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Complementarity and Aggregate Implications of Assortative Matching: A Nonparametric Analysis

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

Abstract

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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Bibliographic Info

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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Handle: RePEc:nbr:nberwo:14860

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  6. Rajeev H. Dehejia, 2002. "Program evaluation as a decision problem," Discussion Papers 0102-23, Columbia University, Department of Economics.
  7. Susan Athey & Scott Stern, 1998. "An Empirical Framework for Testing Theories About Complimentarity in Organizational Design," NBER Working Papers 6600, National Bureau of Economic Research, Inc.
  8. Patrick Legros & Andrew F. Newman, 2003. "Beauty is a Beast, Frog is a Prince: Assortative Matching with Nontransferabilities," Economics Working Papers 0030, Institute for Advanced Study, School of Social Science.
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Cited by:
  1. Debopam Bhattacharya & Pascaline Dupas, 2008. "Inferring Welfare Maximizing Treatment Assignment under Budget Constraints," NBER Working Papers 14447, National Bureau of Economic Research, Inc.
  2. Scott E. Carrell & Bruce I. Sacerdote & James E. West, 2011. "From Natural Variation to Optimal Policy? The Lucas Critique Meets Peer Effects," NBER Working Papers 16865, National Bureau of Economic Research, Inc.
  3. Imbens, Guido & Wooldridge, Jeffrey M., 2009. "Recent Developments in the Econometrics of Program Evaluation," Scholarly Articles 3043416, Harvard University Department of Economics.
  4. Oosterbeek, H. & Ewijk, R. van, 2010. "Gender peer effects in university: Evidence from a randomized experiment," Working Papers 35, Top Institute for Evidence Based Education Research.
  5. Allcott, Hunt, 2011. "Social norms and energy conservation," Journal of Public Economics, Elsevier, vol. 95(9), pages 1082-1095.
  6. Frölich, Markus & Michaelowa, Katharina, 2011. "Peer effects and textbooks in African primary education," Labour Economics, Elsevier, vol. 18(4), pages 474-486, August.

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