Non-Extensive Entropy Econometrics: New Statistical Features of Constant Elasticity of Substitution-Related Models

Second Bwanakare

doi:10.3390/e16052713

Abstract

Power-law (PL) formalism is known to provide an appropriate framework for canonical modeling of nonlinear systems. We estimated three stochastically distinct models of constant elasticity of substitution (CES) class functions as non-linear inverse problem and showed that these PL related functions should have a closed form. The first model is related to an aggregator production function, the second to an aggregator utility function (the Armington) and the third to an aggregator technical transformation function. A q-generalization of K-L information divergence criterion function with a priori consistency constraints is proposed. Related inferential statistical indices are computed. The approach leads to robust estimation and to new findings about the true stochastic nature of this class of nonlinear—up until now—analytically intractable functions. Outputs from traditional econometric techniques (Shannon entropy, NLLS, GMM, ML) are also presented.

Highlights

This paper proposes a new approach for modeling stochastic non-linear inverse problems.The approach is based upon Kullback-Leibler (K-L) relative entropy [1] which is generalized through a Levy-unstable PL process
A constant elasticity of substitution (CES) is a property of Entropy 2014, 16 some supply and utility functions which refers to a particular type of aggregator function combining two or more types of supply inputs or demand items into the aggregate quantity
In the case of the CES production model (CESP) model, we found for q converging to unity a coefficient variation (CV) of 85.3% in the case of K-L, against 0.06% for an optimal q equal to 2.331

Summary

Introduction

This paper proposes a new approach for modeling stochastic non-linear inverse problems. The CET model remains an identity equation, covariate values of which sum up to the explained value of the model, suggesting that national production aggregates two classes of goods (the locally demanded product and the export product). These two goods are supplied through a constant elasticity of technical transformation [3]. Thanks to the proposed non-extensive entropy approach—enabled by PL characterization of CES functions—implications on the stochastic features of these three distinct models are pointed out through robust estimation procedure To our knowledge, this nonlinear class of functions remains analytically intractable when using traditional statistical techniques.

Tsallis Non-Extensive Entropy and Low Frequency Series Modeling

PL and the CES Function

A Generalized Non-Extensive Entropy Econometric Model

Parameter Confidence Area

Model Outputs and Discussion

Concluding Remarks