IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2408.13971.html
   My bibliography  Save this paper

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

Author

Listed:
  • Zhongjian Lin
  • Francis Vella

Abstract

We address the estimation of endogenous treatment models with social interactions in both the treatment and outcome equations. We model the interactions between individuals in an internally consistent manner via a game theoretic approach based on discrete Bayesian games. This introduces a substantial computational burden in estimation which we address through a sequential version of the nested fixed point algorithm. We also provide some relevant treatment effects, and procedures for their estimation, which capture the impact on both the individual and the total sample. Our empirical application examines the impact of an individual's exercise frequency on her level of self-esteem. We find that an individual's exercise frequency is influenced by her expectation of her friends'. We also find that an individual's level of self-esteem is affected by her level of exercise and, at relatively lower levels of self-esteem, by the expectation of her friends' self-esteem.

Suggested Citation

  • Zhongjian Lin & Francis Vella, 2024. "Endogenous Treatment Models with Social Interactions: An Application to the Impact of Exercise on Self-Esteem," Papers 2408.13971, arXiv.org.
    • Handle: RePEc:arx:papers:2408.13971
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2408.13971
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    2. 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.
    3. 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.
    4. 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.
    5. Charles F. Manski, 2013. "Identification of treatment response with social interactions," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-23, February.
    6. Andrea Galeotti & Benjamin Golub & Sanjeev Goyal, 2020. "Targeting Interventions in Networks," Econometrica, Econometric Society, vol. 88(6), pages 2445-2471, November.
    7. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    8. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    9. 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.
    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. Lin, Zhongjian & Hu, Yingyao, 2024. "Binary choice with misclassification and social interactions, with an application to peer effects in attitude," Journal of Econometrics, Elsevier, vol. 238(1).
    12. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    13. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    14. 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.
    15. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 497-529.
    16. Mian Dai & Xun Tang, 2015. "Regulation and Capacity Competition in Health Care: Evidence from U.S. Dialysis Markets," The Review of Economics and Statistics, MIT Press, vol. 97(5), pages 965-982, December.
    17. 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.
    18. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    19. 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.
    20. 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.
    21. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    22. Charles F. Manski, 2000. "Economic Analysis of Social Interactions," Journal of Economic Perspectives, American Economic Association, vol. 14(3), pages 115-136, Summer.
    23. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    24. 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.
    25. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    26. 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.
    27. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    28. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    29. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    30. 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.
    31. Vella, F, 1992. "Simple Tests for Sample Selection Bias in Censored and Discrete Choice Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(4), pages 413-421, Oct.-Dec..
    32. Lin, Zhongjian & Liu, Ruixuan, 2021. "A Multiplex Interdependent Durations Model," Econometric Theory, Cambridge University Press, vol. 37(6), pages 1238-1266, December.
    33. Katja Seim, 2006. "An empirical model of firm entry with endogenous product‐type choices," RAND Journal of Economics, RAND Corporation, vol. 37(3), pages 619-640, September.
    34. 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.
    35. 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.
    36. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Lin, Zhongjian & Hu, Yingyao, 2024. "Binary choice with misclassification and social interactions, with an application to peer effects in attitude," Journal of Econometrics, Elsevier, vol. 238(1).
    3. Yingyao Hu & Zhongjian Lin, 2018. "Misclassification and the hidden silent rivalry," CeMMAP working papers CWP12/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Lin, Zhongjian & Tang, Xun & Yu, Ning Neil, 2021. "Uncovering heterogeneous social effects in binary choices," Journal of Econometrics, Elsevier, vol. 222(2), pages 959-973.
    5. Yann Bramoullé & Habiba Djebbari & Bernard Fortin, 2020. "Peer Effects in Networks: A Survey," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 603-629, August.
    6. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, September.
    7. Áureo de Paula, 2015. "Econometrics of network models," CeMMAP working papers CWP52/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Vincent Boucher & Yann Bramoullé, 2020. "Binary Outcomes and Linear Interactions," AMSE Working Papers 2038, Aix-Marseille School of Economics, France.
    9. Topa, Giorgio & Zenou, Yves, 2015. "Neighborhood and Network Effects," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 561-624, Elsevier.
    10. Chen, Denghui & Kiefer, Hua & Liu, Xiaodong, 2022. "Estimation of discrete choice network models with missing outcome data," Regional Science and Urban Economics, Elsevier, vol. 97(C).
    11. Aristide Houndetoungan, 2024. "Count Data Models with Heterogeneous Peer Effects under Rational Expectations," Papers 2405.17290, arXiv.org.
    12. Paul B. Ellickson & Sanjog Misra, 2011. "Structural Workshop Paper --Estimating Discrete Games," Marketing Science, INFORMS, vol. 30(6), pages 997-1010, November.
    13. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    14. Yoon, Jangsu, 2024. "Identification and estimation of sequential games of incomplete information with multiple equilibria," Journal of Econometrics, Elsevier, vol. 238(2).
    15. Liu, Xiaodong & Zhou, Jiannan, 2017. "A social interaction model with ordered choices," Economics Letters, Elsevier, vol. 161(C), pages 86-89.
    16. Jos'-Antonio Esp'n-S'nchez & 'lvaro Parra, 2018. "Entry Games under Private Information," Cowles Foundation Discussion Papers 2126, Cowles Foundation for Research in Economics, Yale University.
    17. Liu, Nianqing & Vuong, Quang & Xu, Haiqing, 2017. "Rationalization and identification of binary games with correlated types," Journal of Econometrics, Elsevier, vol. 201(2), pages 249-268.
    18. Erhao Xie, 2018. "Inference in Games Without Nash Equilibrium: An Application to Restaurants, Competition in Opening Hours," Staff Working Papers 18-60, Bank of Canada.
    19. Steven T Berry & Giovanni Compiani, 2023. "An Instrumental Variable Approach to Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(4), pages 1724-1758.
    20. Paul Ellickson & Sanjog Misra, 2012. "Enriching interactions: Incorporating outcome data into static discrete games," Quantitative Marketing and Economics (QME), Springer, vol. 10(1), pages 1-26, March.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2408.13971. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.