2022
DOI: 10.3982/ecta18678
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Optimal Decision Rules for Weak GMM

Abstract: This paper studies optimal decision rules, including estimators and tests, for weakly identified GMM models. We derive the limit experiment for weakly identified GMM, and propose a theoretically‐motivated class of priors which give rise to quasi‐Bayes decision rules as a limiting case. Together with results in the previous literature, this establishes desirable properties for the quasi‐Bayes approach regardless of model identification status, and we recommend quasi‐Bayes for settings where identification is a … Show more

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Cited by 13 publications
(14 citation statements)
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“…The optimal test in the presence of weakly identified baseline moments is beyond the scope of the paper. However, the literature has provided several encouraging power results for various conditional tests against the null hypothesis H0:θ=θ0 (e.g., Andrews, Moreira, and Stock (2006), Andrews and Mikusheva (2016a, forthcoming)) and we expect the conditional specification test to inherit these good properties. One may also apply the generic methods of Elliott, Müller, and Watson (2015) to evaluate the efficiency of an ad hoc test with correct size.…”
Section: Theoretical Propertiesmentioning
confidence: 86%
“…The optimal test in the presence of weakly identified baseline moments is beyond the scope of the paper. However, the literature has provided several encouraging power results for various conditional tests against the null hypothesis H0:θ=θ0 (e.g., Andrews, Moreira, and Stock (2006), Andrews and Mikusheva (2016a, forthcoming)) and we expect the conditional specification test to inherit these good properties. One may also apply the generic methods of Elliott, Müller, and Watson (2015) to evaluate the efficiency of an ad hoc test with correct size.…”
Section: Theoretical Propertiesmentioning
confidence: 86%
“…In this limit experiment, as in the finite-sample problem, the goal is to choose an estimator δ, which now maps realizations of g(•) to estimates δ(g, Σ) ∈ A, in a way which yields a low risk E m [L(δ(g, Σ), θ * )], where E m [•] denotes the expectation taken under (2). Andrews and Mikusheva (2022) shows that the risk in the limit experiment lower-bounds the (appropriately scaled) asymptotic risk in the original problem.…”
Section: Settingmentioning
confidence: 99%
“…Specifically, the moment condition E [φ(X, θ)] = 0 should be uniquely solved at θ * , and the sample moment function g n (θ) should be wellseparated from zero, asymptotically, outside infinitesimal neighborhoods of θ * . These point-and strong-identification assumptions are a poor fit for many economic applications, so in Andrews and Mikusheva (2022) we derived an alternative asymptotic efficiency theory for moment condition models with weak and partial identification. There, we showed that under mild conditions the problem of inference on θ * under weak identification reduces, asymptotically, to observing a single realization of a Gaussian process…”
Section: Settingmentioning
confidence: 99%
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