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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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  1. 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.
  2. 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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  8. Card, David & Krueger, Alan B, 1992. "Does School Quality Matter? Returns to Education and the Characteristics of Public Schools in the United States," Journal of Political Economy, University of Chicago Press, vol. 100(1), pages 1-40, February.
  9. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
  10. Rajeev H. Dehejia, 2002. "Program evaluation as a decision problem," Discussion Papers 0102-23, Columbia University, Department of Economics.
  11. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 1-21, June.
  12. William A. Brock & Steven N. Durlauf, 2000. "Interactions-Based Models," Working Papers 00-05-028, Santa Fe Institute.
  13. Susan Athey & Guido Imbens, 2003. "Identification and Inference in Nonlinear Difference-in-Differences Models," Levine's Working Paper Archive 506439000000000079, David K. Levine.
  14. 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.
  15. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
  16. Manski, C.F., 1989. "Nonparametric Bounds On Treatment Effects," Working papers 8909, Wisconsin Madison - Social Systems.
  17. Bryan S. Graham, 2008. "Identifying Social Interactions Through Conditional Variance Restrictions," Econometrica, Econometric Society, vol. 76(3), pages 643-660, 05.
  18. Heckman, James J & Smith, Jeffrey, 1997. "Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 487-535, October.
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