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A Few Graphs Describing the Reagan Presidency

by Mike Kimel

A Few Graphs Describing the Reagan Presidency
Cross posted at the Presimetrics blog.

On February 6, 2011, Ronald Reagan would have been turned 100 years had he been alive. In this post I’d like to share a few graphs from Presimetrics (the book I wrote with Michael Kanell, with graphs and illustrations by Nigel Holmes) which hopefully will give you an idea of how Reagan did as President.

Figure 1 below shows growth rates in real GDP per capita for every administration beginning in 1929, the first year for which the BEA provides data:

Figure 1.

(Note – FDR I was through 1940, FDR II was most of the War years. We broke up the sample that way because there are a lot of people who either out of ignorance or some odd desire to spread BS insist that under FDR, the Great Depression got worse or that growth only picked up with the start of WW2. Either way, I’ve found it is safe to use a person’s pronouncements about FDR as a signal about the accuracy of other things they choose to share. Also note – the remaining graphs in this post focus on the period from 1952 – 2008, as that was the main focus of the book from whence they come.)

As the graph shows, when it comes to real economic growth, Reagan did better than other Republicans. But growth under Reagan was also slower than it was under most of the Democrats since 1929. While the growth rate under Reagan is far less impressive when that last detail is mentioned, it is less impressive still if you remember the definition of GDP:

GDP = Private Consumption + Private Investment + Gov’t Consumption & Investment + Net Exports.

Put another way – if the government borrows a lot and spends what it borrows, it will boost GDP, and that in turn causes real GDP per capita growth to increase. And that is precisely what happened under Reagan:

Figure 2

As we note on page 50 of Presimetrics, early in his term Reagan noted:

Our national debt is approaching $1 trillion. A few weeks ago I called such a figure, a trillion dollars, incomprehensible, and I’ve been trying ever since to think of a way to illustrate how big a trillion really is. And the best I could come up with is that if you had a stack of thousand-dollar bills in your hand only four inches high, you’d be a millionaire. A trillion dollars would be a stack of thousand-dollar bills sixty-seven miles high. The interest on the public debt this year we know will be over $90 billion, and unless we change the proposed spending for the fiscal year beginning October 1st, we’ll add another almost $80 billion to the debt.

We also noted this:

By the time he left office, the national debt, which had been “approaching $1 trillion” had more than doubled to $2.7 trillion, and the stack of thousand-dollar bills that had been 67 miles high was now 193 miles high and rising fast. Interest payments on the debt—“over $90 billion” in 1981—were just shy of $200 billion in Reagan’s last year in office.

Using more relevant measures, real debt per capita (in 2008 dollars) grew from about $10,620 in 1980 to $19,860 in 1988, and from 32 percent of GDP to 51 percent of GDP over the same period. However you slice it, Reagan’s profligacy bore no resemblance to his promises.

All that increased debt creates an obligation to taxpayers, who will, after all, have to repay that debt eventually. One measure we used in the book looks at the impact of that debt obligation – that is, the real net disposable income (i.e., income after current taxes less the increase in the debt per capita):

Figure 3

When you take into account future obligations to pay back debt, Reagan no even longer looks as good as Jimmy Carter. A rising tide, fueled by debt, wasn’t so great at lifting at most people’s boats… unless compared to the tide generated during other Republican presidencies.

But concluding that Reagan was someone to emulate means more than just ignoring the fact that he underperformed most Democrats on economic issues. It also requires means ignoring the fact that Reagan also didn’t particularly care about Republican ideals either, not even the ones he parroted frequently and loudly. For instance, a big source of state and local funding is the federal government. Presidents who truly want to move power away from Washington generally try to increase the transfers from the Federal government to state and local governments. But that is most definitely not what Reagan did:

Figure 4

So what did Reagan excel at, other than outperforming other Republicans on economic issues? Well, it turns out that he was very, very good for the public mood:

Put another way, some Presidents are better with reality, some are better with perception. Reagan was better at the latter.

And if I may, a quote from the book (page 178) about another way Reagan’s administration stood out:

And it’s not just the quantity of crime in Washington that is noteworthy. Some of the plots these folks engage in are—let’s call it like it is—cartoonish. Consider, for instance, the Iran-Contra affair, a convoluted scheme by which American weapons were sold to Iran in exchange for Iran’s exerting influence on Hezbollah, Iran’s terrorist buddies in Lebanon, to release American hostages. (Hezbollah, not incidentally, is thought to be the group responsible for the 1983 U.S. barracks bombings in Lebanon, in which 220 U.S. Marines and 79 international peacekeepers were killed.) To bring the complication of the scheme to the level worthy of a comic-strip villain, much of the loot resulting from the sale of American weaponry to an extremely hostile country would go toward funding the Contras, a rebel group in Nicaragua, thus providing the Contras with a much-needed source of funding that did not involve drug trafficking. A number of administration officials were convicted for their role in the affair. This included the secretary of defense (that would be our friend Weinberger, previously featured in Nixon’s White House), as well as two successive national security advisors (Robert McFarlane and John Poindexter).

The folks who believe, who truly believe, won’t let facts stand in the way of their faith. And the cult of Reagan will continue to live on. Anyone who says Sarah Palin is no Ronald Reagan don’t have the facts on Ronald Reagan.

At this point, I’d normally give you my sources. Since everything here comes from Presimetrics, you’ll find the source for all the data and all the quotes there.

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Tax Rates v. Real GDP Growth Rates, a Scatter Plot

by Mike Kimel

Tax Rates v. Real GDP Growth Rates, a Scatter PlotCross posted at the Presimetrics blog.

This post was submitted by Kaleberg.

In this post, I will look at the relationship between top marginal income tax rates and real GDP growth using a scatter plot.

I am inordinately fond of scatter plots. The nice thing about a scatter plot is that you can present a lot of data in a fairly small space, so rather than just comparing tax rates at time period t against real GDP growth rates from period t to t+1, I can also show real GDP growth rates from period t to t+2, from t to t+3, and from t to t+4. (I.e., the scatter plot shows tax rates at any given time, and the growth rates over one year, two years, three years, and four years.)

The vertical axis is the GDP growth rate, the geometric average for multiple years. The horizontal average is the top marginal tax rate. The one year comparison is shown in dark blue, and each subsequent year is shown with a paler color and a smaller marker.

Figure 1

Data is for the period from 1929 to 2009 (i.e., all the years available from the BEA.)

Lower top marginal tax rates seem to limit economic growth with a rate of about 60% seeming to divide the restricted growth phase from the unrestricted growth phase. There might be a little falloff when the tax rate passes 90%, or there might not. There are lackluster growth rates associated with higher and lower top marginal tax rates. Mediocre growth is not all that hard to achieve. Finally, if high top marginal tax rates had a multi-year effect, we’d see a distinctive pattern in paler blue in this chart, but we don’t. The paler blue, longer term comparisons seem bounded by the single year effect.

The data used in this scatterplot is the same data used to build the bar chart in this this post.

Note from Mike Kimel – as always, if you want the spreadsheet (I have a copy of Kaleberg’s work), send me an e-mail. I’m at my first name dot my last name at, and my first name is “mike.” My last name has only one “m.”

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How Tax Rates Affect Investment and Consumption – A Look at the Data

by Mike Kimel

How Tax Rates Affect Investment and Consumption – A Look at the Data
Cross posted at the Presimetrics blog

This post looks at how changes in the top marginal tax rates affect peoples’ decisions on how much to consume and invest. Ask a libertarian or conservative economist and the answer is obvious – raising tax rates on high income individuals dissuades them from doing productive things – that is to say, it causes them to cut back on working and investing. In the interest of avoiding strawmen at all costs, many libertarians and conservatives might assume that a hike in the tax rates on such individuals can also cause them to cut back on consumption. After all, if tax rates are raised high enough, perhaps people won’t have enough left over to consume as much as they otherwise would. However, the reduction in voluntary activities that take effort (i.e., work, investment) should easily swamp the reduction in consumption, some amount of which is needed for simple survival. Put another way, as tax rates rise the ratio of investment to consumption should fall.

That right there is what’s known as a testable implication, and there’s data aplenty for that purpose. But before we move on to testing this, let me note that the first paragraph actually provides a second, far more familiar testable implication, namely that higher tax rates will generally lead to slower economic growth. While that particular narrative seems to be widely believed even by non-economists, it certainly isn’t borne out by US data from the last eight decades or so:

Figure 1

(Figure 1 first appeared in this post.)

The graph shows that, at least until top marginal tax rates get somewhere above 50% (a bit more precision available here), increasing those rates does not correlate with slower economic growth, but rather with faster increases in real GDP. In fact, raising top marginal tax rates doesn’t have many of the effects many people seem to expect (And incidentally, its worth noting that state level data also produces results the Chicago school and most libertarians don’t expect.)

Now, the reason I mention the data’s irresponsible failure to abide by conservative and/or libertarian philosophies when it comes to tax rates and growth is because I think the relationship between tax rates and economic growth can be at least partly explained by the relationship between tax rates and investment. As I stated here, in my opinion, higher tax rates can lead to more investment. After all, one way a person who owns a business (large or small) can reduce the taxes they pay on profits is to reinvest the profits, which in turn leads to faster economic expansion. Furthermore, the incentive to avoid taxes and reinvest increases as tax rates increase. Of course, at some point, tax rates get high enough to encourage individuals to reinvest even though the “benefits” from more reinvestment, at the margin, are negative. Where that happens, I don’t know, but based on Figure 1, my guess is that it takes a top marginal tax rate above 50%.

So… here’s what libertarians and conservatives should expect to see: as the top marginal tax rises, the ratio of investment to consumption falls.

Here’s what I expect to see: the relationship between the top marginal tax rate and the ratio of investment to consumption is somewhat curved. For top marginal tax rates between 0 and some point X (where X > 50%), an increase in the top marginal rate leads to an increase in investment/consumption. After that, as the top marginal rate rises, we should investment/consumption level off, and for even higher marginal rates, investment/consumption should fall.

So… using top marginal rates from the IRS’ Statistics of Income historical table 23, and national investment and consumption figures from the Commerce Department’s Bureau of Economic Analysis’ National Income and Product Accounts table 1.1.5, we can construct this little graph:

Figure 2

It’s not a perfect quadratic curve, but it sure looks a lot more like what I had in mind than what any conservative or libertarian would expect. FYI, the correlation between the top marginal tax rate the ratio of investment to consumption for top marginal tax rates below 50% is 55%. That is to say, an increase in tax rates increases the ratio of investment to consumption when tax rates are below 50%. On the other hand, the correlation is a negative 11% when tax rates are above 50%. That is to say, increasing tax rates when they are above 50% has a (not particularly strong) negative effect on people’s “invest v. consume” decision.

Put another way – conservatives and libertarians have a very, very flawed theory of the world. At the very least it does not conform at all with historical US data. At all. Which of course has serious consequences; because that theory is somewhat dominant in the political sphere, and has been since the late 60s. The end result – slower economic growth for all of us since the late 60s. That has real consequences for real people – 310 million of us. That should have repercussions for the consciences of economists who peddle this garbage, though apparently it doesn’t.

But that’s for another post. Today, I want to remain clinical. So… what does Figure 2 mean, with respect to Figure 1? It means that, yes, at least until a certain point (somewhere above 50%), raising the top marginal rate both increases the ratio of investment to consumption and the real economic growth rate. Its not outlandish to assume that increasing investment is one of the factors that can increase real economic growth. (Worth exploring more in a post sometime in the future.) Other things matter, of course, but I think investment is up there among factors that matter.

It also means that since we’re keeping tax rates at the level they’ve been for the past decade or so, we shouldn’t expect sustained rapid investment or economic growth any time soon. Don’t expect the 60s or even the 70s again any time soon – we’re in end of the 80s and 00s level taxation, and over the long haul, we’re in for that sort of growth too.

A few closing remarks:

1. 1. This post was partly inspired by an interview I had with George Kenney of Electric Politics. It was a really useful and interesting conversation for me, in part because he pressed me a bit past my comfort level. I understand he’ll have that interview up in a few weeks.

2. 2. I’ve noticed that a number of the graphs I’ve been putting up are not so much quadratic as a bit bimodal. I have been thinking about that for the past few days, and I think that will be my next post on this “kimel curve” approach to world I’ve been following lately.

3. 3. Please, please, please, please, if you object to something in this post and are planning to bring up Romer and Romer, read this first to save me from being embarrassed on your behalf.

4. 4. As always, my spreadsheets are available to anyone who wants them.

5. 5. Between the time I finished my spreadsheet and the time I wrote this post, I read this blurb from Tyler Cowen’s next book. It might be uncharitable of me, but my first thought was to wonder about the odds a libertarian professor would add two and two together, and whether he could remain libertarian if he inadvertently did.

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The Data Shows that State "Beggar Thy Neighbor" Policies Don’t Work.

by Mike Kimel

The Data Shows that State “Beggar Thy Neighbor” Policies Don’t Work.
Cross posted at the Presimetrics blog.

Many states seem to believe a “beggar thy neighbor” approach to taxes works best. That is, the state with the lowest taxes will “steal” business from other states and produce the fastest economic growth. A lot of people seem to believe it works. The data stands in opposition to them.

States raise revenues through a variety of means – state income taxes, property taxes, fines on overdue books, etc. The Tax Foundation , which bills itself as “a nonpartisan tax research group based in Washington, D.C” and which I believe can be fairly described as generally advocating lower taxes in general, provides a file showing the the overall state tax burden and per capita income for every state for each year from 1977 to 2008.

So here’s what I did after the fold.

I took the per capita income, adjusted by the CPI-U, and got the real per capita income, which I then used to compute the percentage growth (or shrinkage) in real per capita from one year to the next for every state and every year from 1977 to 2007. I did the same thing for the US, getting the US average growth in real per capita income from t to t+1 for every year from 1977 to 2007, and subtracted that amount from the state growth rates. This provided the amount by which each state grew (or shrunk) faster (or not) than average, each and every year from 1977 to 2007.

The next step was to take the state tax burden for each state for each year, and subtract from that the average state tax burden for that year. Result: 1,550 combinations of (tax burden for a state in a year less average tax burden for all states for the same year) on one hand, and (growth in real per capita income from one year to the next for a state in a year less the average growth in real per capita income over the same period). In other words, a comparison between being above or below average on tax burdens and being above or below average on real per capita income growth.

Here’s a histogram:

Figure 1

The graph is a bit busy, but let me interpret it. The first bar is for observations for which the tax burden was between 4.25% and 3.75% below (i.e., more 4.25% below, or less than or equal to 3.75% below) the average state tax burden for that year.(sentence updated….dan)
There are 7 observations (figure in purple at the bottom), and the median growth rate for those 7observations was 1.65% slower than the average for that year.

What the graph tells us is that there seem to be two maxima; going the beggar thy neighbor route can lead to faster than average growth, and there is a sweet spot: keeping tax burdens at about 2.5% below average has, historically tended to be associated with growth rates in real per capita income 0.47% above average. However, get too far away from that sweet spot and the doo-doo really hits the fan. The states that keep the tax burdens the lowest also produce the slowest growth, on average.

For states that don’t take the beggar thy neighbor route (i.e., they take a tax and spend approach), things generally go a little better. The sweet spot there – keeping tax burdens about 2% above average – produces growth rates about 0.67% above average. And getting too far away from that sweet spot doesn’t seem to lead to catastrophic outcomes either.

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. This post has an analogous histogram showing the relationship between top marginal tax rates and growth in real GDP for the US from 1929 to the present. This one – the first of several to do so – computes the growth maximizing tax rate for the US economy. I plan to go back to work on the national data analysis in the coming posts, but everyone needs a break now and then.

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 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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Top Marginal Income Tax Rates & Real Economic Growth, a Bar Chart

by Mike Kimel

Top Marginal Income Tax Rates & Real Economic Growth, a Bar Chart
Cross posted at the Presimetrics blog.

The chart below shows tax rates on one axis and the growth rates in real GDP that accompanied those tax rates on the other:

I broke the tax ranges into 5 percentage point increments centered around intuitive numbers (30%, 35%, etc.). Growth rates are the median observed for each range. For ranges which did not occur in the real world, growth rates are left blank.

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, the graph uses data starting in 1929.

Consider 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 data might be useful before going on.

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The top marginal income tax rate should be about 65%…

by Mike Kimel

Cross posted at the Presimetrics blog.

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:

Figure 1

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

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:

Figure 3

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

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.

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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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Why the Economy Stubbornly Insists on Growing More Slowly When Taxes are Lower

by Mike Kimel

An Economic Theory That Uses Micro Forces to Explain Macro Outcomes: Why the Economy Stubbornly Insists on Growing More Slowly When Taxes are Lower

Cross-posted at the Presimetrics blog.

I’ve been writing for years about the fact that a basic piece of economic theory does not apply to real world US data: unless one engages in the sort of assumptions that can justify eating ceramic plates as a cure for leprosy, there is simply no evidence that lower taxes lead to the good stuff we’ve been led to believe over non-cherry picked data sets. Recent examples include this look at the effect top federal marginal rates on various measures of growth, this look at the effect of top federal marginal rates on tax revenues, a different look at federal marginal rates and growth, and this look using state tax levels. I’ve also shown that effective tax rates also have fail to cooperate with theory when looking over the length of presidential administrations – examples include myriad posts and Presimetrics, the book I wrote with Michael Kanell.

I think the reason a lot of people have trouble accepting this is that they see some sort of conflict between this macro fact and and what seems to be a self-evident micro truth – if tax rates get high enough, people will work less. Now, such micro-macro conflicts have existed in the past, and are certainly aren’t unique to economics. One obvious example we all live with is that to each of us, from where we’re standing, the Earth does a pretty good job of appearing to be flat, and yet we know that its actually round(ish). For most applications, from running a marathon to building a house to making toast, assuming that the earth is flat doesn’t hurt, and even simplifies matters. That is to say, for most applications facing critters roughly our physical size, a flat earth is a good model. On the other hand, we’d be much impoverished by sticking to that model at all times, as we’d lose out on satellites, our understanding of weather and geology, a great deal of transoceanic shipping, and Australia.

The same thing is true when it comes to the economy – failing to understand and account for the dichotomy between micro and macro truths is harmful. It has cost us, all 6.8 billion of us, economic growth and wealth, which is to say, it has cost us in quality and length of life. But nobody is trying to explain that dichotomy, in part because so few people see it. There is a profession that should be trying to explain this dichotomy, and that is the economic theorists. However, they seem to be pretending the data isn’t there, so waiting around them to explain it means more loss of quality and length of life. So let me take a crack at it.

In addition to explaining the real world reasonably well, a good theory, in my opinion, should not rely on crazy assumptions. After all, a theory that doesn’t make any sense simply isn’t going to get used even in the unlikely event that it works. So I came up with a theory that relies on only a few assumptions, all of which are sane and which hew pretty close to the real world. My assumptions are these:

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.)
1a. The probability that an economic agent will choose to do any work is inversely related the tax rate. At 100% tax on income, work drops, but not to zero – many of us do some charity work, after all, for which we aren’t compensated at all. On the other hand, not everyone is going to work even if tax rates drop to 0%.
2. Economic actors do not have perfect information about the economy, and are not homogeneous. They have different skillsets and different size, and that limits their opportunities at any given time. On the other hand, some economic actors are sufficiently similar to other economic actors that they could occupy similar economic niches, albeit they wouldn’t necessarily produce identical output.
3. Economic actors come in different sizes. Small players cannot compete with large players on economies of scale. (I get really irritated with the oft-repeated assumption that everyone is the same size, or that any unemployed person can walk into a bank and borrow $1.2 billion to build a chip fab.)
4. Economic actors are at least somewhat risk averse.
5. Many parts of the economy are characterized by economies of scale. At some point those economies of scale may reverse themselves, but economic actors rarely work at points where the diseconomies of scale have become strong.
6. Many parts of the economy are characterized by lumpiness. If an economic player is into hot dog stands, for instance, it can buy one hot dog stand, or two, or three, but it can’t buy 2.7183 hot dog stands.
7. Among the the pieces of the economy characterized by economies of scale and lumpiness are tax evasion/avoidance, which economic actors will engage in due to assumption number 1. That is to say, $1,000 spent on attorneys, accountants and economists in the course of a $100,000 project will gets you less tax evasion/avoidance than the same amount (or even a proportionately larger amount) spent in the course of a $100,000,0000 project.
8. There is a government that collects taxes. (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.)

I trust there aren’t any assumptions on this list that seem particularly heroic or which contradict the real world in any important way. Additionally, I don’t think there’s anything here that a conservative or libertarian would object to either. So I figure we’re good to go.

Let’s focus on one particular economic actor (or entity or firm or player), and let’s put some numbers down for simplicity of keeping track of going on. Say this one actor has $100 million (whether debt or equity is irrelevant to the model) which it can invest – and it can invest all, part, or none of that $100 million. To keep things really simple, say this actor must decide how to allocate its funds between a single $100 million investment and five $20 million investments, each of which has an expected return of X% a year before taxes.

Essentially, this player has four forces acting upon its decision making process.

1. Risk aversion. That makes the actor lean away from the one big project and toward some number of the smaller projects, both to avoid having all its eggs in one basket, and because by avoiding the one big project it doesn’t have to invest the full $100 million. Instead of investing in five small projects, for instance, it can invest in four at a cost of $80 million, and keep $20 million cash.
2. Economies of scale. That makes the actor lean toward the one big project over the five smaller projects.
3. The marginal tax rate. If its too high, that actor will simply sit on its hands. If not, it will invest some amount of its $100 million.
4. Economies of scale in tax avoidance/evasion. That tends to lead toward the one big project over the five smaller projects, since the net benefits of tax avoidance from one big project exceed the net benefits of tax avoidance from several small projects.

Now, forces 1 and 2 push in opposite directions. Force 3 is orthogonal to 1 and 2, and force 4 is parallel to force 2. All of which means it is easy for a player who chooses to invest rather than sit on his hands, and who otherwise is evenly balanced between one large and multiple small projects (or even tilting slightly toward multiple small projects) by forces 1 and 2 to be pushed toward the one big project by force 4. Let me restate – under some circumstances, marginal tax rates are low enough not to preclude investment altogether, but are high enough that due to scale economies, the gains of tax avoidance/evasion from large projects so exceed the gains to tax avoidance/evasion from small projects to make a single large project more desirable than a group of small projects, even though the latter would have been more desirable in the absence of taxes. Furthermore, there is some positive probability that shrinking marginal tax rates reduces force 4 enough to keep this story from being true.

This follows in a straightforward way from the assumptions, and looks a lot like real world situations. I assume its not objectionable even if you’re fortunate not to have ever worked for a Big 4 accounting firm. But, it has important implications. See, by taking the single big project rather than the multiple small projects, our player increases economic growth several ways. These include:

1. Because of project lumpiness, by going the big project route, it has to invest the full $100 million. Had it gone the small project route, there is a positive probability that risk aversion would have led it to invest $80 million (or $60 million) instead, meaning $20 million (or $40 million) would not have been put to work in the economy.
2. It spends less on tax avoidance/evasion services with the single large project than with multiple small projects. Since these services produce a private gain but don’t actually generate output, that reduces the drag on the economy.
3. As noted previously, small players are reluctant to take on big players – sure, it happens, but in general, small players prefer to go up against other small players than against big players. (Think Walmart and the centipede game.) But small players are priced out of the big projects. So if small players find bigger guys entering their potential space, they are more likely to sit on their hands (or focus on what amounts to the smaller, more wasteful projects among options available to them, potentially forcing out the even smaller guys, etc.).

But that is one single player. In a big enough economy, there can be many, many companies and/or individuals of many different sizes in just such a situation. With 310 million people and who knows how many companies in the economy, probabilities add up. (I note that the second benefit of biasing companies toward their largest available projects goes away when you consider the whole economy. After all, while company X saves on accountants/attorneys and economists by picking the larger projects, by leaving the smaller projects to smaller players, those players will be hiring accountants/attorneys and economists as well.)

Note that relaxing a few assumptions makes it even easier to understand why US macro data shows a positive correlation between marginal tax rates and real economic growth. For instance, it isn’t difficult to imagine that the government actually does something useful (i.e., growth generating) with the some of the tax money it collects. Additionally, smaller firms are often more innovative than larger firms, even within the same space (one has to compete somehow). Our little story is one where under many circumstances, smaller firms are more likely to enter the market when tax rates rise than when tax rates fall.

Thus, this little story, while requiring only a few realistic assumptions, does something that as far as I know is unique in the field of economics: it explains why US macro data shows a positive correlation between the top marginal tax rates and economic growth for all but the most cherry picked data sets, and it does it by sticking to micro foundations. I’m sure it could be improved, but but I think its a good start. Your thoughts?

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