Measuring the natural rates, gaps, and deviation cycles

One definition of the natural rate is the (time-varying) steady state equilibrium rate. Then the gap is the difference between the actual and natural rates, or the forecastable movement. Although modern business cycle theories study deviation cycles (cycles in the gap), the NBER business cycle reference dates measure classical cycles (cycles in the actual rate) in the US. Measuring deviation cycles requires detrending, and this motivated the invention of the Beveridge–Nelson (B–N) decomposition. This paper considers multivariate detrending, and proposes a Bayesian approach to the multivariate B–N decomposition. An application of the method to US data gives (i) a joint estimate of the natural rates and gaps of output, inflation, interest, and unemployment with reliable error bands, and (ii) the posterior probabilities of positive gap, recession, and revival. These results may help us to identify the four phases of deviation cycles: expansion, recession, contraction, and revival. Copyright Springer-Verlag Berlin Heidelberg 2014