Simultaneous selection and weighting of moments in GMM using a trapezoidal kernel

This paper proposes a novel procedure to estimate linear models when the number of instruments is large. At the heart of such models is the need to balance the trade off between attaining asymptotic efficiency, which requires more instruments, and minimizing bias, which is adversely affected by the addition of instruments. Two questions are of central concern: (1) What is the optimal number of instruments to use? (2) Should the instruments receive different weights? This paper contains the following contributions toward resolving these issues. First, I propose a kernel weighted generalized method of moments (GMM) estimator that uses a trapezoidal kernel. This kernel turns out to be attractive to select and weight the number of moments. Second, I derive the higher order mean squared error of the kernel weighted GMM estimator and show that the trapezoidal kernel generates a lower asymptotic variance than regular kernels. Finally, Monte Carlo simulations show that in finite samples the kernel weighted GMM estimator performs on par with other estimators that choose optimal instruments and improves upon a GMM estimator that uses all instruments.