Class Size and Sorting in Market Equilibrium: Theory and Evidence

Joint with: Eric Verhoogen

This paper examines how schools choose class size and how households sort in response to those choices. Focusing on the highly liberalized Chilean education market, we develop a model in which schools are heterogeneous in an underlying productivity parameter, class size is a component of school quality, a class-size cap applies to some schools, and households are heterogeneous in income and hence willingness to pay for quality. The model offers an explanation for two distinct empirical patterns: (i) There is an inverted-U relation between class size and household income in equilibrium, which will tend to bias cross-sectional estimates of the effect of class size on

student performance. (ii) Some schools at the class size cap adjust prices and/or enrollments to avoid adding another classroom, which produces stacking at enrollments that are multiples of the class size cap. This results in discontinuities in the relationship between enrollment and

students’ income at those points, violating the assumptions underlying regression-discontinuity (RD) research designs. An implication is that RD approaches should not be applied in settings in which parents have substantial school choice and schools are free to set prices and influence their enrollments.

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