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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 concern. We further propose weighted average power‐optimal identification‐robust frequentist tests and confidence sets, and prove a Bernstein‐von Mises‐type result for the quasi‐Bayes posterior under weak identification. [ABSTRACT FROM AUTHOR]

We propose a positive model of empirical science in which an analyst makes a report to an audience after observing some data. Agents in the audience may differ in their beliefs or objectives, and may therefore update or act differently following a given report. We contrast the proposed model with a classical model of statistics in which the report directly determines the payoff. We identify settings in which the predictions of the proposed model differ from those of the classical model, and seem to better match practice. [ABSTRACT FROM AUTHOR]

We propose a way to formalize the relationship between descriptive analysis and structural estimation. A researcher reports an estimate ĉ of a structural quantity of interest c that is exactly or asymptotically unbiased under some base model. The researcher also reports descriptive statistics γˆ that estimate features γ of the distribution of the data that are related to c under the base model. A reader entertains a less restrictive model that is local to the base model, under which the estimate ĉ may be biased. We study the reduction in worst‐case bias from a restriction that requires the reader's model to respect the relationship between c and γ specified by the base model. Our main result shows that the proportional reduction in worst‐case bias depends only on a quantity we call the informativeness of γˆ for ĉ. Informativeness can be easily estimated even for complex models. We recommend that researchers report estimated informativeness alongside their descriptive analyses, and we illustrate with applications to three recent papers. [ABSTRACT FROM AUTHOR]

Correspondingly, a given distribution I F i may now be consistent with a set HT ht of possible values of I c i .[4] Importantly, though not in general a singleton, for bounded HT ht the set HT ht will typically be limited in size. This alternative relaxation is not nested by the one we define based on bounded neighborhoods HT ht . The set HT ht tells us which values of I c i are consistent with the complete distribution of the observed data. [Extracted from the article]

We introduce the class of conditional linear combination tests, which reject null hypotheses concerning model parameters when a data-dependent convex combination of two identification-robust statistics is large. These tests control size under weak identification and have a number of optimality properties in a conditional problem. We show that the conditional likelihood ratio test of Moreira, 2003 is a conditional linear combination test in models with one endogenous regressor, and that the class of conditional linear combination tests is equivalent to a class of quasi-conditional likelihood ratio tests. We suggest using minimax regret conditional linear combination tests and propose a computationally tractable class of tests that plug in an estimator for a nuisance parameter. These plug-in tests perform well in simulation and have optimal power in many strongly identified models, thus allowing powerful identification-robust inference in a wide range of linear and nonlinear models without sacrificing efficiency if identification is strong. [ABSTRACT FROM AUTHOR]

This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a sufficient statistic for this nuisance parameter in a Gaussian problem and propose conditional tests. These conditional tests have uniformly correct asymptotic size for a large class of models and test statistics. We apply our approach to construct tests based on quasi-likelihood ratio statistics, which we show are efficient in strongly identified models and perform well relative to existing alternatives in two examples. [ABSTRACT FROM AUTHOR]

Conventional tests for composite hypotheses in minimum distance models can be unreliable when the relationship between the structural and reduced-form parameters is highly nonlinear. Such nonlinearity may arise for a variety of reasons, including weak identification. In this note, we begin by studying the problem of testing a "curved null" in a finite-sample Gaussian model. Using the curvature of the model, we develop new finite-sample bounds on the distribution of minimum-distance statistics. These bounds allow us to construct tests for composite hypotheses which are uniformly asymptotically valid over a large class of data generating processes and structural models. [ABSTRACT FROM AUTHOR]