Oona Hathaway provides one of the most influential and impressive reports against the idea that treaties retain a particular political purpose and that they could indeed be subject to congressional executive approval. The foregoing discussion shows that there are countless theories about the qualitative difference between treaties and agreements between Congress and the executive. A common approach to solving such theoretical debates is to focus on empirical evidence. However, as has already been said, both the theoretical and empirical literature do not appear to be conclusive, with the hypotheses of both categories claiming to be supported by quantitative empirical evidence. 103 Formally, it is necessary that the cooperative of interest, in this case the contractual indicator, should not be correlated with the potential result, in the absence of permanence of an agreement, after having included all the control variables. This is also called the adoption of “selection on observables”. If the choice between treaties and agreements between Congress and the executive branch were random, the covariate of interest would not, by definition, be correlated with the possible outcome. In the absence of randomization, the selection on observation hypotheses cannot be verified and is the subject of theoretical debates. In the United States, executive agreements are concluded exclusively by the President of the United States. They are one of three mechanisms through which the United States make binding international commitments. Some authors consider executive agreements to be treaties under international law, as they bind both the United States and another sovereign state. However, under U.S.

constitutional law, executive agreements are not considered treaties within the meaning of the contractual clause of the U.S. Constitution, which requires the Council and the approval of two-thirds of the Senate to be considered a treaty. As explained in the text, survival periods are continuous in nature, with international agreements being able to stop at any time. However, since survival periods are only measured once a year when the TIF is published, the data can be described as continuous data, aggregated by year. For truly continuous data where an event can occur at any time, the Cox proportional-hazard modelFootnote 117 has emerged as the preferred choice for researchers, footnote 118, as it is a semiparametric model based on a few assumptions. The popularity of this model comes from the fact that it can be appreciated without making parametric assumptions about the base hazard rate. . . .