Concerns over free riding in NATO are widespread. An intuitive approach to analyzing free riding is treating it as a systematic pattern of spatial interdependence between the allies: how does a NATO member's defense spending react to changes in other allies' military expenditures? While recent work has found statistically significant free riding (negative spatial interdependence in the outcomes), it suffers from important limitations. First, this research does not adequately account for temporal dependence. Second, it does not quantify the effect of interest. Accounting directly for temporal dependence provides a meaningfully distinct perspective on the within-alliance dynamics, demonstrating that the spatiotemporal effect of free riding is, in fact, more substantial than its short-run effect, challenging inferences of static spatial models. We discuss the relevant practical and theoretical implications.

Decades of research has debated whether women first need to reach a “critical mass” in the legislature before they can effectively influence legislative outcomes. This study contributes to the debate using supervised tree-based machine learning to study the relationship between increasing variation in women's legislative representation and the allocation of government expenditures in three policy areas: education, healthcare, and defense. We find that women's representation predicts spending in all three areas. We also find evidence of critical mass effects as the relationships between women's representation and government spending are nonlinear. However, beyond critical mass, our research points to a potential critical mass interval or critical limit point in women's representation. We offer guidance on how these results can inform future research using standard parametric models.