We propose a novel identification-robust test for the null hypothesis that an estimated New Keynesian model has a reduced form consistent with the unique stable solution against the alternative of sunspot-driven multiple equilibria. Our strategy is designed to handle identification failures as well as the misspecification of the relevant propagation mechanisms. We invert a likelihood ratio test for the cross-equation restrictions (CER) that the New Keynesian system places on its reduced-form solution under determinacy. If the CER are not rejected, sunspot-driven expectations can be ruled out from the model equilibrium and we accept the structural model. Otherwise, we move to a second-step and invert an Anderson and Rubin-type test for the orthogonality restrictions (OR) implied by the system of structural Euler equations. The hypothesis of indeterminacy and the structural model are accepted if the OR are not rejected. We investigate the finite-sample performance of the suggested identification-robust two-step testing strategy by some Monte Carlo experiments and then apply it to a New Keynesian AD/AS model estimated with actual US data. In spite of some evidence of weak identification as for the Great Moderation period, our results offer formal support to the hypothesis of a switch from indeterminacy to a scenario consistent with uniqueness occurring in the late 1970s. Our identification-robust full-information confidence set for the structural parameters computed on the Great Moderation regime turns out to be more precise than the intervals previously reported in the literature through limited-information methods.
