Optimal Amount of Tax Collection

Reader Erisian23 sent me an e-mail linking to comments by David M. Walker, Comptroller General of the United States. Walker, who runs the GAO, said, “Continuing on our current fiscal path would gradually erode, if not suddenly damage, our economy, our standard of living, and ultimately even our domestic tranquility and our national security.”

Additionally, on the subject of how high US tax revenues should be, he responded, “I can’t tell you an exact number … but more than 18.2 percent (of GDP), but below 25 percent.”

Erisian23 notes that 18.2% to 25% is a wide range, and asks whether its possible to narrow that down. The nickel answer… the size of revenues should depend in part on the size government should be. When government gets large enough, at the margin, it is less efficient at creating growth than the private sector, and hence cutting back on the size of government is good in the long run. On the other hand, if government gets small enough, at the margin an extra dollar spent on government services is more efficient at creating growth than the private sector.

So what does growth (in real GDP per capita) look when federal tax receipts are X percent of GDP? Letting A equal 0 to 17% of GDP, B being 17% to 18% of GDP, C being 18% to 19% of GDP, D being 19% – 20% of GDP, and E being 20% to 21% of GDP, and using data going back to 1950 (we have not observed federal tax receipts above 21% of GDP in this time):

_________A______B______C_____D______E
t to t+1__1.48%__2.72%__1.59%__2.12%__0.98%
t to t+2__1.50%__2.58%__1.46%__2.43%__0.91%
t to t+3__1.10%__2.46%__1.47%__2.76%__1.23%
t to t+4__1.55%__2.42%__1.52%__2.45%__1.50%
t to t+5__1.71%__2.38%__1.68%__2.24%__1.66%
t to t+6__1.68%__2.34%__1.77%__2.15%__1.60%
t to t+7__1.71%__2.29%__1.79%__2.30%__1.68%
t to t+8__1.72%__2.30%__1.81%__2.24%__NA

As an example of how to read the table, the annualized growth rate, over a seven year period beginning in a year when tax collections are 18% to 19% of GDP, is 1.79%.

The fastest growth rates, both over the short run and over eight years (I chose not to go longer – after 8 years one is definitely facing a different president’s policies) seem to happen when tax receipts are between 17% and 18% of GDP. However, 19% to 20% of GDP also looks very good – D beats B in several years.

But… if “too little” is collected, this means deficits. Does the same apply to deficits, or at least large ones?

The table below looks at the same thing, but only for those years in which there was a surplus, or a deficit of less than 2% of GDP.

_________A______B______C_____D______E
t to t+1__1.42%__2.51%__2.25%__1.99%__0.98%
t to t+2__1.53%__2.42%__1.96%__1.82%__0.91%
t to t+3__0.84%__2.56%__1.92%__2.28%__1.23%
t to t+4__1.33%__2.66%__1.84%__1.93%__1.50%
t to t+5__1.41%__2.72%__1.89%__1.55%__1.66%
t to t+6__1.24%__2.75%__1.86%__1.44%__1.60%
t to t+7__1.20%__2.69%__1.78%__1.81%__1.68%
t to t+8__1.29%__2.64%__1.71%__1.94%__NA

The benefits of having tax collections fall between 17% and 18% of GDP seem to increase when the country runs a small deficit or a surplus.

And when there is a large deficit?

_________A______B______C_____D______E
t to t+1__1.55%__3.01%__1.09%__2.34%__NA
t to t+2__1.44%__2.62%__1.08%__3.46%__NA
t to t+3__1.88%__2.23%__1.14%__3.56%__NA
t to t+4__2.23%__2.12%__1.29%__3.31%__NA
t to t+5__2.62%__2.04%__1.53%__3.16%__NA
t to t+6__3.00%__1.98%__1.69%__3.09%__NA
t to t+7__3.25%__1.93%__1.79%__2.95%__NA
t to t+8__3.02%__1.94%__1.89%__2.65%__NA

Column B no longer looks all that great. It does in the short term, but at periods longer than a year out, it produces lower growth rates than collecting at 19% to 20% of GDP.

Note an interesting fact… the lowest tax collections- 0 to 17% of GDP, actually exhibit the fastest growth 7 and 8 years out. But… I suspect this is an artifact of the data. Almost half of the observations in which real GDP per capita occurred in the beginning of the Clinton administration, or within 8 years of its beginning. Since that administration was one of relative fiscal responsibility, it is unlikely that the high growth rates of that era were caused by the previous fiscal irresponsibility.

Conclusion…. The data suggests that the fastest rates of growth have been observed when tax receipts have been between 17% and 18% of GDP, but only if the deficits have been kept small (or there is a surplus) at the same time. When deficits are large, its better to collect more – closer to 20% of GDP… presumably to pay off the deficit and pay down debt.

Data
Tax receipts and deficit or surplus as a percentage of GDP from OMB Table 1.3
Real GDP per capita from BEA NIPA Table 7.1.

Note that because tax and deficit data is for fiscal year, I used real GDP per capita for the third quarter of the calendar year.

Administrative notes:
1. As always, my spreadsheets are available upon request, even Thomas Sowell.
2. The cool thing about playing with data is, barring mistakes, one often learns something. When I started this exercise, I would have bet the data would show the optimal federal tax collection would be in the neighborhood of 20% of GDP and up, assuming no deficit.