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Testing the Normality Assumption in the Sample Selection Model with an Application to Travel Demand

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  • van der Klaauw, Bas
  • Koning, Ruud H

Abstract

In this article we introduce a test for the normality assumption in the sample selection model. The test is based on a flexible parametric specification of the density function of the error terms in the model. This specification follows a Hermite series with bivariate normality as a special case. All parameters of the model are estimated both under normality and under the more general flexible parametric specification, which enables testing for normality using a standard likelihood ratio test. If normality is rejected, then the flexible parametric specification provides consistent parameter estimates. The test has reasonable power, as is shown by a simulation study. The test also detects some types of ignored heteroscedasticity. Finally, we apply the flexible specification of the density to a travel demand model and test for normality in this model.

Suggested Citation

  • van der Klaauw, Bas & Koning, Ruud H, 2003. "Testing the Normality Assumption in the Sample Selection Model with an Application to Travel Demand," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 31-42, January.
  • Handle: RePEc:bes:jnlbes:v:21:y:2003:i:1:p:31-42
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    References listed on IDEAS

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    1. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    2. Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-1525, September.
    3. Melenberg, B. & van Soest, A.H.O., 1993. "Semi-parametric estimation of the sample selection model," Discussion Paper 1993-34, Tilburg University, Center for Economic Research.
    4. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    5. Cameron, A Colin & Johansson, Per, 1997. "Count Data Regression Using Series Expansions: With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 203-223, May-June.
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    Cited by:

    1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
    2. Kostov, Philip & Patton, Myles & Moss, Joan E. & McErlean, Seamus, 2005. "Does Gibrat's Law Hold Amongst Dairy Farmers in Northern Ireland?," 2005 International Congress, August 23-27, 2005, Copenhagen, Denmark 24775, European Association of Agricultural Economists.
    3. Picchio, Matteo & Mussida, Chiara, 2011. "Gender wage gap: A semi-parametric approach with sample selection correction," Labour Economics, Elsevier, vol. 18(5), pages 564-578, October.
    4. Spiess, Martin & Kroh, Martin, 2010. "A Selection Model for Panel Data: The Prospects of Green Party Support," EconStor Open Access Articles, ZBW - German National Library of Economics, pages 172-188.
    5. David Greenaway & Richard Kneller & Xufei Zhang, "undated". "Exchange Rates, Exports and FDI: A Microeconometric Analysis," Discussion Papers 08/09, University of Nottingham, GEP.
    6. van den Berg, Gerard J. & van Vuuren, Aico, 2010. "The effect of search frictions on wages," Labour Economics, Elsevier, vol. 17(6), pages 875-885, December.
    7. David Greenaway & Richard Kneller & Xufei Zhang, 2012. "The effect of exchange rates on firm exports and the role of FDI," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 148(3), pages 425-447, September.
    8. repec:spr:reihed:v:58:y:2017:i:4:d:10.1007_s11162-016-9429-8 is not listed on IDEAS
    9. Masuhara, Hiroaki, 2013. "Semiparametric duration analysis with an endogenous binary variable: An application to hospital stays," CIS Discussion paper series 597, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    10. repec:ebl:ecbull:v:3:y:2008:i:42:p:1-13 is not listed on IDEAS
    11. Lindeboom, Maarten & van Doorslaer, Eddy, 2004. "Cut-point shift and index shift in self-reported health," Journal of Health Economics, Elsevier, vol. 23(6), pages 1083-1099, November.
    12. Hiroaki Masuhara, 2008. "Semi-nonparametric count data estimation with an endogenous binary variable," Economics Bulletin, AccessEcon, vol. 3(42), pages 1-13.
    13. David Dreyer Lassen, 2004. "The Effect of Information on Voter Turnout: Evidence from a Natural Experiment," EPRU Working Paper Series 04-03, Economic Policy Research Unit (EPRU), University of Copenhagen. Department of Economics.
    14. Lee Adkins & R. Carter Hill, 2007. "Bootstrap Inferences in Heteroscedastic Sample Selection Models: A Monte Carlo Investigation," Economics Working Paper Series 0710, Oklahoma State University, Department of Economics and Legal Studies in Business.
    15. Michael Pfaffermayr, 2014. "A GMM-Based Test for Normal Disturbances of the Heckman Sample Selection Model," Econometrics, MDPI, Open Access Journal, vol. 2(4), pages 1-18, October.
    16. Eun-Ju Lee & David Eastwood & Jinkook Lee, 2004. "A Sample Selection Model of Consumer Adoption of Computer Banking," Journal of Financial Services Research, Springer;Western Finance Association, vol. 26(3), pages 263-275, December.
    17. van Hasselt, Martijn, 2011. "Bayesian inference in a sample selection model," Journal of Econometrics, Elsevier, vol. 165(2), pages 221-232.
    18. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 535-572, November.
    19. Hiroaki Masuhara, 2007. "Semi-nonparametric estimation of regression-based survival models," Economics Bulletin, AccessEcon, vol. 3(61), pages 1-12.
    20. repec:ebl:ecbull:v:3:y:2007:i:61:p:1-12 is not listed on IDEAS
    21. Claudia PIGINI, 2012. "Of Butterflies and Caterpillars: Bivariate Normality in the Sample Selection Model," Working Papers 377, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.

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