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Anatomy of the Selection Problem

Charles F. Manski
The Journal of Human Resources
Vol. 24, No. 3 (Summer, 1989), pp. 343-360
DOI: 10.2307/145818
Stable URL: http://www.jstor.org/stable/145818
Page Count: 18
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Anatomy of the Selection Problem
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Abstract

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.

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