A Geometric Approach to Nonlinear Econometric Models
Isaiah Andrews, Anna Mikusheva
Econometrica · 2016 · Volume 84 · Issue 3
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.
Keywords
Weak identification, statistical differential geometry, curved exponential family
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