Joe Cardinale and Larry W. Taylor 3097.6 The shape of cycles 325
7.6.1 Durations 327
7.6.2 Amplitudes 327
7.6.3 Cumulative gain 327
7.7 Synchronization of cycles 328
7.7.1 The coincidence indicator 328
7.7.2 Correlation analysis 329
7.7.2.1 Tests based on the method of moments 329
7.7.2.2 Regression-based tests 331
7.8 Unemployment cycles 332
7.8.1 Cycle shapes 332
7.8.2 Synchronization with business cycles 334
7.8.3 Duration analysis 335
7.9 Conclusion 341
7.10 Appendix: LIMDEP 7.0 program for jackknifing duration data 342
7.1 Introduction
An event history is a longitudinal record of specified events. Examples at the indi-
vidual level include dates of schooling, marriage, birth of children, job change,
illness, promotion, retirement and migration. Examples at the aggregate level
include dates of militarized disputes, riots, revolution, economic expansions and
contractions, bull and bear markets, and massive layoffs. Regardless of the under-
lying activity, an event consists of a qualitative change that marks a new phase
for either the individual or the collective. Consider that the beginning of a
bull market marks the end of a bear market and that the beginning of a mili-
tarized interstate dispute marks the end of placid relations between states with
diplomatic ties.
A pertinent issue is whether the probability of exiting a phase, orstate, depends
on its duration. For instance, is a four-hour riot more likely to end within the next
hour than a one-hour riot? Does the likelihood of changing jobs decrease with the
time invested in the current job? Is a young economic expansion more robust to
failure than an old one? If so, we anticipate the end of an old expansion, but are
surprised by the end of a young one.
The demographer sees each of the above questions answered best by a life
table analysis, the biostatistician by a survival analysis, and the engineer by a
reliability or failure-time analysis. The economist tends to view the individual-
specific questions on job change as somehow different from the aggregate-level
question on business cycles, with the question on riots fitting perhaps some-
where in between. In fact, these questions are generally handled by various
sub-disciplines, as the microeconometrician examines individual employment
while the macroeconometrician examines the overall business cycle. Despite the
initial segregation, however, it is now understood that life table, survival, and reli-
ability analyses are intellectually very similar, and that the analysis of business
cycles can be handled in much the same way as that involving promotion and job
change.^1