A Bias in the Seasonally Adjusted Unemployment Series and a Suggested Alternative - Brittain, John A. (The Review of Economics and Statistics, 1959)
T HE Census Bureau reported a decline from 7.2 per cent to 6.8 per cent in the seasonally adjusted ratio of unemployment to labor force between May and June I958 but noted that rate is subject to small statistical and other noneconomic fluctuations. The Bureau further discounted the May-June dip in its July Report, attributing it to technical difficulties arising from application of a percentage seasonal adjustment to the figure for June I958, but there was no hint of a solution to this problem on either occasion.' Less cautious interpretation in the popular press of this improvement in the unemployment rate2 invites the response that the ratio of adjusted employment to adjusted labor force was stable in this period at 92.8 per cent; this implied an unemployment rate unchanged at 7.2 per cent. Furthermore, continued stability in this residual rate would have been accompanied automatically by a climb in the official rate from 6.8 per cent to 8.o per cent by October I958. These figures offer a recent illustration of a chronic inconsistency in the three seasonally adjusted labor force series. Under certain conditions, this intuitively undesirable and systematic discrepancy may widen rapidly and obviously discredit the adjustment process. This note generalizes the criticism of the adjusted United States unemployment series, reports a bias in the standard procedure due to application of a misleading descriptive model, and suggests a residual estimate as an alternative. The general argument can be stated as a hypothesis: Because the standard adjustment is roughly proportional to the unemployment level it will tend to exaggerate the adjustment when unemployment is high and understate it when unemployment is low. Therefore when unemployment is high and the seasonal index increases, the adjusted series will tend to decline; a fall in the seasonal index will tend to produce a rise in the adjusted series. The opposite association or bias exists when unemployment is low. This bias is avoided by the residual alternative. The following section contrasts results of the standard and residual procedures; the second section presents the argument for the above hypothesis and for the superiority of the residual estimate.