A Bayesian method for constructing input-output tables

Abstract

Methods of updating, balancing, disaggregation of Input-Output Tables (IOT) are widely used in applied economic and statistical research (for example, for the calibration of computable general equilibrium models), as well as by statistical services for compilation of IOTs. As compared to the well-known popular methods (RAS, cross-entropy minimization, and their analogs), which provide point estimates of unknown tables, the proposed approach targets estimation of joint probability distribution of input-output (IO) coefficients. With this goal we develop a probabilistic model ofjoint distribution of the IO coefficients as a likelihood function of observed information (for example, output, value added, intermediate demand). This information from newly arrived data is being mixed with prior information of IO parameters (for example, known IOTs from former years) by Bayes rule. The resulting posterior joint distribution can be estimated using Markov chain Monte Carlo (MCMC) sampling methods. The sample of IOTs from the targeted distribution is a set of IO matrices consistent with the observed data, constrains, and also near to the prior information. In contrary to the point estimates, the stochastic IOTs naturally incorporate uncertain information of each estimated IO parameter, taking into account all the multivariate correlation between the cells. The proposed methodology can be applied to updating, interpolation, disaggregation, and balancing of IOTs, and more widely - national accounts. We test the methodology with experimental updating of IO table for the Russian economy for 2003 year, based on tables from 1998 to 2002 years. The results suggest adequacy and computational accessibility of the proposed methodology.