Testing the effects of an unobservable factor: Do marriage prospects affect college major choice?

Abstract

This paper develops an econometric test for whether an unobservable factor jointly influences a choice among multiple alternatives and a subsequent binary outcome. Because only transformed versions of the choice model's unobservables are identified, we combine a copula-based joint model with results on the covariance between ordered and unordered normal variables to recover the covariance between structural shocks, yielding a simulation-based test for a common unobserved factor. Applying it to the National Longitudinal Survey of Youth 1997, we find unobserved marriage prospects significantly influence college major choice. Supporting this, the dependence disappears once stated marriage expectations, elicited before major selection, are included.