De Luca, G., Magnus, JanR. and Peracchi, F. (2022). Sampling properties of the Bayesian posterior mean with an application to WALS estimation Journal of Econometrics, 230(2):299--317.

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    Journal of Econometrics

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.