The democratic peace—the idea that democracies rarely fight one another—has been called “the closest thing we have to an empirical law in the study of international relations.” Yet, some contend that this relationship is spurious and suggest alternative explanations. Unfortunately, in the absence of randomized experiments, we can never rule out the possible existence of such confounding biases. Rather than commonly used regression-based approaches, we apply a nonparametric sensitivity analysis. We show that overturning the negative association between democracy and conflict would require a confounder that is forty-seven times more prevalent in democratic dyads than in other dyads. To put this number in context, the relationship between democracy and peace is at least five times as robust as that between smoking and lung cancer. To explain away the democratic peace, therefore, scholars would have to find far more powerful confounders than those already identified in the literature.

The two-way linear fixed effects regression (2FE) has become a default method for estimating causal effects from panel data. Many applied researchers use the 2FE estimator to adjust for unobserved unit-specific and time-specific confounders at the same time. Unfortunately, we demonstrate that the ability of the 2FE model to simultaneously adjust for these two types of unobserved confounders critically relies upon the assumption of linear additive effects. Another common justification for the use of the 2FE estimator is based on its equivalence to the difference-in-differences estimator under the simplest setting with two groups and two time periods. We show that this equivalence does not hold under more general settings commonly encountered in applied research. Instead, we prove that the multi-period difference-in-differences estimator is equivalent to the weighted 2FE estimator with some observations having negative weights. These analytical results imply that in contrast to the popular belief, the 2FE estimator does not represent a design-based, nonparametric estimation strategy for causal inference. Instead, its validity fundamentally rests on the modeling assumptions.