Testing for separability in structural equations

Separability is an important feature of structural equations, as it implies the absence of unobservable heterogeneity of effects and has significant implications for identification and efficiency of estimation. This paper provides a nonparametric test for separability in structural equations. The test is based on a conditional independence test recently developed by Huang et al. (2013), building on consistent procedures of Bierens (1982, 1990) and Stinchcombe and White (1998). The test is easy to implement and achieves n local power. We apply our test to study interest rate elasticities of loan demand in microfinance and the impact of education on wages.