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Cowles Foundation Discussion Papers

2011

Asymptotics

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Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger Mar 2011

Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger

Cowles Foundation Discussion Papers

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 + γ bounded moments for some γ > 0 in i.i.d. scenarios. In stationary strong mixing time series cases, the same condition suffices, but the magnitude of …


Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger Mar 2011

Identification- And Singularity-Robust Inference For Moment Condition Models, Donald W.K. Andrews, Patrik Guggenberger

Cowles Foundation Discussion Papers

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 …