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.
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.
The problem with this post is that it depends on things that numbers wonks are comfortable with..and misses many (if not all) of the subtler aspects of an economy that make the statistics for a particular time play out the way they do..here’s a few examples….
Tax rates of many differing percentages can have advantageous effects on GDP…BUT they depend on the momentum of the economy in general and the ability of high earners to earn enough to make up for tax payments…higher tax rates also have smaller effects when debt levels are lower..That certainly is not where we are now..In fact, my guess is that higher rates on ANY group making less than a million $ annually would have a severely depressing effect on economic activity.
The age configuration of a society..it’s demographics..are critical to future growth rates. Tax older, retired people even marginally more and my guess is there would be an outsized negative effect.
Economic growth..even smaller rates nearer 3%..let alone GDP growth of 5% or more..require prodigious amounts of credit, borrowing and debt obligation. Lower tax rates can make it easier for businesses and individuals to assume risk, but it’s only one part of the equation. IF you’re not making much money it hardly matters what your tax rate is..you can’t make monthly debt service let alone a profit…
At the end of the day there isn’t going to be a tax rate manipulation solution to our huge problems..it’s going to be a lot more contentious and jarring than that.
65/65
65% top rates and 1965 really did leave us in the Leave it to Beaver territory i remembered as an eight year old? We finally had Civil Rights Acts and were only temporaily escalating in Vietnam (while Westmoreland told us the ‘Boys will be home by Christmas’) and Apollo was on target. Boy the storm clouds of 1968 seemed mostly distant. (If you overlooked the race riots in Detroit and Watts)
I don’t think America ever really hit the sweet spot, but God Damn it 1966 came close. At least for the upper working class white population. My grandparents were still living in fairly grim situations but their kids had houses! and at least one car! and the first kid ever to go to college in each branch’s history!
Ouch. Turns out that the Age of Aquarius we were about to enter wasn’t what it was cracked up to be. Still I was there for ‘Meet the Beatles’.
But as far as taxes go let them show how they produced more material progress on net for everyone on utilitarian ‘Greatest Good for Greatest Number” grounds than that 65 in 65 number. Exactly which cohort of America is better off today than we were in 1966? Color TV aside. And princess phones.
Bruce Webb,
I think your question about “being better off” – even with caveats, leaves it open to the Megan McArdles to insist that the princess phones are the be-all end-all, and that somehow that is proof that lower tax rates are better.
A better question – which cohort today or in the 80s or 90s, even, was more hopeful of the future than its counterpart in 1965?
Greg P,
All I can do is present the data. In the end, that’s all I got. But with all due respect, you have less than that – you are stating your opinion. And everyone has an opinion. I have opinions that are unsupported by data too. I try to change them when the data contradicts them, and I try to confirm them with data when I can or not put myself in a position to act on them when I can’t figure out how to prove or disprove them.
We can either debate based on something small – data and facts – or we can debate based on opinion. And we won’t get anywhere – at least not anywhere that is good for all of us – if we ignore the facts and the data.
You’ve admitted to having serial correlation in your errors. It should be obvious a priori that you have serial correlation in almost every data point that you run. If your dependent *and* independent variables aren’t AR(M) I don’t know what is.
Your estimator does not satisfy the assumptions of OLS, is biased, and is not consistent. Why are you still running regressions?
Mike:
I’m too busy (rewriting a tax course thanks to Congress) to dig through your numbers so i will ask a direct question.
Has the impact of tax credits been factored into the analysis?
Certain tax credits (say the Investment Tax Credit) can make massive difference in capital budgeting models despite whatever the marginal rate is.
Beyond that, I still think there are too many other economic variables to draw any hard and fast conclusions from this, particularly now in a more global economy.
And I repeat, during periods of high marginal rates the economy tended to be dominated by large conglomerates (ATT, ITT, IBM, GM, etc.) and there seemed to be less successful entreprenurial activity (this makes sense from a managerial accounting viewpoint). Is this desirable?
Better than Laffer’s simplisitic stuff though.
Don’t stop. Not too complicated. But would really like it if you’d drop real GDP/cap into your dependent variable column. It’s really a much more useful economic target, and an easy way to factor out population growth as a variable.
Having lived on both sides of the fence since ’39, Ive seen quite a bit of this countries groth as well as its present decline. What is amazing to my eyes, is how the country grew during the years folling the WWII to the 80″s. I believe the tax rates were higher than they are today. The infrastructure, education, even the health care allowed this country to prosper, which I might add also allowed the “Boomer Generation” to achive what they have, from what their parents hard work & sacrifice gave them. This present B & F in my eyes is disgusting as far as giving back, which sure has been lost. As we sit here watching the infrastructure crumble, the Petersons snivel & whine about paying their fair share. I ask the “Q”, just where the hell would you be of this was Afghanistan, Yemen, Sudan, etc. for that’s what we’re going to end up being if this ninsense continues.
Bad Reggression,
As it says in the post… the correlation between errors at time t sand errors at time t plus one is zero point zero four. That is as close to zero as you are likely trouble find. As not stated in the post, also looked at other regular issues that crop up with the errors. Nothing.
I didn’t want to get into anything too technical but, if you are going to comment about am AR(M) process, you should first. Ask yourself whether the dependent variable (not to mention an explanatory variaable) resembles a first difference. The numerator of a percentage change is the first difference.
Yes, a decade ago i would have done something more complicated, but at this stage I like what works and I don’t feel a desperate urge to correct for a condition that a graph of the residuals tells me
Please excuse the errors in spelling, because I need new glasses, but have to await until Medicare will allow replacement. Sorry
Missing the words “isn’t there” at the end of my comment.
Str – I did look at tax burdens in the last post. They’d be folded in.
Steve – there is a lot on my to do list. That is on it.
Norman – thanks.
Agree with Steve R. This is an economics blog. That means doing economics once in a while. Your presentation is far simpler than the average data-based econ journal article.
The Bowdlerization Huck Finn has brought back an expression from a prior effort to boot Twain from libraries – denying a man a steak because the baby can’t chew it. There is no need to shy away from useful presentation just because some part of your potential audience may have problems with it.
To the extent that “Bad Regressions” has a point, he(she?) does not have a conclusion. You should be able to run regressions os as to correct for problems of serial correlation.
Once you have assured yourself that your results are not distorted by serial correlation (or any of the other evils of data caught in the wild), then whatever you have left is the actual power of the analysis. If you come up with anything like the R^2 you are showing now, you can safely ignore assertions that stuff you didn’t mamnage to account for make the stuff you have accounted for invalid. No useful regression analysis explains everything. As soon as you start turning in R^2 figures in the 90+ region, it’s time to go back and figure out which of your independent variables is really just a plug for the dependent variable, or check that you de-trended the data. If you can explain something on the order of 78% of the movement in the dependent variable with movements in the independent variables, you have explained a lot.
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.
Mike. There appears to be a contradiction here. What am I not understanding?
Mike Kimel,
I just came across your posts on this subject and found it fascinating. I have a few comments.
1) My economics PhD dissertation topic is on economic growth and tax structure in the EU so needless to say I think I have something to say on this topic.
2) You are an economist. So when you say “why aren’t more economists doing work on this subject” I’m thinking why aren’t you? (That is, why don’t you try and get it published in a research journal?)
3)There *are* papers on economic growth and taxes, just not too many of them. Most come in two flavors, an older strand focusing on overall tax burden showing mixed results, and a newer strand focusing on tax structure that is much more promising. Without getting into too much detail the latter strand suggests that taxing corporate income is detrimental to and taxing consumption promotes economic growth. There is even a published paper that uses marginal tax rates as variables (the only one I know of):
Young Lee and Roger H. Gordon, “Tax Structure and Economic Growth,” Journal of Public Economics (89), June 2005.
It finds top marginal corporate tax rates are very detrimental to economic growth.
4) Nearly all of the published papers start with an endogenous growth model that include fixed capital investment and population growth rate as explanatory variables (often along with measures of human capital and fiscal variables). Leaving out investment and population puts you squarely in left field. I wonder how your results would hold up if you included these?
5) Your estimation of a quadratic model is innovative (perhaps too much so). No published paper uses such models and despite the fact it is very intuitive and frankly the thought had never occured to me. I plan to include such terms in future regressions and see what happens. Thanks very much for the idea.
6) Despite the fact my research (so far) suggests that higher marginal rates are always bad I’m not a classic American supply sider. I actually suspect that the European model with high consumption tax burden and correspondingly large welfare state to be optimal for long run growth.
8) I have to go and buy your book (I still have a Barnes and Noble gift card from Christmas).
Again, I really enjoyed your posts and hope I get similar work published in a research journal before you do.
Mark A. Sadowski
My “solution” to this would be to properly model the data generating process. This is why everyone from Sims onward ran VAR models since the 1980’s. As I said, everything’s AR(m) and also dependent on all the other variables lags (and perhaps current values).
Of course, there’s a reason why VAR models, which solve the problem I talked about, have died as a methodology as well. Obviously current consumption is dependent on (beliefs about) future income! So we could be correlated with future shocks as well as past.
Additionally, all of these sorts of regressions are vulnerable to the Lucas Critique, which is a death blow as far as I’m concerned. Look for exogenous variation at the least (even that won’t help you in full form).
Personally I prefer writing down a model, and calibrating or estimating it, as you prefer. Writing this sort of model would explicitly give form to the serial correlation that make these regressions explicitly biased.
As to the author’s question: I don’t think that this sort of analysis is worthwhile. There’s no way to do it correctly and simply. You did it simply here, but your numbers aren’t to be trusted. You could do it correctly, but no one would read the blog. I think this sort of exercise is too deceptive to be continued.
Pinelli
while i would tend to agree with you that there are other aspects of an economy that determine growth… or more important, quality of life… and agree that a tax rate manipulation is not a sane way to drive economic policy… i suspect your dicta about the inability of folks to make money under conditions of higher taxes is just more wish fulfillment thinking.
Bad Regressions,
For a minute I thought you were one of my old statistics students having some fun with me, but it occurs to me that you are actually serious. In that vein, I will be serious back.
1. FWIW, in general I avoid using VARs because its a prime example of a tool that exists because the math works, but for which the intuition makes no sense. Peter Kennedy’s chapter on simultaneous equations has a nice, albeit concise treatment of the intuition behind a VAR.
2. In your first comment, you somehow detected serial correlation despite evidence that there is none there. In this comment, you suggest using a method that notoriously goes to pot when there is serial correlation. Worse, in any system approach, you have a lot more places where any problem with the residuals can crop up. Your comments are not consistent with each other.
3. VARs are generally OK for forecasting, but most textbooks will tell you they aren’t all that great for policy analysis. This post is about policy analysis and not forecasting.
4. Take another look at the model specification in the post and think about what you’re saying, er, writing. If you want to assume that the demographics somehow are affected by shocks to real GDP or gov’t spending, that’s one thing, but are you really suggesting its legitimate to forecast changes in the 1929-1932 dummy based on those variables too? I’d love to hear the logic behind that explained. On second thought, I wouldn’t.
beezer,
In general, most economists believe that Fed is in the business of reacting to changes in the economy. For instance, if the economy tanks, the Fed comes running with piles of money to get things moving again. On the other hand, if the economy is running quickly, the Fed pulls some money out of the economy to slow things down.
I’ve commented before that while that effect does happen (the Great Recession being an example), in general, the Fed’s behavior leads rather than follows the economy. Most of the time, the economy runs because the Fed is pumping money into the economy, or slows down because the Fed is draining money from the economy. (I’ve had a few posts – probably time to return to this – showing graphically that changes to the real money supply generally occur before changes to the economy rather than the other way around. I’ve also noted that during some Presidential elections, Greenspan happily moved the economy in ways that would benefit republicans, but that’s another story.)
OK. Now, in this post, the “growth in real GDP” and “change in money supply” variables are in annual data, so they can be thought of as simultaneous. If the standard story were correct, and the Fed was doing what everyone says it is, then a drop in real M1 should not be accompanied by a reduction in real GDP growth. i.e., the sign on the “drop in real M1” dummy should not be negative. Conversely, the sign on the “increase in real M1” dummy should not be positive. We’d have expected to see the signs reversed (i.e., economy collapses, causing the Fed to increase real M1). Incidentally, that would also be a sign that I mis-specified the model by getting which was the dependent and which were the explanatory variables wrong.
Its kind of confusing, so if it still doesn’t make sense let me know.
you should see a positive sign
Mark A. Sadowski,
Thanks for the words of encouragement.
Actually, I would state one big counterexample… but I’m working off of a weak memory from when I was in grad school in the 1990s. Barro had a paper in 1990 that I think mentioned what I’m calling the Kimel curve, but he very specifically did not estimate it on US data. (Not being in academia any more, I can’t get the paper, but I’m thinking of breaking down and buying the thing from JSTOR for $14 to see if my memory is accurate.) If Barro did come up with this, and he didn’t fit US data to it, that would be very odd for a guy like him who is so very good at both theory and empirical work. On the other hand, Barro has some very particular views on taxes, and he really wouldn’t have liked what the model would have spit out… but that would be assuming bad behavior when I’m not even sure my memory is accurate. I really better go ahead and order that paper.
Another good analysis. As you add variables from post-to-post, other than increasing your R, you are very slightly decreasing your optimal TMT rate (originally 67 percent, now down to 59 percent, right?). Your coefficients remain steady enough to maintain your hypothesized curvilinear relationship. That’s important as you continue your exploratory analysis.
BTW, I just heard something interesting and sort of related (the TMT rate issue) so I’ll just share. A university that you see advertized a lot on television pays its president about $5 million, its COO about $3 million, and its president of academics a paltry $800,000 or so. Anecdotal evidence indicates it pays very little to professors and administrative staff and for facilitites and equipment. I sure am glad our tax system is encouraging this kind of behavior.
Problem with economic data, modeling is that they only capture certain time frame, specific circumstances. In the 1960s, the trading partners of Unites States does not include China, the Soviet Bloc countries, the europeans still rebuilding from aftershocks of WWII.
The societal structure are also very different… It was a male dominate society, less equality. More redeeming quality was that the WWII, depression era people are willing to work harder and pay more into the society. I just don’t think the same circumstances exists today.
There were less competition, more government sanctions monopolies in existance in the 60s going to the mid-seventies. Yes the tax rate are higher, yes on paper, the model suggests better “economic” growth. The same set of circumstance just don’t exist today. The living standards are higher today, the cost of living is correspondingly better, and the environment is better too!! Just think of the cost of medicine to extend the quality of life, the length of lifespan today.
Does anyone wants to go back to monopoly such as AT&T- just imagine calling long distance through an operator in those era $$$. Or fly overseas on TWA or Pan Am…$$$ Again, society composition changes, and the tax policies have to change to adapt.
I simply think congress allowed maladaption… Instead of everyone in their respective progressive tax bracket contributing their equal share of taxes now we have so many special tax “incentives.” No one person in the same tax bracket will end up with the same amount of tax… It’s too convoluted. The society have changed from where everyone expects to pay and contribute to a society of “not me!” and/or “let the other person pay!” Is this for better or worse?
It’s like deregulation of airlines… It eventually was good for the consumers but in the process cost a few lives. The tax system needs to evaluate itself and takes out the special treatments… Every in their tax bracket should ended paying ths same regardless of “special circumstance.” An airplane will crash if there’s no proper maintainance. The percentage of taxation is meanless if there is no equal enforcement of rules.
I stopped reading when you denied having admitted you had serial correlation. (See “E(e_t|e_{t+1})!=0”). Reread your first post. If you want to keep running bad regressions keep running them, it’s no business of mine anymore.
Ooops! Sorry for posting that sucker three times. It didn’t show as being posted afetr pressing [post] ; I had to refresh to see what damage I had wrought!
Ooops! Sorry for posting that sucker three times. It didn’t show as being posted afetr pressing [post] ; I had to refresh to see what damage I had wrought!
I like this work, and glad you added in more variables like the fed, very interesting. One question, what income level does the top marginal rate apply, and would that even matter to the analysis?
Bad Regressions,
This is my last response to you. Given how insistent you were, Just on the off chance I was missing something, I regressed the residuals on residuals t-1, residuals t-2, residuals t-3, and residuals t-4.
Adjusted R2 was negative, and the “best” P-value was 0.38. You can continue to believe that somehow, somewhere, residuals from one period affect residuals from the next, you can continue to suggest VARs as a solution, and you can continue forecasting dummy variables. I don’t have time for this kind of nonsense.
Mcwop,
That was actually my plan for the next post, more or less. (That plus the tax rate on the median income earner.) I’m having a very hard time finding income levels before the 1960s for individuals, and before 1947 for families. I might have to sit on this for a bit until I think of where I can get what I need.
Tony Wikrent,
First – I did do the adjunct thing for five years from 2001 to 2006, but I haven’t done it since and its unlikely I’ll have time for the foreseeable. Thus, I don’t qualify for the title “professor.”
Thanks for the info. I will check out the study.
Mike,
I am looking at your posts with real interest, but a poor background in economics. Most of my experience with modeling comes from ecology which ruthlessly steals its ideas from economics. You take a long view approach to the economic modeling, yet the changing global economic environments may lead to non-linear affects to domestic growth, how cofindent are you that this retrospective analysis can provide useful information for future economic growth? Is it common to run simulations and sensitivity analysis to identify important variables in a changing global market? I apologize for asking any questions that would easily be answered with a basic background in economics.
Dan