A Bayesian Method to Reconcile Conflicting Input-Output Data

At the heart of a CGE model lies an input-output (IO) model, i.e., the set of transactions taking place in the economy in the base-line year. For example, the GTAP 7 database consists, to some extent, to a large mult-regional IO model for the year 2004. The compilation of this large data set has to deal with the problem of reconciling potentially inconsistent data. Currently this procedure is performed using simple simple methods (RAS or least square minimization) and a good deal of expert knowledge. In this paper we derive a Bayesian method to obtain a consistent and fully determined set of posteriors when the priors are inconsistent and there is a set of known topological constraints of arbitrary structure. The expression relating priors (inconsistent data) and posteriors (reconciled data) is obtained by the application of the maximum entropy principle and its properties are discussed. In general, the posteriors form a vector of multivariate truncated Gaussian random variables. This distribution approaches the Gaussian distribution in the limit of low uncertainty and the exponential distribution in the limit of high uncertainty. Using invariance considerations we derive a numerical iterative implementation that takes the form of a generalized least squares method. We present a real application (60x60 symmetric IO table) to illustrate the behavior of the method and to compare its performance against conventional methods. The numerical implementation is slightly more complex than conventional methods. However, the adjustment from prior to posterior is more strongly correlated to the initial uncertainty of the data points in the Bayesian method. If the data set is large, it is necessary to store data and perform algebra in sparse format.