A general weighted least squares approach for the projection of input–output tables

In the context of input–output analysis, it is often necessary to update a matrix for a date when only the sum of its columns and rows are known. This projection problem is quite similar to temporal disaggregation. I borrow from this literature a class of solutions for which the exact result can be implemented without iteration. These solutions minimize the adjustment made to the out-of-date matrix and as such can be said optimal according to a chosen criteria. The framework I expose is flexible enough to encompass many of the existing methods and develop new ones. I propose one of such methods to project a matrix between two given benchmarks. I exemplify the technique on 35 years of input–output tables for France and show in particular that the issue of negative cells can be avoided.