Template-Type: ReDIF-Paper 1.0
Series: Tinbergen Institute Discussion Papers
Creation-Date: 2022-02-24
Number: 22-022/III
Author-Name: Giuseppe De Luca
Author-Workplace-Name: University of Palermo
Author-Name: Jan Magnus
Author-Workplace-Name: Vrije Universiteit Amsterdam
Author-Name: Franco Peracchi
Author-Workplace-Name: University of Rome Tor Vergata
Title: Asymptotic properties of the weighted average least squares (WALS) estimator
Abstract: We investigate the asymptotic behavior of the WALS estimator, a model-averaging estimator with attractive finite-sample and computational properties. WALS is closely related to the normal location model, and hence much of the paper concerns the asymptotic behavior of the estimator of the unknown mean in the normal local model. Since we adopt a frequentist-Bayesian approach, this specializes to the asymptotic behavior of the posterior mean as a frequentist estimator of the normal location parameter. We emphasize two challenging issues. First, our definition of ignorance in the Bayesian step involves a prior on the t-ratio rather than on the parameter itself. Second, instead of assuming a local misspecification framework, we consider a standard asymptotic setup with fixed parameters. We show that, under suitable conditions on the prior, the WALS estimator is sqrt(n)-consistent and its asymptotic distribution essentially coincides with that of the unrestricted least-squares estimator. Monte Carlo simulations confirm our theoretical results.
Classification-JEL: C11, C13, C51, C52
Keywords: Model averaging, normal location model, consistency, asymptotic normality, WALS
File-URL: https://papers.tinbergen.nl/22022.pdf
File-Format: application/pdf
File-Size: 811,390 bytes
Handle: RePEc:tin:wpaper:20220022