Government spending as a pecentage of GDP

This New York magazine profile of Paul Krugman contains the following excerpt:

At the board, Krugman started sketching the American government’s expenditures, projected into the future and divided into three subgroups: Social Security, Medicare and Medicaid, and "everything else," which means defense, education, foreign aid, and much more. In 2010, "everything else" required 12 percent of GDP.

By 2030, under the [Rep. Paul] Ryan plan, it would get only 5.25 percent, and by 2050, 3.5. Krugman had run the numbers, and he said that the last time that figure had even approached 3.5 percent was during the Coolidge administration, when the country looked radically different; when, for instance, it had effectively no standing military.

...It was the reduction of "everything else" to a third of its current share that seemed simply impossible. There was a long silence in the classroom. "This is a pretty amazing number," Krugman said. "I try to present both sides, but this is pretty hard to understand."

Krugman's analysis is flawed. The problem with assessing government expenditures as a percentage of GDP is that GDP has been increasing faster than population growth for quite some time -- pretty much since the industrial revolution. Thus, even if government spending as a percentage of GDP is held constant the size of government will still expand. A smaller slice of a bigger pie is often larger than a big slice of a small pie.

Consider 1925, which is roughly the middle of Coolidge's presidency*. At 3.5 percent of GDP, government spending would have been about $27 per person (GDP of $90.6 billion and population of 114.3 million). Adjusted for inflation that's about $333 in 2010 dollars. If the government were to spend 3.5 percent of GDP today, it would amount to $494 billion, or just over $1,600 per person.

If government spending as a percentage of GDP were simply held constant over the last 85 years it nonetheless would have nearly quintupled (x4.8) on a per capita basis!

* As an aside, Calvin Coolidge was a superb president, favoring low taxes and minimal regulation, opposing farm subsidies and racking up a solid record on civil rights (one notably superior to that of Woodrow Wilson).

Update: Conversely, if government expenditures of $1600 per capita were converted into 1925 dollars, it would be the equivalent of $14.8 billion, or 16.3 percent of GDP at the time.