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

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  • De Luca, Giuseppe
  • Magnus, Jan R.
  • Peracchi, Franco

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.

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  • De Luca, Giuseppe & Magnus, Jan R. & Peracchi, Franco, 2022. "Sampling properties of the Bayesian posterior mean with an application to WALS estimation," Journal of Econometrics, Elsevier, vol. 230(2), pages 299-317.
    • Handle: RePEc:eee:econom:v:230:y:2022:i:2:p:299-317
    DOI: 10.1016/j.jeconom.2021.04.008
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    1. Giuseppe Luca & Jan R. Magnus & Franco Peracchi, 2023. "Weighted-Average Least Squares (WALS): Confidence and Prediction Intervals," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1637-1664, April.

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    More about this item

    Keywords

    Normal location model; Posterior moments and cumulants; Double-shrinkage estimators; WALS;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • I21 - Health, Education, and Welfare - - Education - - - Analysis of Education

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