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Dear Economist,

Mathematical techniques and computational experiments have always been tools to complement and interpret data and models.

Quantifier elimination, recognized by Alfred Tarski in the late 1940s as a computable task when working at RAND, was initially considered impractical because of its high complexity (doubly exponentially).

But the task is conceptually quite simple: instead of solving an equation or a system of equations, say x² + bx + c with respect to x, find the conditions on the parameters b and c such that the solutions for x are always positive (or negative or within a given range).

Quantifier elimination can be an incredibly useful tool. The last decades have brought quantifier elimination from a pie-in-the-sky method to a practical tool. Mathematicians were the first to adapt it, then it was used in quantum theory. Over the last three years, the number of applications in economics has been on the rise.

A recent paper from the National Economic Bureau of Research gives example problems for quantifier elimination and compares the available software products to do the actual computation. The paper concludes:

Of the tools we tried, only Mathematica was able to decide all problems in the benchmark set. In fact all 135 could be tackled by Mathematica [in] less than a minute on a laptop computer, with only three of those taking more than ten seconds, ...

And just a few weeks after the aforementioned publication, a preprint was published on the arXiv preprint server that describes a new Mathematica package called TheoryGuru. The package is dedicated to quantifier elimination applications in economics and the social sciences.

We hope this package will be useful for economists. To further foster the use of quantifier elimination, we are offering temporary Mathematica licenses for select researchers in economics and related fields to get you started with the Wolfram Language. If you or your colleagues would be interested in a license, please let us know.

Sincerely,

The Wolfram Publication Watch Team

Inflation has little to do with the Unemployment Rate

Copyright, TheHill.com

The April unemployment rate, released Friday, showed the headline unemployment rate below 4 percent, which has rarely happened in the past 48 years. But a low unemployment rate does not necessarily mean high inflation.

A conventional wisdom, sometimes known as the Phillips curve, holds that low unemployment creates inflation as employers increasingly bid against each other for workers and pass on some of their labor costs to consumers.

One problem with the theory is that low unemployment is not synonymous with high employment. Aside from identifying Americans as either working or being unemployed, federal government statisticians also put adults into a third category: out of the labor force (OLF).

In other words, "unemployed" is just one of two not-working categories, so that both employment and unemployment can fall at the same time if enough people are switching from unemployed to out of the labor force.

The official distinction between unemployed and OLF is whether the not-working person is actively looking for work. This distinction helps to prevent confusing a retiree or a full-time student with a laid-off head of household who is eagerly looking for a new job.

But a number of people are on the margin of looking for work and could be classified either way. During President Obama's first term, the federal government was actively assisting out-of-work people with temporary cash, health and mortgage assistance but only if they said that they were looking for work. That by itself inflated the measured unemployment rate above what it would have been.

When the temporary assistance programs began to expire during 2010 and 2011, that's exactly when the unemployment rate started falling. Some of that drop was a result of additional employment, but an important part of it was just a shift to the OLF form of not working.

To further add to the statistical distortion, the headline unemployment rate is measured as a share of people in the labor force rather than a share of population. When 3.9 percent of the labor force is unemployed, that means that an even lesser percentage of the adult population is unemployed because a great many adults are not in the labor force.

Increases in the number of people classified as OLF can, therefore, reduce the headline unemployment rate without changing the number of people who actually are unemployed.

The chart below shows unemployment (blue) and OLF (red) on the same scale, which is a fraction of the adult population (I have subtracted 28 points from OLF so that the two series come together around 2010).

Around 2010, the two started moving in opposite directions, and this trend continued until about 2016. By that point, unemployment was historically low, in comparison with the population, but employment was not historically high.

What had really changed between 2010 and 2016 was the propensity of people who are out of work to say that they are actively looking.

The most recent year has been different, with unemployment falling yet no real increase in OLF. But that change is fairly small in comparison to the changes from 2010 to 2016.

The other problem with the Phillips curve theory is that it has been backward many times in history; there have been times of rapid economic growth at the same time that inflation was low or even negative.

The takeaway: If you want to understand what is happening with inflation, look somewhere else than the unemployment rate.

How Can I Get Introduced to Automated Reasoning for Economics and Statistics?

I can suggest four resources to get introduced, in order of utility:

1. A new paper on automated econometric reasoning. No economic theory here but being newest it is my most user-friendly paper. Also the analogy with economic theory should be pretty clear.

2. The youtube channel containing two 45-60 minutes seminars I gave, one at Chicago Economics and the second to a Microsoft Research audience that was more computer science than economics.

3. Browse dozens of examples in pdf format.  Even better, execute them yourself using Mathematica.

4. My original paper on automated economic reasoning, whose primary value given (1) is that it contains the economic theory examples.

Click for teaser video

Click for teaser video

Monopolies are unhealthy, but high taxes make the disease worse

Copyright, TheHill.com

Taxes are necessary to fund worthy government activities, but taxes come with side effects. The side effects can be especially harmful in an economy where businesses enjoy monopoly power.

People and businesses individually attempt to reduce their tax burden by doing less of the activities taxed at high rates and more of the activities tax at low rates or by doing activities that aren't taxed at all.

If the primary activities hit with high rates were unpleasant -- pollution is an example -- then thankfully taxes would not only bring revenue to the treasury but also induce people to pollute less.

However, most of the objects of taxation are labor and capital, which are not intrinsically undesirable the way pollution is. The reduction in labor and capital, and ultimately national income, by taxes is a regrettable side effect.

The size of government is ultimately a along the tradeoff between reducing side effects and obtaining tax revenue. 

Former Obama-administration economists, and New York Times economist Paul Krugman, have recently decided to treat corporate income as a kind of pollution that is supposedly a source of tax revenue without adverse consequences. They are confused about how monopolies work. 

We all agree that a real problem with monopolies is that they may charge too much, owing to the fact that by definition they have little concern that a competitor will outbid them. But charging high prices is equivalent to producing too little, because customers' natural reaction to high prices is to buy less.

So the problem with monopolized industries is that they produce too little, and with their lower production levels, they ultimately have less need to hire labor and capital. Taxing monopolies only worsens their low usage of labor and capital. In this way, monopolies are the opposite of pollution.

A second feature of monopolies is that everybody wants to own one! The result is a competition for the ability to have a monopoly. Sometimes this feature of competition for monopoly rights only adds to the problem, as when businesses compete to convince government officials to grant them monopoly power.

Other times, businesses and individuals compete to invent a new product that they can successfully monopolize. Yes, it's too bad for the consumer that the new product costs so much -- that's the first feature of monopoly noted above -- but that's better than having no product at all. Taxing the profits of innovators discourages innovation.

An important aspect of taxing monopoly profits is therefore to understand how the monopoly rights are attained and who benefits from the competition for rights. Certainly, the headline "monopolists" of today, like Facebook, Google, Apple, etc., got their monopoly rights from socially valuable innovation and not government favors.

Are we sure that we want to discourage the next generation of innovators?

None of this is to say that monopoly is a sign of a healthy economic system. It's just that taxes probably make the disease worse. A time of rising monopoly is the time for tax cuts, not increases.

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"

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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.

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

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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.

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

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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.

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

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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.

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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.

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[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.

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: https://upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg/194px-Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg 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.)

Honey, Who Shrank the Economic Pie?

Copyright, TheHill.com

Last week the White House released the latest Economic Report of the President that, following both statute and tradition, begins with a short letter to Congress from President Trump, followed by the detailed annual report of his Council of Economic Advisers.

The period from 2010 should have had relatively rapid growth as the economy recovered from the 2008-09 recession, but it did not. Both the president's letter and the CEA annual report blame the slow growth on federal policy failures during the previous administration.

A lot of research backs up their claim and suggests that higher growth rates are forthcoming if only some of those failures are reversed and not too many new ones are created.

First is the high statutory corporate tax rate that had prevailed for decades prior to 2017 (yes, the "effective rate" was not as high, but a low effective rate is just a symptom of some of the growth-retarding effects of corporate-income taxation.)

The Obama administration agreed that America would benefit if the federal statutory rate were reduced, saying that a reduction would be "as close to a free lunch as tax reformers will ever get."

But they were not enough interested in corporate tax reform to reach a deal with Congress, so the long-overdue rate cut has President Trump's signature on it and is expect to add to economic growth over the next several years.

Second was the so-called federal "stimulus" law of 2009 that was supposed to jumpstart the recovery. But, unlike the stimulus laws in some other countries, such as the United Kingdom, our stimulus did not expand the economic pie by enhancing incentives.

Instead, our stimulus was a redistribution exercise that eroded incentives to work and earn income by expanding food stamps, mortgage subsidies, health insurance assistance and unemployment assistance primarily for people who were unemployed or otherwise had low incomes (the end of the Bush administration did some of this too). The result was less work and less national income for as long as the stimulus lasted.

Third, very soon after the stimulus expired, a new permanent redistribution began to take effect in the form of the Affordable Care Act (ACA). Indeed, the health-insurance assistance provisions of the ACA were presaged in the 2009 stimulus.

As its authors attempt to target assistance to people who they thought needed it most, the ACA unleashes a host of unintended consequences that shrink the economic pie in the process of redistributing it.

Businesses are encouraged to forgo hiring in order to keep their employment below 50 full-time equivalents and to cut workers' hours in order to keep the workweek less than 30 hours. Productive and knowledgeable employees are encouraged to retire early in order to be eligible for taxpayer-funded assistance.

The ACA is also remarkably uneven in its treatment of different sectors, regions and workplace circumstances. Another result is therefore a misallocation of resources away from the most penalized activities to the most favored ones, thereby depressing productivity; i.e., the amount of value that workers create in the marketplace.

Most businesses and households did not react to these incentives because other considerations were dominant, but it only takes a small percent of them who do to make a noticeable dent in the growth rate. If and when the federal government can repeal the ACA or relax its growth-retarding provisions, that will add to the growth rate.

Fourth, other regulations came into effect during the Obama years. Perhaps the leading instance is the 2010 Dodd-Frank financial regulation law. The law is so remarkably complicated that research on its effects will be ongoing for years, and massive complexity is hardly the leading ingredient for economic growth.

But it is likely that new financial regulations have reduced the willingness of banks to lend to small and medium-sized businesses, which further restrains economic activity.

The national economic pie has been smaller due to Obama-era policies, leaving opportunities for subsequent federal policies to enhance economic performance.

Casey Mulligan is a professor of economics at the University of Chicago. His recent research has focused on non-pecuniary incentives to save and work and how the economy affects policy. His two recent books are, "The Redistribution Recession: How Labor Market Distortions Contracted the Economy," and "Side Effects: The Economic Consequences of the Health Reform."

Your job cannot be automated? Then you need to worry!

Copyright, TheHill.com

One of the greatest labor force changes of the 20th century was the movement of workers out of farming. In 1900, more than two out of five workers were in agriculture. Now it is less than two workers out of every 100.

It's not that people stopped eating. Rather, farm machinery and innovation increased the amount of food that could be produced per farm worker by more than a factor of 10. Food got cheaper and that got people to buy more food, but not 10 times as much. The end result has been fewer jobs in agriculture.

Automation is expected to come to other industries and occupations, and it is tempting to forecast less employment for them too. A variety of studies are using engineering information to determine which jobs will be automated next.

While automation may be a question of engineering, job loss is even more a question of economics. A key part of the agriculture story is that people were unwilling to purchase all of the food that farmers were capable of producing, even though food was getting cheaper. But not all industries share this with agriculture. 

Suppose that the automation in agriculture had only been for chicken farming and not for any other food production. Chicken would have gotten cheaper relative to beef, fish, vegetables, fruit, etc., and that would have caused people to buy more chicken and less of other types of food.

Many -- even most -- of the extra chickens produced would have been purchased by consumers, and there would have been less need to reduce employment in chicken farming. 

The most dramatic job losses would have occurred in the food industries like beef and fish that were not automated and that compete with chicken. In other words, jobs that are difficult to automate from an engineering perspective may be exactly the jobs pushed to extinction by automation because they cannot compete.

It all depends on the competitive landscape and how willing are consumers, encouraged by lower prices, to absorb the extra output made possible by automation.

Trucking is a modern example, because engineers are predicting that machines will soon do a lot of the driving formerly done by trucking employees. But the result may be more jobs for people in trucking and fewer jobs for people in railroads, airlines and shipping that compete with trucking (unless they also get more productive at the same time that trucking does).

Another example has occurred in my own profession: Two or three generations ago, a large fraction of economists were employed manually performing the arithmetic of statistical analysis. Then, computers came along to automate that arithmetic, without really automating the tasks done by theoretical economists.

The result was an increase in the fraction of economists doing statistical work, because universities, businesses and government wanted more statistical analysis when computers made it became cheaper and more accurate. The fraction of economists doing theoretical work fell, precisely because their tasks were not automated.

So the more interesting economic question for a worker is not whether his job can be automated but whether he or she will miss out on automation to occur in the workplace of his or her primary competitors.