Identification- and Singularity-Robust Inference for Moment Condition Models

212 Pages Posted: 5 Apr 2019

See all articles by Donald W. K. Andrews

Donald W. K. Andrews

Yale University - Cowles Foundation

Patrik Guggenberger

Pennsylvania State University, College of the Liberal Arts - Department of Economic

Multiple version iconThere are 3 versions of this paper

Date Written: April 4, 2019

Abstract

This paper introduces a new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) test and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2+γ bounded moments for some γ>0. No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions.

The SR-CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi-strong identification (for all k≥p, where k and p are the numbers of moment conditions and parameters, respectively). The SR-CQLR test reduces asymptotically to Moreira’s CLR test when p=1 in the homoskedastic linear IV model. The same is true for p≥2 in most, but not all, identification scenarios.

We also introduce versions of the SR-CQLR and SR-AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR-CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi-strong identification.

Keywords: Asymptotics, Conditional likelihood ratio test, Confidence set, Identification, Inference, Moment conditions, Robust, Singular variance, Test, Weak identification, Weak instruments

JEL Classification: C10, C12

Suggested Citation

Andrews, Donald W. K. and Guggenberger, Patrik, Identification- and Singularity-Robust Inference for Moment Condition Models (April 4, 2019). Cowles Foundation Discussion Paper No. 1978R2, Available at SSRN: https://ssrn.com/abstract=3366443 or http://dx.doi.org/10.2139/ssrn.3366443

Donald W. K. Andrews (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

Patrik Guggenberger

Pennsylvania State University, College of the Liberal Arts - Department of Economic ( email )

524 Kern Graduate Building
University Park, PA 16802-3306
United States

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