Dennis Kristensen, UCL

"Penalised Continuous-Updating GMM Estimators: Shrinking the No-moment Problem"

Abstract

We propose a class of penalised estimators as a solution to the no--moment problem of the GMM Continuously Updated Estimator (CUE). We analyse the finite-sample and asymptotic properties of the CUE and its penalised version, and show that the added penalty reduces finite--sample variability and restores moments. We also analyse the higher--order properties of the penalised version which provides guidelines for how to choose the penalty. Our preferred penalised estimator, which we call the quasi-likelihood GMM (QL--GMM) estimator, uses the log-determinant of the optimal weighting matrix as penalty. This choice of penalty is justified asymptotically since the QL-GMM objective function is the large--sample log--likelihood of the sample moments. The implementation of the penalised estimators are computationally less burdensome compared to the standard CUE, and the former perform well in simulations with significantly smaller variance compared to the latter, while paying only a small price in terms of slightly bigger biases.

Contact person: Anders Rahbek