The Kimel Curve and the Kitchen Sink, Part 1: All Years

by >Mike Kimel

I’ve been writing about the relationship between tax rates and growth since I started blogging in 2006. A lot of those posts have focused on the quadratic relationship between tax rates and growth. That is, it turns out that if you take US data going back to when the BEA started keeping track, 1929, you can easily build a model of the following form:

% 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 have modestly referred to that as the Kimel curve. Now, it turns out that for most variations on that theme I’ve come up with, b is positive, c is negative, and both are significant at the 5% or 10% level. That allows you to find a top marginal tax rate that maximizes growth… which turns out to be somewhere between 60% and 70% depending on how the model is specified.

In this post I want to address a few criticisms by running two additional regressions with more or less the form. Parts of this may get a bit wonky but I’m going to keep it so that even if you’ve never done any statistical analysis, hopefully you’ll be able to follow the outcomes.

In the first regression, I’m going to account for a few additional facts:
1. By going with every single observation the BEA produces, I’ve been accused of “cherry picking.” So I’m going to throw in a dummy variable for Hoover.
2. I’ve been told the only reason growth was so quick during the New Deal was that there was a bounceback effect from the Great Depression… so I’m throwing in a dummy variable for FDR’s peacetime years (i.e., 33-41).
3. I’ve been told WW2 biases the results…. so there’s a third dummy for 1942-1944, the fast growing years in WW2.
4. I’ve also included two demographic variables: the percentage of Americans 35 to 44 and the percentage of Americans 45 – 54. The latter group tends to be the highest income group these days, but in an earlier era more focused on manual labor, those 35 to 44 might have been higher paid.
5. For grins, I threw in a dummy variable which is equal to 1 if the President is a Republican and 0 otherwise.

So… here’s what it looks like:

So what does it all mean? Well, this set of variables explains about 43% of the observed variation in growth rates over the period for which we have data (see the adjusted R2). There’s obviously room to improve the model, variables I’m not accounting for, etc.

The percentage of Americans 35 to 44 has a positive coefficient and is almost significant at 10%. We’re almost at the point where we’d be comfortable saying as that percentage increases, growth increases. The percentage of Americans 45 – 54 has a negative coefficient, but isn’t close to being significant.

Not surprisingly, the Hoover dummy is associated with economic shrinkage, FDR’s peacetime period is associated with positive growth, and 1942 – 1944 is associated with even faster economic growth.

The Republican dummy is not significant – any difference in the growth rate observed between the two parties can be explained by other factors. Which other factors?

Well, the top marginal tax rate and the top marginal tax rate squared are both significant – the former is positive and the latter is negative, which means they trace out the desired upside-down-U shape.

Oh… and the top of the curve happens when tax rates are at 64%. That is, the fastest growth rates seem to occur when the top marginal tax rate is around 64%. Now, I’ve had post after post on this topic, and the top of the curve always seems to occur in more or less in the same place. It isn’t a coincidence folks.

I’ll post results of the second regression in my next post in the series. That regression will focus on the period since Reagan took office and thus will only include data from 1981 to the present. What does it say? Well, a hint: if you don’t like the results shown in this post, you won’t be happy about that one either. But remember, I’m just the messenger. The data is what the data is, and if it isn’t showing what you think it should, its up to you figure out what’s wrong with the analysis or with the data, to pontificate wisely and inaccurately, to ignore the evidence, or to change your mind.

If anyone has a line on a good inequality series with annual data that goes back to 1929, please let me know. I’d like to drop it into the model. I’d also love a good proxy for regulation. Don’t be afraid to offer other suggestions for data to drop into the mix are welcome too. I’m like a DJ, I take requests, but it helps if you can point to whatever data you want me to use.

As always, if you want my spreadsheets drop me a line at “mike” period “kimel” (note – one m only in my last name!!!!) at

Thanks to Bill McBride for pointing toward the demographic data and m. jed for suggesting its use.