes of zoning, growth controls, and impact fees on house prices and construction. Of the limited research that does examine development density, the focus is on large-lot zoning ŽWhite w31x., which may yield limited insights for density constraints on redevelopment in core urban locations. In the second half of this paper we apply the methodology developed here to explain the intensity of restrictions on development density in Shanghai as a function of government objectives. This application builds on the literature on the determinants of regulations. One branch of this research identifies exogenous factors that affect the application of different types of regulations ŽRolleston w25x, Hanushek and Quigley w14x, Dubin et al. w9x, and Brueckner w3x.. A second treats zoning as endogenous ŽWallace w29x, McMillen w19x, McMillen and McDonald w21x, Pogodzinski and Sass w23x, and Thorson w28x.. Like Wallace we compare the prevailing regulations with the objectives of the regulating government. Our work differs in that we examine site-specific density restrictions while Wallace looks at the choice of broad zoning categories. Pogodozinski and Sass include site-specific zoning regulations like building height and setback restrictions in their analysis. However, they focus on single-family homes. We would expect that these constraints are less important than maximum allowed density restrictions are for the urban redevelopment sites we study. The research we present here adds to this literature by broadening the set of tools available to evaluate the effects of land use regulations on urban redevelopment and analyze the determinants of such regulations. In particular we can examine the spatial variation in the site-specific regulatory intensity as opposed to just the choice among a small number of zoning categories. Our empirical analysis of competing interest in regulating land use by different levels of local government in Shanghai relates to the substantial literature on fiscal federalism. This includes growing work on public finance in China. This is in part because of the recent reforms in local public finance described in Wong w32x and Cullen and Fu w6x. As well, Qian and Stiglitz w24x analyze the allocation of power and property rights between central and local governments in China, and Li et al. w17x and Gordon and Li w13x analyze how 3 See Pogodzinski and Sass w22x for a review of the theoretical zoning literature and Fischel w11x for a discussion of empirical work.

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competition among local governments fosters the growth of private enterprises. Other works that bear on our application are Helsley and Strange w16x and Brueckner w3x on strategic interactions between neighboring governments with respect to land use regulations. Our work differs from these two papers in that we examine vertical rather than horizontal interactions. III. MEASURING THE SITE-SPECIFIC DENSITY RESTRICTIONS Consider the development of a site with L square meters of land. Assuming constant returns to scale in the production of real estate space, we can express development density Žthe floor-to-area ratio or FAR. h, as a function of the ratio of capital K to lot size L, h ' QrL s F Ž KrL, 1 . ' f Ž S . ,

Ž 1.

where Q is real estate space Žfloor area., S s KrL is structural density, and the production function F Žy. is concave and homogeneous of degree one. Inverting h s f Ž S . gives S s fy1 Ž h., which in turn implies that the cost function for development density is c Ž h . s iS s ify1 Ž h . ,

Ž 2.

where i is the price of capital. Taking derivatives, the marginal cost of development density is cX Ž h . s irf X Ž S . s irFK ) 0.

Ž 3.

Since F Žy. is concave, the marginal cost of development is increasing in h: cY Ž h . s Ž yirf ⬘ Ž S .

2

. f Y Ž S . ) 0.

Ž 4.

Letting pŽ X . represent the market price of floor space, which varies with location characteristics X and is assumed to be independent of density, and v represent the price of land, the profit of a developer per unit of land is

␲ s p Ž X . h y c Ž h . y v.

Ž 5.

Under perfect competition, free-entry drives profits to zero Ž␲ s 0., which implies v s pŽ X . h y c Ž h. .

Ž 6.

Thus, land price v depends on the price of space pŽ X ., density h, and construction costs cŽ h.. The marginal value of development density is v h s p Ž X . y cX Ž h . .

Ž 7.

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Absent regulatory constraints on density, profit maximizing developers will select density to maximize land value. There is a unique profit maximizing value for density hU that satisfies the FOC, where v hŽ X, hU . s 0. If government land use regulations are binding, then the marginal land value of development density is positive: v h ) 0. Thus, a site-specific measure of v h describes the extent to which density restrictions constrain development at any given site. To implement this methodology empirically, we need more structure. By Euler’s theorem the homogeneity of F Žy. implies h s FK ⭈ S q FL . Substituting S s cŽ h.ri from the definition of cŽ h. in Ž2. and rearranging gives h s FK ⭈ c Ž h . ri q FL .

Ž 8.

Dividing through Ž8., by FK , substituting cX Ž h. s irFK from Ž3., and rearranging we obtain the rate of technical substitution as a function of h: RTS s FLrFK s Ž 1ri . h ⭈ cX Ž h . y c Ž h . .

Ž 9.

Finally, substituting for cŽ h. and cX Ž h. from Ž6. and Ž7. and rearranging gives v h s Ž 1rh . Ž v y i ⭈ RTS . .4

Ž 10 .

Since RTS depends only on h, we require only two variables, the land price v and the development density h to measure the marginal value of density v h . In Section V we use this methodology to examine the extent to which density restrictions bind development at individual sites within a city. To apply Ž10. as an empirical tool we normalize i s 1 and assume a Cobb᎐Douglas production for floor space, F Ž K, L. s ␣ K ␭L1y ␭. The resulting rate of technical substitution is RTS s Ž 1 y ␭ . r␭ Ž hr␣ .

1r ␭

.

Ž 11 .

To generate a suitable linear regression specification, rewrite Eq. Ž10. as z s Ž RTSrh . r Ž 1 y v hrz . ,

Ž 12 .

where z s vrh is land price per meter of buildable space.5 Taking the 4 When h maximizes v, i.e., h s hU , then vh s 0 and Ž10. simplifies to the standard efficient market condition that the ratio of input prices must equal the RTS. This condition is distorted when land use regulations constrain h below the developer’s optimum, yielding a positive vh and an inequality v ) RTS. 5 This measure is common in Asia and Europe. It has a clear interpretation for developers in markets where development sites or ground leases are transferred with the restriction on total buildable floor space. It together with per square meter construction costs gives total costs per square foot meter of building space.

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logarithm of each side gives ln Ž z . s ln Ž RTSrh . y ln Ž 1 y v hrz . .

Ž 13 .

We then substitute the Cobb᎐Douglas RTS from Ž11. and assume that v hrz is sufficiently small that lnŽ1 y v hrz . f yvhrz.6 This yields a simplified expression for Ž13., ln Ž z . s a q b ⭈ ln Ž h . q v hrz ,

Ž 14 .

where a ' lnwŽ1 y ␭.rŽ ␭␣ 1r ␭ .x and b ' Ž1 y ␭.r␭. In the empirical section we want to identify how the constraint varies across sites as a function of location attributes that enter the welfare functions of the municipal and district governments. To do so we specify the constraint on density v hrz as a linear function of location attributes X plus a random error ␧ , so that v hrz s X ⭈ ␥ q ␧ , where ␥ is a vector of coefficients. This gives the reduced form estimating equation, which we implement with GLS: ln Ž z . s a q b ⭈ ln Ž h . q X ⭈ ␥ q ␧ .

Ž 15 .

Given a correct specification of the RTS function, the estimated coefficients in ␥ identify the determinants of the spatial variation in the intensity of the constraints on development density. A positive ␥ indicates that v hrz and thus the density constraint increases in X. IV. LOCAL GOVERNMENT AND DENSITY REGULATIONS IN SHANGHAI We apply the methodology outlined above to examine how the competing interests in land use control between the municipal and district governments in Shanghai affect the spatial pattern of density restrictions. Land is owned by the state in Chinese cities, but at the beginning of the 1990s the government introduced reforms that permitted ground leases Žlasting 75 years for residential uses and 50 years for nonresidential uses. for private development and allowed government owned enterprises to develop sites and lease space at locations they occupied and held the right to use the land.7 These leases not only attracted private Žlargely overseas. capital to develop much needed housing and commercial properties but also provided city governments with valuable revenue to 6 vhrz is the elasticity of land value v with respect to FAR h, which equals zero when h is land-value maximizing but is positive when the density is restricted. According to land prices shown in Table 1, the denominator is sufficiently large that this assumption is likely to hold. 7 For a review of this process we see the World Bank w33x examination of urban and land management in China under the central planning system and the issues in China’s transition to a market economy, Dowall’s description w7x of the establishment of the land market, and Clarke and Howson’s summary w4x of the legal developments in China that have enabled the development of urban real estate markets.

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finance massive infrastructure projects and pay for the resettlement of residents and factories displaced by redevelopment.8 In Shanghai, fiscal responsibilities and administrative authorities are divided between the municipal government and the district governments under its jurisdiction.9 The districts run enterprises, retain tax revenue, and support public housing and a large array of other public services. In 1992, the district governments were given the authority to offer sites for development and negotiate ground lease contracts with private developers. These land use contracts specify the price, allowed land uses, and the maximum allowed floor-to-area ratio. The districts retain 85% of the ground lease revenue to fund their responsibilities for resettling the residents and factories displaced from the site by redevelopment and the municipal government receives the remainder to fund municipal infrastructure projects.10 Our analysis rests on two implicit assumptions. The first is that government officials act in the interests of their respective jurisdictions. Although officials do not have to explicitly answer to residents or business organizations in the jurisdiction, the career prospects of officials depend on both their economic achievements and the absence of unrest in their jurisdiction. The second is that the balance of interests between the different levels of government affects the determination of the maximum allowed density. Although the municipal government approves density levels, districts can influence the process. First, they can exert political pressure for projects with strong local support. They can also compensate the municipal government with side or in-kind payments, such as taking over the municipal government’s role for infrastructure projects. In interviews, Shanghai’s officials indicated that the municipal government is sensitive to the interests of the district governments. The municipal government’s Real Estate Administration and Urban Planning Bureau oversees the pricing of the ground leases offered by the districts and the overall supply of redevelopment sites and land use densities across the city. Following Sun w27x, we expect them to set density regulations that reflect the interaction of the interests and relative bargaining powers of the local district and the municipal governments. These interests should be a function of the net effect of redevelopment at each site on the objectives of each level of 8 Fu et al. w12x examines the background and the pattern of redevelopment in Shanghai during the early 1990s. 9 Responsibilities and powers were devolved to the municipal government and then to the districts during the economic reform. As the central government’s share of Shanghai’s GDP dropped to below 10% in early 1990s, from 60% prior to 1980, individual districts’ fiscal autonomy increased significantly. The budget controlled by individual districts rose, from a fraction of less than 7% of the total budget of the city before 1980, to 53.7% by 1995 ŽShanghai Economic Yearbook, various years.. 10 Liang w18x discusses the fiscal incentives for local governments to promote real estate development within their jurisdiction.

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government, which will depend on both project and local area characteristics. Our empirical analysis identifies these factors and tests whether density restrictions relate to the different government objectives. The net benefit of redevelopment is not divided equally between different levels of government. Both the district and the municipal government have an incentive to loosen restrictions on development densities in order to maximize land lease revenues, which they share.11 The districts experience other positive fiscal benefits from development, such as business tax and real estate revenue, which they retain, as well as any local agglomeration effects of increased development. However, local district governments must finance the resettlement of residents and firms displaced by redevelopment Žsee Dowall w8x.. District governments use retained land lease revenue either to build or purchase housing to accommodate the relocating households. The municipal government experiences a relatively larger share of the negative externalities of increased density. They finance the expansion of public infrastructure needed to ameliorate development-spawned congestion. Their interests are citywide, so they internalize any externalities that may cross over district boundaries, such as the negative effects of a given development on the demand curve faced by other developments, and any wasteful relocation of firms from one district to another. Land lease sales can help both levels meet national policy objectives of eliminating inefficient land uses, which are a result of years of government allocation of resources, and upgrading the quality of the housing stock. V. EMPIRICAL ANALYSIS A. Data Our data consist of 204 land leases granted by the 10 central urban districts in Shanghai to foreign developers for the purpose of redevelopment in 1992᎐1993.12 For each site, we know the location, transaction price, site size, and the permitted use and maximum allowed density ŽFAR. of structures to be redeveloped at the site.13 In all cases these sites are sold for redevelopment. 11 District governments also profit through their wholly owned subsidiary construction companies. These companies frequently joint venture with developers, providing the construction services for the development. These revenues rise with density. The contracts are particularly valuable because the profits from subsidiaries do not have to be shared with the municipal government. 12 These data ŽShanghai Land Administration w26x. exclude leases to local developers, redevelopment by holders of the existing land use rights, and large tracts of land in the Pudong new district east of the CBD, the planned location of the city’s new financial center. 13 The land lease prices are negotiated. Lack of negotiating skill or rent-seeking behavior by government officials could result in land lease prices that are biased measures of market values. Our goal is to examine the variation in land prices across locations. As long as any distortion in the land lease prices is orthogonal to our variables of interest, our estimates will not be biased. To test for ‘‘spatial bias,’’ we compare the price gradient for land lease prices with that of apartments prices for units traded on the free market. We cannot reject the hypothesis that both of these prices are distributed across space in a consistent manner.

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FU AND SOMERVILLE TABLE 1 Descriptive Statistics: District Mean Values of Transaction Specific Variables Mean floor-area-ratio ŽFAR.

Districts

No. of obs.

Pct. residen. only

Mixed and commercial

Huang Pu Hong Kou Nan Shi Lu Wan Zha Bei Jing An Yang Pu Xu Hui Pu Tuo Chang Ning Total

13 19 5 10 10 22 11 46 17 51 204

0.0 31.6 0.0 0.0 0.0 18.2 0.0 43.5 47.1 78.4 38.2

8.00 6.06 7.46 4.84 6.26 4.87 5.27 4.65 5.46 5.86 5.65

Residential only

4.33

3.14 2.72 1.43 2.52 2.63

Mean distance to CBD Žkm.

Mean land price Ž$USrm2.

1.40 2.52 2.97 3.31 3.46 4.53 5.69 7.06 8.76 9.43 6.20

5,433 2,290 2,720 2,290 2,773 2,842 1,755 1,640 1,436 1,160 2,055

Note. Mixed is defined as buildings combining commercial, office, and residential uses.

Table 1 provides the total and by district summary statistics for these data. The districts are sorted by distance to Shanghai’s historic CBD, the mean straight-line distance from their land-lease sites to the intersection of Nanjing East Road and the Bund. Over half of the sites will be redeveloped as ‘‘multipurpose’’ buildings, which include both residential and nonresidential space in the same structure. Most of the remaining sites will be redeveloped as high-rise residential buildings. Site are not evenly distributed across Shanghai’s districts. Figure 1 shows the distribution of land lease sites. There is a concentration of sites in the Chang Ning district near the Hongqiao airport and along the Nanjing West Road and Huaihai West Road commercial corridors. The largest number of land leases is in the Chang Ning district, but 78.4% of these are for residential developments, versus 38.2% citywide. In general, the all-residential projects are located in more distant districts than the all-commercial and mixed projects. As well, they are less dense, with less than half the FAR of multipurpose and commercial developments. To describe local conditions we have land use and population statistics for 48 sub-districts within Shanghai’s 10 urban districts. Unfortunately, the geographic coverage of this data limits us to fewer than 160 projects. Table 2 provides the district level values of the sub-district aggregates. We observe large differences in land use patterns and population density across districts. The CBD district of Huang Pu has a much higher share of commercial and government land uses. In

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FIG. 1. Residential and mixed-usernonresidential developments.

413

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FU AND SOMERVILLE TABLE 2 Descriptive Statistics: Characteristics of Shanghai Urban DistrictsᎏSubdistrict Data

Districts

Population district area Žpoprsq. km.

Populationrresid. land use area Žpoprsq. km.

Commercial and govt. offices share of district land area

Industrial share of district land area

Huang Pu Hong Kou Nan Shi Lu Wan Zha Bei Jing An Yang Pu Xu Hui Pu Tuo Chang Ning Total

70,286 60,890 67,204 55,881 23,647 58,010 18,180 35,193 30,877 41,925 33,920

210,441 159,983 177,817 170,273 174,855 130,028 76,837 110,267 111,543 111,278 124,269

18.82% 5.19% 5.84% 5.42% 2.44% 9.01% 2.07% 6.90% 3.33% 3.51% 4.11%

3.36% 20.67% 14.17% 24.39% 26.12% 16.18% 28.44% 12.81% 27.39% 22.22% 23.63%

Note. Values are the mean of sub-district averages.

general, industrial uses are located away from the CBD though there is still a large share of land dedicated to these uses in the urban core. Older residential stock is distributed throughout the city, but the older stock’s share of sub-district land use concentration is nearly twice as high in the five most central districts. The reverse holds for newer housing stock, with nearly four times the land use share in the five most distant districts. B. Empirical Specification The goal of our empirical application is to identify whether the constraint on density varies across locations in a manner indicative of a balance between the competing interests of the different levels of local government in Shanghai. To do so we use a set of location specific measures that we believe capture the relative interests of the two levels of government in constraining or relaxing development densities at individual land lease sites. These comprise the location attribute variables X in the reduced form regression equation Ž15.. At locations where congestion is more likely to be a problem, we expect that development densities are more restricted, reflecting the interests of the municipal government. Conversely, at those sites where redevelopment will result in greater resettlements costs, we expect local district governments to be more successful in getting the municipal government to relax restrictions on development densities. A third issue is the desire for redevelopment to achieve national land use and housing policy objectives. In this case what matters is type and location of an existing land use. At locations where existing land use is ‘‘inefficient’’ or the existing stock is of poor quality, we expect fewer

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restrictions on redevelopment density, as both the district and the municipal government would favor a more favorable investment environment to make redevelopment viable. We measure the likelihood that congestion is a concern at a site by the presence of congestion-causing land uses and the concentration of redevelopment projects. For the former we use the share of a sub-district’s land in commercial and government office use, as congestion should be rising in this share. If greater potential congestion problems at a location result in tighter constraints on density, then the coefficient on commercialrgovernment land share will be positive. We also expect more potential congestion problems where redevelopment activity is greatest. To measure this concentration we determine the radius of a circle around each land lease site that contains the closest 20% of the total sample. As the radius increases in size, redevelopment is less concentrated and congestion at the site should be lower, which should make the municipal government more lenient on allowed densities.14 Thus, the expected coefficient on this radius variable should be negative. Resettlement costs will increase with the number of households that must be resettled. To describe these expected costs we use the sub-district’s density of population on residential land. District governments may be more successful in lobbying for a relaxation of constraints where resettlement costs are higher, in order to obtain sufficient land lease revenues to pay for resettlement. If so, the estimated coefficient on the population density variable will be negative. The World Bank w33x and others argue that one legacy of the state allocation of land use is excessive factory and warehouse land uses in the urban core.15 Redevelopment of these sites is consistent with central government policy objectives. We thus expect constraints on development density to be relaxed at locations where the existing use is inefficient to encourage their conversion to more appropriate land uses. This is a function of both the extent of industrial and warehouse users on a site and their location. It is industrial land use close to the CBD that is an economically inefficient legacy of central planning, while in more distant locations it is appropriate. To test for this effect we include both the industrialrwarehouse land use share of a sub-district’s land area, the distance to the CBD from individual sites, and the interaction term between them. We do not know the existing use on a site, but the probability that it is industrial or a warehouse is rising in these land uses’ share of sub-district land. We expect that near the CBD, increases in industrial land use share relax density constraints, but this need not hold at greater distances. This should 14 We do not observe redevelopment by current holders of land use rights and local developers. If they have the same distribution across space as land lease sites sold to foreign developers, then excluding them is not a problem. 15 According the the World Bank w33x, industrial users in Chinese cities account for 20 to 30% of urban land as opposed to 6% in Hong Kong and 9% in Seoul. In Shanghai’s 10 core urban districts, industrial users account for 26.7% of land use.

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show up as a negative estimated coefficient on industrial land share and a positive one on the interaction term so that at a certain distance from the CBD, greater industrial and warehouse land use shares no longer result in a relaxation of density restrictions for new development. Shanghai’s older housing stock is of low quality and fails to meet the quality and quantity standards laid out by the central government in Beijing. As above, we would expect a relaxation of density restrictions at sites with older stock to encourage its conversion. We use the older housing stock’s share of sub-district land area to measure the importance of this factor at a location. Increases in this variable should result in less constrained development, so the expected coefficient is negative. C. Regression Results Our empirical analysis estimates Eq. Ž15. using the log of the price of land per building square meter, lnŽ z ., as the dependent variable. The interpretation we place on the results is that, conditional on the correct specification of the RTS, the other variables we include in the regressions constitute elements of the vector X, where X ⭈ ␥ is the linear reduced form estimate of the constraint on density Ž v hrz .. If the estimated coefficients on these variables, the vector ␥ , are positive, then the constraint rises with them. We present these results in Table 3. Although our left hand side variable is a land price and we have location characteristics on the right hand side, this is not a land price equation. These terms only affect the land price if v h ) 0. From Ž10. when v h s 0 the effects of the location characteristics on land price are entirely embodied in the RTS, which we describe by the FAR h. Overall, our results are consistent with the hypotheses regarding government incentives and density restrictions laid out above. In regression Ž1., the estimated coefficient on commercial and government office share of sub-district land use is positive and statistically different from zero. Thus, the constraint rises at locations where congestion is likely to be problematic because when controlling for the maximum allowed FAR, increases in the commercial and government office share of sub-district land use raise the price of land per buildable m2 . The latter only occurs if v h , the measure of the constraint on density, is rising in the land use share. The municipal government loosens density regressions to encourage the conversion of locations that currently have inefficient land uses. For sites within 5.7 kilometers of the CBD, which includes all sites in the districts of Huang Pu, Hong Kou, Nanshi, Lu Wan, and Zha Bei, higher shares of their sub-district’s land in industrial and warehouse use result in reductions in the constraints on density. At these locations, the positive estimated coefficient on the interaction term, which reflects greater constraints, is not large enough to offset the negative estimated coefficient on industrial land use share. For sites further away, which includes all development sites in Chang Ning, the positive

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SITE DENSITY RESTRICTIONS TABLE 3 Variation in Marginal Price of Density: Dependent Variable is logŽLand Price per Buildable m2 . s logŽ z . Dependent variable Location attributes Distance to bund ŽCBD. Commercial and govt. office share of land use Factory and warehouse share of land use InteractionᎏDistance to CBDU factory and warehouse share Distance to closest 20% of all land lease sites Population density on residential land Older residential buildings share of land use Newer residential buildings share of land use RTS parameter lnŽFAR. Constant Number of observations R-squared

Regr. Ž1.

Regr. Ž2.

y0.0731 y0.1084 Ž0.0367. Ž0.0261. 1.504 Ž0.581. y2.2903 y2.7719 Ž0.8961. Ž0.6913. 0.3998 0.5116 Ž0.1652. Ž0.1343. y0.0836 Ž0.0133. y0.0149 y0.0162 Ž0.0051. Ž0.0040.

0.2054 Ž0.0826. 6.2618 Ž0.36520. 148 0.314

0.2197 Ž0.0728. 6.7760 Ž0.2390. 148 0.363

Regr. Ž3.

Regr. Ž4.

Regr. Ž5.

y0.0849 y0.0497 Ž0.0349. Ž0.0293. 0.964 1.146 Ž0.586. Ž0.431. y2.2439 y2.3189 Ž0.8393. Ž0.8089. 0.4325 0.3871 Ž0.1571. Ž0.1589. y0.0755 Ž0.0141. y0.0135 Ž0.0040. y0.2490 Ž0.3048. 0.2968 Ž0.2878.

y0.0771 Ž0.0222.

0.2247 Ž0.0753. 6.4983 Ž0.3365. 148 0.375

0.2056 Ž0.0843. 5.996 Ž0.267. 158 0.300

y2.4950 Ž0.6886. 0.4360 Ž0.1413. y0.0873 Ž0.0173.

y0.5308 Ž0.3298. y0.1344 Ž0.2998. 0.2108 Ž0.0740. 6.5905 Ž0.2352. 158 0.376

Note. Standard errors are in parentheses. All regressions use a White correction for heteroscedasticity. All location attributes except ‘‘Distance to the bund’’ are sub-district aggregates.

interaction term dominates. These results support the hypothesis that constraints are relaxed to encourage the redevelopment of locations with inefficient land uses. The discussion in the previous section suggests that at sites where districts face higher costs of resettling residents displaced by redevelopment, municipal officials are more willing to lower constraints on development densities to increase land lease revenues available to the districts to pay for resettlement. When controlling for the allowed FAR, increases in the population density on residential land lower land prices per buildable m2 . The implication is that development density is less constrained where resettlement costs are likely to be higher. In regressions Ž2. ᎐ Ž5. we test the robustness of these results. The differences across regression specifications are that we allow the degree of concentration of redevelopment sites around a given location to measure congestion effects and

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we examine whether the condition of the existing stock Žshare of land use occupied by old vs newer residential structures. affects decisions on the maximum allowed density. In regression Ž2. we replace the share of land in commercial and government office use with a measure of the concentration of redevelopment. The estimated coefficient is negative. As redevelopment is less concentrated and more spread out, which occurs when the radius of a circle around a given site that encompasses the closest 20% of other redevelopment sites is larger, density at the site is less constrained. The estimated coefficient values indicate that the constraint on density is more sensitive to changes in the concentration measure than commercial and government office land share variable. We cannot directly estimate constraint elasticities because we do not have a cost of capital.16 However, the ratio of two constraint elasticities will be the same as the ratio of two land price elasticities. Thus, comparing relative elasticities or relative effects on land prices of two variables will tell us to which of the two variables the density constraint is most sensitive. A one standard deviation increase in the measure of the concentration of redevelopment has a 68% greater effect on land prices, and thus on the intensity of the density constraint, than does a one standard deviation increase in the commercial and government office share of district land use. The former’s elasticity at the mean is 130% larger. In regression Ž3. we include both measures. Together their effects operate in the same way, though with smaller estimated coefficients. As well, the drop in the coefficient value is smaller for the concentration measure. Taken together these results confirm the hypothesis presented above that the municipal government is more aggressive in restricting densities at locations where congestion is likely to be a bigger problem. As explained above, in areas where the housing stock is older, we expect densities on redevelopment projects to be less constrained. Just as with industrial land use share, the share of a sub-district’s land occupied by older housing stock describes the probability that the site under study was occupied by older low quality housing prior to redevelopment. In regressions Ž4. and Ž5. we replicate regressions Ž1. and Ž2., but replace population density with the share of land used for older and newer residential structures. Because of the correlation between these values and population densityᎏolder units are much smaller yielding higher population densitiesᎏwe cannot fully differentiate between the objective of replacing the older stock and higher resettlement costs by including all three variables in a regression. In both regressions the estimated coefficient on the share of land in a sub-district used for older housing is negative, though only in regression Ž5. is it statistically different

16 We normalized i s 1 in the model, but that is not appropriate for estimating the actual level of vh .

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from zero with 90% confidence. However, the coefficient on the older stock is consistently at least one standard error lower than coefficient on newer stock, which is never even close to being statistically different from zero. The older stock’s share of land use has a relatively small effect on the density constraints; its elasticity is less than 50% than that of population density, and the same applies to the relative elasticities. Our results depend on a correct specification of the RTS. We assume that the production function is Cobb᎐Douglas for convenience, but clearly other nonCES specifications are possible. Fu et al. w12x shows that Shanghai has approximately a monocentric form, in which case distance to the CBD will be correlated with the RTS. Consequently to control for possible specification bias, and to operate with the interaction term, we include the distance to the CBD as a right hand side variable in all regressions in Table 3.17 For robustness we tested additional approximations for RTS and alternative approaches to estimate v h .18 The general pattern of our results holds in all cases. We cannot rule out possible specification bias, but our results are robust across different specifications. The coefficient on distance also indicates that constraints are falling with distance. This is consistent with the perception that it is in Shanghai’s inner core that congestion is most problematic and where negative externalities from development are greatest. The results in Table 3 may suffer from simultaneity bias. Our determinants of the density constraints v hrz, the X vector, all reflect the historic growth path and construction decisions taken prior to 1992, so they should not be a function of the dependent variable lnŽ z .. However, the land price z and the allowed FAR h Žhence RTS. are jointly determined through land lease negotiations. The regression error ␧ in Eq. Ž15. represents the noise in density constraint v hrz rather than in land price z, so we do not expect it to be correlated with RTS. To ensure that our estimates are not biased due to potential simultaneity, in Table 4 we replicate the regressions in Table 3 instrumenting for lnŽFAR.. Our instruments are the log of the distance to the airport, the square of distance to the CBD, a dummy indicating whether the development is 100% residential, and a predicted value of the FAR at a site

17

In general, the restrictions on density tend to weaken with distance from the CBD, but the estimated coefficient is only statistically different from zero when it picks up a left out variable effect from commercial and government office land share in regressions Ž2. and Ž5.. 18 Using different production function functional forms we obtained similar regression results. We also took the partial derivative of z s vrh and rearranged it to get vh s z h h q vrh. Using an estimated sample mean value for z h we computed site specific values for vh . Regressing this measure vh directly on X also yielded qualitatively similar results.

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FU AND SOMERVILLE TABLE 4 Variation in Marginal Price of DensityᎏIV for Density ŽFAR.: Dependent Variable is logŽLand Price per Buildable m2 . s logŽ z . Dependent variable

Location attributes Distance from bund

Regr. Ž1.

Regr. Ž2.

y0.0926 y0.1236 Ž0.0386. Ž0.0271. Commercial and govt. office 1.367 Ž0.587. share of land use Factory and warehouse share y2.5104 y2.9309 Ž0.9217. Ž0.7181. of land use Interactionᎏdistance to CBDU 0.4501 0.5488 Ž0.1677. Ž0.1366. factory and warehouse share Distance to closest 20% of all y0.0776 Ž0.0144. land lease sites Subdistrict populationrland y0.0134 y0.0146 Ž0.0052. Ž0.0044. in residential use Older residential buildings share of land use Newer residential buildings share of land use RTS parameter IV for lnŽFAR. 0.0884 0.1098 Ž0.1021. Ž0.0877. Constant 6.508 9.963 Ž0.368. Ž0.239. Number of observations 148 148 R-squared 0.287 0.339

Regr. Ž3.

Regr. Ž4.

Regr. Ž5.

y0.1033 y0.0667 Ž0.0355. Ž0.0334. 0.8681 1.049 Ž0.5873. Ž0.440. y2.4650 y2.5014 Ž0.8655. Ž0.8307. 0.4798 0.4207 Ž0.1583. Ž0.1615. y0.0699 Ž0.0150. y0.0121 Ž0.0044. y0.3141 Ž0.3262. 0.1723 Ž0.3091.

y0.0931 Ž0.0244.

0.1075 Ž0.0859. 6.725 Ž0.323. 148 0.348

0.1048 Ž0.1066. 6.271 Ž0.341. 158 0.300

y2.6448 Ž0.7003. 0.4643 Ž0.1411. y0.0841 Ž0.0179.

y0.5798 Ž0.3505. y0.2475 Ž0.3312. 0.1076 Ž0.0971. 6.836 Ž0.284. 158 0.356

Note. Standard errors are in parentheses. All regressions use a White correction for heteroscedasticity. All location attributes except ‘‘Distance to the Bund’’ are subdistrict aggregates. Instruments for lnŽFAR. include distance to airport, square of distance to CBD, log of non-parametric smoothed estimate of FAR, and a residential project dummy.

using Cleveland and Devlin’s locally weighted regression w5x methodology.19 As predicted, the coefficients on the determinants of the restrictions on density are largely unchanged, but the use of imperfect instruments for FAR means statistical significance fails. 19

A first stage regression of lnŽFAR. on the instruments produces an adjusted R 2 of 0.38, and the estimates of all coefficients except the type of land use dummy are of the expected sign and statistically different from zero. We follow McMillen w20x and use Cleveland and Devlin’s locally weighted regression w5x to obtain a smoothed value estimate of FAR at a given site as a distance-weighted average of FAR from the closest 20% of the sample. Smoothing captures broad influences, but excludes idiosyncratic site-specific effects. Unlike maximum allowed FAR, the semi-parametric smoothed estimate of FAR is not a function of the land price per buildable m2 .

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VI. CONCLUSION In this paper we present a methodology for measuring and analyzing the variation in density restriction on individual urban development sites. This allows a site specific estimate of the constraints imposed on developments. We apply the methodology to a unique set of data covering long-term leases for urban redevelopment sites in Shanghai in the early 1990s. For these sites, the district and the municipal governments share control over the supply of land and the allowed redevelopment density. Our objective in the empirical analysis is to evaluate how different interests between the two levels of government influence the outcomes of urban redevelopment. We find that the measured deviation of redevelopment density from its unconstrained level is consistent with a set of tradeoffs faced by the regulating authorities. In particular, concerns for congestion raise the restriction on redevelopment densities. However, higher resettlement costs and greater inefficiency in the existing land use tend to lower the restriction. The methodology for measuring the constraint makes these empirical results reliable; absent these restrictions, the observed FAR would be sufficient to explain the variation in land prices. Our findings have several implications for future research on land markets, particularly in transition economies. First, we demonstrate that the structure of revenue and power sharing between different levels of local government clearly affects the pattern of redevelopment. Second, the endogeneity of land use regulation introduces a new dimension of path-dependence into urban development. Incentives that determine land use regulation policies at different levels of local government depend in part on the existing land use conditions. This path-dependence can be of particular significance for transition economies because the initial land use pattern in these emerging urban land markets is much distorted from the market equilibrium Žsee Bertaud and Renaud w2x.. Both of these observations lead to a particularly important question for future research, that is, how the differences in the incentives facing local governments affect the adjustment of urban forms towards their market equilibrium.

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