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Tobit Model Estimation and Sliced Inverse Regression

22 Pages Posted: 3 Nov 2008  

Lexin Li

North Carolina State University

Jeffrey S. Simonoff

New York University (NYU) - Leonard N. Stern School of Business; New York University (NYU) - Department of Information, Operations, and Management Sciences

Chih-Ling Tsai

University of California, Davis - Graduate School of Management

Date Written: 2006

Abstract

It is not unusual for the response variable in a regression model to be subject to censoring or truncation. Tobit regression models are a specific example of such a situation, where for some observations the observed response is not the actual response, but rather the censoring value (oftenzero), and an indicator that censoring (from below) has occurred. It is well-known that the maximum likelihood estimator for such a linear model (assuming Gaussian errors) is not consistent if the error term is not homoscedastic and normally distributed. In this paper we consider estimation in the Tobit regression context when those conditions do not hold, as well as when the true response is an unspecified nonlinear function of linear terms, using sliced inverse regression (SIR). The propertiesof SIR estimation for Tobit models are explored both theoretically and based on Monte Carlo simulations. It is shown that the SIR estimator has good properties when the usual linear model assumptions hold, andcan be much more effective than other estimators when they do not. An example related to household charitable donations demonstrates the usefulness of the estimator.

Keywords: Dimension reduction, Heteroscedasticity, Nonnormality, Single-index model

Suggested Citation

Li, Lexin and Simonoff, Jeffrey S. and Tsai , Chih-Ling, Tobit Model Estimation and Sliced Inverse Regression (2006). Statistics Working Papers Series, Vol. , pp. -, 2006. Available at SSRN: https://ssrn.com/abstract=1293148

Lexin Li (Contact Author)

North Carolina State University ( email )

Hillsborough Street
Raleigh, NC 27695
United States

Jeffrey S. Simonoff

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
New York, NY NY 10012
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

Chih-Ling Tsai

University of California, Davis - Graduate School of Management ( email )

One Shields Avenue
Davis, CA 95616
United States

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