This paper analyzes the conditions under which consistent estimation can be achieved in instrumental variables (IV) regression when the available instruments are weak and the number of instruments, K_n, goes to infinity with the sample size. We show that consistent estimation depends importantly...

In parametric, nonlinear structural models, a classical sufficient condition for local identification, like Fisher (1966) and Rothenberg (1971), is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We derive an analogous result for the...

Using many moment conditions can improve efficiency but makes the usual generalized method of moments (GMM) inferences inaccurate. Two-step GMM is biased. Generalized empirical likelihood (GEL) has smaller bias, but the usual standard errors are too small in instrumental variable settings. In...

In an effort to improve the small sample properties of generalized method of moments (GMM) estimators, a number of alternative estimators have been suggested. These include empirical likelihood (EL), continuous updating, and exponential tilting estimators. We show that these estimators share a...

This paper uses control variables to identify and estimate models with nonseparable, multidimensional disturbances. Triangular simultaneous equations models are considered, with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar...

For conditional heteroskedasticity models, the authors study the identification condition that is required for consistency of a non-Gaussian quasi-maximum-likelihood estimator. They show that, if the conditional mean is zero or if a symmetry condition is satisfied, then the identification...

Conditional moment restrictions can be combined through GMM estimation to construct more efficient semiparametric estimators. This paper is about attainable efficiency for such estimators. We define and use a moment tangent set, the directions of departure from the truth allowed by the moments,...

This paper presents a simple two-step nonparametric estimator for a triangular simultaneous equation model. The authors use series approximations that exploit the additive structure of the model. The first step comprises the nonparametric estimation of the reduced form and the corresponding...

The purpose of this note is to show how semiparametric estimators with a small bias property can be constructed. The small bias property (SBP) of a semiparametric estimator is that its bias converges to zero faster than the pointwise and integrated bias of the nonparametric estimator on which it...