Volume 24, Number 3 (Summer) 1989
Manski, Charles F. 1989. "Anatomy of the Selection Problem." Journal of Human Resources 24(3):341-360.
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.
The author is a professor of economics at the University of Wisconsin-Madison and is affiliated with the Institute for Research on Poverty. This research is supported by National Science Foundation Grant SES-8808276 and by funding to the Institute for Research on Poverty from the U.S. Department of Health and Human Services. The author is grateful to Irving Piliavin for posing the empirical issue that stimulated him to take a fresh look at the selection problem. He has benefited from discussions with Arthur Goldberger and from the opportunity to present this work in a conference at Wingspread and in seminars at Brown, Cornell, and Harvard University.
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