To Consolidate or Not to Consolidate, That Is the Question: Optimal School Size and Teacher Incentive Contracts (2010)

INTRODUCTION Over the last few decades the US school system has received much attention from researchers and administrators on a variety of issues such as incentive pay and accountability (Holmstrom & Milgrom, 1991; Kane & Staiger, 2002); school (Lee & Smith, 1997; Umphrey, 2002); school consolidations (Antonucci, 1999); curriculum decisions (Goodlad & Su, 1992); education accessibility (Dunn, 1992); and overall school reform (Allen & Dale, 1995). The No Child Left Behind Act of 2001 motivates further research in to these areas of study. We bring together several facets of these discussions by examining the cross implications of school and consolidations with incentive teacher pay and accountability in the classroom. A general trend over the past century, and the main motivation for our inquiry, has been the wide-scale consolidation of elementary and secondary schools and districts. Enrollment per school has substantially increased since 1900, from 62.44 to 506.29 while the number of districts has correspondingly decreased; see Table 1. While consolidation of disparate community schools is frequently justified by appealing to economies of scale, it has precipitated many difficulties. One such difficulty is the loss of teacher and curriculum control suffered by formerly localized school administrators and parents, losses that can be attributed to the increasing physical and bureaucratic distance between teachers, administrators, and parents. To address these difficulties, various accountability schemes have been implemented in recent years, including incentive pay. The general premise of incentive-pay is straightforward: replace the eroded control structure with a formal incentive structure that optimally aligns teacher effort with administrative objectives. Unfortunately, even within incentive pay paradigms, any number of pervasive inefficiencies can arise when designing and implementing an incentive contract. For this reason, it is crucial that the design phase be guided by sound theory that is flexible enough to incorporate the relevant institutional features of the education system. Designing just such a framework and its implication on school is the focus of this paper. Cutshall (2003) describes a number of recent political events that suggest a growing concern over the negative effects of consolidated schools, and thus a general call to open a serious dialogue about school sizes. In particular, there is an important interaction between incentive contracts and school size. Bard, Gardener, and Wieland (2005) provide an excellent review on the history of school consolidation in the US, issues, solutions, and the literature related to school (see also Barker and Gump (1964), Driscoll, Halcoussis, and Svorny (2003), Garbarino (1980), and Lee and Smith (1997)). One conclusion of Bard, Gardener, and Wieland is that the estimates of optimal school size range dramatically depending on researcher and time period. Indeed, their further conclusion that the literature lacks a cohesive model for the determination of school partly motivates this work. While some of this work is based on solid statistical analyses, others are case studies (i.e., Kirkpatrick (1998) notes that one of the poorest of New York City's sub-districts moved from among the worst rated to among the best by re-creating schools with 200-300 students each). We add to this discussion by presenting a model of school that incorporates the positive effects of incentive contracts and inspection (possibly by parents). The remainder of the paper is organized into five sections. In the following sections of this paper, we present the context and background of the administrative realities surrounding decisions about incentive pay and school size, our principal-agent model of incentive contracting with an auditor, and finally an example that shows school based on reasonable numerical estimates of our model. …