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Conditional Moment Tests for Normality in Bivariate Limited Dependent Variable Models: a Monte Carlo Study

  • Riccardo LUCCHETTI

    ()

    (Universita' Politecnica delle Marche, Dipartimento di Economia)

  • Claudia PIGINI

    ()

    (Universita' Politecnica delle Marche, Dipartimento di Economia)

In this paper, we run a Monte Carlo analysis of the finite-sample performance of an Information Matrix Test put forward by Smith (1985) for bivariate censored models. We use the bivariate probit model and Heckman selection model as examples.;Approximating the finite-sample distribution of this test statistic by its asymptotic distribution can lead to very misleading results: its size is severely distorted even in samples that common practice would judge to be perfectly adequate for asymptotics. This is especially true when the correlation coefficient is far from zero.;Power properties of the test statistic are investigated by using bivariate t(6) and x2(1) alternatives. The test has very low power against leptokurtosis, especially in the bivariate probit case, while power against asymmetry appears to be much more satisfactory.;In general, the performance of the Information Matrix test seems to be related to the amount of information on the latent variables which survives the censoring mechanism. A somewhat improved version of the test can be obtained, in some cases, by a careful choice of the moment conditions to employ.

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Paper provided by Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali in its series Working Papers with number 357.

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Length: 37
Date of creation: Jun 2011
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Handle: RePEc:anc:wpaper:357
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  1. 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.
  2. Anthony Murphy, 2005. "Score Tests of Normality in Bivariate Probit Models," Econometrics 0512004, EconWPA.
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  4. Gao, Chuanming & Lahiri, Kajal, 2000. "Further consequences of viewing LIML as an iterated Aitken estimator," Journal of Econometrics, Elsevier, vol. 98(2), pages 187-202, October.
  5. Hall, A.R., 1984. "The Information Matrix Test for the Linear Model," The Warwick Economics Research Paper Series (TWERPS) 250, University of Warwick, Department of Economics.
  6. Gabriel Montes-Rojas, 2011. "Robust Misspecification Tests for the Heckman's Two-Step Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 30(2), pages 154-172.
  7. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, March.
  8. Bera, Anil K & Jarque, Carlos M & Lee, Lung-Fei, 1984. "Testing the Normality Assumption in Limited Dependent Variable Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(3), pages 563-78, October.
  9. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  10. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
  11. Orme, Chris, 1990. "The small-sample performance of the information-matrix test," Journal of Econometrics, Elsevier, vol. 46(3), pages 309-331, December.
  12. Skeels, Christopher L. & Vella, Francis, 1999. "A Monte Carlo investigation of the sampling behavior of conditional moment tests in Tobit and Probit models," Journal of Econometrics, Elsevier, vol. 92(2), pages 275-294, October.
  13. Chesher, Andrew & Irish, Margaret, 1987. "Residual analysis in the grouped and censored normal linear model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 33-61.
  14. Pagan, Adrian & Vella, Frank, 1989. "Diagnostic Tests for Models Based on Individual Data: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S29-59, Supplemen.
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