Estimating the Rahn Curve: Or, How Government Inhibits Economic Growth

UPDATED 12/28/11 — This update incorporates GDP and government spending statistics for 2010 and corrects a minor discrepancy in the estimation of government spending. Also, there are new, easier-to-read graphs. The bottom line is the same as before: Government spending and everything that goes with it (including regulation) is destructive of economic growth.

*   *   *

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 accumulates with the size of government.)

Politics & Prosperity, “The Rahn Curve at Work,” July 7, 2010

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

Returning to “The Rahn Curve at Work”:

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.

Here is a graphic look at the historical relationship between government spending and GDP growth:

(Source notes for this graph and those that follow are at the bottom of this post.)

The regression lines are there simply to emphasize the long-term trends. The relationship between government spending as a percentage of GDP (G/GDP) and real GDP growth will emerge from the following graphs. There are chronological gaps because the Civil War, WWI, the Great Depression, and WWII distorted the relationship between G/GDP and economic growth. Large wars inflate government spending and GDP. The Great Depression saw a large rise in G/GDP, by pre-Depression standards, even as the economy shrank and then sputtered to a less-than-full recovery before the onset of WWII.

The graphs paint a consistent picture: Higher G/GDP means lower growth. There is one inconsistency, however, and that is the persistence of growth in the range of 2 to 4 percent during the post-WWII era, despite G/GDP in the range of 25-45 percent. That is not the kind of growth one would expect, given the relationships that obtain in the earlier eras. (The extrapolated trend line for 1946-2009 comes into use below.)

There are at least five plausible — and not mutually exclusive — explanations for the discrepancy. First, there is the difficulty of estimating GDP for years long past. Second, it is almost impossible to generate a consistent estimate of real GDP spanning two centuries; current economic output is vastly greater in volume and variety than it was in the early days of the Republic. Third, productivity gains (advances in technology, management techniques, and workers’ skills) may offset the growth-inhibiting effects of government spending, to some extent. Fourth, government regulations and active interventions (e.g., antitrust activity, the income tax) have a cumulative effect that operates independently of G/GDP. Regulations and interventions may have had an especially strong effect in the early 1900s (see the second graph in this post). The effects of regulations and interventions may diminish with time because of  adaptive behavior (e.g., “capture” of regulatory bodies).

Finally, and perhaps most importantly, there is the shifting composition of government spending. At relatively low levels of G/GDP, G consists largely of government programs that usurp and interfere with private-sector functions by diverting resources from productive uses to uses favored by politicians, bureaucrats, and their patrons. Higher levels of G/GDP — such as those we in the United States have known since the end of WWII — are reached by the expansion of the welfare state. Government spending (at all levels) on so-called social benefits accounted for only 7 percent of G and 0.8 percent of GDP in 1929; in 2009, it accounted for 36 percent of G and 15 percent of GDP. The provision of “social benefits” brings government into the business of redistributing income, which discourages work, saving, and capital formation to some extent, but doesn’t impinge directly on commerce. Therefore, I would expect G to be less damaging to GDP growth at higher levels of G/GDP — which is the message to be found in the contrast between the experience of 1946-2009 and the experience of earlier periods.

With those thoughts in mind, I present this empirical picture of the relationship between G/GDP and GDP growth in the United States:

The intermediate points, unfortunately, are missing because of the chronological gaps mentioned above. But, as indicated by the five earlier graphs, it is entirely reasonable to infer from the preceding graph a strong relationship between GDP growth and changes in G/GDP throughout the history of the Republic.

It is possible to obtain a rough estimate of the downward sloping portion of the Rahn curve by focusing on two eras: the post-Civil War years 1866-1890 — before the onset of “progressivism,” with its immediate and strong negative effects — and the post-WWII years 1946-2009. Thus:

My rough estimate is appropriately “fuzzy” and somewhat more generous than Daniel Mitchell’s, which is indicated by the heavy black line. In light of my discussion of the shifting composition of G as G/GDP becomes relatively large, I  have followed the slope of the trend line for 1792-2010; that is, every 1 percentage-point increase in G/GDP yields a decrease in the growth rate of about 0.06 percent. That seemingly small effect becomes a huge one when G/GDP rises over a long period of time (as has been the case for more than a century, with no end in sight).

Maximum GDP growth seems to occur when G/GDP is 2-4  percent. That is somewhat less than the 7-percent share of GDP that was spent on national defense, public order, and safety in 2010. The excess represents additional “insurance” against predators, foreign and domestic. (The effectiveness of the additional “insurance” is a separate question, though I am inclined to err on the side of caution when it comes to defense and law enforcement. Those functions are not responsible for the economic woes facing America’s taxpayers.)

If G/GDP reaches 55 percent — which it will if present entitlement “commitments” are not curtailed — the “baseline” rate of growth will shrink further: probably to less than 2 percent. And thus America will remain mired in its Mega-Depression.

*     *     *

Source notes:

Estimates of real and nominal GDP, back to 1790, come from the feature “What Was the U.S GDP Then?” at MeasuringWorth.com.

Estimates of government spending (federal, State, and local) come from USgovernmentspending.com; Statistical Abstracts of the United States, Colonial Times to 1970: Part 2. Series Y 533-566. Federal, State, and Local Government Expenditures, by Function; and the Bureau of Economic Analysis (BEA), Table 3.1. Government Current Receipts and Expenditures (lines 34, 35).

I found the amount spent by governments (federal, State, and local) on national defense and public order and safety by consulting BEA Table 3.17. Selected Government Current and Capital Expenditures by Function.

The BEA tables cited above are available here.

*    *    *

Related posts: Go to “Favorite Posts” and browse V. Economics: Principles and Issues.

Advertisement