See part 1 here.

In the last decade, there has been a growing quantitative statistical research literature that seeks to determine the factors that are most associated with nuclear proliferation. These include factors affecting the supply of nuclear-weapons-enabling technologies such as the sharing of sensitive technology and materials (Fuhrmann 2009; Kroenig 2009) as well as factors affecting the demand for nuclear weapons, such as enduring rivalries and military disputes (Bleek 2010; Jo and Gartzke 2007; Singh and Way 2004). Of particular interest are studies that assess the effect of the nuclear nonproliferation treaty (NPT) on nuclear proliferation. These studies have found a variety of different results. Matthew Fuhrmann and Yonatan Lupu created a useful summary of these studies shown in the table below. 6 of the 13 quantitative studies that assessed the correlation between the NPT and nuclear proliferation found that the treaty had a negative correlation with proliferation and 7 of 13 found mixed results or no significant relationship.


(Fuhrmann and Lupu 2016)

While these quantitative studies have been useful in understanding variables that are correlated with nuclear weapons programs and nuclear proliferation, they have shortcomings in their ability to credibly identify the causes of proliferation. This is significant because understanding the causes of nonproliferation is important to understanding how nonproliferation in the future might change with different variables, such as defections from the nuclear nonproliferation treaty, further nuclear proliferation, or the expiration of the New START treaty.

The principal shortcomings of these analyses are:

  1. Data quality and availability
  2. The data generating process

(1) Data quality and availability issues include the uncertainty around the start and end of nuclear programs and small sample sizes.(2) The data generating process issue is more fundamental and comes about because countries themselves choose whether to join the treaty based on whether they view it as in their interest to join the treaty. Just inferring from the dataset, we cannot know whether a given country joined the NPT because they were not planning on proliferating anyway, or if they were planning on proliferating and the NPT changed their incentives in such a way so that they felt compelled to join the treaty, and once a member of the treaty they found pursuing a nuclear weapon unattractive or impossible.

On (1), because nuclear programs are usually closely guarded secrets, there is significant uncertainty around the dependent variable of many analyses: which states had nuclear weapons programs and when they started and ended these programs. In addition, the small number of cases of successful nuclear proliferation limits the statistical power of these analyses and makes their findings less robust. The result is that small changes to how certain events are coded based on interpretation of the historical evidence or additions or subtractions of a small number of events to the sample based on new evidence can reduce the robustness and even change the substantive findings of the analysis (Montgomery and Sagan 2009; Sagan 2011).

            While these issues make statistical analysis difficult, a more fundamental problem is (2): the data generating process. This makes statistically identifying the causal drivers of nuclear proliferation extremely difficult even if the data were accurate and plentiful. To illustrate this point, we can imagine an ideal experiment that would help us to understand the effect of the NPT on nuclear proliferation. This ideal experiment would involve creating a version of the world where the NPT never existed, and then comparing this world to the observed historical world with the NPT. We could then compare the difference in outcomes for a given country in the two worlds. If we find that a lot of countries proliferate in the non-NPT world but do not proliferate in the NPT world, then we can conclude that the NPT plays a significant role causing less proliferation. Unfortunately, this experiment is impossible since history only happened once and we do not have a time machine to go back in time and create a new history with no NPT.

Another good alternative would be to find “natural experiments” in which countries were randomly assigned membership into the NPT. As long as this NPT “treatment” is random, then we can compare the group of countries that were given the NPT treatment with the group of countries that were not. If the frequency of proliferation in the NPT treated group was significantly lower than the non-treated group, then we can conclude that the NPT plays a significant role in causing less proliferation. Unfortunately, we cannot do this experiment either. The reason is that the decision to join the NPT is a non-random strategic decision made by country leaders. We can imagine one type of country (type 1) that joined the treaty and was also not interested in nuclear weapons in the first place. Type 1 countries gladly join the NPT because joining the treaty does not change their prior plans, and they get the benefit of nuclear technology sharing that comes with the treaty and they avoid the scorn of other countries that want to maximize treaty participation. In this case, the NPT is not constraining the type 1 country’s proliferation because it would not have proliferated with or without the treaty. We can imagine another type of country (type 2) that was planning on pursuing nuclear weapons. However, due to a combination of pressure from their allies, the carrot of nuclear technology sharing, and fear of becoming an international pariah by eschewing the norm of joining the NPT, the type 2 country reluctantly chooses to join the NPT. After joining, the type 2 country is now unable to proliferate because IAEA safeguards monitor potential proliferation activities, and some countries are willing to enforce the NPT through sanctions and the threat or use of force.

There also may be countries that do not squarely fall into type 1 or type 2, further complicating this issue. We could imagine a type 3 country that under one set of leaders decided to ratify the NPT, but then another set of leaders came to power with nuclear ambitions and regretted the decision of the past regime to join the NPT. While the new regime may want to withdraw from the treaty, they may find it difficult to do so due to the spectacle that kicking out international safeguards inspectors would draw and the degree to which it would make their nuclear plans clear to powerful countries that might try to stop them through sanctions and the threat or use of force.  

Unfortunately, we cannot observe whether countries that joined the NPT are type 1, type 2, or type 3 in the dataset. It would be nice if countries that joined the treaty would declare their type, but countries have an incentive to represent themselves as type 1 even if they are type 2 or 3 because they do not want to attract suspicion. Alternatively, a type 1 country may be widely suspected of being type 2 or type 3 even if they never had any intention of pursuing nuclear weapons. Ultimately, all of these types join the NPT, and there is no way definitive way to know a country’s type. Therefore, we cannot accurately estimate the role that the NPT actually played in constraining proliferation with this research design.

This question of the effect that the NPT has on nuclear proliferation, unfortunately, falls into a class of questions that econometricians Josh Angrist and Jörn-Steffen Pischke call FUQ’d  (Fundamentally Unidentified Questions) (Angrist and Pischke 2008). With these questions, the potential explanatory variable (e.g. NPT participation) is so entangled with other variables that credibly isolating its causal effect on the outcome variable of interest (e.g. nuclear proliferation) is unfortunately not possible given the limitations of the data generating process.

Fuhrmann and Lupu provide a clever way to get around this problem in their 2016 article Do Arms Control Treaties Work? Assessing the Effectiveness of the Nuclear Nonproliferation Treaty. This article attempts to overcome the problem of non-random sorting into the NPT by creating a statistical model that considers a number of variables, including an estimated probability of NPT ratification (Fuhrmann and Lupu 2016). Fuhrmann and Lupu compare two country-years (i.e. a given country in a given year) that are very similar in the statistical model, but where one country had joined the NPT and where one did not. In this way, they create a matched sample of treatment and control country-years with two very similar country-years where one is given the NPT treatment and one is not. They argue that this research design brings us closer to establishing a causal connection between NPT membership and nuclear proliferation by ameliorating the problem of non-random treatment (the treatment being whether the country joined the NPT) because in theory, their model captures a states’ preferences towards pursuing nuclear weapons.

They then compare the control and treatment countries to estimate the effect of the NPT on proliferation. They run a regression using this matched sample, and they determine that the NPT had a significant constraining effect on whether a country pursued nuclear weapons or successfully proliferated in a given year.They conclude that the estimated annual probability of nuclear weapons pursuit for non-NPT members is 6.65%, whereas the estimated probability for NPT members is 1.14%.

This study represents the most advanced effort at causally identifying the effect of the NPT on nonproliferation, and their findings are significant. However, their study does not fully overcome the issue of non-random sorting. As they acknowledge in their paper, their model is not a perfect measure of state preferences for nuclear weapons in a given year because they cannot fully account for all the relevant variables. This is omitted variable bias: i.e. the variables that they cannot measure might skew their results one way or the other. There is reason to think that omitted variables bias may indeed be present because countries have an incentive to hide information that would suggest they want nuclear weapons so as not to arouse suspicion. Despite this issue, their analysis goes further than past statistical analyses in addressing the issue of the data generating process. If we assume that omitted variables bias is limited — and their sensitivity analyses show that omitted variable bias would have to be quite large to directionally change their findings — then these results are strong statistical evidence that the NPT had a large effect on limiting proliferation.

            So where does this leave us? Fuhrmann and Lupu’s analysis represents a significant step forward in addressing the data generating process issue that makes credible identification difficult and provides the most credible statistical answer yet on the causal effect that the NPT has had on proliferation. Because we are not able to generate random assignment of the treatment effect (the NPT), however, we cannot be sure that the relationship is causal. There may be other statistical techniques that can provide more credible evidence, such as a clever instrumental variable, but the question of the causal effect of the NPT on nuclear proliferation may remain FUQ’d (a Fundamentally Unidentifiable Question). In lieu of statistical analysis, we can use in-depth studies of historical cases to infer the preferences of states to determine if the NPT did seem to have a constraining effect on these countries; though some of the issues that plague quantitative analysis, such as knowing precisely when a nuclear program starts are stops, still affect case study analysis. In addition, there is more theoretical work to do to better understand the logic that explains how the NPT works (see Part 1). Given the destructive power of nuclear weapons, the importance of nuclear weapons in international security, and the degree to which understanding this logic could inform other arms control treaties such as those covering biological weapons, chemical weapons, missile defense, cybersecurity, and autonomous weapons, understanding this logic is an important area for future research.

Works Cited

Angrist, Joshua D., and Jörn-Steffen Pischke. 2008. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton university press.

Bleek, Philipp C. 2010. “Why Do States Proliferate? Quantitative Analysis of the Exploration, Pursuit, and Acquisition of Nuclear Weapons.” Forecasting Nuclear Proliferation in the 21st Century 1: 159–192.

Fuhrmann, Matthew. 2009. “Spreading Temptation: Proliferation and Peaceful Nuclear Cooperation Agreements.” International Security 34 (1): 7–41.

Fuhrmann, Matthew, and Yonatan Lupu. 2016. “Do Arms Control Treaties Work? Assessing the Effectiveness of the Nuclear Nonproliferation Treaty.” International Studies Quarterly 60 (3): 530–539.

Jo, Dong-Joon, and Erik Gartzke. 2007. “Determinants of Nuclear Weapons Proliferation.” Journal of Conflict Resolution 51 (1): 167–194.

Kroenig, Matthew. 2009. “Importing the Bomb: Sensitive Nuclear Assistance and Nuclear Proliferation.” Journal of Conflict Resolution 53 (2): 161–80. https://doi.org/10.1177/0022002708330287.

Montgomery, Alexander H., and Scott D. Sagan. 2009. “The Perils of Predicting Proliferation.” Journal of Conflict Resolution 53 (2): 302–328.

Sagan, Scott D. 2011. “The Causes of Nuclear Weapons Proliferation.” Annual Review of Political Science 14: 225–244.

Singh, Sonali, and Christopher R. Way. 2004. “The Correlates of Nuclear Proliferation: A Quantitative Test.” Journal of Conflict Resolution 48 (6): 859–885.