Benchmarking and reconciliation with time-varying cross-coefficients

In this paper, the authors propose a method to obtain explicit solutions for simultaneous benchmarking and reconciliation problems for a system of variables when the cross-restrictions use time-varying coefficients. The method is based on a hierarchical Bayesian model with a normal-gamma specification for the prior distributions. The proposed solution provides explicit (not sequential) feasible estimations, including measurements for its statistical accuracy. One interesting feature of the proposed procedure is that it allows users to include one or several performance indicators and to estimate disaggregated values for incomplete years. The method is applied to obtain Quarterly Regional Accounts for the Spanish economy.