To maximize real economic growth in the United States, the top marginal income tax rate should be about 65%, give or take about ten percent. Preposterous, right? Well, it turns out that’s what the data tells us, or would, if we had the ears to listen.

This post will be a bit more complicated than my usual “let’s graph some data” approach, but not by much, and I think the added complexity will be worth it. So here’s what I’m going to do – I’m going to use a statistical tool called “regression analysis” to find the relationship between the growth in real GDP and the top marginal tax rate. If you’re familiar with regressions you can skip ahead a few paragraphs.

Regression analysis (or “running regressions”) is a fairly straightforward and simple technique that is used on a daily basis by economists who work with data, not to mention people in many other professions from financiers to biologists. Because it is so simple and straightforward, a popular form of regression analysis (“ordinary least squares” or “OLS”) regression is even built into popular spreadsheets like Excel.

I think the easiest way to explain OLS is with an example. Say that I have yearly data going back to 1952 for a very small town in Nebraska. That data includes number of votes received by each candidate in elections for the city council, number of people with jobs, and number of city employees convicted of graft. If I believed that the votes incumbents received rose with the number of people jobs and fell with political scandals, I could have OLS return an equation that looks like:

Number of incumbent votes =

B0 + B1*employed people + B2*employees convicted of graft

B0, B1, and B2 are numbers, and OLS selects them in such a way as to minimize the sum of squared errors you get when you plug the data you have into the equation.

Think of it this way – say the equation returned was this:

Number of incumbent votes in any given year

= 28 + 0.7*employed people – 20*employees convicted of graft

That equation tells us that the number of incumbent votes was equal to 28, regardless of how many people were employed or convicted of graft. (Bear in mind – that first term, the constant term as it is called, sometimes gives nonsensical results by itself and really is best thought of as “making the equation add up.”) The second term (0.7*employed people) tells us that every additional employed person generally adds 0.7 votes. The more people with jobs, the happier voters are, and thus the more likely to vote for the incumbent. Of course, not everyone with a job will be pleased enough to vote for the incumbent. Finally, the last term (- 20*employees convicted of graft) indicates that every time someone in the city government is convicted of graft, incumbents lose 20 votes in upcoming elections due to an increased perception that the city government is lawless.

Now, these numbers: 28, 0.7, and -20 are made up in this example, but they wouldn’t have been arrived at randomly. Instead, remember that together they form an equation. The equation has a very special characteristic, but before I describe that characteristic, remember – this is statistics, and statistics is an attempt to find relationships based on data available. The data available for number of people employed and number convicted of graft – say for the year 1974 – can be plugged into the equation to produce an estimate of the number of votes. That estimate can then be compared to the actual number of votes, and the difference between the two is the model’s error. In fact, there’s an error associated with every single observation (in our example, there’s one observation per year) used to estimate the model. Errors can be positive or negative (the estimate can be higher than the actual or lower), or even zero in some cases.

OLS regression picks values (the 28, 0.7, and -20 in our example) that minimize the sum of all the squared errors. That is, take the error produced each year, square it, and add it to the squared errors for all the other years. The errors are squared so that positive errors and negative errors don’t simply cancel each other out. (Remember, the LS in OLS are for “least squares” – the least squared errors.) You can think of OLS as adjusting each value up or down until it spots the combination that produces the lowest total sum of squared errors. That adjustment up and down is not what is happening, but it is a convenient intuition to have unless and until you are someone who works with statistical tools on a daily basis.

Note that there are forms of regression that are different from OLS, but for the most part, they tend to produce very similar results. Additionally, there are all sorts of other statistical tools, and for the most part, for the sort of problem I described above, they also tend to produce similar outcomes.

I gotta say, after I wrote the paragraphs above, I went looking for a nice, easy representation of the above. The best one I found is this this download of a power point presentation from a textbook by Studenmund. It’s a bit technical for someone whose only exposure to regressions is this post, but slides eight and thirteen might help clarify some of what I wrote above if it isn’t clear. (And having taught statistics for a few years, I can safely say if you’ve never seen this before, it isn’t clear.)

OK. That was a lot of introduction, and I hope some of you are still with me, because now it is going to get really, really cool, plus it is guaranteed to piss off a lot of people. I’m going to use a regression to explain the growth in real GDP from one year to the next using the top marginal tax rate and the top marginal squared. (In other words, explaining the growth in real GDP from 1994 to 1995 using the top marginal rate in 1994 and the top marginal rate in 1994 squared, explaining the growth in real GDP from 1995 to 1996 using the marginal rate in 1995 and the top marginal rate in 1995 squared, etc.) If you aren’t all that familiar with regressions, you might be asking yourself: what’s with the “top marginal rate squared” term? The squared term allows us to capture acceleration or deceleration in the effect that marginal rates have on growth as marginal rates change. Without it, we are implicitly forcing an assumption that the effect of marginal rates on growth are constant, whether marginal rates are five percent or ninety-five percent, and nobody believes that.

Using notation that is just a wee bit different than economists generally use but which guarantees no ambiguity and is easy to put up on a blog, we can write that as:

% change in real GDP, t to t+1 = B0 + B1*tax rate, t + B2*tax rate squared, t

Top marginal tax rates come from the IRS’ Statistics of Income Historical Table 23, and are available going back to 1913. Real GDP can be obtained from the BEA’s National Income and Product Accounts Table 1.1.6, and dates back to 1929. Thus, we have enough data to start our analysis in 1929.

Plugging that into Excel and running a regression gives us the following output:

For the purposes of this post, I’m going to focus only on those pieces of output which I’ve color coded. The blue cells tell us that the equation returned by OLS is this:

% Change in Real GDP, t to t+1 = -0.15 + 0.63*tax rate, t – 0.48* tax rate squared, t

From an intuition point of view, the model tells us that at low tax rates, economic growth increases as tax rates increase. Presumably, in part because taxes allow the government to pay for services that enhance economic growth, and in part because raising tax rates, at least at some levels, actually generates more effort from the private sector. However, the benefits of increasing tax rates slow as tax rates rise, and eventually peak and decrease; tax rates that are too high might be accompanies by government waste and decreased private sector incentives.

The green highlights tell us that each of the pieces of the equation are significant. That is to say, the probability that any of these variables does not have the stated effect on the growth in real GDP is very (very, very) close to zero.

And to the inevitable comment that marginal tax rates aren’t the only thing affecting growth: that is correct. The adjusted R Square, highlighted in orange, provides us with an estimate of the amount of variation in the dependent variable (i.e., the growth rate in Real GDP) that can be explained by the model, here 17.6%. That is – the tax rate and tax rate squared, together (and leaving out everything else) explain about 17.6% of growth. Additional variables can explain a lot more, but we’ll discuss that later.

Meanwhile, if we graph the relationship OLS gives us, it looks like this:

Figure 2

(You might need to click on the figure to see the whole thing depending on your browser.)

So… what this, er, (if I may be so immodest) “Kimel curve” shows is a peak – a point an optimal tax rate at which economic growth is maximized. And that optimal tax rate is about 67%.

Does it pass the smell test? Well, clearly not if you watch Fox News, read the National Review, or otherwise stick to a story line come what may. But say you pay attention to data?

Well, let’s start with the peak of the Kimel curve, which (in this version of the model) occurs at a tax rate of 67% and a growth rate of 5.85%. Is that reasonable? After all, a 5.85% increase in real GDP is fast. The last time economic growth was at least 5.85% was in the eighties (it happened twice, when the top rate was at 50%). Before that, you have to go back to the late ‘60s, when growth rates were at 70%. It isn’t unreasonable, then, to suggest that growth rates can be substantially faster than they are now at tax rates somewhere between 50% and 70%. (That isn’t to say there weren’t periods – the mid-to-late 70s, for instance, when tax rates were about 70% and growth was mediocre. But statistics is the art of extracting information from many data points, not one-offs.)

What about low tax rates – the graph actually shows growth as being negative. Well… the lowest tax rates observed since growth data has been available have been 24% and 25% from 1929 to 1932… when growth rates were negative.

What about the here and now? The top marginal tax rate now, and for the foreseeable future will be 35%; the model indicates that on average, at a 35% marginal tax rate, real GDP growth will be a mediocre 1.1% a year. Is that at all reasonable? Well, it turns out so far that we’ve observed a top marginal rate of 35% in the real worlds six times, and the average growth rate of real GDP during those years was about 1.4%. Better than the 1.1% the model would have anticipated, but pretty crummy nonetheless.

So, the model tends to do OK on a ballpark basis, but its far from perfect – as noted earlier, it only explains about 17.6% of the change in the growth rate. But what if we improve the model to account for some factors other than tax rates. Does that change the results? Does it, dare I say it, Fox Newsify them? This post is starting to get very long, so I’m going to stick to improvements that lie easily at hand. Here’s a model that fits the data a bit better:

From this output, we can see that this version of the Kimel curve (I do like the sound of that!!) explains 36% of the variation in growth rate we observe, making it twice as explanatory as the previous one. The optimal top marginal tax rate, according to this version, is about 64%.

As to other features of the model – it indicates that the economy will generally grow faster following increases in government spending, and will grow more slowly in the year following a tax increase. Note what this last bit implies – optimal tax rates are probably somewhat north of 60%, but in any given year you can boost them in the short term with a tax cut. However, keep the tax rates at the new “lower, tax cut level” and if that level is too far from the optimum it will really cost the economy a lot. Consider an analogy – steroids apparently help a lot of athletes perform better in the short run, but the cost in terms of the athlete’s health is tremendous. Finally, this particular version of the model indicates that on average, growth rates have been faster under Democratic administrations than under Republican administrations. (To pre-empt the usual complaint that comes up every time I point that out, insisting that Nixon was just like Clinton in your mind is not the point here. The point is that in every presidential election at least since 1920, the candidate most in favor of lower taxes, less regulation and generally more pro-business and less pro-social policy has been the Republican candidate.)

Anyway, this post is starting to get way too lengthy, so I’ll write more on this topic in the next few posts. For instance, I’d like to focus on the post-WW2 period, and I’m going to see if I can search out some international data as well. But to recap – based on the simple models provided above, it seems that the optimal top marginal tax rate is somewhere around 30 percentage points greater than the current top marginal rate. The recent agreement to keep the top marginal rate where it is will cost us all through slower economic growth.

—

As always, if you want my spreadsheet, drop me a line. I’m at my name, with a period between the mike and my last name, all at gmail.com.

Added Dec 26, 2010. It occurs to me that I should probably explain why I used taxes at time t to explain growth from t to t+1, rather than using taxes at time t+1. (E.g., taxes in 1974 are used to explain growth from 1974 to 1975, and not to explain growth from 1973 to 1974.) Some might argue, after all, that that taxes affect growth that year, and not in the following year. There are several reasons I made the choice I did:

1. When changes to the tax code affecting a given year are made, they are typically made well after the start of the year they affect.

2. Most people don’t settle up on taxes owed in one year until the next year. (Taxes are due in April.)

3. Causation – I wanted to make sure I did not set up a model explaining tax rates using growth rather than the other way around.

4. It works better. For giggles, before I wrote this line, I checked. The fit is actually better, and the significance of the explanatory variables is a bit higher the way I did it.

We have several tax rates:

- individual earned income tax rates

- corporate rates

- capital gains rates

The capital gains taxes are to take account of earned income captured in capital gains, but inflation distorts the measurement of such gains, so the rates were cut to compensate. However, circa the 80s, the idea was that cutting the capital gains rate would boost growth. However, in the 80s, 90s, and 00s, the capital gains tax cuts seemed to drive pump and dump asset bubbles. The economy is boosted for a few years until the bubble bursts.

A related tax incentive is investment expensing which defers taxes – instead of capitalizing investment and depreciating, it is expensed saving current taxes but increasing taxes paid as the capital generates revenue.

Tariffs and sales taxes aren’t major factors since WWII at the Federal level, but in general, States with higher tax rates have had higher growth rates, at least until Federal revenue transfers mitigated the poor policy of low taxes in places like Texas; the heavy military spending in the South, for example, paid for the development without high local taxes.

Tax hikes are generally for specific purposes that have sufficient merit to justify the “sacrifice” – Reagan doubling the gas tax in 1993, for example, to fund road repairs, which had been neglected as inflation devalued the gas tax last hiked when Eisenhower was president.

[...] Cross posted at the Presimetrics blog. [...]

[...] This post was mentioned on Twitter by bartezzini. bartezzini said: To maximize real economic growth the top marginal tax rate should be about 65%: Comments http://goo.gl/fb/Q7qLx [...]

Interesting that the Heavy Hitters seems to get a similar result:

http://www.econ.berkeley.edu/~saez/derive.pdf, p. 224-226.

Ryan,

Thanks for the reminder. Saez (& Picketty) do a lot of interesting work.

I think there are a couple issues with your analysis which obviously reflects a lot of thought so I hope you take this as constructive suggestions and not an attack.

1) There are plenty of taxes other than the top federal marginal rate and they are not held constant across the relevant periods. (To illustrate their significance, I note that in my case, I pay SS, Medicare, state, local and property taxes equal to about 50% of my federal taxes so these other taxes are significant and that is without taking into account sales tax, utility taxes, airline taxes, my allocable share of corporate and business taxes, and the numerous hidden or implicit taxes out there). So it seems they should be factored in to have a rigorous analysis.

2) As I think you begin to acknowledge toward the end, the tax base is very different across these time periods and that would appear to be a material variation that needs to be pinned down to isolate the meaning of the marginal tax rate as well.

Last, I hope the rest of your Christmas Day involved less wonkery than this post.

mark,

1) Until very recently, I rarely worked with marginal rates for that reason. Presimetrics (the book) focuses on overall tax burdens, as do many of the posts I wrote on Angry Bear. But people kept telling me marginal rates were the way to go, and I’ve decided that since the public thinks in terms of marginal rates, at least for the time being much of my focus goes there. There’s no point in doing this kind of work without making an attempt to get the message across, and sometimes you have to dress up like a clown to do it.

2) This is first of a number of posts I hope to write on the topic. It will take a while to drill down to what is going on.

3) Spent time with the family.

[...] this post a quick follow up to my previous post on optimal tax rates that appeared at the Presimetrics blog and Angry Bear blogs. There will be a lot more follow-ups, but it occurs to me that a look a the [...]

The IRS data goes back to 1913, so I decided to try the same thing with US GDP data from Measuring Worth:

http://www.measuringworth.com/usgdp/

Going back to 1913 and using the initial formula, I end up with:

% change in real GDP, t to t+1 = -0.032432966 + 0.002216068*tax rate, t + -1.58602E-05*tax rate squared, t

X1 T-stat: 2.035750302

X2 T-stat: -1.652669372

Adjusted R-Squared: 0.054136429

I don’t think I screwed it up, but that’s what I’ve said to myself before handing in most tests I’ve screwed up. The source material for the period 1913-1928 seems pretty legit:

http://www.measuringworth.com/uscompare/sourcegdp.php

Hi Ed,

I don’t think you made a mistake. Frankly, the model I built is a bit simple, and may not apply outside the period for which I had data.

That said, the GDP data you used originates with the Historical Statistics of the US. I’m always reluctant to use it. (You’ll find I only use it, as in one of the posts on David R. Henderson, to show that someone using it is doing so in a misleading way.) The reason I avoid it is that despite its imprimatur (the Historical Statistics of the US kind of is a project that a number of scholars have worked on with support from the Census), its calculated too far after the fact.

GDP, at least as we know it, originated when the Dep’t of Commerce hired Simon Kuznets to start trying to estimate the size of the country. He made his first estimate (of 1929) somewhere around 1932, if memory serves. The figures from the Historical Statistics of the US were produced years later. I believe they had fewer resources available than the Dep’t of Commerce staff did (and does today – the BEA, is a branch of the Dep’t of Commerces) to work on the project, but more damning is that there’s a “feel” to the process that you aren’t going to have thirty some years later.

But… back to my model. Clearly it needs a lot more variables to adequately explain the US even for the time period I used, and I do intend to improve on it in posts in the near term. I have some ideas, but I also take suggestions.

Thanks for responding. Is OLS the best unbiased estimator for this purpose?

Since you’re taking suggestions…energy prices and the change in the working age population make sense as variables. Interest rates would as well, but there’s probably a hefty endogeneity problem. Capturing the effect of the previous year’s growth or contraction is probably important: recession followed by higher than average growth, et cetera.

Cheers!

Mike,

You use the analogy of an athlete and steroids, which got me thinking. Perhaps the analogy of muscle building exercise using weights would work here. If we assume the GDP maps to muscle power, then taxation could be analogous to the weights lifted or resistance that the economy is exerting against. When there is not enough resistance the muscle growth is suboptimal (i.e. the economy is being lazy), as is the case for too much resistance. Or, without pain (of taxes) there is no gain.

Fritz.

[...] the process of building a rigorous “econometric model.” (Some basic material appeared at the Presimetrics and Angry Bear [...]

“the Dep’t of Commerce hired Simon Kuznets to start trying to estimate the size of the country. ”

They should gone down the street and asked the US Geological Survey. )

Seriously though, Kuznets really didn’t get down to brass tacks until WWII. But for its military purposes, there’s no way Congress in the 1940s would’ve put up with the, for lack of a better word, indicative planning that Kuznets, Robert Nathan and the exiled Jean Monnet did for the War Production Board (cf. Congress quickly eliminating the “Public Resources Planning Board” for its post-war planning efforts).

http://books.google.com/books?id=bMp3jxlTxugC&lpg=PA143&pg=PA143

If I remember correctly, even after the war, Input-Output analysis work continued to be funded through the Air Force.

[...] 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 [...]

[...] on this topic, looking at a range of data from a range of sources, e.g., Kimel, Presimetrics, Tax Rates that Maximize Growth, Dec. 25, 2010. States that follow the [...]

This “analysis”, and I use that term extremely loosely, would have failed in any statistics 101 class. Look at the graph. It says that with a 0% marginal income tax rate that the economy would contract at a rate of 15% per year. It says that the economy would contract with a top marginal tax rate of anything less than about 33%. Does that make any sense to any of you whatsoever? If somehow it does, then that would imply that the US economy should have been contracting all during the years before it had an income tax. Maybe I have my economic history wrong, but I don’t think that was the case.

On the first day of my freshman year statistics course in college my professor told me that the worst thing one can do is use the same set of data to both develop a model and then test it. By definition, you will get good results when you do that. However, the model’s predictive value is likely to be meaningless. I suggest the author use his model on pre-1913 years to see how accurately it predicts US growth in those years. I suspect it will be wildly off.

:sigh: same problem here. Prove to me first that GDP growth doesn’t lag tax rates. Common sense might suggest that a reduction in tax rates in, say, the middle of 2006 may not effect GDP growth in 2006 due to the time needed for money ciruclation to take place.

First, show that tax rates in year one have an apparent causal relationship on GDP growth in year 1. If that’s not the case, you have to change your model. You may need to regress the data so that tax rates in year 1 impact GDP growth in year 2, year 3, or whatever is most appropriate. Your assumptions haven’t been proven, and I would bet may very well be wrong.

And if your assumptions are wrong, your conclusions are invald.

Bruce Berger,

1. This is a simple model. In fact, the point was to make it as simple as possible – it only includes the bare minimum number of variables needed to get a quadratic term.

2. No model predicts very well for situations too far out the range of the observations used in developing it. The minimum tax rate observed during the period for which I have data is 24%. Of course, with a simplistic model (see comment 1 again) and rates that never dropped below 24%, predictions for growth at the 15% rates may not be accurate. But if I didn’t show them, someone like you would come around and accuse me of hiding something.

3. I keep mentioning in post after post that I avoid doing analyses with GDP data prior to 1929 because those are unofficial estimates made decades after the fact rather than the official BEA-generated series. I can’t vouch for that work. Can you?

4. “On the first day of my freshman year statistics course in college my professor told me that the worst thing one can do is use the same set of data to both develop a model and then test it.” I agree fully. Oh wait, you’re implying that’s happening in the post. Where? Where is that happening in the post?

Cwill,

1. That’s the tax rate at time t influencing the growth rate from t to t+1. Put another way, the tax rate in 1948 is assumed to affect the growth rate from 1948 to 1949.

2. My latest post (here: http://www.presimetrics.com/blog/?p=531) looks at tax rates at time t and how they affect growth rates from time t to t+10. I hope you aren’t going to argue that tax rates in 1973 were caused by the growth rate that occurred from 1973 to 1983.

Mike,

2. Your model still predicts negative GDP growth with maximum marginal tax rates of 25%. Those would hardly qualify as being “too far outside of the range of observations”. Yet it makes no common sense to draw such a conclusion. In the long run real GDP growth is a function of total hours worked and productivity growth. So unless you think somehow that a 25% top marginal tax rate would result in population decline and/or negative productivity growth there is no way that anyone in their right mind would conclude that we would have negative GDP growth over any reasonable length of time, but that is the conclusion of your model.

3. Try it on pre-1929 data, just for fun. The robustness of the GDP data doesn’t matter particularly much because your model prediction will be dramatically wrong. What was the US top marginal tax rate prior to the introduction of an income tax? Was it zero? Was it 10%? Who knows, but I am guessing it was less than 30%. So unless the US GDP contracted in the first 137 years, in its history, and I am not sure there is an economic historian in the world that would claim that, your model will have the direction of GDP growth wrong. Just for laughs what do you think is the order of magnitude difference in a 1% positive annual growth rate or a 1% negative annual growth rate compounded over 137 years? It is 15 times!

4. Yes, that is precisely what you have done. You have developed a model that may or may not have validity. You now need to test its robustness on out of sample data. You mention testing it on other countries’ data. That would be a good place to start. Alternatively, if you only trust US data from 1929 on, you should have split the 1929 to present data in two. You could have used one half of the sample to determine your model parameters and then tested it on the other half of the sample. My guess is that the Great Depression years so skewed the data that you will not be able to produce a model that works. That is the point. You have assumed a stable distribution, while the Great Depression showed that the distribution is anything but stable. Fitting your model to that data makes for a nice story, but is of no predictive value. I think it probably fit your political view to have the Great Depression years included in your model estimation because those happened to coincide with relatively low marginal tax rates. But that doesn’t make for good statistical analysis.

Without testing on out of sample data you have nothing. You should not “publish” results until you have done so. And while you can say that it is only a “simple model” and that you want to do further study that did not keep you from drawing the very strong conclusion, “The recent agreement to keep the top marginal rate where it is will cost us all through slower economic growth.”

No serious economist would use this model to predict the growth maximizing tax rate. First, this post is methodologically flawed. The whole idea of using time-series data has been shown to be largely flawed. Cross-country variations have proven to be much more accurate. Not surprisingly, cross country data have generally shown the opposite of what you have found: higher and more progressive taxes mean less growth, less entrepeunership, less investment, and less labor supply.

Second, your variable of the marginal tax rate is flawed. You have to realize that the marginal tax rate kicked in at different income levels at different points in history. Before the 1980s, we had 14 different brackets, meaning that the highest tax rate affected a smaller segment of the population. Likewise, we had many more deductions during this period, meaning that the top tax rate affected even fewer.

However, neither of these things relate to the largest problem with your post: you assume correlation equals causation. As you admitted, many different factors contribute to economic growth. Almost everyone would agree that the conditions for economic growth not relating to the tax rate were better during the decades immediatley following the second World War than they have been for the past 30 or so years.

Regardless, the whole idea of the growth maximizing tax rate being 65% is absurd. Most estimates for the REVENUE maximizing tax rate are lower than 65%. I would love to meet an economist who thinks the growth maximizing tax rate is higher than the revenue maximizing tax rate.

Even most left wing economists would reject a 65% tax rate. It is universally accepted int he economics world that incentives do matter with regard to taxes, and a 65% tax rate would serve as a huge disincentive.

I conclude by saying that this post was not done with intellectual honesty. You looked at one cherry picked set of data, and then you ignored how absurd your conclusion was. It does not take an economist to know that a 65% tax rate will harm growth.

Jim Timmy,

” The whole idea of using time-series data has been shown to be largely flawed. Cross-country variations have proven to be much more accurate.”

Really? When did that happen? Did anyone inform some of the really well-known economists? For instance, someone had better stop Robert Barro (http://www.economics.harvard.edu/faculty/barro/files/Barro%2BRedlick%2Bpaper%2B_2_.pdf) and fast. I’ve also quoted Romer and Romer a whole bunch of times, and they keep updating their paper. I can go on, but clearly you’re not being serious.

” Not surprisingly, cross country data have generally shown the opposite of what you have found: higher and more progressive taxes mean less growth, less entrepeunership, less investment, and less labor supply.”

Yes. I remember how in the early and mid-90s they showed Argentina was the country to emulate. A few years later, it was Russia. More recently there was some to-do about the Baltic states, Ireland, Hungary, Poland, and Spain. Put another way… without a decent time series, its easy to stop before the consequences have set in.

“Second, your variable of the marginal tax rate is flawed. You have to realize that the marginal tax rate kicked in at different income levels at different points in history. ”

Yes. And as pointed out here (http://www.presimetrics.com/blog/?p=525), that actually isn’t a problem.

“However, neither of these things relate to the largest problem with your post: you assume correlation equals causation.”

Here (http://www.presimetrics.com/blog/?p=531) I look at how tax rates in one year affect growth rates over the subsequent ten years. Things don’t change much. Its an odd correlation that stays that stable without having any correlation whatsoever.

“Almost everyone would agree that the conditions for economic growth not relating to the tax rate were better during the decades immediatley following the second World War than they have been for the past 30 or so years.”

Not sure I’d agree. But would most of us agree that conditions were better in the 1930s? Because real economic growth was much faster from 1932 to 1940 (or, if you want to really cherry pick, 1932 to 1938) than it was in the past decade too. Or the past six decades for that matter.

I’m going to jump to the end…

“You looked at one cherry picked set of data, and then you ignored how absurd your conclusion was. It does not take an economist to know that a 65% tax rate will harm growth.”

I looked at every observation beginning when the BEA began computing GDP. That is, I looked at every observation available using US data. Every single one. To the best of my knowledge, that is the longest reliable set of official data available from any country in the world. It is over 8 decades of data. And you call that cherry-picking? Seriously?

Mike Kimel,

I was probably too strong in criticizing time series data. However, it is quite misleading to use the mid 20th century as proof that higher marginal tax rates INCREASE growth. As Scott Winship Explains:

“It is certainly true that wage growth has been slower since 1973 than in the two previous decades. But that isn’t a realistic bar to use. The U.S. was the only major economy left standing after World War II, and there was little foreign competition putting downward pressure on manufacturing wages and jobs. The period between WWII and 1973 was anomalous—it could not have been expected to have lasted.

The other way to judge middle-class living standards in the U.S. is to compare them to those in other countries. The Luxembourg Income Study shows that at most points in the income distribution (the 25th percentile, the median, the 75th percentile), income in the U.S. exceeds that in nearly all European countries, including Sweden, the model for many on the left. (The most accessible evidence on this is in a 2002 article in the journal Daedalus by Christopher Jencks.) Determining how to incorporate publicly provided benefits such as education and health care is very complicated, but the evidence we have indicates that American middle-class living standards are at worst comparable to those in European nations.”

Thats the important thing to remember. Countries with lower marginal tax rates have grown faster than countries with higher marginal tax rates. You write:

“Yes. I remember how in the early and mid-90s they showed Argentina was the country to emulate. A few years later, it was Russia. More recently there was some to-do about the Baltic states, Ireland, Hungary, Poland, and Spain. Put another way… without a decent time series, its easy to stop before the consequences have set in.”

Many Eastern European countries with flat and low taxes have performed very well in the past 10 or 20 years, the same is true of Ireland. Just because some of these countries have run into problems recently does not mean that those many years of fast growth never happened, and I certainly don’t think low tax rates are too blame for the recent problems.

Likewise, Argentina did have some success with market reforms, but high inflation has plagued them recently. I hope you don’t argue that free market polices led to this high inflation.

The real success story in South America is Chile. After aggressive free market reforms, the economy turned around and was dubbed the “Chilean Miracle”. In your response, you ignore this.

Other countries with free market policies have also been very successful, just look at Singapore or Hong Kong (both of these countries have very low marginal tax rates and very high growth rates).

You also left a couple of my questions unanswered. I pointed out that correlation does not equal causation. Just because the relationship holds for 10 years does not mean that there is causation. There are many complex factors affecting economic growth.

The reason I called your data “cherry picked” is not because it was not reliable. Your data started in 1929, and you explained why it did. However, the result would have been very different had it started earlier. The Gilded Age had no income tax and rapid economic growth. Including this in your analysis would significantly lower your estimate for the growth maximizing tax rate.

Finally, you never answered my most important question. How exactly can you account for, theoretically, the fact that a 65% tax rate supposedly maximizes growth?

Would you really argue that incentives are so unimportant that a 65% tax rate would maximize growth. And how exactly do you explain the fact that your estimate for the growth maximizing tax rate is higher than most estimates for the REVENUE maximizing tax rate?

These questions need to be answered. As Robert Lucas has shown, macroeconomic analysis needs to be consistent with microeconomic observations.