Testing instrument validity in sample selection models

This paper proposes tests for instrument validity in sample selection models with non-randomly censored outcomes. Such models commonly invoke an exclusion restriction (i.e., the availability of an instrument affecting selection, but not the outcome) and additive separability of the errors in the selection process. These assumptions allow us to both point identify and bound the outcome distribution of the subpopulation of the always selected, whose outcomes are observed irrespective of the instrument value. As the point must lie within its bounds, this yields two testable inequality constraints. We apply our tests to two instruments conventionally exploited for the estimation of female wage equations: non-wife/husband's income and the number of (young) children. Considering eight empirical applications, our results suggest that the former is not a valid instrument, while the validity of the latter is not refuted on statistical grounds.