Monday, September 1, 2014

Capital, corporations, and a post for labor day.

(note: this post turned out to be way longer than I meant it to be, so I should take the time to cut it down.  But I want to get it out on Labor Day, a day dedicated to workers rather than owners of capital.  I put a line about halfway down; there's a bunch below the line, but I'll understand if you want to stop there.  Actually, I'll understand if you want to stop here.  Follow your whim.)

Let’s see…I said I would talk about taxing capital.  Before I do that, I want to clarify something from my last post.  It will probably give you some indication of my age if I tell you that William of Ockham was a personal friend of mine when I was young, and I always admired his razor.  Simplicity is good.  When I said in my last post that we should raise corporate income tax rates and increase the deductions available to corporations to drive the effective tax on corporations to zero, I didn’t mean that we should multiply their number or complexity, only the total size of the deductions they provide. 

The comment about my advanced age was largely because the discussion about capital taxation, which has been raised repeatedly by at least one segment of the corporate tax discussion, seems to be dominated by a result that is often called “classic”---and that was first published well after I completed my trip through the graduate program in economics, and well after the turbulence of my early career had landed me in a job where instead of doing economics I supervise engineering project.  It dates to the mid-1980s.  It’s called, in the usual academic shorthand, by the names of the people who first offered it, and in particular to  Christophe Chamley and Kenneth Judd: it’s called the Chamley-Judd result, sometimes even the Chamley-Judd Theorem. The theorem claims that we should not tax returns to capital at all, and that all taxes should be paid by labor.
To understand what Chamley and Judd are getting at, you have to understand that the “capital” they have in mind is tangible capital, not financial capital: plant and equipment, computers, office buildings, hammers, cranes, trucks, tools, but not bonds or other financial assets.   This kind of capital is the stuff that economists want to put into a production function that looks something like this: Q=f(L, K), which means that the total quantity produced is a function of the labor used and the capital they have to work with.  The Chamley-Judd theorem, which is pretty interesting if used reasonably, shows that under a bunch of very restrictive conditions the optimal rate of taxation on the income earned by owning this kind of capital is zero---and they mean optimal in the long run for workers even though the workers will have to pay additional taxes to make up for the revenues lost by eliminating taxes on capital income.  Sometimes politicians and some economists use this theorem to justify proposals to decrease taxes on corporations, although usually not to zero.  (There are other inputs to this discussion that come to a different optimal rate by relaxing some of the restrictive conditions required to get the Chamley-Judd result.  A recent paper by Thomas Piketty and Emmanuel Saez found that the optimal taxation of inherited capital was as high as 60%. ) 

Here’s a sample of the kinds of things people say, more or less as an argument to stop taxing corporate dividends, from the Library of Economics and Liberty:

“let me sum up a key implication of Chamley-Judd: 

Under standard, pretty flexible assumptions, it's impossible to tax capitalists, give the money to workers, and raise the total long-run income of workers.    

Not, hard, not inefficient, not socially wasteful, not immoral: Impossible…

Good economic policy doesn't try to do things that are impossible.  And if the world works roughly the way Chamley and Judd assume it does, a long run policy that redistributes total income from capitalists to workers is impossible.  “

To which the proper response is:  wow.  This isn’t the usual let’s-reduce-the-rate-and-eliminate-loopholes-to-be-revenue-neutral argument.  It isn’t the end-double-taxation-of-corporate-income argument.  This is a theorem, proved with mathematical rigor, that shows that it’s bad for workers in the long run to tax either corporations or dividends at all, at least if “corporations” and “capital” are interchangeable words, so that taxing corporate income is the same thing as taxing capital.

Well, since I said in my last post that I want to drive effective corporate taxes (not corporate tax rates!) to zero I probably should not question the Chamley-Judd result; I should just go with it as a statement not just about capital but about corporations.  But I have some reservations about how applicable it really is to whatever it is that corporate taxes (or even taxes on corporate dividends) tax.  First, as we noted before, the capital considered leaves out any incomes corporations receive from bonds, mortgages, insurance or any other financial capital.  But the model doesn’t include human capital either, or non-capital human progress; all labor is the same, present and future.  Actually, all capital is the same too, which means it doesn’t include the kind of intellectual capital that is embodied in technological progress in production, and which is often created through the labor of workers (for example, by workers called "engineers").   A different formulation of the model argument might conclude that we should never tax the income of engineers.  I’m not by any means the only one to recognize all of these things; here’s Steve Randy Waldman on it:

In empirical fact, 'human capital' and its more sociable, incorporeal twin 'institutional capital' seem to be much more important predictors of the growth path of an economy than physical capital. Europe and Japan bounce back quickly after war devastates their infrastructure. But imagine that a Rapture clears the Earth and pre-agrarian nomads take possession of perfect gleaming factories. I think you will agree that production does not recover so fast. Human and institutional capital dominate physical capital...

Further, while physical capital grows by virtue of nonconsumption, it seems plausible that human capital development is proportionate to its use, which would render a tax penalty on 'wages' particularly destructive. Fundamentally, Chamley-Judd logic suggests that we should tax least the factor most capable of expanding to engender economic growth. You don’t have to be a new-age nut to believe that human and institutional development, which yield return in the form of wages, may well be that factor. It is perfectly possible, under this logic, that the roles of capital and labor are reversed, that the optimal tax on labor should be zero or even negative, because returns to physical and financial capital are so enhanced by human talent that even capitalists are better off paying a tax to cajole it.”

The model also barely recognized the existence of government except as some external agency that for some reason sucks away taxes every year and uses the funds to buy some of the produced goods and make them magically disappear.  In other words, in this model government doesn’t actually do anything, it just costs money and gobbles things that could otherwise be consumed by its citizens.  And the theory doesn’t include corporate reputation, or branding, or business relationships, business culture, or any culture for that matter, at least not in a straightforward manner, so taxing corporations and corporate dividends is not quite the same as taxing capital in the sense that Chamley and Judd have intended.  Finally, the equation above is about how to produce things, not to sell them (there is often an unstated presumption in these small models that anything produced will be sold, which, of course, would immediately eliminate the need for advertising, which in turn would be a real downer for any future season of “Mad Men”), and production is only increased in the model by adding more labor (not improving it), or adding more capital (not improving it), or both.  (If value of a company were the same as the value of the physical capital owned by the company, then the book value would be the same as tangible book value, which excludes all kinds of values that are not tangible assets.  Needless to say, those are not the same thing and never the same value.  And even total book value doesn’t contain every asset that makes a share worthwhile or makes a company profitable; if that were true, the ratio of price to book value would always be 1.  It isn’t. )

So “corporate profits” and “returns to capital” are not the same thing.  But it’s still worth a look at Chamley Judd, because the model makes at least one very good point, which, frankly, is all you can expect of a model that so heroically simplifies the world.  This is what I think much of the world of conservative economists fails to understand, not only about this but about a lot of small models that make a point, such as the modern version of Ricardian Equivalence.   It’s a parable.  It describes a simple lesson, one lesson, not a complete panoramic intellectual tapestry of the meaning of life.  And in particular, models that assume away unemployment or demand failures are completely at odds with the tapestry and meaning of life.  So the models are good for illustrating their single lessons, but they are useless as a basis for policy.


There are (at least) two basic ideas that appear to me to drive the result: that an increased rate of investment in new capital will raise wages over time, in the long run, enough to compensate workers for accepting the total burden of funding the government without any help from a tax on capital income, and that a reduction of tax rates on capital will induce increased rate of investment in new capital.  Let’s look at both of them. 

The first relies on the assumption that capital accumulates over time and labor doesn’t, as Dr. Waldmann observed in the link above; if we encourage the formation of this cumulative capital workers in the future will have more capital to work with, and so their labor will be more valuable---and so their wages will be higher.  Taxing labor more heavily might discourage labor in the short run, but lower labor availability right now, in the world the model describes, won’t impact next year’s production possibilities, since the same amount of raw labor will be available then.  But if taxing capital discourages capital formation, that does impact next year’s possibilities, and the following year’s, and all future years’ possibilities.  In the long run, accumulation of capital will raise production and productivity of workers so much that the increased rate of taxes on workers to pay capital-income’s share of the cost of government will simply be overwhelmed by increased wages.  So the specific lesson within the model is that the cumulative formation of capital in the production function is in the best interests of workers even if encouraging capital formation means higher short run taxes on labor.

But the generalized lesson, given how the model comes to its conclusions, is that anything that cumulatively increases production possibilities should be encouraged even if that means that we have to pay higher tax rates in the short run.   And if that’s the generalized lesson, then why stop with privately owned capital?  Why not include the accumulation of national infrastructure as an input to the production function?  Or the human capital that is created by public schools?  Or the intellectual capital that is created or at least seeded by government research?  Surely a similar model that includes a government that doesn’t just gobble goods and make them vanish, but instead turns them into additional public capital, human capital, and intellectual capital that are cumulative inputs to the production function, would show that higher taxes to pay for those things are justified by long run increases in productivity.  I don’t plan to create a model like that just for this blog post---way, way too much work---but the underlying generalized logic of Chamley-Judd sounds like it would lead to that conclusion.   Also, a similar model would show that if the value of capital is cumulatively enhanced by technological progress created by labor, then the owners of capital should be willing to pay some taxes in order to reduce the tax burden on those workers to induce them to work more, and to create more cumulative technological change. 

The second basic idea that is required for this theorem is that the level of investment in new capital is a function of the return to capital, which is decreased by the tax rate on capital---lower tax rates, higher after-tax return, more investment.  If that’s not true, then why lower rates?  The workers would get nothing out of paying a higher share of the cost of government if the sacrifice didn’t induce more capital formation.  

So is that true?  Certainly it’s true that a lower tax rate would increase the after tax returns to the owners of capital, but is it true that the rate of investment in new capital depends largely on the after-tax returns to owners of capital?  That’s what the usual train of thought that’s drilled into us a undergrads would lead us to expect. 

Here’s a graph from FRED (Federal Reserve Economic Data).  The blue line is private nonresidential fixed investment as a share of GDP.  The red line is the best measure I could come up with on short notice for average after-tax return on investment; it’s total corporate after tax profits as a share of nonfinancial corporate business nonfinancial assets.  Hey, it’s not perfect, particularly since corporate profits are a function of a lot more than just the owned capital, but it’s something.

I don’t know about you, but I don’t see an exact correlation between these two lines. 

Well, then, if it’s not after tax profits, what does drive private nonresidential fixed investment?  Good question.  It’s clearly not just interest rates either, or investment would have soared after 2008 when the interest rate was driven down close to zero.

I have a theory: it’s all driven by magical creatures.   No, really.  The link is to my second post in this blog, where I said:

I do have a kind of faith in something beyond the mathematics that moves the economic world.  I believe that there is a group of magical creatures out there, a special kind of creature that makes the economy come alive; when they arrive in large numbers, businesses pop into existence like mushrooms in the woods after a spring rain; when they arrive jobs are created, and wealth is created.  When they leave, jobs are lost, wealth is lost and businesses die.  Really.  I’m not making this up, and I’m not the only one who believes in these creatures.  Sober businessmen know about them and seek them out, and spend large amounts of money hoping to coax them from their hiding places. 

We call these creatures ‘customers’.”

In this case, it’s not really the customers themselves that make businesses invest in new productive capacity.  It’s the belief that customers are coming, that when the new capacity comes online and starts producing stuff that there will be customers out there to buy it.  There is a regularity I notice in the graph above in the investment/GDP line: it always seems to have a downward slope during or before recessions (the gray vertical bars). 

In terms of the model we’ve been talking about, though, this means that the way to induce increased investment in each year is to convince investors that there will be enough customers available with enough income in the following years to buy all the new product their investment will enable them to make.   Which is a problem: the providers of labor get about 70% of total national income; owners of capital and land get the rest.  Reducing taxes on the income from capital won’t, by itself, create a rosy vision of a future teeming with consumers.  But reducing taxes on wages might…and increasing taxes on wages, in that case, would produce exactly the opposite of the effect presumed by Chamley-Judd.


  1. "You should be teaching this stuff, not managing a bunch of engineers from the Netherlands or anyplace else! Retire early and start a second career in academia!" says Craig, who had technical difficulties posting his comment.

  2. This is a test, this is only a test...