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

Giuseppe De Luca (), Jan Magnus and Franco Peracchi
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Jan Magnus: Vrije Universiteit Amsterdam

No 22-022/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: Model averaging; normal location model; consistency; asymptotic normality; WALS (search for similar items in EconPapers)
JEL-codes: C11 C13 C51 C52 (search for similar items in EconPapers)
Date: 2022-02-24
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Working Paper: Asymptotic properties of the weighted-average least squares (WALS) estimator (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20220022

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