A GRAS variant solving for minimum information loss: An erratum

Junius and Oosterhaven (2003, hereafter J&O) proposed an information-theoretic approach, which they called “GRAS”, to solve the problem of adjusting matrices with negative entries. In Lemelin (2009), I demonstrated that the J&O target function was not equivalent to Kullback-Leibler’s (1951, hereafter K-L) cross-entropy measure. In fact, I reformulated the problem using K-L’s cross-entropy to show that the reformulated problem yields a different solution. In addition, my paper extended the approach to adjustment problems, intractable via GRAS, where row sums, column sums or both are constrained to zero. The world table of country international investment positions (IIP) is an example: the worldwide sum of assets, minus liabilities, of any given category (row sums) must be zero; but individual countries’ net worth, or IIP (column sums), may be positive or negative. I illustrated this in Table 6. Unfortunately, that table was not the one that I used to generate Tables 7 and 8. As a matter of fact, given the sign-preserving property of the adjustment procedure, Table 6 is incompatible with results displayed in Tables 7 and 8. This error was mine. The proper table is now displayed here. All other numerical examples presented in Lemelin (2009) are correct.