¹ Hathaway, Oona A., Treaties' End: The Past, Present, and Future of International Lawmaking in the United States, 117 Yale L.J. 1236, 1239 (2008)CrossRefGoogle Scholar (pointing out that “virtually no other country” has a two-track procedure of making international law like the United States does).

² U.S. Const. Art. II, § 2, cl. 2.

³ Wallace McClure, International Executive Agreements: Democratic Procedure Under the Constitution of the United States 378 (1941) (arguing that the treaty should be replaced by the executive agreement, safe for the exception where “no public opinion exists and no question as to [the treaties’] acceptability arises”); Borchard, Edwin, Book Review: International Executive Agreements: Democratic Procedure Under the Constitution of the United States, 42 Colum. L. Rev. 887 (1942)CrossRefGoogle Scholar (rebutting McClure's argument, characterizing it as unconstitutional); see also Borchard, Edwin, Shall the Executive Agreement Replace the Treaty?, 53 Yale L.J. 664 (1944)CrossRefGoogle Scholar (characterizing executive agreements as the weaker commitment device).

⁴ See, e.g., United States v. Belmont, 301 U.S. 324 (1937); United States v. Pink, 315 U.S. 203 (1942); Dames & Moore v. Regan, 453 U.S. 654 (1981).

⁵ Koh, Harold H., Treaties and Agreements as Part of Twenty-First Century International Lawmaking, in Digest of United States Practice in International Law 91, 91–92 (Guymon, CarrieLyn D. ed., 2012)Google Scholar.

⁶ This number is based on a count of treaty documents in Library of Congress approved by the 111th, 112th, 113th, or 114th United States Congress. See https://www.congress.gov.

⁷ According to the data used here, 524 executive agreements were concluded under President Obama during his first term alone.

⁸ See Hathaway, supra note 1.

⁹ Id. at 1312; see also Curtis A. Bradley, International Law in the U.S. Legal System 76 (2015) (pointing out that one of the reasons for the popularity of the executive agreements is that it is “much easier to conclude the growing number of international agreements without submitting them for approval by two-thirds of the Senate”).

¹⁰ Bradley, supra note 9, at 81.

¹¹ Hathaway, supra note 1, at 1285 (arguing that historical conventions explain the use of the treaty). Bradley, Curtis A. & Morrison, Trevor W., Historical Gloss and the Separation of Powers, 126 Harv. L. Rev. 411, 474 (2012)Google Scholar (arguing that the use of the treaty can at least partially be explained through selective senatorial attention paid to “major” agreements).

¹² Don Oberdorfer, Incremental Step: Pact Far Short of Carter's Initial Goal, Wash. Post (May 11, 1979).

¹³ Edward Epstein & Anna Badkhen, U.S., Russia to Slash Nuclear Arsenals/Bush Wins Concessions—Putin Gets Formal Treaty, SFGate (May 14, 2002).

¹⁴ Seth Mydans, Marcos Flees and Is Taken to Guam; U.S. Recognizes Aquino as President, N.Y. Times (Feb. 26, 1986).

¹⁵ Setear, John K., The President's Rational Choice of a Treaty's Preratification Pathway: Article II, Congressional-Executive Agreement, or Executive Agreement?, 31 J. Legal Stud. S5 (2002)CrossRefGoogle Scholar; Martin, Lisa L., The President and International Commitments: Treaties as Signaling Devices, 35 Presidential Stud. Q. 440 (2005)CrossRefGoogle Scholar.

¹⁶ Schultz, Kenneth A., Domestic Opposition and Signaling in International Crises, 92 Am. Pol. Sci. Rev. 829 (1998)CrossRefGoogle Scholar; Yoo, John, Rational Treaties: Article II, Congressional-Executive Agreements, and International Bargaining, 97 Cornell L. Rev. 1 (2011)Google Scholar.

¹⁷ Setear, supra note 15; Lisa L. Martin, Democratic Commitments: Legislatures and International Cooperation 64 (2000).

¹⁸ For the reasons causing the State Department to consider an agreement out of force, see infra at 14.

¹⁹ Hathaway, supra note 1, at 1239 (pointing out that “virtually no other country” has a two-track procedure of making international law like the United States does).

²⁰ U.S. Const. Art. II, § 2, cl. 2.

²¹ Their supposed constitutional basis is the subject of debate and will be detailed momentarily.

²² North American Free Trade Agreement Implementation Act, Pub. L. No. 103-182, 107 Stat. 2057 (1993).

²³ Uruguay Round Agreements Act, Pub. L. No. 103-465, 108 Stat. 4809 (1994).

²⁴ Hathaway, supra note 1, at 1256 (conducting a search for congressional-executive agreements that have been approved ex post and finding only a “small number” of such agreements).

²⁵ Treaties and Other International Agreements: The Role of the United States Senate, 106 Comm. Print 5 (2001) (detailing that presidents have claimed as a basis general executive authority in Article II, Section 1 of the Constitution; his power as commander in chief in Article II, Section 2, Clause 1; his treaty negotiation power in Article II, Section 2, Clause 2; his authority to receive ambassadors in Article II, Section 3; and his duty toward the faithful execution of laws in Article II, Section 3).

²⁶ 1 U.S.C. 112b(a) (1979). It is important not to “fetishize” this triptych of treaties, congressional-executive agreements, and sole executive agreements. Indeed, most recent scholarship has called attention to its unsuitability in categorizing two recent agreements, namely the Paris Climate Change Agreement and the Iran Nuclear Deal. See Galbraith, Jean, From Treaties to International Commitments: The Changing Landscape of Foreign Relations Law, 84 U. Chi. L. Rev. 1675 (2017)Google Scholar; Koh, Harold H., Triptych's End: A Better Framework to Evaluate 21st Century International Lawmaking, 126 Yale L.J. F. 338 (2017)Google Scholar. Since this Article is interested in the substantive difference between executive agreements and treaties concluded between 1982 and 2012 and does not discuss novel forms of international agreements, there is little need to move beyond this traditional distinction.

²⁷ See Vienna Convention on the Law of Treaties, Art. 2(1)(a), opened for signature May 23, 1969, 1155 UNTS 331 [hereinafter VCLT].

²⁸ See Arthur W. Rovine, Digest of United States Practice in International Law 195 (Office of the Legal Adviser, Department of State 1974). For a general overview of the history of U.S. agreements under the VCLT, see Frankowska, Maria, The Vienna Convention on the Law of Treaties Before United States Courts, 28 Va. J. Int'l L. 281 (1987)Google Scholar.

²⁹ Bradley, supra note 9, at 90 (“Most scholars … believe that the president's authority to enter into sole executive agreements is substantially narrower than the president's authority to enter into Article II treaties.”); Louis Henkin, Foreign Affairs and the United States Constitution (1996) (describing the view that the president will seek the Senate's approval only for “prudential reasons” as “unacceptable”).

³⁰ See McClure, supra note 3, 4, 247 (finding that 1,200 of 2,000 agreements have been concluded as congressional-executive agreements and using this as a basis to advance a basis for legitimizing their use); see also Wright, Quincy, The United States and International Agreements, 38 AJIL 341, 354 n. 62 (1944)CrossRefGoogle Scholar (reversing previous views based on “Congressional and executive practice”); Ackerman, Bruce & Golove, David, Is NAFTA Constitutional?, 108 Harv. L. Rev. 799, 868 (1995)CrossRefGoogle Scholar (demonstrating how McClure's narrative makes consistent practice a necessary and sufficient condition for interchangeability. Also discussing Wright's shift in views.). See generally McDougal, Myers S. & Lans, Asher, Treaties and Congressional-Executive Agreements or Presidential Agreements: Interchangeable Instruments of National Policy: I, 54 Yale L.J. 181 (1945)Google Scholar; McDougal, Myers S. & Lans, Asher, Treaties and Congressional-Executive Agreements or Presidential Agreements: Interchangeable Instruments of National Policy: II, 54 Yale L.J. 534 (1945)Google Scholar (arguing that a need for flexibility justifies perfect interchangeability of treaties and congressional-executive agreements).

³¹ See Ackerman & Golove, supra note 30, at 861.

³² Borchard, Edwin, The Proposed Constitutional Amendment on Treaty-Making, 39 AJIL 537, 538 (1945)CrossRefGoogle Scholar (describing the rise of the executive agreement as an “encroachment on the treaty-making power”); Berger, Raoul, The Presidential Monopoly of Foreign Relations, 71 Mich. L. Rev. 1, 48 (1972)CrossRefGoogle Scholar (criticizing the idea of “adaptation by usage” as grounds for constitutional interpretation); Tribe, Laurence H., Taking Text and Structure Seriously: Reflections on Free-Form Method in Constitutional Interpretation, 108 Harv. L. Rev. 1221, 1249 (1995)CrossRefGoogle Scholar (criticizing Ackerman's extension on interpretive methods; even though he acknowledges that the Constitution is silent on many questions of separation of powers in foreign affairs, Tribe argues that the Treaty Clause is clear in making Advice and Consent the exclusive method for treaty approval).

³³ Yoo, John C., Laws as Treaties?: The Constitutionality of Congressional-Executive Agreements, 99 Mich. L. Rev. 757 (2001)CrossRefGoogle Scholar (arguing against both “transformationists” who introduce the idea of constitutional moments, as well as “exclusivists” who view treaties as the only means to enact binding international agreements).

³⁴ There is some remaining debate as to whether congressional-executive agreements can be used in the rare occasions where the agreement falls outside of the congressional powers enumerated in Article I of the Constitution. See, e.g., Hathaway, supra note 1, 1339.

³⁵ Koh, supra note 5, at 91–93 (describing perfect legal substitutability as the “long-dominant view” and pointing out that legal academia rejected opposing conclusions); Koh, supra note 26, at 339 (describing the debate as “long ago settled”).

³⁶ The approved draft of the Restatement (Fourth) is conspicuously silent on the matter of interchangeability, but there is no indication that this silence provides support to those arguing against interchangeability. The drafters of Restatement (Fourth) make clear that they focus on Article II treaties only and leave other international agreements unaddressed. See Restatement (Fourth) of the Foreign Relations Law of the United States, § 113, Reporters’ Note 8 (Mar. 20, 2017). So far, there seems to be little indication of a change in the scholarly debate. See, e.g., Bradley, Curtis A., Exiting Congressional-Executive Agreements, 67 Duke L.J. 1615 (2018)Google Scholar (viewing treaties and congressional-executive agreements as largely interchangeable even after the approval of the draft of Restatement (Fourth)).

³⁷ Restatement (Third) of the Foreign Relations Law of the United States, § 303, cmt. e (1987).

³⁸ See McClure, supra note 3, at 363 (reducing the treaties’ relevance to a small subset of non-controversial issues); see also Louis Henkin, Constitutionalism, Democracy, and Foreign Affairs 60 (1990) (finding that the executive agreement is the more democratic tool); see also Ackerman & Golove, supra note 30, at 916 (concluding that the rise of the congressional-executive agreement promotes “[e]fficacy, democracy [and] legitimacy”).

³⁹ Hathaway, supra note 1, at 1317.

⁴⁰ Id. at 1319.

⁴¹ Id. at 1336 (“[T]he President is on the whole likely to find it more difficult to withdraw unilaterally from a congressional-executive agreement than an Article II treaty.”). Some scholars cast doubt on the claim that presidents can withdraw from treaties more easily than from congressional-executive agreements. As Koremenos and Galbraith point out, many agreements in the UN Treaty Collection have withdrawal provisions that would allow a president to lawfully exit an agreement regardless of the form in which it has been concluded. See Barbara Koremenos, The Continent of International Law: Explaining Agreement Design 124 (2016) (finding that 70% of agreements have withdrawal provisions, based on a random sample of treaties in the UN Treaty Collection); Galbraith, supra note 26, at 1720 (arguing that withdrawal provisions give successors of the current president an easy way to legally withdraw from a treaty). For doctrinal challenges to the claim that treaties can be withdrawn from more easily, see Bradley, supra note 36.

⁴² Hathaway, supra note 1, at 1239–40 (“Although there are patterns to the current practice of using one type of agreement or another, those patterns have no identifiable rational basis.”).

⁴³ Id. at 1304.

⁴⁴ 108 AJIL Unbound (2014), available at https://www.cambridge.org/core/journals/american-journal-of-international-law/ajil-unbound; see also Bradley, supra note 9, at 85 (agreeing with Hathaway that the different use of treaties and executive agreements does not reflect any discernable logic).

⁴⁵ Bradley & Morrison, supra note 11, at 474.

⁴⁶ So labeled by Martin, supra note 17, at 53.

⁴⁷ Terry M. Moe & William G. Howell, The Presidential Power of Unilateral Action, 15 J. L. Econ. & Org. 132, 163 (describing how simply labeling an agreement “executive agreement” rather than “treaty” would allow the president to set foreign policy without having to involve the Senate); see also Matthew A. Crenson & Benjamin Ginsberg, Presidential Power: Unchecked and Unbalanced 321 (2007) (arguing that Franklin D. Roosevelt's use of the executive agreement was motivated by a desire to circumvent the Senate).

⁴⁸ Lawrence Margolis, Executive Agreements and Presidential Power in Foreign Policy 45 (1986).

⁴⁹ Setear, supra note 15 (describing a signaling model in non-formal terms).

⁵⁰ Martin, supra note 15 (providing a formal signaling model in which the cost of the agreement determines its credibility).

⁵¹ For a detailed discussion of the supposed difference in political costs, see Setear, supra note 15, at S14.

⁵² Martin believes the cost differential to be greatest for the difference between sole executive agreements and treaties, but she extends her argument to the difference between congressional-executive agreements and treaties. See Martin, supra note 15, at 447.

⁵³ Id. at 456.

⁵⁴ For a detailed description of these proxies, see id. at 454.

⁵⁵ Setear, supra note 15, at S16; Martin, supra note 17, at 64; Posner, Eric A. & Goldsmith, Jack L., International Agreements: A Rational Choice Approach, 44 Va. J. Int'l L. 113, 124 (2003)Google Scholar.

⁵⁶ Posner & Goldsmith, supra note 55. at 124.

⁵⁷ Fearon, James D., Domestic Political Audiences and the Escalation of International Disputes, 88 Am. Pol. Sci. Rev. 577 (1994)CrossRefGoogle Scholar (detailing audience costs for presidents who back down). Martin, supra note 17, at 64 (applying the audience cost rationale to senators).

⁵⁸ Schultz, supra note 16; Yoo, supra note 16, at 25; Posner & Goldsmith, supra note 55, at 124.

⁵⁹ In relative terms.

⁶⁰ See infra Table 3, which identifies the proportion of agreements made in the form of a treaty for a number of different countries. See also Table 2 in the online appendix for a full list of countries.

⁶¹ Hathaway, supra note 1, at 1258 (presenting a table of absolute treaty usage).

⁶² For a discussion on the importance and difficulty of measuring compliance with international agreements, see Downs, George W., Rocke, David M. & Barsoom, Peter N., Is the Good News About Compliance Good News About Cooperation?, 50 Int'l Org. 379 (1996)CrossRefGoogle Scholar.

⁶³ For instance, it is difficult to compare a breach of a tax treaty to compliance with a nuclear weapons reduction treaty. See Simmons, Beth A., Treaty Compliance and Violation, 13 Ann. Rev. Pol. Sci. 273 (2010)Google Scholar for examples of the fragmented nature of studies on treaty compliance.

⁶⁴ Downs, George W. & Jones, Michael A., Reputation, Compliance, and International Law, 31 J. Legal Stud. S95, S104 (2002)CrossRefGoogle Scholar (presenting a model built on the notion that reliability is the ability to perform even in light of shocks).

⁶⁵ For one attempt at codifying the propensity for shocks to occur by issue area, as well as for a discussion of the downsides of this approach, see Koremenos, Barbara, Contracting Around International Uncertainty, 99 Am. Pol. Sci. Rev. 549, 554 (2005)CrossRefGoogle Scholar.

⁶⁶ Martin, supra note 15, at 448 (“At times, U.S. allies demand that long-standing executive agreements be transformed into formal treaties, explicitly stating that such changes would signal U.S. long-term commitment.”); Yoo, supra note 16, at 41 (“[T]his reading of the Constitution removes from the nation's tool chest an instrument that could … lead to the most durable international agreements.”); Hathaway, supra note 1, at 1316 (“[T]he bar in Congress is generally higher for Article II treaties—which might be thought to create a stronger assurance of political durability.”).

⁶⁷ Treaties in Force: A List of Treaties and other International Agreements of the United States (1929–2017) [hereinafter TIF]. The dataset is limited to agreements concluded since 1982 because its construction requires cross-references with the Kavass’ Guide of Treaties in Force, which was first published in 1982. For the first time since 1957, the State Department did not release a separate edition of TIF for the years 2013 and 2014, which makes it impossible to tell the exact year in which agreements went out of force during that two-year window. The analysis thus ends in 2012.

⁶⁸ See U.S. Department of State, A Guide to the United States Treaties in Force (Igor I. Kavass ed., 1982–2016).

⁶⁹ See, e.g., U.S. Department of State, A Guide to the United States Treaties in Force, at vii (Igor I. Kavass ed., 2016) (“[T]here is very little correlation between the bilateral subject categories and the multilateral subject headings. The Treaties in Force does not have either a numerical or a subject list of bilateral and multilateral agreements in force. Neither does it attempt to draw agreements together in other manners of retrieval convenient to researchers.”).

⁷⁰ This procedure is accurate, save for some exceptions caused by idiosyncrasies in the publication process. For instance, the Guide (2011) lists the START I agreement as having been indexed in TIF (2010) and not indexed in TIF (2011), even though the agreement expired on December 5, 2009 (The corresponding identifier is KAV 3172, see U.S. Department of State, A Guide to the United States Treaties in Force 870 (Igor I. Kavass ed., 2011)). This is due to the fact that the treaty expired too close to the TIF's 2010 publication deadline. However, all agreements are equally affected by idiosyncrasies in the underlying publication mechanism, which makes it unlikely for these errors to introduce biases in the estimation.

⁷¹ See, e.g., Treaties in Force: A List of Treaties and other International Agreements of the United States, at i (1982).

⁷² For empirical evidence, see Crocker, Keith J. & Masten, Scott E., Mitigating Contractual Hazards: Unilateral Options and Contract Length, 19 RAND J. Econ. 327 (1988)CrossRefGoogle Scholar. For a theoretical assessment with regards to treaty-making, see Helfer, Laurence R., Exiting Treaties, 91 Va. L. Rev. 1579 (2005)Google Scholar (describing that an easy termination of a treaty may make its conclusion more attractive for those who do not intend to comply regardless of cost).

⁷³ See Hathaway, supra note 1, at note 49. It is possible that she misses some acts, as the process requires a manual search of the Statute at Large; however, it is the most comprehensive list to date.

⁷⁴ For each statute, a manual search is conducted for all executive agreements between the United States and the party mentioned in the act within a two-year window prior to the passing of the legislation. Not every act actually authorizes an executive agreement in the treaty. For example, the South African Democratic Transition Support Act of 1993 encourages investments and trade in South Africa. See South African Democratic Transition Support Act of 1993, Pub. L. No. 103-149, 107 Stat. 1503 (1993). It can thus reasonably be construed as authorizing prior investment and trade agreements between the United States and South Africa. However, there has not been any such agreement in the years preceding the act that is included in TIF. Indeed, the first investment agreement was concluded shortly after the statute was enacted.

⁷⁵ This choice rests on the rationale that the sitting president at the time when the agreement was signed has the greatest influence on its content. However, all results are substantively identical if instead using a categorical variable for the president under which the agreement went into force. The relevant regressions are included in the online appendix.

⁷⁶ Martin, supra note 15, at 454 (describing LPPC scores).

⁷⁷ Congressional Quarterly Weekly Report, Cong. Q. (1982–2012). Unity scores are the share of party members voting with their party in party unity votes. Party unity votes are those votes in which a majority of democrats vote in one direction and a majority of republicans vote in the other direction. For instance, if 85% of democrats voted in favor of a bill and 90% of republicans voted against it, then the voting unity scores for that particular bill would be 0.85 for democrats and 0.9 for republicans. These values are averaged across all roll calls for a given year. Note that unity scores are sometimes reported in percentages, e.g., 85 instead of 0.85 and 90 instead of 0.9. To increase readability of the relevant coefficients, I use unity scores as decimals.

⁷⁸ For an overview of possible sources, see Hoffman, Marci, United States, in Sources of State Practice in International Law 529 (Gaebler, Ralph F. & Shea, Alison A. eds., 2d ed. 2014)Google Scholar.

⁷⁹ The Case Act provides that these agreements only need to be transmitted “to the Committee on Foreign Relations of the Senate and the Committee on International Relations of the House of Representatives under an appropriate injunction of secrecy to be removed only upon due notice from the President.” 1 U.S.C. 112b(a) (1979).

⁸⁰ Hathaway combines multiple sources, leading to a total number of 3,119 agreements in the period of 1980–2000. See Hathaway, supra note 1, at 1258–60. In contrast, the dataset used here contains 6,148 agreements in the same period.

⁸¹ See note 28.

⁸² Hathaway, supra note 1, at 1259 (“[S]eparating executive agreements that are congressionally authorized from those that are not requires a painstaking search for authorizing legislation. To determine whether an agreement is a congressional-executive agreement, it is necessary to search the Statutes at Large prior to the date the agreement went into effect for terms related to that subject area. Then it is necessary to read each statute to determine whether it actually authorizes the relevant international agreements.”) (footnote omitted).

⁸³ See McLaughlin, C.H., The Scope of the Treaty Power in the United States II, 43 Minn. L. Rev. 651, 721 (1958)Google Scholar (calculating that 5.9% of agreements between 1883 and 1957 were concluded as sole executive agreements, or “Presidential agreements”); see also International Agreements: An Analysis of Executive Regulations and Practices, at 22, Senate Committee on Foreign Relations, 95th Cong., 1st Sess. (1977) (calculating that 5.5% of agreements from 1946–1972 relied exclusively on executive authority).

⁸⁴ Infra at 84.

⁸⁵ For example, commentators have observed recent efforts by developing countries to amend, supersede, or exit from bilateral investment treaties (BITs) with the United States. These efforts are fueled by information about the negative domestic effects of BITs and treaty interpretations that tend to favor investors. For a thorough discussion, see Lavopa, Federico M., Barreiros, Lucas E. & Bruno, Victoria M., How to Kill a BIT and Not Die Trying: Legal and Political Challenges of Denouncing or Renegotiating Bilateral Investment Treaties, 16 J. Int'l Econ. L. 869 (2013)CrossRefGoogle Scholar.

⁸⁶ Otherwise, the omission simply increases the standard errors of the estimate.

⁸⁷ A similar argument applies to agreements falling into desuetude. Whether an agreement is still actively relied on cannot be observed, is a subjective determination and we lack a clear theory for why the rate of active reliance to inactivity should differ for treaties and executive agreements.

⁸⁸ Janet M. Box-Steffensmeier & Bradford S. Jones, Event History Modeling: A Guide for Social Scientists 2 (2004) (describing the different terminology that survival models are referred to).

⁸⁹ The agreement is in force at least until 2012, possibly longer.

⁹⁰ Cox, David R., Regression Models and Life Tables, 34 J. Royal Stat. Soc'y 187 (1972)Google Scholar.

⁹¹ See, e.g., Tian, Lu, Zucker, David & Wei, L. J., On the Cox Model with Time-Varying Regression Coefficients, 100 J. Am. Stat. Ass'n 172, 172 (2005)Google Scholar (“The most popular semiparametric regression model for analyzing survival data is the proportional hazards (PH) model.”) (citation omitted). For examples in international law, see Elkins, Zachary, Simmons, Andrew T. Guzman & Beth A., Competing for Capital: The Diffusion of Bilateral Investment Treaties, 1960–2000, 60 Int'l Org. 811, 828 (2006)CrossRefGoogle Scholar (estimating adoption times for bilateral investment treaties using a Cox model); Simmons, Beth A., International Law and State Behavior: Commitment and Compliance in International Monetary Affairs, 94 Am. Pol. Sci. Rev. 819, 823 (2000)CrossRefGoogle Scholar (relying on the Cox model to estimate time until states accept commitments under IMF Articles of Agreement Article VIII).

⁹² The Cox model is of the form

$$h_i\lpar {t{\rm \vert} x_i} \rpar = h_0\lpar t \rpar e^{x_i^{\prime} \beta} $$

where i is the individual agreement, t is a period in time, x denotes a set of covariates, and h denotes the hazard rate, i.e. the probability for an event to occur.

⁹³ Jeffrey S. Peake, Executive Agreements as a Foreign Policy Tool During the Bush and Obama Administrations, at 2 (Apr. 16, 2015), available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2594414. See also Bradley, Curtis A. & Goldsmith, Jack L., Presidential Control Over International Law, 131 Harv. L. Rev. 1201, 1211 (2018)Google Scholar (“Both the average number of treaties transmitted per presidential year during [President Obama's] Administration (4.75) and the percentage of treaties receiving Senate consent (39%) are by far the smallest in the modern period measured since President Truman… .”).

⁹⁴ Valentine v. United States ex rel. Neidecker, 299 U.S. 5, 8 (1936).

⁹⁵ Ntakirutimana v. Reno, 184 F.3d 419, 437 (5th Cir. 1999) (DeMoss, J., dissenting).

⁹⁶ See Yoo, supra note 33, at 812 (arguing that extradition does not clearly fall under one of the enumerated powers conferred to Congress); see also Hathaway, supra note 1, at 1346–48.

⁹⁷ See Panayiota, Alexandropoulos, Enforceability of Executive-Congressional Agreements in Lieu of an Article II Treaty for Purposes of Extradition: Elizaphan Ntakirutimana v. Janet Reno, 45 Vill. L. Rev. 107, 113–14 (2000)Google Scholar (arguing that the Supreme Court in Valentine has clearly determined the legality of an extradition pursuant to an executive agreement); see also Klarevas, Louis, The Surrender of Alleged War Criminals to International Tribunals: Examining the Constitutionality of Extradition via Congressional-Executive Agreement, 8 UCLA J. Int'l L. & For. Aff. 77, 107 (2003)Google Scholar (providing further cases to support the interpretation that Valentine authorizes extradition based on an executive agreement).

⁹⁸ It cannot be ruled out that the importance of agreements within a subject category varies more strongly than the importance of agreements between subject categories. This possibility is discussed below, infra at 87–88.

⁹⁹ Due to data sparsity, not all country fixed effects can be accurately estimated, which is why this specification is included separately.

¹⁰⁰ The country is Mexico, the president is Reagan, and the subject is defense.

¹⁰¹ Note that the analysis only considers agreements concluded between 1982 and 2000 to take into account the fact that ex post congressional-executive agreements are not identified beyond that window.

¹⁰² For similar approaches in the sensitivity analysis of causal estimates, see Weiwei, Liu, Kuramoto, S. Janet & Stuart, Elizabeth A., An Introduction to Sensitivity Analysis for Unobserved Confounding in Non-Experimental Prevention Research, 14 Prevention Sci. 570 (2013)Google Scholar.

¹⁰³ Formally, it is required that the covariate of interest, here the treaty indicator, is uncorrelated with the potential outcome, here an agreement's durability, after the inclusion of all control variables. This is also referred to as the assumption of “selection on observables.” If the choice between treaties and congressional-executive agreements was random, the covariate of interest would, by definition, be uncorrelated to the potential outcome. However, absent randomization, the selection on observables assumption remains unverifiable and subject to theoretical debate.

¹⁰⁴ Recall, however, that including subject matter fixed effects does not cause large changes in the coefficients. In order for more nuanced selection effects to fully explain the results, one would have to assume that the within-category selection effects are stronger than the between-category selection effects, for example, that the average difference between two tax agreements explains more variation than the average difference between a tax agreement and an arms limitation agreement.

¹⁰⁵ For instance, HeinOnline's U.S. Treaties and Agreements Library offers access to the full text of a large number of international agreements.

¹⁰⁶ Alschner, Wolfgang, Seiermann, Julia & Skougarevskiy, Dmitriy, Text of Trade Agreements (ToTA)—A Structured Corpus for the Text as Data Analysis of Preferential Trade Agreements, 15 J. Empirical Legal Stud. 648 (2018)CrossRefGoogle Scholar (describing the creation and subsequent analysis of a database of 448 preferential trade agreements).

¹⁰⁷ Michael Waibel, Fair and Equitable Treatment as Boilerplate (not yet published, 2018) (examining the text of “fair and equitable treatment” clauses in investment treaties).

¹⁰⁸ See Hathaway, supra note 1, at 1307; see also Hathaway, Oona A., Presidential Power Over International Law: Restoring the Balance, 119 Yale L.J. 140, 260 (2009)Google Scholar.

¹⁰⁹ See Hathaway, supra note 1, at note 49.

¹¹⁰ Balanced Budget Downpayment Act, Pub. L. No. 104-99, § 201(a), 110 Stat. 26, 34 (1996).

¹¹¹ There were a few attempts in the Senate to waive the act which were rejected.

¹¹² Of the five legislative acts not related to trade, only one is an implementation act. The others address a larger set of policy goals. In addition to the 1996 Balanced Budget Downpayment Act, see Atomic Energy Act – Exemption, Pub. L. No. 109-401, 120 Stat. 2726 (2006) (including detailed provision which waive certain requirements of the Atomic Energy Act of 1954, and map out the legal framework for a proposed, future agreement between the United States and India); South African Democratic Transition Support Act of 1993, Pub. L. No. 103-149, 107 Stat. 1503 (1993) (a general act setting out United States policy with respect to the South African transition process after Apartheid); Support for East European Democracy (SEED) Act of 1989, Pub. L. No. 101-179, 103 Stat. 1298 (1989) (a general act including many provision designed “[t]o promote political democracy and economic pluralism in Poland and Hungary …”). The exception is the Agreement for Cooperation Concerning Peaceful Uses of Nuclear Energy, Pub. L. No. 99-183, 99 Stat. 1174 (1985) (codified at 42 U.S.C. § 2156 (2000)) (authorizing a prior agreement between the United States and China on the peaceful use of nuclear energy).

¹¹³ See Bradley, supra note 36; Galbraith, supra note 26; Bradley, Curtis A. & Helfer, Laurence R., Treaty Exit in the United States: Insights from the United Kingdom or South Africa?, 111 AJIL Unbound 428 (2017)CrossRefGoogle Scholar.

¹¹⁴ Guzman, Andrew T., A Compliance-Based Theory of International Law, 90 Calif. L. Rev. 1823, 1880 (2002)CrossRefGoogle Scholar.

¹¹⁵ Beth A. Simmons, Mobilizing for Human Rights: International Law in Domestic Politics 120 (2009). See also Guzman, Andrew T. & Meyer, Timothy L., International Soft Law, 2 J. Legal Analysis 171 (2010)CrossRefGoogle Scholar.

¹¹⁶ Some scholars are thus critical of the potential for reputational mechanisms to explain compliance. See, e.g., Brewster, Rachel, Unpacking the State's Reputation, 50 Harv. Int'l L.J. 231, 249 (2009)Google Scholar.

¹¹⁷ Cox, David R., Regression Models and Life Tables, 34 J. Royal Stat. Soc'y 187 (1972)Google Scholar.

¹¹⁸ In general, see Lin, Danyu Y., Wei, L. J. & Ying, Z., Checking the Cox Model with Cumulative Sums of Martingale-Based Residuals, 80 Biometrika 557, 557 (1993)CrossRefGoogle Scholar (“The proportional hazards model with the partial likelihood principle … has become exceedingly popular for the analysis of failure time observations.”) (citations omitted); see also Tian, Zucker & Wei, supra note 91, at 172 (“The most popular semiparametric regression model for analyzing survival data is the proportional hazards (PH) model.”) (citation omitted). For examples in international law, see Elkins, Guzman & Simmons, supra note 91, at 828 (estimating adoption times for bilateral investment treaties using a Cox model); Simmons, supra note 91, at 823 (2000) (relying on the Cox model to estimate time until states accept commitments under IMF Articles of Agreement Article VIII).

¹¹⁹ Kalbfleisch, John D. & Prentice, Ross L., Marginal Likelihoods Based on Cox's Regression and Life Model, 60 Biometrika 267 (1973)CrossRefGoogle Scholar.

¹²⁰ Through maximization of the associated likelihood function.

¹²¹ Efron, Bradley, The Efficiency of Cox's Likelihood Function for Censored Data, 72 J. Am. Stat. Ass'n 557 (1977)Google Scholar.

¹²² The complementary log-log discrete model (or c-log-log model) is of the form

$$h_i\lpar {t{\rm \vert} x_i} \rpar = 1-\lpar {1-h_0\lpar {t_i} \rpar } \rpar ^{e^{x_i^{\prime} \beta}} $$

or, if linearized,

$$\log \lpar {-\log \lpar {1-h\lpar t \rpar } \rpar } \rpar = \alpha _j + x_i^{\prime} \beta $$

where j denotes grouped time intervals. Note that

$$a_j = \log \lpar {-\log \lpar {1-h_0\lpar {t_j} \rpar } \rpar } \rpar $$

is an interval-specific complementary log-log transformation of the baseline hazard rate, h ₀(t _j). This means that the baseline hazard rate is allowed to vary with each interval, thus imposing only mild parametric assumptions.

¹²³ John D. Kalbfleisch & Ross L. Prentice, The Statistical Analysis of Failure Time Data 47 (2d ed. 2002). The statement refers to the continuous-time proportional-hazards model, where observations have been grouped by time. McCullagh shows that this model is identical to the complementary log-log discrete model, see McCullagh, Peter, Regression Models for Ordinal Data, 42 J. Royal Stat. Soc'y, Ser. B (Methodological) 109 (1980)Google Scholar.

¹²⁴ See Hertz-Picciotto, Irva & Rockhill, Beverly, Validity and Efficiency of Approximation Methods for Tied Survival Times in Cox Regression, 53 Biometrics 1151 (1997)CrossRefGoogle ScholarPubMed; Chalita, Liciana V.A.S., Colosimo, Enrico A. & Demétrio, Clarice G. B., Likelihood Approximations and Discrete Models for Tied Survival Data, 31 Communications in Statistics-Theory and Methods 1215 (2002)CrossRefGoogle Scholar; Borucka, Jadwiga, Methods of Handling Tied Events in the Cox Proportional Hazard Model, 2 Studia Oeconomica Posnaniensia 91 (2014)Google Scholar.

¹²⁵ Chalita, Colosimo & Demétrio, supra note 124, at 1220.

¹²⁶ Grambsch, Patricia M. & Therneau, Terry M., Proportional Hazards Tests and Diagnostics Based on Weighted Residuals, 81 Biometrika 515 (1994)CrossRefGoogle Scholar.

¹²⁷ Eric Vittinghoff, David V. Glidden, Stephen C. Shiboski & Charles E. McCulloch, Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models 237 (2d ed. 2012) (“The Schoenfeld test is widely used and gives two easily interpretable numbers that quantify the violation of the proportional hazards assumption. However, … in large samples they may find statistically significant evidence of model violations which do not meaningfully change the conclusions.”).

¹²⁸ Paul D. Allison, Survival Analysis Using SAS: A Practical Guide 173 (2d ed. 2010) (pointing out that interactions with time are commonly suppressed and that the estimates are nonetheless meaningful averages); see also Paul Allison, Event History and Survival Analysis 43 (2d ed. 2014) (“Even when the proportional hazards assumption is violated, it is often a satisfactory approximation. Those who are concerned about misspecification would often do better to focus on the possibilities of omitted explanatory variables, measurement error in the explanatory variables, and informative censoring.”).

¹²⁹ Indeed, such a scenario is comparable to the process of fitting a linear regression model to non-linear data. The reason why the OLS regression is so popular in many social scientific applications is that the obtained coefficients can still reasonability be interpreted as average covariate effects, even though the data generating process is non-linear. That is why the linearity assumption is hardly ever validated.