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Heckman sample-selection estimators under heteroskedasticity

Author

Listed:
  • Alyssa H. Carlson

    (University of Missouri)

  • Wei Zhao

    (Truist Bank)

Abstract

This article provides a practical guide for Stata users on the conse- quences of heteroskedasticity in sample-selection models. We review the properties of two Heckman sample-selection estimators, full-information maximum likelihood and limited-information maximum likelihood (LIML), under heteroskedasticity. In this case, full-information maximum likelihood is inconsistent, while LIML can be consistent in certain settings. For the LIML estimator under heteroskedasticity, we show that standard Stata commands are unable to produce correct standard errors and instead suggest the community-contributed command gtsheckman (Carlson, 2022, Statistical Software Components S459109, Department of Economics, Boston College; 2024, Stata Journal 24: 687–710). Because heteroskedasticity affects the performance of these two estimators, we also offer guidance on how to test for heteroskedasticity and the conditions needed for the LIML estimator to be consis- tent. The Monte Carlo simulations illustrate that the suggested testing procedures perform well in terms of appropriate size and power.

Suggested Citation

  • Alyssa H. Carlson & Wei Zhao, 2025. "Heckman sample-selection estimators under heteroskedasticity," Stata Journal, StataCorp LLC, vol. 25(1), pages 212-236, March.
    • Handle: RePEc:tsj:stataj:v:25:y:2025:i:1:p:212-236
    DOI: 10.1177/1536867X251322971
    Note: to access software from within Stata, net describe http://www.stata-journal.com/software/sj25-1/st0772/
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    Keywords

    sample selection; heteroskedasticity; limited-information max- imum likelihood; LIML; full-information maximum likelihood; FIML; Breusch– Pagan test; Hausman test;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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