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Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors

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  • Jiaying Gu
  • Thomas M. Russell

Abstract

This paper considers (partial) identification of a variety of counterfactual parameters in binary response models with possibly endogenous regressors. Our framework allows for nonseparable index functions with multi-dimensional latent variables, and does not require parametric distributional assumptions. We leverage results on hyperplane arrangements and cell enumeration from the literature on computational geometry in order to provide a tractable means of computing the identified set. We demonstrate how various functional form, independence, and monotonicity assumptions can be imposed as constraints in our optimization procedure to tighten the identified set. Finally, we apply our method to study the effects of health insurance on the decision to seek medical treatment.

Suggested Citation

  • Jiaying Gu & Thomas M. Russell, 2021. "Partial Identification in Nonseparable Binary Response Models with Endogenous Regressors," Papers 2101.01254, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2101.01254
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    1. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-270, March.
    2. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Beresteanu, Arie & Molchanov, Ilya & Molinari, Francesca, 2012. "Partial identification using random set theory," Journal of Econometrics, Elsevier, vol. 166(1), pages 17-32.
    4. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 45(3), pages 809-829, August.
    5. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    6. Christopher Baum & Yingying Dong & Arthur Lewbel & Tao Yang, 2012. "Binary choice models with endogenous regressors," SAN12 Stata Conference 9, Stata Users Group.
    7. Sukjin Han & Sungwon Lee, 2019. "Estimation in a generalization of bivariate probit models with dummy endogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 994-1015, September.
    8. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    9. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    10. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    11. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Viewpoint: Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics, Canadian Economics Association, vol. 45(3), pages 809-829, August.
    12. Jiaying Gu & Roger Koenker, 2018. "Nonparametric maximum likelihood methods for binary response models with random coefficients," Papers 1811.03329, arXiv.org, revised Jan 2020.
    13. Heckman, James & Pinto, Rodrigo, 2015. "Causal Analysis After Haavelmo," Econometric Theory, Cambridge University Press, vol. 31(1), pages 115-151, February.
    14. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
    15. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    16. Yingying Dong & Arthur Lewbel, 2015. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 82-105, February.
    17. 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.
    18. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    19. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    20. Arthur Lewbel, 2007. "Coherency And Completeness Of Structural Models Containing A Dummy Endogenous Variable," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1379-1392, November.
    21. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    22. Florian Gunsilius, 2019. "A path-sampling method to partially identify causal effects in instrumental variable models," Papers 1910.09502, arXiv.org, revised Jun 2020.
    23. 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.
    24. Charles F. Manski, 2007. "Partial Identification Of Counterfactual Choice Probabilities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1393-1410, November.
    25. Hendry,David F. & Morgan,Mary S., 1997. "The Foundations of Econometric Analysis," Cambridge Books, Cambridge University Press, number 9780521588706, January.
    26. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    27. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    28. Richard W. Blundell & Richard J. Smith, 1989. "Estimation in a Class of Simultaneous Equation Limited Dependent Variable Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(1), pages 37-57.
    29. 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.
    30. Andrew Chesher & Adam M. Rosen, 2014. "An instrumental variable random‐coefficients model for binary outcomes," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 1-19, June.
    31. Alfred Galichon & Marc Henry, 2011. "Set Identification in Models with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1264-1298.
    32. 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.
    33. James J. Heckman & Rodrigo Pinto, 2018. "Unordered Monotonicity," Econometrica, Econometric Society, vol. 86(1), pages 1-35, January.
    34. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    35. Patrick Bajari & Christina Dalton & Han Hong & Ahmed Khwaja, 2014. "Moral hazard, adverse selection, and health expenditures: A semiparametric analysis," RAND Journal of Economics, RAND Corporation, vol. 45(4), pages 747-763, December.
    36. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    37. 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.
    38. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2023. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," Econometrica, Econometric Society, vol. 91(1), pages 107-146, January.
    39. Joseph Bennett, 1956. "Determination of the number of independent parameters of a score matrix from the examination of rank orders," Psychometrika, Springer;The Psychometric Society, vol. 21(4), pages 383-393, December.
    40. Ilya S. Molchanov, 1998. "A Limit Theorem for Solutions of Inequalities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 235-242, March.
    41. Alexander Torgovitsky, 2019. "Partial identification by extending subdistributions," Quantitative Economics, Econometric Society, vol. 10(1), pages 105-144, January.
    42. Ichimura, Hidehiko & Thompson, T. Scott, 1998. "Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution," Journal of Econometrics, Elsevier, vol. 86(2), pages 269-295, June.
    43. Amy Finkelstein & Kathleen McGarry, 2006. "Multiple Dimensions of Private Information: Evidence from the Long-Term Care Insurance Market," American Economic Review, American Economic Association, vol. 96(4), pages 938-958, September.
    44. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
    45. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    46. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    47. 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.
    48. Cardon, James H & Hendel, Igal, 2001. "Asymmetric Information in Health Insurance: Evidence from the National Medical Expenditure Survey," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 408-427, Autumn.
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