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On Testing Sample Selection Bias under the Multicollinearity Problem

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  • Yamagata. T.

Abstract

This paper examines and compares the finite sample performance of the existing tests for sample selection bias, especially under the multi-collinearity problem pointed out by Nawata (1993). The results show that under such multicollinearity problem, (i) the t-test for sample selection bias based on the Heckman and Greene variance estimator can be unreliable; (ii) the standard t-test (Heckman 1979) and the asymptotically efficient Lagrange multiplier test (Melino 1982) have correct size but very little power; (iii) however, the likelihood ratio test following the maximum likelihood estimation remains powerful.

Suggested Citation

  • Yamagata. T., 2005. "On Testing Sample Selection Bias under the Multicollinearity Problem," Cambridge Working Papers in Economics 0522, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0522
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    1. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    2. Orme, Chris, 1990. "The small-sample performance of the information-matrix test," Journal of Econometrics, Elsevier, vol. 46(3), pages 309-331, December.
    3. Angelo Melino, 1982. "Testing for Sample Selection Bias," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(1), pages 151-153.
    4. Nawata, Kazumitsu, 1995. "Estimation of sample-selection models by the maximum likelihood method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(3), pages 299-303.
    5. Olsen, Randall J, 1980. "A Least Squares Correction for Selectivity Bias," Econometrica, Econometric Society, vol. 48(7), pages 1815-1820, November.
    6. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    7. Siu Fai Leung & Shihti Yu, 2000. "Collinearity and Two-Step Estimation of Sample Selection Models: Problems, Origins, and Remedies," Computational Economics, Springer;Society for Computational Economics, vol. 15(3), pages 173-199, June.
    8. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    9. Leung, Siu Fai & Yu, Shihti, 1996. "On the choice between sample selection and two-part models," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 197-229.
    10. Francis Vella, 1998. "Estimating Models with Sample Selection Bias: A Survey," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 127-169.
    11. Nawata, Kazumitsu, 1994. "Estimation of sample selection bias models by the maximum likelihood estimator and Heckman's two-step estimator," Economics Letters, Elsevier, vol. 45(1), pages 33-40, May.
    12. Olsen, Randall J, 1982. "Distributional Tests for Selectivity Bias and a More Robust Likelihood Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(1), pages 223-240, February.
    13. Greene, William H, 1981. "Sample Selection Bias as a Specification Error: Comment," Econometrica, Econometric Society, vol. 49(3), pages 795-798, May.
    14. Nawata, Kazumitsu, 1993. "A note on the estimation of models with sample-selection biases," Economics Letters, Elsevier, vol. 42(1), pages 15-24.
    15. Kazumitsu Nawata & Michael McAleer, 2001. "Size Characteristics Of Tests For Sample Selection Bias: A Monte Carlo Comparison And Empirical Example," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 105-112.
    16. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
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    Cited by:

    1. Campbell, Randall C. & Nagel, Gregory L., 2016. "Private information and limitations of Heckman's estimator in banking and corporate finance research," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 186-195.
    2. Zhang, Fan, 2011. "Distributional impact analysis of the energy price reform in Turkey," Policy Research Working Paper Series 5831, The World Bank.
    3. Yamagata, Takashi, 2006. "The small sample performance of the Wald test in the sample selection model under the multicollinearity problem," Economics Letters, Elsevier, vol. 93(1), pages 75-81, October.
    4. Zhao, Shangwei & Xie, Tian & Ai, Xin & Yang, Guangren & Zhang, Xinyu, 2023. "Correcting sample selection bias with model averaging for consumer demand forecasting," Economic Modelling, Elsevier, vol. 123(C).
    5. Verbič, Miroslav & Spruk, Rok, 2011. "Aging population and public pensions: theory and evidence," MPRA Paper 38914, University Library of Munich, Germany.
    6. Quattri, Maria A. & Ozanne, Adam & Wang, Xioabing & Hall, Alastair R., 2011. "On The Role Of The Brokerage Institution In The Development Of Ethiopian Agricultural Markets," 85th Annual Conference, April 18-20, 2011, Warwick University, Coventry, UK 108941, Agricultural Economics Society.
    7. Fan Zhang, 2015. "Energy Price Reform and Household Welfare: The Case of Turkey," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).

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    More about this item

    Keywords

    Sample selection bias; t-test; Wald test; likelihood ratio test; Lagrange multiplier test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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