What Drives Arms Races?

Much of the early work on arms races centered on trying to understand what drives the acquisition of armaments. A great deal of this literature was inspired by the Richardson equations (Richardson, 1939).² Richardson was interested in understanding what would have an impact on the “defenses” of a pair of states in competition with one another. Note that his writing referred to defenses, not military expenditures. Figure 1 displays the Richardson equations.

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Figure 1. Lewis Richardson’s “Linear theory of two nations.”

Where:

x, y are the defenses of x and yk, l are the defense coefficients of x and yα‎, β‎ are the fatigue coefficients of x and yg, h are the grievance coefficients of x and y

Richardson assumed that for two states in an arms competition the changes in their defenses would be a function of three things:

The form of the Richardson equations suggested that the coefficients could be estimated by statistical analysis. And there were numerous efforts to do so. Typically researchers used military expenditures as their indicator for defenses.

This is only a brief review of Richardson’s work on arms races (see Leeds & Morgan, 2012, for a good review of arms race studies over the entire time period). This article only references a few additional key studies and discuss the issues and main problems of this research. It begins by noting that through time the methodologies used to explore arms races became more sophisticated. As well, the quantity and quality of data improved. But findings were inconsistent.

A significant focus of this research was to evaluate whether arms expenditures were externally driven or internally driven. If the changes in state A’s defenses were driven by State B’s defenses and vice versa, this suggests the two states were in an arms race against one another. But it was possible that a state’s defenses were driven by internal factors. In Richardson’s formulation, high levels of previous defense would lead to a decrease in current defense due to the costs of building and maintaining a large military. But a number of quantitative researchers embraced—or at least allowed for—a different interpretation. They argued that the military, the defense industry, and portions of the government would press a state to have higher and higher levels of expenditure. That is, while Richardson believed the coefficients for α‎ and β‎ would be negative, other researchers argued they would be positive.

Of course, one could argue that the signs of α‎ and β‎ could be treated as an empirical question: Just estimate the coefficients for a particular pair of states and see what happens. But generally studies were not this atheoretical. Most work involved a great deal of thought about the underlying causal mechanisms that drive changes in defense. Nevertheless, there was a sense that the results of the statistical analysis would serve to clarify the relationships being studied.

Unfortunately the empirical studies did not all point in the same direction for a particular (potential) arms race. Looking at the United States and the Soviet Union, Majeski and Jones (1981, p. 273) found “no causal relations exist between the military expenditure series” of those two countries. On the other hand, at roughly the same time the results of Wallace’s (1980, p. 271) study of the military expenditures of the United States and the Soviet Union “offer[ed] no support whatever to those who are convinced that the arms race results from the ineluctable nature of the political or economic system on either side. Rather, it would appear that both superpowers are reacting to external [emphasis in original] rather than internal stimuli.” There were a number of differences between these two studies. But the fact that these two well-done studies come to completely opposite conclusions (and there are other examples as well) is—to say the least—disheartening. As Moll and Luebbert note in their review of arms races models (1980, p. 166): “The common failure of statistical tests to discriminate among various models indicates that there are fundamental problems with either the explanatory power of the models or the discriminating ability of the tests. Which is the real difficulty remains a subject for future research.”

Of course, if one varies statistical techniques, data, and spatial temporal domain, this may have an impact on the results. But for research based on the Richardson equations there was another issue that led to inconsistent findings about whether particular dyads were engaged in an arms competition or were being driven by internal factors. Consider two polar cases: one in which both states in a dyad are driven internally and the other in which both states in a dyad are driven externally. If both states are driven internally and each is growing at a constant rate there will be a solid correlation between the data series of the two states (i.e., it will look like an externally driven arms race).³ And if both states are driven externally by each other’s defenses the relationship within each state to its own previous level of defenses should be strong (i.e., an externally driven arms race may look like a situation in which both states are driven by internal forces). So regardless of whether a dyad is purely driven internally or whether there is a pure arms race in a dyad, there should be a high degree of correlation between (a) the defenses of both sides, and (b) within each state its defenses and its previous defenses. This is only a simplistic depiction of the relationships, but it should convey the essence of the issue (see Stoll, 1982). To illustrate one aspect of this argument consider the simple set of correlations displayed in Table 1.

Table 1 shows the correlations of military expenditures among European members of NATO from 1960 through 1990.⁴ As you can see the correlations are fairly high. In fact, the average correlation is .70 and it rises to .88 if Portugal is removed. At the risk of being painfully obvious, none of the members of the dyads of European NATO countries were engaged in an arms race against each other; they were allied to one another. The point is that simply looking at military expenditure patterns is a poor way to judge whether countries are engaged in an arms race against one another.

So the earlier generation of arms race studies did not come to firm conclusions about whether particular dyads were engaged in an arms race or whether their increases in defenses were driven by something else (in particular by internal factors). While the sophistication of studies increased, as did the quality of the data, consensus was not achieved.

Do Arms Races Lead to War?

The second major area of research was whether states involved in arms races were likely to end in war. The belief that arms races lead to war was one of the main motivations for Richardson’s work; he felt that arms races were a primary cause of World War I. This was also the prime motivation of Huntington’s work (1958). Post World War II, this was a very important question for the obvious reason that an arms competition between the superpowers that ended in war might result in a nuclear exchange and the killing of millions and millions of people.

While a number of theoretical approaches were applied to this question, the two most prominent approaches were the spiral model and the deterrence model (Levy & Thompson, 2010, pp. 30–31). In the spiral model, states take actions against each other (increasing their defenses) for defensive purposes. However, while each state regards its own actions as defensive, each sees the other state’s states actions as offensive. Consequently the defensive actions of each state will be misperceived as offensive and lead to war.

While the spiral model focuses on the unintended consequences of defensive actions, the deterrence model focuses on the failure of states to take sufficient action to convince other states that if a war is fought they will lose. That is, war comes about if a state fails to increase its defenses sufficiently to dissuade the other state from attacking.

Each line of reasoning is plausible. What is less plausible is that it is an either–or situation (Levy & Thompson, 2010, p. 31). It seems more likely that sometimes one model would apply and that in other situations the other model would apply. So, the critical issue is what distinguishes these two situations. Uncovering the factors that differentiate the validity of these two perspectives is a far more difficult and demanding task. And one that was not directly addressed in most of the early literature on arms races.

There is another important issue. How do we select cases to study to evaluate whether arms races lead to war? There were a large number of studies that looked at this relationship. But how did researchers studying this question identify arms races?

One approach was used by Huntington (1958). Huntington (1958) was the first well-known effort to gather information on a series of arms races and draw general conclusions as opposed to a deep dive into a particular arms race. He relied on his study of history to identify 13 arms races from 1840 through the Cold War.⁵ And of course, instead of creating one’s own list of arms races one could use the consensus of historians to identify a number of races or even a single race for close study. But it seems likely that any two scholars would not achieve a complete consensus on arms races; that is, which states were involved and the years of the arms race. As well this entire approach is unlikely to be as rigorous as one that relies on quantitative measures. A different approach was used by Wallace (1979). He looked at major power dyads involved in militarized interstate disputes. Militarized interstate disputes occur when a state explicitly threatens, displays, or uses military force (Palmer, d’Orazio, Kenwick, & Lane, 2015). Wallace created an index for the military expenditures of each of the two states in a dispute over the previous ten years. He then multiplied the two indices together. He inferred that the higher the value of this multiplicative index, the more rapid the military growth in the dyad and the greater the chance of the dispute ending in war. His empirical analysis supported this assertion.

There were a number of issues with his research. One was that many of the major power dyads that ended in war were associated with the World Wars (i.e., these cases were not independent of one another). There were also several issues about his multiplicative index. First the multiplicative index could produce a large value even if one side’s value was very small; that is, while one state in the dyad may have rapidly increased its military expenditures, the index could produce a large value even if the other state was showing only small increases in military expenditures. This is not an arms race. A second issue with the index was that if the expenditures of both sides were declining for the first nine years but turned up in the last year the index would have a positive value. Finally, no one was able to replicate the index. As well as noted by Leeds and Morgan (2012, p. 144) a number of follow-up studies (Altfeld, 1983; Diehl, 1983; Weede, 1980) found a much weaker relationship than Wallace.

The broader issue is about the basic research design used by Wallace. He did not examine whether arms races lead to war. He looked at dyads that engaged in militarized interstate disputes and asked whether if prior to the dispute the dyad engaged in rapid military growth. If so, Wallace predicted (and his results—with the caveats of other studies noted above—supported this) that the states were very likely to engage in war.

For the moment let us accept Wallace’s findings. Understanding the conditions under which a dyad that engages in a militarized interstate dispute is more likely to end in war is a contribution to understanding why wars happen. But it does not explain the relationship between arms races and war. Even if we accept Wallace’s index as a valid indicator his research design does not allow for the possibility that there may be many arms races that are not associated with disputes. Including these cases may produce very different conclusions about the linkage between arms races and war.

Singletons

Move Away From Using Total Military Expenditures

Most arms race studies—regardless of when they were published—rely on total military expenditures. Some use this as the main variable of interest. There are two alternative variants. One involves what is usually viewed as defense effort (or burden); this is military expenditures divided by the GDP of the country. The other involves an over-time measure involving increases in total military expenditures and/or military personnel; in addition, some studies use defense effort (or burden) over time. On the surface these measures seem like a good approach. And these measures avoid the issues which arise if a researcher tries to construct indicators based on elements such as military hardware or military personnel, as well as attempting to consider elements of quality. It can be difficult to construct good measures of these alternative measures. But there are substantial drawbacks to using total military expenditures.

First, when dealing with arms races involving the United States in the post–World War II era, what about United States war involvements (in particular, Korea and Vietnam)? If you are conducting an arms race study involving the United States during the time periods of those wars and use a measure based on total military expenditures, then all of the resources that the United States was devoting to the wars will be counted toward the arms race. This makes absolutely no sense. To be sure, this may be an extreme case, but nevertheless it illustrates one way that total aggregate military expenditures figures can be misleading. Arms race studies cannot use total military expenditures when one or both states are engaged in a war with countries that are not involved in the arms race. Of course, one could use a measure of military expenditures that removed the amount being spent on the war(s) involving the state. But determining this amount may not be a simple task.

There are additional issues with military expenditures that are not so simple to resolve. During the Cold War there were extensive efforts both in and out of government to determine the level of military expenditures of the Soviet Union. While there were differences among scholars about the actual level of expenditures of the Soviet Union, there was general agreement on one thing: The official figure for defense that was released by the Soviet government was too low. Among those who were trying to provide more accurate estimates of Soviet military expenditures there were two general approaches.

The first was the residual approach (Becker, 1964). The premise of this approach was that the total Soviet budget contained all the military expenditures of the Soviet Union, but that significant portions of military expenditures were in other budget lines. With an economy based on central planning, everything had to be accounted for. So, if there was spending for defense that was not in the defense budget it had to be located in other parts of the Soviet budget. The residual approach can be illustrated using defense spending in the United States. If the United States builds nuclear weapons, the expenditure for this is not in the defense budget; it is in the budget of the Department of Energy. Furthermore, one can argue that when it comes to outer space, some of United States defense capability has been funded by NASA. But there was a significant difference between the United States and the Soviet Union during the Cold War. First, for the Soviet Union there were more budget lines outside the defense budget that contained spending for the military. Second, the Soviets were trying to hide their total military expenditures, while the “extra” expenditures outside the United States defense budget were (and still are) widely known and fairly easy to include in a budget figure for defense.

So the issue of obtaining an accurate figure for the Soviet budget involved significant effort. It involved estimating the proportion of other budget lines that were part of military expenditures and adding these figures to the Soviet military budget. Since the government of the Soviet Union was trying to keep this secret, there was considerable uncertainty about which additional categories of their budget—and in some cases how much of a budget category—should be added to the “official” Soviet military expenditure budget. This was not an arbitrary process, but different researchers could reach different conclusions about how much of other lines in the Soviet budget should be part of the Soviet military budget.

The second method to create a figure for the total military budget of the Soviet Union was the direct costing method (GlobalSecurity.org., 2016). This involved calculating the cost of individual items (e.g., a specific type of Soviet tank) and then aggregating by the total number of such items. In particular, United States firms were asked to estimate how they would build Soviet military equipment and how much this would cost. Their expenditure estimates were used to compute the total Soviet military budget. But there was a significant problem with this approach. In the United States, labor was (and is) very expensive, so it was (is) efficient to use as much capital as possible. But in the Soviet Union the opposite was true; capital was expensive and labor was cheap. Thus using estimates of the way the United States would build military equipment and then converting this into Soviet military expenditures produced much higher estimates for military items for the Soviet Union than building items the way the Soviets did.

This brief description makes one thing clear: The link between total military capability and total military expenditures may not be simple or direct, and reasonable people can reach very different conclusions. There is no better illustration of this disconnect than the results of the Team B exercise in the 1970s (Cahn, 1993). In the 1970s a great deal of pressure from conservatives in the United States was directed at the CIA’s evaluation of the threat from the Soviet Union. As a result “Team B” was created. A group of conservative critics of the CIA received security clearances and were given access to the same information the CIA used to create its estimates of a variety of things about the Soviet military. Team B concluded that the CIA had significantly underestimated Soviet military capabilities in a number of areas.

Following this exercise (although there was no official acknowledgement that Team B had anything to do with it), the CIA doubled its estimate of the proportion of the Soviet economy that was devoted to the military. This also meant that the estimate of Soviet military expenditures was doubled. But the CIA did not increase its estimate of any element of the Soviet military. To be absolutely clear, the revision of the Soviet military expenditures was not accompanied by a revision of the amount of hardware, personnel, or any other element of the actual military forces of the Soviet Union. The CIA decided that, while the Soviet military was no larger than they initially calculated, the Soviets were far less efficient then the CIA had thought. Consequently, they doubled their estimate of the proportion of the Soviet economy that was devoted to their military.

One can take different positions on the CIA revision. One point of view is that if the Soviet Union was devoting this much effort to the military, they were incredibly dangerous and likely to engage the United States in military conflict (i.e., why devote so much to the military if they didn’t intend to use it?). Alternatively, one could argue that any country that needed to devote so much of their economy to produce a military of that size was bound to encounter significant economic difficulties. But from the point of view of using military expenditures as a gauge of military capability, the fact that the CIA could revise its estimates and double the expenditure figure for the Soviet Union should raise questions for those who feel that military expenditures are the best way to measure military capability. I note as well that the estimation of Soviet military expenditures was considered to be—quite rightly—a very important question. The United States government spent a great deal of effort and resources to calculate this figure. The level of these resources dwarfs the effort that scholars (whether individuals or groups) could do. But even with a large amount of resources, it was not simple or straightforward to generate estimates.

Some may feel that the machinations to create a figure for the military expenditures of the Soviet Union—while perhaps interesting—are a historical footnote. But currently, those interested in military expenditures face a new challenge: How much does China spend on its military? As with the Soviet Union during the Cold War, there is a consensus that the Chinese are not transparent about their military budget. Of course, no one disputes that the United States is spending considerably more on its military than China is spending. But what are the Chinese spending? The recent study of Cordesman with Kendall (2016) offers the following data for the Chinese military expenditure budget in 2015 from a variety of sources (note: all figures are in billions of U.S. dollars):

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Chinese official figure:	141.1
US Department of Defense:	180.0
SIPRI15	214.5
IISS16	314.0

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As you can see, there is a wide range of estimates. Lack of transparency—the same problem that existed for Soviet military expenditures—makes it difficult to produce a reliable estimate for Chinese military expenditures. Of course, estimating military expenditures for most countries is not as difficult as producing a figure for China. But the Chinese example reinforces the point that using expenditures as a measure of military power is not always simple and straightforward.

There is a second issue that makes using total military expenditures problematic even if one is confident that there are no issues with the expenditure figures themselves. If the dynamics of an arms race (let us assume it is between just two states) are measured by total military expenditures, this implies that the competition involves all the armed services of both states. But this is—to say the least—implausible. For example, Huntington (1958) lists 13 arms races from 1840 to the Cold War. For each of these races Huntington lists only a single service; for example, he classifies the Cold War arms race between the United States and the Soviet Union as only involving nuclear weapons.

Of course, one could argue that Huntington was not correct; that is, arms races typically involve more than one military service. But consider the Military Balance 1989–1990 (International Institute for Strategic Studies, 1989); in 1989 (the year many people would argue is the last year of the Cold War), it reported the active duty army of United States was 766,500. The active duty army of the Soviet Union was 1,596,000. Given that the United States army was a bit less than half the size of the Soviet army, it is hard to argue that there was arms race between the two armies. And the classic naval arms race between Great Britain and Germany around the turn of the 20th century was clearly not matched by one between the armies of these two countries. Of course, it is possible that two states can be racing each other in more than one service. But even if one wants to use military expenditures to tap military power researchers should treat arms races as between individual services (although if one assumes that a pair of states are engaged in arms races across multiple services, these individual races may need to be modelled as linked to one another).

Scholars need to seriously consider whether the appropriate measure of arms races is not expenditures at all but is something more directly related the armaments. For example Stoll (2006) identified a number of naval competitions in which states established goals in terms of the number of capital ships:

There are other examples of states having goals for their navies tied to ship totals, particularly the number of capital ships. While the operationalization of capital ship changed through time (see Modelski & Thompson, 1988, pp. 50–96), it always meant that capital ship was the type of ship would be part of the battle line in a major naval engagement. Governments commonly used ship counts—not expenditures—to estimate naval capability.

There were also a number of efforts during the Cold War to construct indicators of the nuclear balance between the United States and the Soviet Union (see, e.g., Barash, 1986; Eden, 1989; Pry, 1990a, 1990b; Speed, 1980). Some of these measures were quite complicated, and the scholars did not always reach the same conclusion. But all focus on weapons (their number and characteristics), not military expenditures.

Finally, there were a number of efforts to estimate the balance of conventional forces between NATO and the Warsaw Pact during the Cold War. That is, a number of analysts believed that just using expenditure data was not the best way to evaluate the force balance. Two examples are Kaufman (1983) the Congressional Budget Office (1988) and Epstein (1988).

I am not suggesting that using measures of the appropriate military power will always be simple. In fact in most instances it will be difficult. But given the major problems with using total military expenditures I believe the study of arms races should move in this direction.

The Start of an Arms Race Is Not Always a Dyadic-Level Decision

Virtually all work on arms races treats the onset as a dyadic-level decision, which of course it is. But the empirical work assumes both states decide in the same year to compete against one another. Think about this for a moment. Does this make sense? It is not as if there is a meeting between the two states and they reach an agreement to engage in an arms competition. Of course, if two states see each other as rivals, it is reasonable to expect that the two states may engage in an arms competition, but they need not reach that decision in the same year.

Several examples were listed earlier of simple rules that are well documented among naval historians, but note that they all are about single states. They do not always reference a specific target state. Additionally, consider the situation concerning major power navies after the Russo-Japanese War of 1904–1905. The consensus among naval historians is that Japan was sizing its navy to the United States Navy, and the United States was sizing its navy to that of Great Britain. So the size of each of these navies was tied to another navy but not to each other.

As far as the British are concerned, virtually all scholars of naval competitions would assert that Germany and Great Britain engaged in a naval arms race from 1898 to either 1912 or 1914. There is also significant evidence that the leadership of the German navy began to size their navy to Great Britain’s in 1898, but when justifying its budget request in the British Parliament the Royal Navy did not mention the German navy until 1900.¹⁸ These examples—admittedly all about navies—suggest that while there are arms race dyads we are better off thinking in terms of armaments targeting. That is, state A begins to size one of its military services to that of state B. Shortly afterwards state B decides that state A is doing this and begins to size its military service to that of state B. This would probably happen quickly, but there may be a gap of a few years before it occurs. Our research on arms races should acknowledge this and not automatically assume that two states pick the same year to start sizing their military forces to the other state.