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

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, illustrating this with 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. Second, we propose possible solutions based on sign restrictions and an augmented moment approach. We show the identification of our approach and propose a consistent estimation procedure. Our Monte Carlo simulations illustrate the underidentification issue and finite sample performance of our proposed estimator. Lastly, we show that the problem persists in many alternative models of the regressor but disappears in some models under stronger assumptions.