In this paper the natural connection between information theory and entropy econometrics is investigated and discussed. After reviewing the basics of the generalized maximum entropy (GME) estimation rule, we develop the post-data (posterior) solutions for different discrete and continuous priors (for the pre-specified supports for all the unknown parameters). We then show that the choice of entropy is a natural choice that results in the independence of the post-data (posteriors) signal and noise estimators. A derivation of the super-resolution (continuous limit) of the GME and the relationship between information, efficience and inference are discussed as well.