Anatomy of the Selection Problem

This article considers anew the problem of estimating a regression E(y|x) when realizations of (y, x) are sampled randomly but y is observed selectively. The central issue is the failure of the sampling process to identify E(y|x). The problem faced by the researcher is to find correct prior restrictions which, when combined with the data, identify the regression. Two kinds of restrictions are examined here. One, which has not been studied before, is a bound on the support of y. Such a bound implies a simple, useful bound on E(y|x). The other, which has received much attention, is a separability restriction derived from a latent variable model.

[1]  R. Gronau.  Wage Comparisons--A Selectivity Bias , 1973, Journal of Political Economy.

[2]  D. McFadden.  Tchebyscheff bounds for the space of agent characteristics , 1975 .

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

[4]  M. Hurd.  Estimation in truncated samples when there is heteroscedasticity , 1979 .

[5]  Consistent Sets of Estimates , 1982 .

[6]  P. Schmidt,et al.  An Investigation of the Robustness of the Tobit Estimator to Non-Normality , 1982 .

[7]  Prakasa Rao.  Nonparametric functional estimation , 1983 .

[8]  Arthur S. Goldberger,et al.  ABNORMAL SELECTION BIAS , 1983 .

[9]  R. Lalonde.  Evaluating the Econometric Evaluations of Training Programs with Experimental Data , 1984 .

[10]  Edward E. Leamer,et al.  Consistent Sets of Estimates for Regressions with Errors in All Variables , 1984 .

[11]  Hal R. Varian,et al.  Non-parametric analysis of optimizing behavior with measurement error , 1985 .

[12]  J. Powell,et al.  Semiparametric Estimation Of Bivariate Latent Variable Models , 1987 .

[13]  H. Bierens.  Advances in Econometrics: Kernel estimators of regression functions , 1987 .

[14]  P. Robinson.  ROOT-N-CONSISTENT SEMIPARAMETRIC REGRESSION , 1988 .

[15]  Charles F. Manski,et al.  Analog estimation methods in econometrics , 1988 .

[16]  C. Manski.  Identification of Binary Response Models , 1988 .

[17]  James J. Heckman,et al.  Choosing Among Alternative Nonexperimental Methods for Estimating the Impact of Social Programs: the Case of Manpower Training , 1989 .

[18]  W. Härdle.  Applied Nonparametric Regression , 1991 .