Simultaneity in Binary Outcome Models with an Application to Employment for Couples

TL;DR

This paper develops a dynamic panel data model for binary outcomes with simultaneity, applying it to study employment within households and revealing significant dependence influenced by ethnicity.

Contribution

It introduces a dynamic, fixed-effects bivariate binary outcome model with simultaneous equations, combining likelihood and moments methods for estimation.

Findings

Dependence in household employment varies by ethnicity.

The model accounts for unobserved household heterogeneity.

Significant within-household employment dependence found.

Abstract

Two of Peter Schmidt's many contributions to econometrics have been to introduce a simultaneous logit model for bivariate binary outcomes and to study estimation of dynamic linear fixed effects panel data models using short panels. In this paper, we study a dynamic panel data version of the bivariate model introduced in Schmidt and Strauss (1975) that allows for lagged dependent variables and fixed effects as in Ahn and Schmidt (1995). We combine a conditional likelihood approach with a method of moments approach to obtain an estimation strategy for the resulting model. We apply this estimation strategy to a simple model for the intra-household relationship in employment. Our main conclusion is that the within-household dependence in employment differs significantly by the ethnicity composition of the couple even after one allows for unobserved household specific heterogeneity.