The theory behind the Rahn Curve is simple — but not simplistic. A relatively small government with powers limited mainly to the protection of citizens and their property is worth more than its cost to taxpayers because it fosters productive economic activity (not to mention liberty). But additional government spending hinders productive activity in many ways, which are discussed in Daniel Mitchell’s paper, “The Impact of Government Spending on Economic Growth.” (I would add to Mitchell’s list the burden of regulatory activity, which grows even when government does not.)

What does the Rahn Curve look like? Mitchell estimates this relationship between government spending and economic growth:

The curve is dashed rather than solid at low values of government spending because it has been decades since the governments of developed nations have spent as little as 20 percent of GDP. But as Mitchell and others note, the combined spending of governments in the U.S. was 10 percent (and less) until the eve of the Great Depression. And it was in the low-spending, laissez-faire era from the end of the Civil War to the early 1900s that the U.S. enjoyed its highest sustained rate of economic growth.

In an earlier post, I ventured an estimate of the Rahn curve that spanned most of the history of the United States. I came up with this relationship:

**Real rate of growth = -0.066(G/GDP) + 0.054**

To be precise, it’s the annualized rate of growth over the most recent 10-year span, as a function of G/GDP (fraction of GDP spent by governments at all levels) in the preceding 10 years. The relationship is lagged because it takes time for government spending (and related regulatory activities) to wreak their counterproductive effects on economic activity. Also, I include transfer payments (e.g., Social Security) in my measure of G because there’s no essential difference between transfer payments and many other kinds of government spending. They all take money from those who produce and give it to those who don’t (e.g., government employees engaged in paper-shuffling, unproductive social-engineering schemes, and counterproductive regulatory activities).

When G/GDP is greater than the amount needed for national defense and domestic justice — no more than 0.1 (10 percent of GDP) — it discourages productive, growth-producing, job-creating activity. And because G weighs most heavily on taxpayers with above-average incomes, higher rates of G/GDP also discourage saving, which finances growth-producing investments in new businesses, business expansion, and capital (i.e., new and more productive business assets, both physical and intellectual).

I’ve taken a closer look at the post-World War II numbers, because of the marked decline in the rate of growth since the end of the war:

Here’s the result:

**Real rate of growth = -0.364(G/GDP) + 0.0626(BA/GDP) – 0.000287(FR) + 0.0537
**

Again, it’s the annualized rate of growth over a 10-year span, as a function of G/GDP (fraction of GDP spent by governments at all levels) in the preceding 10 years, and two new terms. The first new term, BA/GDP, represents the constant-dollar value of private nonresidential assets (i.e., business assets) as a fraction of GDP, averaged over the preceding 10 years. The second new term, FR, represents the average number of Federal Register pages, in thousands, for the preceding 10-year period.

The equation has a good r-squared (0.729) and is highly significant (F-value = 4.16E-13). The p-values of the coefficients and intercept are also highly significant (7.43E-08, 1.67E-08, 0.00011, and 0.0014). The standard error of the estimate is 0.0059, that is, about 6/10 of a percentage point. I found no other intuitively appealing variables that add to the explanatory power of the equation.

What does the equation portend for the next 10 years? Based on G/GDP, BA/GDP, and FR for the most recent 10-year period (2006-2015), the real rate of growth for the next 10 years will be about 1.7 percent. The earlier equation yields an estimate of 2.9 percent. The new equation wins the reality test, as you can tell by the blue line in the graph above.

In fact the year-over-year rates of real growth for the past four quarters (2015Q3 through 2016Q2) are 2.2 percent, 1.9 percent, 1.6 percent, and 1.2 percent. So an estimate of 1.7 percent for the next 10 years looks rather optimistic.

And it probably is. If G/GDP were to rise from 0.381 (the average for 2006-2015) to 0.43, the rate of real growth would fall to zero, even if BA/GDP and FR were to remain at their 2006-2015 levels. (And FR is much more likely to rise than to fall.) It’s easy to imagine G/GDP hitting 0.43 with a Democrat president and Democrat-controlled Congress mandating “free” college educations, universal “free” health care, and who knows what else.