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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 actual 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?

Update on Dec 12, 8:32 PM – corrected typos on assumptions 3 and 5.

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

  1. Sandwichman says:

    Occam’s razor, Mike.

    A simpler explanation is that lower taxes do act as an incentive for employed people to work more hours but that there is not a direct relationship between hours worked and output. In fact, longer hours can lead to reduced output. In short, the microeconomic incentives are pecuniary but the macroeconomic results are measured in real output, not in aspirations or opportunity costs.

    • Mike Kimel says:

      I have argued in the past something, er, parallel, which is that at the margin, the private sector may not be more efficient than the public sector at generating output based on where we are right now. But that’s another story.

      The problem with ” lower taxes do act as an incentive for employed people to work more hours but that there is not a direct relationship between hours worked and output. In fact, longer hours can lead to reduced output.” is that while this is true at some point, I’m not sure we can conclude that we’re at that point. Would we really generate more output with a 35 hour workweek? But that’s all I have on this right now. I feel I’m missing an important implication of your comment, so let me sleep on it.

  2. Sandwichman says:

    “Would we really generate more output with a 35 hour workweek?”

    I would say a very definite “yes”, based on projection from the historical trend up to mid-20th century. The New Deal, World War II and the Cold War brought in very substantial changes to the compensation structure for labor and to the policy priorities of organized labor. These changes effectively derailed a “persistent and significant” historical trend of progressive decline in the duration of working time. That trend reflected a response to the effects of technology, in terms both of productivity and the value of leisure.

    Just as an example, projecting the 1909-1957 trend forward to 2009 suggests that something like a 32-hour workweek with five weeks annual vacation would be optimal for output.

  3. Professor Plum says:

    You’re math isn’t really up to the standards of economic proofs…

    “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″

    Now since orthogonality requires zero correlation in mathematical terms (literally, that is the definition) and parallelism requires perfect correlation (again, a definition) and the orthogonal vector to any parallel line is by definition orthogonal with all other lines parallel, we are left with the odd scenario that Force 4 (the value of economies of scale in tax avoidance) has zero correlation with Force 3 (marginal tax rates).

    This is fairly easy to disprove as the value of tax avoidance is by definition zero when marginal tax rates are zero (zero times anything is zero) and positive when marginal tax rates are positive. Hence there is correlation and your theory (or at least the pseudo-mathematical explanation) is worthless.

    Go back to your day job.

    • Mike Kimel says:

      Wow. I go through the effort of telegraphing how I would respond to this particular objection (“For most applications… assuming that the earth is flat doesn’t hurt, and even simplifies matters….. On the other hand, we’d be much impoverished by sticking to that model at all times” – you didn’t think that was a random example, did you?) and they still show up.

      OK. Here goes. Assume the earth is round. (We’ll stick to three dimensions, no need to bring up glomes.) The equator and, say, the tropic of capricorn are parallel. A skyscraper built on the equator can be perpendicular to the equator but avoid the tropic of capricorn altogether. On the other hand, one can put a line that goes through the earth and is perpendicular to both. With higher dimensions we have many more possibilities.

      I suspect you understood that piece of the post was metaphoric, but you clearly didn’t notice the syntactic ambiguity built in. Now go back to teaching something that isn’t true. Presumably your comment was intended to justify that.

  4. Professor Plum says:

    A skyscraper built on the equator can indeed be perpendicular to the equator and avoid the tropic of capricorn altogether. That would make perfect sense as the height (for example — could also be width, color, etc) has no impact on the Equator and therefore no impact on the Tropic of Capricorn. Zero correlation. Again, that is the definition of orthogonal.

    However, your proof requires that the value of tax avoidance have no relationship to the level of marginal tax rates. Since that is clearly false, we can conclude that your proof is false.

    You are making several errors in your analysis, the simplest one being a dependence on an accounting relationship, GDP, with “growth”. I can grow GDP by restricting economic activity (cutting imports, subsidizing exports) or by targeting savings (reducing the incentive to save) or by growing an inefficient public sector while monetizing the debt.

    You are, as Keynes best articulated, “the slave[s] of some defunct economist.” His economic theories are shyte, but he did have a gift with words.

  5. [...] at Angry Bear and Presimetrics, Mike Kimel makes his usual brilliant case for the stupidity of right-wing and many orthodox [...]

  6. Hi. Econ blogger One Salient Oversight here. I have published an article which examines the monetary base and how changes in it when compared to inflation can be used to predict recessions.


    Please feel free to comment there. Thx.

    • Mike Kimel says:

      To anyone who read One Salient Oversight’s comments. OSO is not a trained economist, but he pays a lot of attention to the field. I can’t say I always agree with him, but he often has some provocative and thoughtful things to say that would not have occurred to insiders. It often takes standing away from the trees to get a good look at the forest.

  7. [...] 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 [...]

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