Identification‐ and singularity‐robust inference for moment condition models

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.

Using arbitrary precision arithmetic to sharpen identification analysis for DSGE models

“…Under local identification failure, the information matrix is singular. Thus, we need to set some eigenvalues to exact zero and adjust the degrees of freedom accordingly, as in Qu (2014) and Andrews and Guggenberger (2019). For these adjustments, knowledge about the number of locally unidentified parameters is important.…”

Simple estimation of semiparametric models with measurement errors

“…Finally, one can test the strength of identification of the model parameters or even conduct identification-robust inference (e.g., Stock and Wright, 2000;Kleibergen, 2005;Guggenberger and Smith, 2005;Guggenberger, Ramalho, and Smith, 2012;Andrews and Mikusheva, 2016;Andrews, 2016;Andrews and Guggenberger, 2019).…”

A Powerful Subvector Anderson–rubin Test in Linear Instrumental Variables Regression With Conditional Heteroskedasticity

“…Deriving (3.22) under all possible drifting sequences Wn is technically tedious and involves, e.g., also consideration of so-called sequences of nonstandard weak identification (see Andrews and Guggenberger, 2019, hereafter AG, for more discussion). If (3.22) is not already implied by the restrictions in the parameter space F Het below then the asymptotic size results should simply be interpreted for sequences of parameter spaces F Het,n that impose additional restrictions on F Het such that (3.22) holds.…”