Top Marginal Tax Rates and Real Economic Growth, Part 2
by Mike Kimel
Top Marginal Tax Rates and Real Economic Growth, Part 2
A few weeks I wrote a post looking at the correlation between the top marginal tax rate in a given year and the growth in real GDP per capita over subsequent years. This post is the first of several follow-ups. It will provide a simple way to estimate the optimal top marginal tax rate – that is, the tax rate at which economic growth is maximized. It will also deal with a weakness that vexes many economic studies, namely how do you estimate the effect of taxation on growth using historical data without ignoring the fact that the economy has changed a great deal over the time period for which we have data?
Let’s start with the second issue first. An honest critique of my previous post, and of similar studies, is that saying “the economy grew faster in year X when the tax rates were higher/lower than in year Y” can be problematic if years X and Y are separated by decades. This is particularly true if there is a clear trend in the data. (For the statistically minded, this is the unit root problem.) In a perfect world for estimating the effect of taxes, the following conditions would be true:
i. we would only compare years that are not too far apart
ii. we would be able to observe the entire range of top marginal tax rates during the period in which we made the comparison
So how do we do both things (as much as is possible) at once? What I came up with is this: use rolling blocks of time. In the example below, we have the growth in real GDP per capita from one year to the next in the third column and the tax rate in the fourth column. The fifth column shows the correlation over the next five years between columns 3 and 4.
So, for example, the t to t+1 (1 year) growth rate from 1985 to 1989 and the tax rate at year t from 1985 to 1989 (see red outlined boxes) have a correlation of .424 (red shaded cell). The correlation is positive, which is to say, during those years, faster growth occurred in the years in which tax rates were higher. When five years in a row have the same tax rate, it is not possible to calculate a correlation (see the purple blocks). Otherwise, there is a correlation calculated for every year.
So, in any given year for which it is possible to compute a correlation, we have:
a. a top marginal tax rate
b. an indication as to whether growth rates increase or decrease as that top marginal tax rate changes over the next few years
Note that in every case, the comparison is over a very short period of time – in this instance 5 years. The effect of increasing and decreasing tax rates is only compared within 5 year blocks of time. The unit root problem goes away.
The data could be organized into buckets. I organized mine as follows:
I. 20% or more, but less than 25%
II. 25% or more, but less than 30%
III. 30% or more, but less than 35%
Using data beginning in the Eisenhower administration, I then took the median correlation for each bucket and graphed (median) correlations on the y axis against tax rates on the x axis:
So how do we interpret this? Well, when the top marginal tax rate is very low, the correlation between the top
marginal tax rates and economic growth rate is positive. In other words, when tax rates are low, increasing the tax rates is associated with faster economic growth. As tax rates rise, the marginal benefits to further tax rate increases shrink, as evidenced by the (mostly) decreasing size of the bars. Through the 50% to 55% bracket, the correlations are positive. (Note – in all four years falling into that tax bracket, the tax rate was 50%.)
And then we get to the 65% or more and less than 70% tax bracket and correlations are negative. (Note – there was one year in which the tax rate fell into that bracket, and in that year the tax rate was 69.5%.) That means that any further increases in tax rates are associated with slower economic growth. Conversely, decreases in tax rates are associated with faster economic growth.
This also suggests the optimal top marginal tax rate is somewhere between 50% and 69.5%.
Here’s the same graph, but going back to 1929, the first year for which the BEA published data:
Conclusions, at least about where the optimal tax rate sits, don’t change. (There are a few other things that do change, but for the purposes of this post we can ignore them.)
The post is getting long, so I’m going to wrap it up with some housecleaning:
1. The mechanism describing how tax rates affect growth is described in my earlier post on this topic
2. In this post, we only looked at the effect of tax rates in year t on growth rates from year t to year t+1. But, as stated in the previous post, the effect of taxation lasts for more than a single year, and we will explore this further in later posts.
3. Click on the links for data on the top marginal income tax bracket from the IRS and growth in real GDP per capita (from NIPA table 7.1).
4. I made the spreadsheet used to produce the earlier post and this one interactive, with a few primitive menus. I will happily send them to anyone who requests them in the next few weeks. You can use the menus to change many of the assumptions I made in these posts and see how they change the graphs. If you want the spreadsheets please email at my first name (which happens to be mike) dot my last name (which happens to be kimel – note only one m in my last name!) at gmail dot com.
You did an alpha beta model like what we use for forecasting to predict a forecast in a beginning life cycle of the product as opposed to a declining forecast or end of life of product. The alpha predicted the determination of the increase.
I think I get what you meant, and if so, the answer is yes.
Your post has several nice charts and a great many numbers. Though not quite as many as a good Lambert post might have. I suppose that that is a good start in an effort to understand the interactions of complex economic phenomenon. The text is a bit wordy, though not nearly as full as a Beverly Mann post might be.
This is an interesting conclusion with which to conclude your post, “Conclusions, at least about where the optimal tax rate sits, don’t change. (There are a few other things that do change, but for the purposes of this post we can ignore them.)” Pardon me for asking, but what is one to conclude from the data presented in the post? Otherwise it is all as clear as a bell, though the bell is an auditory stimulus and your post is strictly cognitive.
A better writer could have covered the same material with more clarity and brevity. So for that you have my apologies.
Basically, in the post I show that the top marginal income tax rate that maximizes economic growth lies between 50% and 65%. I did the analysis with two sets of data – once with data from 1953 to the present, and once with data going back to 1929 (which is as far as we have official, Bureau of Economic Analysis approved data). That’s where I note the conclusions don’t change regardless of the choice of data.
The wordiness was due to my attempt to be thorough given that the conclusions fly in the face of conventional wisdom. I wanted to be sure someone so inclined could replicate what I did and would not attribute the results to cherry picking. (Note that I also provide a little interactive spreadsheet to anyone who wants it, which of course makes replication that much easier, and also makes it easier to check whether the results are due simply to sample selection.)
An additional issue that added to the length is that I was trying to deal with this:
Without dealing that issue, the post would have been much, much simpler.
Anyway, let me think about how this post could be done simpler.
“Anyway, let me think about how this post could be done simpler.” Kimel
No, stop there. My primary reaction to the post was to wonder why people keep trying to create a causal link between a taxes and general economic performance. Note I said, “trying to create” not trying to prove that there is such a link. You’re picking one variable, tax rate at one end of the scale for one form of taxation, to compare with general economic activity during a given period of time. In a nut shell, one variable of such minor consequence doesn’t mean shit….., Oh excuse me, pardon the invective. Lost my cool for a moment.
Taxation is for the purpose of funding a government. Taxation of income is thought to be a fair way to accomplish this purpose, government funding that is. Those who benefit most from government activities are expected to support the government more directly and more generously. Paying one’s taxes is patriotic. Is there some optimal level of taxation? Yes, that level which funds the government in the manner that seems most productive, i.e. which pays the bills. Studying the effect of tax rates on GDP is the playing field of those who prefer to pay no tax at all. Comparison of the two variables does not compute. One is too small to determine effect of the other. And the other has an amorphous character which confounds otherwise disparate variables making them appear to in some way be linked, as when a marginal tax rate is thought to influence an entire economic system.
Said in another way, you’re looking backwards at a multivariate phenomenon and hoping to establish a causal relationship with one variable. That variable, rate of taxation, having been established for an entirely different purpose than the causal influence that you are looking for. Taxes are not intended to influence some aspect of the general economy. Taxes are levied for the purpose of funding government activities. An economy has a multitude of variable agents effecting its ebb and flow. Why not look back at wages and develop some high minded theory regarding the relationship between wage rates and GDP fluctuations? At least wages are at the front end of economic transactions. Taxes are the result of such activities. To look for a cause from an effect is like putting the cart before the horse. Once you’re playing that game any result gains legitimacy. Because of the nature of the variables being compared the door to obfuscating the argument swings wide open allowing for an analysis that supports any side of the argument.
The standard assumption is that a higher tax rate causes the after-tax return to be lower so investors will make fewer investments and this will have a negative impact on growth.
But we could make just the opposite argument. A lower after tax returns implies that you income and wealth would be lower. But you are trying to maximize your income and/or wealth. Consequently, you will invest more so as to increase you income and/or wealth to offset the negative impact of the higher tax.
Why isn’t this conclusion just as valid as the standard assumption?
Neither really applies, Spencer, because investment income (whether dividends or long-term capital gains) is not subject to the top income tax rate.
The real question is, given two cabbies, one who works 40 hours per week and the other works 60 hours per week, why should the more industrious of the two be taxed at a higher rate? How is that FAIR by any definition of that word?
Let us take two individuals of similar intellect and upbringing. One works his @$$ off in school and becomes an Engineer, then a Patent Attorney, while the other muddles through life taking it easy and working as a plumber. How is it FAIR to tax one at a higher rate than the other?
Warren, Thanks for bringing up the old “why is that fair” argument, but applying it in a spurious manner. Higher levels of income are taxed at higher rates because, by definition, the greater the income, the greater the benefit from the economy and what ever it is in that economy that allows for some to earn so much more than others. If you’re benefiting more from economic activity then you owe it to yourself as a good investment strategy to continue to support the government and society that makes your better earnings possible. And we all know that most truly wealthy people have inherited aq large portion of that wealth creating yet another form of their debt to society.
You are wrong. This post and the earlier one establish a correlation between tax rates today and growth rates in the future. if tax rates aren’t going some way toward “causing” growth rates then there is one hell of a coincidence. I will have follow up posts which will make the the coincidence theory that much more unlikely.
I described a mechanism for how tax rates affect growth in the earlier post. The link to that post is at the top of this one.
Even an under grad would know that correlation is necessary for causation, but hardly demonstrates a causal relationship between two variables. There are so many possible reasons why both the tax rate and the level of GDP activity may be effected by similar circumstances and, therefore, may have correlated levels of activity.
As I said before, I intend to keep adding to what I wrote in follow ups to this post and the coincidence, if that is what it is, will seem increasingly unlikely. As an unrelated appetizer, check out this post from a bit ago:
Here’s a coincidence in which tax collections over a two year period period correlate very highly with growth rates over the subsequent 6 years. Of course, it’s a specific 2 years of taxes and subsequent six years that don’t tie to business cycles either. Anyway, feel free to retain your opinion and I will do my coincidence thing with the data.
Mike, I’m not saying that the data don’t show some level of “coincidence” as you put it. Think about this for a minute. If the economy is growing strong during any particular span of time I would expect that tax receipts would also be growing. When economics are working people are earning more. Thereby they will pay more taxes. Does it follow that one thin has caused the other? Or does increasing income define a growing economy? Nor do we know any better that the increase in earnings was brought about by the higher tax rate.
My point is that rates of taxation are minutia measures when considering an effect on an entire economic system. People are motivated to earn as much as an economy will bear. It’s unlikely that someone is turning down more pay because of higher marginal rates on the additional income. Nor is a business that has good apparent profit potential going to be lacking entrepreneurs due to the effect of taxes on profits.
With all due respect, perhaps you all miss the point that the marginal upper income people are mare likely to be able and allowed to off shore profits through corporate inversions, with deferred interest and capital gains tax avoidance schemes. Why should the wealthy in essence be allowed to pull their profits, earned interest and capital gains out of our country where the money is no longer circulated for the benefit of our economy. The average middle class workers and wage earners are not allowed so much to play this game.The top 10%ers are being allowed to hoard and sit on trillions over seas waiting forever for a more favorable tax treatment is killing our economy. The top 10% in income earned over 90% of our countries new wealth creation I read somewhere .Where is the push back or discussion of this predatory globalization in the TPP that so many idiots want to support?
“Higher levels of income are taxed at higher rates because, by definition, the greater the income, the greater the benefit from the economy and what ever it is in that economy that allows for some to earn so much more than others.”
A flat tax does that, too. That is not an argument for a graduated tax.
“If you’re benefiting more from economic activity then you owe it to yourself as a good investment strategy to continue to support the government and society that makes your better earnings possible.”
Feel free to do so: https://www.pay.gov/public/form/start/23779454/
“And we all know that most truly wealthy people have inherited [a] large portion of that wealth creating yet another form of their debt to society.”
No, most truly wealthy people created a product or service priced where lots of people want to buy it.
“The top 10%ers are being allowed to hoard and sit on trillions over seas waiting forever for a more favorable tax treatment is killing our economy.”
So lets get some sensible tax policies so the U.S. becomes the tax haven of choice.
Who knew that the only difference between a Patent Attorney and a plumber was how hard they worked in school?
I guess the same people who think working as a plumber your entire life is “taking it easy”.
Any chance that effective tax rates can be matched to this theory instead of marginal tax rates? Not a big fan at all of using marginal tax rates for anything.
I have used tax burdens a lot in the past. One example:
“Who knew that the only difference between a Patent Attorney and a plumber was how hard they worked in school?”
What’s your explanation — that one is smarter than the other?
“I guess the same people who think working as a plumber your entire life is ‘taking it easy.'”
Life is like chess — if you make poor decisions early on, you are in for a miserable game.