A Bayesian Approach to Matrix Balancing Transformation of Industry-Level Data under NACE Revision

Abstract

We apply Bayesian inference to estimate transformation matrix that converts
vector of industry outputs from NACE Rev. 1.1 to NACE Rev. 2 classification.
In formal terms, the studied issue is a representative of the class of matrix
balancing (updating, disaggregation) problems, often arising in the field of multisector economic modelling. These problems are characterised by availability
of only partial, limited data and a strong role for prior assumptions, and are
typically solved using bi-proportional balancing or cross-entropy minimisation
methods. Building on Bayesian highest posterior density formulation for
a similarly structured case, we extend the model with specification of prior
information based on Dirichlet distribution, as well as employ MCMC sampling.
The model features a specific likelihood, representing accounting restrictions in
the form of an underdetermined system of equations. The primary contribution,
compared to the alternative, widespread approaches, is in providing a clear
account of uncertainty.