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 multi-sector 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.

We propose a Bayesian approach to estimating productive capital stocks and depreciation rates within the production function framework, using annual data on output, employment and investment only. Productive capital stock is a concept related to the input of capital services to production, in contrast to the more common net capital stock estimates, representing market value of fixed assets. We formulate a full Bayesian model and employ it in a series of illustrative empirical examples. We find that parameters of our model, from which the time-path of capital is derived, are weakly identified with the data at hand. Nevertheless, estimation is feasible with the use of prior information on the production function parameters and the characteristics of productivity growth. We show how precision of the estimates can be improved by augmenting the model with an equation for the rate of return.