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Selection and Endogenous Treatment Models with Social Interactions: An Application to the Impact of Exercise on Self-Esteem

Author

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  • Lin, Zhongjian

    (Emory University)

  • Vella, Francis

    (Georgetown University)

Abstract

We address the estimation of sample selection and endogenous treatment models with social interactions. To model the interaction between individuals in an internally consistent matter we employ a game theoretic approach based on the use of a discrete Bayesian game. We overcome the substantial computational burden this introduces through a sequential version of the nested fixed point algorithm. We describe how our methodology can be applied to a large class of commonly employed models. We employ our approach to examine the impact of an individual's frequency of exercise on her level of self esteem in a setting where an individual's exercise frequency is treated as endogenous and is potentially influenced by her belief of her friends' exercise frequency.

Suggested Citation

  • Lin, Zhongjian & Vella, Francis, 2021. "Selection and Endogenous Treatment Models with Social Interactions: An Application to the Impact of Exercise on Self-Esteem," IZA Discussion Papers 14167, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp14167
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    References listed on IDEAS

    as
    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    2. Willis, Robert J & Rosen, Sherwin, 1979. "Education and Self-Selection," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages 7-36, October.
    3. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    4. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July.
    5. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    6. Horst, Ulrich & Scheinkman, Jose A., 2006. "Equilibria in systems of social interactions," Journal of Economic Theory, Elsevier, vol. 130(1), pages 44-77, September.
    7. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    8. 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.
    9. Haiqing Xu, 2018. "Social Interactions In Large Networks: A Game Theoretic Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(1), pages 257-284, February.
    10. 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.
    11. Lewbel, Arthur & Tang, Xun, 2015. "Identification and estimation of games with incomplete information using excluded regressors," Journal of Econometrics, Elsevier, vol. 189(1), pages 229-244.
    12. Charles F. Manski, 2000. "Economic Analysis of Social Interactions," Journal of Economic Perspectives, American Economic Association, vol. 14(3), pages 115-136, Summer.
    13. Áureo de Paula & Xun Tang, 2012. "Inference of Signs of Interaction Effects in Simultaneous Games With Incomplete Information," Econometrica, Econometric Society, vol. 80(1), pages 143-172, January.
    14. Edward Vytlacil & James J. Heckman, 2001. "Policy-Relevant Treatment Effects," American Economic Review, American Economic Association, vol. 91(2), pages 107-111, May.
    15. Federico Ciliberto & Charles Murry & Elie Tamer, 2021. "Market Structure and Competition in Airline Markets," Journal of Political Economy, University of Chicago Press, vol. 129(11), pages 2995-3038.
    16. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    17. Wan, Yuanyuan & Xu, Haiqing, 2014. "Semiparametric identification of binary decision games of incomplete information with correlated private signals," Journal of Econometrics, Elsevier, vol. 182(2), pages 235-246.
    18. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
    19. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    20. Lung-fei Lee & Ji Li & Xu Lin, 2014. "Binary Choice Models with Social Network under Heterogeneous Rational Expectations," The Review of Economics and Statistics, MIT Press, vol. 96(3), pages 402-417, July.
    21. Philipp Eisenhauer & James J. Heckman & Edward Vytlacil, 2015. "The Generalized Roy Model and the Cost-Benefit Analysis of Social Programs," Journal of Political Economy, University of Chicago Press, vol. 123(2), pages 413-443.
    22. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    23. Arthur Lewbel & Xun Tang, 2010. "Identification and Estimation of Games with Incomplete Information Using Excluded Regressors, Second Version," PIER Working Paper Archive 12-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 20 Mar 2012.
    24. 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.
    25. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    26. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    27. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    28. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    29. Antoni Calvó-Armengol & Eleonora Patacchini & Yves Zenou, 2009. "Peer Effects and Social Networks in Education," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1239-1267.
    30. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    31. Zhongjian Lin & Haiqing Xu, 2017. "Estimation of social‐influence‐dependent peer pressure in a large network game," Econometrics Journal, Royal Economic Society, vol. 20(3), pages 86-102, October.
    32. Bo E. Honoré & Luojia Hu, 2020. "Selection Without Exclusion," Econometrica, Econometric Society, vol. 88(3), pages 1007-1029, May.
    33. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 70, Elsevier.
    34. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 33-58.
    35. 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.
    36. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    37. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    38. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
    39. Jorge Balat & Sukjin Han, 2018. "Multiple Treatments with Strategic Interaction," Papers 1805.08275, arXiv.org, revised Sep 2019.
    40. 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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    Cited by:

    1. Michael P. Leung, 2024. "Causal Interpretation of Estimands Defined by Exposure Mappings," Papers 2403.08183, arXiv.org, revised Mar 2024.
    2. Michael P. Leung & Pantelis Loupos, 2022. "Graph Neural Networks for Causal Inference Under Network Confounding," Papers 2211.07823, arXiv.org, revised Mar 2024.

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    More about this item

    Keywords

    endogenous treatment; sample selection; social interactions; sequential estimation; exercise; self-esteem;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • Z2 - Other Special Topics - - Sports Economics

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