Greenhouse Emission Forecast as an Inverse Stochastic Problem: A Cross-Entropy Econometrics Approach

This paper proposes the non-extensive entropy econometric approach to predict regional cross-industry greenhouse emissions within a country, based on imperfect knowledge of industrial and regional aggregates. The solution of this stochastic inverse problem is applied to Poland. Non-extensive entropy should remain a valuable device for econometric modelling even in the case of low frequency series since outputs provided by the Gibbs-Shannon entropy approach correspond to the Tsallis entropy limiting case of the Gaussian law when the Tsallis q-parameter equals unity. We, therefore, set up a q-Tsallis-Kullback-Leibler entropy criterion function with a priori consistency constraints, including the environmental Kuznets econometric model and regular conditions. As in the case of Shannon-Gibbs-based entropy models, we found that the Tsallis entropy estimator also belongs to the family of Stein estimators, meaning that smaller probabilities are shrunk and higher probabilities dominate in the solution space. Fortunately, adding more pertinent data to the model priors will enhance parameter precision and then allow for the recovery of the real influence of smaller events. The q-Tsallis-Kullback-Leibler entropy index is computed for different scenarios of the Kuznets model. The model outputs continue to conform to empirical expectations. In spite of the close to unity q-Tsallis parameter, this Tsallis related approach reflects higher stability for parameter computation in comparison with the Shannon-Gibbs entropy econometrics technique.