GEL statistics under weak identification

Guggenberger, Patrik; Ramalho, Joaquim J.S.; Smith, Richard J.

doi:10.1016/j.jeconom.2012.05.009

Cited by 22 publications

(37 citation statements)

References 70 publications

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“…For a certain parameter space of null distributions

{scriptF}_{0}

, AG1 establishes correct asymptotic size for Kleibergen's CLR tests that are based on (what AG1 calls) moment‐variance‐weighting (MVW) of the orthogonalized sample Jacobian matrix, combined with a rank statistic, such as the Robin and Smith () rank statistic. Tests of this type have been considered by Guggenberger, Ramalho, and Smith (). AG1 also determines a formula for the asymptotic size of Kleibergen's CLR tests that are based on (what AG1 calls) Jacobian‐variance‐weighting (JVW) of the orthogonalized sample Jacobian matrix, which is the weighting suggested by Kleibergen.…”

Section: Discussion Of the Related Literaturementioning

confidence: 99%

Identification‐ and singularity‐robust inference for moment condition models

Andrews¹,

Guggenberger

2019

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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.

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“…For a certain parameter space of null distributions

{scriptF}_{0}

Section: Discussion Of the Related Literaturementioning

confidence: 99%

Identification‐ and singularity‐robust inference for moment condition models

Andrews¹,

Guggenberger

2019

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“…Standard inferential tools such as LR and Wald test statistics no longer have the standard limiting normal or chi-square distributions. A number of methods have been proposed to ameliorate this problem, primarily related to score or Lagrange multiplier statistics as discussed in section 4; see, e.g., Kleibergen (2005), Guggenberger et al (2012) and Otsu (2006). Newey and Windmeijer (2009) obtains the limiting properties of GMM and (G)EL when there are many weak moments and, in particular, shows that the respective variance matrices are in ated in comparison to the standard variance matrix expression given in section 3 for e cient 2SGMM and GEL.…”

Section: Discussionmentioning

confidence: 99%

Recent Developments in Empirical Likelihood and Related Methods

Parente

Smith

2014

Annu. Rev. Econ.

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This article reviews a number of recent contributions to estimation and inference for models de ned by moment condition restrictions. The particular emphasis is on the generalised empirical likelihood class of estimators as an alternative to generalised method of moments. Estimation methods for parameters de ned through moment restrictions and their properties are described with tests of overidentifying moment restrictions and parametric hypotheses. Computational issues are discussed together with some proposals for their amelioration. Higher order and other properties are also addressed in some detail. Models speci ed by conditional moment restriction models are considered and a discussion of the adaptation of these methods to weakly dependent data is given.

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“…Its objective is to develop powerful tests whose asymptotic null rejection probability is controlled uniformly over a parameter space that allows for weak instruments. 3 Under the assumption that the unrestricted structural parameters are strongly identified, the above robust full vector procedures can be adapted by replacing the unrestricted structural parameters by consistently estimated counterparts; see Stock and Wright (2000), Kleibergen (2004Kleibergen ( , 2005, Guggenberger and Smith (2005), Otsu (2006), and Guggenberger, Ramalho, and Smith (2012), among others, for such adaptations of the AR, LM, and CLR tests to subset testing. 2 An applied researcher is, however, typically not interested in simultaneous inference on all structural parameters, but in inference on a subset, like one component, of the structural parameter vector.…”

Section: Introductionmentioning

confidence: 99%

“…Tests of a subset hypothesis are substantially more complicated than tests of a joint hypothesis since the unrestricted structural parameters enter the testing problem as additional nuisance parameters. 3 Under the assumption that the unrestricted structural parameters are strongly identified, the above robust full vector procedures can be adapted by replacing the unrestricted structural parameters by consistently estimated counterparts; see Stock and Wright (2000), Kleibergen (2004Kleibergen ( , 2005, Guggenberger and Smith (2005), Otsu (2006), and Guggenberger, Ramalho, and Smith (2012), among others, for such adaptations of the AR, LM, and CLR tests to subset testing. Under the assumption of strong identification of the unrestricted structural parameters, the resulting subset tests were proven to be asymptotically robust with respect to the potential weakness of identification of the hypothesized structural parameters and, trivially, have non-worse power properties than projection-type tests.…”

Section: Introductionmentioning

confidence: 99%

On the Asymptotic Sizes of Subset Anderson-Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression

et al. 2012

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We consider tests of a simple null hypothesis on a subset of the coefficients of the exogenous and endogenous regressors in a single-equation linear instrumental variables regression model with potentially weak identification. Existing methods of subset inference (i) rely on the assumption that the parameters not under test are strongly identified, or (ii) are based on projection-type arguments. We show that, under homoskedasticity, the subset Anderson and Rubin (1949) test that replaces unknown parameters by limited information maximum likelihood estimates has correct asymptotic size without imposing additional identification assumptions, but that the corresponding subset Lagrange multiplier test is size distorted asymptotically.

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GEL statistics under weak identification

Cited by 22 publications

References 70 publications

Identification‐ and singularity‐robust inference for moment condition models

Identification‐ and singularity‐robust inference for moment condition models

Recent Developments in Empirical Likelihood and Related Methods

On the Asymptotic Sizes of Subset Anderson-Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression

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