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Asymptotic properties of the weighted-average least squares (WALS) estimator

Giuseppe De Luca (), Jan R. Magnus and Franco Peracchi ()
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Jan R. Magnus: Vrije Universiteit Amsterdam and Tinbergen Institute

No 2203, EIEF Working Papers Series from Einaudi Institute for Economics and Finance (EIEF)

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, 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 √n-consistent and its asymptotic distribution essentially coincides with that of the unrestricted least-squares estimator. Monte Carlo simulations confirm our theoretical results.

Pages: 36 pages
Date: 2022, Revised 2022-03
New Economics Papers: this item is included in nep-ban and nep-ore
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