Time is Not A Theoretical Variable

Carter and Signorino (2010) (hereinafter "CS") add another arrow, a simple cubic poly nomial in time, to the quiver of the binary time series-cross-section data analyst; it is al ways good to have more arrows in one's quiver. Since comments are meant to be brief, I will discuss here only two important issues where I disagree: are cubic duration polyno mials the best way to model duration dependence and whether we can substantively in terpret duration dependence. But first, I should make it clear that I agree with CS, amongst other issues, that adding duration dummies to the logit specification is inferior to adding a smooth function of du ration to that specification. In Beck, Katz, and Tucker (1998) (hereinafter "BKT"), we noted that the duration dummies (which are simply the grouped duration analogue of the Cox [1972] proportional hazards model "baseline hazards") are estimated very im precisely (especially for loner durations). We then suggested that we expected the baseline hazard function to be reasonably smooth and hence could be better modeled by as a smooth function of time. CS's discussion of separation provides another reason to prefer smooth functions of time to the duration dummies. CS argue that a simple cubic polynomial in time is about as good, and more easily interpretable, than a cubic spline. BKT suggested a natural cubic spline because at the time, it was the best smoother available in the widely used package Stata and we wanted to appeal to the applied researcher.1 In the ensuing decade, R has become popular and today I would recommend researchers use mgcv in R or, if the prefer to stay with Stata, fracpoly. I agree with CS that choice of knots can be difficult. These newer and now easily available programs allow the user to specify a more intuitive "degree of smoothing" (or "band width") parameter and so avoid the knot selection problem.2 Today, there is no need to choose between only the somewhat awkward natural cubic spline and the somewhat Procrustean cubic polynomial. Moreover, there is no reason to choose the latter because it is easier to get intuitive graphs; both routines mentioned make it easy to get plots of the baseline hazard against time. Before leaving splines, it should be noted that CS's position on knots in splines reflects our discipline's general uneasiness with allowing researchers to make decisions about issues such as smoothness that require some art. CS's position here is logically