Economics Letters 45 (1994) 33-40 0165-1765/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved 33 Estimation of sample selection bias models by the maximum likelihood estimator and Heckman’s two-step estimator Kazumitsu Nawata”’ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Department of Social and International Relations, University of Tokyo, 3-8-l Komaba, M eguro- ku, Tokyo 1.53, Japan Department of Economics, University of W estern Australia, Nedlands, Perth W A 6009, Australia Received 28 June 1993 Final revision 3 November 1993 Accepted 8 November 1993 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Abstract In this paper, methods of estimating models with sample selection biases are analyzed. Finite sample properties of the maximum likelihood estimator (MLE) and Heckman’s two-step estimator are compared using Monte Carlo experiments. JEL classification: C34 1. Introduction Econometric models with sample selection biases (type II Tobit models) are widely used in various fields of economics. Unlike other types of econometric models, the maximum likelihood estimator (MLE) is seldom used because of its computational difficulty. Heckman (1976, 1979) proposed a simple two-step estimator. However, Heckman’s estimator sometimes performs poorly [Wales and Woodland (1980), Nelson (1984), Paarsch (1984), and Nawata (1994)]. In this paper, a method of calculating the MLE is considered, and the finite sample properties of the MLE and Heckman’s two-step estimator are compared using Monte Carlo experiments. Although Heckman’s two-step estimator performs well when there is not a high degree of multicollinearity between the hazard ratio and explanatory variables, it performs poorly when there is a high degree of multicollinearity between them. * Correspondence to: Kazumitsu Nawata, Department of Social and International Relations, University of Tokyo, 3-8-l Komaba, Meguro-ku, Tokyo 153, Japan. ’ I wish to thank Michael McAIeer and Paul Miller for their helpful comments. The program used in this paper, for calculating the MLE, is available through the author. SSDI 0165-1765(93)00369-Y