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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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  • Bryan S. Graham & Guido W. Imbens & Geert Ridder, 2009. "Complementarity and Aggregate Implications of Assortative Matching: A Nonparametric Analysis," NBER Working Papers 14860, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:14860
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    References listed on IDEAS

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    2. Bryan S. Graham, 2008. "Identifying Social Interactions Through Conditional Variance Restrictions," Econometrica, Econometric Society, vol. 76(3), pages 643-660, May.
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    Cited by:

    1. Ciccone, Antonio & Garcia-Fontes, Walter, 2014. "Gender Peer Effects in School, a Birth Cohort Approach," Working Papers 14-19, University of Mannheim, Department of Economics.
    2. Bryan S. Graham & Guido Imbens & Geert Ridder, 2016. "Identification and efficiency bounds for the average match function under conditionally exogenous matching," CeMMAP working papers CWP10/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. 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.
    4. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    5. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    6. Oosterbeek, Hessel & van Ewijk, Reyn, 2014. "Gender peer effects in university: Evidence from a randomized experiment," Economics of Education Review, Elsevier, vol. 38(C), pages 51-63.
    7. Robert W. Fairlie & Florian Hoffmann & Philip Oreopoulos, 2014. "A Community College Instructor Like Me: Race and Ethnicity Interactions in the Classroom," American Economic Review, American Economic Association, vol. 104(8), pages 2567-2591, August.
    8. Allcott, Hunt, 2011. "Social norms and energy conservation," Journal of Public Economics, Elsevier, vol. 95(9), pages 1082-1095.
    9. Frölich, Markus & Michaelowa, Katharina, 2011. "Peer effects and textbooks in African primary education," Labour Economics, Elsevier, vol. 18(4), pages 474-486, August.
    10. 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.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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