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Complementarity and Aggregate Implications of Assortative Matching: A Nonparametric Analysis

  • Bryan S. Graham
  • Guido W. Imbens
  • Geert Ridder

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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14860.

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Date of creation: Apr 2009
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Publication status: published as Bryan S. Graham & Guido W. Imbens & Geert Ridder, 2014. "Complementarity and aggregate implications of assortative matching: A nonparametric analysis," Quantitative Economics, Econometric Society, vol. 5, pages 29-66, 03.
Handle: RePEc:nbr:nberwo:14860
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  12. Bhattacharya, Debopam, 2009. "Inferring Optimal Peer Assignment From Experimental Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 486-500.
  13. Manski, Charles F, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 531-42, July.
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