Preliminary and incomplete

Comments welcome This paper focuses on the efficient estimation of a finite dimensional parameter in a linear model where the number of potential instruments is very large or infi-nite. It is well-known that the instrumental variables (IV) estimator has poor small sample properties when the number of instruments is large. In order to improve these small sample properties, we propose three modified IV estimators based on three different ways of inverting the covariance matrix of the instruments. These methods are based on the spectral decomposition of the covariance matrix and in-volve a regularization or smoothing parameter. We show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound under some standard assumptions. Moreover, we derive the analytic expression of the mean square error (MSE) of the estimators and propose to select the value of the regularization parameter that minimizes the approximated MSE. The simulations show that these new estimators have good small sample properties