# 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%
etc.

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: Figure 2
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.