The basic logic underlying parametric event history models is to directly model the time dependency exhibited in event history data. This is easily done by specifying a distribution function for the failure times. If the researcher suspects that the risk of an event occurrence is increasing, or “rising” over time, for example, then one may specify a distribution function that accounts for such a relationship. Social scientists, and in particular, political scientists, have made use of parametric methods to understand such phenomena as coalition durations (King et al. 1990; Warwick 1992), the survival of political leaders (Bueno de Mesquita and Siverson 1995), and the duration of military conflicts (Bennett and Stam 1996). Parametric models for political analysis would seem most reasonable when there exists a strong theoretical expectation regarding the “shape” of the hazard rate (or by extension, survival times), conditional on the covariates included in the model. Under such conditions, correctly specifying the distribution function will yield slightly more precise estimates of the time dependency in the data as well as more precise estimates of covariate parameters than nonparametric approaches in small samples (Collett 1994); however, if the distribution of failure times is parameterized incorrectly (for any size sample) then the nice interpretations afforded parametric models may not hold (Bergström and Edin 1992).

We make this cautionary note primarily because parametric methods directly specify the shape of the hazard rate. This will happen even if the parameterization is wrong.