In the traditional GDP equation of Y = C + I + G + NX all public expenditure is lumped together as one sum. It seems to me that we should consider whether the government expenditure is on consumption or capital goods. Doing so would give us a more accurate sense both of total investment and of the concept of "crowding out."Yes, that is exactly correct. The traditional National Income Accounts identity separates private consumption C from private investment I but does not make the same distinction for public spending G. For many purposes, that decomposition is too crude, and it is useful to separate public consumption from public investment.
It is, however, hard to decide which government expenditures should count as public investment. Here are a few things that the government buys:
- Office buildings
- Military equipment
- Healthcare for a child
- Healthcare for a middle-aged person
- Healthcare for a senior in the last days of his life
Education, for example, is a combination of investment and consumption. I suppose it depends on how much a person is enjoying school and perhaps on what he is studying. A person learning auto repair in a public vocational school is accumulating human capital, and the teacher's salary is arguably a government capital expenditure. But would you say the same thing for the salary of the soccer coach?
Some of the same ambiguities arise in the measurement of private investment. For example, spending on college tuition is counted as private consumption, not investment. If we counted spending on human capital as investment, U.S. saving and investment would be higher as a percentage of GDP than they are under current measurement conventions.
Human capital becomes particularly vexing once we recognize that the most important input into its production is students' time. Maybe your high-school students should be viewed as members of the labor force who are employed producing human capital. That perspective would require a very different measurement of GDP and its components.