تخمین ادغام شده مکانی با یک برنامه برای تحکیم منطقه مدرسه

This paper develops a spatial merger estimator to explain political integration generally and then applies this method to a wave of school district mergers in the state of Iowa during the 1990s. Our estimator is rooted in the economics of matching and thus accounts for three important features of typical merger protocol: two-sided decision making, multiple potential partners, and spatial interdependence. Rather than simply explaining when a particular region is likely to experience a wave of political integration, our method allows us to explore the factors driving which specific subregional mergers take place. This allows us to explore how those districts that merge choose with which of their neighbors to do so. Our results highlight the importance of state financial incentives for consolidation, economies of scale, diseconomies of scale, and a variety of heterogeneity measures in this particular application. We also demonstrate the power of our estimator, relative to existing estimators, to detect a statistically significant role for heterogeneity factors. While our application is limited to school district consolidation, our method can be adapted to include the salient features of many spatial integration problems.

Economists have made considerable progress in the analysis of matching problems. In some applications, such as in the choice of roommates, there are few restrictions on who can match with whom. In many applications, however, spatial considerations place important restrictions on the set of potential partners. The political integration of contiguous jurisdictions, such as countries or school districts, are examples of such spatial matching problems. The annexation of suburbs by neighboring cities is another prominent example. Similar issues arise when considering mergers of firms for whom geographic location is an important characteristic. Hospitals (see Dranove and White, 1994) and real estate multiple listing services are two examples of industries with recent merger activity and in which the mergers are strongly influenced by firm location. In this paper, we develop a method for analyzing patterns of spatial mergers. To provide an example of the methodology, we examine school district consolidation activity in Iowa in the 1990s. As Fig. 1 shows, the number of school districts in the United States has declined precipitously over the twentieth century, so the application to school district mergers is a historically salient one. The method could, however, be applied in any spatial merger context for which the researcher has access to the complete map of jurisdictional borders or the boundaries of firm-level territories.The theoretical literature on endogenous borders has flourished: Alesina and Spolaore, 1997 and Alesina and Spolaore, 2003, Bolton and Roland (1997), and Persson and Tabellini (2000) have focused on the role of potential cost-savings associated with integration as well as the role of heterogeneity in discouraging integration. There is less empirical work, however, examining why political integration occurs in some cases but not others. One reason for the slow progress in this area is the lack of econometric models of jurisdictional merger decisions, reflecting methodological challenges associated with three standard features of merger protocol. First, mergers must typically be approved by voters in both districts (that is, there is two-sided decision making); standard discrete choice models, such as the logit, are designed for single agent decision making. Second, in addition to deciding whether or not to merge, districts typically have multiple borders and thus must decide with whom to merge. Third, merger decisions are spatially interdependent. That is, if two districts 1 and 2 merge, then the choice set is altered for all districts sharing a border with either 1 or 2. While the bivariate probit model of Poirier (1980) accounts for the first feature and the multinomial logit model accounts for the second feature, we know of no estimators that simultaneously account for all three of these features of merger protocol. These three features are all relevant in the institutional context of school district consolidation; they are likely to be relevant, if in weaker forms, for nearly all spatial merger applications. To overcome these limitations of existing estimators, we first develop an econometric model of discrete choice that accounts for these three key features of the merger protocol. We model this merger environment as a matching game in which jurisdictions choose a partner from the set of adjacent districts, and our approach thus allows for two-sided decision making, multiple potential partners, and spatial interdependence. While existence and uniqueness of equilibrium are not generally guaranteed in such models, we show that under a seemingly reasonable restriction on preferences, which we refer to as symmetry in match quality, a unique stable matching exists. Moreover, this stable matching can be calculated via a simple iterative algorithm. Finally, we develop a simulation-based estimator, which we refer to as a spatial merger estimator, which uses this iterative algorithm in order to calculate the probability of a merger between any two adjacent districts in stable matchings. To illustrate the value of the spatial merger estimator, we then apply this methodology through an analysis of school district mergers in Iowa during the 1990s. Over 50 mergers involving more than 100 districts occurred during this period (see Fig. 2), and, due to these mergers, the number of districts fell from 430 in 1991, the first year included in the analysis, to 371 in 2002, the final year in the analysis. Our findings highlight the role of potential factors in these merger decisions. First, regarding the role of size, small districts are much more likely to merge, suggesting that they benefit from any economies of scale associated with consolidation due to the spreading of fixed costs over more taxpayers. On the other hand, large districts may experience diseconomies of scale. Second, we find that like districts are more likely to merge, suggesting an important role for heterogeneity. We also find an important role for state financial incentives in encouraging these mergers. Finally, we show that our estimator is significantly better than existing methods in terms of detecting the role of heterogeneity in driving merger decisions.The paper proceeds as follows. In Section 2, we describe the methodology and findings of the existing literature. 3 and 4 develop the theoretical and econometric framework, which is then applied to school districts mergers in Iowa in Section 5. Finally, Section 6 concludes.

In this paper, we develop an empirical approach to the study of jurisdictional mergers. This method is rooted in the economics of matching and thus overcomes several methodological problems with existing estimators. In particular, our approach allows for two-sided decision making, multiple potential merger partners for each district, and spatial interdependence in merger decisions. Applying this method to a spate of school district mergers in Iowa during the 1990s, our results demonstrate the importance of state subsidies and the limited role of heterogeneity in explaining the patterns of mergers in Iowa during this time period. In a comparison with existing estimators, we demonstrate the relative power of our estimator to detect a statistically significant role for heterogeneity factors. One caveat is that the results of this analysis, which abstracts from racial heterogeneity, may not generalize to other states and time periods. Iowa has very little racial heterogeneity, and, as noted above, other studies, such as Alesina et al. (2004), have found a strong role for such heterogeneity in terms of predicting the number of school districts within U.S. counties. The methodology we develop, however, could be adapted to consider racial and other sources of heterogeneity. We anticipate that this methodology will be useful in analyzing spatial integration in a variety of applications, particularly those analyzing more recent and ongoing boundary changes, which benefit from the availability of geocoded boundary data.