Measuring the Natural Rates, Gaps, and Deviation Cycles∗

The natural rate is the equilibrium rate under flexible prices, and the gap is the difference between the actual and natural rates. Since prices adjust eventually, the Beveridge–Nelson (B–N) decomposition gives the statistical counterparts of the two notions. Measuring cycles in the gap is of interest from the new neoclassical synthesis perspective. The Bayesian multivariate B–N decomposition gives a joint estimate of the natural rates and the gaps of output, inflation, interest, and unemployment with reliable error bands, and the posterior probabilities of positive gap, recession, and revival, which help to identify the four phases of cycles. JEL codes: C11, C32, C82, E32