314 Economic Cycles
nent component asPt=yt− 1 , the temporary effect is now the growth rate since
zt=yt=yt−yt− 1. Marking time by examining positive and negative values of
ztdefines the classical business cycle.
We make a distinction here between growth cycles and gap ordeviationcycles.
For growth cycles, we seek turning points inyt; there is no reason to specify a
trend curve. For gap cycles, however, we seek deviations from a specified trend
curve. In contrast, Zarnowitz and Ozyildirim (2006), among others, classify a
gap cycle as a special type of growth cycle. For their gap analysis, Zarnowitz and
Ozyildirim recommend that the trend curve be determined by the classical non-
parametric phase-average-trend (PAT) algorithm of Boschan and Ebanks (1978).
Zarnowitz and Ozyildirim then argue that a gap analysis is more informative than
a direct growth-rate analysis in the study of national output. First, they argue
that growth rates over short time spans are very erratic and must be smoothed
with complex moving averages that potentially distort patterns. Second, they find
that the timing of growth rates is very different from that of the corresponding
level series. Of course, an alternative interpretation of the second finding is that
the growth cycle is providing different information than is the classical business
cycle.
7.2.3.2 Filtering procedures
The specification of any trend curve is somewhat arbitrary. However, Zarnowitz
and Ozyildirim (2006) find that the PAT algorithm produces a nonlinear trend
curve that smoothly transits from higher to lower growth. They also find that
the trend from the PAT algorithm fits as well as a log-linear trend, the stochastic
Beveridge and Nelson (1981) trend, the local linear trend of Harvey (1989), the
Hodrick–Prescott (1997) trend, and Rotemberg’s (1999) heuristic trend.
Intuitively, different types of trends produce different types of temporary compo-
nents. For instance, King and Rebelo (1993) show that the temporary component
from the Hodrick–Prescott (HP) trend is a two-sided weighted average of growth
rates. However, if the data-generating process is the pure random walk, yt =
yt− 1 + (^) t, Harding and Pagan (2005) show that the HP temporary component is
well represented by a weighted average of current and lagged values of the growth
rates with slowly declining weights. In contrast, the Beveridge–Nelson temporary
component for the random walk is degenerate since the permanent component
isyt.
The point is this. It is easy to think that all temporary components are mea-
suring the same thing as long as each is a stationary process; however, this is
not the case. For business cycles, the litmus test appears to be whether the turning
points match well with those of the NBER. Consider that, for quarterly observations
on GDP, Hamilton (1989) compares his estimated latent-structure probabilities
with turning points in aggregate activity. He demonstrates that his estimate of
P(s∗t= 0 |FT)is generally greater than 0.5 during recessions and less than 0.5 dur-
ing expansions. On the other hand, the very flexible BBQ algorithm of Harding
and Pagan (2002) also yields turning points that accord well with those of the
NBER.^5