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On Testing Sample Selection Bias Under the Multicollinearity Problem

  • Takashi Yamagata
  • Chris Orme

This paper reviews and extends the literature on the finite sample behavior of tests for sample selection bias. Monte Carlo results show that, when the “multicollinearity problem” identified by Nawata (1993) is severe, (i) the t-test based on the Heckman-Greene variance estimator can be unreliable, (ii) the Likelihood Ratio test remains powerful, and (iii) nonnormality can be interpreted as severe sample selection bias by Maximum Likelihood methods, leading to negative Wald statistics. We also confirm previous findings (Leung and Yu, 1996) that the standard regression-based t-test (Heckman, 1979) and the asymptotically efficient Lagrange Multiplier test (Melino, 1982), are robust to nonnormality but have very little power.

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Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 24 (2005)
Issue (Month): 4 ()
Pages: 467-481

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Handle: RePEc:taf:emetrv:v:24:y:2005:i:4:p:467-481
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  1. Greene, William H, 1981. "Sample Selection Bias as a Specification Error: Comment," Econometrica, Econometric Society, vol. 49(3), pages 795-98, May.
  2. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
  3. 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 765-99, July.
  4. 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.
  5. Melino, Angelo, 1982. "Testing for Sample Selection Bias," Review of Economic Studies, Wiley Blackwell, vol. 49(1), pages 151-53, January.
  6. Olsen, Randall J, 1980. "A Least Squares Correction for Selectivity Bias," Econometrica, Econometric Society, vol. 48(7), pages 1815-20, November.
  7. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
  8. 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.
  9. Orme, Chris, 1990. "The small-sample performance of the information-matrix test," Journal of Econometrics, Elsevier, vol. 46(3), pages 309-331, December.
  10. Leung, S.F. & Yu, S., 1992. "On the Choice Between Sample Selection and Two-Part Models," RCER Working Papers 337, University of Rochester - Center for Economic Research (RCER).
  11. 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.
  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 223-40, February.
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