Identification- and Singularity-Robust Inference for Moment Condition

Donald Andrews () and Patrik Guggenberger

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

Abstract: This paper introduces two new identification- and singularity-robust conditional quasi-likelihood ratio (SR-CQLR) tests and a new identification- and singularity-robust Anderson and Rubin (1949) (SR-AR) test for linear and nonlinear moment condition models. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For two of the three tests, all that is required is that the moment functions and their derivatives have 2 + gamma bounded moments for some gamma > 0 in i.i.d. scenarios. In stationary strong mixing time series cases, the same condition suffices, but the magnitude of gamma is related to the magnitude of the strong mixing numbers. For the third test, slightly stronger moment conditions and a (standard, though restrictive) multiplicative structure on the moment functions are imposed. For all three tests, 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 two SR-CQLR tests are shown to be asymptotically efficient in a GMM sense under strong and semi-strong identification (for all k greater than or equal to p; where k and p are the numbers of moment conditions and parameters, respectively). The two SR-CQLR tests reduce asymptotically to Moreira's CLR test when p = 1 in the homoskedastic linear IV model. The first SR-CQLR test, which relies on the multiplicative structure on the moment functions, also does so for p greater than or equal to 2

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)
Pages: 154 pages
Date: 2015-01
New Economics Papers: this item is included in nep-ecm
Note: Includes supplemental material
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Related works:
Working Paper: Identification- and Singularity-Robust Inference for Moment Condition (2019)
Working Paper: Identification- and Singularity-Robust Inference for Moment Condition (2018)
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