The effects of moratoria on residential development: evidence from a matching approach.

During the last decade, the state of Maryland was one of the fastest growing states in the United States. As a consequence, the state has implemented an aggressive and comprehensive "smart growth" initiative. One of the most popular of these smart growth policies is the Adequate Public Facility Ordinance (APFO), which has been used in some counties of Maryland since the 1970s. Under these laws, new subdivisions are ostensibly permitted only where there is sufficient capacity in public facilities, such as schools, roads, and public utilities capacity. Local regulators set a quantifiable minimum standard for the level of service of a public facility that must exist for new development to be approved.

An APFO is a spatially explicit growth management tool, in that new development is presumably temporarily denied in specific areas and implicitly redirected to other areas. Surprisingly, despite their extensive use, very little is known about the effects of these policies on new residential development. The purpose of this paper is to shed light on this issue by evaluating the effects of an APFO on new residential development in Howard County, Maryland.

The effectiveness of land use controls has been the subject of only a modest amount of literature over the last two decades. The early empirical literature (surveyed in Fischel 1990) on the efficiency of growth controls presumed that the motivation for the growth controls was to restrict supply to raise prices for existing house owners. In this literature, growth controls were deemed inefficient, by definition, and empirical evidence of rising housing prices constituted evidence of their effectiveness but also their inefficiency.

More recent literature acknowledged that rising housing prices are not, in and of themselves, evidence of inefficiency. As Engle, Navarro, and Carson (1992) point out, if there are amenity values associated with growth controls, then demand for houses in the higher-amenity regions will shift out, causing rents to rise. Thus, rather than distorting the market, growth controls could be an attempt to correct for externalities. Higher rents in areas of growth controls could be the result of either rent-seeking behavior by owners of developed land to decrease supply (Brueckner 1995; Helsley and Strange 1995; and Brueckner and Lai 1996) or attempts by local governments to internalize congestion and other externalities, with resulting increased local amenities and therefore increased demand (Brueckner 1990; Engle, Navarro, and Carson 1992; Helsley and Strange 1995; Sakashita 1995). Contemporary theoretical work has investigated the distributional effects of different types of growth policies (Bento, Franco, and Kaffine 2006).

The key econometric difficulty in this literature results from the fact that growth controls emerge in a nonrandom fashion throughout the landscape, which is a classic selection problem. Therefore studies that treat growth controls as exogenous are unable to measure the causal effects of these policies. In addition, measuring the effects on housing prices is an indirect measurement; in this article, we directly measure the impact on new residential development activity.

We overcome this selection problem by using matching methods, first proposed by Rosenbaum and Rubin (1983). Matching methods represent a nonparametric alternative to linear regressions. The logic of matching is rather simple. First, we match policy areas based on the predicted probability or propensity, of being under a moratorium, which is a function of their observed characteristics. Second, once we have the distribution of estimated propensity scores of policy areas that are under moratoria, the treatment group, and policy areas that are not, the control group, we compare the two densities and measure the extent of their differences. The difference represents the impact of the moratorium on new residential development or the average treatment effect on the treated observations, which is our test statistic.

We illustrate this methodology with a unique dataset for Howard County, Maryland, where an APFO has been in effect since 1993. We evaluate the effects of this policy on new residential development in the four years following its enactment.

Methodological Framework

The key problem with measuring the effects of APFOs on new residential development is that not all policy areas have the same likelihood of being under a moratorium. In fact, one would expect that faster growing policy areas as well as policy areas that are close to reaching capacity for one of the public facilities that is being regulated (e.g., roads or schools) are more likely to be under moratoria. This results in a classic nonrandom treatment assignment, and as a consequence, traditional regression analysis may not capture the true effects of the policy on residential development. We overcome this problem with matching methods.

In this study we utilize a class of estimators called propensity score-matching estimators, first suggested by Rosenbaum and Rubin (1983) and now quite prevalent in the literature. This is especially true in labor economics where the evaluation of job training programs is fraught with nonrandom selection issues (e.g., Dehejia and Wahba 2002; Lechner 2002; Smith and Todd 2005a) and the approach has started to make its way into the environmental and agricultural economics literature (e.g., List et al. 2003; Lynch, Gray, and Geoghegan 2007). We follow the standard matching procedure described in detail in classic references such as Heckman and Robb (1986), Heckman, Ichimura, and Todd (1997), and Heckman et al. (1998). In addition, we implement small sample methods suggested by Frolich's (2004) Monte Carlo analysis.

Let [Y.sub.1] be the potential outcome in the "treated" state, which is the number of new residential units developed in the policy area that adopted a moratorium and [Y.sub.0] the potential outcome that would have happened in these policy areas had they not adopted a moratorium. We call these potential outcomes because we observe only one of ([Y.sub.1], [Y.sub.0]) for each policy area. Let D = 1 indicate a policy area that adopted the moratorium and D = 0 indicate a policy area that did not. Finally, let X be a vector of observed covariates affecting both the choice of adoption and outcomes. In the next section, we discuss each of these covariates in great detail. These include, for example, the rate of residential growth of the policy area and the level of congestion of the public facility.

Our parameter of interest--the impact of moratoria on new residential development measured as the number of new housing units constructed--is the mean effect of being in a policy area that has a moratorium versus an observationally equivalent policy area, as measured by X, that it is not under a moratorium. Formally, the parameter of interest is:

(1) [[DELTA].sup.TT] = E([Y.sub.1] - [Y.sub.0]|D = 1)

where [[DELTA].sup.TT] denotes the average treatment effect on the treated observations.

The matching method consists of finding a "surrogate" for [Y.sub.0], since we do not observe [Y.sub.0] for this treated observation (i.e., D = 1). The task of propensity score estimators is to define an estimator for E([Y.sub.0] | D = 1) using an appropriate subset of the D = 0 data. Matching estimators pair each treated observation with one or more observationally similar nontreated observations, using the conditioning variables, X, to identify the similarity. This procedure is justified if it can be argued that conditional on these X's, outcomes are independent of the selection process. Rosenbaum and Rubin (1983) proved this independence condition holds conditional on the propensity score P(X) as well, which leads to the propensity score matching method.

The steps to estimate the model are: (a) estimate a probit model of moratoria adoption, and then using the estimated coefficients, predict the probability of the moratorium adoption for each observation, which is the propensity score, P(X); (b) divide the data into the treatment group (the policy areas that were in fact under moratoria) and the control group (the policy areas that were not under moratoria but had similar characteristics to the areas that are under moratoria), using the propensity scores; (c) estimate a counterfactual for each treated observation ([Y.sub.1] |D = 1, P[X]) based on ([Y.sub.0] | D = 0, P[X]) using the Epanechnikov kernel as suggested by Frolich (2004). This conditional mean difference, E([Y.sub.1] - [Y.sub.0] | D = 1, P[X]), measures the impacts of the moratoria on new residential development and is called the average treatment on the treated, [[DELTA].sup.TT], from equation (1).

The matching estimator has two primary advantages over traditional estimators such as least squares. First, a traditional regression approach relies on a functional form assumption to construct a relevant counterfactual for each treated observation, which is troubling in areas of sparse data. In a matching procedure, all treated observations that do not have comparable observations in the control group, are dropped. This phenomenon is referred to as a failure of the common support. Second, the kernel-weighted counterfactual provides a nonparametric estimate of the mean impact. Kernel weights allow untreated observations close, in propensity score, to their treated counterparts to be weighted higher than observations at more distant propensity scores when constructing counterfactuals for each treated observation. These advantages minimize the impact of functional form restrictions present in traditional regression estimators.

Dataset and Overview of the Trends in Moratoria Adoption

To implement the analysis, we compiled the most detailed data available on school district boundaries, moratoria designations for elementary schools in 1994, new residential development, and other relevant determinants of the adoption of moratoria and residential development in Howard County, Maryland. This section describes the data sources and presents basic summary statistics.

School District Boundaries, Moratorium, and Other School-Related Data

There are 32 school districts in Howard County. Information regarding school district boundaries and designations of elementary school moratoria in 1993 were obtained from Howard County Planning Office. For each of the school districts, we have also collected information on the capacity of the different schools and percentage of new enrollees and graduates from elementary schools. We use the percentage of overcapacity for the own school district as well as the percentage of overcapacity for the nearest neighboring school district in the model. (1)

Residential Development Data

We supplement the data on school districts and moratoria designations, with data on new residential development between 1994 and 1997 from the Maryland Property View dataset and the Howard County Tax and Assessment data. These data are disaggregated at the parcel level. To capture development pressure three key variables were constructed for each observation: the number of potential lots from undeveloped land based on zoning laws; the percentage of potential lots subdivided in the previous 3 years; and the percentage of subdivided lots that became sold homes in the last year. The subdivision data were obtained from the actual subdivision database used by the county to track subdivisions from the planning stage to approval.

Census Data, Community Characteristics, and Other Determinants of Development

We have matched the school district data and the parcel-level data on residential development with several census variables measured at the census block. This process consisted of overlapping the census blocks with the school district maps. Whenever a census block belonged to two school districts, we assigned the acreage of the census block that corresponds to each district and allocated the census variables accordingly.

We used the census data to create several variables. These variables aim to capture the population composition as well as the average characteristics of the housing stock. These include: percentage of nonwhite, percentage of children less than five years old, percentage of household income more than 100K, percentage of college educated and the percentage of housing stock valued more than 300K. Finally, we calculated the distances of the centroids of each census block to Washington, D.C. and Baltimore, MD, the two major employment centers for the county.

Table 1 presents a short description of the different variables. Because of the different spatial units of our datasets--school districts, parcels, and census block--we have chosen the final unit of observation for the study to be the census block, as this will capture all the relevant spatial variation on key variables within school districts.

Trends in Moratoria Adoption

Figure 1 presents a map of the school district boundaries highlighting those that were under moratoria in 1994. Of the 32 school districts, 8 school districts were under moratoria. Interestingly, there appears to be a spatial pattern in the adoption of moratoria, with most of these school districts located in the eastern part of Howard County.

Table 2 presents summary statistics for the full sample and a breakdown of census blocks belonging to school districts that were under moratoria in 1994 and those that were not. When comparing census blocks that belong to school districts under moratoria against those that do not, we notice the following important trends. Not surprisingly, the percentage of school overcapacity in treated census blocks (those under moratoria) is distinctly higher than the untreated census blocks (those not under moriatoria): 23% versus 9%, as is the percentage of school overcapacity in neighboring school district: 11% versus 6%. Second, it appears that the untreated census blocks, are wealthier--measured both by the value of existing homes and the percentage of high-income households.

Results

We begin our discussion of results by reexamining the characteristics of the treated versus untreated census blocks after the matching to illustrate the advantages of the matching techniques. We then display the propensity scores in a map to visualize the matching process. Finally, we present the average treatment effects [[DELTA].sup.TT]. We consider the effects of the 1994 moratoria on 1994-1997 new residential development.

Summary Statistics After Matching

By constructing a counter-factual that looks identical to the treated in observable covariates, the matching approach essentially eliminates "outliers" from the original dataset. Table 2 illustrates this point clearly. First, comparing the "treated" versus the "matched treated" columns, we note that the number of treated observations drop from 42 to 31. That is, 11 observations were considered "off support," as there were no untreated observations in the control group with "close enough" propensity scores to these 11 observations. Second, we note that the differences in some of the variables in the treated and untreated groups are reduced substantially. For example, the differences in the percent of school capacity filled and the percent of nearest neighbor's school capacity filled are now much smaller, illustrating that the matching method removes from the dataset treated observations that do not have comparable untreated matches.

[FIGURE 1 OMITTED]

Spatial Distribution of Propensity Scores

Figure 2 displays the map of Howard County and the propensity scores for the different census blocks. The figure reveals some interesting spatial patterns. First, most of the matched census blocks--that is untreated census blocks with relatively higher probability of being under moratoria--seem to be located in the eastern part of the county and right next to census blocks that were treated, so neighboring census blocks have similar characteristics for predicting the probability of adoption of a moratorium. Second, of the 238 census blocks, 157 had a probability greater that 0.01 of being treated, while only 86 have a probability greater than 0.26.

[FIGURE 2 OMITTED]

Effects on New Residential Development

Table 3 presents the results from the propensity score matching model. We evaluate the effects of the 1994 moratoria policy on new residential development in the year of enactment and three subsequent years. The table presents the unmatched mean differences between treated and controls as well as the mean differences after matching, using the Epanechnikov kernel-matching estimator ("Epan" in table 3). Bootstrapped standard errors were calculated and all results are derived from propensity score regressions that pass strict regression based balancing tests as described in Smith and Todd (2005a).

The table highlights the following key results. First, the 1994 moratorium does indeed reduce new residential development. Second, the effects are significant for the two years immediately after the policy is enacted. In 1994, the effect of the policy is to reduce new home construction by five units in the census blocks that were treated, despite the fact that all these census blocks have a similar stock of approved subdivisions. This implies a total county reduction of 155 units or approximately 7% of the projected growth for 1994 based on the county's General Plan. The effect of the policy is even stronger one-year after, perhaps a result of the supply restriction induced by the moratoria in the previous year, i.e., there are no new subdivisions approvals from which homes can be built. In 1995, the effect of the policy is to reduce new development by approximately 202 units in the county, corresponding to 9%. After two years, the policy no longer produces any statistically significant effect.

Conclusions

This paper applied modern matching techniques to evaluate the effects of APFOs on new residential development in Howard County, Maryland. Our results suggest that the policy indeed slowed new development in the two years after it has been enacted. The total reduction in new development during this two-year period corresponded to approximately 355 new housing units, 8 percent of the projected county growth for these two years.

We thank Nancy Bockstael for providing some of the data used, Jeff Bronow and Sharon Melis from the Howard County Planning Department for additional data and policy information, and Joel Landry for outstanding research assistance.

References

Bento, A.M., S.F. Franco, and D. Kaffine. 2006. "The Efficiency and Distributional Impacts of Alternative Anti-Sprawl Policies." Journal of Urban Economics 59:121-41.

Brueckner, J.K. 1990. "Growth Controls and Land Values in an Open City." Land Economics 66:237-48.

Brueckner, J.K. 1995. "Strategic Control of Growth in a System of Cities." Journal of Public Economics 57:393-416.

Brueckner, J.K., and F.C. Lai. 1996. "Urban Growth Controls with Resident Landowners." Regional Science and Urban Economics 26:125-43.

Engle, R., P. Navarro, and R. Carson. 1992. "On the Theory of Growth Controls." Journal of Urban Economics 32:269-83.

Dehejia, R.H., and S. Wahba. 2002. "Propensity Score-Matching Methods for Nonexperimental Causal Studies." The Review of Economics and Statistics 84:151-61.

Fischel, W. A. 1990. Do Growth Controls Matter: A Review of Empirical Evidence on the Effectiveness and Efficiency of Local Government Land Use Regulation. Cambridge, MA: Lincoln Institute of Land Policy.

Frolich, M. 2004. "Finite-Sample Properties of Propensity-Score Matching and Weighting Estimators." The Review of Economics and Statistics 86:77-90.

Heckman, J.J., H. Ichimura, J.A. Smith, and P.E. Todd. 1998. "Characterizing Selection Bias Using Experimental Data." Econometrica 66:1017-98.

Heckman, J.J., H. Ichimura, and P. Todd. 1997. "Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme." The Review of Economic Studies 64:605-54.

Heckman, J.J., and R. Robb. 1986. "Alternative Method for Solving the Problem of Selection Bias in Evaluating the Impact of Treatments on Outcomes." In H. Wainer, ed. Drawing Inferences from Self-Selected Samples. Berlin, Germany: Springer-Verlag, pp. 63-107.

Helsley, R.W., and W.C. Strange. 1995. "Strategic Growth Controls." Regional Science and Urban Economics 25:435-60.

Lechner, M. 2002. "Program Heterogeneity and Propensity Score Matching: An Application to the Evaluation of Active Labor Market Policies." The Review of Economics and Statistics 84:205-20.

List, J., D.L. Millimet, P.G. Fredriksson, and W.W. McHone. 2003. "Effects of Environmental Regulation on Manufacturing Plant Births: Evidence from a Propensity Score Matching Estimator." The Review of Economics and Statistics 85:944-52.

Lynch, L., W. Gray, and J. Geoghegan. 2007. "Are Farmland Preservation Programs Easement Restrictions Capitalized into Farmland Prices? What Can a Propensity Score Matching Analysis Tell Us?" Review of Agricultural Economics 29 (3):502-9.

McMillen, D.P., and J.F McDonald. 2002. "Land Values in a Newly Zoned City." The Review of Economics and Statistics 84:62-72.

Rosenbaum, P.R., and D.B. Rubin. 1983. "The Central Role of the Propensity Score in Observational Studies for Causal Effects." Biometrika 70:41-55.

Sakashita, N. 1995. "An Economic Theory of Urban Growth Control." Regional Science and Urban Economics 25:427-34.

Smith, J.A., and P.E. Todd. 2005a. "Does Matching Overcome LaLonde's Critique of Nonexperimental Estimators?" Journal of Econometrics 125:305-53.

--. 2005b. "Rejoinder." Journal of Econometrics 125:365-75.

(1) We scale the neighboring school capacity using the distance in kilometers between the centroid of the observation and the actual address of the neighboring school.

Antonio Bento is Associate Professor in the Department of Applied Economics and Management, Cornell University, Charles Towe is Ph.D. Candidate in the Department of Agricultural and Resource Economics, University of Maryland and Jacqueline Geoghegan is Associate Professor in the Department of Economics, Clark University.

This article was presented in a principal paper session at the AAEA annual meeting (Portland, OR, July 2007). The articles in these sessions are not subjected to the journal's standard refereeing process. Table 1. Variable Definitions Variable Short Description Acres Acreage of census block/elementary

school district distBA Distance to Baltimore in km distDC Distance to DC in km pctSchFull Percentage of school capacity

filled--100 pctSchFullNeigh Percentage of nearest neighbor's

school capacity filled--100

(normalized by distance to the

nearest school) pctEntrantsYr Percentage of new enrollees in

elementary school pctWithDrawYr Percentage of graduates from

elementary school existingHomePr Median sales price of existing

homes/1000 newHomePremium Percentage premium for new home nonWhite Percentage non white ageLessThan5 Percentage of population less than

5 years of age highIncome Percentage of household incomes

> 100k collegeEduc Percentage college educated expHouse Percentage of housing stock

valued >300k potentialSubdivUnits Number of potential lots from

undeveloped land based on

zoning regulations recentSubdivRate Percentage of potential lots

subdivided in the previous 3 years pctOfSubdivBlt Percentage of subdivided lots which

became sold homes in the last year Table 2. Summary Statistics (Before Matching and After Matching)

Full Sample Treated

Mean Std Dev. Mean Std Dev. acres 651.472 1205.021 359.713 289.913 distBA 23.875 5.772 23.985 4.406 distDC 38.459 5.162 35.666 7.018 pctSchFull 12.386 25.315 22.771 17.379 pctSchFullNeigh 6.83 12.201 10.642 10.084 pctEntrantsYr 8.053 3.652 8.029 3.149 pctWithDrawYr 6.778 3.811 8.048 3.351 existingHomcPr 276.495 373.588 260.463 371.031 newHomePremium 19.979 46.612 19.520 61.986 nonWhite 19.844 11.826 18.894 8.573 ageLessThan5 9.055 2.375 10.134 2.553 highlncome 22.651 13.782 18.281 12.647 collegeEduc 72.735 14.638 70.823 13.847 expHouse 14.212 18.303 10.413 14.329 potentialSubdivUnits 321.960 432.378 356.261 400.237 recentSubdivRate 4.589 10.143 5.995 14.119 pctOfSubdivBlt 56.228 298.391 11.512 32.370 No. of observations 198 42

Untreated Matched Treated

Mean Std Dev. Mean Std Dev. acres 739.767 1354.845 351.352 313.411 distBA 23.841 6.077 22.878 4.527 distDC 39.304 4.122 37.681 7.188 pctSchFull 9.243 26.519 24.775 17.315 pctSchFullNeigh 5.677 12.576 10.904 9.835 pctEntrantsYr 8.059 3.800 7.455 3.006 pctWithDrawYr 6.394 3.869 6.894 2.818 existingHomcPr 281.347 375.443 296.882 448.050 newHomePremium 20.118 41.102 26.551 74.454 nonWhite 20.104 12.660 19.161 9.583 ageLessThan5 8.728 2.226 9.525 2.645 highlncome 23.974 13.876 20.278 12.58 collegeEduc 73.313 14.864 72.480 13.003 expHouse 15.362 19.239 10.323 12.522 potentialSubdivUnits 311.579 442.377 284.581 303.809 recentSubdivRate 4.164 8.604 5.320 14.904 pctOfSubdivBlt 69.760 339.198 12.858 36.639 No. of observations 156 31

Matched Untreated

Mean Std Dev. acres 360.597 366.092 distBA 22.549 3.533 distDC 38.561 4.057 pctSchFull 27.728 13.567 pctSchFullNeigh 8.271 15.476 pctEntrantsYr 7.629 3.423 pctWithDrawYr 6.871 3.628 existingHomcPr 310.585 487.726 newHomePremium 30.087 58.957 nonWhite 18.898 8.207 ageLessThan5 9.508 2.157 highlncome 211.201 11.898 collegeEduc 73.371 14.335 expHouse 10.444 13.330 potentialSubdivUnits 318.179 298.354 recentSubdivRate 5.171 9.968 pctOfSubdivBlt 8.647 71.784 No. of observations 31 Table 3. Propensity Score Matching Results

On Support Off Support Outcome-Number of Houses

Built 1994 # Control 152 0 # Treated 31 11 Outcome-Number of Houses

Built 1995 # Control 152 0 # Treated 31 11 Outcome-Number of Houses

Built 1996 # Control 152 0 # Treated 31 11 Outcome-Number of Houses

Built 1997 # Control 152 0 # Treated 31 13

Differences in Outcome Means

Unmatched Epan kernel Outcome-Number of Houses

Built 1994 # Control 11.95 7.74 # Treated 6.23 2.74 Outcome-Number of Houses [[DELTA].sub. -500 *

Built 1995 TT] - 5.71 # Control 12.05 9.28 # Treated 6.06 2.74 Outcome-Number of Houses [[DELTA].sub. -6.54 *

Built 1996 TT] - 5.98 # Control 9.92 4.27 # Treated 6.04 4.25 Outcome-Number of Houses [[DELTA].sub. -0.02

Built 1997 TT] - 3.88 # Control 7.44 5.96 # Treated 6.78 4.60

[[DELTA].sub. -1.36

TT] - 0.66 Note: Significance levels: * :5%. The bandwidths are 0.09 for 1994, 0.41 for 1995, 0.16 for 1996. 0.02 for 1997. [[DELTA].sub.TT] denotes average treatment on treated.