Class size and sorting in market equilibrium: Theory and evidence

This paper examines how schools choose class size and how households sort in response to thosechoices. Focusing on the highly liberalized Chilean education market, we develop a model inwhich schools are heterogeneous in an underlying productivity parameter, class size is a componentof school quality, households are heterogeneous in income and hence willingness to pay forschool quality, and schools are subject to a class-size cap. The model offers an explanation fortwo distinct empirical patterns observed among private schools that accept government vouchers:(i) There is an inverted-U relationship 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 (or enrollments) to avoid adding anotherclassroom, which produces stacking at enrollments that are multiples of the class size cap. Thisgenerates discontinuities in the relationship between enrollment and household characteristicsat those points, violating the assumptions underlying regression-discontinuity (RD) research designs.This result suggests that caution is warranted in applying the RD approach in settings inwhich parents have substantial school choice and schools are free to set prices and influence theirenrollments.