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Testing exclusion restrictions and additive separability in sample selection models

Huber, Martin ; Mellace, Giovanni

In: Empirical Economics, 2014, vol. 47, no. 1, p. 75-92

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    Title
    • Testing exclusion restrictions and additive separability in sample selection models
    Author
    • Huber, Martin. Department of Economics, SEW, University of St. Gallen, Varnbüelstrasse 14, 9000, St. Gallen, Switzerland
    • Mellace, Giovanni. Department of Economics, SEW, University of St. Gallen, Varnbüelstrasse 14, 9000, St. Gallen, Switzerland
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:325969
    Summary
    Standard sample selection models with non-randomly censored outcomes assume (i) an exclusion restriction (i.e., a variable affecting selection, but not the outcome) and (ii) additive separability of the errors in the selection process. This paper proposes tests for the joint satisfaction of these assumptions by applying the approach of Huber and Mellace (Testing instrument validity for LATE identification based on inequality moment constraints, 2011) (for testing instrument validity under treatment endogeneity) to the sample selection framework. We show that the exclusion restriction and additive separability imply two testable inequality constraints that come from both point identifying and bounding the outcome distribution of the subpopulation that is always selected/observed. We apply the tests to two variables for which the exclusion restriction is frequently invoked in female wage regressions: non-wife/husband's income and the number of (young) children. Considering eight empirical applications, our results suggest that the identifying assumptions are likely violated for the former variable, but cannot be refuted for the latter on statistical grounds.