Estimation of Type 3 Tobit models using symmetric trimming and pairwise comparisons

Abstract This paper considers estimation of the semiparametric Type 3 Tobit model. We construct two-step estimators that use the ideas of symmetric trimming and pairwise comparisons which have been proposed for the censored regression model by Powell (1986) and Honore and Powell (1994). The estimators are consistent and asymptotically normal under two identifying assumptions: conditional symmetry and independence between the errors and regressors. The ideas and techniques are also implementable in other selection models that are variations of the basic Type 3 Tobit model. We demonstrate this by applying the proposed method in estimating an empirical model considered by Udry (1994).

[1]  Andrew Chesher,et al.  Asymptotic expansions of the informa-tion matrix test statistic , 1991 .

[2]  John C. Ham,et al.  Unemployment, discouraged workers and female labour supply , 1998 .

[3]  K. Nawata.  Robust estimation based on grouped-adjusted data in censored regression models , 1990 .

[4]  I. James,et al.  Linear regression with censored data , 1979 .

[5]  Andrew Chesher,et al.  Residual analysis in the grouped and censored normal linear model , 1987 .

[6]  H. L. Le Roy,et al.  Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; Vol. IV , 1969 .

[7]  J. Powell,et al.  Least absolute deviations estimation for the censored regression model , 1984 .

[8]  James L. Powell,et al.  Symmetrically Trimmed Least Squares Estimation For Tobit Models , 1986 .

[9]  W. Newey,et al.  Asymmetric Least Squares Estimation and Testing , 1987 .

[10]  J. Powell,et al.  Nonparametric and Semiparametric Methods in Econometrics and Statistics , 1993 .

[11]  D. Andrews.  CONSISTENCY IN NONLINEAR ECONOMETRIC MODELS: A GENERIC UNIFORM LAW OF LARGE NUMBERS , 1987 .

[12]  J. Heckman.  The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models , 1976 .

[13]  Christopher Udry,et al.  Risk and Insurance in a Rural Credit Market: An Empirical Investigation in Northern Nigeria , 1994 .

[14]  P. J. Huber.  The behavior of maximum likelihood estimates under nonstandard conditions , 1967 .

[15]  Bo E. Honoré,et al.  Pairwise difference estimators of censored and truncated regression models , 1994 .

[16]  Gregory M. Duncan.  A semi-parametric censored regression estimator , 1986 .

[17]  D. Pollard,et al.  Simulation and the Asymptotics of Optimization Estimators , 1989 .

[18]  Songnian Chen.  Semiparametric median estimation of the Type 3 Tobit model , 1994 .

[19]  J. Horowitz.  A distribution-free least squares estimator for censored linear regression models , 1986 .

[20]  R. N. Rosett.  A Statistical Model of Friction in Economics , 1959 .

[21]  Myoung-jae Lee,et al.  QUADRATIC MODE REGRESSION , 1993 .

[22]  Lung-fei Lee.  Semiparametic Nonlinear Least-Squares Estimation of Truncated Regression Models , 1992, Econometric Theory.

[23]  Songnian Chen.  Semiparametric estimation of the type-3 Tobit model , 1997 .

[24]  Lung-fei Lee,et al.  Semiparametric two-stage estimation of sample selection models subject to Tobit-type selection rules , 1994 .

[25]  Choon-Geol Moon,et al.  A Monte Carlo Comparison of Semiparametric Tobit Estimators , 1989 .

[26]  Moshe Buchinsky.  Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study , 1995 .

[27]  J. Heckman.  Sample selection bias as a specification error , 1979 .

[28]  Bo E. Honoré,et al.  Trimmed LAD and Least Squares Estimation of Truncated and Censored Regression Models with Fixed Effects , 1992 .

[29]  L. Fernandez.  Non-parametric maximum likelihood estimation of censored regression models , 1986 .