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Identification- and Singularity-Robust Inference for Moment Condition

Donald W. K. Andrews () and Patrik Guggenberger
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Donald W. K. Andrews: Cowles Foundation, Yale University, http://economics.yale.edu/people/donald-w-k-andrews
Patrik Guggenberger: Dept. of Economics, Penn State University

No 1978R2, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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+? bounded moments for some ?>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 (search for similar items in EconPapers)
JEL-codes: C10 C12 (search for similar items in EconPapers)
Date: 2015-01, Revised 2019-01
Note: Includes supplemental material
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