Sampling properties of the Bayesian posterior mean with an application to WALS estimation

Giuseppe De Luca; Jan R. Magnus; Franco Peracchi

doi:10.1016/j.jeconom.2021.04.008

Sampling properties of the Bayesian posterior mean with an application to WALS estimation

Giuseppe De Luca^*, Jan R. Magnus, Franco Peracchi

^*Corresponding author for this work

Econometrics and Data Science

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Abstract

Many statistical and econometric learning methods rely on Bayesian ideas. When applied in a frequentist setting, their precision is often assessed using the posterior variance. This is permissible asymptotically, but not necessarily in finite samples. We explore this issue focusing on weighted-average least squares (WALS), a Bayesian-frequentist ‘fusion’. Exploiting the sampling properties of the posterior mean in the normal location model, we derive estimators of the finite-sample bias and variance of WALS. We study the performance of the proposed estimators in an empirical application and a closely related Monte Carlo experiment which analyze the impact of legalized abortion on crime.

Original language	English
Pages (from-to)	299-317
Number of pages	19
Journal	Journal of Econometrics
Volume	230
Issue number	2
Early online date	5 Jun 2021
DOIs	https://doi.org/10.1016/j.jeconom.2021.04.008
Publication status	Published - Oct 2022

Bibliographical note

Funding Information:
We thank Domenico Giannone, Henk Pijls, and Giorgio Primiceri for useful discussions, and an Associate Editor and three anonymous referees for their positive and constructive comments. Giuseppe De Luca acknowledges financial support from MIUR, Italy , PRIN PRJ-0324 .

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Double-shrinkage estimators
Normal location model
Posterior moments and cumulants
WALS

UN SDGs

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10.1016/j.jeconom.2021.04.008

Sampling properties of the Bayesian posterior mean with an application to WALS estimationFinal published version, 735 KBLicence: Article 25fa Dutch Copyright Act

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title = "Sampling properties of the Bayesian posterior mean with an application to WALS estimation",

abstract = "Many statistical and econometric learning methods rely on Bayesian ideas. When applied in a frequentist setting, their precision is often assessed using the posterior variance. This is permissible asymptotically, but not necessarily in finite samples. We explore this issue focusing on weighted-average least squares (WALS), a Bayesian-frequentist {\textquoteleft}fusion{\textquoteright}. Exploiting the sampling properties of the posterior mean in the normal location model, we derive estimators of the finite-sample bias and variance of WALS. We study the performance of the proposed estimators in an empirical application and a closely related Monte Carlo experiment which analyze the impact of legalized abortion on crime.",

keywords = "Double-shrinkage estimators, Normal location model, Posterior moments and cumulants, WALS",

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AU - Magnus, Jan R.

AU - Peracchi, Franco

N1 - Funding Information: We thank Domenico Giannone, Henk Pijls, and Giorgio Primiceri for useful discussions, and an Associate Editor and three anonymous referees for their positive and constructive comments. Giuseppe De Luca acknowledges financial support from MIUR, Italy , PRIN PRJ-0324 . Publisher Copyright: © 2021 Elsevier B.V.

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KW - Posterior moments and cumulants

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Sampling properties of the Bayesian posterior mean with an application to WALS estimation

Abstract

Bibliographical note

Keywords

UN SDGs

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