Calzolari, Giorgio and Fiorentini, Gabriele (1993): Estimating variances and covariances in a censored regression model. Published in: Statistica No. 53 (1993): pp. 323339.

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Abstract
When the coefficients of a Tobit model are estimated by maximum likelihood their covariance matrix is typically, even if not necessarily, associated with the algorithm employed to maximize the likelihood. Covariance estimators used in practice are derived by: (1) the Hessian (observed information), (2) the matrix of outer products of the first derivatives of the loglikelihood (OPG version), (3) the expected Hessian (estimated information), (4) a mixture of 1 and 2 (White's QML covariance matrix). Significant differences among these estirnates are are usually interpreted as an indication of misspecification. From our Monte Carlo study this seems not to be true, unless the sample size is really very large. Even in absence of misspecification, large differences are encountered in small samples, and the sign of the differences is almost systematic. This suggests that the choice of the covariance estimator is not neutral and the results of hypotheses testing may be strongly affected by such a choice.
Item Type:  MPRA Paper 

Original Title:  Estimating variances and covariances in a censored regression model 
Language:  English 
Keywords:  Tobit model, maximum likelihood, hessian matrix, outer products matrix, covariance estimators 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C34  Truncated and Censored Models ; Switching Regression Models C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C24  Truncated and Censored Models ; Switching Regression Models ; Threshold Regression Models 
Item ID:  22598 
Depositing User:  Giorgio Calzolari 
Date Deposited:  10. May 2010 12:53 
Last Modified:  18. Feb 2013 00:31 
References:  T. AMEMIYA (1983), A comparison of the Amemiya GLS and the LeeMaddakzTrost G2SLS in a simultaneous equations Tobit model, "Journal of Econometrics", 23, pp. T. AMEMIYA (1984), Tobit models: a survay, "Journal of Econometrics", 24, pp. 361. T. AMEMIYA (1985), Advanced Econometrics, Basil Blackwell, Oxford. A. ARABMAZAR, P. SCHMIDT (1981), Further evidence on the robustness of the Tobit estimator to heteroscedasticity, "Journal of Econometrics", 17, pp. 253258. A. ARABMAZAR, P. SCHMIDT (1982), An investigation of the robustness of the Tobit estimators to nonnormality, "Econometrica", 50, pp. 10551069. BANCA D'ITALIA (1988), Modello mensile del mercato monetario, Banca d'Italia, Servizio studi, Temi di discussione, n. 108, Roma. E.R. BERNDT, B.H. HALL, R.E. HALL, J.A. HAUSMAN (1974), Estimation and inference in nonlinear structural models, "Annals of Economic and Social Measurement", 3, pp. 653665. G. CALZOLARI, L. PANATTONI (1988a), Alternative estimators of FIML covariance matrix: a Monte Carlo study, "Econometrica", 56, pp. 701714. G. CALZOLARI, L. PANATTONI (1988b), Finite sample performance of the robust Wald test in simultaneous equation systems, "Advances in Econometrics", vol.7, ed. by G.F. Rhodes Jr. and T.B. Fomby, JAI Press, Greenwich, pp. 163191. A. CHESHER, I. JEWITT (1987), The bias of a heteroskedasticity consistent covariance matrix estimator, "Econometrica", 55, pp. 12171222. P.S. DHRYMES (1986), Limited dependent variables, "Handbook of Econometrics", ed. by Z. Griliches and M.D. Intrilligator, NorthHolland Publishing Co., vol. 3, Amsterdam, pp. 15671631. B. EFRON, D.V. HINKLEY (1978), Assessing the accuracy of the maximum likelihood estimator: observed versus expected fisher information, "Biometrika", 65, pp. 457487. R.C. FAIR (1977), A note on computation of the Tobit estimates, "Econometrica", 45, pp. 17231727. R.P.H. FISHE, G.S. MADDALA, R.P. TROST (1979), Estimation of a heteroscedastic Tobit model, "Manuscript", University of Florida. L. FLOOD, A. TASIRAN (1989), A comparison of system Tobit estimations, University of Gothenburg, Discussion Paper presented at the "European Meeting of the Econometric Society", Munich. A.S. GOLDBERGER (1964), Econometric Theory, John Wiley & Sons, New York. C. GOURIEROUX, A. MONFORT, A. TROGNON (1984), Pseudo maximum likelihood methods: theory, "Econometrica", 52, pp. 681700. W.H. GREENE (1985), LIMDEP, user's manual, Graduate School of Business Administration, New York University, New York. W.E. GRIFFITHS, R.C. HILL, P.J. POPE (1987), Small samples properties of probit model estimators, "Journal of the American Statistical Association", 82, pp. 929937. B.H. HALL (1984), Software for the computation of Tobit model estimates, "Journal of Econometrics", 24, pp. 215222. J.J. HECKMAN (1976), The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimators for such models, "Annals of Economic and Social Measurement", 5, pp. 475492. J.G. MACKINNON, H. WHITE (1985), Some heteroskedasticityconsistent covariance matrix estimators with improved finite sample properties, "Journal of Econometrics", 29, pp. 305325. G.S. MADDALA (1983), Limiteddependent and qualitative variables in economics, Cambridge University Press, Econometric Society Monographs n. 3. T.A. MROZ (1987), The sensitivity of an empirical model of married women's hours of work to economic and statistical assumptions, "Econometrica", 55, pp. 765799. F.D. NELSON (1981), A test for misspecification in the censored regression model, "Econometrica", 49, pp. 13171329. F.D. NELSON, L. OLSON (1978), Specification and estimation of a simultaneous equation model with limited dependent variables, "International Economic Review", 19, pp. 695710. F.D. NELSON, N.E. SAVIN (1988), The nonmonotonicity of the power function of the Wald test in nonlinear models, The University of Iowa, Department of Economics, working paper. W.K. NEWEY (1987), Specification tests for distributional assumption in the Tobit model, "Journal of Econometrics", 34, pp. 125145. R.J. OLSEN (1978), Note on the uniqueness of the maximum likelihood estimator of the Tobit model, "Econometrica", 46, pp. 12111215. R.W. PARKS, N.E. SAVIN (1990), The choice of coefficients covariance matrix estimator: outer product versus hessian, The University of Iowa, Department of Economics, working paper. J.L. POWELL (1983), Asymptotic normality of the censored and truncated least absolute deviations estimators, Stanford University, IMSSS, "Technical Report", n. 395. I.R. PRUCHA (1984), On the estimation of the variance covariance matrix of maximum Likelihood estimators in nonlinear simultaneous equation systems: a Monte Carlo study, University of Maryland, Department of Economics, Working paper nn.8414. P.M. ROBINSON (1982), On the asymptotic properties of estimators of models containing limited dependent variables, "Econometrica", 50, pp. 2741. P.A. RUUD (1986), Consistent estimation of limited dependent variable models despite misspecification of distribution, "Journal of Econometrics", 32, pp.157187. R.C. SICKLES, P. SCHMIDT (1978), Simultaneous equation models with truncated dependent variables: a simultaneous Tobit model, "Journal of Economics and Business", 31, pp. 1121. R.J. SMITH (1987), Testing the normality assumption multivariate simultaneous limited dependent variable models, "Journal of Econometrics", 34, pp. 105125. J. TOBIN (1958), Estimation of relationships for limited dependent variables, "Econometrica", 26, pp. 2436. H. WHITE (1980), A heteroskedsaticityconsistent covariance matrix estimator and a direct test for heteroskedasticity, "Econometrica", 48, pp. 817838. H. WHITE (1982), Maximum likelihood estimation of misspecified models, "Econometrica", 50, pp. 125. H. WHITE (1983), Corrigendum, "Econometrica", 51, p. 513. A.D. WITTE (1980), Estimating the economic model of crime with individual data, "Quarterly Journal of Economics", 94, pp. 5784. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/22598 