Models for Arms races
After the Second World War the USA and Russia started the so called Arms races. The races were not only taking place with respect to nuclear bombs but also with respect to delivery systems of nuclear weapons. The common idea behind arms races is that there are at least two countries which affect each other to generate more or better weapons.
In my classes on structural equation models the students had to learn to transform verbal statements in equations. An example, which illustrates very well the attraction of this transformation, was the arms race because as soon as the equations are formulated one can simply illustrate the consequences of arms races. In verbal statements these consequences are not so clear.
For this exercise I used a text of Richardson (1960) who had made models of arms races. He starts with a speech of the Defense minister of “Jedesland” (this is a German expression for every country) :
In my classes on structural equation models the students had to learn to transform verbal statements in equations. An example, which illustrates very well the attraction of this transformation, was the arms race because as soon as the equations are formulated one can simply illustrate the consequences of arms races. In verbal statements these consequences are not so clear.
For this exercise I used a text of Richardson (1960) who had made models of arms races. He starts with a speech of the Defense minister of “Jedesland” (this is a German expression for every country) :
Next, Winston Churchill is cited on a point of view which presents another aspect of the process of arms races. In 1923, Churchill spoke about the constraints which exist with respect to armaments:
I suggested in the exercise the following: “These two statements give an indication of the way nations decide about their defense budgets. Try to formulate on the basis of these two verbal reports a causal theory which might explain arms races. Restrict the theory to only two nations which behave in the same way.”
First of all the students had to look for relevant variables and then for the effects between these variables. The sentences about pacifism are funny but irrelevant. The next sentence suggest the relevant variables “state of unrest” , further more the “menaces” which are supposed to come from the other country and these variables will “increase the defense budget of the own country”. From the text of Churchill follows that there is a limiting effect of the “expenses for defense” on the increase of the defense budget. This analysis suggests the following causal effects for country A and B taking into account that countries A and B behave in the same way.
First of all the students had to look for relevant variables and then for the effects between these variables. The sentences about pacifism are funny but irrelevant. The next sentence suggest the relevant variables “state of unrest” , further more the “menaces” which are supposed to come from the other country and these variables will “increase the defense budget of the own country”. From the text of Churchill follows that there is a limiting effect of the “expenses for defense” on the increase of the defense budget. This analysis suggests the following causal effects for country A and B taking into account that countries A and B behave in the same way.
This so called path diagram suggests that Country A feels obliged to increase its defense budget and as a consequence country B feels obliged to do the same. The only moderating effect comes from the negative effect of the already spent budget.
This process is understandable for all students and the process can be transformed in equations introducing time delays and they can compute what happens under different conditions through time. In this sense this exercise was very illustrative for formalization of verbal theories.
This process is understandable for all students and the process can be transformed in equations introducing time delays and they can compute what happens under different conditions through time. In this sense this exercise was very illustrative for formalization of verbal theories.
Test on real data
Another issue is of course whether this model represents what happens in reality. One can use linear models like we did in the exercise or more complex nonlinear models like Richardson formulated in 1980 and Hamblin et al. in 1977 using differential equations. However all three models did not fit to data which I found about the number missiles of the USA and the Soviet Union between 1959 and 1977.
As one can see the USA produced missiles when the USSR did not have them or only very few. On the other hand the USSR continued to produce more and more missiles when the USA had already stopped with the production of new missiles. This suggests that this process does not looks like the suggested arms race model generally accepted. This raises the question what else was going on?
Another issue is of course whether this model represents what happens in reality. One can use linear models like we did in the exercise or more complex nonlinear models like Richardson formulated in 1980 and Hamblin et al. in 1977 using differential equations. However all three models did not fit to data which I found about the number missiles of the USA and the Soviet Union between 1959 and 1977.
As one can see the USA produced missiles when the USSR did not have them or only very few. On the other hand the USSR continued to produce more and more missiles when the USA had already stopped with the production of new missiles. This suggests that this process does not looks like the suggested arms race model generally accepted. This raises the question what else was going on?
An alternative model
It is interesting that the decision makers involved in this process suggested an alternative process. First of all in his memoirs Khrushchev is quoted to have said the following:
It is interesting that the decision makers involved in this process suggested an alternative process. First of all in his memoirs Khrushchev is quoted to have said the following:
Although Krushchev states this argument in terms of the existence of the weapon in the hands of the USA, it would also be valid if the USSR realized that they could develop this weapon and so expected the other could develop this as well. This was typically the case during WW II. The USA realized that they could develop a nuclear bomb and that was enough to start a big research and production program to develop the bomb because they thought that Germany could develop it as well. This turned out not to be true after the war. So only the idea that one can develop a better weapon can lead to the production of it.
Another question is how many of these weapons should be made. These weapons were used for “assured deterrence”. According to McNamara that meant that one should have the “ability to inflict at all times and under all foreseeable conditions an unacceptable degree of damage upon any single aggressor - or combination of aggressors – even after absorbing a surprise attack”. Based on this argument one can determine a number above which one does not need to produce more missiles for assured destruction.
The combination of these two arguments suggests that each country will start the production of the new weapon as soon as they realize that they can make it and fear that the other can do it too. This production will go on till the level is reached which is necessary for assured damage.
Such a process can also be specified in a mathematical model. It would lead to far to explain this here but it can be found in my paper. This model did not specify influence of the other country, nevertheless this model fitted very well to the data as can be seen in the figure presented at the side.
Another question is how many of these weapons should be made. These weapons were used for “assured deterrence”. According to McNamara that meant that one should have the “ability to inflict at all times and under all foreseeable conditions an unacceptable degree of damage upon any single aggressor - or combination of aggressors – even after absorbing a surprise attack”. Based on this argument one can determine a number above which one does not need to produce more missiles for assured destruction.
The combination of these two arguments suggests that each country will start the production of the new weapon as soon as they realize that they can make it and fear that the other can do it too. This production will go on till the level is reached which is necessary for assured damage.
Such a process can also be specified in a mathematical model. It would lead to far to explain this here but it can be found in my paper. This model did not specify influence of the other country, nevertheless this model fitted very well to the data as can be seen in the figure presented at the side.
Why did the US stop earlier than the USSR?
One would expect that the USA should need more missiles to realize assured destruction than the USSR given that the USSR is much larger in size than the USA. This is however not what we see in this picture. Therefore other variables should play a role in this process. Here President Eisenhower can help us out because he has said:
One would expect that the USA should need more missiles to realize assured destruction than the USSR given that the USSR is much larger in size than the USA. This is however not what we see in this picture. Therefore other variables should play a role in this process. Here President Eisenhower can help us out because he has said:
Implicitly he suggests that the political elite has become captive of a scientific- technological elite which invents each time new weapons. In this specific case what happened was that the industry had developed the MIRV or Multiple Independently –targetable Re-entry Vehicle. That means that they could launch with one new type of missile several warheads which independently could be directed to different targets. Therefore one needs much less missiles because with one missile one could destroy different targets. This idea was certainly known in 1967 and therefore the USA stopped the production of the original missiles and started the production of the MIRV´s in 1970. So the stop of the production of the old missiles in 1967 was not because an absolute saturation level was reached as McNamara suggested, but because they were aware that they could produce a better weapon for the same purpose. The production of the MIRVS continued for 7 years and fitted well to the model I had developed without taking into account the production of that weapon by the USSR. In fact the USSR did not have that weapon at that time therefore it continued to produce the old missiles to get closer to their chosen level of assured destruction.
Conclusion
At least in the development of missiles an arms race can´t be observed. The only way the countries affected each other was because they feared that the other could do the same as they could. Besides that the production process was determined by the technical capacity of the military industry and the innovations they produced. This process has led to an extremely dangerous situations during the “cold war” which easily could have ended very “warm”.
One may wonder if one could have prevented this risk. After the development of the first nuclear bomb by the USA, several scientists were so shocked by the result that they suggested that the bomb should not be used. They suggested that the devastating power of this weapon should be shown to representatives from all over the world and after that the United Nations should make an agreement to ban this weapon. Unfortunately this proposal has been rejected, the bomb was used in Japan, the development of these weapons and delivery systems went on and we have been lucky to have survived this “Cold War”.
At least in the development of missiles an arms race can´t be observed. The only way the countries affected each other was because they feared that the other could do the same as they could. Besides that the production process was determined by the technical capacity of the military industry and the innovations they produced. This process has led to an extremely dangerous situations during the “cold war” which easily could have ended very “warm”.
One may wonder if one could have prevented this risk. After the development of the first nuclear bomb by the USA, several scientists were so shocked by the result that they suggested that the bomb should not be used. They suggested that the devastating power of this weapon should be shown to representatives from all over the world and after that the United Nations should make an agreement to ban this weapon. Unfortunately this proposal has been rejected, the bomb was used in Japan, the development of these weapons and delivery systems went on and we have been lucky to have survived this “Cold War”.