Testing Exclusion Restrictions in Nonseparable Triangular Models

In recent years, estimators for nonseparable models have been developed that rely on (an) instrumental variable(s) for identification. The exclusion restriction in triangular models can be reformulated and causally decomposed under the Settable Systems extension to the Pearl Causal Model due to Chalak & White (2012). We propose two new ways of testing the exclusion restriction, one based on testing conditional independence nonparametrically and one based on multivariate conditional mutual information. Unlike existing tests for overidentifying restrictions, the proposed tests are applicable in the just identified case. An important field of application is randomized trials with partial compliance, since for that case, the exclusion restriction is not only refutable, but also confirmable. The first approach, conditional independence testing, is illustrated by the application of the nonparametric test of equality of conditional densities of Li, Maasoumi & Racine (2009) to examples from medicine and economics.