# Tax Rates over Time, GDP Growth Rates, and Tax Collections

Forgive the long post. This one is a bit complicated.

Last week I had a post showing that, based on information available in the year 2000, the top of the Laffer curve for the highest marginal personal income tax rate was probably in the neighborhood of between 42.4% and 51.4%. I noted that based on this, GW’s promises to “pay off the debt, deliver meaningful tax relief and address needed priorities, while preserving nearly a trillion dollars as protection against uncertainties” were just as ludicrous at the time as they look now.

The post received many comments. Among the most substantive criticisms was one from happyjuggler0, who stated: “[b]ehavioral changes occur with changes in tax rates. It ought not to be too surprising to think that a tax rate cut in one year will yield lower revenues the next year unless the rates are in the stupidly high category…. At the same time, a hike in tax rates would likely also yield higher revenues in the year after the hike.”

To extend his comment, in a given year, if taxes are cut, collections will be lower, but eventually people will adjust, work harder, leading to a faster growing economy and greater tax collections. Happyjuggler0 also indicated that looking at taxes as a percentage change of GDP makes no sense because as taxes go up, it could stifle growth. Therefore, if tax collections as a percentage of GDP fall after taxes are reduced, it could be the case that tax collections are increasingly rapidly, but GDP is rising even more rapidly. These are classic arguments, and they make sense. But do they fit the facts?

Let’s begin by looking at happyjuggler0’s second point – do tax cuts lead to increased growth? We can simply take the correlation between real GDP growth and tax rates, but that happyjuggler0 could again, rightfully point out, that perhaps over time, the effect of taxes is different than their effect over the short haul. Presumably, 5 years is enough time for taxpayers to change their behavior – instead of looking at the highest marginal tax rates in any given year, we will look at the “five year average of the highest marginal tax rates” (i.e., that year, and the preceding four years).

The following table shows the average of the “five year average of the highest marginal tax rates” for each sample period. It also shows the correlation between the “five year average of the highest marginal tax rates” and the growth rate of real GDP in any given year.

Sample Av High Correlation

1950 – 2000___68.87____0.11

1960 – 2000___64.10____0.12

1970 – 2000___56.64___-0.04

1980 – 2000___48.96____0.00

1990 – 2000___37.36____0.70

How to interpret this? Well, it seems over the entire 50 year sample, there is a slight positive correlation between five year average tax rates and the growth rate in real GDP. In other words, an increase in the five year average of the highest marginal tax rate tends be associated with higher growth in real GDP. From the 1970- 2000, the correlation is slightly negative, from 1980 to 2000 it is pretty much zero, and from 1990 to 2000, it is positive and high.

Results are essentially the same if the “five year average of the highest marginal tax rates” are lagged by a year, if the Clinton years are excluded, or if the ten year average is used instead of the five year average. Therefore, it doesn’t seem like there is much of a pattern, indicating that there probably isn’t much relationship between the highest average tax rate over the past five years and the growth rate in real GDP. (If there is any relationship, it is that as taxes rise, it seems that growth rates increase. This seems to be especially true in recent years, and has manifested itself more as tax rates have dropped.)

Given the lack of a relationship between tax rates and growth rates in GDP, the argument for tax cuts bringing in more revenue essentially means that tax cuts lead to higher tax revenues as a percentage of GDP.

The table below shows the average of the “five year average of the highest marginal tax rates” for each sample period, and the correlation between the “five year average of the highest marginal tax rates” and tax revenues as a percentage of GDP in any given year.

Sample Av High Correlation

1950 – 2000___66.44___-0.36

1960 – 2000___60.93___-0.26

1970 – 2000___53.60___-0.17

1980 – 2000___45.30____0.11

1990 – 2000___35.65____0.55

This produces results similar to those in the earlier post… it would seem that the top of the Laffer curve for the five year average of the highest marginal tax rate appears to be somewhere between 45.3% and 53.6%.

Now… here is where it get its interesting…. the table below considers the correlation between the “ten year average of the highest marginal tax rates” and tax revenues as a percentage of GDP in any given year.

Sample Av High Correlation

1950 – 2000___68.87___-0.45

1960 – 2000___64.10___-0.41

1970 – 2000___56.64___-0.35

1980 – 2000___48.96___-0.28

1990 – 2000___37.36___-0.37

In other words, this table suggests that over a ten year period, the higher the highest average tax rate, the less taxes are collected. (I note – leaving out the Clinton years, the familiar Laffer curve shape appears, with a “high point” between 63% and 70%.)

A recap:

1. There is a slight positive correlation between average tax rates over a five year period (and a ten year period) and growth rates in GDP. Therefore, over the long run, the higher the tax rate, the faster the economy grows. This would imply that those subject to the highest marginal rate spend their money is not as efficient at creating wealth than the government.

2. Fitting a Laffer curve to one year (as in the previous post) or five year average highest marginal tax rates, we find that the tax rate bringing in the highest revenues over a one or five year period is somewhere in the neighborhood of 50%.

3. The higher the ten year highest marginal rates, the lower the tax revenues as a percentage of GDP.

The results seem somewhat contradictory (to me at least). For both 1 and 3 to be true, an increase in the highest marginal tax bracket would, over a ten year period, lead to slight increases in GDP growth but decreases in tax revenues over the same period. Additionally, at current tax rates, that would also lead to more tax revenues over a five year period.

(For those interested in something more technical, I also tried running some regressions for each sample period. The regressions took two forms: 1) dependent variable: tax receipts, explanatory variables: 5 year and 10 year average highest marginal tax rate, and one year lagged tax receipts, and 2) the same regressions but without one year lagged receipts). In almost all cases, the coefficients on both five and ten year average highest rates were significant, with the former being positive and the latter being negative, one exception being the regression for the 1990s alone, leaving out lagged tax receipts, in which case the ten year variable was not significant.)

At this point, I’m flummoxed. I think one of the following must be the case:

a. Findings 1, 2, and 3 are all true

b. Findings 1 and 2 are true, finding 3 is an artifact of the data

c. Finding 3 is true, findings 1 and 2 are artifacts of the data.

My guess, and perhaps its just my bias, is that Finding 3 is just an artifact of the data, but I can’t explain it, and at this point its run up against the amount of time I’m willing to give it. Perhaps it’s a good thesis topic (hint hint hint to any graduate students).

So… I’ll throw it open. Anybody know what’s going on?

Postscript. As always, my spreadsheets are available to anyone who wants them.

Postscript 2. In the comment section, commentor Reason provides a simple explanation for what might be going on. To rephrase Reason’s point:

Tax rates fall leading to greater concentration of income at the high end, as tax cuts tend to be focused on the high income earners. While this doesn’t lead to increased growth in the economy as a whole (and possibly leads to slower growth overall), it does increase the amount of income that is subject to taxes, leading to (in the long run) greater taxes being collected. Ironically, this policy of benefiting high income individuals also benefits the government, but not most of the population. Somehow this doesn’t strike me as being the way Laffer tells it, but unlike with the supply-siders story, it does seem to fit the facts.