Non-extensive entropy econometrics and CES production models: Country case study

Abstract

In many situations, official statistics institutions (OSI) and researchers try to produce statistics with the assisted-model methodology based on incomplete or poor quality data from an unknown data generating system that may display power-law (PL). The ubiquity of PL - measured for high frequency series phenomena and then Big Data - in natural phenomena or manmade complex systems is supported by a vast, recent literature. When, additionally, the number of parameters to be estimated is higher than the related observed points, we are dealing with a non-ergodic inverse problem. This article treats the particular case of aggregated time series characterized by PL and explains how to solve this kind of inverse problem through non-extensive cross-entropy econometrics (NCEE). This is a model-assisted methodology which can be seen as a coincident junction of three scientific disciplines: non-additive statistics, the Kullback-Leibler statistical information theoretic, and the traditional econometrics from the Cowles Commission. This paper provides links to comparative, empirical literature on this technique, which include an application to national production modelling through a constant elasticity of technical substitution (CETS) function.