Focused econometric estimation for noisy and small datasets: A Bayesian Minimum Expected Loss estimator approach

TL;DR

This paper introduces a Bayesian Minimum Expected Loss (MELO) estimator tailored for noisy and small datasets, improving estimation accuracy for functions of parameters by explicitly focusing on the quantity of interest.

Contribution

It develops a novel MELO estimator that outperforms traditional plug-in methods in small sample and noisy data scenarios, with comparable asymptotic properties.

Findings

MELO estimator yields lower standard errors in small, noisy datasets.

Simulation shows improved accuracy over traditional methods.

Asymptotic properties are similar to existing plug-in estimators.

Abstract

Central to many inferential situations is the estimation of rational functions of parameters. The mainstream in statistics and econometrics estimates these quantities based on the plug-in approach without consideration of the main objective of the inferential situation. We propose the Bayesian Minimum Expected Loss (MELO) approach focusing explicitly on the function of interest, and calculating its frequentist variability. Asymptotic properties of the MELO estimator are similar to the plug-in approach. Nevertheless, simulation exercises show that our proposal is better in situations characterized by small sample sizes and noisy models. In addition, we observe in the applications that our approach gives lower standard errors than frequently used alternatives when datasets are not very informative.