Time is money: An empirical examination of the effects of regulatory delay on residential subdivision development

Regional Science and Urban Economics 51 (2015) 25–36

Contents lists available at ScienceDirect

Regional Science and Urban Economics journal homepage: www.elsevier.com/locate/regec

Time is money: An empirical examination of the effects of regulatory delay on residential subdivision development☆ Douglas H. Wrenn a,⁎, Elena G. Irwin b,1 a

Department of Agricultural Economics, Sociology, and Education, Pennsylvania State University, 112A Armsby Building, University Park, PA 16802, United States Department of Agricultural, Environmental, and Development Economics, The Ohio State University, 316 Agricultural Administration Building, 2120 Fyffe Road, Columbus, OH 43210, United States

b

a r t i c l e

i n f o

Article history: Received 2 July 2014 Received in revised form 23 December 2014 Accepted 28 December 2014 Available online 6 January 2015 JEL classification: R14 R12 R52 Keywords: Land development Land use regulations Urban spatial structure

a b s t r a c t Variation in regulatory costs over time and across different types of investment projects creates risk for developers who hold land. These so-called implicit costs, which arise as a result of regulatory delay in the land development process, are hypothesized to be potentially large, but empirical evidence of their influence on development outcomes is limited. Using a unique micro-level data set on parcel-level subdivision development that includes data on the timing of subdivision approvals, we test the effects of implicit costs that arise as a result of increased subdivision approval times on the timing and pattern of residential subdivision development. Consistent with theory, we find that these regulation-induced implicit costs reduce the probability of subdivision development on any given parcel. In addition, we find that systematic variation in regulation-induced implicit costs across space has reduced development in more heavily regulated urbanized areas intended for development and intensified development in less regulated exurban areas located farther away. The results provide a new explanation of scattered, low-density urban development as the result of optimal land development with multiple development options and heterogeneous regulatory costs. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Land development projects are often risky investments. Because development projects take time to complete risks related to future revenues and costs can significantly alter investment behavior. This is especially true when those future risks are outside the control of the investor. New land use regulations that are enacted after the start of a project or existing land use regulations that are differentially applied based on the time and place of a project can impose such risks. The main implication of such regulations is often to extend the time that it takes to complete a project thus increasing the implicit costs associated with the project. These so-called implicit costs arise from any regulation-induced delay in the completion of a given real asset investment project, which increases costs by extending the time required to tie up capital and delays revenue generation by postponing the time of sale of the asset (Mayer and Somerville, 2000). Because these costs are not explicit their impact on development outcomes and the

☆ This research is supported by a cooperative agreement with the U.S. Forest Service Northern Research Station, National Science Foundation DEB-0410336 and Grant No. 0423476 and the James S. McDonnell Foundation. ⁎ Corresponding author. Tel.: +1 814 865 9216; fax: +1 814 865 3746. E-mail addresses: [email protected] (D.H. Wrenn), [email protected] (E.G. Irwin). 1 Tel.:+1 614 292 6449; fax: +1 614 292 0078.

http://dx.doi.org/10.1016/j.regsciurbeco.2014.12.004 0166-0462/© 2015 Elsevier B.V. All rights reserved.

resulting inefficiencies that are introduced in the land market are unlikely to be fully anticipated by policymakers.2 While many land use regulations represent de jure increases in the explicit costs of land development, e.g., impacts fees or taxes, real options theory suggests that a de facto increase in implicit costs can have an even larger impact on housing and land market investments (Pindyck, 1993; Bar-Ilan and Strange, 1996; Mayer and Somerville, 2000; Quigley and Raphael, 2005; Gyourko and Saiz, 2006). However, despite this theoretical interest in implicit costs, there is little empirical evidence of how these costs influence housing markets. Mayer and Somerville (2000) provide one of the few empirical investigations using metro-level data on housing starts and a national survey of planners to estimate the impact of regulation-induced increases in expected approval times on the number of new houses being built. They divide regulations between those that add explicit costs and those that induce cost increases by extending approval times. They find that regions with increased approval times for subdivisions can have up to 45% fewer starts and elasticities that are more than 20% lower, and that those regulations that lengthen the approval process serve to decrease the supply response the most. Their results provide key evidence of the potentially

2

In economic terms, they are neither endogenous to the developer nor anticipated.

26

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

large impact that implicit costs can have on housing supply.3 However, the aggregate scale of analysis precludes consideration of how implicit costs influence individual development decisions and the spatial structure of land markets within an individual metropolitan region. Other empirical studies of regulation and housing markets focus on the overall impact of regulatory stringency on housing supply at a metropolitan level (Green et al., 2005; Glaeser and Gyourko, 2005; Glaeser et al., 2005, 2006; Ortalo-Magne and Prat, 2007; Paciorek, 2011). These studies largely confirm the relationship between increased regulatory stringency and a reduction in housing supply at the regional scale, but are also unable to identify the impact of implicit costs on micro-level investment decisions from their aggregate measure of regulatory stringency. On the other hand, parcel-level models of residential development have considered the impact of specific land use regulations on the timing, density, and spatial pattern of land development (Newburn and Berck, 2006; McConnell et al., 2006; Cunningham, 2006, 2007; Towe et al., 2008). These studies provide a number of interesting insights about the relationship between spatially-heterogeneous regulations and the timing, density, and location of development, but do not consider the role of implicit costs. The purpose of this paper is to investigate the impact of regulatoryinduced delay on the investment decisions of individual land developers and the spatial distribution of residential development. First, given their non-diversifiable nature, we hypothesize that an increase in the implicit costs associated with regulatory delay should delay the optimal timing of starting a given subdivision project (Pindyck, 1993). In the context of the land development investment problem, any policy that extends the time that it takes to gain final approval for a project will extend the time that capital must be tied up, thereby increasing costs and reducing the probability of the investment. Second, we hypothesize that differences in the intensity with which smaller versus larger subdivisions (in terms of number of buildable lots created) are regulated imply meaningful differences in their implicit costs that favor the development of lower cost, smaller subdivisions. An implication of this second hypothesis is that, because smaller subdivisions tend to occur farther from the urban areas, this difference in implicit costs has fostered greater exurban development. We test these hypotheses using data from an exurban to suburban county located in the Baltimore, Maryland metropolitan region that grew rapidly over our study time period from 1995 to 2007. We construct a parcel-specific measure of expected implicit costs using data on the spatial, temporal, and parcel characteristics of previouslyapproved development projects to estimate a measure of expected approval time for each undeveloped parcel in each year from 1995 through 2007. We use this measure as a proxy for the actual implicit costs of regulatory delay in a series of discrete-time duration models that include a variety of controls for parcel-level explicit costs, land prices, and the prices of housing services. The identification strategy relies on the model specification providing sufficient controls so that our measure of implicit costs is uncorrelated with any omitted variables that may influence implicit costs. The absence of an exogenous shift in the regulatory environment and the lack of a viable instrumental variable for these implicit costs make this a difficult assumption to test. Instead, we examine the potential for omitted viable bias by estimating a series of models that control for a range of other parcel-level and neighborhood effects and subject our model to a series of powerful tests.4 Our findings confirm the hypotheses that implicit costs resulting from regulation-induced delay exert a significant influence on both 3 A number of more-recent papers have extended the idea of regulatory delay and the impact that this delay has on the “right to build” and found very similar results in terms of reductions in the both the timing and quantity of housing supply and attendant rise in the overall level of housing prices (Glaeser and Ward, 2009; Paciorek, 2011; Murphy, 2013). 4 This approach is similar to the one used in Albouy et al. (2013). In the absence of a clear instrumental variable strategy, the author's propose testing the robustness of the findings using a series of model specifications and powerful controls.

the overall development process and the spatial pattern of development. We demonstrate through a series of robustness checks that, even after controlling for a number of other spatially and temporally varying factors, the sign and significance of our implicit cost result continues to hold. We find that a 1% increase in average expected approval time results in a decrease in the probability of development by 0.94%, suggesting that the overall impact of implicit costs on the probability of conversion is fairly unit elastic. Our results also reveal significant spatial variation in the impact of implicit costs on the location of development. Using the coefficient estimates from our preferred model, we compare the baseline probability predictions before and after a onemonth increase in expected approval times between areas of the county primed for development and those restricted or protected from development. The results reveal that the predicted probability of development is greater in more restricted development areas. Moreover, we find that a one-month increase in expected approval time leads to a 13% reduction in the probability of development in areas primed for development, but that only leads to an 8% reduction in areas not primed for development. Both of these results are counter to the intentions of most of the policies restricting growth in our study region and suggest that at least some of the increased sprawl in the region may be the result of spatial heterogeneity in the way land use policies are applied. This paper makes several contributions to the literature on land use regulation and urban spatial structure. The role of heterogeneity in generating discontinuous development patterns has long been emphasized in the theoretical literature (Mills, 1981; Wheaton, 1982; Newburn and Berck, 2011), but empirical evidence thus far has been lacking. Instead, previous empirical studies have focused on the role of demand-side amenities and disamenities and the role of these local land use spillovers in generating scattered suburban and exurban land development (Irwin and Bockstael, 2002; Walsh, 2007; Klaiber and Phaneuf, 2010). Using a unique parcel-level panel data set on subdivision development, we provide the first empirical evidence of the impact of implicit costs associated with the supply of residential land on individual land conversion decisions and on the spatial structure of land markets. Our main results are that implicit costs due to increased approval times for subdivision projects significantly influence the timing and spatial distribution of subdivision development and in ways that generate unintended consequences for the spatial pattern of development. The results offer a new explanation of scattered, low-density residential development as the outcome of heterogeneous regulatory costs and optimal land development decision making. In next section, we present our basic theoretical framework. In Section 2, we present our empirical model followed by Section 3, which briefly describes our study region and policy context in terms of land use regulations and shows descriptively, using our unique micro-level dataset of subdivision approval times, how it is entirely possible that spatial differences in these approval times could be leading to more urban expansion and a fragmentation a pattern that most counties are looking to change. Section 5 presents our data and the construction of our implicit cost variables, Section 6 presents our results, and Section 7 concludes. 2. Conceptual framework Our conceptual framework follows from Pindyck (1993) who developed a theoretical model describing how implicit costs impact real asset investment decisions. Implicit costs are defined as increased project costs that follow from increased approval times.5 In our study region 5 Pindyck (1993) considers two types of costs — technical costs, which vary with the decisions made by the investors, and input costs, that change regardless of the actions taken by the investor. In the context of the investment option facing the land developer, these input costs are analogous to the implicit costs generated by regulatory delay — i.e., the time that it takes to get final approval for a subdivision often changes as a result of factors, such as changes in land use regulation, that are outside of the control of the land developer.

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

new subdivisions go through a two-step approval process. Owners of raw land first apply for conditional subdivision approval. The county then grants final approval of the plan conditional on meeting a number of regulatory requirements. The time required to meet these requirements can take anywhere from a few months to several years and can create a considerable lag between the initial application by the developer and the actual start of the project. It is this expected approval time, between the time that the developer first applies for conditional approval and the time by which the developer expects to gain final approval, which is of primary interest here. This lag in the development process implies an opportunity cost6 and thus, if larger projects translate into increased capital expenditures through the impact of implicit costs on the time value of money, then an increase in future approval times should decrease the probability of development for these projects. Hence, we treat the optimal investment decision as the developer's decision to seek approval for a given subdivision project and focus on how the expected approval time influences this decision. To formalize the role of heterogeneous approval times across multiple development options, suppose an atomistic developer, m∈{1,…,M}, is faced with the choice of which type of residential subdivision development project to undertake. Projects differ based on the maximum level of allowable capital investment, which is determined by zoning regulations for a given location. Developers must borrow capital to acquire the raw land and pay a fixed amount in every period to service this debt. Costs vary with the type of project because of differences in location and the allowable capital investment, which imply differences in regulations, approval times, and time to build. To determine the payoffs for each project i, the developer will choose t to maximize the following equation: τ X s F i ðt þ τÞ ¼ V i ðt þ τÞ− β C i ðsÞ−P i ðt þ τÞ;

ð1Þ

s¼0

where Fi(t + τ) is the total value from a given investment project i started in period t but with the returns realized in period τ, Vi(t + τ) is the payoff from project i, β is the discount rate, Ci(s) is a fixed coupon payment paid by the developer in every period that the project is active,7 and Pi(t + τ) is the full loan or principal amount used to buy the raw land parcel at the beginning of the project and must be repaid in full at the time of completion, τ. Given the expected payoff for each type of project i, the developer will then choose the project that maximizes the expected payoff across all projects i ∈ {1,…,I}. As is clear from this equation, returns are only realized at the end of the project, but costs occur throughout the time period over which the project is active. If the project length does not vary across the different projects, the developer's optimal choice will be determined by the relative payoffs and other costs associated with each option. However, if one project is located in an area subject to more stringent regulation that delays the project approval time, then the optimal choice will also depend crucially on this relative time difference. As the differences in approval times rise relative to the differences in payoffs and other costs, the optimal investment decision will be increasingly determined by the option with the faster approval time. In our case, we hypothesize that the differences in approval times between the more regulated suburban versus exurban areas will favor development in the lesser regulated exurban areas, at the margin, and lead to lower overall density and greater urban expansion in the region. 6 Bar-Ilan and Strange (1996) were the first authors to build this delay process into a real options model and demonstrate that its impact of spatial development patterns in an urban economic model. 7 The costs that are incurred over time are net any returns that may be generated from the raw land while the developer awaits approval, e.g., from agricultural production. We assume that conditions of growth, e.g., due to growing population or rising incomes over time, imply that the costs of holding raw land in this urbanizing area are greater than agricultural returns in any given period and therefore per period costs Ci are assumed to be greater than zero.

27

3. Econometric model Given the dynamic nature of the subdivision investment decision, we model the optimal timing of land conversion using a duration model (Irwin and Bockstael, 2002; Cunningham, 2007; Towe et al., 2008; Bulan et al., 2009). Duration models take account of the fact that an action taken in period t implies the action was not taken in any previous period (T b t), which is essence of an optimal stopping investment decision. In our model the random variable of interest, t, is the time until a first-stage subdivision event occurs, and we are interested in the impact of a set of covariates, Xmt, for a parcel m, in period t, on the probability that a parcel will convert from an undeveloped state to a developed state in a given time period by submitting an initial subdivision application. In a duration model the observations in the data are actually spells or observations, over time, of the same observational unit and realizations of this process can be characterized by the following density function, f ðt Þ ¼ Probðt ≤Tbt þ dt Þ;

ð2Þ

and its corresponding cumulative density function, Z F ðt Þ ¼

t 0

f ðsÞds ¼ PrðT ≤t Þ; t ≥0;

ð3Þ

where T denotes the random duration time of conversion and t is one realization of that random variable. Eq. (3) specifies the cumulative probability of failure, or converting, so subtracting this value from one gives S(t), which is probability of surviving, or not converting, before time t. The survival function serves as a control in the likelihood function for censored observations, which do not experience an event during the observation period for the data. The values contributed by the density function are for those observations that do experience an event. Combining Eqs. (2) and (3) produces the hazard function: λðt Þ ¼ Probðt ≤Tbt þ dtjT ≥t Þ ¼

f ðt Þ : S ðt Þ

ð4Þ

The hazard function is the instantaneous probability of an event occurring in the time interval dt given that it has not occurred up to that point. To facilitate this estimation, the general form for the parametric proportional hazard model is given by the following equation: 0

λðt Þ ¼ λ0 ðt Þe

X β

;

ð5Þ

where the baseline hazard, λ0(t), which is identical across all observations, is shifted proportionally by changes in a vector of covariates, X, and the coefficients capture the significance and the magnitude of the change in those covariates on the baseline hazard. In our model, the data matrix X contains those cost and revenue variables that are most likely to impact the timing of land conversion including our empirical measure of implicit costs or expected approval time specified below. Given that our data are only available at yearly time steps, we use the discrete-time duration method developed by Beck et al. (1998). The authors show that a simple binary logit specification with time fixed effects provides a similar fit to the data as the continuous-time duration model when the data have a large number of ties. Applying their model to the duration model in Eq. (5) produces the following probability function:

Probðymt

 0  e− X βþτt−t0 ; ¼ 1jX Þ ¼ λðtjX Þ ¼ 0 1 þ e−ðX βþτt−t0 Þ

ð6Þ

28

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

Fig. 1. Baltimore/Washington, D.C. MSA.

which is a basic logit probability model with time fixed effects included. The time fixed effects are included to model the baseline hazard and account for the censored nature of the data, which results in an unbalanced pooled panel. The logit likelihood is specified in the standard fashion.

4. Study region and policy environment The study region for our paper is Carroll County, Maryland (Fig. 1). Carroll is an urban fringe county located within the Baltimore/Towson metropolitan statistical area. While predominantly rural for much of its history, the county has witnessed rapid population growth since the 1960s with population more than doubling in the last 40 years. In response to these growth pressures, the county passed its first comprehensive zoning plan in 1963, which restricted development density to one house per acre in all areas of the county without public sewer facilities. Increased growth in the 1970s led to the passage of a second comprehensive plan in 1978, which included a massive down zoning of 70% of the land in the county to low-density agricultural zoning. This zoning class has a stated density of one house per 20 ac, but its actual effective density is closer to one house per 15 ac due to some flexibility that was built into the law to accommodate residential development on agricultural parcels. Specifically, each parcel located in an agriculture zoning area and having at least 6 ac of land is allowed to create two buildable lots; each additional lot requires an addition 20 ac. Apart from several small adjustments made in 1989, these same restrictions have been in place in the county since 1978.8 The 1963 comprehensive plan also provided the first formal procedure for the creation of large major and small minor residential subdivisions. Large subdivisions consist of any development with four or more buildable lots at the time of development and require the installation of streets, storm water management facilities, and other infrastructure. Small developments consist of two or three buildable lots and are not subject to any infrastructure requirements. In addition, while approval of large subdivisions requires a formal public hearing, small subdivisions can simply be approved by the chairmen of the planning board without a formal hearing. According to county planning officials, in most cases small developments can gain approval in less than two or three months; large developments, however, require an open public 8 Given the amount of land in the county that falls within the agriculture zoning class and the drastic difference in density between this class and the other four zoning classes in the county, the estimation and analysis in the remainder of this paper will differentiate between these two areas by classifying all agricultural areas as low-density suburban and exurban development areas and the other four classes as high-density urban development areas.

Fig. 2. Subdivision development as of 2007.

hearing as well as the approval of numerous county agencies, which can significantly increase the time until approval. Despite the intention of these regulations to control exurban and rural development, Carroll County has experienced a significant amount of residential development outside of traditional development envelopes. Our data show that over 60% of all subdivisions created from 1995 through 2007 were platted in agriculturally zoned areas and that of these 82% were small minor developments. Fig. 2 shows the location of all subdivision activity in the county as of 2007 broken out by subdivision type. It is clear from this figure that, while both types of developments contribute to fragmentation, the minor developments are more concentrated in more remote, exurban areas. To provide additional motivation it is instructive to get a sense of the unconditional relationships between different types of subdivision developments and their approval times.9 Table 1 shows the distribution of approval times for all of the subdivisions in our data set. Sections 1 and 2 of Table 1 break approval times out by subdivision size as determined by minor, medium major, and large major subdivisions. The categories are based on the number of lots created. It is clear that minor developments take a less time to get approved and that this difference holds across the entire distribution. Given that most minor subdivision developments take place in more remote locations, this lends support to our hypothesis that variation in regulation induced implicit costs has fostered exurban development. In Section 3, we compare approval times based on the commute times to the urban boundary via the roads network. From these results, it is clear that: (1) the number of projects increases with distance; (2) the average approval time falls with distance; and (3) the decrease in approval times with distance holds across the distribution. Once again, if these advantages translate into increased value for developers, then we would expect the increased activity in more exurban areas to be, to some extent, the result of relative differences in the value of the investment. Finally, we investigate how approval times vary inside versus outside areas intended for development. Sections 4 and 5 of Table 1 show the distributions for approval times for completed subdivisions broken out by areas inside and outside

9 The data used in this descriptive analysis is from our dataset on subdivision approval times for Carroll County from 1991–2007 and consists of 653 subdivisions that gained approval during that period and for which the total time of approval was less than or equal to 72 months. We chose 72 months as our cutoff as this was the 99th percentile from the raw data. A full description of these data is contained in Section 5.

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36 Table 1 Approval time data. Time (months) (1) Major versus minor Major developments Minor developments (2) Large, medium, and small (lot count) Large major developments (over 9 lots) Small major developments (4 to 9 lots) Minor developments (3) Travel time to Baltimore City TravTimeBalt ≤ 34 Min. 34 b TravTimeBalt ≤ 38 38 b TravTimeBalt ≤ 42 42 b TravTimeBalt (4) Zoning class AgZoning Non-AgZoning (5) Metro services No sewer Sewer

Mean

25th

50th

75th

N

18.33 6.25

8 3

14 4

25 8

261 392

21.51 14.96 6.25

10 5 3

17.5 11 4

25 18 8

133 128 392

16.27 13.81 12.37 10.44

5 4 3 3

11 9 7 5

25 20 16 13

137 138 166 212

9.63 16.25

3 7

4 13

11 25

397 256

11.61 19.31

3 8

6 14

14 28

547 106

of agricultural areas and inside and outside of areas with public sewer. It is clear that significant differences also persist between these two areas: subdivisions outside of agricultural areas and parcels outside of areas with public sewer experience much faster approval times. Since the majority of these areas are located in exurban areas of the county, it is plausible that these differences may create advantages for exurban developments, which could increase the probability and amount of development activity in these areas. 5. Data and construction of variables To formally test the effects of heterogeneous implicit costs from regulatory delay on subdivision development outcomes, we construct a micro panel data set of the subdivision and land development process in Carroll County from 1995–2007. First, we join the parcel boundary GIS shapefile for the county with data on the parcel characteristics from the county's tax assessor's database and data on the subdivisioning process from the Maryland historical archives.10 By matching the individual parcels from our GIS database with a series online plat maps, we are able to determine the subdivision to which each parcel belongs and a date for when each subdivision development was granted final approval. From 1924 through the end of 2007 there were 1942 residential subdivisions developed in Carroll County. Of these, 1117 were majors and 825 were minors. Second, we incorporate data on the status and timing of parcels enrolled in one of the several land preservation programs during our time period. This permits us to control for when a parcel has forgone its development rights and drops out of the sample of developable parcels. Finally, we reconstruct the history of the subdivision approval process in the county by matching subdivision names with information on their stages of development gathered from the official minutes from the planning commission's monthly meetings. Given that the county only started collecting electronic data starting in 1991, we only have data on approvals for subdivisions that started the develop process after 1990. The final cross-sectional data for this paper includes all parcels that, as of the end of 1994, were eligible to be subdivided into at least two buildable lots according to the current zoning. We use all parcels that were located in one of five zoning classes in the county: agricultural, conservation, and residential (specifically, R40, R20, and R10), which in total account for 95% of the land in the county. The final data set includes a total of 3829 parcels of which 382 (10%) initiated the 10 After a subdivision gains final approval from the county zoning commission the plat of that development becomes public record and is recorded and stored at the Maryland historical archives. These plats and the information contained on them are available to the public online at the following address: www.plats.net.

29

development process by applying for conditional subdivision approval between 1995 and 2007. The final panel data set, after stacking the data over our 13-year observation period, consists of 45,433 observations, which we designate as Zmt, where m is the cross-section ID for the parcel and t is the time period that the parcel is observed. In the remainder of this section, we explain the construction of the implicit cost variable. 5.1. Implicit cost variable To capture the impact of implicit costs on developers' decisions to initiate a new subdivision project, we use our data on historical subdivision approvals to form a temporally and spatially-varying prediction of expected approval time for each undeveloped parcel in our data set.11 Starting in 1995 and continuing through 2007, we use past approval outcomes to form predictions for those parcels in the dataset that are yet undeveloped. While theory produces a clear prediction for the expected sign of the coefficient on implicit costs, the model does not provide explicit guidance on how developers form their expectations. One option is to write out the explicit structural decision making process of the developers, estimate it based off of available data on past approval outcomes and on the characteristics of the developers, and then use that structure, coefficients, and additional data on undeveloped parcels to form out-of-sample expectations for undeveloped parcels. However, we lack sufficient data on the individual characteristics of landowners. We do, however, have data on past approval outcomes as well as data on the characteristics of every parcel and its spatial location relative to zoning, major roads, and metropolitan centers. Using these data, we can specify a relationship between the parcel characteristics, past approval times, and the location of the parcel to generate credible predictions of expected approval time for each parcel.12 We investigate two separate estimation methods to produce these implicit cost predictions—a parametric prediction method based on a linear least squares model (OLS) and a nonparametric method based on a nearest-neighbor mean-value matching algorithm. We then compare the two methods using AIC values from a series of duration models and pick the prediction method that provides the best fit to the data. 5.1.1. Parametric prediction The following OLS model is specified for each of our 13 time periods: 0

lnAT st ¼ Zone þ Time þ X st βk þ εst ;

ð7Þ

where lnATst is the natural log of the approval time of subdivision s in time period t, Zone is a fixed effect for the zoning class in which the approved subdivision is located, Time is a time fixed (each model contains data from more than one year – i.e., the model for 1995 contains data from 1991 to 1994 – so this variable is fixed effect for the years contained in each model), and XstV and εst are the observed and unobserved characteristics and spatial attributes of the completed subdivision parcels, respectively. The model in Eq. (7) is estimated using only completed subdivision developments or those developments that have completed the entire approval process at which time the actual approval time, in months, is 11 While there is only one planning board for the entire county, the composition of this planning board is made up of representatives from both city and county districts and this composition varies over time as the county has elections for members of the planning board. Given that we only have approval data for a single county, we rely on variation in the composition of the planning board over time to identify the impact of past approvals on the probability of development. 12 This process, of using past approval times and the characteristics and spatial location of those approvals to form predictions, is very similar to the “comps” technique used by real estate appraisers to develop selling prices for newly-listed home. As long as we are able to incorporate all of the information that was available to potential developers in each time period in forming our predictions, then our method should be fairly close to other comparable methods used on the demand side of the market.

30

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

revealed in the data. One limitation of our data is that we only have approval-time data beginning in 1991. Thus, to estimate the model in Eq. (7) and form our predictions in 1995, we can only use data on subdivision approvals for the four-year period from 1991 to 1994. To keep our models, estimates, and predictions consistent, we estimate each of our models using only the previous four years of data and include time fixed effects in each model to control any unobservable macro-level and county-level trends. In addition to the zoning and time fixed effects, we hypothesize that the approval time of a proposed subdivision is dependent on other observable characteristics associated with the parcel as represented by XstV . First, we expect approval times to decline with distance and account for this by including both the distance to the center of Baltimore as well as the distance to the nearest primary road. The main reason for this is that being close to the city or a major is likely associated with more dense development and congestion. Thus, planning boards a more likely to require new developments to conduct transportation studies to determine how much extra traffic is going to be added to already congested roads. If this increases approval times, then being further from major roads or the city will decrease the time to approval. Next, we include the following four variables to control for the physical characteristics that are most impacted by land use policy in the county: ExHouse, which is an indicator for whether a parcel already has an existing house on the property; FloodZone, which is an indicator for whether a parcel is in a 100-year flood zone; PercentForest, which is the percentage of the parcel that is covered by forest; and ZonedLotCapacity, which is the zoned density for the parcel according to the zoning and the area of the parcel. We expect the coefficient on the existing-house variable to be negative, given that many minor developments take place as splits from existing farms and these minor subdivisions have a much shorter approval time. We include FloodZone as a proxy for parcels that are located near water or other environmentally sensitive areas, which may require additional environmental impact assessments to be approved. We include PercentForest to proxy for the impact of Maryland's Forest Conservation Law, which imposes a strict set of rules and regulations for how forest cover on a parcel is handled at the time of development. Finally, we note that the zoning class variables are relative to the excluded class, agricultural zoning, and we expect each of the included fixed effects to be positive relative to the agricultural zoning class Table 2 provides the summary statistics for the variables used in each of our 13 OLS models. To produce our implicit cost predictions, we use the following equation: 0

d ¼ lnZone d þZ β c lnAT mt mt k ;

ð8Þ

generated from these estimates. These predictions are then merged with main panel data set and used as our parametric measure of implicit costs. 5.1.2. Nonparametric prediction While parametric models provide a clear mechanism for out-ofsample predictions, they also rely on parametric assumptions and variables that may not be entirely credible. We compare these parametric predictions with a simple nonparametric mean-value calculation of expected approval time that is generated using a minimal set of assumptions. To do so we assume that potential developers form their expectations of approval times based only on the relative spatial and temporal distance of their undeveloped parcel from previously approved subdivision parcels in their same zoning class. That is, in each period an undeveloped parcel uses approval-time data for subdivisions approved in the previous four years and in the same zoning class to form a mean-value statistic, which is used as their measure of expected approval time. The main empirical challenge with this nonparametric technique is in deciding how much data (how many previous subdivision events) to use in forming the mean-value statistics. As is the case with any nonparametric modeling technique there is a tradeoff between increased bias and variance. In the case of one-dimensional estimates, such as strictly spatial estimates, this is straight forward. However, our data contains information in both space and time, which makes the tradeoff less clear. Given that we have greater variation in space than time, we give preference to the spatial dimension by constructing our nearestneighbor data sets based first, on spatial neighbors and second, on temporal neighbors. More specifically, in each time period that a parcel is undeveloped we choose first the closest parcels in space (from among those that were approved in the previous four years) and then the closest parcels in time. We iterate in this fashion picking neighbors until we meet a specific count of neighbors set by our number-ofneighbors restriction in our algorithm. We then use these data to form a mean-value estimate that serves as our prediction for expected approval time for each parcel. We repeat this process for each of the 13 years of our data and we vary the number of neighbors from 20 to 110 in increments of 10. To determine the optimal number of neighbors to use in estimating our main model, we estimate a series of duration models each with a different nearest-neighbor specification used for the implicit cost variable and pick the one that minimizes the AIC statistic for those models. The results from these series of duration models are shown in Fig. 3. To compare this optimum with the output produced from using our parametric predictions, we also plot the OLS predictions. From this figure,

where the coefficients are those estimated from the models in Eq. (7) and the data matrix, Zmt, is the data matrix for all of the data used in the main panel data model. The hats on the coefficients indicate that d , is a prediction they are estimates and the outcome prediction, lnAT mt

Table 2 Variables for parametric prediction model.

TravTimeBalt (minutes) DisttoPrimeRd (km) ExHouse FloodZone PercentForest ZonedLotCapacity AgZoning ConservZoning R40Zoning R10R20Zoning

N

Mean

S.D.

Min.

Max.

653 653 653 653 653 653 653 653 653 653

39.62 1.38 0.49 0.23 26.21 19.87 0.61 0.14 0.09 0.17

6.93 1.39 0.50 0.42 25.98 49.20 0.49 0.34 0.28 0.37

25 0 0 0 0 2 0 0 0 0

63 9 1 1 100 478 1 1 1 1

Fig. 3. AIC statistics.

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

we observe that the AIC optima from the nonparametric implicit cost prediction are all below the AIC statistic from the OLS model. We also observe that the data set using 50 nearest neighbors is the optimal choice overall. Based on these results, we use will use the nonparametric cost prediction method based on 50 nearest neighbors in the remainder of the paper.

5.2. Other variables In addition to implicit costs a land developer is impacted by numerous other factors in making his or her decision to convert raw land into a residential subdivision. Two of the most important factors are the final price of housing, or the price of housing services, and the price of land per acre, which is an input into the housing production function. To construct our measure of housing prices, we follow Sieg et al. (2002) and estimate a series of hedonic models that permit us to separate out the pure price of housing services for each census tract and time period from the quantity value of housing. Unfortunately we lack sufficient data to follow the same procedure for developing an estimate of the price of land as an input in the production function of housing. Instead, we develop a parcel and time-period (yearly) specific prediction of land price per acre based on a semi-log land price regression using 3770 transactions of raw land over the period of 1995–2007. We control for parcel-level attributes by including variables that proxy for the physical features of the parcels; we control for broad trends in the price per acre of raw land by including a series of fixed effects for the Regional Planning District (RPD) in which the parcel is located. Details of both of these estimation procedures and their results can be found in the Appendix A. The remaining variables used in our duration models are included to control for additional explicit and opportunity costs that may impact the decision of a land developer to convert his or her parcel. The variable Sewer is an indicator for whether a parcel has public sewer and water access. While we hypothesized that sewer access plays a role in determining the level of implicit costs we also expect that there may be explicit fees associated with sewer access. Since we do not have actual data on these costs, we include a dummy variable for sewer to account for these unobserved costs. Two variables, Soil1 and Soil2, represent the percentage of class 1 and class 2 soils on the parcel and are included to

Table 3 Summary statistics. Description

Variable name

Parametric prediction (OLS) Nonparametric prediction House prices (100 s of $) Land price (100 s of $ per acre) Has sewer Class 1 soil (%) Class 2 soil (%) Over 15% slope (% of parcel) Forest cover (% of parcel) Located in flood plane Travel time to Baltimore (min.) Distance to primary road

ImplicitCosts

10.23

5.54

1.05

82.88

ImplicitCosts

12.24

5.08

4.02

23.33

Has an existing structure Area of parcel (acres) Number of buildable lots by zoning Eligible for land preservation program

HsPrice100 LndPrice100

Mean

S.D.

Min.

Max.

713.90 265.39 353.58 1511.51 173.06 231.16 5.00 2650.82

Sewer Soil1 Soil2 Slope

0.15 41.54 53.94 17.28

0.36 43.33 43.57 29.25

0.00 0.00 0.00 0.00

1.00 100.00 100.00 100.05

PercentForest FloodZone TravTimeBalt (Minutes) DisttoPrimeRd (km) ExHouse Area ZonedLotCapacity

32.45 0.24 41.04

32.53 0.43 8.05

0.00 0.00 23.18

100.60 1.00 65.51

1.17

1.34

0.00

9.98

0.50 32.34 8.54

0.50 40.86 25.39

0.00 0.46 2.00

1.00 370.00 653.00

0.25

0.43

0.00

1.00

EaseElig

31

proxy for the explicit costs of excavating and grading a parcel in preparation for the development. Both of these are estimated relative to the worst class, class 3, and we expected their influence to be positive. The variable Slope is defined as the percentage of each parcel with relief of 15% or greater. The variables PercentForest and FloodZone are the same as those defined above and the percentage of forest cover on the parcel and whether the parcel was located in a flood zone, respectively. As with sewer, we expected these variables to have a direct and indirect impact. Indirectly, they impact development through policies, such as the Forest Conservation Act, that are designed to regulate them. Directly, however, they proxy for the direct costs of developing a parcel — clearing trees and stumps from land is expensive and adds explicit costs to a project. TravTimeBalt and DisttoPrimeRd, which are, once again, measures of accessibility and capture the direct impact of being close to the city center or a major highway on the probability of development. Thus, we expect this probability to decrease with distance from the city as well as with distance from a primary road. We include the following set of variables as controls for the opportunity cost of land: Area, which is the size of the parcel in acres; EaseElig, which is a time-varying indicator variable for whether a parcel is eligible for easement in each period13 and a proxy for the opportunity cost of preservation; and ZonedLotCapacity, which represents the zoned density of parcel. A larger parcel is advantageous for both development and agriculture and therefore the effect of Area is ambiguous. On the other hand, the variable EaseElig is expected to have a negative effect on the probability of development while ZonedLotCapacity is expected to increase the payoff from development and therefore increase the probability of conversion. Table 3 provides the summary statistics of all the variables used to estimate the duration models. In addition we also include a full set of time fixed effects in each of the discrete-time duration models to control unobserved macro and county-level changes that occur during our observation period. 6. Results In this paper, we estimate a discrete-time duration model based interval nature of our data. As shown in Beck et al. (1998), estimating a binary logit model with time fixed effects provides a good approximation to a continuous-time piece-wise exponential parametric proportional hazard model. One concern, however, is that the results from our model may be impacted by this parametric specification. To address this issue, we also estimated our duration model using a semiparametric Cox proportional hazard model. The results from this model were very similar the results using our discrete-time duration model, so we do not include them given limited space. 6.1. Duration model estimates The results from our duration models are shown in Table 4. The model includes time fixed effects and the standard errors are bootstrapped (300 reps) and clustered at the parcel level.14 All of our variables have the expected sign. An increase in the price of housing

13 To be eligible for preservation, a parcel must be greater than 50 acres and have more that 50% of class one and class two soils combined or be between 25 and 50 acres with similar soils makeup and border a previously-preserved parcel. Thus, eligibility is based off of the size of the parcel, the percentage of the certain soil types, and the proximity of a parcel to other parcels that have preserved in the past. Because of this final clause, some parcels that were not eligible at the beginning of our study period may have become eligible later on. 14 Our approval-time and price variables are estimated in first-stage regressions and then included in the duration model. Thus, they are generated regressors, which could bias, downward, our standard errors. We control for this bias using a nonparametric bootstrap method based on the panel (parcel ID) nature of the data. We thank a reviewer for pointing this out.

32

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

Table 4 Duration results.

Table 5 Elasticity calculations.

Variables

Coef.

St. err.

Variables

Coef.

St. err.

HsPrice100 LndPrice100 ImplicitCosts Sewer Soil1 Soil2 Slope PercentForest FloodZone TravTimeBalt (minutes) DisttoPrimeRd (km) ExHouse Area ZonedLotCapacity EaseElig Constant Log likelihood

0.001⁎⁎ −0.002⁎⁎ −0.078⁎⁎ 0.760⁎⁎ 0.005 0.002 −0.002 −0.005⁎⁎ −0.341⁎⁎ −0.021⁎⁎ 0.130⁎⁎

0.001 0.001 0.022 0.221 0.005 0.005 0.002 0.002 0.125 0.006 0.034 0.123 0.002 0.002 0.193 0.849

HsPrice100 LndPrice100 ImplicitCosts Sewer Soil1 Soil2 Slope PercentForest FloodZone TravTimeBalt (Minutes) DisttoPrimeRd (km) ExHouse Area ZonedLotCapacity EaseElig

1.020⁎⁎ −0.379⁎⁎ −0.949⁎⁎ 0.116⁎⁎

0.510 0.103 0.263 0.033 0.190 0.245 0.038 0.058 0.033 0.255 0.036 0.061 0.064 0.010 0.046

0.047 0.002 0.004⁎⁎ −0.384⁎⁎ −3.325⁎⁎ −2120.822

Notes: The model includes time fixed effects to account for the baseline hazard. The standard errors are bootstrapped (300 reps) and clustered at the parcel level. ⁎ Significant at 10% level. ⁎⁎ Significant at 5% level.

0.192 0.083 −0.040 −0.177⁎⁎ −0.083⁎⁎ −1.020⁎⁎ 0.151⁎⁎ 0.024 0.068 0.031⁎⁎ −0.093⁎⁎

Notes: The standard errors were calculated using the Delta method. ⁎ Significant at 10% level. ⁎⁎ Significant at 5% level.

6.2. Robustness checks

services, which increases the payoff from development, is found to increase the likelihood of conversion. On the other hand, an increase in the price per acre of raw land, an input to housing production, leads to a fall in the likelihood of conversion. We find expected positive signs for the sewer access and better soils variables and the expected negative sign for forest percentage, parcels located in flood zones, and parcels with very steep slopes, although only the sewer access, forest percentage, and flood-zone variables are significant. We also find the expected signs and significance for our accessibility variables. The variable for travel time to the center of Baltimore is negative and significant, implying a negative conversion gradient relative to the city center. Distance to primary roads is found to increase the probability of conversion, which implies that people like access to the city, but prefer to not be right next to a major highway. We also find, consistent with previous work (Towe et al., 2008), that having the option to preserve the land reduces the likelihood of development and increased building capacity as determined by zoning increases the likelihood of development. Finally, we observe that the coefficient on our measure of implicit costs has the expected negative sign and is significant at the 5% level. This result, which is consistent with the predictions from our theoretical model, implies that as the expectation of approval time increases, all else equal, the probability of a parcel converting to a residential subdivision falls. The results in Table 4 provide an indication of the sign and significance for the various coefficients, but they do not have a direct interpretation in probability or elasticity space. One approach is to calculate the marginal effects for each point in the data for an infinitesimal change in the underlying variable and take the average over all of the data to get the average marginal effect for each variable. However, are more intuitive approach is to create unitless comparison across variables and models by generating an elasticity change for a 1% change in each variable. The elasticity results from our duration model are shown in Table 5. The coefficients were generated using the average elasticities for the full data and the standard errors were calculated using the Delta method. The result for our implicit cost variable is negative and significant and the coefficient value in implies that for a 1% increase in average expected approval time the probability of development falls by 0.94%, which is a fairly unit elastic measure for changes in implicit costs. Thus, it can be expected that for a 1% increase in the average expected approval time in the county there will be a proportional decrease in the overall likelihood of subdivision development.

Given the absence of an exogenous regulatory shift and lack of appropriate instrumental variables, an unavoidable concern with our results is the potential for unobservable factors operating at different spatial and temporal scales that are correlated with our measure of implicit costs. While we control for time-varying macro-level trends using time fixed effects there are likely other unobserved factors operating at the parcel, census-tract, and regional level that could be determining development timing apart from implicit costs. In this section, we present a series of models controlling for a range of other parcel-level and regional effects and demonstrate that even after controlling for all of these factors the sign and significance of our implicit cost result continues to hold. The results from these robustness checks are shown in Models 1–4 in Table 6.15 In Model 1, we control for the possibility that very small, two-lot projects could be the result of a different economic process. In many urban fringe counties these two-lot projects often get developed directly by the landowner (as opposed to having the land sold to a developer who then develops the parcel his or herself) and the lots are sold directly by the landowner. While we have information on the developer and landowners names and address, we do not know anything about the relationship between the landowner and the people who buy the houses and lots that are created (apart from some level of rough deduction based on names, which is not sufficient). So, as a test that these twolot developments are not produced by a different behavioral process and are driving our results, in Model 1 we drop all two-lot subdivisions as well as those parcels that are zoned to accommodate only a two-lot subdivision. The results from this model show that even after dropping these developments and parcels the impact of implicit costs on the development decision is still significant. In Models 2 and 3, we address the potential for endogeneity that may exist between our prediction of expected approval time and the error structure in the discrete-time duration model — i.e., parcel-level time-invariant unobservables that may be correlated with our approval-time variable. First, there is the potential for temporal endogeneity between the data used to form the prediction and the errors in the duration model. However, this issue has been accounted

15 In all of the models in Table 6 we only present the results for the implicit cost variable to conserve on space. Most of the other coefficients remain the same although some are not significant after the inclusion of the census-tract fixed effects.

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

33

Table 6 Robustness checks. Model 1a

ImplicitCosts⁎ ImplicitCostsFE rho Log likelihood N

Model 2b

Model 3c

Model 4d

Model 5e

Coef.

St. err.

Coef.

St. err.

Coef.

St. err.

Coef.

St. err.

Coef.

St. err.

−0.060⁎⁎

0.023

−0.070⁎⁎ −0.039 0.231 −1885.371 41,584

0.029 −0.032

−4E−04⁎⁎

2E−04

−0.083⁎⁎

0.033

−0.076⁎⁎

0.035

−1533.131 33,863

45,433

−2096.218 45,433

−2063.744 45,433

a

Results are for the duration model after dropping all two-lots developments and parcels eligible for only a two-lot subdivision based on zoning. Results are for the duration model after controlling for parcel-level unobservables using the fixed effects technique for nonlinear models suggested by Zabel (1992). The likelihood ratio statistcs for the RE term are: Statistic = 1.58; p-value = 0.104. c Results are for a linear probability model with parcel fixed effects. d Results are for the duration model with census-tract fixed effects. Standard errors are clustered at census tract level. e Results are for the duration model with time-by-planning district fixed effects. Standard errors are clustered at the planning district level. ⁎ Significant at 10% level. ⁎⁎ Significant at 5% level. b

for by our strategy of modeling the initial decision to start the development project and not the final approval date. Thus, by using only previously-developed, and completed, subdivisions to form the predictions and not past data on the undeveloped parcels we can control for temporal correlations between the error structures in the two models. However, even after accounting for the temporal effects by modeling the initial starting decision it is still possible that unobserved timeinvariant effects in the prediction could be correlated with those same unobservables in the duration model. If this is true, then the correlation would produce inconsistent and inefficient parameter estimates for our measure of implicit cost. One solution to this problem is to run a fixed effects model and difference out the unobservables. In theory, it is possible to estimate a fixed effects model within the logit framework by exploiting the linear exponential nature of the error distribution and estimating a conditional likelihood function, which uses the time-averaged value of the dependent variable as a sufficient statistic. However, given the nonlinear nature of our duration model and the sparse nature of our dependent variable this is not possible as it would imply excluding all parcels that did not subdivide during our study period. To provide a solution to this problem, and test the robustness of our results, we apply two other econometric methods, which allow us to use the full data set and test for the presence of parcel-level unobservables. First, we employ the technique for handling endogeneity in nonlinear models suggested by Zabel (1992). Specifically, we build correlation into the model by first, specifying an individual random effect, γm, for each parcel; and second, by defining that individual random effect as a function of both the initial value of the implicit cost variable in the first period and the individual random effect for each parcel: δm = ImplicitCostsFE1Vθ + γm,16 where γm is a time-invariant random effect distributed standard normal with a correlation terms defined by ρ, and ImplicitCostsFE1 is the value for our implicit cost variable in the first period of the data (1995). This FE variable serves as a proxy for individual-specific fixed effects and controls for time-invariant effect for each parcel that may cause correlation between our measure of implicit cost and the standard error in the duration model. To estimate this model we drop the first year of data (1995) and estimate the model using only data and developments from 1996 to 2007. The results from this process (Model 2, Table 6) produce a significant and negative coefficient for our implicit cost variable. The fixed effects term, while it is also negative, is not significant even at the 10% level.

16 The role played by the random effect in the discrete-time duration model is the identical to that played by the “frailty” term that captures individual heterogeneity in the continuous-time duration models (Lancaster, 1990; Kalbfleisch and Prentice, 1980).

In addition, the ρ term for the significance of correlation across time for the same parcels is positive, but a likelihood ratio test produces an insignificant result at the 10% level. From these results it does not appear that endogenous correlation between our prediction and the error structure in the duration model is a significant problem. Moreover, we do not find any indication of serial correlation across time for the same parcels. Our second technique addresses parcel-level endogeneity by estimating a panel data linear probability model with parcel-level fixed effects. While this method does not allow for the identification of time-invariant parcel variables (soils, slopes, etc.), it does provide a very robust test of our approval-time variable, which varies over space and time, by netting out all time-invariant parcel-level unobservables. The results from this estimation are shown in Model 3 in Table 6. While the coefficients are not directly comparable to the nonlinear models, the coefficient for our approval-time variable still has the appropriate sign and is significant at the 5% level suggesting that unobservables are not a big issue and our parcel-level variables are doing a good job of controlling for the factors most important to landowners in making their development decisions. In the final two models in Table 6, we control for higher-level unobservable factors that may be biasing our results. In Model 4, we include a full set of census-tract fixed effects in the model in addition to the time fixed effects and the other covariates. The census-tract fixed effects control for the impact of income, demographics, and other time-invariant policy effects that may be impacting the conversion decisions of developers. We also cluster the standard errors in this model at the census tract level and not at the parcel level.17 Once again, the results from this process produce a negative and significant coefficient value for our implicit cost variable. Our final model, Model 5, includes a full set of fixed effects at the regional planning district level as well as interactions between each of these (6) and our year fixed effects (13).18 Regional planning districts are agglomerations of smaller census tracts and serve at planning areas for the Baltimore Metropolitan Council. As before, the results for our implicit cost variable continue to hold even with the inclusion of the full set of interaction terms. Given the results from the previous four models, we conclude that our prediction variable provides a robust proxy for the impact of

17 In our previous models we clustered the standard errors at the parcel level. However, if there is an unspecified spatial error process in the data it could bias downward our standard errors. One potential solution to this is to cluster the errors at a larger spatial scale. We follow this logic and cluster at the census tract and planning district in Models 4 and 5 in Table 6. We thank an anonymous reviewer for pointing this out. 18 We choose to interact our time variables with the fixed effects at the regional planning district level because of collinearity problems when trying to do it at the census tract level.

34

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

regulation-induced implicit cost. While we cannot conclusively rule out the possibility that unobserved factors are still at play, we conclude that the robustness of the results across these different model specifications provide reasonable evidence of the impact that implicit costs, as represented by expected approval time by the county planning agency, have on the likelihood of development. 6.3. Spatial analysis of elasticities The second part of this research focuses on how regulatory delay and spatial variation in the application of land use policy as it flows through implicit costs impacts the location of development. If spatial variation exists, and if the differences are more pronounced between areas primed for development and those that are not, then it is possible that these differences could be leading to increased exurban development and urban spatial expansion. While precisely quantifying this result is difficult, our model provides a sufficient framework for providing at least some idea of how this result may be impacting development patterns in our study region. To quantify the impact of these relative changes in implicit costs across space, we use the results and data from our model in a simple simulation exercise. First, we combine the parameter estimates and the variance-covariance matrix from the duration model with a set of draws (1000) from a standard normal distribution to generate a set of random draws from our estimated parameter distribution in a method similar to Krinsky and Robb (1986). Second, we use each draw from the simulated parameter distribution to compute the predicted probability of development for each parcel as well as the coefficient and standard error of this probability by taking the mean and standard deviation over the draws from the parameter distribution. Third, we add a one-month increase to our implicit cost variable and repeat the simulation generating a new coefficient and standard error for the new data set (following the one-month change). Finally, we calculate the percent change in the predicted probability of development before and after the change and calculated the coefficients, standard errors, and percentage changes for parcels located in areas primed for development and those that are not. The results from our simulation exercise are shown in Table 7. As expected, a one-month increase in expected approval time decreases the predicted the probability of development in all cases. However, as the last column clearly demonstrates, the decrease is much larger for parcels located in areas primed for development. For example, for parcels located in areas with public sewer facilities a one-month increase leads to more than a 13.3% decline in the probability of development. Similarly, for parcels located in non-Ag. zoning categories a similar one-month increase in expected approval time leads to an 11.9% decline in the probability of development. Both of these results support our hypothesis – that it is heterogeneity in land use regulation and the application of land use policies that may be leading to increased urban expansion – and shed light on the fact that many of the policies that were designed to control growth are actually combining to create a relative advantage for more remote development and increased sprawl. While the results from this paper do not assess any welfare measure to this type of development, they do provide clear evidence that policy induced implicit costs that differentially impact parcels based on space can impact the spatial pattern of development in an urban areas and lead to increased fragmentation. 7. Conclusions The process of converting raw land to a residential subdivision development often requires considerable time and capital and is subject to many uncertainties. It is influenced by many factors including the physical characteristics of the parcel, local market conditions, the price of raw land, housing prices, and local regulatory policies impacting the type and location of development. While many of these factors lead to

Table 7 Results of spatial analysis. Scenario

Baseline Coef

(1) Change based on sewer availability No sewer Sewer (2) Change based on Ag. zoning Ag. zoning Non-Ag. zoning

New St. err

Coef

Change (%) St. err

0.0089 0.0022 0.0082 0.0021 −8.233 0.0079 0.0025 0.0068 0.0022 −13.298 0.0105 0.0019 0.0099 0.0025 −6.427 0.0068 0.0026 0.0061 0.0018 −11.871

Notes: The results in this table are for a one month change in implicit costs. The standard errors were calculated using the simulation method in Krinsky and Robb (1986).

explicit changes in the costs or revenues for a particular development project, others impact development via non-diversifiable changes in the costs of the investment project. These so-called implicit costs to a development, which are outside of the control of the land developer, can have significant impacts of the timing and type of development project undertaken. In this paper, we focus on a specific type of implicit cost related to land development that arises from increased regulatory stringency, which translates into increased approval times for development projects. This subsequently alters the cost and revenue streams for those development projects. Our hypotheses, based on both theory and unique data from our study region, are that increases in regulationinduced implicit costs will both reduce the probability of a developer initializing a subdivision project and favor smaller subdivision development with lower implicit costs. Given that these smaller developments tend to be located farther away in less regulated exurban areas, the implication is that this heterogeneity in implicit costs has resulted in greater urban sprawl and fragmentation. Using a unique data set on subdivision approval times from an urban fringe county in Maryland, we generate a nonparametric measure of implicit costs based on past approval-time data and use that variable as a proxy for implicit costs in a series of proportional hazard models. The results from our model produce coefficients that are consistent with theory, showing that as implicit costs increase, the probability of starting a development project decreases. Specifically, we find that a 1% increase in average expected approval time results in a decrease in the probability of development by 0.94%, suggesting that the overall impact of implicit costs on the probability of conversion is fairly unit elastic. The results from our model continue to hold even under a series of rigorous robustness checks. While we cannot conclusively rule out the possibility of remaining correlation between unobserved variables and the implicit costs variable, we conclude that the results provide reasonable evidence of the impact of implicit costs. Assuming that the nonparametric, nearest-neighbor variable provides a sufficient proxy for the revealed preference information available to potential developers, this result is significant in that it provides micro-level evidence of the impact of implicit costs on investment decisions. While a number of inter-urban, aggregate studies have shown that expected approval times matter for aggregate housing supply, this is the first paper to demonstrate its impact on micro-level behavioral decisions. The results from our spatial analysis also confirm the predictions from our spatial theoretical model. As the relative advantage, in term of expected approval times and implicit costs, increase for more exurban parcels, the likelihood of development increases in those areas and the responsiveness decreases. These results provide the first empirical evidence of the important role that cost heterogeneities, generated by land use regulation, play in influencing land development outcomes and urban spatial patterns and underscore the importance of supply-side factors that, to-date, have received limited empirical attention.

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

value for the price of housing service for each census tract and time period in our model.19 Summary statistics for our house price variables over all parcels and time periods are given in Table A.1.

Appendix A A.1. House prices In addition to the impact of implicit costs, a land developer is impacted by numerous other factors in making his or her decision to convert raw land into a residential subdivision. Two of the most important factors are the final price of housing, or the price of housing services, and the price of land per acre, which is an input into the housing production function. In this section, we demonstrate our method for developing measures of both the price of housing and price per acre of land for each parcel in our data set. All of the house and land-price data as well as the characteristics of those data, such as the attributes of the house or parcel and its location in the county, were taken from Maryland's state-side transactions database, Maryland Property View. The process of cleaning these data and removing outliers, separating raw land sales from the sales of housing and land combined, and matching these transactions with the larger data set required considerable work. We have excluded the description of this process because of limitations on space, but the description is available upon request. To construct our measure of housing prices, we follow Sieg et al. (2002) and estimate a series of hedonic models that permit us to separate out the pure price of housing services at the census tract level from the quantity index of housing that is determined by physical and lot-specific factors of the house. To do this, we estimate the following housing-price hedonic regression model for each of the 13 years of our observation period: 0

X ji βk þε ji

P ji ¼ ρ j e

35

:

ðA:1Þ

The dependent variable, Pjt, is the real transaction price (in 2000 $) for house i in census tract j, the coefficient ρj is a fixed effect for the census tract in which the house is located, and XjiV and εji are the observable and unobservable attributes for house i, respectively. We control for the physical, lot, and neighborbood-specific attributes of the house by combining our house price data with tax assessor's data for each house. The variables used in each our hedonic regressions are given in Table A.1. Table A.1 Summary statistics for housing transactions: 1995–2007. Variable

Mean

St. dev.

Min.

Max.

Log real house price (2000 $) Travel time to Baltimore Inside of a subdivision Area (acres) Square footage Age (years) New house Structure quality (1–6) Has a garage Has airconditioning Is brick Number of bathrooms Townhouse indicator N = 31,602

12.22 36.92 0.81 1.05 1816.28 19.02 0.21 3.57 0.62 0.84 0.01 1.86 0.16

0.44 6.74 0.39 2.75 751.87 24.49 0.41 0.78 0.49 0.37 0.09 0.67 0.36

10.94 25.35 0.00 0.00 800.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

13.83 64.49 1.00 125.00 9600.00 150.00 1.00 8.00 1.00 1.00 1.00 6.00 1.00

Taking the natural log of both of sides of Eq. (A.1) gives the following price function: 0

lnP ji ¼ lnρ j þ X ji βk þ ε ji ;

A.2. Land prices To proxy for the price of land as an input in the production function of housing, we develop a parcel and time period specific prediction of land price per acre based on a semi-log land price regression using 3770 transactions of raw land over the period of 1995–2007. We control for parcel-level attributes by including variables that proxy for the physical features of the parcels; we control for broad trends in the price per acre of raw land by including a series of fixed effects for the Regional Planning District (RPD) in which the parcel is located. RPDs are agglomerations of the smaller census tracts that are used by the Baltimore Metropolitan Council in evaluating housing and labor markets, evaluating policy, and making recommendations for future interventions. While we would ideally like to include fixed effects at the census tract level, as we did in our models for the price of housing services, it is not possible in the land price regressions as the number of land sales is too small. So, we include the RPD fixed effects and use the variation in the other parcel-level variables within each RPD to form our predictions. To form our yearly parcel-level predictions, we estimate the following land price hedonic regression in each time period: 0

lnPPAri ¼ lnRPDr þ X ri βk þ εri ;

ðB:1Þ

where lnPPAri is the natural log of the real price per acre of land for parcel i in RPD r, lnRPDr is a fixed effect for the RPD in which the parcel is located, and XriV and εri are the observable and unobservable characteristics of the parcels, respectively. The summary statistics for the data used in Eq. (B.1) are shown in Table B.1. Because our land transactions data set includes sales of both raw land (34%) as well as improved lots (66%), we include a fixed effect for whether a parcel was located inside of a previously developed subdivision as well. Table B.1 Summary statistics for land transactions: 1995–2007. Variable

Mean

St. dev.

Min.

Max.

Log real land price (2000 $ per acre) Travel time to Baltimore Inside of a subdivision Area (acres) Distance to primary road Number of buildable lots by zoning Quarter 1 Quarter 2 Quarter 3 Quarter 4 Reg. plan dist. 1 Reg. plan dist. 2 Reg. plan dist. 3 Reg. plan dist. 4 Reg. plan dist. 5 Reg. plan dist. 6 N = 3770

10.54 39.40 0.66 5.32 1.28 38.11 0.22 0.30 0.23 0.25 0.16 0.23 0.13 0.18 0.23 0.07

1.07 7.10 0.47 13.30 1.22 69.93 0.41 0.46 0.42 0.43 0.37 0.42 0.34 0.39 0.42 0.26

6.85 22.92 0.00 0.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

13.24 64.58 1.00 250.00 9.36 799.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

After running the model in Eq. (B.1) for each of our time periods, we use the coefficients from that model to form predictions, for each parcel

ðA:2Þ

which, as is shown in Sieg et al. (2002), can be taken as a pure price function with values of ρj giving the price of housing service for each census tract. Repeating this process for each of our 13 years gives us a

19 This same method of estimating the price of housing services has been applied in numerous other structural models of housing demand and supply (see Klaiber and Phaneuf, 2010; Bayer et al., 2009, and Walsh, 2007, among others).

36

D.H. Wrenn, E.G. Irwin / Regional Science and Urban Economics 51 (2015) 25–36

in our main data set (Zrm), of the price per acre of land using the following equation: 0

d ¼ lnRPD d þZ β c lnPPA rm r rm k :

ðB:2Þ

To form these predictions, we zero out the coefficient for whether a parcel was located inside of a subdivision and use the remaining data for each undeveloped parcel in our data set to develop a prediction for the price per acre of raw land. Coming up with a good measure of raw land prices is notoriously difficult. While it is known that houses are bundles composed of both the physical features of the house as well as the land on which the house is build, it is not easy to separate the two. If the researcher does possess data on land sales, apart from house, as we do, it becomes somewhat easier. However, there still remains the challenge of using past sales as a means of predicting future values. While our method is admittedly imperfect, given the richness of our data set, in terms of being able to control for parcel and subdivision factors, we believe our predictions come fairly close to the actual values that would have prevailed on the market. As a test of our approach, we examined the mean values, by year, of the real price per acre of land broken out by parcels with and without sewer service and outside and inside of the agricultural zoning areas. As expected, the value of parcels with sewer services, which allow for much more dense development, are significantly higher than those without and rise quite steeply over the last part of our study period. On par with what we would expect, the prices for parcels with sewer services approach $80,000 an acre by the end of our observation period. The results and intuition for parcels located outside and inside of agricultural zoning areas provide additional support of our method. References Albouy, D., Graf, W., Kellogg, R., Wolff, H., 2013. Climate amenities, climate change, and American quality of life. NBER Working Paper 18925. Bar-Ilan, A., Strange, W., 1996. Urban development with lags. J. Urban Econ. 39, 87–113. Bayer, P.N., Keohane, N., Timmins, C., 2009. Migration and hedonic valuation: the case of air quality. J. Environ. Econ. Manag. 58, 1–14. Beck, N., Katz, J., Tucker, R., 1998. Taking time seriously: time-series-cross-section analysis with a binary dependent variable. Am. J. Polit. Sci. 42, 1260–1288. Bulan, L., Mayer, C., Somerville, C.T., 2009. Irreversible investment, real options, and competition: evidence from real estate development. J. Urban Econ. 65, 237–251. Cunningham, C., 2006. House price uncertainty, timing of development, and vacant land prices: evidence for real options in Seattle. J. Urban Econ. 59, 1–31.

Cunningham, C., 2007. Growth controls, real options, and land development. Rev. Econ. Stat. 89, 343–358. Glaeser, E.G., Gyourko, J., 2005. Urban decline and durable housing. J. Polit. Econ. 113, 345–375. Glaeser, E.G., Ward, B., 2009. The causes and consequences of land use regulation: evidence from greater Boston. J. Urban Econ. 65, 265–278. Glaeser, E.G., Gyourko, J., Saks, R., 2005. Why is Manhattan so expensive? J. Law Econ. 48, 331–370. Glaeser, E.G., Gyourko, J., Saks, R., 2006. Urban growth and housing supply. J. Econ. Geogr. 6, 71–89. Green, R., Malpezzi, S., Mayo, S., 2005. Metropolitan-specific estimates of the price elasticity of supply of housing, and their sources. Am. Econ. Rev. 2, 334–339. Gyourko, J., Saiz, A., 2006. Construction costs and the supply of housing structure. J. Reg. Sci. 46, 661–680. Irwin, E.G., Bockstael, N., 2002. Interacting agents, spatial externalities and the endogenous evolution of residential land use patterns. J. Econ. Geogr. 2, 31–54. Kalbfleisch, J., Prentice, R., 1980. The Statistical Analysis of Failure Time Data. John Wiley and Sons, New York. Klaiber, H.A., Phaneuf, D., 2010. Valuing open space in a residential sorting model of the twin cities. J. Environ. Econ. Manag. 60, 57–77. Krinsky, I., Robb, L., 1986. On approximating the statistical properties of elasticities. Rev. Econ. Stat. 68, 715–719. Lancaster, T., 1990. The Econometric Analysis of Transition Data. Cambridge University Press, New York, NY. Mayer, C., Somerville, C.T., 2000. Land use regulation and new construction. Reg. Sci. Urban Econ. 30, 639–662. McConnell, V., Walls, M., Kopits, E., 2006. Zoning, TDRs, and the density of development. J. Urban Econ. 59, 440–457. Mills, D., 1981. Growth, speculation, and sprawl in a monocentric city. J. Urban Econ. 10, 201–226. Murphy, A., 2013. A dynamic model of housing supply. Manuscript. Newburn, D., Berck, P., 2006. Modeling suburban and rural-residential development beyond the urban fringe. Land Econ. 82, 481–499. Newburn, D., Berck, P., 2011. Exurban development. J. Environ. Econ. Manag. 62, 323–336. Ortalo-Magne, F., Prat, A., 2007. The political economy of housing supply: homeowners, workers, and voters. Discussion Paper: London School of Economics. Paciorek, A., 2011. Essays on Housing Supply and House Price Volatility. (Ph.D Dissertation). University of Pennsylvania. Pindyck, R., 1993. Investments of uncertain cost. J. Financ. Econ. 34, 53–76. Quigley, J., Raphael, S., 2005. Regulation and the high cost of housing in California. Am. Econ. Rev. 95, 323–328. Sieg, H., Smith, V.K., Banzhaf, H.S., Walsh, R., 2002. Interjurisdictional housing prices in location equilibrium. J. Urban Econ. 52, 131–153. Towe, C., Nickerson, C., Bockstael, N., 2008. An empirical examination of the timing of land conversions in the presence of farmland preservation programs. Am. J. Agric. Econ. 90, 613–626. Walsh, R., 2007. Endogenous open space amenities in a locational equilibrium. J. Urban Econ. 61, 319–344. Wheaton, W., 1982. Urban residential development under perfect foresight. J. Urban Econ. 12, 1–21. Zabel, J., 1992. Estimating fixed and random effects models with selectivity. Econ. Lett. 40, 269–272.