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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 thedoi:10.5964/meth.4529 fatcat:axllmmezjvalfit3dxzbw5wwcq