Separating Hyperplanes

The US spends way more on healthcare

Matthew Martin 3/17/2014 03:04:00 PM

The Sydney Morning Herald, weighing in on Australia's healthcare debate, tells us that total healthcare cost is directly proportional to private financing of healthcare. As an American, and a healthcare econometrician, I found their graph interesting on a number of levels:

First, as an American, holy cow! We spend a ton on healthcare compare to these guys. It's even worse when you realize that this graph is in terms of percent of GDP, but the US also has somewhat higher GDP per capita than most of these other countries, meaning we are paying even more, comparatively, than the graph indicates.

However, as an econometrician, while I don't particularly doubt the central claim that private insurance is the most expensive way to organize a healthcare system, this is clearly not a valid regression line. If you treat the US as an outlier, which it clearly is, then observed the correlation between private funding and health expenditure pretty much disappears. Just look at how the error terms change as we move up the regression line in the graph--even heteroskedasticity assumes that the distribution of the error terms is symmetric about the trend line, whereas here we can clearly see that the errors above trend get smaller as you move up the trend-line, while errors below get bigger. This is not how you do OLS.