Joe Cardinale and Larry W. Taylor 3357.8.3 Duration analysis
If expansions, or upswings, in the unemployment rate exhibitpositive duration
dependence,then upswings with longer maturities have a higher chance of ter-
minating than those with shorter maturities. The hazard tends to rise with the
duration of the event, and the average duration is greater than the standard devi-
ation. In the opposite case, callednegative duration dependence,the hazard tends
to fall with the duration of the event, and the average duration is less than the
standard deviation.Duration independenceis characterized by neither of the above
cases. For instance, the probability that unemployment exits an expansionary state
and enters a contractionary state is constant regardless of how long the upswing
has lasted.
The average duration of 22 months for upswings is more than twice the sample
standard deviation of 10 months; this suggests that rises in unemployment exhibit
positive duration dependence. Likewise, the average duration of 48 months for
downswings is larger than the sample standard deviation of 30 months; this also
suggests positive duration dependence, though such descriptive evidence is not
as strong as it is for upswings. We can formally test for duration dependence by
using the discrete-time SB and GMD tests from Ohn, Taylor and Pagan (2004). We
subtract months from each of the observed durations to be consistent with our
BBQ censoring rules.^16
We analyze upswings and downswings separately. Under the null hypothesis
of duration independence, the estimated termination probability for upswings is
0.076, but the estimated termination probability for downswings is only 0.025.
However, neither SB nor GMD indicate duration dependence for either upswings
or downswings. Finite-samplep-values are obtained through a parametric boot-
strap algorithm, with the discrete-time geometric density corresponding to the
null hypothesis of duration independence. Sensitivity analysis is performed by
varying the termination probability to account for sampling variability in esti-
mation. Since our calculatedp-values are always considerably greater than 0.10,
we cannot reject the null hypothesis that the probability of exiting a state of
national unemployment is independent of its duration at the 10% significance
level. As a further robustness check, we also employ the asymptotic LSBt-test and
the continuous-timeW-test from Shapiro and Wilk (1972). The distribution ofW
depends neither on the termination probability nor on the minimum phase, with
finite-sample critical values tabulated by Shapiro and Wilk (1972). Consistent with
SB and GMD, neither LSB norWreject duration independence for either upswings
or downswings in unemployment.
In comparision, Ohn, Taylor and Pagan (2004) find some evidence that post-war
economic contractions exhibit positive duration dependence, though there is no
such evidence for post-war expansions. However, such lack of evidence is not too
surprising in light of the small number of completed cycles. For instance, post-
war sample sizes are too small to employ the chi-square goodness-of-fit test for
comparison with SB and GMD.