A Geometric Approach to Nonlinear Econometric Models

Abstract

Conventional tests for composite hypotheses in minimum distance models can be unreliable when the relationship between the structural and reduced-form parameters is highly nonlinear. Such nonlinearity may arise for a variety of reasons, including weak identification. In this note, we begin by studying 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. These bounds allow us to construct tests for composite hypotheses which are uniformly asymptotically valid over a large class of data generating processes and structural models.