The aim of this article is to characterize the saturation spaces that appear in inverse problems. Such spaces are defined for a regularization method and the rate of convergence of the estimation part of the inverse problem depends on their definition. Here we prove that it is possible to define...

In this paper, I develop a quasi empirical likelihood estimator that has good finite-sample properties when there are many moment conditions. I show that the quasi empirical likelihood estimator, which uses semiparametric efficient estimation, is an approximation to the empirical likelihood...

We construct higher order expressions for Wald and Lagrange multiplier (LM) GMM statistics that are based on 2step and continuous updating estimators (CUE). We show that the sensitivity of the limit distribution to weak and many instruments results from superfluous elements in the higher order...

This paper concerns a new statistical approach to instrumental variables (IV) method for nonparametric structural models with additive errors. A general identifying condition of the model is proposed, based on richness of the space generated by marginal discretizations of joint density...

We show that the higher order biases of instrumental variable statistics in the strong instrument case indicate the degeneracy of the first order asymptotic distributions of these statistics under weak or many instrument asymptotics. We express the higher order approximations using an estimator...

In this paper we use optimal-instrument and new finite-sample methods to test the empirical relevance of the New Keynesian Phillips curve (NKPC) equation. Unlike generalized method of moments-based methods, these generalized Anderson-Rubin tests are immune to the presence of weak instruments,...

The fact that weak instruments lead to spurious inference is now widely recognized. In this paper we ask whether spurious inference occurs more generally in weakly identified models. To distinguish between models where spurious inference will occur from those where it does not, we introduce the...

In this paper we analyze GMM with semi-weak instruments. This case includes the standard GMM and the nearly-weak GMM. In the nearly-weak GMM the correlation between the instruments and the first order conditions decline at a slower rate than root T. We find an important difference between the...

This lecture explores conditions under which there is identification of the impact on an outcome of exogenous variation in a variable which is endogenous when data are gathered. The starting point is the Cowles Commission linear simultaneous equations model. The parametric and additive error...