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Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case

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  • Arthur Lewbel

    (Boston College)

Abstract

Lewbel (2012) provides an estimator for linear regression models containing an endogenous regressor, when no outside instruments or other such information is available. The method works by exploiting model heteroscedasticity to construct instruments using the available regressors. Some authors have considered the method in empirical applications where an endogenous regressor is binary (e.g., endogenous Diff-in-Diff or endogenous binary treatment models), without proving validity of the estimator in that case. The present paper shows that the assumptions required for Lewbel’s estimator can indeed be satisfied when an endogenous regressor is binary.

Suggested Citation

  • Arthur Lewbel, 2016. "Identification and Estimation Using Heteroscedasticity Without Instruments: The Binary Endogenous Regressor Case," Boston College Working Papers in Economics 927, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:927
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    References listed on IDEAS

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    1. 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.
    2. Arthur Lewbel, 2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80.
    3. 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.
    4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    5. Christopher Baum & Yingying Dong & Arthur Lewbel & Tao Yang, 2012. "Binary choice models with endogenous regressors," SAN12 Stata Conference 9, Stata Users Group.
    6. M. Shahe Emran & Virginia Robano & Stephen C. Smith, 2014. "Assessing the Frontiers of Ultrapoverty Reduction: Evidence from Challenging the Frontiers of Poverty Reduction/Targeting the Ultra-poor, an Innovative Program in Bangladesh," Economic Development and Cultural Change, University of Chicago Press, vol. 62(2), pages 339-380.
    7. Klein, Roger & Vella, Francis, 2010. "Estimating a class of triangular simultaneous equations models without exclusion restrictions," Journal of Econometrics, Elsevier, vol. 154(2), pages 154-164, February.
    8. 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.
    9. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "Nonparametric identification of regression models containing a misclassified dichotomous regressor without instruments," Economics Letters, Elsevier, vol. 100(3), pages 381-384, September.
    10. Todd Prono, 2014. "The Role Of Conditional Heteroskedasticity In Identifying And Estimating Linear Triangular Systems, With Applications To Asset Pricing Models That Include A Mismeasured Factor," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 800-824, August.
    11. 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.
    12. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "A note on the closed-form identification of regression models with a mismeasured binary regressor," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1473-1479, September.
    13. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
    14. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(3), pages 776-799, June.
    15. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    16. Christopher F Baum & Arthur Lewbel & Mark E Schaffer & Oleksander Talavera, 2012. "Instrumental variables estimation using heteroskedasticity-based instruments," United Kingdom Stata Users' Group Meetings 2012 07, Stata Users Group.
    17. Hoang, Trung X. & Pham, Cong S. & Ulubaşoğlu, Mehmet A., 2014. "Non-Farm Activity, Household Expenditure, and Poverty Reduction in Rural Vietnam: 2002–2008," World Development, Elsevier, vol. 64(C), pages 554-568.
    18. Le Moglie, Marco & Mencarini, Letizia & Rapallini, Chiara, 2015. "Is it just a matter of personality? On the role of subjective well-being in childbearing behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 453-475.
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    More about this item

    Keywords

    Simultaneous systems; linear regressions; endogeneity; identification; heteroscedasticity; binary regressors; dummy regressors; linear probability model; logit; probit;
    All these keywords.

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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