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:
(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:
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.
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.
Great post. Never met you, but my mental image is that you’re rather awkwardly dressed, needing two pairs of pants, a loin cloth, and an atheletic supporter to…uh…. hoist your equipment.
Mr Kimel, To take this one step further, perhaps the other blogs, those who know how, even perhaps miracle makers, can/will give this the exposure that is needed today in the country. I believe it’s time for a full frontal assualt on the disinformation of those who are in effect, tearing down/destroying the very fabric that is the United Stated of America.
What’s infuriating is that (with all respect) these numbers are not rocket science, you don’t need special equipment to extract them, and they have been sitting there for decades silently refuting the libertarian tax cut ideology which, frankly, only exists because a cadre of pundits have been broadcasting it for decades.
If I plan to drive to Florida and use a broken compass where north was swapped for south, and consistently find snowdrifts instead of beaches, the answer is NOT to soap over the windows and keep navigating among the polar bears.
Of course, this is exactly what one does if trying to convince one’s passengers that those snowdrifts really are pure white beach sand, and the predatory bears are actually big, white cows.
Well here is the crux (BTW I agree with your post mostly)
“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.”
This assumes that we have a well-functioning, market based economy. Though the US is better than anywhere else, I would say that this is not the case and has been getting worse over time. The Feds have far more than a thumb on the scale anymore. They pick winners. for a timely example – GM is selling 25% of its output to the USG.
Secondly, the libertarian assumption assumes (more or less) that we are already on the wrong side of the Laffer curve (for a lack of a better decription – don’t go on about the curve). At our current tax rate the US is not even close. And the increases we are talking about are minor at best.
I would bet $100 they don’t take you up on you offer though!
Islam will change
Setting aside the well-known correlation/causation problem, are you trying to argue that raisng taxes increases GDP?
LOL…Mike can speak for himself when he gets home from work, but Mike is saying what he says. No strawmen please.
I don’t know what he’s saying, but I would argue that that’s generally the case, yes. Because in the real world, governments generally spend *more* efficiently than the private sector, for a number of reasons. For instance, governments spend money on public goods, which tends to be an efficient way to spend money; the private sector pretty much by definition can’t do this as it requires taxation to avoid free-rider effects. And however inefficient, governments are more likely to spend money on useful things (education, health care) than on, say, Cabbage Patch dolls. Government direct outlays tend to go more to poorer individuals who will spend it (welfare, pensions) rather than wealthier individuals who will hoard it or use it to destroy the economy with exotic financial instruments (dividends).
Now the modern US government is perhaps working hard at becoming an exception to this rule, as it spends less and less on public goods, education, and redistribution while spending more and more on useless things (bank bailouts, corporate subsidies, excessive prison and security expenditures, and above all the military). But it’s really an outlier as governments go.
Yes, there is value in public goods spending, and the argument is often bypassed in the rush to cut taxes, and the value of the two wars we are in now appears negated by the same group who pushed for the expense as a public good but used deficit spending as the way….first time I believe ever done this way.
So look to who is advocating such measures in order to discount them first. Then look to see if fiscle response people are still standing. I also encourage voters to look at who is pushing the non-deficit social security issue instead of the medicare problem.
SS could be dealt with in ten years as Arne suggests, in a deflationarry environment and lower payrolls overall…then, of course, the problem will be better defined, although it is clear to some now. Or take it off the table for twenty cents a week for the moment until the SS haters club dies off.
Then take the assumptions in the NYT to task along the same lines. Some obvious choices were left out.
Calling the hardwork done by some of the Bears as quibbles is disengenious at best, and debating issues that are being fought with massive amounts of political monies and advertising is a lesson in futility. I agree with spencer and buffpilot that it will be wasted energy to date…these issues are framed in ways that are important but bypass the economic realities and caveats.
if I remember correctly, some of the first mention in the healthcare debate was caught by a Bear, the MLR formulas, and still is discounted after a serious of amount of energy was spent following the ins and outs of that debate.
Purple Library Guy, I don’t think you fully understand the arguments you are throwing out. Some are just plain wrong. Some are completely unpersuasive.
1. Yes, the market fails when it comes to public goods, free rider problems, and other sorts of issues. However, this makes up an extremely small portion of economic activity. More importantly, there is a second part to this that you don’t address: why is the state more efficient rather than just as inefficient or worse?
2. I think you must be a little blinded by what you want to be true when you say that the government usually spends money on useful things rather than “Cabbage Patch Dolls”. I can leave aside your assumption that education and health care are always more useful than toys, and just ask what government you have been following that spends money on useful things. The War on Drugs, Medicare Part D, wars in the middle east, buying up bad debt, and agricultural subsidies all must be funded by very usefully spent dollars, correct?
3. Look up Gini coefficients for after-tax and transfer income distributions in the country. Our government expenditures are demonstrably shifted towards the wealthy. If you can name one currently active government program that doesn’t provide noncompetitive profit to a corporation, I will be surprised.
4. Dividends is not a good example of “exotic financial instruments”.
And yet, though she knows the burdens under which I labor, the ex-GF (i.e., the wife) keeps complaining about my attire.
Here at Angry Bear, readers sometimes inform Dan of material they have seen elsewhere, and sometimes he posts it. Other blogs operate the same way. I’d be grateful if you dropped a note with other bloggers about this post.
Noni – I can’t argue. This is not rocket science, and its been done before. Still no traction though.
I’m hoping to see Henderson offer the bet to Krugman.
Less well known – lack of correlation is equal to lack of causality. That’s all this post showed.
I am … troubled that the windows of smaller time frames tend to have the values <50%. (All the yellow is to the left.) I wonder if this pattern (yellow blocks on the left, not the overall pattern) is an artifact of sampling, somehow. I haven't thought this through. But seeing those blocks cluster concerns me, and the notion that there might be some sampling bias makes me wonder about the robustness of the overall result.
Or, phrased differently, lets suppose this pattern is real. Let’s suppose that increasing tax on the top marginal tax rate increases GDP — or that the correlation, not the causation, is real. (To be careful.) Why would we see that correlation less than 50% of observations only when the window of time is 40 years or less?
Don’t disagree with the result, but trying to understand this aspect.
On point 4 apologies, I was unclear–I meant that where taxes went to redistribution, dividends (the “taxes” taken from corporate revenues, mostly going to the wealthy) tended to get reinvested in exotic financial instruments. But looking at it that’s not what I said–my parallelism was faulty.
Your point 3 is addressed in my last paragraph. The US government has been captured by wealthy private interests to an unusual, perhaps unprecedented degree. But even so, actual government expenditures even in the US, while skewed towards the wealthy, are probably less skewed towards the wealthy than is the remainder of the economy.
On point 2, consider the degree to which much of the private economy is deeply useless. It was calculated a few years ago that the amount of money dedicated to advertising, marketing and PR in the US came to $4,000 annually for every man woman and child in the country. Now consider the size of the FIRE section of the economy and how much of that is useless or actively counterproductive. Then there are negative externalities, the deep inefficiency of private compared to public health care delivery (it seems reasonable to suppose that the difference between private- and public- dominated health care alone costs the US 7% of GDP, that representing the difference between US expenditures and average-ish first world expenditures for generally better coverage). Plus, the payroll for upper management layers alone in the private sector has to account for quite a bit of inefficiency . . . people talk about government waste, but nobody in government’s getting paid millions per year. I could go on for pages . . . but the stuff I’ve already mentioned probably represents, oh, easily 20, 25% of US GDP . . . now consider that the private sector itself isn’t even close to 100% of the economy, so what proportion of private US output is waste? Lots and lots, and it seems more all the time.
I’ve been thinking about it too. I hope to write a post about that soon. But I don’t have a very well thought out explanation. Here’s what I am thinking right now:
1. Over short periods, cutting taxes does produce faster economic growth, but over longer periods, keeping taxes low creates costs (either more debt or less government spending). Think of it this way – some sugar before a sprint might make you run faster during the race, but continue consuming sugar regularly throughout the day, every day, and you’ll have a problem. What’s good for the short haul is not good for the long haul.
2. With only a few exceptions, there isn’t all that much variation between tax rates for relatively short windows. But there is huge variation between bigger windows. And I suspect it is possible that when tax rates are relatively stable, a small decrease in tax rates does produce more growth, though on the whole, much higher taxes are still preferable. For instance, going from 35% to 30% might produce some benefits, but going from 35% to 70% might produce even more benefits. The fact that there might benefits to either the small decrease or the big increase could be possible because change of any sort is good after a while (as it means some old loopholes are covered up along with the changes in tax rates).
3. Different tax rates “create” different economic structures. A tax cut might be a good thing (at least in the short run), but when you have taxes at very low rates, it might be (not what a libertarian would believe, but then they wouldn’t believe the data either) encouraging people to think in terms of taxes rather than producing things. Not sure how to test for this.
Sorry but that’s all I have right now. No conclusions, but results that hold up over a very long period of time. You may recall that I found something similar with state taxes as well, so its doubtful this is spurious even if we don’t understand it.
If tax rates are cut over long periods of time, and deficit spending continues to be the norm, could the impact of increased debt service payments be a factor? Kind of like compound interest in reverse? Same for the effects of inflation rates over time? Just curious.
But as I understand it, your resampling scheme only looks at differences of one to five years, right? (t – 1 to t; to, t to t+5). I might not understand it. (How doe t-1 to t, differ from, t to t+1 ?)
Let’s think only of the t to t+5; a five year difference between tax and GDP. And we consider each (?) 40-year window of data, let’s say, with the correlation (simple r?) between tax and GDP. And then look at what percent of 40-year windows have a positive correlation. We’re still only looking at the effect of tax on GDP five years later, right? Just through multiple (every) 40-year blocks? The 40-year blocks (or 50 year, or 60 year) essentially just determine the ni for each subset of data, right?
It still sounds like the yellow being on the left is some kind of sampling effect. E.g., if there were one period of time with an anomalous tax and GDP pattern that only showed a negative correlation in small (<40) or a positive correlation in large (>40) year blocks. I’m not sure what that would be without looking at the actual data.
A link to the data is in the PS to the post. If you want my original excel file with the work in it, I’ll be happy to send it to you.
Drop me a line at mike period and my last name, all at gmail dot com.
Hi, Mike. Thanks for the offer, but I think my other work will keep me from looking over these data. Mostly just wanted to point out the pattern. It is considerate of you, though, and I appreciate the offer.
I guess it is too much to ask for our taxes to be understood by the rest of us. It should not be this confusing about who pays what. – Heath Jordan