# Tax Rates and Economic Growth Over Ten Year Time Horizons, plus Why a Flat Tax Would Result in Much Slower Economic Growth

by **Mike Kimel**

**Tax Rates and Economic Growth Over Ten Year Time Horizons, plus Why a Flat Tax Would Result in Much Slower Economic Growth**

Last week I had a post looking at the the real GDP growth maximizing income tax rate using both top marginal income tax rates and and “average marginal” “all-in” tax rates for all taxpayers (including those who paid nothing) computed by Barro & Sahasakul. The post noted that the optimal top marginal rate was in the neighborhood of 64%, a finding that corresponds with many other posts I’ve written on the topic. The post also noted that the Barro-Sahasakul rates were not as useful at explaining economic growth as the top marginal income tax rates.

David Altig of the Atlanta Fed commented on the piece here, but he essentially had one very gently delivered criticism and one follow-up comment. The criticism is that my post did not consider long run effects – for each year, it looked at how the tax rate that year would affect growth in real GDP from that year to the next. The comment was that the post’s results did not correspond with results of a paper he published in the AER with Auerbach, Kotlikoff, Smetters and Walliser. (Ungated version here. The paper

uses a new large-scale dynamic simulation model to compare the equity, efficiency, and macroeconomic effects of five alternative to the current U.S. federal income tax. These reforms are a proportional income tax, a proportional consumption tax, a flat tax, a flat tax with transition relief, and a progressive variant of the flat tax called the ‘X tax.’

In his post, Altig provides this graph:

The graph shows that according to the Altig et. al simulation model, after about ten years, the growth maximizing tax (among the types they simulated) is a flat tax. I read the paper this afternoon, and while I have a few small quibbles (some of them raised by the authors themselves, to their credit), having done a bit of simulation work myself, I think there is one thing that is worth mentioning and which I can cover in this forum: results of a simulation must fit known facts.

Now… I think there is a quick and dirty way regression that can account for both a long range analysis and to test the notion of whether the cause of rapid economic growth is best served by a progressive tax system or a flat tax. Here’s what I have in mind:

equation 1: annualized growth in real GDP, t to t+10 = f(top marginal income tax rate, top marginal income tax rate squared, bottom marginal income tax rate, bottom marginal income tax rate squared)

The quadratic terms allow us to find the growth maximizing tax rates, as I’ve done in so many posts before. And by including both top and bottom marginal rates, we can compute the optimal growth maximizing top marginal rate and the growth maximizing bottom marginal rate. And… if a flat tax is the best tax, the optimal bottom rate should be more or less equal to the optimal top rate.

As in the previous post, data ran back to 1929, the first year for which real GDP was computed by the BEA. Top marginal and bottom marginal rates came from the IRS Statistics of Income Table 23.

So here are the results, as spit out by Excel.

What this tells us is that each of the components of equation 1 are significant. For top marginal rates, we have the expected shape, and if you work it out (either with calculus or by plugging the numbers into a spreadsheet) you’ll find that the model claims the optimal rate is about 67%, and that getting tax rates there from the current 35% would add about 1.4% a year to real GDP growth.

For the bottom marginal income tax rate, things are a bit more complicated… it turns out that the expected quadratic shape isn’t there. In fact, the model indicates that tax rates should be as low as possible. In the range from 0 to 100, 0 is best. The model also provides support for the Milton’s Friedman negative income tax rate, though I’d say results are bit shakier there as rates were never at or below zero during the sample for which we have data. If I were to do it again, I think I’d specify the bottom marginal rate differently – no quadratic shape – but right now I gotta go. I would note – I’d also add a few other variables, both to account for the small degree of patterns that appear in the residuals and frankly, just to make the model more realistic. But its fairly clear – especially since I keep getting results that more or less the same no matter how I approach the problem, that better specification wouldn’t change the results all that much. They might push estimates of the top marginal rate down a bit, but its fairly clear that top marginal rates well above where they are now will lead to much faster economic growth.

And of course, the other thing we learn… because the effect of top and bottom rates are so very different, and relative to where they are now, pull economic growth in different directions, it makes no sense for the top rate and the bottom rate to be in close vicinity. Put another way – a flat tax is a very bad idea, at least when it comes to generating economic growth.

As always, if you want my spreadsheet, drop me a line via e-mail with the name of this post. My e-mail address is my first name (mike), my last name (kimel – with one m only), and I’m at gmail.com.

(Rdan…post was modified at 10 am to include the link to Altig’s post)

It’s interesting how different the results are when you simulate based on economics principles as opposed to observing the real world.

kaleberg,

That is precisely why I keep stating that economics today is roughly where astronomy was before Tycho Brahe came around, which makes it more comparable to astrology than astronomy. The tools are there to take the leap and actually become a science – Brahe used nothing more than his eyeballs and heck of a lot of patience, after all. In fact, I think the sophisticated tools are one of the things that keep getting in the way because they allow for easy obfuscation – in most cases, that isn’t even deliberate.

But in the end, in economics we always, always come back to Maier’s law: if the facts don’t conform to theory, they must be disposed of.

Altig is a first rate economist. He’s a big cheese at research at the Fed, teaches at the U of Chicago business school, and this paper came out in the AER. These are the best bona fides you can produce in economics. I have been reading his blog for years, and I don’t see any evidence he’s deliberately shading anything (unlike so many others).

Which tells you, even a first rate practioner like Altig will go off the rails when following today’s economic principles. Macroeconomic theory is wrong, wrong, wrong, and wrong.

Well, interesting that Laffer had it correct, be it for the wrong end of the income spectrum.

As hind sight is 20/20, thinking about the fact that the lower in income one goes, the more of a bite taxes become as it relates to autonomous consumption, it would seem to reason that yes, taxes inhibit consumption which relates to economic growth.

Being that we are a consumption driven economy, it would seem to reason that the over riding goal for developing policy for our economy would be to balance the maximizing of consumption with the minimizing of economic (ultimately political) power.

Progressive taxation I believe was the ancient concept used in the USA.

Hi Mike — First, let me apologize for missing the byline. My mistake. More substantively, I appreciate your effort here, though it doesn’t quite settle the issue in my mind. Your regressions are based on a tax regime that is income-based, and the lesson that I drew fom the paper I cited was that the dynamics and long-run effects might be very different if tax reform fundamentally changes the tax base. So here is one of those instances where I think the Lucas critique needs to be taken seriously. This is not to say that your conclusions are wrong — or right. It is just to say that the identification problem has to be confronted directly.

Thanks for the nice words above, and for the useful conversation.

DB,

Well, Laffer was looking at tax revenue, whereas I’m looking at growth. The two are related, but don’t necesarilly correlate.

Dave Altig,

Thanks for stopping by, and no need to apologize about the byline. Having Dan post my stuff with both our names appearing on the same post can be confusing and you aren’t the first to make that mistake as a result. (The fault for how we do this here lies with me, not with Dan.)

The Lucas Critique (for readers who aren’t professional economists) is the idea that the public adapts to the policies that are in play at any given time and reacts accordingly. Thus, we collectively behave as we behave in part because of the existing tax structure, and we’d collectively behave differently under a different tax structure. Lucas, as I recall, went on to say the result is that you can’t use aggregate macro data to compare results of alternative policies.

Even assuming something like a strong version of the Lucas Critique is true (and while I have only kept up with the literature very sporadically since leaving grad school, I understand that the literature is far from definitive on whether the Lucas Critique applies at all), there is still the problem that for a flat tax to be growth maximizing, you need the folks at the low end of the income scale, the middle, and the top end of that scale to react the same way to a marginal rate of X%. (I guess you don’t if you say that some portion of the public doesn’t affect the economy very much, but I don’t think anyone argues that.) That should be true regardless of whether we have a flat or a progressive tax, and this post indicates it isn’t true under a progressive tax.

It also is hard to argue that everyone reacts the same to the same X% tax rate if you think in terms of marginal propensity to consume taking into account that some folks make Y and some make many multiples of Y.

And then there is another explanation based on microfoundaitions: http://www.angrybearblog.com/2010/12/simple-explanation-for-strange-paradox.html Note that this explanation doesn’t work for folks whose primary source of income is a W-2 or who have so little income that their ability to save is negligible.

In the end, regardless of the Lucas Critique, for a flat tax to be optimal even in theory requires that taxpayers of vastly different income levels react the same way to a tax rate of X%. But the evidence, including that in this post, points to people reacting differently to tax rates depending on their income levels.

Yes, Laffer looked at revenue, however, the full response is that revenue would go up because taxes going down increased economic activity.