Sunday, March 4, 2018

NYTimes Packs Five Ungrounded Economic Opinions in Two Sentences

Some misconceptions about tax incidence have been getting a lot of press, but Paul Krugman's column from last week is particularly efficient at perpetuating them:

"How much of a trickle-down effect depends on a bunch of technical factors: what share of corporate profits represents monopoly rents rather than returns to capital, how responsive inflows of foreign capital are to the U.S. rate of return.  Enthusiasts claim that the tax cut will eventually go 100% to workers; most serious modelers think the number is more like 20 or 25 percent."

Of course I am not a "serious modeler", but let's break this down:
  1. "Enthusiasts claim that the tax cut will eventually go 100% to workers"

  2. Actually, the White House Council of Economic Advisers, I, and anyone else using the standard supply and demand model claims that MORE THAN 100% of the tax cut will eventually go to workers. The analysis is in pdf here and executable Mathematica notebook here.

  3. "what share of the capital stock is even affected by the corporate tax rate"

  4. This extension of the supply and demand model only strengthens the conclusion, because now workers not only have to pay for the revenue received by the treasury and for the productivity lost due to less aggregate capital, but also the productivity lost due to the misallocation of capital between activities covered by the statutory corporate rate and activities not covered. The analysis is here. Perhaps the proponents of this argument are thinking that the tax does less damage when it covers less capital. Maybe, but for sure it brings in less revenue too, and Krugman is referring to damage as a percentage of revenue.

  5. "what share of corporate profits represents monopoly rents rather than returns to capital"

  6. Krugman and the others do not give any citation to "serious modeling" of monopoly rents (monopoly rents = free lunch is not a serious model by any definition). But it looks to me that adding monopoly rents to the model also strengthens the conclusion, because now workers not only have to pay for the revenue received by the treasury, the productivity lost due to less aggregate capital, the productivity lost due to the misallocation of capital, but also exacerbation of the productivity lost due to monopoly. The analysis is here and in the links therein.

  7. "how responsive inflows of foreign capital are to the U.S. rate of return"

  8. This is a red herring. All of the models that I have cited make the assumption most charitable to Krugman's conclusions: namely that foreign capital inflows are completely unresponsive (they are closed-economy models!). Nevertheless, they conclude that labor pays more than 100 percent of the corporate-income tax.

These counterintuitive results, and many more, are treated in the forthcoming Chicago Price Theory textbook by Sonia Jaffe, Robert Minton, Casey B. Mulligan, and Kevin M. Murphy.

Corporate-income Tax Incidence with Imperfect Competition

Summary: Labor Losses in an Economy with Imperfect Competition May Be Even Greater than Labor Losses in a Perfectly Competitive Economy, Which Themselves are Sizable

Two kinds of distortions are both important and easy to handle in the standard models of capital taxation: the distortion in terms of the total amount of capital and the distortion of the distribution of capital among activities that are differentially taxed.  In the long run, the deadweight loss of these distortions and other distortions comes entirely out of wages.

Raising the corporate-income tax rate adds to the total-capital and capital-composition distortions.[1]  Therefore wages are reduced more in the long run than revenue is enhanced (if at all).  In other words, labor pays more than 100 percent of the corporate-income tax.

But proponents of corporate-income taxation have asserted that, not withstanding the above, labor is scarcely harmed by the tax because of the prevalence of “monopoly.”  If such assertions are to be taken seriously, they need to be accompanied by some more detailed economic reasoning, which is provided below.

The abbreviated version is this: if policy goals (e.g., fighting monopolies) are pursued with oblique policy instruments (e.g., the corporate-income tax or, in New-Keynesian fashion, monetary policy), then unintended consequences abound.

Market Power is Uneven

Any reasonable view of market power has to acknowledge that market power is uneven: that industries, regions, etc., have different percentage gaps between price and marginal cost; between factor prices and marginal products.  If market power is important, then even a low-rate corporate-income tax likely adds significantly to already existing distortions because the tax-free economy is not well approximated as first best (in terms of the amount of capital or its composition).[2]

Rent Seeking: People Like Profits and Will Pursue Them

A third type of distortion has to do with rent seeking, which refers to activities that people and businesses do to obtain market power or government favors.  These include advertising, inventing new products, merging businesses, or lobbying public officials.

A number of factors determine the direction of the effect of corporate taxation on the deadweight losses associated with rent seeking (hereafter, DWRS).  One is whether the social return to rent seeking exceeds the private return.  Arguably inventing new products or merging businesses could benefit consumers beyond its benefit to the businesses taking these actions. One element in the rent seeking calculus is therefore to quantify the gap between social and private return.  The gap may well be negative, but it is usually too extreme to assert that all rent seeking is a waste.

The second element is the direction and magnitude of the effect of the corporate tax on rent seeking.  Are corporations more rent-seeking intensive than noncorporations?  Are corporations able to deduct their rent-seeking efforts from income for the purpose of determining their corporate-income tax liability?  Will the extra treasury revenue itself motivate socially costly rent seeking to influence how it is distributed?  This last point is particularly important because, in the neighborhood of a zero tax rate, the corporate tax creates far more tax revenue than it destroys rewards to monopoly (at large tax rates, see below).

These are all reasons why a higher corporate rate could encourage rent-seeking.[3]  To the extent that the corporate tax encourages rent seeking in some instances and discourages it in others, we need to know the net effect, weighted by the social benefit or damage associated with each instance.

With all of these factors determining the DWRS, we cannot rule out the possibility that corporate taxation adds to DWRS and therefore adds to the amount that the tax reduces wages as compared to the amount it would reduce wages in an economy with no rent seeking, which itself is in excess of the amount of revenue obtained from the tax.  If so, we can conclude even more confidently that labor pays more than 100 percent of the corporate-income tax because all three types of deadweight loss are adding to the tax’s burden on labor (a specific and rigorous demonstration is here as pdf and here as executable Mathematica notebook).

An interesting and ironic case is when rent seeking is labor-intensive, or otherwise deductible from the corporate income tax.  Here the corporate tax encourages rent seeking by reducing the price of rent-seeking inputs.  Ironically, if you use monopoly as a pejorative term, then you have to acknowledge that yet another cost of the corporate-income tax is wasteful rent seeking.  On the other hand, if you think that monopoly rents motivate socially valuable R&D, then one of the benefits of the corporate tax is that it encourages that R&D (but see my advice below on using less oblique policy measures).

A Proper Tax-Incidence Formula Does Not Merely Enter the "Monopoly Profit Share" as a Subtraction

The amount of DWRS is related to the amount of rents to be sought, which we might roughly describe as the “share of corporate profits that represent monopoly rents.”  The amount would be small if there are few rents to be had.

In contrast, the amount of the other two deadweight losses (capital amount and composition) depends on the level of the tax rate.  At high tax rates, the capital amount and composition dominate DWRS, and labor is paying more than 100 percent of the corporate-income tax at the margin.

Note that even if the corporate-income tax reduces DWRS more than enough to offset what it adds to the other two deadweight losses, that does not mean that labor benefits from the tax.  It means that labor pays less than 100 percent of it.  Moreover, for the reasons cited above, simply subtracting the monopoly-rent share in a tax-incidence analysis is a wild exaggeration, if not directionally incorrect, of how the true incidence differs from simpler models that have no DWRS.

Advice: Forgo Oblique and Uncertain Policy Instruments

Perhaps most important, the deadweight costs of capital amount and composition are direct consequences of the corporate tax.  In contrast, the benefit, if any, of corporate taxation coming through DWRS is indirect and uncertain, and presumably we could do better by attacking these problems more directly with antitrust enforcement, policing election fraud, supporting well-designed systems to encourage the supply of intellectual property, etc.

[1] The capital-composition distortion could in principle get better if (a) the non-corporate tax rate were sufficiently greater than the corporate rate and (b) little of the corporate activity could avoid the tax (e.g., through loopholes).
[2] We might get lucky that the corporate tax falls on the sectors that already have too much capital and sales, although the assertion that the corporate sector is full of monopolies suggests the opposite (the usual complaint about monopolies is that they charge too much and produce too little).  There is also the concern that the corporate tax falls on sectors that are labor-intensive (Harberger 1962) thereby depressing the aggregate demand for labor even beyond its effect on the capital stock.
[3] Arguably the people and businesses most productive at rent seeking have already obtained tax exemptions for themselves, so that raising the tax rate only encourages more exemption seeking.

Saturday, March 3, 2018

Robots: Leibniz' dream is coming true in economics

Gottfried Leibniz, one of the legends in the history of mathematics, envisioned that human reasoning would one day be automated, thereby resolving a great many disputes among experts. He wrote (translated from German at WikiQuote from his 1688 "The characteristics of the art in order to make science fair"):

[...] if controversies were to arise, there would be be no more need of disputation between two philosophers than between two calculators. For it would suffice for them to take their pencils in their hands and to sit down at the abacus, and say to each other (and if they so wish also to a friend called to help): Let us calculate.
image credit: Public domain.

More recently, Obama administration economists Furman and Summers claimed that only a fraction of the revenue loss from a corporate-income tax cut benefits labor. But the standard supply and demand model says the opposite.

Summers, as well as Nobel Laureate Paul Krugman, rejected this result, asserting that it depends on "what share of the capital stock is even affected by the corporate tax rate."

The supply and demand model readily accommodates the fact that the statutory corporate rate does not apply to much of the nation's capital. Now a machine has proven the supply-demand result, without assuming any functional form for the aggregate production function, and without restricting the share of capital that is subject to the tax (except that the share cannot be zero or negative).

You can view the proof in pdf here, or as an executable Mathematica notebook here.

For another economics dispute between Krugman and I that was resolved by machine, see here.

(They also incorrectly claim that "monopoly" overturns the result too. See here, and here. For some machine analysis of the issue, see the pdf here and the executable Mathematica notebook here.)