Tommaso Proietti 4171950 1960 1970 1980 1990 2000–5
0510
Output gap1950 1960 1970 1980 1990 20000.51.0Posterior probabilities of high variance state P (St = 1|y)0.0 0.5 1.0 1.5510
Posterior density trend variance parameters
σηa^2 σηb^20.00 0.25 0.50 0.75 1.00 1.25 1.5051015Posterior density cycle variance parameters
σκa^2 σκb^2–0.1 0.0 0.1 0.2 0.3 0.410
20
30
Inflation loadings parameters
−θψ 1 θψ 0 +θψ 1
0.80 0.85 0.90 0.95 1.002040Transition probabilities
T 11 T 00Figure 9.8 Bayesian estimation of the bivariate output gap model with Markov-switching in
the variances of the trend and cycle disturbances (GM specification). Point and 95% interval
estimates of the output gap; posterior probabilities of the high volatility state,P(St= 1 |y),
and posterior densities of variance and loadings parameters
potential, and established an empirical law of strict proportionality between cycli-
cal unemployment and the output gap. Hence, Okun’s law is meant to imply that
output and the unemployment rate share a common cycle.
Against this background, Clark (1989) estimated a bivariate model of US real
output and unemployment such that output and unemployment are decomposed
into two unrelated permanent components and the comovements between the
two series result from the presence of a common cycle, represented as an AR(2)
stationary component. Apel and Jansson (1999) obtained estimates of the NAIRU
and potential output for the UK, the US and Canada, based on an unobserved
components model of output, inflation and unemployment rates.
Another important multivariate extension of the basic bivariate model is thepro-
duction function approach(PFA) to the estimation of potential output and the output
gap, according to which potential output is obtained from the trend, or “nonin-
flationary,” levels of its structural determinants, such as productivity and factor
inputs. This approach is currently one of the most popular methods of measuring
potential output among statistical agencies being employed by the OECD (2001),