Identification robust Inference in GMM Models Using Stability Restrictions

Brown University, Providence RI

Investigators

Abstract

Structural change, typically induced by policy regime shifts, is a common feature of dynamic economic models. The proposed research shows that such changes can be used constructively to improve the identification of structural parameters that are stable over time. This insight is used to develop novel econometric methods that generalize the widely used generalized method of moments (GMM). The proposed methods yield improved inference in models that are used for the analysis of macroeconomic policy, so they have the potential to be widely used in practice. The proposed reseach focuses on time series models that are speci…ed in terms of a set of moment conditions. A leading example is Euler equation models whose parameters are assumed to be stable in the face of policy regime shifts or changes in the volatility of economic shocks. However, the scope of the proposed methods of inference extends beyond this specific example. The contribution of the proposed research is twofold. First, it makes a formal case for using stability restrictions (e.g., immunity to the Lucas critique) as a source of identification of the stable structural parameters in economic models, or put di¤erently, for using structural change to identify stable dynamic causal e¤ects. The key insight is that changes in the distribution of the data induced by, for example, policy regime shifts, provide additional exogenous variation that can be usefully exploited for inference. This information is ignored by the usual GMM approach that relies only on full-sample exclusion or cross-equation restrictions to identify the structural parameters of the model. The second contribution is to develop new econometric methods for structural inference that exploit the information in stability restrictions and require only mild assumptions about the nature of instability in the distribution of the data. Specifically, they do not require any prior knowledge about the incidence, number and timing of breaks. Because no assumptions about identification are required, the main regularity conditions are strictly weaker than those used to justify the stability tests that are widely used in applied work. Therefore, the scope of the proposed methods is very wide. Application of the proposed methods to a widely used new Keynesian macroeconomic model shows that these methods are very useful in practice. Intellectual Merit: This research, which is in collaboration with Leandro Magnusson (Tulane U), is important to advancing knowledge in the field of economics by developing essential new quantitative methods with transformative potential. Broader Impact: (i) The project will provide essential tools for the evaluation of models used for economic policy. (ii) the results will be broadly disseminated to enhance scientific understanding through presentations in conferences, and publication in peer-reviewed academic journals.