Complementarity and Aggregate Implications of Assortative Matching: A Nonparametric Analysis∗

This paper presents methods for evaluating the effects of reallocating an indivisible input across production units. When production technology is nonseparable such reallocations, although leaving the marginal distribution of the reallocated input unchanged by construction, may nonetheless alter average output. Examples include reallocations of teachers across classrooms composed of students of varying mean ability and altering assignment mechanisms for college roommates in the presence of social interactions. We focus on the effects of reallocating one input while holding the assignment of another, potentially complementary input, fixed. We present a class of such reallocations – correlated matching rules – that includes the status quo allocation, a random allocation, and both the perfect positive and negative assortative matching allocations as special cases. Our econometric approach involves first nonparametrically estimating the production function and then averaging this function over the distribution of inputs induced by the new assignment rule. Formally our methods build upon the partial mean literature (e.g., Newey 1994, Linton and Nielsen 1995). We derive the large sample properties of our proposed estimators and assess their small sample properties via a limited set of Monte Carlo experiments. An application, assessing the effects of spousal sorting on child education (e.g., Kremer 1996), concretely illustrates our methods. JEL Classification: C14, C21, C52