IDEAS home Printed from https://ideas.repec.org/a/wly/quante/v5y2014ip29-66.html
   My bibliography  Save this article

Complementarity and aggregate implications of assortative matching: A nonparametric analysis

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/quan.2014.5.issue-1.x
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    2. Bryan S. Graham, 2008. "Identifying Social Interactions Through Conditional Variance Restrictions," Econometrica, Econometric Society, vol. 76(3), pages 643-660, May.
    3. Brock, William A. & Durlauf, Steven N., 2001. "Interactions-based models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.),Handbook of Econometrics, edition 1, volume 5, chapter 54, pages 3297-3380, Elsevier.
    4. Keisuke Hirano & Jack R. Porter, 2009. "Asymptotics for Statistical Treatment Rules," Econometrica, Econometric Society, vol. 77(5), pages 1683-1701, September.
    5. Dehejia, Rajeev H., 2005. "Program evaluation as a decision problem," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 141-173.
    6. Charles F. Manski, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 531-542.
    7. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.),Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366, Elsevier.
    8. Bruce Sacerdote, 2001. "Peer Effects with Random Assignment: Results for Dartmouth Roommates," The Quarterly Journal of Economics, Oxford University Press, vol. 116(2), pages 681-704.
    9. Patrick Legros & Andrew F. Newman, 2007. "Beauty Is a Beast, Frog Is a Prince: Assortative Matching with Nontransferabilities," Econometrica, Econometric Society, vol. 75(4), pages 1073-1102, July.
    10. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," Review of Economic Studies, Oxford University Press, vol. 64(4), pages 487-535.
    11. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    12. Bhattacharya, Debopam, 2009. "Inferring Optimal Peer Assignment From Experimental Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 486-500.
    13. 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.
    14. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    15. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    16. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Achyuta Adhvaryu & Vittorio Bassi & Anant Nyshadham & Jorge A. Tamayo, 2020. "No Line Left Behind: Assortative Matching Inside the Firm," NBER Working Papers 27006, National Bureau of Economic Research, Inc.
    3. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Taehoon Kim & Jacob Schwartz & Kyungchul Song & Yoon-Jae Whang, 2019. "Monte Carlo Inference on Two-Sided Matching Models," Econometrics, MDPI, Open Access Journal, vol. 7(1), pages 1-15, March.
    10. Frölich, Markus & Michaelowa, Katharina, 2011. "Peer effects and textbooks in African primary education," Labour Economics, Elsevier, vol. 18(4), pages 474-486, August.
    11. 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.
    12. Bryan S. Graham, 2019. "Network Data," NBER Working Papers 26577, National Bureau of Economic Research, Inc.
    13. 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.
    14. Bryan S. Graham, 2019. "Dyadic Regression," Papers 1908.09029, arXiv.org.
    15. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    16. Bryan S. Graham, 2019. "Network Data," NBER Working Papers 26577, National Bureau of Economic Research, Inc.
    17. Allcott, Hunt, 2011. "Social norms and energy conservation," Journal of Public Economics, Elsevier, vol. 95(9), pages 1082-1095.
    18. Yifan Gong & Charles Ka Yui Leung, 2019. "When education policy and housing policy interact: can they correct for the externalities?," GRU Working Paper Series GRU_2019_031, City University of Hong Kong, Department of Economics and Finance, Global Research Unit.
    19. 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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:quante:v:5:y:2014:i::p:29-66. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: http://edirc.repec.org/data/essssea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.