Joe Cardinale and Larry W. Taylor 325prior expansion and/or contraction should be included in the set of explana-
tory variables. The usual asymptotict-ratio can then be employed to determine
if such effects are important. Thus, with a set of appropriate explanatory variables,
either predetermined or strictly exogenous, one can account for certain types of
dependence that cannot be handled by simply segmenting the time line.
Unobserved, or neglected, heterogeneity is inherently a problem of omitted vari-
ables. As a practical consideration, however, the sample sizes encountered in the
study of economic cycles are generally too small to consider many explanatory
variables. Explanatory variables are used to control for heterogeneity in the exit
probabilities. Bover, Arellano and Bentolila (2002) develop logistic discrete hazard
models that can accommodate unobserved heterogeneity. In their microecono-
metric study of about 27,000 unemployment spells of Spanish men, they explicitly
control for unemployment benefits, age, education, head of household status, and
dummies for economic sector and year of unemployment. A second model is esti-
mated with time-varying macroeconomic variables, such as the growth rate in GDP
and sectoral unemployment rates, substituting for the sectoral and time dummy
variables. Autonomous shift dummies,a(t), are included in both models to cap-
ture flexible additive duration dependence. A dummy variable is included for each
possible exit time, with time marked at monthly intervals.
Bover, Arellano and Bentolila (2002) treat the length of unemployment benefits
as predetermined, though not strictly exogenous, since knowledge about future
benefits can influence job choice and especially the decision to re-enter the labor
market. The distinction between predetermined and strictly exogenous variables
is fairly unimportant unless there is unobserved heterogeneity. In that case, pre-
determined variables are effectively endogenous, and it is necessary to maximize
the joint mixture likelihood for the unemployment and benefit durations. This is
accomplished, in part, by introducing a discrete unobserved random variable with
finite support. Additional parameters are thus included to model the unobserved
heterogeneity.
In the macroeconometrics literature on business cycles, however, post-war sam-
ple sizes of about ten spells preclude the possibility of estimating models that are
rich in parameters. As a partial solution, segmenting the time line into pre-war
and post-war is sufficient to control for omitted variables that vary across, but not
within, the segments. Since any residual heterogeneity inducesnegativeduration
dependence, expansions and contractions may appear to be self-perpetuating even
if this premise is false. On the other hand, Diebold and Rudebusch (1990) and Ohn,
Taylor and Pagan (2004) find evidence ofpositive, not negative, duration depen-
dence in the American business cycle. Thus, at least thedirectionof such duration
dependence cannot be caused by residual, or neglected, heterogeneity.
7.6 The shape of cycles
Duration dependence concerns the shape of the hazard function. If the hazard
function slopes upward, there is positive duration dependence; if downward, there