Under-Identification of Structural Models Based on Timing and Information Set Assumptions

Abstract: We revisit identification based on timing and information set assumptions in structural models, which have been used in the context of production functions, demand equations, and hedonic pricing models (e.g. Olley and Pakes (1996), Blundell and Bond (2000)). First, we demonstrate a general under-identification problem using these assumptions in a simple version of the Blundell-Bond dynamic panel model. In particular, the basic moment conditions can yield multiple discrete solutions: one at the persistence parameter in the main equation and another at the persistence parameter governing the regressor. We then show that the problem can persist in a broader set of models but disappears in models under stronger timing assumptions. We then propose possible solutions in the simple setting by enforcing an assumed sign restriction and conclude by using lessons from our basic identification approach to propose more general practical advice for empirical researchers.