Immune Subjects and Durations

“All at Risk?: A Split Population, Competing Risks Approach” – working paper

There are many ways in which states can resolve their disputes over issues. They could peacefully settle their differences, through negotiation—bilateral talks, third-party mediation, etc. Alternatively, states could settle their differences through military force. What happens, though, if some disputes have zero chance of being settled through military force, or zero chance of being settled peacefully? Are our hypothesis tests, and the inferences we make from them, still accurate?

I suggest there is reason to be skeptical of our inferences’ accuracy. Despite the scenario’s simplicity, our current empirical tools are incapable of accommodating it. The scenario is an example of causal heterogeneity: the population of cases is not uniformly at risk of experiencing all possible events. Standard empirical tools assume causal homogeneity as a prerequisite for producing accurate estimates (which allow for accurate inferences to be made).

Specifically, the causal heterogeneity problem comes in two distinct forms:

1. A competing-risks problem (e.g., disagreements can be resolved in multiple ways, vs. just one)
2. A split-population problem (e.g., some disagreements are not at risk for being resolved with military force, vs. all being at risk; some disagreements are not at risk for being resolved with peaceful negotiation, vs. all being at risk)

Estimators exist to handle each form separately (for an overview, see Box-Steffensmeier and Jones 2004; for example applications, see: Quiroz Flores 2012; Svolik 2008). However, no tool exists to handle them jointly.

I develop a split-population, competing-risks survival estimator capable of investigating questions that are characterized by this scenario. I use Monte Carlo simulations to demonstrate that estimates regarding a covariate’s effect on the probability of an event occurring will be biased if a case is immune to experiencing the event (i.e., it is not at risk). I also use Monte Carlos to show my estimator does not suffer from such a bias. I then use democratic reversals to demonstrate one potential application of the estimator.