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Journal of Econometric Methods

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2156-6674
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Bivariate Non-Normality in the Sample Selection Model

Claudia Pigini
Published Online: 2014-08-19 | DOI: https://doi.org/10.1515/jem-2013-0008

Abstract

Since the seminal paper by [Heckman, J. J. 1974. “Shadow Prices, Market Wages, and Labor Supply.” Econometrica 42: 679–694], the sample selection model has been an essential tool for applied economists and arguably the most sensitive to sources of misspecification among the standard microeconometric models involving limited dependent variables. The need for alternative methods to get consistent estimators has led to a number of estimation proposals for the sample selection model under non-normality. There is a marked dichotomy in the literature that has developed in two conceptually different directions: the bivariate normality assumption can be either replaced, by using copulae, or relaxed/removed, relying on semi- and non-parametric estimators. This paper surveys the more recent proposals on the estimation of the sample selection model that deal with distributional misspecification giving the practitioner a unified framework of both parametric and semi/non-parametric options.

This article offers supplementary material which is provided at the end of the article.

Keywords: bivariate normality; copulae; maximum likelihood; sample selection model; semiparametric methods

References

  • Ahn, H., and J. L. Powell. 1993. “Semiparametric Estimation of Censored Selection Models with a Nonparametric Selection Mechanism.” Journal of Econometrics 58: 3–29.CrossrefGoogle Scholar

  • Amemiya, T. 1984. “Tobit Models: A Survey.” Journal of Econometrics 24: 3–61.CrossrefGoogle Scholar

  • Andrews, D. W. K., and M. M. A. Schafgans. 1998. “Semiparametric Estimation of the Intercept of a Sample Selection Model.” Review of Economic Studies 65: 497–517.CrossrefGoogle Scholar

  • Arabmazar, A., and P. Schmidt. 1982. “An Investigation of the Robustness of the Tobit Estimator to Non-Normality.” Econometrica 50: 1055–1063.CrossrefGoogle Scholar

  • Bhat, C. R., and N. Eluru. 2009. “A Copula-Based Approach to Accommodate Residential Self-Selection Effects in Travel Behavior Modeling.” Transportation Research Part B: Methodological 43: 749–765.CrossrefGoogle Scholar

  • Cavanagh, C., and R. P. Sherman. 1998. “Rank Estimators for Monotonic Index Models.” Journal of Econometrics 84: 351–381.CrossrefGoogle Scholar

  • Chesher, A., and M. Irish. 1987. “Residual Analysis in the Grouped and Censored Normal Linear Model.” Journal of Econometrics 34: 33–61.CrossrefGoogle Scholar

  • Cosslett, S. R. 1983. “Distribution-Free Maximum Likelihood Estimator of the Binary Choice Model.” Econometrica 51: 765–782.CrossrefGoogle Scholar

  • Cosslett, S. 1991. “Semiparametric Estimation of a Regression Model with Sample Selectivity.” In Nonparametric and Semiparametric Methods in Econometrics and Statistics, edited by G. T. W. A. Barnett, J. L. Powell, 175–197. Cambridge: Cambridge University Press.Google Scholar

  • Das, M., W. K. Newey, and F. Vella. 2003. “Nonparametric Estimation of Sample Selection Models.” Review of Economic Studies 70(1): 33–58.Google Scholar

  • De Luca, G. 2008. “Snp and Sml Estimation of Univariate and Bivariate Binary-Choice Models.” Stata Journal 8: 190–220.Google Scholar

  • Eberth, B., and M. D. Smith. 2010. “Modelling the Participation Decision and Duration of Sporting Activity in Scotland.” Economic Modelling 27: 822–834.CrossrefPubMedGoogle Scholar

  • Froelich, M. 2006. “Non-Parametric Regression for Binary Dependent Variables.” Econometrics Journal 9: 511–540.CrossrefGoogle Scholar

  • Gabler, S., F. Laisney, and M. Lechner. 1993. “Seminonparametric Estimation of Binary Choice Models with an Application to Labor Force Participation.” Journal of Business and Economic Statistics 11: 61–80.Google Scholar

  • Gallant, A. R., and D. W. Nychka. 1987. “Semi-Nonparametric Maximum Likelihood Estimation.” Econometrica 55: 363–390.CrossrefGoogle Scholar

  • Gallant, A. R. 1981. “On the Bias in Flexible Functional Forms and an Essentially Unbiased Form: The Fourier Flexible Form.” Journal of Econometrics 15: 211–245.CrossrefGoogle Scholar

  • Genius, M., and E. Strazzera. 2008. “Applying the Copula Approach to Sample Selection Modelling.” Applied Economics 40: 1443–1455.CrossrefGoogle Scholar

  • Gourieroux, C., A. Monfort, E. Renault, and A. Trognon. 1987. “Generalised Residuals.” Journal of Econometrics 34: 5–32.CrossrefGoogle Scholar

  • Gozalo, P. and O. Linton. 1994. “Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically.” Cowles Foundation Discussion Papers 1075, Cowles Foundation for Research in Economics, Yale University.Google Scholar

  • Greene, W. H. 2002. Econometric Analysis. fifth edition, Upper Saddle River, NJ: Prentice Hall.Google Scholar

  • Gronau, R. 1974. “Wage Comparisons-A Selectivity Bias.” Journal of Political Economy 82: 1119–1143.CrossrefGoogle Scholar

  • Hasebe, T., and W. P. Vijverberg. 2012. “A Flexible Sample Selection Model: A GTL-Copula Approach.” IZA Discussion Papers 7003, Institute for the Study of Labor (IZA).Google Scholar

  • Hayfield, T., and J. S. Racine. 2008. “Nonparametric Econometrics: The Np Package.” Journal of Statistical Software 27: 1–32.Google Scholar

  • Heckman, J. J. 1974. “Shadow Prices, Market Wages, and Labor Supply.” Econometrica 42: 679–694.CrossrefGoogle Scholar

  • Heckman, J. J. 1976. “The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for such Models.” Annals of Economic and Social Measurement 5: 120–137.Google Scholar

  • Heckman, J. J. 1979. “Sample Selection Bias as a Specification Error.” Econometrica 47: 153–161.CrossrefGoogle Scholar

  • Heckman, J. J. 1990. “Varieties of Selection Bias.” American Economic Review 80: 313–318.Google Scholar

  • Heckman, J. J., and R. J. Robb. 1985. “Alternative Methods for Evaluating the Impact of Interventions.” In Longitudinal Analysis of Labor Market Data, edited by J. Heckman and B. Singer, 156–245. Cambridge: Cambridge University Press, chapter 4.Google Scholar

  • Horowitz, J. L. 1992. “A Smoothed Maximum Score Estimator for the Binary Response Model.” Econometrica 60: 505–531.CrossrefGoogle Scholar

  • Hussinger, K. 2008. “R&d and Subsidies at the Firm Level: An Application of Parametric and Semiparametric Two-Step Selection Models.” Journal of Applied Econometrics 23: 729–747.CrossrefGoogle Scholar

  • Ichimura, H. 1993. “Semiparametric Least Squares (sls) and Weighted Sls Estimation of Single-Index Models.” Journal of Econometrics 58: 71–120.CrossrefGoogle Scholar

  • Klein, R. W., and R. H. Spady. 1993. “An Efficient Semiparametric Estimator for Binary Response Models.” Econometrica 61: 387–421.CrossrefGoogle Scholar

  • Lee, L. -F. 1982. “Some Approaches to the Correction of Selectivity Bias.” Review of Economic Studies 49: 355–372.CrossrefGoogle Scholar

  • Lee, L. -F. 1983. “Generalized Econometric Models with Selectivity.” Econometrica 51: 507–512.CrossrefGoogle Scholar

  • Lee, L. -F. 1984. “Tests for the Bivariate Normal Distribution in Econometric Models with Selectivity.” Econometrica 52: 843–863.CrossrefGoogle Scholar

  • Li, Q., and J. S. Racine. 2007. Nonparametric Econometrics: Theory and Practice. Princeton, NJ: Princeton University Press.Google Scholar

  • Lucchetti, R., and C. Pigini. 2013. “A Test for Bivariate Normality with Applications in Microeconometric Models.” Statistical Methods & Applications 22: 535–572.CrossrefGoogle Scholar

  • Manski, C. F. 1989. “Anatomy of the Selection Problem.” Journal of Human Resources 24: 343–360.CrossrefGoogle Scholar

  • Manski, C. 1975. “Maximum Score Estimation of the Stochastic Utility Model of Choice.” Journal of Econometrics 3: 205–228.CrossrefGoogle Scholar

  • Martins, M. F. O. 2001. “Parametric and Semiparametric Estimation of Sample Selection Models: An Empirical Application to the Female Labour Force in Portugal.” Journal of Applied Econometrics 16: 23–39.CrossrefGoogle Scholar

  • Melenberg, B., and A. Van Soest. 1993. “Semi-Parametric Estimation on the Sample Selection Model.” Working papers 9334, Tilburg-Center for Economic Research.Google Scholar

  • Montes-Rojas, G. V. 2011. “Robust Misspecification Tests for the Heckman’s Two-Step Estimator.” Econometric Reviews 30: 1–19.Google Scholar

  • Mroz, T. A. 1987. “The Sensitivity of an Empirical Model of Married Women’s Hours of Work to Economic and Statistical Assumptions.” Econometrica 55: 765–799.CrossrefGoogle Scholar

  • Nadaraya, E. A. 1964a. “On Estimating Regression.” Theory of Probability and Its Applications 9: 141–142.CrossrefGoogle Scholar

  • Nadaraya, E. A. 1964b. “On Nonparametric Estimation of Density Functions and Regression Curves.” Theory of Probability and Its Applications 10: 134–137.Google Scholar

  • Newey, W. K., J. L. Powell, and J. R. Walker. 1990. “Semiparametric Estimation of Selection Models: Some Empirical Results.” American Economic Review 80: 324–328.Google Scholar

  • Newey, W. K. 1988. “Two-Step Series Estimation of Sample Selection Models.” European Meeting of the Econometric Society.Google Scholar

  • Newey, W. K. 1999a. “Consistency of Two-Step Sample Selection Estimators Despite Misspecification of Distribution.” Economics Letters 63: 129–132.CrossrefGoogle Scholar

  • Newey, W. K. 1999b. “Two-Step Series Estimation of Sample Selection Models.” Working paper 99–04, Massachusetts Institute of Technology (MIT), Department of Economics.Google Scholar

  • Newey, W. K. 2009. “Two-Step Series Estimation of Sample Selection Models.” Econometrics Journal 12: 217–229.CrossrefGoogle Scholar

  • Olsen, R. J. 1980. “A Least Squares Correction for Selectivity Bias.” Econometrica 48: 1815–1820.CrossrefGoogle Scholar

  • Pagan, A., and A. Ullah. 1999. Nonparametric Econometrics. New York, NY, USA: Cambridge University Press.Google Scholar

  • Pagan, A. and F. Vella. 1989. “Diagnostic Tests for Models Based on Individual Data: A Survey.” Journal of Applied Econometrics 4: S29–S59.CrossrefGoogle Scholar

  • Powell, J. L., J. H. Stock, and T. M. Stoker. 1989. “Semiparametric Estimation of Index Coefficients.” Econometrica 57: 1403–1430.CrossrefGoogle Scholar

  • Powell, J. L. 1987. “Semiparametric Estimation of Bivariate Latent Variable Models.” Working Paper 8704, Social Systems Research Institute, University of Wisconsin-Madison.Google Scholar

  • Powell, J. L. 1994. “Estimation of Semiparametric Models.” North-Holland, Handbook of Econometrics 4: 2443–2521.Google Scholar

  • Prieger, J. E. 2002. “A Flexible Parametric Selection Model for Non-Normal Data with Application to Health Care Usage.” Journal of Applied Econometrics 17: 367–392.CrossrefGoogle Scholar

  • Puhani, P. 2000. “The Heckman Correction for Sample Selection and its Critique.” Journal of Economic Surveys 14: 53–68.CrossrefGoogle Scholar

  • Racine, J. S. 2008. Nonparametric Econometrics: A Primer. volume 3, Foundations and Trends in Econometrics.Google Scholar

  • Robinson, P. M. 1988. “Root- N-Consistent Semiparametric Regression.” Econometrica 56: 931–954.CrossrefGoogle Scholar

  • Ruud, P. A. 1986. “Consistent Estimation of Limited Dependent Variable Models Despite Misspecification of Distribution.” Journal of Econometrics 32: 157–187.CrossrefGoogle Scholar

  • Schwiebert, J. 2012. “Analyzing the Composition of the Female Workforce-A Semiparametric Copula Approach.” Discussion Paper dp-503, Leibniz University Hannover, Institute of Labor Economics.Google Scholar

  • Skeels, C. L., and F. Vella. 1999. “A Monte Carlo Investigation of the Sampling Behavior of Conditional Moment Tests in Tobit and Probit Models.” Journal of Econometrics 92: 275–294.CrossrefGoogle Scholar

  • Smith, M. D. 2003. “Modelling Sample Selection Using Archimedean Copulas.” Econometrics Journal 6: 99–123.CrossrefGoogle Scholar

  • Smith, R. J. 1987. “Testing the Normality Assumption in Multivariate Simultaneous Limited Dependent Variable Models.” Journal of Econometrics 34: 105–123.CrossrefGoogle Scholar

  • Smith, R. J. 1989. “On the Use of Distributional Mis-Specification Checks in Limited Dependent Variable Models.” The Economic Journal 99 (395), Supplement: Conference Papers, 178–192.Google Scholar

  • Trivedi, P. K., and D. M. Zimmer. 2007. Copula Modeling: An Introduction for Practitioners. Foundations and Trends in Econometrics, Boston, Massachussets:Now Publishers.Google Scholar

  • van der Klaauw, B., and R. H. Koning. 2003. “Testing the Normality Assumption in the Sample Selection Model with an Application to Travel Demand.” Journal of Business & Economic Statistics 21: 31–42.Google Scholar

  • Vella, F. 1998. “Estimating Models with Sample Selection Bias: A Survey.” Journal of Human Resources 33: 127–169.CrossrefGoogle Scholar

  • Vuong, Q. H. 1989. “Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses.” Econometrica 57: 307–333.CrossrefGoogle Scholar

  • Watson, G. S. 1964. “Smooth Regression Analysis.” Sankhya, A 26(4): 359–372.Google Scholar

About the article

Corresponding author: Claudia Pigini, Department of Economics, University of Perugia, Via A. Pascoli 20 – Perugia, Italy, E-mail:


Published Online: 2014-08-19

Published in Print: 2015-01-01


Citation Information: Journal of Econometric Methods, Volume 4, Issue 1, Pages 123–144, ISSN (Online) 2156-6674, ISSN (Print) 2194-6345, DOI: https://doi.org/10.1515/jem-2013-0008.

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