Testing Additive Separability of Error Term in Nonparametric Structural Models

This article considers testing additive error structure in nonparametric structural models, against the alternative hypothesis that the random error term enters the nonparametric model nonadditively. We propose a test statistic under a set of identification conditions considered by Hoderlein et al. (2012), which require the existence of a control variable such that the regressor is independent of the error term given the control variable. The test statistic is motivated from the observation that, under the additive error structure, the partial derivative of the nonparametric structural function with respect to the error term is one under identification. The asymptotic distribution of the test is established, and a bootstrap version is proposed to enhance its finite sample performance. Monte Carlo simulations show that the test has proper size and reasonable power in finite samples.