When health care spending (or military spending or education) is tallied as a "percentage of GDP," doesn't that GDP figure include that same health spending? If you remove all that double-dipping, what would those percentages look like?
Thank you for your question. Indeed, part of the expenditure in health expenditure and defense will count towards total GDP. The reason why the total GDP (including health expenditure or defense expenditure themselves) is used as a denominator to calculate the health expenditure as a percent of the GDP is because it gives us an idea about how much we spend on health relatively to the total amount of output we produced as a country in a whole year. In that sense, the usual statistics seem to be the more adequate way to look at the problem.
Now, if you would like to know how much we spend in Health relative to the GDP excluding Health related output we would need to exclude each of its items of the GDP before calculating the ratio. A back of the envelope calculation that assumes that all health expenditure is part of the GDP would be, using data from the World Bank (data.worldbank.org/indicator/SH.XPD.TOTL.ZS) for the U.S. in 2012:
Health Expenditure as a proportion of GDP: 17.9%
Health Expenditure as a proportion of non-health related GDP: 21.8%
For Defense (data.worldbank.org/indicator/MS.MIL.XPND.GD.ZS)
Defense Expenditure as a proportion of GDP: 3.8%
Defense Expenditure as a proportion of non-defense GDP: 3.95%