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There's a good argument to be made that the Great Depression caused WWII. The German Republic was brand new, and the economic devastation was far more than its tenuous prestige could support. As an alternative, extremist parties like the communists and the Nazis, neither of which wanted a Republic at all, were greatly strengthened. In the 1930 election enough Germans voted for the anti-republican parties that it wasn't possible for the Republic to create a government without them. The Nazis were invited into the government, and Hitler's ambition did the rest. In happier economic times this would not have happened.
WWI on the other hand, was mostly the result of the surpassing incompetence of the German monarch, Kaiser Wilhelm II. Here's an excerpt from his wikipedia page to give you an idea:
German foreign policy under Wilhelm II was faced with a number of significant problems. Perhaps the most apparent was that Wilhelm was an impatient man, subjective in his reactions and affected strongly by sentiment and impulse. He was personally ill-equipped to steer German foreign policy along a rational course.
He fired Otto von Bismarck, easily the most talented German politician and diplomat of the age (in fact, the man responsible for there being a German Kaiser in the first place), and instead surrounded himself with people who could be counted on to tell him only things he wanted to hear. The subsequent disconnect from reality had rather sad effects.
The spark that started the war happened in Austria-Hungary. But rather than try to contain things, Wilhelm at every stage fanned the flames. He became convinced that Russia, France, and England were all in cahoots against him, and then proceeded to take pre-emptive measures that ensured that in short order they were.
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In their book "Generations," William Strauss and Neil Howe argue that there is a correlation between economic crises and American wars.
A decade-long economic crisis "no taxation without representation" in 1765–1775 led to the American Revolution; the Depression of the 1850s led to the Civil War, and the Great (and global) Depression of the 1930s led to World War II (with America being one of the greatest participants in both the depression and the war).
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Correlations? Yes. Causations? No.
War and economy are different metrics. Both world economic crisis and world wars are huge historical events with multiple, far-reaching causes. Is there then a direct path, from a general crisis to a world-wide war? Well, no.
Put simply, since war and economy do not work at the same "plane", you can have a huge, broad, deadly war and still have huge economic growth, like in colonial America, or in Afghanistan, or in Persia prior to Alexander's conquests. Afghanistan has been a country on permanent civil war since the '80 has economically grown consistently, at a fast pace. This principle works from local wars to worldwide wars.
Also, a single "causation" to large scale events, like world wars, cannot be ascertained. Even when an economic crisis sets the stage for a large conflict, you cannot rule out the technological advances, diplomacy, or any other factor that leaders leveraged to actually decide to go to war (aka: true, direct causes).
Many examples in the timelines I build for HistoryTimeline.com have given me the idea that that wars and economy are obviously related, but that they really have different natures, and can be quite unnafected. Many, many times war is brought by economic growth. Just some examples: Nigeria after decolonization (oil prosperity), the conquest of Old Kingdom of Egypt, also the Islamic conquests.The Islamic conquests, truly a world war of their time, are a good example. They targeted prosperous areas so they could tax them.