The Kimel Curve and the Kitchen Sink, Part 1: All Years
by >Mike Kimel
I’ve been writing about the relationship between tax rates and growth since I started blogging in 2006. A lot of those posts have focused on the quadratic relationship between tax rates and growth. That is, it turns out that if you take US data going back to when the BEA started keeping track, 1929, you can easily build a model of the following form:
% change in real GDP from t to t+1 = a + b*Top Marginal Tax Rate at time t
+ c* Top Marginal Tax Rate squared at time t
I have modestly referred to that as the Kimel curve. Now, it turns out that for most variations on that theme I’ve come up with, b is positive, c is negative, and both are significant at the 5% or 10% level. That allows you to find a top marginal tax rate that maximizes growth… which turns out to be somewhere between 60% and 70% depending on how the model is specified.
In this post I want to address a few criticisms by running two additional regressions with more or less the form. Parts of this may get a bit wonky but I’m going to keep it so that even if you’ve never done any statistical analysis, hopefully you’ll be able to follow the outcomes.
In the first regression, I’m going to account for a few additional facts:
1. By going with every single observation the BEA produces, I’ve been accused of “cherry picking.” So I’m going to throw in a dummy variable for Hoover.
2. I’ve been told the only reason growth was so quick during the New Deal was that there was a bounceback effect from the Great Depression… so I’m throwing in a dummy variable for FDR’s peacetime years (i.e., 33-41).
3. I’ve been told WW2 biases the results…. so there’s a third dummy for 1942-1944, the fast growing years in WW2.
4. I’ve also included two demographic variables: the percentage of Americans 35 to 44 and the percentage of Americans 45 – 54. The latter group tends to be the highest income group these days, but in an earlier era more focused on manual labor, those 35 to 44 might have been higher paid.
5. For grins, I threw in a dummy variable which is equal to 1 if the President is a Republican and 0 otherwise.
So… here’s what it looks like:
So what does it all mean? Well, this set of variables explains about 43% of the observed variation in growth rates over the period for which we have data (see the adjusted R2). There’s obviously room to improve the model, variables I’m not accounting for, etc.
The percentage of Americans 35 to 44 has a positive coefficient and is almost significant at 10%. We’re almost at the point where we’d be comfortable saying as that percentage increases, growth increases. The percentage of Americans 45 – 54 has a negative coefficient, but isn’t close to being significant.
Not surprisingly, the Hoover dummy is associated with economic shrinkage, FDR’s peacetime period is associated with positive growth, and 1942 – 1944 is associated with even faster economic growth.
The Republican dummy is not significant – any difference in the growth rate observed between the two parties can be explained by other factors. Which other factors?
Well, the top marginal tax rate and the top marginal tax rate squared are both significant – the former is positive and the latter is negative, which means they trace out the desired upside-down-U shape.
Oh… and the top of the curve happens when tax rates are at 64%. That is, the fastest growth rates seem to occur when the top marginal tax rate is around 64%. Now, I’ve had post after post on this topic, and the top of the curve always seems to occur in more or less in the same place. It isn’t a coincidence folks.
I’ll post results of the second regression in my next post in the series. That regression will focus on the period since Reagan took office and thus will only include data from 1981 to the present. What does it say? Well, a hint: if you don’t like the results shown in this post, you won’t be happy about that one either. But remember, I’m just the messenger. The data is what the data is, and if it isn’t showing what you think it should, its up to you figure out what’s wrong with the analysis or with the data, to pontificate wisely and inaccurately, to ignore the evidence, or to change your mind.
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If anyone has a line on a good inequality series with annual data that goes back to 1929, please let me know. I’d like to drop it into the model. I’d also love a good proxy for regulation. Don’t be afraid to offer other suggestions for data to drop into the mix are welcome too. I’m like a DJ, I take requests, but it helps if you can point to whatever data you want me to use.
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As always, if you want my spreadsheets drop me a line at “mike” period “kimel” (note – one m only in my last name!!!!) at gmail.com.
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Thanks to Bill McBride for pointing toward the demographic data and m. jed for suggesting its use.
Instead of looking at the president’s pary, how about looking at the make up of the Congress?
Regarding inequality: Emmanuel Saez at Berkley has nice data on this, tracing back to 1913 (http://g-mond.parisschoolofeconomics.eu/topincomes/).
Cheers for the great work!
The increasing emphasis on individual ownership versus societal ownership of income might make the problem of induction rear its ugly head if this analysis were used to back a top marginal rate of 60-70%.
If the era of high top marginal tax rates was so effective, why was there a need to implement the alternative minimum tax in the late 1960s to fix the tax system’s inability to address the wealthiest citizens? Also, this comes across as a reactionary theory given history. The result of the high top marginal tax era left the nation in a decade long period of stagflation. In fact, the 70s saw a sustained double digit Misery Index reaching its all time high in 19t80. Knowing this end result, the reason for growth during the 40s, 50s, and 60s may have been due to the successive wars the nation fought during these years.
If economics is a science, then this theory should apply to other national economies and address the caveats/outliers in history. Or is it only specific to the United States?
If you read Presimetrics, you might recall why we believe the President and not Congress is in the driver’s seat.
How could I forget Picketty and Saez? Will look at the series. Thanks.
And thanks for the kind words.
I just report it. But the post above could be used to argue at least for a return to Clinton era rates.
Kevin,
1. The AMT had to do with people escaping the tax. Remember… this was an era where a number of fixes were put in place to make sure people paid their “fare share.” This is when a singe social security number or FIT had to be attached to everything.
2. You may have noticed that the slowdown happened to coincide with the Oil Embargo and ended a few years after the second Oil Embargo. Conversely, we’ve had three periods since 1920 or so when tax rates were reduced to 35% or below for several consecutive years. Those periods, by coincidence, included the start of the Great Depression, the S&L Crisis, and the Great Recession. There was no Oil Embargo though. Which means that a 70% top marginal rate is bad and a 35% marginal rate is good for growth?
3. I’ve stated a number of times, I don’t believe economics is a science. Specifically, I’ve noted that I believe Economics is where astronomy was before Tycho Brahe, which means that given how many of its practioners behave, in general economics bears precisely the same resemblance to science as astrology.
Nevertheless, this sentence does not follow: “If economics is a science, then this theory should apply to other national economies and address the caveats/outliers in history. “
Part of what makes an optimum is cultural factors. It isn’t hard to see why the optimal tax rates would be higher in Denmark than in Mexico. Besides, optimal rates might change over time (cultural factors change over time) and might not even be computable (it depends on the B and C in the regression, right?).
Hmmm:
~155 taxpayers making ~$200,000 in the late sixties escaping all income taxes is not indicative of a failure of the progressive tax system. Its a loophole just like the Wendy Gramm Energy Loophole which passed with th Financial Services Modernization Act.
So Mike what is your argument for not having a top marginal income tax rate of, oh, say 60 percent? Other than some judgment about “political realities” that is.
“The Republican dummy is not significant”
I suspect the only reason you added the ‘Republican’ variable was to use this phrase…. 🙂
“The Republican dummy is not significant”
I suspect the only reason you added the ‘Republican’ variable was to use this phrase…. 🙂
At some point, you have to acknowledge that one of the parties is lying to everyone in a very big way.
1. The AMT had to do with people escaping the tax.
The fact that they had to implement the AMT demonstrates that the tax system advocated in the post had serious flaws.
2. You may have noticed that the slowdown happened to coincide with the Oil Embargo and ended a few years after the second Oil Embargo.
One, there was no second Oil Embargo unless you are counting the one of 1967 that had little effect. Two, by December of 1970 unemployment increased 42% from the previous year and inflation was already at 5.8%. This is two years before the Oil Embargo of 1973 which lasted all of five months and was not enough to baffle economists and the world’s strongest nation for an entire decade.
3. I’ve stated a number of times, I don’t believe economics is a science.
Yet you attempt to describe some underlying law/relationship between growth and tax rates through loose correlation while leaving out demonstrable changes in the income levels affected by the top tax rate and the overall tax system.
Nevertheless, this sentence does not follow: “If economics is a science, then this theory should apply to other national economies and address the caveats/outliers in history. “
The statement demonstrates how science describes (or at least attempts) some embedded rationality in the world. Faraday’s law attempts to describe a relationship that applies everywhere and if there were caveats, it has to be able to explain them.
Part of what makes an optimum is cultural factors.
And there have been huge cultural shifts since the early 80s in the United States. The fact is, correlation does not imply causation. Declining world pirate populations are not responsible for increased temperatures even though we can show a strong correlation between the two.
200k in 1968 is equivalent to about 1.24 million in 2010 dollars. If you’re okay with them not paying taxes today, then you aren’t an advocate of a progressive tax system. Also, this doesn’t begin to describe the system the AMT attempted to address. 155 did not pay a single cent in taxes, but the number who paid less than 15% was rumored to be many magnitudes higher. Let’s put it this way: enough to threaten the entire tax system.
PJR,
Cultures change. Collectively we’ve “learned” that the system that produced the fastest peacetime growth rates in this country’s history (see 1933-1941) actually produced disaster, not to say evil. Once enough people have come to believe that taxation is theft, it can actually have real consequences on growth.
1. “The fact that they had to implement the AMT demonstrates that the tax system advocated in the post had serious flaws. “
Listen, one works with the data available. There are also differences in the data that goes into GDP today and in the 1940s. If you believe that some people evading taxes is a reason to say tax rates had no effect, that’s up to you.
“One, there was no second Oil Embargo unless you are counting the one of 1967 that had little effect. “
Over the years I’ve had people tell me about how JFK raised tax rates, how Reagan balanced the budget, how the economy tanked under FDR, and a myriad of things. This is the first time I’ve heard of a second Oil Embargo occurring in 1967. Its particularly odd given the first one happened in 1973. If it wasn’t obvious, I was referring to this:
http://www.google.com/#sclient=psy-ab&hl=en&source=hp&q=%22second+oil+embargo%22&pbx=1&oq=%22second+oil+embargo%22&aq=f&aqi=&aql=1&gs_sm=e&gs_upl=8829l9926l1l10134l2l2l0l0l0l0l462l462l4-1l1l0&bav=on.2,or.r_gc.r_pw.r_cp.,cf.osb&fp=b4c14b174b3e10f4&biw=1600&bih=756
🙂
pvdl,
First, the other party has its own, er, failures to deal with reality. I focus on the effect of taxation in my blogging so its the party that fails there that looks bad with the stuff I write. If we could magically make everyone in America face reality on taxation, a lot of people who like me feel that taxation is the biggest issue might move on to issue number two or number three… which might make the other party look bad. I just don’t have time to deal with more than one issue.
That said, there is a differenc between ignorance and lying. My own opinion… the rank and file, and even people like Paul Ryan, believe. But there are a lot of people with training in economics who work with data. My own opinion is that folks like Glenn Hubbard or Robert Barro, or even someone like Thomas Sowell, know precisely what they’re doing and it speaks extremely poorly of economists in general that there isn’t a mass exodus whenever one of those people walks into the room.
1. I was referring to this
Yes, you confuse oil embargo and the effects of revolution in a single country in the Middle East. In response to the 1979 events in Iran, other OPEC nations increased production, so the term ‘oil embargo‘ is incorrect unless it has to fit one’s narrative. In 1973, OPEC stopped its oil exports to the United States, which is why it’s labeled an oil embargo. The U.S. imposed trade sanctions against Iran in 1995, yet it’s never referred as an oil embargo nor did it cause stagflation.
2. This is the first time I’ve heard of a second Oil Embargo occurring in 1967.
http://www.jstor.org/pss/2536897
An oil embargo occurred in ’67, so you’re either mistaken about the number or their label.
3. Listen, one works with the data available.
Yet you admit to leaving out data. When asked about the variance of income that the top marginal tax rate has been applied, it’s been dismissed as a trivial data set. Yet any rational reader knows there is a different impact when the maximum rate is applied to the top 50% vs the top 20% vs the top 5%, etc.
People are open to the idea of finding an optimum tax rate structure. However, studies where the conclusion was made beforehand does little to win anyone over.
If Picketty and Saez don’t work out for you, Census once did a number of series on income distribution. Oddly, those data stopped around 1986, and have disappeared from the Census website. It is preserved here:
http://web.archive.org/web/20070626183417/http://www.census.gov/hhes/www/income/histinc/p60no231_tablea3.pdf
Don’t you have a monetary policy variable in the model?
Kevin,
“ In response to the 1979 events in Iran, other OPEC nations increased production”
True, but irrelevant. The gas lines in 1979 are not a figment of people’s imagination. I note that I was in Brazil at the time and I distinctly remember there were gas lines in Brazil at the time too. (I’ve written about the reaction of the Brazilian government to that, and how the Brazilian government took steps which have led to the point where Brazilians can buy tri-flex vehicles today.)
And of course, it didn’t cause stagflation. Events in 1979 cannot possibly have caused a phenomenom that began in 1973. But they can keep stagflation going when good policy has weakened that stagflation. Growth during the first three years of the Carter administration was rapid (see: http://www.bea.gov/national/xls/gdpchg.xls)
As to the 1967 embargo…. I wasn’t born yet. But the article you mention says that it was “ineffective, costly and thus unsuccessful.” If a tree falls in a forest…
“Yet you admit to leaving out data. When asked about the variance of income that the top marginal tax rate has been applied, it’s been dismissed as a trivial data set. “
I’ve covered this before:
1. The correlation between the top rate and the bottom rate from 1929 to the present was 52%. I think its reasonable to assume that the corrrelation between the top rate and the second highest rate was quite a bit higher than that…. which means that when the top tax rate went up, you had a tax hike whether you were in the top income bracket or whether you were a bit below it.
2. I keep hearing from Republicans that its the folks at the top that drive the economy. If that’s the case, does it matter how many non-captains of industry are snared in the net as long as the captains of industry are affected?
“However, studies where the conclusion was made beforehand does little to win anyone over.”
Yes. Now point how I made the conclusion beforehand.
Nope. Another thing to add to the list.
My favorite NIPA table, which made the degree of tax evasion obvious, disappeared from the BEA’s website a few years ago. I know the feeling.
Still…. I need a series that is as long as the growth series, ideally.
Mike,
“If you believe that some people evading taxes is a reason to say tax rates had no effect, that’s up to you.”
Look…I appreciate the effort, and majority of the time you offer some good points, and you make access to data alot easier for some people, which is always a good thing…BUT
From my research…..the tax system didn’t operate the way it was written in the code over the years. Yes….rates were higher in the past, but very few paid them due to either not making enough to be in them, or the vast loopholes and incentives that were built into the system, and the lack of accountablity. Over the years your basic analysis always white washes this fact, and to me, that really does you a major dis-service. I can understand the complexity of trying to nail this down, and the only thing I can say is keep building on it, but you aren’t there yet. You are entitled to believe that a top rate of 65% will maximize growth…….just don’t expect me to believe it…….I need actual proof before I can make decision.
And again…..It just cracks me up that no matter which way you decide to dice up this data, you just will not leave the FDR and before out of the analysis. As I explained before I know exactly why you have to keep him in the loop….it gives me quite the chuckle. If it weren’t the for FDR administration, and the big shift to Socialism during those years you guys on the left would have just a hell of a time pushing this agenda. But…that’s O.k.!
True, but irrelevant. The gas lines in 1979 are not a figment of people’s imagination.
If someone is trying to describe the situation as an oil embargo, increased oil production from the OPEC nations, ex-Iran, is the most relevant fact. Embargoes are not defined as cartels increasing their trade to outside nations.
Long gas lines can be caused by numerous events, as many on the east coast this past August can tell us. Hurricanes, as far as I know, are not synonymous with oil embargoes. Another cause for long gas lines is a shift in price control policy, as was the case in 1979.
Growth during the first three years of the Carter administration was rapid
Rapidly increasing inflation also describes Carter’s presidency. The purchasing power of $17k, the average salary in 1978, would have eroded to $12.5k if held through the final three years of his administration. A loss of more than 25% affects all citizens’ economic behavior and it’s the reason central banks the world over do everything they can to combat it. Left unchecked, inflation ruins economies.
As to the 1967 embargo…. I wasn’t born yet.
I’ll help you out then. The events of 1967 fit the description of an oil embargo much better than the 1979 situation.
I’ve covered this before:
1.The correlation between the top rate and the bottom rate from 1929 to the present was 52%.
And yet the question is yet to be addressed. Correlation between the top and bottom rate tells us NOTHING about how the top 20% (or 10% or 5%) were affected by changes in the maximum rate. Most Americans in the top 1% did not fall in the top tax rate category in 1951. In fact, few in the top 10% found themselves in the top brackets.
And I’ll make this point as I did before: According to the conclusions of the study, all GDP growth problems will be solved if we set a tax rate of 64% to anyone making more than 1.5 billion a year, leaving everyone else alone.
Should we change the capital gains rate? It won’t affect GDP growth according to the study, as long as the top rate is about 64%. Should we emulate the 40s/early 50s and not tax dividends? How about the corporate tax rate? Not even mentioned.
2. I keep hearing from Republicans that its the folks at the top that drive the economy.
That theory and its counter will never be proved/disproved due to its generalization. Do you need the ‘folks at the top’ to be engaged in the economy? Yes. Does that mean they’re driving it? Who knows.
Yes. Now point how I made the conclusion beforehand.
Sure, but first let’s get the record straight: You began the study with a blank slate and no bias whatsoever when it came to tax policy?
Kevin,
1. When I mentioned rapid growth in the first three years of the Carter admin, I meant rapid growth adjusted for inflation. The link I provided included inflation adjusted. And I hope you’re not trying to blame Carter for inflation.. Inflation is the fault of the Fed and predates Carter. (Think of the WIN buttons Ford was peddling.).
2. “I’ll help you out then. The events of 1967 fit the description of an oil embargo much better than the 1979 situation. “
I’ll help you out. The EIA keeps nominal and real prices for gasoline: http://www.eia.gov/totalenergy/data/annual/showtext.cfm?t=ptb0524
The increase in real prices from 66 to 67 was 5 cents a gallon, and in 68 prices fell. Put another way… the effect of the 67 embargo was smaller than the random changes that occur in many other years.
By contrast, the non-embargo of 79 saw a real price hike of 40 cents a gallon in 70 and 53 cents in the year after.
With all due respect, I don’t think your story fits the data (be it the existence of gas lines or the changes in prices). The data points to oil being an issue in 79 but not in 67.
“ And yet the question is yet to be addressed. Correlation between the top and bottom rate tells us NOTHING about how the top 20% (or 10% or 5%) were affected by changes in the maximum rate. “
Um, yes, it does. If two rates move together, and one rate moves, the other rate moves too.
“Sure, but first let’s get the record straight: You began the study with a blank slate and no bias whatsoever when it came to tax policy?”
I’ve been doing this for 4 years. I’ve taken requests for years about what to include in the models from people who don’t like the results. I am still waiting to add something that changes the result. So yes, I started with a bias. But over the years I’ve included every suggestion I could from people who had the opposite bias. Results didn’t change. Now I’m revisiting the exercise.
Darren,
“It just cracks me up that no matter which way you decide to dice up this data, you just will not leave the FDR and before out of the analysis.”
From the post: “I’ll post results of the second regression in my next post in the series. That regression will focus on the period since Reagan took office and thus will only include data from 1981 to the present.”
Its coming. I’ve already done the work but haven’t had a chance to write it up. I suggest you work on your tapdancing in the meanwhile.
I’m interested in the spread around these estimates. Can we add partial r^2 values, or SE’s around the coefficients? (Or both?)
Maybe that is one reason your r^2 is only 0.49.
When it comes to blogging, I use Excel for a number of reasons. Excel does put out more diagnostics than I’m printing… I’ve been trying to keep it simple but will add some more info in the future. Apologies.
Just as a for your info… the lower 95% upper 95% for the coefficient on tax rates is positive, and for tax rate squared is negative… so no matter what we end up with a quadratic.
Creating at matrix (5%, 95% for tax rates along the top, 5%, 95% tax rate squared along the side) and plugging in gives us maxima at:
5%, 5%: 7%
95%, 5%: 64%
5%, 95%: 62%
95%, 95%: >100%
1. When I mentioned rapid growth in the first three years of the Carter admin, I meant rapid growth adjusted for inflation.
So you believe that high inflation is not a concern as long as there is fast growth? And you’re okay an annual inflation rate of 13% as long as GDP growth exceeds it? Even after confronting the fact that stagflation was a huge issue during this time period, you still champion it? I know you’re not in the Volcker camp or the Hayek camp… I can’t think of an economic theory your ‘high inflation is okay” argument gels with today.
2. The data points to oil being an issue in 79 but not in 67.
You’re having a rough time with what the definition of an embargo is. It’s either that or the concept of ’cause and effect’ is yet to take root. An embargo is not defined by price increases. If you believe that then tell us what oil embargo took place in the past year that caused gas prices to spike. Maybe we can give you a couple of years to bring out the “Oil Embargo of 2011” theory. Even after admitting that OPEC nations increased oil production and trade to make up for the revolution in Iran, you still claim there was a Great Oil Embargo of 1979 and that, when it ended, stagflation ceased to exist. The facts are, there was an oil embargo in 1967 and 1973 and OPEC did not cease its oil trades with the U.S. in 1979.
3 Um, yes, it does. If two rates move together, and one rate moves, the other rate moves too.
The fact that you can’t address the question is indicative of your entire perspective. Were there times where the tax payers in the top quintile, but outside the top vigintile (or decile, percentile, etc) were not affected by a change in the top marginal rate? Yes. Does your study take these changes into account? No. Do you understand this question? I don’t know, but you can never address it.
4- I’ve been doing this for 4 years.
You’ve been doing this for that long, yet your premise is still (paraphrasing) “the top marginal tax rate level is the major underlying determinant to GDP growth”.
Mike the culture that has changed is among those in the top 1 percent. If you imposed a 60 percent marginal top tax bracket on them–that is, raise the current bracket to 60 percent from 35 percent–they’d scream theft and poverty and class warfare. But that change would reduce them to living on annual incomes comparable, in inflation-adjusted terms, roughly to what their counterparts were receiving in the early 1980s under Reagan. That might be unacceptable today to anyone within that (sub-)culture.
You MIGHT be correct that these people would react to the intolerable situation in a way that has consequences for growth–I assume you mean negative consequences because of their new culture. In their former culture, your data suggest positive consequences, even by those coming out of the “roaring 20s” culture. But you must have a “theory” about their behavior here.
I find your analysis fascinating. My primary complaint is your use of GDP for the dependent variable. It has serious flaws as a measure of the economic well-being of the country. Not all economic activities are created equal.
For example, the WWII era may have been one of high growth in GDP, but many consumer staples were rationed (meat, cheese, butter, gas, oil, sugar coffee, etc.) A dollar spent building a tank or a bomb doesn’t contribute to the wealth of the country as much as a dollar spent building a car or washing machine.
Similarly, government payments to farmers not to grow food during the Great Depression may have added to the GDP, but I doubt that it actually increased the economic output of the country.
Unfortunately, I don’t have a good suggestion how this shortcoming should be addressed. At a minimum, it seems that changes in the national debt should be included. I also think that an accurate measure of real economic output would account for government spending (or at least some portion of it) in a different manner than spending by the private sector.