  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.
