Detecting identification failure in models with conditional moment restrictions: A bootstrap approach

Abstract

This paper proposes a simple graphical diagnostic for global identification failure that can arise when point-identifying conditional moment restrictions are converted into unconditional ones. Our procedure uses the standard bootstrap to generate an empirical distribution of the GMM estimator. We illustrate that the standard bootstrap successfully reproduces the key features of the GMM estimator’s sampling distribution in such non-standard cases. Specifically, the bootstrap distribution becomes multi-modal in the presence of multiple solutions and flat or widely dispersed when the parameter is set-identified. This visual distinction provides a useful diagnostic and helps researchers to detect and understand the nature of the identification problem. Monte Carlo simulations support the usefulness of our approach.