I revisit the question of indeterminacy in US monetary policy using limited-information identification-robust methods. I find that the conclusions of Clarida, Galí, and Gernter (2000) that policy was inactive before 1979 are robust, but the evidence over the Volcker-Greenspan periods is inconclusive. I show that this is in fact consistent with policy being active over that period. Problems of identification also arise because policy reaction has been more gradual recently. At a methodological level, the paper demonstrates that identification issues should be taken seriously, and that identification-robust methods can be informative even when they produce wide confidence sets. (E31, E32, E52, E65,)

We review the main identification strategies and empirical evidence on the role of expectations in the New Keynesian Phillips curve, paying particular attention to the issue of weak identification. Our goal is to provide a clear understanding of the role of expectations that integrates across the different papers and specifications in the literature. We discuss the properties of the various limited-information econometric methods used in the literature and provide explanations of why they produce conflicting results. Using a common dataset and a flexible empirical approach, we find that researchers are faced with substantial specification uncertainty, as different combinations of various a priori reasonable specification choices give rise to a vast set of point estimates. Moreover, given a specification, estimation is subject to considerable sampling uncertainty due to weak identification. We highlight the assumptions that seem to matter most for identification and the configuration of point estimates. We conclude that the literature has reached a limit on how much can be learned about the New Keynesian Phillips curve from aggregate macroeconomic time series. New identification approaches and new datasets are needed to reach an empirical consensus.

This paper studies inference in models that are identified by moment restrictions. We show how instability of the moments can be used constructively to improve the identification of structural parameters that are stable over time. A leading example is macroeconomic models that are immune to the well-known (Lucas (1976)) critique in the face of policy regime shifts. This insight is used to develop novel econometric methods that extend the widely used generalized method of moments (GMM). The proposed methods yield improved inference on the parameters of the new Keynesian Phillips curve.

We consider tests of a simple null hypothesis on a subset of the coefficients of the exogenous and endogenous regressors in a single-equation linear instrumental variables regression model with potentially weak identification. Existing methods of subset inference (i) rely on the assumption that the parameters not under test are strongly identified, or (ii) are based on projection-type arguments. We show that, under homoskedasticity, the subset Anderson and Rubin (1949) test that replaces unknown parameters by limited information maximum likelihood estimates has correct asymptotic size without imposing additional identification assumptions, but that the corresponding subset Lagrange multiplier test is size distorted asymptotically.