COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1773 Estimation and Inference with Weak, Semi-strong, and Strong Identification Donald W. K. Andrews and Xu Cheng October 2010 This paper analyzes the properties of standard estimators, tests, and
confidence sets (CS's) in a class of models in which the parameters 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, including maximum
likelihood (ML), least squares (LS), quantile, generalized method of moments (GMM),
generalized empirical likelihood (GEL), minimum distance (MD), and semi-parametric
estimators. The consistency/lack-of-consistency and asymptotic distributions of the
estimators are established under a full range of drifting sequences of true distributions.
The asymptotic size (in a uniform sense) of standard tests and CS's is established. The
results are applied to the ML estimator of an ARMA(1, 1) model and to the LS estimator of
a nonlinear regression model. |
