Estimation of Behavioral Parameters of CGE Models For the 28 EU Countries

(A) Presenter

Second Bwanakare, University of Information Technology and Management in Rzeszow

(B) Category

Mature idea awaiting possible call

(C) Partners needed

- CGE modeler for the interpretation of model outputs
- Economist or statistician for statistical data gathering and processing

Research project objectives

The objective of the project is to implement a power law(PL)-based econometric parameter estimation approach, known in recent literature as non-extensive (cross)entropy econometrics [Golan, Judge and Miller, 1996; Bwanakare, 2013, 2014], to solve a large class of non-linear inverse problems.
Unlike most of traditional econometrical techniques, non-particular hypotheses are imposed on such generalized entropy model which combines the second universal law of thermodynamics with the Bayesian information processing rule. On a theoretical ground, a PL will be described in connection with Tsallis non-additive statistics. Then, formalism related to Tsallis nonextensive cross-entropy econometrics will be set up in the context of a Bayesian rule.
A mathematical relationships between a generic constant elasticity of substitution (CES) function, a PL and statistical inference characterization of the new estimator will be also presented. On empirical side, this will allow for parameter estimation of CES(supply and demand side) for 28 EU countries. Thanks to this new PL-based statistical procedure, obtained parameters are robust since data generating system (CES model) displays PL characteristics plausibly with a closed-form. Nevertheless, in this case we deal with a Levy’s law instable processes. Therefore an analytical cross-analysis of outputs will be also presented. In particular, different levels of elasticity of substitution between production or demand factors of the 28 EU countries will be shown and discussed under the hypothesis that these countries are dwelling on different economic growth paths – in the sense of Solow and new endogenous growth models.

Research methodology

Power-law (PL) formalism is known to provide an appropriate framework for canonical modeling of nonlinear systems. After having presented the PL nature of CES function, we will estimate 28 models of CES production or demand functions as non-linear inverse problem. Statistical data – available on the EUROSTAT database, will be grouped in accordance with variables defining CES production or demand function. An information-theoretic formalism will be introduced and q-generalization of Kullback-Leibler (K-L) information divergence criterion function- with a priori consistency constraints will be proposed as a new methodology to solve this class of complex models. Related inferential statistical indices will be also computed. Outputs from traditional competitive econometric techniques (Shannon entropy, NLLS, GMM, ML) will be presented and as well. Having obtained model estimates of each country, a
cross-comparison of CES parameters will be carried out in the context of economic growth theory.

Research project impact

The main impact of the project will be due to the estimation of the parameters of CES characterized by a higher precision on a basis of a true data generating model. A constellation of different levels of elasticity of substitution between factors for a variety of EU countries should suggest insights on the position – on the growth path, for each of the countries in the context of recent growth models. Next, estimated parameters will allow EU community of macroeconomists to revisit a variety of general equilibrium (or quasi-equilibrium) models built upon hazardously calibrated CES parameters. 
The impact of this project could be of crucial importance for the future of general equilibrium
modeling. In fact, analogical technics could be also used in the case of utility and technical transformation models that both require a large-scale macroeconomic modeling.

Justification - basic research

The proposed estimation technique of power law-based non-extensive entropy econometrics is a new, robust devise for illbehaved inverse problem. In essence, this approach constitutes the junction of two distinct concepts: Tsallis-oriented non-additive statistics- then the generalized second law of thermodynamics, and the Bayesian generalized method of moments. Rival traditional econometric techniques are not conceptually adapted to solving such complex inverse problems. In recent years, power law-based Tsallis entropy has shown its multidisciplinary character through its various applications in many fields, including financial ones.
Its popularity can be attributed to its trans-disciplinary properties of describing with higher accuracy heavy tail non-ergodic phenomena. However, the link between power law (PL) and macroeconomic phenomena has been neglected—probably because of the facility use and interpretation of the Gaussian family of laws, which are globally sufficient for time (or space) aggregated data. In light of recent literature, the amplitude and frequency of macroeconomic fluctuations do not substantially diverge from many extreme events, natural or human-related, once explained at the same time-or space, scale by power law. Recent developments in information-theoretic built upon Tsallis non-additive statistics show that long range correlation and observed time invariant scale structure of high frequency series may still be conserved—in some classes of non-linear models, e.g. CES models—through a process of time (or space) aggregation of statistical data. In such a case, the proposed non-extensive entropy econometrics approach should show a higher estimated parameter efficiency over existing competitive procedures. Next, when aggregated data converge to the Gaussian attractor, as generally happens, outputs from Gibbs-Shannon entropy coincide with those derived through Tsallis entropy. In general, when the model involved displays less complexity (with well-behaved data matrix) and remains closer to Gaussian law, computed outputs by both entropy econometrics approaches should coincide or approximate those derived through most classical econometric approaches. Thus, the proposed non-ergodic approach could be at least as good as the existing estimation techniques. On empirical grounds, this more general approach helps in ensuring stability of the estimated parameters and in solving some classes of, up to now, intractable non-linear models.