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Penalised Continuous-Updating GMM Estimators: Shrinking the No-moment Problem
The GMM Continuous Updating Estimator (CUE) is known to suffer from large finite—sample variability in general. The variability may be so large that the CUE’s do not have any moments. We first identify the underlying cause for this adverse behaviour of the CUE’s, namely the weighting matrix entering the CUE objective function. We then propose to resolve this problem by introducing a class of penalised CUE’s, where large values of this weighting matrix are penalised. We 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 CUE, which we call the quasi-likelihood GMM (QL-GMM) estimator, uses the log-determinant of the optimal weighting matrix as penalty. Through simulations, we find that in practice the penalised CUE dominates the standard CUE both in terms of computational and statistical properties: The former is a lot easier to compute and comes with significantly smaller variances compared to the latter. The variance reduction comes with only a small price in terms of slightly bigger biases.
Date:
21 February 2025, 14:15
Venue:
Manor Road Building, Manor Road OX1 3UQ
Venue Details:
Seminar Room C
Speaker:
Dennis Kristensen (University College London)
Organising department:
Department of Economics
Part of:
Nuffield Econometrics Seminar
Booking required?:
Not required
Audience:
Members of the University only
Editor:
Edward Valenzano
