Much discussion has happened on this site regarding income tax rates, government spending, and the health of the economy. Certainly I’ve had some preconceived notions of what’s best, as has pretty much everyone else here.
I decided to be more open-minded and run a more thorough analysis of the relationships among taxes, government spending, and the economy. I collected data on GDP, government revenues, and government spending, from 1913 to 2008. I also collected data on inflation and population, so that I could normalize the results against changes in the real value of nominal dollars, and against the inherent growth effects that result from larger populations. I chose 1913 as the starting year because it was the first year of the federal income tax.
In some cases, I have normalized government revenues and spending as a ratio to overall GDP. Where I did this, the intent is to recognize that the effect on the economy of government collecting taxes or spending money will necessarily be related to the size of the levies and expenditures relative to the overall economy. That is, government spending $1B in a $3B economy should be expected to have a substantial impact, while spending the same $1B in a $3T economy should be expected to have minimal impact, being a thousandth as much a part of the economy.
In all cases, I looked at GDP in the same year as inputs, as well as one to five years offset, to account for the time it takes for economic impact to propagate throughout the economy.
I performed regression analyses against a number of possible inputs, looking for a statistically significant correlation between the input and the output of year-over-year change in per-capita GDP in real dollars (i.e., adjusted for inflation).
It took numerous iterations, which I will be happy to explain if I’m asked to, but I don’t want to bore you with the details otherwise. Perhaps a sidebar article is in order, if you all want to read it.
The most significant correlations I found were when combining spending as a percentage of GDP at an offset of two years (S%GO2), and income tax as a percent of government revenues with an offset of one and two years (IT%RO1 and IT%RO2). The combined R2 was 0.36, indicating that these combined inputs accounted for 36% of the variance in GDP growth. The spending coefficient was 0.26, meaning that each increase of 1% in government spending relative to GDP corresponded to an increase of roughly 0.26% in GDP growth two years later. Oddly enough, the coefficients for income tax as a percent of government revenues were nearly equal but opposite for offset years one and two. That is, for a one-year offset, higher percentages of government revenues coming from income taxes corresponded to a decrease in GDP growth, while the opposite is true for a two-year offset. You can see what I mean in the below table.
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | -0.02851 | 0.020875 | -1.36562 | 0.1755 | -0.06999 | 0.012971 |
| S%GO2 | 0.260125 | 0.066184 | 3.930333 | 0.000167 | 0.128619 | 0.391631 |
| IT%RO1 | -0.3683 | 0.073444 | -5.01478 | 2.69E-06 | -0.51424 | -0.22237 |
| IT%RO2 | 0.376671 | 0.083202 | 4.52721 | 1.84E-05 | 0.211351 | 0.541991 |
I could find no statistically significant correlation between GDP growth and any of the following:
- Income tax as a percentage of GDP
- Overall tax revenues as a percentage of GDP
- Non-income tax revenues as a percentage of GDP
- Deficit spending as a percentage of GDP
- Bottom and top income tax rates
I also tried including and excluding the size of the national debt as a percentage of GDP. While the size of the national debt was borderline statistically significant, it had a tiny R2 (0.003) and it didn’t impact the multivariable regression analysis.
I ran one other set of tests, looking for a correlation between increases in government spending and changes in private sector spending. Specifically, I was looking for evidence that increased government spending crowds out the private sector, a theory that has been brought up repeatedly in the comments on this site. Again, I looked at offsets from zero to five years. For this set, because income tax was not important, I went from 1794 to 2008, so as to have more data points. I could find no statistically significant relationship between the two.
The regression analysis suggests that the most important thing the federal government can do to improve the economy (among the fiscal levers of spending, taxing, and running deficits) is to spend money. It doesn’t matter whether it’s spending money collected via taxes or created via deficit spending.
So, based on nearly a century of data, we can conclude that there is statistically significant evidence to support the hypothesis that Keynes was right, at least within the range of values experienced over the past century. More government spending corresponds to more growth in the economy.
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Interesting analysis. I have a couple questions, if I may:
1) Did your analysis rule out the possibility that economic growth caused growth in government spending (via increased tax revenues) rather than the reverse? How did you accomplish this?
2) How did you calculate the effective marginal tax rates over time? That alone could take years.
a) Which income tax rates did you use? There are often several which combine to make up the effective marginal income tax rate.
b) The published tax rates are only starting points and do not account for the various deductions and credits and other tax games. Did you incorporate these?
3) If you managed to obtain genuine marginal income tax rates over time, did your analysis examine economic growth before and after substantial increases/decreases in the effective marginal tax rate?
Thanks.
Bart,
1) Yes. It should come as no surprise that increased revenues had an exceptionally high correlation to increased spending, but in a non-offset kind of way. But there was no statistical correlation between GDP growth and spending growth (at least to the standard 95% confidence that I used everywhere else), and the R-squared was 0.01.
2) and 3) I didn’t calculate effective marginal tax rates. I looked at the highest marginal tax rate. I recognize that there may be something of value to look at with respect to the relative tax rates on different segments of the population, but for the purposes of this analysis I was eliminating the progressiveness of the tax structure from the equation.
“More government spending corresponds to more growth in the economy.”
This tell us nothing and simply reiterates what we already know from definitions and formulas learned in Economics 101.
You’re making a very simple argument. That being that “growth in the economy” = Gross Domestic Product.
And we know that GDP = Private Consumption + Gross Investment + Government Spending + (Exports – Imports).
What you’re saying is that, “Make Government Spending bigger, assume all else is constant, and voila, GDP is bigger.”
And, in theory, you’re right. The problem is that it’s not that simple. You don’t simply increase G and not have any long-term effect on C, I, or (X-I).
Looked at another way, I challenge you on something on the same grounds you and many liberals argue against the Laffer Curve by asking the people who say a lower tax rate equals higher tax revenues, “Why not take the rate to zero?”
My riposte, then, is if more government spending equates economic growth, why not make it considerably larger, even “infinite”? Wouldn’t that translate into unfettered economic growth, in theory?
Michael:
BD: Did your analysis rule out the possibility that economic growth caused growth in government spending (via increased tax revenues) rather than the reverse? How did you accomplish this?
Yes. It should come as no surprise that increased revenues had an exceptionally high correlation to increased spending, but in a non-offset kind of way. But there was no statistical correlation between GDP growth and spending growth (at least to the standard 95% confidence that I used everywhere else), and the R-squared was 0.01.
There is a high correlation between increased tax revenues and increased government spending, but there is no correlation between the economic growth that causes increased tax revenues and increased government spending? That makes no sense. Are you including recessionary drops in GDP in your GDP “growth” data?
2) and 3) I didn’t calculate effective marginal tax rates. I looked at the highest marginal tax rate. I recognize that there may be something of value to look at with respect to the relative tax rates on different segments of the population, but for the purposes of this analysis I was eliminating the progressiveness of the tax structure from the equation.
With respect, your calculations are useless then.
The rates should cover at least the folks paying most of the income taxes.
Even if you limit the analysis to the top rate, you have to incorporate all the taxes on income and then reduce the rate by all the deductions taken and credits received. For example, the nominal top income tax rate dropped from over 70% to 28% in the 80s, but this does not include the increase in corporate and SS income tax rates, the elimination of a slew of deductions and credits or the drop in capital gains. In reality folks were not paying nearly 70% before the reforms if they had access to a competent CPA.
@Bart,
There is a high correlation between increased tax revenues and increased government spending, but the reason that tax revenue increases have lower correlation to GDP is that the tax structures have been changed so many times that it generates a surprising amount of noise. For example, in 1808 there was growth in GDP, but tax revenues dropped nearly 20%. There are literally dozens of similar examples I can point to over any time period. It looks even worse if we just cover 1913 to 2008.
I presume, based on this statement, that you don’t understand how multivariable regression analyses work. All I did was test the null hypothesis that the top margin of tax rate affects GDP growth in a statistically significant way. I could not find a statistical connection between the top rate and GDP growth. I drew no conclusions beyond that with respect to tax rates. I had considered that it might be enough to show a correlation, but it’s not.
In other words, you’re pointing to something that may have an impact on the portion outside the 36% accounted for in government spending, but that hardly makes my calculations useless.
Michael:
I am assuming you are properly applying your multivariable regression analyses. My contention is with the data you are using in that analysis and your rather grandiose claim that the results prove Keynes was right. Instead, this appears to be a case of garbage in, garbage out.
For example, using the nominal top tax rate fails the quality test (no effective tax rates) and the quantity test (a tiny percentage of the population which bears only around a quarter of the tax burden). What then does it matter whether there is allegedly no statistically significant correlation between the nominal top tax rate and GDP growth over whatever time period you are measuring since the nominal top tax rate is largely meaningless?
Michael,
It’s pointless to respond to Bart. His ideology prevents his brain from allowing information contrary to his beliefs from interfering with his faith.
It seems to me that the inclusion of total revenue is a decent substitute for “effective amount of tax collected”, as they are highly correlated.
Since the nominal top tax rate is “largely meaningless” I guess Bart just came out in favor of letting the Bush tax cuts expire on the wealthy. Oddly inconsistent, but no more than I’ve come to expect.
Bart,
In the final analysis, I excluded the nominal top tax rate because it didn’t show statistical significance. In other words, it was left out of my conclusion. Effective tax rates may have influence aside from government spending. I’m looking into that. But even if it does, that effect is statistically separate from the effect of government spending.
The only thing I concluded based on the data is that increased government spending corresponds to better GDP performance two years afterward.
Michael:
I look forward to your refined work.
I very much enjoyed this analysis and look forward to future articles with a similar informative, analytical approach.