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Central to many inferential situations is the estimation of rationalfunctions of parameters. The mainstream in statistics and econometricsestimates these quantities based on the plug-in approach without considerationof the main objective of the inferential situation. We propose the BayesianMinimum Expected Loss (MELO) approach focusing explicitly on the function ofinterest, and calculating its frequentist variability. Asymptotic properties ofthe MELO estimator are similar to the plug-in approach. Nevertheless,simulation exercises show that our proposal is better in situationscharacterized by small sample sizes and noisy models. In addition, we observein the applications that our approach gives lower standard errors thanfrequently used alternatives when datasets are not very informative.

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