Valid Two-Step Identification-Robust Confidence Sets for GMM

In models with potentially weak identification, researchers often decide whether to report a robust confidence set based on an initial assessment of model identification. Two-step procedures of this sort can generate large coverage distortions for reported confidence sets, and existing procedures for controlling these distortions are quite limited. This paper introduces a generally applicable approach to detecting weak identification and constructing two-step confidence sets in GMM. This approach controls coverage distortions under weak identification and indicates strong identification, with probability tending to 1 when the model is well identified

Identification of and correction for publication bias

Some empirical results are more likely to be published than others. Such selective publication leads to biased estimates and distorted inference. This paper proposes two approaches for identifying the conditional probability of publication as a function of a study's results, the first based on systematic replication studies and the second based on meta-studies. For known conditional publication probabilities, we propose median-unbiased estimators and associated confidence sets that correct for selective publication. We apply our methods to recent large-scale replication studies in experimental economics and psychology, and to meta-studies of the effects of minimum wages and de-worming programs

Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak instrument asymptotics with an unknown error distribution

Weak Identification in Maximum Likelihood: A Question of Information

In this paper we connect the discrepancy between two estimates of Fisher information, one based on the quadratic variation of the score and the other based on the negative Hessian of the log-likelihood, to weak identification. Classical asymptotic approximations assume that these two estimates are asymptotically equivalent, but we show that this equivalence fails in many weakly identified models, which can distort the behavior of the MLE. Using a stylized DSGE model we show that the discrepancy between information estimates is large when identification is weak.National Science Foundation (U.S.) (NSF Graduate Research Fellowship, grant no. 1122374)Alfred P. Sloan Foundation (Fellowship)Massachusetts Institute of Technology (Castle-Krob Career Development Chair

Maximum Likelihood Inference in Weakly Identified DSGE Models

This paper examines the problem of weak identification in maximum likelihood, motivated by problems with estimation and inference a multi-dimensional, non-linear DSGE model. We suggest a test for a simple hypothesis concerning the full parameter vector which is robust to weak identification. We also suggest a test for a composite hypothesis regarding a sub-vector of parameters. The suggested test is shown to be asymptotically exact when the nuisance parameter is strongly identified, and in some cases when the nuisance parameter is weakly identified. We pay particular attention to the question of how to estimate Fisher's information, and make extensive use of martingale theory

A Geometric Approach to Weakly Identified Econometric Models

Many nonlinear Econometric models show evidence of weak identification, including many Dynamic Stochastic General Equilibrium models, New Keynesian Phillips curve models, and models with forward-looking expectations. In this paper we consider minimum distance statistics and show that in a broad class of models the problem of testing under weak identification is closely related to 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 Anderson-Rubin-type statistics, which we show can be used to detect weak identification and to construct tests robust to weak identification. We apply the new method to a small-scale DSGE model and show that it provides a significant improvement over existing methods

Optimal Decision Rules for Weak GMM

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

Robust Two-Step Confidence Sets, and the Trouble with the First Stage F-Statistic

When weak identification is a concern researchers frequently calculate confidence sets in two steps, first assessing the strength of identification and then, on the basis of this initial assessment, deciding whether to use an identification-robust confidence set. Unfortunately, two-step procedures of this sort can generate highly misleading confidence sets, and we demonstrate that two-step confidence sets based on the first stage F-statistic can have extremely poor coverage in linear instrumental variables models with heteroskedastic errors. To remedy this issue, we introduce a simple approach to detecting weak identification and constructing two-step confidence sets which we show controls coverage distortions under weak identification in general nonlinear GMM models, while also indicating strong identification with probability tending to one if the model is well-identified. Applying our approach to linear IV we show that it is competitive with approaches based on the first-stage F-statistic under homoscedasticity but performs far better under heteroskedasticity

Replication data for: "Valid Two-Step Identification-Robust Confidence Sets for GMM"

Replication data for: "Valid Two-Step Identification-Robust Confidence Sets for GMM