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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\u2010equation restrictions (CER) that the New Keynesian system places on its reduced\u2010form solution under determinacy. If the CER are not rejected, sunspot\u2010driven expectations can be ruled out from the model equilibrium and we accept the structural model. Otherwise, we move to a second\u2010step and invert an Anderson and Rubin\u2010type 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\u2010sample performance of the suggested identification\u2010robust two\u2010step 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 \u2018Great Moderation\u2019 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\u2010robust full\u2010information confidence set for the structural parameters computed on the \u2018Great Moderation\u2019 regime turns out to be more precise than the intervals previously reported in the literature through \u2018limited\u2010information\u2019 methods. 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