A Proposed Bet for Professors Bryan Caplan and David R. Henderson

by Mike Kimel

A Proposed Bet for Professors Bryan Caplan and David R. Henderson (and Anyone Else Who Believes Lower Taxes Generate Faster Economic Growth)
Cross posted at the Presimetrics blog.

Professors Caplan and Henderson,

Both of you have had recent posts that indicate you have some enthusiasm for betting on economic outcomes. (Your co-blogger at Econlog, Arnold Kling seems less enthusiastic about bets, and thus I have not addressed him by name here.) I have a few criticisms of your approach to betting. The first is that, frankly, y’all are betting on some rather peripheral issues. Why not cut to the chase? Why not propose a bet on something vital to your way of thinking but with which many people disagree? For example, as libertarians you believe that lower marginal tax rates on the “producer class” result in faster economic growth in a well-functioning, more or less market based economy, and that this outcome can be observed in the US economy. (Forgive the wordiness, but I want to be precise so you don’t think I’m trying to trap you up in a technicality or some oddball example.) I believe you are generally wrong, at least about the US economy. Many people share your beliefs, and many people share mine, so this would be an ideal topic on which to bet if your goal is to prove a point.

Another criticism I have of the bets I’ve seen you propose is that your bets tend to be based on a small number of events, typically one or a handful of observations occurring over ten years or less. But that is too short a period to leave out the effect of random fluctuations, acts of God, or long running conditions. For example, though I haven’t verified the data myself, I understand that it has been pointed out that had the Julian Simon bet (a favorite of Professor Henderson’s) occurred a few years later results would have been different. A truly fair bet would look at more data. In fact, an ideal bet would look at many different overlapping long time periods. Results over ten year windows, twenty windows, thirty year windows, etc., would all combined to ensure that the results aren’t just an artifact of the data.

Another safeguard which helps get at a “true outcome” rather than some random fluctuation is to consider whether the effect you are looking at can have lags of different lengths. For example, it may be that the marginal tax rate in 2010 might affect growth rates from 2009 to 2010, or from 2010 to 2011, or from 2010 to some later year. After all, as any libertarian would say, if you pay less in taxes this year, it means more money in your pocket this year. Since you spend more efficiently than the government, that creates more growth this year, and that additional growth has positive effects next year too. Of course, at some point, the future effects of today’s tax rates dissipate. Not having a precise theory, it probably pays to consider several of these “effect periods” to (perhaps) coin a term.

The third problem I have with your bets is that, frankly, it takes too long to find out who won. Professor Henderson indicates in one post that he’ll probably be settling up with the estate of fellow bettor. If bets are intended as a way to help move the field, not to say the bettors beliefs, forward, results have to come in more quickly to make an appreciable difference. Now, at first glance, this last complaint kind of clashes with my previous criticism that ten years of data is just not enough. But if you think about it, there’s an easy way to square the circle: the obvious solution is to bet on outcomes that occurred on the past.

Now, before you say that’s silly, hear me out. You wouldn’t (dare I say couldn’t?) be a libertarian if you didn’t believe that historically, economic growth in the US was faster when the marginal income tax rates on what you would term the productive class were lower than when they were higher. And in the unlikely event you’ve read anything I’ve written, whether on the Presimetrics or Angry Bear blogs, or the book I cowrote with Michael Kanell, you would be aware that I am pretty certain the US economy is not characterized by such a relationship between marginal tax rates and economic growth. Simply put, what each of us knows about the past contradicts what the other knows. At least one of us has to be wrong.

Given how bet-happy you all are, and your core beliefs, I would have expected you to propose this one (not necessarily to me, who you no doubt don’t know from Adam) a long time ago. To be precise, here’s the bet I would have expected you to issue:

For the vast majority (say, at least 70%) of overlapping windows, the correlation between top marginal individual income tax rate and the growth in real GDP will be negative. Windows of data to be considered are ten years long, twenty years long, etc., through sixty or seventy years long. Growth rates to be compared with marginal tax rates at time period t include t – 1 to t, t to t+1, t to t+2, t to t+3, t to t+4, and t to t+5.

Now, I could see variations of that bet. For instance, Professor Henderson has indicated in a recent working paper that he doesn’t believe National Accounts data for the WW2 years are accurate, so perhaps he would structure the bet to only use data from 1946 on, rather than the 1929 on which is possible with the official BEA data. Alternatively, perhaps t to t+5 might seem a little much to consider, or perhaps one would prefer to include t to t+x where x is something larger than 5. Nevertheless, this is very close to the bet I would have expected to be proposed from people with strong libertarian beliefs who like to engage in wagers on economic outcomes.

One other thing – notice that I indicate the correlations should be negative well over half the time. I have yet to hear a libertarian hedge when he/she tells me about the benefits of lower taxes. Getting a touch above 50% just doesn’t fit that with that sort of certainty, and is more akin to random fluctuation, is it not? (But don’t worry, where we’re going, the distinction between 50.00001% and something more appropriate to your level of certainty won’t matter.)

What is left is to consider – what should have been the size of the bet we should have expected to see. Now, Professor Caplan has recently noted:

But why are small sums enough to deter 95%+ of the people who disagree with me? I see two main reasons:

1. We aren’t just betting $100. We’re betting $100 plus reputation plus bragging rights. That’s why I prefer to bet the famous. The Simon-Ehrlich victory wouldn’t have been nearly as awesome if Simon bet a random Malthusian.

2. Many spouses, perhaps most, disapprove of betting. They think you’re irresponsible when you bet, and stupid when you lose. Imagine how badly they’d react if the stakes were $25k! Even the victor might find himself stuck in the doghouse.

So… $100 plus bragging rights is about right. Of course, I’m not famous, so I doubt the bet would have been issued to me. I would have taken the $100 bet, though, if offered. More – well, probably not, despite my certainty, given item number 2. Nevertheless, I am surprised that neither of you offered this bet to someone.

But here’s the thing. You would have lost that bet. And we’re not talking by a smidge, we’re talking by a country mile… or seventeen and a half.

Here’s what I get:


by Mike KimelFigure 1.

(Note – you might have to click on the figure to see it in full. It seems to cut off on my browser. The same is true of the next figure.)

The way to read this graph…. consider the cell with t to t+3 on the horizontal and 50 years on the vertical. That cell has 62.1% in it. That indicates that of the 29 fifty year windows in which you can measure the growth in real GDP from a given year to three years later, 18 of them (or 62.1% of them) show a positive correlation between the top marginal tax rate. That is to say, in 62.1% of those windows, growth is faster when top marginal tax rates are higher than when tax rates are lower.

Notice… most of the squares have numbers above 50% in them. That means, in most situations we considered, more often than not, the correlations between marginal tax rates and growth rates are positive, not negative. When the negative correlations do occur, they tend to occur over the very short term. Put another way – they have negative repercussions that hit later. (And yes, that is what the table indicates.) Over longer periods of time, the percentage of time positive correlations are observed approaches 100%. This cannot in any way be reconciled with libertarian theory.

FWIW, the table above represents a grand total of 1,652 observed correlations between the top marginal tax rate and growth rates of real GDP. 56.5% of those correlations are positive.

Note… I haven’t included it in the table, but for giggles I checked the t to t+10 results. For ten and twenty year windows, the percentages are below 50%. For thirty year windows and up, the percentages are above 50% and go above 70% at 40 year windows and hit 100% at the 70 year windows. Put another way… t to t+10 looks an awful lot like t to t+4.

Now, say you’re Professor Henderson and you want to discard the data through the end of WW2. In that case, you come out looking even worse:

Figure 2.

Now, 64.6% of all the correlations observed are positive.

Now, this post is starting to get awfully long, so let me wrap it up. I think you should offer this bet. In fact, my advice to any libertarian or conservative is to offer to make this bet. Sure, its easy for me to say, because the bet goes against you, but I promise if you offer the bet or something similar I will refrain from jumping in so I’m not making that suggestion for personal gain. The reason I think you should offer this bet is that, knowing you’d lose gives only a few options:

1. You can change your beliefs.
2, You can tapdance into the opposite result. To some extent, that’s where the economic profession is now. There are any number of studies by well known academics that show that cutting taxes lead to faster economic growth under some or most conditions, and they all require either weird special cases or assumptions that, frankly, could be used to show that a 400 year old sketch of a chicken is a nuclear submarine.
3. You can pretend none of this ever happened.
4. You can show there is a problem with what I have done or proposed.

Now, its possible I’ve made a mistake, but to repeat myself, if you’ve read anything I’ve written before, you’ll find that I’ve been on a “the data shows that lower taxes do not equal faster economic growth” kick for a long time. I’ve gotten here every which way, using data from all sorts of sources and at all levels of granularity. In this case, I’m guessing that if you included windows of 11, 12, 13, etc. years, you might push the percentage of positive correlations down. For all I know, with judicious fiddling, you might even get to a point where a slight majority of cases have a negative correlation. I don’t have an institute or a university paying me to make this sort of argument and I’m running out of spare time this afternoon. But even if you got that percentage down a bit – the libertarian position is not that lower taxes lead to faster economic growth somewhere around half the time, is it? And frankly, it would take a heck of a lot to get that number down for a Henderson post-WW2 look. And no matter what, you aren’t going to escape one more detail – over longer periods of time, the correlations are overwhelmingly positive. I’d hate be touting the benefits of lower taxes and having to explain that fact.

Moving on, the problem with option 2, the status quo, or option 3, is that its simple enough to show what I’ve shown. The results are there. As noted above, I’ve done this sort of thing so many times, so many ways, with so many different data sets, and at so many levels of granularity. Sooner or later someone that other folks do listen to will discover the same thing. Then what?

As to option 1, well, Upton Sinclair said it best a long time ago, “It is difficult to get a man to understand something when his job depends on not understanding it.” And frankly, its hard to see GMU or the Mercatus Institute or Hoover or even the blog where you write keeping you on if you start telling people that higher top marginal rates are correlated with faster economic growth. You have a lot to lose if you change your beliefs.

So if you can’t take any of these options, you really need a different approach. And what’s better than going on the offensive? Offer up the bet. Sound confident- a true believer would insist that correlations between lower taxes and faster growth should be there 90% of the time, right? Heck, issue odds. Do that and people might assume you know the results favor your position. People are lazy, and they don’t check. That’s why so many people believe so many things that simply don’t hold up when confronted by data.

Sincerely,

Mike Kimel

PS. The Excel file containing the data and analysis that went into this post is published as a webpage here. I’m not quite sure why but the ten year results seem to have acquired an error upon uploading into google. Everything else seems OK, but should anyone want the original Excel file, drop me a line at mike period and my last name, all at gmail dot com.

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