A Geometric Approach to Weakly Identified Econometric Models

Many nonlinear Econometric models show evidence of weak identification. In this paper we consider minimum distance statistics and show that in a broad class of models the problem of testing under weak identification is closely related to the problem of testing a curved null in a finite-sample Gaussian model. Using the curvature of the model, we develop new finite-sample bounds on the distribution of minimum-distance statistics, which we show can be used to detect weak identification and to construct tests robust to weak identification. We apply our new method to new Keynesian Phillips curve and DSGE examples and show that it provides a significant improvement over existing approaches.