For GDP purposes, do economists classify education spending as consumption, investment, or gov't spending?

For GDP purposes, do economists classify education spending as consumption, investment, or gov't spending?
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I don’t think you can make that kind of generalization, lumping public and private education together. I’ve only taken AP Macroeconomics so I’m certainly no expert, but I would think that publicly funded education would fall under government spending; spending for private education, on the other hand, would be considered investment and consumption, depending on the type of spending, since a private school is a business. Even then, though, that’s a large generalization, the types of spending would have to be further broken down.
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