The effects of war on the workforce

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I'm not sure that deaths decrease the active population

Historically speaking there are periods when war is conducted only by professional military (in which case there is no effect on the labor force), and periods where war is conducted by citizen/soldier/militia. Different sides in the same war may have different participation rates. Military service in most wars is a very tiny fraction of total population. I believe military service is generally less than 10% of the population - meaning that the change in labor force participation is effectively insignificant.

I'm not sure that women are mobilized in all wars.

I'm not sure that there was a vast surge in female employment during the Napoleonic wars or even during the Vietnam war. I know that modern specialists in women's history question the extent to which women's participation in the labor force actually surged during WWII. Women's participation in the labor force probably shifted between segments, but may not have risen significantly. (My girlfriend has written several papers on this, but I haven't learned to boil down her thesis into a sound bite that fits neatly on SE).

I'm not sure how you're defining "Active Population"

Inventing your own term here makes it very difficult to provide an answer with references and citations. I think you should probably research employment to population ratio or other standard terms of use. The interesting question is whether the war pulls people out of the idle class into the working class. Even the unemployment rates only measure the proportion of the population that chooses to seek work - it ignores those who have given up, or choose not to participate (because they're wealthy, because they're handicapped, because they are criminal, etc.)

I think it is safer and more accurate to say that the allocation of the labor force shifts from private enterprise (butter) to mandated production (guns). The proportion of the GDP that is shifted is probably much more important than the labor force participation.

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