Across states, there is little correlation between a state’s marriage rate or cohabitation rate and own population. Within states, there is a positive (no) correlation between a state’s marriage (cohabitation) rate and its population growth rate. The Cobb-Douglas marriage matching function (CDMMF), which extends the Choo-Siow MMF to include peer effects, can rationalize these correlations. The model is easy to estimate. The CDMMF is estimated using panel data across US states from 1990 to 2010. The estimated model replicates the above scale effects. These effects are not sufficient to explain the large recent declines in the gains to marriage.

In this paper, we discuss the key conditions for the identification and estimation of the local average treatment effect (LATE, Imbens and Angrist, 1994): the valid instrument assumption (LI) and the monotonicity assumption (LM). We show that the joint assumptions of LI and LM have a testable implication that can be summarized by a sign restriction defined by a set of intersection bounds. We propose an easy-to-implement testing procedure that can be analyzed in the framework of Chernozhukov, Lee, and Rosen (2013) and implemented using the Stata package of Chernozhukov, Kim, Lee, and Rosen (2013). We apply the proposed tests to the "draft eligibility" instrument in Angrist (1991), the "college proximity" instrument in Card (1993) and the "same sex" instrument in Angrist and Evans (1998).

We analyze the empirical content of the Roy model, stripped down to sector-specific unobserved heterogeneity and self-selection on the basis of potential outcomes. We characterize sharp bounds on the joint distribution of potential outcomes and testable implications of the Roy model. We apply these bounds to derive a measure of departure from Roy self-selection, so as to identify prime targets for intervention. Special emphasis is put on the case of binary outcomes. We analyze a Roy model of college major choice in Canada and Germany and take a new look at the underrepresentation of women in science, technology, engineering, and mathematics.