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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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Cited by:
  1. Robert W. Fairlie & Florian Hoffmann & Philip Oreopoulos, 2011. "A Community College Instructor Like Me: Race and Ethnicity Interactions in the Classroom," NBER Working Papers 17381, National Bureau of Economic Research, Inc.
  2. 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.
  3. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 168-196.
  4. Guido Imbens & Jeffrey Wooldridge, 2008. "Recent developments in the econometrics of program evaluation," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP24/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
  6. 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.
  7. Antonio Chiccone & Walter Garcia-Fontes, 2014. "Gender Peer Effects in School, a Birth Cohort Approach," Working Papers 2014-07, FEDEA.
  8. Frölich, Markus & Michaelowa, Katharina, 2011. "Peer effects and textbooks in African primary education," Labour Economics, Elsevier, Elsevier, vol. 18(4), pages 474-486, August.
  9. Allcott, Hunt, 2011. "Social norms and energy conservation," Journal of Public Economics, Elsevier, Elsevier, vol. 95(9), pages 1082-1095.
  10. Antonio Ciccone & Walter Garcia-Fontes, 2014. "Gender peer effects in school, a birth cohort approach," Economics Working Papers 1424, Department of Economics and Business, Universitat Pompeu Fabra.

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