Coordinated testing for identification failure and correct model specification

原文摘要

We develop a specification test for GMM and Minimum Distance (MD) inference that is: (i) robust to weak identification; (ii) easy to implement and broadly applicable; and (iii) has meaningful power. Our specification test is based on a conditional inference approach: information about the existence of strongly identified directions in the parameter space is exploited to define a data-dependent critical value, which, in turn, increases the power of the resulting specification test by reducing the conservativeness of the corresponding critical value used to carry out the approach. This conditional or coordinated testing approach relies on a novel test of weak identification that is more powerful than existing procedures and is compatible with mixed identification strengths - that is, subvector and/or directions in the parameters space that display different strengths of identification (e.g. weak and non-weak). Furthermore, we show that in both cases, specification testing and testing for weak identification, an empirical measure of identification strength can be used to enhance testing power by eliciting less conservative critical values when appropriate. This new testing approach is illustrated using three applications: discrete choice models with simultaneity and the New Keynesian Philips curve (in a GMM framework), as well as Asset Pricing models with stochastic volatility and leverage (in a MD framework).

摘要来源：OpenAlex