Statistical studies of the determinants of defense expenditures have been criticized on two counts: (a) most of them do not test the hypotheses of causality that they include, but simply use them as a point of departure, and (b) those that do test causality are restricted to conceptual models with very few explanatory variables. The objective of this paper is to study the defense expenditures of the USA and the USSR, explicitly avoiding these two limitations. This is done using elementary statistical methods in somewhat unorthodox ways. The conclusions of the analyses are carefully compared with those obtained by other authors and the differences encountered are explained as far as possible. The analyses and comparisons show that the defense expenditures of the USA are determined by their own inertia and by political factors within the country, while those of the USSR are determined by their own inertia and the conditions of relations with the USA. The interest of these results is not in their novelty, but in the fact that they are obtained with procedures designed to provide a more solid foundation.