Cross-posted at the Angry Bear blog.

I often post about the relationship between the top marginal tax rate and economic growth, which I’ve noted can be described this way:

% change in real GDP from t to t+1 = a + b*Top Marginal Tax Rate at time t

+ c* Top Marginal Tax Rate squared at time t

(I’ve modestly described that relationship as the “Kimel curve.”)

I’ve done this many times, and have added all sorts of things to the curve, but in every case, the results are more or less the same: the top marginal tax rate that maximizes growth is somewhere in the neighborhood of about 64%, give or take about 5%.

Its usually my practice to use all data available when I’m estimating that relationship. That means going back to 1929, the first year for which the BEA keeps data on real GDP. In part that’s because I get accused of cherrypicking if I don’t use all the data available. But lately I’ve started getting accused of somehow trying to bias results by using all the data available.

So I’m going to run a version of the model similar to the one I ran last week, but I’m going to start with data from 1981, which is when Reaganomics set in.

The specific model I’m going to estimate is this

% change in real GDP from t to t+1 = a + b*Top Marginal Tax Rate at time t

+ c* Top Marginal Tax Rate squared at time t

+ d* % of pop 35 – 44 at time t

+ e* % of pop 45 – 54 at time t

+ f* President is a Republican (Y/N) at time t

Here are the results:

Figure 1

If the numbers are too small click here.

A few things to note: the percentage of the population 35 to 44 is not significant, though it was significant when data going back to 1929 was used. Conversely, the percentage of the population 45 to 54 was not significant with data going back to 1929, but is significant here. What that tells me is that for much of the period from 1929 to the present, the percentage of the population 35 to 44 was one of the more important demographics for driving growth. However, more recently, the population 45 to 54 has become more important reflecting the reduced importance of manual labor.

The Republican dummy wasn’t significant when using data going back to 1929… and it isn’t significant in the more recent period either.

But what really matters, in my opinion at least, is this: the coefficients on the top marginal tax rate and the top marginal tax rate squared are both significant. The former is positive and the latter is negative. That means the Kimel curve applies to the period since 1981 to the present as well.

The growth maximizing tax rate obtained when using data for the period from 1981 on is 44%, about 20 percentage points below the top marginal rate obtained when using data going back to 1929. So, why the difference? I don’t know, but I have some ideas:

1. The period from 1981 on includes one observation where the tax rate was above 50% (i.e., 1981, when the economy was in a recession), several at 50%, and the rest below. The model simply hasn’t “observed” higher tax rates and the growth rates associated with those higher tax rates.

2. Prior to Reagan, the public was more accepting of the idea that tax rates should be higher. Reagan changed the zeitgeist. The government became the problem, not the solution, and taxes, well taxes came to be viewed as theft.

My guess is that its a combination of both factors. But even if you lean primarily toward the second reason, and assume the optimal tax rate has shifted down over time… its still well above where tax rates are now.

In fact, tax rates have been below 40% since 1987. The annualized growth rate in real GDP during the 23 years from 1987 to 2010 was 2.6%. The last time real GDP grew that slowly during a 23 year period was… well, who knows – it never happened before then in the time since the BEA has been keeping data. If you decide to, well, cherry pick and leave out the Great Recession… the annualized growth rates in real GDP from 1987 to 2007 was a hair over 3% a year. Previous to that, the last time annualized growth rates were that low for the same number of years occurred at the end of World War 2. Put another way… the period from 1987 on may have been a success in terms of keeping tax rates low, but it has been a failure in terms of economic growth, as the only time the economy has done worse was when it switched out of a command economy and went immediately into a recession. (I can’t help but notice that the only time when the economy did worse happened to come during what David R. Henderson refers to as the Post War Economic Miracle.) Better policy would get us faster economic growth and that would be good for everyone, even those paying the highest marginal rates.

Housekeeping… GDP data came from the BEA and tax rates came from the IRS.

A few other comments… the correlation between residuals at time t and time t+1 in the model estimated is about 16.5%. One could do other checks, but it seems very, very unlikely that autocorrelation is a problem here. Of course, we’re also missing some important variables… the fit could be a lot higher. I’ll start incorporating some of the suggestions I received from readers after the last post.

As always, if you want my spreadsheet, drop me a line. I’m at my first name (mike) period my last name (kimel – note only one m) at gmail.com.

I’d love to see some kind of lagged regression factor reflecting public R&D and/or non-defense public investment as %s of GDP. The problem would be that the fruits of those investments will not come to fruition in t + 1. You’d have to something with the numbers to reflect the prior ten-year average or something. But then, you’re the economist!

I was thinking of R&D as something to throw in. Its a slow process but over time hopefully I’ll expand things in that direction.

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