V. Empirical Results
The heterogeneity in principals’ skills across geography is evaluated first and is
shown in table 1. To illustrate the differences across geographic strata, the sum of
squares in years teaching and previous experience is calculated and recalculated after
differing the data along successively narrower levels of geography. The descriptive
statistics in table 1 indicate school principals become more homogeneous as the level of
geography narrows, although substantial variation remains within school districts. After
differencing the data by the state mean, the variation in each skill falls by just under ten
percent relative to the level calculated for the undifferenced data. Although minimum
qualification standards for principals are set primarily by the states, over ninety percent of
the total variation in both skills originates within-state. Mean differences across
metropolitan areas account for approximately five percent of the residual variation in the
two skills. Further differencing the variables by school district cumulatively decreases
variation in teaching experience by nineteen percent and previous principal experience by
twenty-two percent. Approximately eighty percent of the total variation in the two skills
exists within the school districts, indicating the degree of possible labor mismatch in the
market for principals.
Regression models are used to test for the determinants of the skills mismatch.
Table 2 presents three models in which the standard deviation in teaching experience
within school districts is regressed on metropolitan area and school district
characteristics. Models estimating the heterogeneity in previous principal experience
were found statistically insignificant and are not shown.6 Model I is distinguished from
II in table 2 by the covariate measuring district-wide mean teaching experience. Model
6 Models estimating composite measures of skills were also insignificant.