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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 econometric methods for measuring the average output effect of reallocating an indivisible input across production units. A distinctive feature of reallocations is that, by definition, they involve no augmentation of resources and, as such, leave the marginal distribution of the reallocated input unchanged. Nevertheless, if the production technology is nonseparable, they may alter average output. An example is the reallocation 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 small changes in the status quo allocation. Our analysis leaves the production technology nonparametric. Identification therefore requires conditional exogeneity of the input to be reallocated given the potentially complementary (and possibly other) input(s). We relate this exogeneity assumption to the pairwise stability concept used in the game theoretic literature on two‐sided matching models with transfers. 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. Our methods build upon the partial mean literature, but require extensions involving boundary issues and the fact that the weight function used in averaging is itself estimated. We derive the large‐sample properties of our proposed estimators and assess their small‐sample properties via a limited set of Monte Carlo experiments. Our characterization of the large‐sample properties of estimated correlated matching rules uses a new result on kernel estimated “double averages,” which may be of independent interest.

Suggested Citation

  • 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, March.
  • Handle: RePEc:wly:quante:v:5:y:2014:i::p:29-66
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    1. Bryan S. Graham & Guido W. Imbens & Geert Ridder, 2020. "Identification and Efficiency Bounds for the Average Match Function Under Conditionally Exogenous Matching," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 303-316, April.
    2. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    3. Adhvaryu, Achyuta & Bassi, Vittorio & Nyshadham, Anant & Tamayo, Jorge, 2020. "No Line Left Behind: Assortative Matching Inside the Firm," CEPR Discussion Papers 14554, C.E.P.R. Discussion Papers.
    4. Isaiah Andrews & Toru Kitagawa & Adam McCloskey, 2018. "Inference on winners," CeMMAP working papers CWP31/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. 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.
    6. 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.
    7. 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.
    8. Bryan S. Graham, 2019. "Network Data," NBER Working Papers 26577, National Bureau of Economic Research, Inc.
    9. Ciccone, Antonio & Garcia-Fontes, Walter, 2014. "Gender Peer Effects in School, a Birth Cohort Approach," CEPR Discussion Papers 10042, C.E.P.R. Discussion Papers.
    10. Bandyopadhyay, Siddhartha & Cabrales, Antonio, 2020. "Pricing group membership," MPRA Paper 102255, University Library of Munich, Germany.
    11. Bryan S. Graham, 2019. "Dyadic Regression," Papers 1908.09029, arXiv.org.
    12. Anton Badev, 2021. "Nash Equilibria on (Un)Stable Networks," Econometrica, Econometric Society, vol. 89(3), pages 1179-1206, May.
    13. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    14. Alexandra de Gendre & Nicolás Salamanca, 2020. "On the Mechanisms of Ability Peer Effects," Melbourne Institute Working Paper Series wp2020n19, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    15. Zhong, Xiaohan & Zhu, Lin, 2021. "The medium-run efficiency consequences of unfair school matching: Evidence from Chinese college admissions," Journal of Econometrics, Elsevier, vol. 224(2), pages 271-285.
    16. 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.
    17. Tarun Jain & Nishtha Langer, 2019. "Does Whom You Know Matter? Unraveling The Influence Of Peers' Network Attributes On Academic Performance," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 141-161, January.
    18. Taehoon Kim & Jacob Schwartz & Kyungchul Song & Yoon-Jae Whang, 2019. "Monte Carlo Inference on Two-Sided Matching Models," Econometrics, MDPI, vol. 7(1), pages 1-15, March.
    19. Allcott, Hunt, 2011. "Social norms and energy conservation," Journal of Public Economics, Elsevier, vol. 95(9), pages 1082-1095.
    20. Frölich, Markus & Michaelowa, Katharina, 2011. "Peer effects and textbooks in African primary education," Labour Economics, Elsevier, vol. 18(4), pages 474-486, August.
    21. Bryan S. Graham, 2019. "Network Data," CeMMAP working papers CWP71/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    22. 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.

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    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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