future search costs for the school district. This possibility also exists for an
underqualified principal.
The expected skills mismatch, D, is determined by the function (2) D = f (t, x, z)
where t is the number of discrete time periods of search, x is a vector of labor market
characteristics and z represents characteristics of the individual school district. Search
time, t, is the school district’s only choice variable. If the school district evaluates a
random sample from the skills distribution in each period, a larger t would imply an
increased probability of observing a potential school administrator whose skills fall
within an arbitrarily small D.
The labor market variables in x, primarily urban size and density, can be
considered endowments to the district. At a given period, a greater density or total urban
population will produce a larger number of potential matches, resulting in a smaller
predicted skills mismatch, a smaller D (see Wheeler, 2001). Differences in D within an
individual school district may partially reflect differences in the criteria the school district
uses to hire administrators for its schools. The school district characteristics in z measure
within-district heterogeneity and are included to capture possible variation in qk in
equation 1.
The hiring process involves trading off expected mismatch and search costs.
Given an optimal search effort by the school district, characteristics in the local labor
market will partially determine the quality of the matches, which can be measured by the
variation in labor skills among the hired principals.