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.