Second Bwanakare
ARTICLE

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ABSTRACT

Shannon-Kullback-Leibler cross-entropy (SKLCE) is particularly useful when ergodic system inverse problems require a solution. Though empirical application using the Shanon-Gibbs approach has recently met with notable success, it suffers from its ergodicity, constraining all micro-states of the system to appear with identical odds. The present document aims at extending applications of a non-extensive cross-entropy model (NECE) for balancing an input output stochastic system. The model then postulates that economic activity is characterized by long run complex behavioural interactions between economic agents and/or economic sectors. Applying scaling property of a Power-law we present a model which successfully balances a Polish national social accounting matrix (SAM) expected to exhibit Warlasian general equilibrium features. The Rao-Cramer-Kullback inferential information indexes are proposed. We note that increasing relative weight on the disturbance component of the dual criterion function leads to higher values of the q-Tsallis complexity index while smaller disturbance weights produce q values closer to unity, the case of Gaussian distribution.
The great advantage of the approach presented over rival techniques is its allowing for the generalisation of Gaussian law enabled by its capability of including heavy tall distributions. The approach also constitutes a powerful instrument for the assessment of complexity in the analysed statistical system thanks to the q-Tsallis parameter.

KEYWORDS

q-Generalization of K-L information divergence, social accounting matrix

REFERENCES

Abe S., Bagci G. B., (2004), Constraints and Relative Entropies in Non-extensive Statistical Mechanics, arXiv:cond-mat/0404253.

Aslan M., (2005), Turkish Financial Social Accounting Matrix, http://ssrn.com/abstract=782729 or http://dx.doi.org/10.2139/ssrn.782729.

Bottazzi G., Cefi s E., Dosi G., Secchi A., (2007), Invariances and Diversities in the Patterns of Industrial Evolution: Some Evidence from Italian Manufacturing Industries, Small Business Economics, 29 (1), 137–159.

Bwanakare S., (2013a), Methodologie pour la Balance d’une Matrice de Comptabilite Sociale par l’Approche de l’Entropie : le Cas du Gabon, http://www.numilog.com/236150/Methodologie-pourla-balance-d-une-matrice-de-comptabilite-sociale-par-l-approche-econometrique-de-l-entropie---lecas-du-Gabon.ebook.

Bwanakare S., (2013b), Non-extensive Entropy Econometrics for Low Frequency Series: Robust Estimation of National Accounts -Based Models, monograph, work under publication by De Gruyter Open Champernowne D. G., (1953), A Model of Income Distribution, The Economic Journal, 63 (250), 318–351.

Chisari O. O., Mastronardi L. J., Romero C. A., (2012), Building an Input-Output Model for Buenos Aires City, MPRA Paper No. 40028, July.

Dragulescu A., Yakovenko V. M., (2001), Exponential and Power-law Probability Distributions of Wealth and Income in the UK and the USA, Elsevier, Physica A., 299 213–221.

Foley D. K., Smith E., (2008), Classical Thermodynamics and Economic General Equilibrium Theory, Elsevier, Journal of Economic Dynamics & Control 32, 7–65.

Fujiwara Y., Aoyama H., Di Guilmi C. , Gallegati M., (2004), Gibrat and Pareto–Zipf revisited with European fi rms, Physica A: Statistical Mechanics and its Applications, 344 (1), 112–116.

Gabaix X., (2008), Power Laws in Economics and Finance, http://www.nber.org/papers/w14299.

Ikeda Y., Souma W., (2008), International Comparison of Labour Productivity Distribution, Cornell University Library, arXiv:0812.0208v4.

Jaynes E. T., (1994), Probability Theory: The Logic of Science, Washington University, USA.

Kullback S., Leibler R. A., (1951), On Information and Suffi ciency, Annals of Mathematical Statistics, 22, 79–86.

Maasoumi E., (1993), A Compendium to Information Theory in Economics and Econometrics, Econometric Reviews, 12 (2), 137–181.

Mantegna R. N., Stanley H. E., (1999), Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press, Cambridge.

Nielsen F., Nock R., (2012), A Closed-form Expression for the Sharma-Mittal Entropy of Exponential Families, Journal of Physics A, 45, 032003. doi:10.1088/1751–8113/45/3/032003.

Pukelsheim F., (1994), The Three Sigma Rule, American Statistical Association, 48 (2), 88–91.

Pyatt G., Round J. I. (eds.), (1985), Social Accounting Matrices: A Basis for Planning, The World Bank, Washington, D. C.

Rak R., Kwapień J., Drożdż S., (2007), Nonextensive Statistical Features of the Polish Stock Market Fluctuations. Physica A, 374, 315–324.

Robinson S., El-Said M., (2000), GAMS Code for Estimating a Social Accounting Matrix (SAM) Using Cross Entropy (CE) Methods, IFPR Institute, Washington, TMD discussion paper no. 64.

Scrieciu S. S., Blake A., (2005), General Equilibrium Modelling Applied to Romania (GEMAR): Focusing on the Agricultural and Food Sectors, Impact Assessment Research Centre, Working Paper Series, Paper No: 11 / 2005.

Shannon C. E., (1948), A Mathematical Theory of Communication, The Bell System Technical Journal, 27, 379–423 & 623–656.

Shen E. Z., Perloff J. M., (2001), Maximum Entropy and Bayesian Approaches to the Ratio Problem, Journal of Econometrics, 104 (2), 289–313.

Tomaszewicz Ł., Trębska J., (2013), Flow of Funds Accounts in the System of National Accounts, in: Bardazzi R., Ghezzi L., Macroeconomic Modelling for Policy Analysis, Firenze University Press, Firenze, 49–63.

Tsallis C., (2009), Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World, Springer, Berlin.

Tsallis C., Mendes R. S., Plastino A. R., (1998), The Role of Constraints within Generalized Nonextensive Statistics, Physica A.: Statistical Mechanics and its Applications, North-Holland.

Venkatesan R. C., Plastino A., (2011), Deformed Statistics Kullback-Leibler Divergence Minimization within a Scaled Bregman Framework, arXiv:1102.1025v3.

Wing S. I., (2004), Computable General Equilibrium Models and Their Use in Economy-Wide Policy Analysis, Technical Note No. 6, MIT Joint Program on the Science and Policy of Global Change, Massachusetts Institute of Technology.

Zellner, A. (1991), Bayesian Methods and Entropy in Economics and Econometrics, in: Grandy Jr., W. T, Schick L. H., (eds.), Maximum Entropy and Bayesian Methods, Boston, Kluwer, 17–31.

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