Using Weighted Least Squares to Deflate Input-Output Tables

This article proposes a balancing procedure for the deflation of input-output (I-O) tables from the viewpoint of users. This is a 'subjective' variant of the Weighted Least Squares (WLS) method, already known in the literature. It is argued that it is more flexible than other methods, and it is shown that SWLS subsumes the first-order approximation of RAS as a special case. Flexibility is due to the facts that (a) users can attach differential 'reliability' weights to first (unbalanced) estimates, depending on the confidence they have in the different parts of their pre-balancing work, (b) differently from RAS, one is not bound to take any row or column total as exogenously given, and (c) additional constraints can be added to it. The article describes also how SWLS was utilised to estimate a yearly (1959-2000) series of constant-price I-O tables for the Italian economy.