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Tax Rates and Economic Growth Over Ten Year Time Horizons, plus Why a Flat Tax Would Result in Much Slower Economic Growth

by Mike Kimel

Tax Rates and Economic Growth Over Ten Year Time Horizons, plus Why a Flat Tax Would Result in Much Slower Economic Growth

Last week I had a post looking at the the real GDP growth maximizing income tax rate using both top marginal income tax rates and and “average marginal” “all-in” tax rates for all taxpayers (including those who paid nothing) computed by Barro & Sahasakul. The post noted that the optimal top marginal rate was in the neighborhood of 64%, a finding that corresponds with many other posts I’ve written on the topic. The post also noted that the Barro-Sahasakul rates were not as useful at explaining economic growth as the top marginal income tax rates.

David Altig of the Atlanta Fed commented on the piece here, but he essentially had one very gently delivered criticism and one follow-up comment. The criticism is that my post did not consider long run effects – for each year, it looked at how the tax rate that year would affect growth in real GDP from that year to the next. The comment was that the post’s results did not correspond with results of a paper he published in the AER with Auerbach, Kotlikoff, Smetters and Walliser. (Ungated version here. The paper

uses a new large-scale dynamic simulation model to compare the equity, efficiency, and macroeconomic effects of five alternative to the current U.S. federal income tax. These reforms are a proportional income tax, a proportional consumption tax, a flat tax, a flat tax with transition relief, and a progressive variant of the flat tax called the ‘X tax.’

In his post, Altig provides this graph:

Figure 1.

The graph shows that according to the Altig et. al simulation model, after about ten years, the growth maximizing tax (among the types they simulated) is a flat tax. I read the paper this afternoon, and while I have a few small quibbles (some of them raised by the authors themselves, to their credit), having done a bit of simulation work myself, I think there is one thing that is worth mentioning and which I can cover in this forum: results of a simulation must fit known facts.

Now… I think there is a quick and dirty way regression that can account for both a long range analysis and to test the notion of whether the cause of rapid economic growth is best served by a progressive tax system or a flat tax. Here’s what I have in mind:

equation 1: annualized growth in real GDP, t to t+10 = f(top marginal income tax rate, top marginal income tax rate squared, bottom marginal income tax rate, bottom marginal income tax rate squared)

The quadratic terms allow us to find the growth maximizing tax rates, as I’ve done in so many posts before. And by including both top and bottom marginal rates, we can compute the optimal growth maximizing top marginal rate and the growth maximizing bottom marginal rate. And… if a flat tax is the best tax, the optimal bottom rate should be more or less equal to the optimal top rate.

As in the previous post, data ran back to 1929, the first year for which real GDP was computed by the BEA. Top marginal and bottom marginal rates came from the IRS Statistics of Income Table 23.

So here are the results, as spit out by Excel.

Figure 2.

What this tells us is that each of the components of equation 1 are significant. For top marginal rates, we have the expected shape, and if you work it out (either with calculus or by plugging the numbers into a spreadsheet) you’ll find that the model claims the optimal rate is about 67%, and that getting tax rates there from the current 35% would add about 1.4% a year to real GDP growth.

For the bottom marginal income tax rate, things are a bit more complicated… it turns out that the expected quadratic shape isn’t there. In fact, the model indicates that tax rates should be as low as possible. In the range from 0 to 100, 0 is best. The model also provides support for the Milton’s Friedman negative income tax rate, though I’d say results are bit shakier there as rates were never at or below zero during the sample for which we have data. If I were to do it again, I think I’d specify the bottom marginal rate differently – no quadratic shape – but right now I gotta go. I would note – I’d also add a few other variables, both to account for the small degree of patterns that appear in the residuals and frankly, just to make the model more realistic. But its fairly clear – especially since I keep getting results that more or less the same no matter how I approach the problem, that better specification wouldn’t change the results all that much. They might push estimates of the top marginal rate down a bit, but its fairly clear that top marginal rates well above where they are now will lead to much faster economic growth.

And of course, the other thing we learn… because the effect of top and bottom rates are so very different, and relative to where they are now, pull economic growth in different directions, it makes no sense for the top rate and the bottom rate to be in close vicinity. Put another way – a flat tax is a very bad idea, at least when it comes to generating economic growth.

As always, if you want my spreadsheet, drop me a line via e-mail with the name of this post. My e-mail address is my first name (mike), my last name (kimel – with one m only), and I’m at

(Rdan…post was modified at 10 am to include the link to Altig’s post)

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Optimal Tax Rates for Generating Economic Growth According to Barro-Sahasakul Tax Data

By Mike Kimel

Optimal Tax Rates for Generating Economic Growth According to Barro-Sahasakul Tax Data

This piece is a bit more wonky than what I normally post.

I recently re-read “Macroeconomic Effects from Government Purchases and Taxes” by Barro & Redlick. I was struck by how different the conclusions they make about taxes are from what you get if you simply make a bar chart of the top marginal rate at any given time versus the growth rate over the next year.

Now, obviously, Barro & Redlick take a completely different approach… but at the bottom of everything is the data set they use (see Table 1 of the above referenced paper and this explanation of the “Barro-Sahasakul” data set). To cut to the chase, they use estimates of the average marginal tax rates paid by taxpayers rather than the top marginal rate that I used in the bar chart referenced above. Their overall marginal rate is made up of not just federal tax rates, but also social security tax rates, and even estimates of the state tax rates. It should be noted the Barro is an average rate, and since the average includes non-filers (who pay zero), the Barro rate is often well below the top marginal rate. The top Barro rate is 41.8% which occurred in 1981 (compared to top marginal rates of 90%+ from 1951 and through 1963). The Barro rate is also not correlated with the top marginal income tax rate (correlation going back to 1929 is -30%).

A lot of work clearly went into producing this overall marginal rate (I’m going to call it the “Barro tax rate” for simplicity). But does it explain economic growth rates any better than the top marginal rate?

I ran a quick and dirty regression…

Growth in real GDP from t to t+1 = f(Barro Tax Rate, Barro Tax Rate Squared, Top Marginal Income Tax Rate, Top Marginal Income Tax Rate Squared)

Data ran back to 1929, the first year for which real GDP was computed by the BEA. Top marginal rates came from the IRS Statistics of Income Table 23. And the Barro Tax Rate came from Table 1 of the Barro & Redlick paper. Since Barro rates are computed only through 2005, that’s when the analysis stops.

Results were as follows:

Figure 1

(Note… the errors got big during leading up to WW2, but I don’t think that invalidates this quick and dirty look.)

Here’s what I get out of this:

1. There is definitely a quadratic relationship between tax rates in one period and real economic growth the next.
2. If you’re going to pick either the Barro rate or the top marginal income tax rate, go with the latter. Its clearly better at explaining economic growth rates.
3. There may be something to be said about using the Barro rate and the top marginal income tax rate together. They do explain different things.

If you compute the “optimal tax rate” – the rate that maximizes economic growth implied by the regression – you get a Barro rate of 25% and a top marginal income tax rate of 64%. The optimal Barro rate was last seen in 1966, when the top marginal rate was 70% and the bottom rate was 14%. I’m guessing from this, and from looking at the Barro rate series, that this would imply that if you want to maximize growth, the top rate should be raised to about 64% and the tax burden on folks at the lower end of the income scale should be lowered. I’m not sure Barro would be pleased with these results.

I may return to this, but my next post should be the next in the series on GDP growth and the S&P 500.

As always, if you want my spreadsheet, drop me a line with the name of this post. I’m at my first name (mike), my last name (kimel – with only one m) at BTW… this spreadsheet contains a lot more wonky goodness!

Thanks to Sandi Saunders for getting me started wading through this particular pile of weeds.

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More on Illinois’ income tax increase –thinking about globalization

by Linda Beale

More on Illinois’ income tax increase –thinking about globalization
crossposted with Ataxingmatter

As states continue to face difficult times and vulnerable residents unemployed by the Great Recession come to the end of their ropes with the last of their unemployment support checks (those unemployed for 99 weeks don’t get any more help under the latest extension), the rhetoric continues to escalate.

As I noted in my last post on Illinois’ decision to increase its personal and corporate income tax rates (See Illinois Senate Bill 2505, signed into law by Gov. Quinn on Jan. 13), tax increases–especially those that require people and companies of wealth and power to kick in a fairer share of the tax burden–may well make sense even as the country deals with the continuing fallout of the banksters’s binge of casino speculation.  Governor Quinn noted when signing the Illinois legislation that the tax increase was need to stave off fiscal insolvency.   The 5% individual income tax rate applies until January 2015, at which time the rate reverts to 3.75% for ten years and then 3.25% after 2025.

The right wing’s preferred solution– to see the states fire public employees or at the least reneg on their earlier commitments to fund pensions (which generally permitted them to hire highly skilled employees at lower wages than would otherwise have been possible)– would only make grave matters much worse. There are important programs to be funded in the states, and ultimately a higher tax burden that is allocated to those who can best pay it may be the best solution.  Management efficiencies need to be undertaken, and wasteful spending and corruption stifled, but in many cases those savings are relatively small.  The “no new taxes” mantra that has dominated public discourse under the Chicago School thinking has kept states from dealing forthrightly with these issues for decades.

Wisconsin’s new governor, right-winger Scott Walker, is a perfect illustration of the zany rhetoric and gamesmanship being played about tax matters all across this country.  He has said he would spurn federal stimulus money and ditch a planned high-speed rail line between Madison and Milwaulkee.  See James warren, Wisconsin Sounds Off, but Misses the Point, New York Times, Jan 15, 2011.  High speed rail is the wave of the future, and the US needs to catch that wave soon or be left behind.   Walker’s rhetoric here seems designed to please wealth and power (and the kooks in the “tea party” who are foolish enough to think that federal monies for infrastructure is a waste of “their” tax money), but move the state in the opposite direction from where it needs to go.  Walker has also gone on the air in a campaign intended to take advantage of corporate dislike of the Illinois tax hike, inviting corporations to “escape to Wisconsin.”

James Warren’s piece in the Friday New York Times challenges that sentiment.  Seems that the Illinois personal rate (5%) is probably less than taxation under the progressive scale of 4.6% to 7.75% in Wisconsin.  And if Caterpillar or some other big corporation were to move to Wisconsin, it would face a higher rate of 7.9% compared to the 7% rate passed for Illinois.    So Walker’s rhetoric is just that–trying to make hay out of the mere fact that Illinois increased its tax rates.  As Warren points out, politicians need to start thinking about what is good for the region and “not just poach others’ enterprises”.  

We need to think strategically, as globalization has made it much easier for companies to move to greener pastures–not just other states, but out of the states.  Congress could help that by eliminating the provision in the Code that permits companies to move active business assets abroad without paying tax on the built-in gain.  In fact, Congress ought really to consider revamping the entire reorganization provisions in the Code.  We have seen that too big to fail banks are costly for us.  Rather than aiding consolidation of companies through nonrecognition provisions, what if we made reorganizations more difficult and costly?  Combine that with a renewed anti-trust vigor, and encourage smaller businesses to stay in this country.  Localvore could take on a new meaning.

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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.

Figure 1

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.


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The Tax Rate that Maximizes Economic Growth, Part 2… With Tax Burdens Too

by Mike Kimel

The Tax Rate that Maximizes Economic Growth, Part 2… With Tax Burdens Too!Cross posted at the Presimetrics blog.

This post continues my look at the relationship between taxes and growth (what I modestly called the “Kimel curve”), which I will continue expanding on over a series of posts. Today I want to look at marginal rates, effective tax burdens, and how each or both affect growth rates. As an added bonus for non-economists and folks who don’t deal with statistics on a daily basis, I will also expand a bit on regression analysis and the process of building a rigorous “econometric model.” (Some basic material appeared at the Presimetrics and Angry Bear blogs).

To begin… its no secret that marginal tax rates don’t always have all that much to do with the amount that taxpayers actually pay. This is especially true for folks with extremely high incomes, particularly if a big chunk of their income doesn’t come with a W-2 attached. (Don’t take my word for it – I’ll give you a number later in the post.)

So, while the Kimel curve equation I provided last week dealt with the effect of the top individual federal marginal tax rate on economic growth, this week I want to throw the federal “tax burden” into the mix. The tax burden is simply the percentage of income that actually gets paid in taxes, which we can calculate as the personal current federal taxes divided by personal income. The former comes from line 2 of NIPA Table 3.2. The latter came from line 1 of NIPA Table 2.1.

(If you’re new to my posts, the NIPA tables, or National Income and Product Accounts tables, are computed by the the Bureau of Economic Analysis of the Commerce Department, the agency responsible for computing GDP. They also keep track of a lot of other interesting data about the US economy.)

Real GDP comes from any number of tables on the BEA website – let’s just pull ‘em from here this time around. And of course, we need top individual marginal tax rates IRS’ Statistics of Income Historical Table 23.

Before we go on, let’s just note that the correlation between the tax burden and the top marginal rate from 1929 to 2008 is 4.5%, which is to say, pretty close to zero.

Now, I’m setting up a simple model of growth as follows:

Growth in Real GDP, t to t+1 = B0 + B1*Top Marginal Tax Rate, t

+ B2*Top Marginal Tax Rate Squared, t

+ B3*Tax Burden, t

+ B4*Tax Burden Squared, t

As I mentioned in the previous post, I’m throwing in the X and X squared terms to account for the fact that the effect of variable X on growth rates can change as X rises or falls. For example, maybe when tax rates are low, increasing taxes has only a small effect on growth, but as tax rates rise, further increases in those tax rates can have a very big effect on growth. I’m also fitting the model using a regression. If none of this makes sense, or you don’t remember how to interpret a regression, please take a look here again.

OK. So we let it rip, and get this ouput:

Figure 1, Regression 1 Output

So now we can just go ahead and compute the optimal tax rate and optimal tax burden, right? Well, not so fast. Just because we ran a regression doesn’t mean its any good. Last week we discussed some of the diagnostics you can find in the output above, but what I didn’t mention is that you really should look at the error terms of the regression as well. The errors, or residuals, in a “good” regression look like they came out of a shotgun – they don’t have any obvious patterns. Patterns in the residuals from a regression mean something is systematically wrong with the way the model being estimated fits the data, and if something is systematically wrong, it can (and should be) fixed. Worse still, one of the mathematical assumptions of regression analysis is that you didn’t specify a model that has something systematically wrong with it, which means that the output of a regression is misleading in various ways if you there is something systematically wrong with the model. (In practice, you will never see a perfect shotgun pattern, but you want to shoot for something close.)

But, errors in this regression do show a pattern:

Figure 2, Residuals Diagram 1

As the graph above shows, the errors tend to be pretty big in the beginning, and they tend to shrink over time. Since OLS regressions maximize the sum of squared errors, big errors early on mean the model is putting an overemphasis on the early years. Additionally, the correlation between the errors in one period and the errors in the next are about 50%; big errors tend to be followed by big errors, small errors by small errors, positive errors by positive errors, and negative errors by negative errors. Now, if you’re in a Ph.D. program where showing you have chops is a big deal, you’ll deal with this using any number of cool sounding techniques, each of which is built on a number of assumptions that are truly horrifying if you stop and think about it. But if you’re long gone from academia, and spent a decade post grad school working with these cool sounding techniques, you might have gotten smart and comfortable enough to have rediscovered the KISS rule. If that’s the case, you’ll take a look a second look at the residual graph, and conclude a few things:

1. The 1929 – 1932 recession was a major outlier early on

2. The early part of the US’ involvement in WW2 (starting in 1940- think lend lease, and other gov’t expenditure) is a major outlier

So you might, as a first pass, create a couple of dummies – one for the 1929 – 1932 recession, and another for “major US involvement in WW2” aka 1940 – 1944. A dummy variable takes a value of 1 or 0, which amounts to “yes the condition is met” or “no the condition is not met.”

Rerun the regression with those dummies and you get a regression with these residuals:

Figure 3, Residuals Diagram 2

I’ve kept the scale in this graph the same as on the other. Notice… most of the big errors have dropped away, much of the “heavy early on” pattern is gone, and the correlation between errors in one period and errors the next has dropped quite a bit. A simple fix, and we’re good enough to move on for now. Here’s the output:

Figure 4, Regression 2 Output

Notice… the new model (using tax data and a couple dummies alone) explains about 57% of the variation in the growth in real GDP. Also… the tax burden is not significant. (The P-values are too far above a “significant” value such as 0.01, 0.05, or 0.1 depending on how strict you want to be, or how many asterisks you want to put in your paper.) The two dummies, not surprisingly, are significant; growth was slower than the model would otherwise predict during the 1929-1932 recession/depression, and faster than the model would otherwise predict during the 1940-1944 period when the US gov’t ramped up its involvement in the War. (BTW… anyone thinking that war is a way to promote economic growth should consider we’ve had a number of other wars during this period. What was unique about 1940-1944 was the degree to which the government decided to run the economy.)

The top marginal tax rate and top marginal rate squared are both significant, and we can use them to compute a top marginal rate that maximizes growth (at least in this model). That figure is (drumroll): 62%. Pretty close to the 67% we computed using last week’s model. And nothing like what Congressman Ryan is likely to glean from reading Atlas Shrugs…

By the way, the list of things I want to look at in future posts, in no particular order, includes:

1. Is the post-WW2 (or post 1963, or post 1981, or post 1986) era different?

2. What is the effect of different demographic groups?

3. Does this work for other forms of growth?

4. Does this type of model always provide an “optimal” result? Does this apply to states? What about other countries?

5. What about other types of taxes, such as corporate taxes? Should we focus on the tax rates paid by middle income earners rather than (or in addition to) tax rates paid by folks at the top?

6. What about the national debt? Or government spending? Or other variables?

7. Does the political party of the President or the Congress matter?

8. What is the effect of the Fed on all of this?

9. How do we know whether this is all merely correlation or is there any sign of causality going on here?

10. Given that this isn’t rocket science, why aren’t “real economists” doing stuff like this? (I would be derelict in not mentioning this paper by Pietro Peretto at Duke, which provides a model showing that “the endogenous increase in the tax on dividends necessary to balance the budget has a positive effect on growth.”)

This seems to have the potential to become the Mike Kimel full-employment act, though sadly, it isn’t my job and it doesn’t pay. Running regressions is quick and easy, and interpreting them (and spotting pitfalls) is second nature to someone who works with them on a daily basis, but pulling data, sorting it and organizing, and even just thinking about that data is very, very time consuming. So please have some patience as its going to take a while to get somewhere. Also… I will probably have occasional posts on other topics in the meanwhile as well.

All that said, one of my goals with these posts is to give non-economists a view of the way this sort thing is (or should be) done in the profession. If I’m not explaining enough, or not keeping it intuitive enough, let me know.

Finally, as always, my spreadsheets are available to anyone who wants ‘em. This one has some cool info that I didn’t get a chance to use in this post, including corporate income, corporate taxes, and some demographic information. If you want to play along at home, or even move ahead of my posts, drop me a line and I’ll send you what I have. Até à próxima, pessoal.

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A Simple Explanation for a Strange Paradox: Why the US Economy Grew Faster When Tax Rates Were High, and Grew Slower When Tax Rates Were

by Mike Kimel

A Simple Explanation for a Strange Paradox: Why the US Economy Grew Faster When Tax Rates Were High, and Grew Slower When Tax Rates Were Low
Cross posted at the Presimetrics blog.

If you are familiar with my writing, you know that for years I have been covering the proverbial non-barking dog: the textbook relationship between taxes and economic growth, namely that higher marginal rates make the economy grow more slowly, is not borne out in real world US data.

Sure, there are a whole raft of academic studies that claim to show just that, but all of them, without fail, rely on rather heroic assumptions, and most of them throw in cherry picked data sets to boot. Leaving out those simple assumptions tends to produce empirical results that fail to abide by the most basic economic theory. This is true for data at the national level and at the state and local level.

Making matters more uncomfortable (and thus explaining all the heroic assumptions and cherry picking of data in the academic literature) is that the correlations between tax rates and economic growth are actually positive. That is to say, it isn’t only that we do not observe any relationship between tax rates and economic growth, in general it turns out that faster economic growth accompanies higher tax rates, not lower ones, and doesn’t take fancy footwork to show that. A few simple graphs and that’s that.

Now, obviously I sound like a lunatic writing this because it goes so far against the grain, but a) I’ve been happy to make my spreadsheets available to any and all comers, and b) others have gotten the same results on their own. Being right in ways that are easily checkable mitigates my being crazy (or a liar, for that matter), but it doesn’t change the uncomfortable fact that data requires a lot of torture before conforming to theory. And yet, that’s the road most economists seem to take, which explains why economics today is as useless as it is. It also speaks poorly of economists. The better approach is come up with theory that fits the facts rather than the other way around.

I’ve tried a few times to explain the relationship that I’ve pointed out so many times, but I never came up with anything that felt quite right. I think I have it now, and it’s very, very simple. Here goes.

1. Economic actors react to incentives more or less rationally. (Feel free to assume “rational expectations” if you have some attachment to the current state of affairs in macro, but it won’t change results much.)
2. There is a government that collects taxes on income. (Note – In a nod to the libertarian folks, we don’t even have to assume anything about what the government does with the taxes. Whether the government burns the money it collects in a bonfire, or uses it to fund road building and control epidemics more efficiently than the private sector can won’t change the basic conclusions of the model.)
3. People want to maximize their more or less smoothed lifetime consumption of stuff plus holdings of wealth. More or less smoothed lifetime consumption means that if given the choice between more lifetime consumption occurring, with the proviso that it happens all at once, or a bit less lifetime consumption that occurs a bit more smoothly over time, they will generally prefer the latter. Stuff means physical and intangible items. People also like holding wealth at any given time, even if they don’t plan to ever spend that wealth, because wealth provides safety, security, and prestige, and for some, the possibility of passing on some bequest.

(If the first two look familiar, they were among 8 assumptions I used last week in an attempt to get where I’m going this time around. Note that I added two words to the second assumption. More on last week’s post later.)

Due to assumptions 1 and 3, people will want to minimize their tax burden at any given time subject provided it doesn’t decrease their lifetime consumption of stuff plus holdings of wealth. Put another way – all else being equal, peoples’ incentive to avoid/evade taxes is higher when tax rates are higher, and that incentive decreases when tax rates go down. Additionally, most people’s behavior, frankly, is not affected by “normal” changes to tax rates; raise or lower the tax rates of someone getting a W-2 and they can’t exactly change the amount of work they do as a result. However, there are some people, most of whom have high actual or potential incomes and/or a relatively large amount of wealth, for whom things are different. For these people, some not insignificant amount of their income in any year comes from “investments” or from the sort of activities for which paychecks can be dialed up or down relatively easily. (I assume none of this is controversial.)

Now, consider the plight of a person who makes a not insignificant amount of their income in any year comes from “investments” or from the sort of activities for which paychecks can be dialed up or down relatively easily, and who wants to reduce their tax burden this year in a way that won’t reduce their total more or less smoothed lifetime consumption of stuff and holdings of wealth. How do they do that? Well, a good accountant can come up with a myriad of ways, but in the end, there’s really one method that reigns supreme, and that is reinvesting the proceeds of one’s income-generating activities back into those income-generating activities. (i.e., reinvest in the business.) But ceteris paribus, reinvesting in the business… generates more income in the future, which is to say, it leads to faster economic growth.

To restate, higher tax rates increase in the incentives to reduce one’s taxable income by investing more in future growth.

A couple acknowledgements if I may. First, I would like to thank the commenters on my last post at the Presimetrics and Angry Bear blogs, as well as Steve Roth for their insights as they really helped me frame this in my mind.

Also, I cannot believe it took me this long to realize this. My wife and I are certainly not subject to the highest tax rate, and yet this is a strategy we follow. At the moment, we are able to live comfortably on my income. As a result, proceeds from the business my wife runs get plowed back into the business. This reduces our tax burden, and not incidentally, increases our expected future income.

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