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

Listed author(s):
  • van der Klaauw, Bas
  • Koning, Ruud H

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.

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Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 21 (2003)
Issue (Month): 1 (January)
Pages: 31-42

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Handle: RePEc:bes:jnlbes:v:21:y:2003:i:1:p:31-42
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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. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
  3. Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-1525, September.
  4. Melenberg, B. & Van Soest, A., 1993. "Semi-Parametric Estimation on the Sample Selection Model," Papers 9334, Tilburg - Center for Economic Research.
  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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