# The Tax Rate that Maximizes Economic Growth, Part 3

by Mike Kimel

The Tax Rate that Maximizes Economic Growth, Part 3… With Gov’t Spending, Money Supply and Demographics
Cross posted at the Presimetrics blog.

Today I will build a model that explains over three quarters of the annual movement in real GDP between 1929 and the present. The model depends on marginal tax rates, government spending, the Fed, and demographic trends. This post isn’t light reading and will demand a bit of attention, but I’m going to try to make it worth your while. Let’s just say there’s a lot here that contradicts what you’ll read in your standard economics textbook.

This post continues the “Kimel curve” theme I’ve been following for the past few weeks, namely that there is a top that maximizes the growth of real GDP. That is relatively easy to find: run a regression with growth in real GDP as the dependent variable, and the top marginal income tax rate and the top marginal income tax rate squared as explanatory variables. (If you haven’t seen any posts in this series, or aren’t familiar with regression analysis, you might want to take a look the first post in the series .) Official and relatively reliable data for GDP is available going back to 1929. The growth maximizing top marginal tax rate according to that simple model is in the neighborhood of 65%.

This week I’d like to add a few other variables that I think might affect growth. The first is government spending; for a long time there has been a debate in this country about whether government spending can boost the economy.

Another variable I want to add is the Fed’s behavior. If you’ve read Presimetrics, the book I wrote with Michael Kanell, you know this is a variable I think has a huge effect on the economy, and not quite in the way textbooks tell you. So I’m going to add two variables, both of which are dummies. As I’ve noted in a couple posts, a dummy variable takes a value of one or zero, which also amounts to a “yes” or a “no.” The first of these Fed behavior dummy variables tells us whether the real money supply increased a lot. I’m defining that as a situation when the median 3 month change in real M1 throughout the year exceeded 1%. (Real M1, obviously, being just M1 adjusted for inflation.) The second Fed behavior dummy variable looks at whether there’s a big drop in the real money supply; that is, the variable is true when the median 3 month change in real M1 was a decrease of greater than 0.5%. Why the asymmetry between big increases (over 1%) and big decreases (over 0.5%)? Simple –the money supply should grow over time if only to keep up with population increases.

Moving on… the model contains two demographic variables. One is the percentage of the population between 35 and 54 years of age. That is to say, the proportion of people in more or less their prime earning years. (I imagine prime earning years was closer to 35 in 1929, and has moved closer to 54 today as manual labor has become a less important piece of the economy.) I’m also including the percentage of the population that is above 70 years of age; on average, most people in that demographic are not active in the work force.

Finally, I’ve included one more dummy variable for the 1929 to 1932 period. I’m not ready to explain that collapse yet, so I’ve included this variable if only to indicate that there is something different about those years than other years for which we have data.

So here’s what we get when we run a regression in Excel.

Figure 1

To interpret… the adjusted R2 (light blue) tells us that the model explains about 76% of the variation in the growth in real GDP. (If you’re interested – I did some residual analysis and the usual batch of things to be worried about come up with nothing. E.g., the correlation between et and et+1 = 0.04.)

Tax rates and tax rates squared are significant (green cells). We get the same curve that has showed up in previous posts on this topic, but in this instance, the fastest real GDP growth occurs when the top marginal tax rate is 59%. A bit lower than the 65% figure from earlier models, but close enough… and pretty far away from what most economists and politicians and talk show hosts will tell you. Like it’s a surprise such folks are wrong.

And on the topic of those folks being wrong… government spending is significant, contributes to growth, and does so at an increasingly faster rate as government spending increases. (Burnt orange.) On the other hand, it doesn’t necessarily pay for itself. In future posts I’d like to split out government spending, as I have a feeling different forms of government spending have different effects.

What about the Fed? Well, it turns out the economy grows faster when the Fed increases the money supply quickly, and grows more slowly when the Fed decreases the money supply. Not a surprise if you read my book, but… you may recall your econ courses that taught you the Fed is supposed to try to boost the economy when it is in the doldrums, and slow the economy when its growing too quickly. If the Fed really behaved that way, big increases in real M1 would be accompanied by slow economic growth, and big decreases in real M1 would be accompanied by fast economic growth. This is yet another indication of something I’ve pointed out many times before – historically, either the folks on the Fed’s board don’t know what they’re doing, or they’re doing something different than most economists believe they’re doing. Since they’re political appointees, I’d bet on both.

1929 – 1932 is negative and significant. No surprise.

Demographics – the prime earning demographic is positive and significant. The more people in that demographic, the faster the economy grows. No surprise, but a big negative – that demographic hit a peak in 2001. It drifted down very slowly since, but its not going up any more. The elderly contingent, on the other hand, is not significant.

OK. So… the idea that if we want to maximize economic growth, the top marginal rate is somewhere well north of what most people believe seems to survive over a number of different posts. Here’s one reason why. Here’s another. I’ll have a few more posts on the topic – this little exercise keeps raising more and more questions in my mind.

But a question – are these posts getting too complicated for a blog? More graphs? Comments?

Data sources:

Real GDP and real gov’t spending from NIPA Table 1.1.6

Top individual marginal income tax rates from the IRS’ Statistics of Income historical table 23

M1 comes from a number of different sources. M1 from prior to 1947 is available biannually (June and December) from documents in the FRASER collection of the Federal Reserve Bank of St. Louis. Specifically, data from prior to 1946 came from here, and data from 1941 to 1947 came from here. The data was “monthleycized” using a simple linear transformation. FRASER also contains monthly data from 1947 to 1958 in this document . Finally, another St. Louis Fed database, FRED, contains monthly M1 from 1959 to the present.

Inflation adjustments were computed using monthly and yearly CPI-U figures from the BLS.

Population figures were obtained (and organized painstakingly) from various Census sources: pre-1980s, 1980s, 1990s, and 2000s. (I’m certain there was an easier way…)

As always, my spreadsheets are available to anyone who wants them. Drop me a line at my first name, period my last name, at gmail period com. And note my first name in the e-mail address is mike. An “m” gets you someone else whose patience is starting wear thin. Also, on the subject of “m”s – my last name has only one. Because a lot of people have been asking for my spreadsheets as of late, to make things easier please tell me the the name of this post, the date it appeared, and where it appeared.

Thanks.