Econometric Balancing of a Social Accounting Matrix Under a Power-law Hypothesis

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.