ON THE BIAS OF MULTIPLIER ESTIMATES

This paper considers the bias of the matrix of multipliers when the un derlying data are random. The traditional approach is to specify the s tochastic nature of the input coefficients directly. It is shown that this approach implies a transactions table which is biased in a most u nbalanced 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, ei ther the biases are zero, or positive biases are canceled out by negat ive biases in the sense that their weighted average is zero. The condi tions are based on the idea that information on aggregates is more exa ct than information on their details. The usual asumptions of independ ence and unbiasedness of the individual errors are avoided. The result s are shown to have a direct interpretation in connection with the RAS -updating procedure.