IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1805.08275.html
   My bibliography  Save this paper

Multiple Treatments with Strategic Interaction

Author

Listed:
  • Jorge Balat
  • Sukjin Han

Abstract

We develop an empirical framework to identify and estimate the effects of treatments on outcomes of interest when the treatments are the result of strategic interaction (e.g., bargaining, oligopolistic entry, peer effects). We consider a model where agents play a discrete game with complete information whose equilibrium actions (i.e., binary treatments) determine a post-game outcome in a nonseparable model with endogeneity. Due to the simultaneity in the first stage, the model as a whole is incomplete and the selection process fails to exhibit the conventional monotonicity. Without imposing parametric restrictions or large support assumptions, this poses challenges in recovering treatment parameters. To address these challenges, we first establish a monotonic pattern of the equilibria in the first-stage game in terms of the number of treatments selected. Based on this finding, we derive bounds on the average treatment effects (ATEs) under nonparametric shape restrictions and the existence of excluded exogenous variables. We show that instrument variation that compensates strategic substitution helps solve the multiple equilibria problem. We apply our method to data on airlines and air pollution in cities in the U.S. We find that (i) the causal effect of each airline on pollution is positive, and (ii) the effect is increasing in the number of firms but at a decreasing rate.

Suggested Citation

  • Jorge Balat & Sukjin Han, 2018. "Multiple Treatments with Strategic Interaction," Papers 1805.08275, arXiv.org, revised Sep 2019.
    • Handle: RePEc:arx:papers:1805.08275
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1805.08275
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. Charles F. Manski, 2013. "Identification of treatment response with social interactions," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-23, February.
    3. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    4. Andrew Chesher & Adam Rosen, 2012. "Simultaneous equations for discrete outcomes: coherence, completeness, and identification," CeMMAP working papers 21/12, Institute for Fiscal Studies.
    5. Matthew Gentzkow & Jesse M. Shapiro & Michael Sinkinson, 2011. "The Effect of Newspaper Entry and Exit on Electoral Politics," American Economic Review, American Economic Association, vol. 101(7), pages 2980-3018, December.
    6. Michael J. Dickstein & Eduardo Morales, 2015. "What do Exporters Know?," NBER Working Papers 21351, National Bureau of Economic Research, Inc.
    7. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    8. Sheetal Sekhri, 2014. "Wells, Water, and Welfare: The Impact of Access to Groundwater on Rural Poverty and Conflict," American Economic Journal: Applied Economics, American Economic Association, vol. 6(3), pages 76-102, July.
    9. Wolfram Schlenker & W. Reed Walker, 2016. "Airports, Air Pollution, and Contemporaneous Health," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(2), pages 768-809.
    10. Austan Goolsbee & Chad Syverson, 2008. "How Do Incumbents Respond to the Threat of Entry? Evidence from the Major Airlines," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(4), pages 1611-1633.
    11. Kenneth Y. Chay & Michael Greenstone, 2003. "The Impact of Air Pollution on Infant Mortality: Evidence from Geographic Variation in Pollution Shocks Induced by a Recession," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 1121-1167.
    12. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
    13. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    14. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, May.
    15. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, September.
    16. Konrad Menzel, 2016. "Inference for Games with Many Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(1), pages 306-337.
    17. Eduardo Morales & Michael Dickstein, 2015. "What do Exporters Know?," 2015 Meeting Papers 139, Society for Economic Dynamics.
    18. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    19. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    20. Michael J. Dickstein & Eduardo Morales, 2015. "What do Exporters Know?," Discussion Papers 15-026, Stanford Institute for Economic Policy Research.
    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. Hoshino, Tadao & Yanagi, Takahide, 2023. "Treatment effect models with strategic interaction in treatment decisions," Journal of Econometrics, Elsevier, vol. 236(2).
    2. 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).
    3. Bora Kim, 2020. "Analysis of Randomized Experiments with Network Interference and Noncompliance," Papers 2012.13710, arXiv.org.
    4. Han, Sukjin, 2021. "Identification in nonparametric models for dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 132-147.

    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. Balat, Jorge F. & Han, Sukjin, 2023. "Multiple treatments with strategic substitutes," Journal of Econometrics, Elsevier, vol. 234(2), pages 732-757.
    2. Lina Zhang & David T. Frazier & D. S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Papers 2009.02642, arXiv.org, revised Sep 2022.
    3. Han, Sukjin & Yang, Shenshen, 2024. "A computational approach to identification of treatment effects for policy evaluation," Journal of Econometrics, Elsevier, vol. 240(1).
    4. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    5. Chen, Xuan & Flores, Carlos A. & Flores-Lagunes, Alfonso, 2015. "Going Beyond LATE: Bounding Average Treatment Effects of Job Corps Training," IZA Discussion Papers 9511, Institute of Labor Economics (IZA).
    6. Gu, Jiaying & Russell, Thomas M., 2023. "Partial identification in nonseparable binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 528-562.
    7. Bhattacharya, Jay & Shaikh, Azeem M. & Vytlacil, Edward, 2012. "Treatment effect bounds: An application to Swan–Ganz catheterization," Journal of Econometrics, Elsevier, vol. 168(2), pages 223-243.
    8. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    9. Alexander Torgovitsky, 2019. "Partial identification by extending subdistributions," Quantitative Economics, Econometric Society, vol. 10(1), pages 105-144, January.
    10. Mourifié, Ismael, 2015. "Sharp bounds on treatment effects in a binary triangular system," Journal of Econometrics, Elsevier, vol. 187(1), pages 74-81.
    11. Possebom, Vitor, 2018. "Sharp bounds on the MTE with sample selection," MPRA Paper 89785, University Library of Munich, Germany.
    12. Li, Chuhui & Poskitt, D.S. & Zhao, Xueyan, 2019. "The bivariate probit model, maximum likelihood estimation, pseudo true parameters and partial identification," Journal of Econometrics, Elsevier, vol. 209(1), pages 94-113.
    13. Machado, Cecilia & Shaikh, Azeem M. & Vytlacil, Edward J., 2019. "Instrumental variables and the sign of the average treatment effect," Journal of Econometrics, Elsevier, vol. 212(2), pages 522-555.
    14. Chesher, Andrew, 2013. "Semiparametric Structural Models Of Binary Response: Shape Restrictions And Partial Identification," Econometric Theory, Cambridge University Press, vol. 29(2), pages 231-266, April.
    15. Shakeeb Khan & Arnaud Maurel & Yichong Zhang, 2023. "Informational Content of Factor Structures in Simultaneous Binary Response Models," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 385-410, Emerald Group Publishing Limited.
    16. Sokbae Lee & Bernard Salanié, 2018. "Identifying Effects of Multivalued Treatments," Econometrica, Econometric Society, vol. 86(6), pages 1939-1963, November.
    17. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Kédagni, Désiré, 2023. "Identifying treatment effects in the presence of confounded types," Journal of Econometrics, Elsevier, vol. 234(2), pages 479-511.
    19. Wooyoung Kim & Koohyun Kwon & Soonwoo Kwon & Sokbae Lee, 2018. "The identification power of smoothness assumptions in models with counterfactual outcomes," Quantitative Economics, Econometric Society, vol. 9(2), pages 617-642, July.
    20. Vira Semenova, 2023. "Aggregated Intersection Bounds and Aggregated Minimax Values," Papers 2303.00982, arXiv.org, revised Jun 2024.

    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:1805.08275. 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.