We have introduced in this paper new variants of two methods for projecting Supply and Use Tables that are based on a distance minimisation approach (SUT-RAS) and the Leontief model (SUT-EURO). We have also compared them under similar and comparable exogenous information, i.e.: with and without exogenous industry output, and with explicit consideration of taxes less subsidies on products. We have conducted an empirical assessment of all of these methods against a set of annual tables between 2000 and 2005 for Austria, Belgium, Spain and Italy. From the empirical assessment, we obtained three main conclusions: (a) the use of extra information (i.e. industry output) generally improves projected estimates in both methods; (b) whenever industry output is available, the SUT-RAS method should be used and otherwise the SUT-EURO should be used instead; and (c) the total industry output is best estimated by the SUT-EURO method when this is not available.

The main objective of this paper is to revisit the Euro method in a critical and constructive way. We have analysed some arguments against the Euro method published recently in the literature as well as some other relevant aspects of the SUT-Euro and SUT-RAS methods not covered before. Although not being the Euro method perfect, we believe that there is still space for the use of the Euro method in updating/regionalizing Supply and Use tables.

We present a multidimensional generalization of the GRAS method (nD-GRAS) for the estimation of multiple matrices in an integrated framework. The potential applications of this method in regional and multi-regional input-output analyses based on national/regional accounts frameworks are many. We provide two real applications, a 3D-GRAS that estimates a use table at basic prices jointly with valuation matrices for Denmark; and a 4D-GRAS for estimating intercountry input-output tables with OECD data. We show that higher dimensional GRAS methods provide more consistent and accurate estimates than those with lower number of dimensions. We provide the analytical closedform solution and the RAS-like algorithm for an easy operationalization.