Joe Cardinale and Larry W. Taylor 317h(x)xCFR IFR IFRA NBUFigure 7.1 Hazard functions for various life distributions
seasonal effects such as holidays or inclement weather, and IFRA hazards are special
cases of NBU hazards. A completely analogous situation holds for DFR, DFRA and
NWU distributions.
The graphical approach of Cutler and Ederer (1958) is nonparametric and avoids
some of the dangers of relying too heavily on parametric methods. For instance, in
the emerging area of forensic economics, Bonanomi, Gaughan and Taylor (1998)
use the flexible nonparametric life table method in the estimation of lost profits
when the plaintiff claims lost customers due to an alleged transgression. How-
ever, in the general economics literature, Sichel (1991) advocates using parametric
methods to increase the power of tests for duration dependence. In the politi-
cal science literature, Bennett (1999) and Zorn (2000) observe that the parametric
Weibull model is the most widely-used form. Bennett also cautions that Cox’s semi-
parametric proportional hazards model does not allow forprecisionconcerning the
hazard function.
Precisely wrong results, however, are hardly helpful. Ohn, Taylor and Pagan
(2004) show that the Weibull model is insufficient to capture the richness of eco-
nomic contractions and expansions, and Taylor (2007) shows that the Weibull
model is highly misleading for militarized interstate disputes. Attempts to apply
more flexible continuous-time methods have met with mixed success. Diebold,
Rudebusch and Sichel (1993), for example, apply their nonlinear exponential
linear model to business cycle data that mostly duplicates the results from the
Weibull model. Zuehlke (2003) applies the nonlinear model of Mudholkar, Sri-
vastava and Kollia (1996) that allows hazards to be monotonically increasing,
monotonically decreasing, U-shaped or inverted U-shaped. However, Ohn, Tay-
lor and Pagan (2004) observe that none of these shapes adequately describes the
hazard functions for pre-World War II constructions and expansions. Even for the
small samples encountered in the business cycle literature, nonparametric analysis
provides valuable insights that parametric analysis fails to uncover.