On the bias of multiplier estimates

This paper considers the bias of the matrix of multipliers when the underlying data are random. The traditional approach is to specify the stochastic nature of the input coefficients directly. It is shown that this approach implies a transactions table which is biased in a most unbalanced way. Next the practitioner's point of view, i.e., taking the transactions table as the source of random errors, is adopted. One of the results states that, within each row of the multiplier matrix, either the biases are zero, or positive biases are canceled out by negative biases in the sense that their weighted average is zero. The conditions are based on the idea that information on aggregates is more exact than information on their details. The usual asumptions of independence and unbiasedness of the individual errors are avoided. The results are shown to have a direct interpretation in connection with the RAS-updating procedure.