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Efficient peer effects estimators with group effects

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  • Kuersteiner, Guido M.
  • Prucha, Ingmar R.
  • Zeng, Ying

Abstract

We study linear peer effect models where peers interact in groups and individual’s outcomes are linear in the group mean outcome and characteristics. We allow for unobserved random group effects as well as observed fixed group effects. The specification is in part motivated by the moment conditions imposed in Graham (2008). We show that these moment conditions can be cast in terms of a linear random group effects model and that they lead to a class of GMM estimators with parameters generally identified as long as there is sufficient variation in group size or group types. We also show that our class of GMM estimators contains a Quasi Maximum Likelihood estimator (QMLE) for the random group effects model, as well as the Wald estimator of Graham (2008) and the within estimator of Lee (2007) as special cases. Our identification results extend insights in Graham (2008) that show how assumptions about random group effects, variation in group size and certain forms of heteroscedasticity can be used to overcome the reflection problem in identifying peer effects. Our QMLE and GMM estimators accommodate additional covariates and are valid in situations with a large but finite number of different group sizes or types. Because our estimators are general moment based procedures, using instruments other than binary group indicators in estimation is straight forward. Our QMLE estimator accommodates group level covariates in the spirit of Mundlak and Chamberlain and offers an alternative to fixed effects specifications. This model feature significantly extends the applicability of Graham’s identification strategy to situations where group assignment may not be random but correlation of group level effects with peer effects can be controlled for with observable group level characteristics. Monte-Carlo simulations show that the bias of the QMLE estimator decreases with the number of groups and the variation in group size, and increases with group size. We also prove the consistency and asymptotic normality of the estimator under reasonable assumptions.

Suggested Citation

  • Kuersteiner, Guido M. & Prucha, Ingmar R. & Zeng, Ying, 2023. "Efficient peer effects estimators with group effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 2155-2194.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:2155-2194
    DOI: 10.1016/j.jeconom.2023.02.013
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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Steven G. Rivkin & Eric A. Hanushek & John F. Kain, 2005. "Teachers, Schools, and Academic Achievement," Econometrica, Econometric Society, vol. 73(2), pages 417-458, March.
    3. Bryan S. Graham, 2008. "Identifying Social Interactions Through Conditional Variance Restrictions," Econometrica, Econometric Society, vol. 76(3), pages 643-660, May.
    4. Bramoullé, Yann & Djebbari, Habiba & Fortin, Bernard, 2009. "Identification of peer effects through social networks," Journal of Econometrics, Elsevier, vol. 150(1), pages 41-55, May.
    5. Guido M. Kuersteiner & Ingmar R. Prucha, 2020. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," Econometrica, Econometric Society, vol. 88(5), pages 2109-2146, September.
    6. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    7. Vincent Boucher & Yann Bramoullé & Habiba Djebbari & Bernard Fortin, 2014. "Do Peers Affect Student Achievement? Evidence From Canada Using Group Size Variation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(1), pages 91-109, January.
    8. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    9. Paul Goldsmith-Pinkham & Guido W. Imbens, 2013. "Social Networks and the Identification of Peer Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 253-264, July.
    10. Raj Chetty & John N. Friedman & Nathaniel Hilger & Emmanuel Saez & Diane Whitmore Schanzenbach & Danny Yagan, 2011. "How Does Your Kindergarten Classroom Affect Your Earnings? Evidence from Project Star," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 1593-1660.
    11. Marcel Fafchamps & Simon Quinn, 2018. "Networks and Manufacturing Firms in Africa: Results from a Randomized Field Experiment," The World Bank Economic Review, World Bank, vol. 32(3), pages 656-675.
    12. Jing Cai & Adam Szeidl, 2018. "Interfirm Relationships and Business Performance," The Quarterly Journal of Economics, Oxford University Press, vol. 133(3), pages 1229-1282.
    13. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    14. Robert Garlick, 2018. "Academic Peer Effects with Different Group Assignment Policies: Residential Tracking versus Random Assignment," American Economic Journal: Applied Economics, American Economic Association, vol. 10(3), pages 345-369, July.
    15. Esther Duflo & Pascaline Dupas & Michael Kremer, 2011. "Peer Effects, Teacher Incentives, and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya," American Economic Review, American Economic Association, vol. 101(5), pages 1739-1774, August.
    16. Esther Duflo & Emmanuel Saez, 2003. "The Role of Information and Social Interactions in Retirement Plan Decisions: Evidence from a Randomized Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 815-842.
    17. Stinebrickner, Ralph & Stinebrickner, Todd R., 2006. "What can be learned about peer effects using college roommates? Evidence from new survey data and students from disadvantaged backgrounds," Journal of Public Economics, Elsevier, vol. 90(8-9), pages 1435-1454, September.
    18. Scott E. Carrell & Bruce I. Sacerdote & James E. West, 2013. "From Natural Variation to Optimal Policy? The Importance of Endogenous Peer Group Formation," Econometrica, Econometric Society, vol. 81(3), pages 855-882, May.
    19. Liu, Xiaodong & Lee, Lung-fei, 2010. "GMM estimation of social interaction models with centrality," Journal of Econometrics, Elsevier, vol. 159(1), pages 99-115, November.
    20. Kelejian, Harry H. & Prucha, Ingmar R., 2002. "2SLS and OLS in a spatial autoregressive model with equal spatial weights," Regional Science and Urban Economics, Elsevier, vol. 32(6), pages 691-707, November.
    21. Scott E. Carrell & Richard L. Fullerton & James E. West, 2009. "Does Your Cohort Matter? Measuring Peer Effects in College Achievement," Journal of Labor Economics, University of Chicago Press, vol. 27(3), pages 439-464, July.
    22. Lee, Lung-fei, 2007. "Identification and estimation of econometric models with group interactions, contextual factors and fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 333-374, October.
    23. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    24. Adam S. Booij & Edwin Leuven & Hessel Oosterbeek, 2017. "Ability Peer Effects in University: Evidence from a Randomized Experiment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 547-578.
    25. Angrist, Joshua D., 2014. "The perils of peer effects," Labour Economics, Elsevier, vol. 30(C), pages 98-108.
    26. David J. Zimmerman, 2003. "Peer Effects in Academic Outcomes: Evidence from a Natural Experiment," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 9-23, February.
    27. Aaron Sojourner, 2013. "Identification of Peer Effects with Missing Peer Data: Evidence from Project STAR," Economic Journal, Royal Economic Society, vol. 123(569), pages 574-605, June.
    28. Charles F. Manski, 1993. "Identification of Endogenous Social Effects: The Reflection Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 531-542.
    29. Jonathan Guryan & Kory Kroft & Matthew J. Notowidigdo, 2009. "Peer Effects in the Workplace: Evidence from Random Groupings in Professional Golf Tournaments," American Economic Journal: Applied Economics, American Economic Association, vol. 1(4), pages 34-68, October.
    30. Bruce Sacerdote, 2001. "Peer Effects with Random Assignment: Results for Dartmouth Roommates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(2), pages 681-704.
    31. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 225-238.
    32. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    33. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves, 2014. "Endogenous peer effects: local aggregate or local average?," Journal of Economic Behavior & Organization, Elsevier, vol. 103(C), pages 39-59.
    34. Frijters, Paul & Islam, Asad & Pakrashi, Debayan, 2019. "Heterogeneity in peer effects in random dormitory assignment in a developing country," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 117-134.
    35. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    36. Kang, Changhui, 2007. "Classroom peer effects and academic achievement: Quasi-randomization evidence from South Korea," Journal of Urban Economics, Elsevier, vol. 61(3), pages 458-495, May.
    37. Harry H. Kelejian & Ingmar R. Prucha & Yevgeny Yuzefovich, 2006. "Estimation Problems In Models With Spatial Weighting Matrices Which Have Blocks Of Equal Elements," Journal of Regional Science, Wiley Blackwell, vol. 46(3), pages 507-515, August.
    38. Xu Lin, 2010. "Identifying Peer Effects in Student Academic Achievement by Spatial Autoregressive Models with Group Unobservables," Journal of Labor Economics, University of Chicago Press, vol. 28(4), pages 825-860, October.
    39. Lung-fei Lee & Xiaodong Liu & Xu Lin, 2010. "Specification and estimation of social interaction models with network structures," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 145-176, July.
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    More about this item

    Keywords

    Social interaction; Peer effect; Random group effect; Quasi-maximum likelihood estimator; Spatial model;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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