Let's start at the beginning.

The key early empirical work was "Arms and Insecurity" by Richardson (pusblished posthumously in 1960) https://www.google.com/books/edition/Arms_and_insecurity/XYfeAQAACAAJ?hl=en
With the data available at the time, Richardson argued that there didn't seem to be much of a relationship
Things really picked up steam with a debate in the Journal of Conflict Resolution between Michael Wallace and Erich Weede
For IR scholars who work with IR data, this piece is notable as it is the first piece to use what we now call "Militarized Interstate Dispute" (MID) data. He used these "serious disputes" to create a sample of state-to-state pairs that were likely to enter arms races
For his outcome variable, Wallace identified which of these dyads entered war (23 out of 99).

Note: I think the 96 is a typo
How did he capture whether an Arms Race was actually taking place within a dyad? Well, that's where things get tricky, which Wallace admits
So what does he do? He uses the military expenditure data from COW and then draws on this book
That book has a table (Table 1) that literally lists a bunch of values that can be used to create a polynomial
As he describes in this footnote, those polynomials can be used to take the expenditure values from the previous 10 years to produce a "time rates of change of national arms levels"
Multiplying the "times rates of change of national arms levels" of both states in the dyad gives the "Arms Race Index" value for that dyad during the year of a dispute
All of these steps produce a dataset that Wallace reproduces in his Table 1
If you look at the whole dataset, you'll notice that Russia is in A LOT of the dyads.

I've talked about this before https://twitter.com/ProfPaulPoast/status/1204745930144174080
So what does Wallace find? His findings are pretty self-explanatory: Arms Races and War are VERY closely associated
The main concern is that most of the "war" dispute-dyads come from just two events: World War I and World War II.
Accounting for this problem severly weakens the finding, though the overall relationship of arms racing being associated with war onset remains
But both Wallace and Weede agree that there seems to be a relationship between arms racing and war onset.
She reevaluates all of the previous work. She finds that the differences between Diehl and Wallace is largely due to differences in measuring arms race (namely, the weights they place on the pre-ceeding years)
What did she find? That Arms races are positively correlated with war onset
Note that she uses "Horn Arms Race". Horn used a different measure of arms racing from Wallace or Diehl
Sample found that the Arms Race and War Onset relationship held for pre-1945, but not since 1945.
Of course, I wonder if this post-1945 "null" is driven by the Cold War not actually becoming a direct war? 🤔
So arms races might be wasteful and they surely don't help to resolve tensions. But the data say that, since 1945 at least, they haven't been strongly associated with war onset.

So maybe they are not all THAT bad? 🤷‍♂️🤔

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