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A Simple Estimator for Binary Choice Models with Endogenous Regressors
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A Simple Estimator for Binary Choice Models with Endogenous Regressors

Author

Listed:
  • Yingying Dong

    (California State University, Fullerton)

  • Arthur Lewbel

    (Boston College)

Abstract

This paper provides a few variants of a simple estimator for binary choice models with endogenous or mismeasured regressors, or with heteroskedastic errors. Unlike control function methods, which are generally only valid when endogenous regressors are continuous, the estimators proposed here can be used with limited, censored, continuous, or discrete endogenous regressors, and they allow for latent errors having heteroskedasticity of unknown form, including random coefficients. The variants of special regressor based estimators we provide are numerically trivial to implement. We illustrate these methods with an empirical application estimating migration probabilities within the US.

Suggested Citation

  • Yingying Dong & Arthur Lewbel, 2004. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Boston College Working Papers in Economics 604, Boston College Department of Economics, revised 15 Jun 2012.
    • Handle: RePEc:boc:bocoec:604
    Note: Previously circulated as "Simple Estimators for Binary Choice Models with Endogenous Regressors"
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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. Dong, Yingying, 2010. "Endogenous regressor binary choice models without instruments, with an application to migration," Economics Letters, Elsevier, vol. 107(1), pages 33-35, April.
    3. Shaikh, Azeem M. & Vytlacil, Edward, 2008. "Endogenous binary choice models with median restrictions: A comment," Economics Letters, Elsevier, vol. 98(1), pages 23-28, January.
    4. Khan, Shakeeb & Lewbel, Arthur, 2007. "Weighted And Two-Stage Least Squares Estimation Of Semiparametric Truncated Regression Models," Econometric Theory, Cambridge University Press, vol. 23(2), pages 309-347, April.
    5. John Kennan & James R. Walker, 2011. "The Effect of Expected Income on Individual Migration Decisions," Econometrica, Econometric Society, vol. 79(1), pages 211-251, January.
    6. 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.
    7. Matzkin, Rosa L., 1986. "Restrictions of economic theory in nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 42, pages 2523-2558, Elsevier.
    8. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 835-864.
    9. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," Cowles Foundation Discussion Papers 1718, Cowles Foundation for Research in Economics, Yale University, revised Mar 2010.
    10. Christopher Baum & Yingying Dong & Arthur Lewbel & Tao Yang, 2012. "Binary choice models with endogenous regressors," SAN12 Stata Conference 9, Stata Users Group.
    11. 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.
    12. Amaresh K. Tiwari & Pierre Mohnen & Franz C. Palm & Sybrand Schim Loeff, 2008. "Financial Constraint and R&D Investment: Evidence from CIS," Palgrave Macmillan Books, in: Cees Beers & Alfred Kleinknecht & Roland Ortt & Robert Verburg (ed.), Determinants of Innovative Behaviour, chapter 10, pages 217-242, Palgrave Macmillan.
    13. Stefan Hoderlein, 2009. "Endogenous Semiparametric Binary Choice Models with Heteroscedasticity," Boston College Working Papers in Economics 747, Boston College Department of Economics, revised 29 Sep 2014.
    14. 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.
    15. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72, Elsevier.
    16. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    17. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    18. Ai, Chunrong & Gan, Li, 2010. "An alternative root-n consistent estimator for panel data binary choice models," Journal of Econometrics, Elsevier, vol. 157(1), pages 93-100, July.
    19. Stewart, Mark B., 2005. "A comparison of semiparametric estimators for the ordered response model," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 555-573, April.
    20. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    21. 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.
    22. Bo E. Honore & Arthur Lewbel, 2002. "Semiparametric Binary Choice Panel Data Models Without Strictly Exogeneous Regressors," Econometrica, Econometric Society, vol. 70(5), pages 2053-2063, September.
    23. Juan Carlos Escanciano & David Jacho‐Chávez & Arthur Lewbel, 2016. "Identification and estimation of semiparametric two‐step models," Quantitative Economics, Econometric Society, vol. 7(2), pages 561-589, July.
    24. Ichimura, Hidehiko & Lee, Sokbae, 2010. "Characterization of the asymptotic distribution of semiparametric M-estimators," Journal of Econometrics, Elsevier, vol. 159(2), pages 252-266, December.
    25. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, March.
    26. Lewbel, Arthur & Schennach, Susanne M., 2007. "A simple ordered data estimator for inverse density weighted expectations," Journal of Econometrics, Elsevier, vol. 136(1), pages 189-211, January.
    27. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    28. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(1), pages 32-51, February.
    29. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    30. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    31. Denis Cogneau & Eric Maurin, 2001. "Parental Income and School Attendance in a Low-Income Country : A Semi-parametric Analysis," Working Papers 2001-08, Center for Research in Economics and Statistics.
    32. Goux, Dominique & Maurin, Eric, 2005. "The effect of overcrowded housing on children's performance at school," Journal of Public Economics, Elsevier, vol. 89(5-6), pages 797-819, June.
    33. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    34. 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.
    35. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532.
    36. Arthur Lewbel & Susanne M. Schennach, 2003. "A Simple Ordered Data Estimator For Inverse Density Weighted Functions," Boston College Working Papers in Economics 557, Boston College Department of Economics, revised 01 May 2005.
    37. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    38. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
    39. Lewbel, Arthur & McFadden, Daniel & Linton, Oliver, 2011. "Estimating features of a distribution from binomial data," Journal of Econometrics, Elsevier, vol. 162(2), pages 170-188, June.
    40. 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.
    41. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    42. 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.
    43. 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.
    44. 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.
    45. Chesher, Andrew, 2009. "Excess heterogeneity, endogeneity and index restrictions," Journal of Econometrics, Elsevier, vol. 152(1), pages 37-45, September.
    46. 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.
    47. Jeremy T. Fox & David H. Hsu & Chenyu Yang, 2012. "Unobserved Heterogeneity in Matching Games with an Application to Venture Capital," NBER Working Papers 18168, National Bureau of Economic Research, Inc.
    48. Shakeeb Khan & Denis Nekipelov, 2018. "Information structure and statistical information in discrete response models," Quantitative Economics, Econometric Society, vol. 9(2), pages 995-1017, July.
    49. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549.
    50. Edward Vytlacil & Nese Yildiz, 2007. "Dummy Endogenous Variables in Weakly Separable Models," Econometrica, Econometric Society, vol. 75(3), pages 757-779, May.
    51. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    52. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    53. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106.
    54. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
    55. Hong, Han & Tamer, Elie, 2003. "Endogenous binary choice model with median restrictions," Economics Letters, Elsevier, vol. 80(2), pages 219-225, August.
    56. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    57. repec:bla:obuest:v:63:y:2001:i:5:p:517-33 is not listed on IDEAS
    58. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    59. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics.
    60. Jacho-Chávez, David T., 2009. "Efficiency Bounds For Semiparametric Estimation Of Inverse Conditional-Density-Weighted Functions," Econometric Theory, Cambridge University Press, vol. 25(3), pages 847-855, June.
    61. Briesch, Richard A. & Chintagunta, Pradeep K. & Matzkin, Rosa L., 2010. "Nonparametric Discrete Choice Models With Unobserved Heterogeneity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 291-307.
    62. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    63. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090.
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    More about this item

    Keywords

    Binary choice; Binomial Response; Endogeneity; Measurement Error; Heteroskedasticity; discrete endogenous; censored; random coefficients; Identification; Latent Variable Model.;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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