7

Economic Cycles: Asymmetries,

Persistence, and Synchronization

Joe Cardinale and Larry W. Taylor

Abstract
Marking upswings and downswings for a time series{yt}provides insights that are not immediately
obvious, but may be meaningful to academics, policy makers, and the general public. The mean
and standard deviation of durations, as well as the amplitude and steepness of a given phase,
yield fruitful insights about cycle asymmetries and persistence. Expansions and contractions in
one series can then be compared to those in another to determine whether their respective cycles
are synchronized. However, our primary focus here is on classical nonparametric methods for the
analysis of duration, dating back to the seminal work of Burns and Mitchell (1946), Cutler and
Ederer (1958), Bry and Boschan (1971), and Cox (1972). Although our specific application is to
unemployment cycles, the ideas and techniques discussed in this chapter apply to a wide variety
of micro- and macroeconometric studies.

7.1 Introduction 309
7.2 Marking time 310
7.2.1 Reasons for marking time 311
7.2.2 Techniques for marking time 311
7.2.2.1 BBQ 311
7.2.2.2 Markov chain models 312
7.2.3 Detrending the series 313
7.2.3.1 Output gaps versus growth rates 313
7.2.3.2 Filtering procedures 314
7.3 The discrete-time hazard function 315
7.3.1 Hazard plots 315
7.3.2 Benchmark hazards 316
7.4 Testing for duration dependence 318
7.4.1 The nature of duration independence 318
7.4.2 Weak-form tests 318
7.4.2.1 The GMD test 319
7.4.2.2 The SB test 319
7.4.3 Strong-form tests 321
7.5 Modeling with covariates 321
7.5.1 The logit model 323
7.5.1.1 The LSB test 323
7.5.1.2 A comparison with Cox’s model 324
7.5.2 Predetermined variables and unobserved heterogeneity 324
308