Econometrica: Sep 2012, Volume 80, Issue 5

Estimation and Inference With Weak, Semi‐Strong, and Strong Identification

https://doi.org/10.3982/ECTA9456
p. 2153-2211

Donald W. K. Andrews, Xu Cheng

This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) for parameters that are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification. This covers a class of models estimated using maximum likelihood (ML), least squares (LS), quantile, generalized method of moments, generalized empirical likelihood, minimum distance, and semi‐parametric estimators.

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Supplemental Material

Supplement to "Estimation and Inference with Weak, Semi-strong, and Strong Identification"

This appendix includes (i) a heuristic description of the approach of the paper, (ii) additional assumptions, (iii) proofs, and (iv) verification of the assumptions, additional tables and figures, and simulation details for (a) the ARMA (1,1) model, (b) the nonlinear regression model, and (c) the LIML example. 

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Supplement to "Estimation and Inference with Weak, Semi-strong, and Strong Identification"

This zip file contains the replication files for the manuscript.

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