Survival and Death in International Trade - Discrete-Time Durations of EU Imports

In the existing literature, the duration of trade has typically been analyzed using either descriptive Kaplan-Meier methods or a Cox regression approach. While the latter has the advantage of allowing for explanatory variables, it is designed for the analysis of continuous duration times, whereas trade flows are observed for discrete time intervals. The purpose of this paper is to point out why it is inappropriate to analyze the duration of trade with continuous- rather than discrete-time models, and to illustrate the implications of the model choice in an empirical application to EU trade. Briefly, there are three major problems with the continuous-time models. First, such models face problems in the presence of many tied duration times, with a risk of biased estimation coefficients and standard errors. Second, it is very difficult to properly control for unobserved heterogeneity, which can cause spurious duration dependencies, as well as parameter biases. Third, the Cox model – which, by far, is the most commonly used model – imposes the restrictive and empirically questionable assumption of proportional hazards. By contrast, discrete-time models, such as probit, logit and complementary log-log models have no difficulty dealing with ties; unobserved heterogeneity can easily be controlled for; and one is not forced to assume proportional hazards. Applying both continuous- and discrete-time models to detailed data on imports to EU15 countries from 139 exporters for the period 1962-2006, we find evidence in support of the arguments against the Cox model, and conclude that researchers that use a Cox model might run a serious risk of getting incorrect results.