Complementarity and Aggregate Implications of Assortative Matching: A Nonparametric Analysis

By Bryan S. Graham, Guido W. Imbens, Geert Ridder. 2014

75 citations recorded by the source corpus.

This paper presents methods for evaluating the effects of reallocating an indivisible input across production units, taking into account resource constraints by keeping the marginal distribution of the input fixed. When the 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. We focus on the effects of reallocating one input, while holding the assignment of another, potentially complementary, input fixed. We introduce 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. We also characterize the effects of local (relative to the status quo) reallocations. For estimation we use a two-step approach. In the first step we nonparametrically estimate the production function. In the second step we average the estimated production function over the distribution of inputs induced by the new assignment rule. These methods build upon the partial mean literature, but require extensions involving boundary issues. We derive the large sample properties of our proposed estimators and assess their small sample properties via a limited set of Monte Carlo experiments.

Subfields: Economics and Econometrics, Education, Management Science and Operations Research

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Citations in the corpus

Inferring Optimal Peer Assignment From Experimental Data (2009, methodology): “Graham et al. (2005) compared a fixed set of matching rules between two continuous inputs with fixed marginals.”
A Distributional Framework for Matched Employer Employee Data (2019, background): “In an additively separable economy between workers and firms, such as under the AKM model, there should be no effect of the reallocation on mean log-earnings (e.g., Graham et al., 2014).”
From Natural Variation to Optimal Policy? The Importance of Endogenous Peer Group Formation (2013, unknown): “Our assignment algorithm uses nonlinear peer effects estimates from the historical pre-treatment data, in which students were randomly assigned to peer groups.”