Forget the Doughnut. Meet the Wedge.

Mar 11 JDN 2458189

I just finished reading Kate Raworth’s book Doughnut Economics: Seven Ways to Think Like a 21st-Century Economist; Raworth also has a whole website dedicated to the concept of the Doughnut as a way of rethinking economics.

The book is very easy to read, and manages to be open to a wide audience with only basic economics knowledge without feeling patronizing or condescending. Most of the core ideas are fundamentally sound, though Raworth has a way of making it sound like she is being revolutionary even when most mainstream economists already agree with the core ideas.

For example, she makes it sound like it is some sort of dogma among neoclassical economists that GDP growth must continue at the same pace forever. As I discussed in an earlier post, the idea that growth will slow down is not radical in economics—it is basically taken for granted in the standard neoclassical growth models.

Even the core concept of the Doughnut isn’t all that radical. It’s based on the recognition that economic development is necessary to end poverty, but resources are not unlimited. Then combine that with two key assumptions: GDP growth requires growth in energy consumption, and growth in energy consumption requires increased carbon emissions. Then, the goal should be to stay within a certain range: We want to be high enough to not have poverty, but low enough to not exceed our carbon budget.

Why a doughnut? That’s… actually a really good question. The concept Raworth presents is a fundamentally one-dimensional object; there’s no reason for it to be doughnut-shaped. She could just as well have drawn it on a single continuum, with poverty at one end, unsustainability at the other end, and a sweet spot in the middle. The doughnut shape adds some visual appeal, but no real information.

But the fundamental assumptions that GDP requires energy and energy requires carbon emissions are simply false—especially the second one. Always keep one thing in mind whenever you’re reading something by environmentalists telling you we need to reduce economic output to save the Earth: Nuclear power does not produce carbon emissions.

This is how the environmentalist movement has shot itself—and the world—in the foot for the last 50 years. They continually refuse to admit that nuclear power is the best hope we have for achieving both economic development and ecological sustainability. They have let their political biases cloud their judgment on what is actually best for humanity’s future.

I will give Raworth some credit for not buying into the pipe dream that we can somehow transition rapidly to an entirely solar and wind-based power grid—renewables only produce 6% of world energy (the most they ever have), while nuclear produces 10%. And nuclear power certainly has its downsides, particularly in its high cost of construction. It may in fact be the case that we need to reduce economic output somewhat, particularly in the very richest countries, and if so, we need to find a way to do that without causing social and political collapse.

The Dougnut is a one-dimensional object glorified by a two-dimensional diagram.

So let me present you with an actual two-dimensional object, which I call the Wedge.

On this graph, the orange dots plot actual GDP per capita (at purchasing power parity) on the X axis against actual CO2 emissions per capita on the Y-axis. The green horizonal line is a CO2 emission target of 3 tonnes per person per year based on reports from the International Panel on Climate Change.


As you can see, most countries are above the green line. That’s bad. We need the whole world below that green line. The countries that are below the line are largely poor countries, with a handful of middle-income countries mixed in.

But it’s the blue diagonal line that really makes this graph significant, what makes it the Wedge. That line uses Switzerland’s level of efficiency to estimate a frontier of what’s possible. Switzerland’s ratio of GDP to CO2 is the best in the world, among countries where the data actually looks reliable. A handful of other countries do better in the data, but for some (Macau) it’s obviously due to poor counting of indirect emissions and for others (Rwanda, Chad, Burundi) we just don’t have good data at all. I think Switzerland’s efficiency level of $12,000 per ton of CO2 is about as good as can be reasonably expected for most countries over the long run.

Our goal should be to move as far right on the graph as we can (toward higher levels of economic development), but always staying inside this Wedge: Above the green line, our CO2 emissions are too high. Below the blue line may not be technologically feasible (though of course it’s worth a try). We want to aim for the point of the wedge, where GDP is as high as possible but emissions are still below safe targets.

Zooming in on the graph gives a better view of the Wedge.


The point of the Wedge is about $38,000 per person per year. This is not as rich as the US, but it’s definitely within the range of highly-developed countries. This is about the same standard of living as Italy, Spain, or South Korea. In fact, all three of these countries exceed their targets; the closest I was able to find to a country actually hitting the point of the wedge was Latvia, at $27,300 and 3.5 tonnes per person per year. Uruguay also does quite well at $22,400 and 2.2 tonnes per person per year.

Some countries are within the Wedge; a few, like Uruguay, quite close to the point, and many, like Colombia and Bangladesh, that are below and to the left. For these countries, a “stay the course” policy is the way to go: If they keep up what they are doing, they can continue to experience economic growth without exceeding their emission targets.


But the most important thing about the graph is not actually the Wedge itself: It’s all the countries outside the Wedge, and where they are outside the Wedge.

There are some countries, like Sweden, France, and Switzerland, that are close to the blue line but still outside the Wedge because they are too far to the right. These are countries for whom “degrowth” policies might actually make sense: They are being as efficient in their use of resources as may be technologically feasible, but are simply producing too much output. They need to find a way to scale back their economies without causing social and political collapse. My suggestion, for what it’s worth, is progressive taxation. In addition to carbon taxes (which are a no-brainer), make income taxes so high that they start actually reducing GDP, and do so without fear, since that’s part of the point; then redistribute all the income as evenly as possible so that lower total income comes with much lower inequality and the eradication of poverty. Most of the country will then be no worse off than they were, so social and political unrest seems unlikely. Call it “socialism” if you like, but I’m not suggesting collectivization of industry or the uprising of the proletariat; I just want everyone to adopt the income tax rates the US had in the 1950s.

But most countries are not even close to the blue line; they are well above it. In all these countries, the goal should not be to reduce economic output, but to increase the carbon efficiency of that output. Increased efficiency has no downside (other than the transition cost to implement it): It makes you better off ecologically without making you worse off economically. Bahrain has about the same GDP per capita as Sweden but produces over five times the per-capita carbon emissions. Simply by copying Sweden they could reduce their emissions by almost 19 tonnes per person per year, which is more than the per-capita output of the US (and we’re hardly models of efficiency)—at absolutely no cost in GDP.

Then there are countries like Mongolia, which produces only $12,500 in GDP but 14.5 tonnes of CO2 per person per year. Mongolia is far above and to the left of the point of the Wedge, meaning that they could both increase their GDP and decrease their emissions by adopting the model of more efficient countries. Telling these countries that “degrowth” is the answer is beyond perverse—cut Mongolia’s GDP by 2/3 and you would throw them into poverty without even bringing carbon emissions down to target.

We don’t need to overthrow capitalism or even give up on GDP growth in general. We need to focus on carbon, carbon, carbon: All economic policy from this point forward should be made with CO2 reduction in mind. If that means reducing GDP, we may have to accept that; but often it won’t. Switching to nuclear power and public transit would dramatically reduce emissions but need have no harmful effect on economic output—in fact, the large investment required could pull a country out of recession.

Don’t worry about the Doughnut. Aim for the point of the Wedge.

I’m not sure environmentalists understand what the word “consumption” means to economists.

Feb 25 JDN 2458175

Several times now I’ve heard environmentalists repeat variants of this line: “Capitalist economies depend on consumption; therefore capitalism is incompatible with environmental sustainability.”

A recent example comes from this article on QZ arguing that “conscious consumerism” isn’t viable for protecting the environment:

In short, consumption is the backbone of the American economy—which means individual conscious consumerism is basically bound to fail. “70% of GDP in the US is based on household consumption. So all the systems, the market, the institutions, everything is calibrated to maximize consumption,” Brown told me in a later interview. “The whole marketing industry and advertising invents new needs we didn’t know we had.”

Consumption. You keep using that word… I do not think it means what you think it means.

To be clear, let me say that I basically agree that “conscious consumerism” isn’t good enough. There are a few big things you can do to reduce your carbon footprint, like moving to California (or better yet, Scandinavia), becoming vegetarian, driving a hybrid car (or not driving at all), and not flying on airplanes. Aside from that, your consumer choices are not going to have a large impact. There is a huge amount of greenwashing that goes on—products that present themselves as eco-friendly which really aren’t. And these things by themselves are not enough. A 2012 study by the European Roundtable on Sustainable Consumption and Production found little or no difference in long-run carbon footprint between people who claim to be “green consumers” and people who don’t.

Moreover, there is a strong positive correlation between a country’s GDP and its carbon footprint. The list of countries with the highest carbon emissions looks a lot like the list of countries with the highest GDP.

But there is still substantial variation in the ratio of GDP to carbon emissions. Scandinavia does extremely well, at over $5,000 per ton (as does France, thanks to nuclear energy), while most European countries make about $3,000 per ton, the US is at about $2,000 per ton, and the very most carbon-intensive economies like China, the UAE, and South Africa only make about $1,000 per ton. China produces more carbon emissions per capita than Denmark despite having only one-third the standard of living (at purchasing power parity). Emissions also vary a great deal by states within the US; California’s per-capita emissions are comparable to France’s, while Wyoming’s are worse than the UAE’s.

This brings me to my main point, which is that economists don’t mean the same thing by the word “consumption” that environmentalists do. The environmentalist meaning might be closer to common usage: When something is consumed, we think of it as being destroyed, despoiled, degraded. (It’s even an archaic euphemism for tuberculosis.) So I can see why you would think that if our economy is 70% “consumption” that must make capitalism terrible for the environment: An economy that is 70% destruction, despoliation, and degradation does sound pretty bad.

But when economists use the word “consumption”, what we actually mean is private household expenditure. Our economy is 70% “consumption” in the sense that 70% of the dollars spent in GDP are spent by private individuals as opposed to corporations or the government. Of the $19.7 trillion of US GDP, $13.6 trillion was personal consumption expenditures. That’s actually 69%, but it’s okay to round up to 70%. The rest is made up of $3.4 trillion in government spending, $3.3 trillion in private investment, and a loss of $0.6 trillion from our trade deficit.

There’s no particular connection between private household expenditure and destruction, despoliation, or degradation. In fact, the most destructive form of GDP is obviously military spending, which is not counted as “consumption” in the National Income and Product Accounts but rather as “government expenditure”. Military spending is almost pure waste from an ecological perspective; it consumes mind-boggling amounts of fossil fuels in addition to causing death and destruction. The US military produces almost as much total carbon emissions as the entire country of Denmark.

In fact, the vast majority of private household expenditure in highly-developed countries is in the form of services—over $9.2 trillion in the US. The top four categories for expenditure on services in the US are housing/utilities, healthcare, finance, and food service. I can at least see how housing and utilities would be related to ecological impact—concrete and steel are very carbon-intensive, as is electricity if you’re not using nuclear or renewables. But healthcare, finance, and food service? When environmentalists point to the fact that 70% of our economy is consumption as evidence of the fundamental unsustainability of capitalism, this amounts to asserting that the reason we can’t prevent global warming is that there are so many nurses, accountants, and waiters.

Of course, most people don’t quite grasp what economists mean when we use the word “consumption”, so it makes for a nice talking point for environmentalists. You can conjure images of degradation and destruction while citing the respected authority of the National Income and Product Accounts. If you were already left-wing otherwise (as most environmentalists are), you can make it seem as though the problem is capitalism itself, the very structure of an economy built upon “consuming” the Earth.

In reality, there is enormous variation between countries in terms of their carbon efficiency, and in fact the most carbon-efficient nations are all those that have the highest degrees of political and economic freedom—which is to say, social democracies. One can debate whether social democracies like Denmark and Sweden are “truly capitalist”, but they definitely have free-market economies with large private sectors. On a global and historical scale, there’s really not that much difference between Denmark and the United States (compare to the USSR, or China, or Burkina Faso, or Medieval Japan, or Classical Rome). And if the US isn’t capitalist, who is?

My advice? Don’t talk about consumption at all. Talk about carbon emissions. Don’t ignore variation in GDP/carbon ratios: If the world copied China, we’d all have a per-capita income of $15,500 and emissions of 7.6 tons of carbon per person per year; but if the world copied Denmark, we’d all have a per-capita income of $51,000 and emissions of 6.8 tons of carbon per person per year. (Granted, even 6.8 is still too high; the targets I’ve seen say we need to be at about 3.0 by 2030. But Denmark has also been trending downward in emissions, so we could copy them on that too.) Reducing our standard of living wouldn’t save us if it meant being like China, and maintaining it wouldn’t hurt us if it meant being like Denmark.

I definitely agree that focusing on consumer choices isn’t good enough. Focus on policy. Carbon taxes, bans on unconventional extraction (e.g. offshore drilling, fracking), heavy investment in solar and nuclear energy, large reforestation projects, research into soil sequestration and ocean seeding. Demand these things from all politicians of all parties at all levels of government always. Don’t take no for an answer—because millions of people will die if we don’t stop climate change.

But I don’t think nurses, accountants, and waiters are the problem—and it doesn’t hurt for people to become vegetarian and buy hybrid cars.

What about a tax on political contributions?

Jan 7, JDN 2458126

In my previous post, I argued that an advertising tax could reduce advertising, raise revenue, and produce almost no real economic distortion. Now I’m going to generalize this idea to an even bolder proposal: What if we tax political contributions?

Donations to political campaigns are very similar to advertising. A contest function framework also makes a lot of sense: Increased spending improves your odds of winning, but it doesn’t actually produce any real goods.

Suppose there’s some benefit B that I get if a given politician wins an election. That benefit could include direct benefits to me, as well as altruistic benefits to other citizens I care about, or even my concern for the world as a whole. But presumably, I do benefit in some fashion from my favored politician winning—otherwise, why are they my favored politician?

In this very simple model, let’s assume that there are only two parties and two donors (obviously in the real world there are more parties and vastly more donors; but it doesn’t fundamentally change the argument). Say I will donate x and the other side will donate y.

Assuming that donations are all that matter, the probability my party will win the election is x/(x+y).

Fortunately that isn’t the case. A lot of things matter, some that should (policy platforms, experience, qualifications, character) and some that shouldn’t (race, gender, age, heightpart of why Trump won may in fact be that he is tall; he’s about 6’1”.). So let’s put all the other factors that affect elections into a package and call that F.

The probability that my candidate wins is then x/(x+y) + F, where F can be positive or negative. If F is positive, it means that my candidate is more likely to win, while if it’s negative, it means my candidate is less likely to win. (If you want to be pedantic, the probability of winning has to be capped at 0 and 1, but this doesn’t fundamentally change the argument, and only matters for candidates that are obvious winners or obvious losers regardless of how much anyone donates.)

The donation costs me money, x. The cost in utility of that money depends on my utility function, so for now I’ll just call it a cost function C(x).
Then my net benefit is:
B*[x/(x+y)+F] – C(x)

I can maximize this by a first-order condition. Notice how the F just drops out. I like F to be large, but it doesn’t affect my choice of x.

B*y/(x+y)^2 = C'(x)

Turning that into an exact value requires knowing my cost function and my opponent’s cost function (which need not be the same, in general; unlike the advertising case, it’s not a matter of splitting fungible profits between us), but it’s actually possible to stop here. We can already tell that there is a well-defined solution: There’s a certain amount of donation x that maximizes my expected utility, given the amount y that the other side has donated. Moreover, with a little bit of calculus you can show that the optimal amount of x is strictly increasing in y, which makes intuitive sense: The more they give, the more you need to give in order to keep up. Since x is increasing in y and y is increasing in x, there is a Nash equilibrium: At some amount x and y we each are giving the optimal amount from our perspective.

We can get a precise answer if we assume that the amount of the donations is small compared to my overall wealth, so I will be approximately risk-neutral; then we can just say C(x) = x, and C'(x) = 1:

B*y/(x+y)^2 = 1
Then we get essentially the same result we did for the advertising:

x = y = B/4

According to this, I should be willing to donate up to one-fourth the benefit I’d get from my candidate winning in donations. This actually sounds quite high; I think once you take into account the fact that lots of other people are donating and political contributions aren’t that effective at winning elections, the optimal donation is actually quite a bit smaller—though perhaps still larger than most people give.

If we impose a tax rate r on political contributions, nothing changes. The cost to me of donating is still the same, and as long as the tax is proportional, the ratio x/(x+y) and the probability x/(x+y) + F will remain exactly the same as before. Therefore, I will continue to donate the same amount, as will my opponent, and each candidate will have the same probability of winning as before. The only difference is that some of the money (r of the money, to be precise) will go to the government instead of the politicians.

The total amount of donations will not change. The probability of each candidate winning will not change. All that will happen is money will be transferred from politicians to the government. If this tax revenue is earmarked for some socially beneficial function, this will obviously be an improvement in welfare.

The revenue gained is not nearly as large an amount of money as is spent on advertising (which tells you something about American society), but it’s still quite a bit: Since we currently spend about $5 billion per year on federal elections, a tax rate of 50% could raise about $2.5 billion.

But in fact this seriously under-estimates the benefits of such a tax. This simple model assumes that political contributions only change which candidate wins; but that’s actually not the main concern. (If F is large enough, it can offset any possible donations.)
The real concern is how political contributions affect the choices politicians make once they get into office. While outright quid-pro-quo bribery is illegal, it’s well-known that many corporations and wealthy individuals will give campaign donations with the reasonable expectation of influencing what sort of policies will be made.

You don’t think Goldman Sachs gives millions of dollars each election out of the goodness of their hearts, do you? And they give to both major parties, which really only makes sense if their goal is not to make a particular candidate win, but to make sure that whoever wins feels indebted to Goldman Sachs. (I guess it could also be to prevent third parties from winning—but they hardly ever win anyway, so that wouldn’t be a smart investment from the bank’s perspective.)

Lynda Powell at the University of Rochester has documented the many subtle but significant ways that these donations have influenced policy. Campaign donations aren’t as important as party platforms, but a lot of subtle changes across a wide variety of policies add up to large differences in outcomes.

A political contribution tax would reduce these influences. If politicians’ sole goal were to win, the tax would have no effect. But it seems quite likely that politicians enjoy various personal benefits from lobbying and campaign contributions: Fine dinners, luxurious vacations, and so on. And insofar as that is influencing politicians’ behavior, it is both obviously corrupt and clearly reduced by a political contribution tax. How large an effect this would be is difficult to say; but the direction of the effect is clearly the one we want.

Taxing donations would also allow us to protect the right to give to campaigns (which does seem to be a limited kind of civil liberty, even though the precise interpretation “money is speech” is Orwellian), while reducing corruption and allowing us to keep close track on donations that are made. Taxing a money stream, even a small amount, is often one of the best ways to incentivize close monitoring of that money stream.

With a subtle change, the tax could even be made to bias in favor of populism: All you need to do is exempt small donations from the tax. If say the first $1000 per person per year is exempt from taxation, then the imposition of the tax will reduce the effectiveness of million-dollar contributions from Goldman Sachs and the Koch brothers without having any effect on $50 donations from people like you and me. That would technically be “distorting” elections—but it seems like it might be a distortion worth making.

Of course, this is probably even less likely to happen than the advertising tax.

The potential of an advertising tax

Jan 7, JDN 2458126

Advertising is everywhere in our society. You may see some on this very page (though if I hit my next Patreon target I’m going to pay to get rid of those). Ad-blockers can help when you’re on the Web, and premium channels like HBO will save you from ads when watching TV, but what are you supposed to do about ads on billboards as you drive down the highway, ads on buses as you walk down the street, ads on the walls of the subway train?

And Banksy isn’t entirely wrong; this stuff can be quite damaging. Based on decades of research, the American Psychological Association has issued official statements condemning the use of advertising to children for its harmful psychological effects. Medical research has shown that advertisements for food can cause overeating—and thus, the correlated rise of advertising and obesity may be no coincidence.

Worst of all, political advertising distorts our view of the world. Though we may not be able to blame advertising per se for Trump; most of his publicity was gained for free by irresponsible media coverage.

And yet, advertising is almost pure rent-seeking. It costs resources, but it doesn’t produce anything. In most cases it doesn’t even raise awareness about something or find new customers. The primary goal of most advertising is to get you to choose that brand instead of a different brand. A secondary goal (especially for food ads) is to increase your overall consumption of that good, but since the means employed typically involve psychological manipulation, this increase in consumption is probably harmful to social welfare.

A general principle of economics that has almost universal consensus is the Pigou Principle: If you want less of something, you should put a tax on it. So, what would happen if we put a tax on advertising?

The amazing thing is that in this case, we would probably not actually reduce advertising spending, but we would reduce advertising, which is what we actually care about. Moreover, we would be able to raise an enormous amount of revenue with zero social cost. Like the other big Pigovian tax (the carbon tax), this a rare example of a tax that will give you a huge amount of revenue while actually yielding a benefit to society.

This is far from obvious, so I think it is worth explaining where it comes from.

The key point is that advertising doesn’t typically increase the overall size of the market (though in some cases it does; I’ll get back to that in a moment). Rather that a conventional production function like we would have for most types of expenditure, advertising is better modeled by what is called a contest function (something that our own Stergios Skaperdas at UCI is actually a world-class expert in). In a production function, inputs increase the total amount of output. But in a contest function, inputs only redistribute output from one place to another. Contest functions thus provide a good model of rent-seeking, which is what most advertising is.

Suppose there’s a total market M for some good, where M is the total profits that can be gained from capturing that entire market.
Then, to keep it simple, let’s suppose there are only two major firms in the market, a duopoly like Coke and Pepsi or Boeing and Airbus.

Let’s say Coke decides to spend an amount x on advertising, and Pepsi decides to spend an amount y.

For now, let’s assume that total beverage consumption won’t change; so the total profits to be had from the market are always M.

What advertising does is it changes the share of that market which each firm will get. Specifically, let’s use the simplest model, where the share of the market is equal to the share of advertising spending.

Then the net profit for Coke is the following:

The share they get, x/(x+y), times the size of the whole market, M, minus the advertising spending x.

max M*x/(x+y) – x

We can maximize this with the usual first-order condition:

y/(x+y)^2 M – 1 = 0

(x+y)^2 = My

Since the game is symmetric, in a Nash equilibrium, Pepsi will use the same reasoning:

(x+y)^2 = Mx

Thus we have:

x = y

(2x)^2 = Mx

x = M/4

In this very simple model, each firm will spend one-fourth of the market’s value, and the total advertising spending will be equal to half the size of the market. Then, each company’s net income will be equal to its advertising spending. This is a pretty good estimate for Coca-Cola in real life, which spends about $3.3 billion on advertising and receives about $2.8 billion in net income each year.

What would happen if we introduce a tax? Let’s say we introduce a proportional tax r on all advertising spending. That is, for every dollar you spend on advertising, you must pay the government $r in tax. The really remarkable thing is that companies who advertise shouldn’t care what we make the tax; the only ones who will care are the advertising companies themselves.

If Coke pays x, the actual amount of advertising they receive is x – r x = x(1-r).

Likewise, Pepsi’s actual advertising received is y(1-r).

But notice that the share of total advertising spending is completely unchanged!

(x(1-r))/(x(1-r) + y(1-r)) = x/(x+y)

Since the payoff for Coke only depends on how much Coke spends and what market share they get, it is also unchanged. Since the same is true for Pepsi, nothing will change in how the two companies behave. They will spend the same amount on advertising, and they will receive the same amount of net income when all is said and done.

The total quantity of advertising will be reduced, from x+y to (x+y)(1-r). That means fewer billboards, fewer posters in subway stations, fewer TV commercials. That will hurt advertising companies, but benefit everyone else.

How much revenue will we get for the government? r x + r y = r(x+y).

Since the goal is to substantially reduce advertising output, and it won’t distort other industries in any way, we should set this tax quite high. A reasonable value for r would be 50%. We might even want to consider something as high as 90%; but for now let’s look at what 50% would do.

Total advertising spending in the US is over $200 billion per year. Since an advertising tax would not change total advertising spending, we can expect that a tax rate of 50% would simply capture 50% of this spending as revenue, which is to say $100 billion per year. That would be enough to pay for the entire Federal education budget, or the foreign aid and environment budgets combined.
Another great aspect of how an advertising tax is actually better than a carbon tax is that countries will want to compete to have the highest advertising taxes. If say Canada imposes a carbon tax but the US doesn’t, industries will move production to the US where it is cheaper, which hurts Canada. Yet the total amount of pollution will remain about the same, and Canada will be just as affected by climate change as they would have been anyway. So we need to coordinate across countries so that the carbon taxes are all the same (or at least close), to prevent industries from moving around; and each country has an incentive to cheat by imposing a lower carbon tax.

But advertising taxes aren’t like that. If Canada imposes an advertising tax and the US doesn’t, companies won’t shift production to the US; they will shift advertising to the US. And having your country suddenly flooded with advertisements is bad. That provides a strong incentive for you to impose your own equal or even higher advertising tax to stem the tide. And pretty soon, everyone will have imposed an advertising tax at the same rate.

Of course, in all the above I’ve assumed a pure contest function, meaning that advertisements are completely unproductive. What if they are at least a little bit productive? Then we wouldn’t want to set the tax too high, but the basic conclusions would be unchanged.

Suppose, for instance, that the advertising spending adds half its value to the value of the market. This is a pretty high estimate of the benefits of advertising.

Under this assumption, in place of M we have M+(x+y)/2. Everything else is unchanged.

We can maximize as before:

max (M+(x+y)/2)*x/(x+y) – x

The math is a bit trickier, but we can still solve by a first-order condition, which simplifies to:

(x+y)^2 = 2My

By the same symmetry reasoning as before:

(2x)^2 = 2Mx

x = M/2

Now, total advertising spending would equal the size of the market without advertising, and net income for each firm after advertising would be:

2M(1/2) – M/2 = M/2

That is, advertising spending would equal net income, as before. (A surprisingly robust result!)

What if we imposed a tax? Now the algebra gets even nastier:

max (M+(x+y)(1-r)/2)*x/(x+y) – x

But the ultimate outcome is still quite similar:

(1+r)(x+y)^2 = 2My

(1+r)(2x)^2 = 2Mx

x = M/2*1/(1+r)

Advertising spending will be reduced by a factor of 1/(1+r). Even if r is 50%, that still means we’ll have 2/3 of the advertising spending we had before.

Total tax revenue will then be M*r/(1+r), which for r of 50% would be M/3.

Total advertising will be M(1-r)/(1+r), which would be M/3. So we managed to reduce advertising by 2/3, while reducing advertising spending by only 1/3. Then we would receive half of that spending as revenue. Thus, instead of getting $100 billion per year, we would get $67 billion, which is still just about enough to pay for food stamps.

What’s the downside of this tax? Unlike most taxes, there really isn’t one. Yes, it would hurt advertising companies, which I suppose counts as a downside. But that was mostly waste anyway; anyone employed in advertising would be better employed almost anywhere else. Millions of minds are being wasted coming up with better ways to sell Viagra instead of better treatments for cancer. Any unemployment introduced by an advertising tax would be temporary and easily rectified by monetary policy, and most of it would hit highly educated white-collar professionals who have high incomes to begin with and can more easily find jobs when displaced.

The real question is why we aren’t doing this already. And that, I suppose, has to come down to politics.

“DSGE or GTFO”: Macroeconomics took a wrong turn somewhere

Dec 31, JDN 2458119

The state of macro is good,” wrote Oliver Blanchard—in August 2008. This is rather like the turkey who is so pleased with how the farmer has been feeding him lately, the day before Thanksgiving.

It’s not easy to say exactly where macroeconomics went wrong, but I think Paul Romer is right when he makes the analogy between DSGE (dynamic stochastic general equilbrium) models and string theory. They are mathematically complex and difficult to understand, and people can make their careers by being the only ones who grasp them; therefore they must be right! Nevermind if they have no empirical support whatsoever.

To be fair, DSGE models are at least a little better than string theory; they can at least be fit to real-world data, which is better than string theory can say. But being fit to data and actually predicting data are fundamentally different things, and DSGE models typically forecast no better than far simpler models without their bold assumptions. You don’t need to assume all this stuff about a “representative agent” maximizing a well-defined utility function, or an Euler equation (that doesn’t even fit the data), or this ever-proliferating list of “random shocks” that end up taking up all the degrees of freedom your model was supposed to explain. Just regressing the variables on a few years of previous values of each other (a “vector autoregression” or VAR) generally gives you an equally-good forecast. The fact that these models can be made to fit the data well if you add enough degrees of freedom doesn’t actually make them good models. As Von Neumann warned us, with enough free parameters, you can fit an elephant.

But really what bothers me is not the DSGE but the GTFO (“get the [expletive] out”); it’s not that DSGE models are used, but that it’s almost impossible to get published as a macroeconomic theorist using anything else. Defenders of DSGE typically don’t even argue anymore that it is good; they argue that there are no credible alternatives. They characterize their opponents as “dilettantes” who aren’t opposing DSGE because we disagree with it; no, it must be because we don’t understand it. (Also, regarding that post, I’d just like to note that I now officially satisfy the Athreya Axiom of Absolute Arrogance: I have passed my qualifying exams in a top-50 economics PhD program. Yet my enmity toward DSGE has, if anything, only intensified.)

Of course, that argument only makes sense if you haven’t been actively suppressing all attempts to formulate an alternative, which is precisely what DSGE macroeconomists have been doing for the last two or three decades. And yet despite this suppression, there are alternatives emerging, particularly from the empirical side. There are now empirical approaches to macroeconomics that don’t use DSGE models. Regression discontinuity methods and other “natural experiment” designs—not to mention actual experiments—are quickly rising in popularity as economists realize that these methods allow us to actually empirically test our models instead of just adding more and more mathematical complexity to them.

But there still seems to be a lingering attitude that there is no other way to do macro theory. This is very frustrating for me personally, because deep down I think what I would like to do as a career is macro theory: By temperament I have always viewed the world through a very abstract, theoretical lens, and the issues I care most about—particularly inequality, development, and unemployment—are all fundamentally “macro” issues. I left physics when I realized I would be expected to do string theory. I don’t want to leave economics now that I’m expected to do DSGE. But I also definitely don’t want to do DSGE.

Fortunately with economics I have a backup plan: I can always be an “applied micreconomist” (rather the opposite of a theoretical macroeconomist I suppose), directly attached to the data in the form of empirical analyses or even direct, randomized controlled experiments. And there certainly is plenty of work to be done along the lines of Akerlof and Roth and Shiller and Kahneman and Thaler in cognitive and behavioral economics, which is also generally considered applied micro. I was never going to be an experimental physicist, but I can be an experimental economist. And I do get to use at least some theory: In particular, there’s an awful lot of game theory in experimental economics these days. Some of the most exciting stuff is actually in showing how human beings don’t behave the way classical game theory predicts (particularly in the Ultimatum Game and the Prisoner’s Dilemma), and trying to extend game theory into something that would fit our actual behavior. Cognitive science suggests that the result is going to end up looking quite different from game theory as we know it, and with my cognitive science background I may be particularly well-positioned to lead that charge.

Still, I don’t think I’ll be entirely satisfied if I can’t somehow bring my career back around to macroeconomic issues, and particularly the great elephant in the room of all economics, which is inequality. Underlying everything from Marxism to Trumpism, from the surging rents in Silicon Valley and the crushing poverty of Burkina Faso, to the Great Recession itself, is inequality. It is, in my view, the central question of economics: Who gets what, and why?

That is a fundamentally macro question, but you can’t even talk about that issue in DSGE as we know it; a “representative agent” inherently smooths over all inequality in the economy as though total GDP were all that mattered. A fundamentally new approach to macroeconomics is needed. Hopefully I can be part of that, but from my current position I don’t feel much empowered to fight this status quo. Maybe I need to spend at least a few more years doing something else, making a name for myself, and then I’ll be able to come back to this fight with a stronger position.

In the meantime, I guess there’s plenty of work to be done on cognitive biases and deviations from game theory.

Influenza vaccination, herd immunity, and the Tragedy of the Commons

Dec 24, JDN 2458112

Usually around this time of year I do a sort of “Christmas special” blog post, something about holidays or gifts. But this year I have a rather different seasonal idea in mind. It’s not just the holiday season; it’s also flu season.

Each year, influenza kills over 56,000 people in the US, and between 300,000 and 600,000 people worldwide, mostly in the winter months. And yet, in any given year, only about 40% of adults and 60% of children get the flu vaccine.

The reason for this should be obvious to any student of economics: It’s a Tragedy of the Commons. If enough people got vaccinated that we attained reliable herd immunity (which would take about 90%), then almost nobody would get influenza, and the death rate would plummet. But for any given individual, the vaccine is actually not all that effective. Your risk of getting the flu only drops by about half if you receive the vaccine. The effectiveness is particularly low among the elderly, who are also at the highest risk for serious complications due to influenza.

Thus, for any given individual, the incentive to get vaccinated isn’t all that strong, even though society as a whole would be much better off if we all got vaccinated. Your probability of suffering serious complications from influenza is quite low, and wouldn’t be reduced all that much if you got the vaccine; so even though flu vaccines aren’t that costly in terms of time, money, discomfort, and inconvenience, the cost is just high enough that a lot of us don’t bother to get the shot each year.

On an individual level, my advice is simple: Go get a flu shot. Don’t do it just for yourself; do it for everyone around you. You are protecting the most vulnerable people in our society.

But if we really want everyone to get vaccinated, we need a policy response. I can think of two policies that might work, which can be broadly called a “stick” and a “carrot”.

The “stick” approach would be to make vaccination mandatory, as it already is for many childhood vaccines. Some sort of penalty would have to be introduced, but that’s not the real challenge. The real challenge would be how to actually enforce that penalty: How do we tell who is vaccinated and who isn’t?

When schools make vaccination mandatory, they require vaccination records for admission. It would be simple enough to add annual flu vaccines to the list of required shots for high schools and colleges (though no doubt the anti-vax crowd would make a ruckus). But can you make vaccination mandatory for work? That seems like a much larger violation of civil liberties. Alternatively, we could require that people submit medical records with their tax returns to avoid a tax penalty—but the privacy violations there are quite substantial as well.

Hence, I would favor the “carrot” approach: Use government subsidies to provide a positive incentive for vaccination. Don’t simply make vaccination free; actually pay people to get vaccinated. Make the subsidy larger than the actual cost of the shots, and require that the doctors and pharmacies administering them remit the extra to the customers. Something like $20 per shot ought to do it; since the cost of the shots is also around $20, then vaccinating the full 300 million people of the United States every year would cost about $12 billion; this is less than the estimated economic cost of influenza, so it would essentially pay for itself.

$20 isn’t a lot of money for most people; but then, like I said, the time and inconvenience of a flu shot aren’t that large either. There have been moderately successful (but expensive) programs incentivizing doctors to perform vaccinations, but that’s stupid; frankly I’m amazed it worked at all. It’s patients who need incentivized. Doctors will give you a flu shot if you ask them. The problem is that most people don’t ask.

Do this, and we could potentially save tens of thousands of lives every year, for essentially zero net cost. And that sounds to me like a Christmas wish worth making.

The Irvine Company needs some serious antitrust enforcement

Dec 17, JDN 2458105

I probably wouldn’t even have known about this issue if I hadn’t ended up living in Irvine.

The wealthiest real estate magnate in the United States is Donald Bren, sole owner of the Irvine Company. His net wealth is estimated at $15 billion, which puts him behind the likes of Jeff Bezos or Bill Gates, but well above Donald Trump even at his most optimistic estimates.

Where did he get all this wealth?

The Irvine Company isn’t even particularly shy about its history, though of course they put a positive spin on it. Right there on their own website they talk about how it used to be a series of ranches farmed by immigrants. Look a bit deeper into their complaints about “squatters” and it becomes apparent that the main reason they were able to get so rich is that the immigrant tenant farmers whose land they owned were disallowed by law from owning real estate. (Not to mention how it was originally taken from Native American tribes, as most of the land in the US was.) Then of course the land has increased in price and been passed down from generation to generation.

This isn’t capitalism. Capitalism requires a competitive market with low barriers of entry and trade in real physical capital—machines, vehicles, factories. The ownership of land by a single family that passes down its title through generations while extracting wealth from tenant farmers who aren’t allowed to own anything has another name. We call it feudalism.

The Irvine Company is privately-held, and thus not required to publish its finances the way a publicly-traded company would be, so I can’t tell you exactly what assets its owns or how much profit it makes. But I can tell you that it owns over 57,000 housing units—and there are only 96,000 housing units in the city of Irvine, so that means they literally own 60% of the city. They don’t just own houses either; they also own most of the commercial districts, parks, and streets.

As a proportion of all the housing in the United States, that isn’t so much. Even compared to Southern California (the most densely populated region in North America), it may not seem all that extravagant. But within the city of Irvine itself, this is getting dangerously close to a monopoly. Housing is expensive all over California, so they can’t be entirely blamed—but is it really that hard to believe that letting one company own 60% of your city is going to increase rents?

This is sort of thing that calls for a bold and unequivocal policy response. The Irvine Company should be forced to subdivide itself into multiple companies—perhaps Irvine Residential, Irvine Commercial, and Irvine Civic—and then those companies should be made publicly-traded, and a majority of their shares immediately distributed to the residents of the city. Unlike most land reform proposals, selecting who gets shares is actually quite straightforward: Anyone who pays rent on an Irvine Company property receives a share.

Land reform has a checkered history to say the least, which is probably why policymakers are reluctant to take this sort of approach. But this is a land reform that could be handled swiftly, by a very simple mechanism, with very clear rules. Moreover, it is entirely within the rule of law, as the Irvine Company is obviously at this point an illegitimate monopoly in violation of the Sherman Antitrust Act, Clayton Antitrust Act, and Federal Trade Commission Act. The Herfindahl-Hirschman Index for real estate in the city of Irvine would be at least 3600, well over the standard threshold of 2500 that FTC guidelines consider prima facie evidence of an antitrust violation in the market. Formally, the land reform could be accomplished by collecting damages in an amount necessary to purchase the shares at the (mandatory) IPO, then the beneficiaries of the damages paid in shares would be the residents of Irvine. The FTC is also empowered to bring criminal charges if necessary.

Oddly, most of the talk about the Irvine Company among residents of Irvine centers around their detailed policy decisions, whether expanding road X was a good idea, how you feel about the fact that they built complex Y. (There’s also a bizarre reverence for the Irvine Master Plan; people speak of it as if it were the US Constitution, when it’s actually more like’s five-year revenue targets. This is a for-profit company. Their plan is about taking your money.) This is rather like debating whether or not you have a good king; even if you do, you’re still a feudal subject. No single individual or corporation should have that kind of power over the population of an entire city. This is not a small city, either; Irvine has about three-quarters of the population of Iceland, or a third the population of Boston. Take half of Donald Bren’s $15 billion, divide it evenly over the 250,000 people of the city, and each one gets $30,000. That’s a conservative estimate of how much monopolistic rent the Irvine Company has extracted from the people of Irvine.

By itself, redistributing the assets of the Irvine Company wouldn’t solve the problem of high rents in Southern California. But I think it would help, and I’m honestly having trouble seeing the downsides. The only people who seem to be harmed are billionaires who inherited wealth that was originally extracted from serfs. Like I said, this is within the law, and wouldn’t require new legislation. We would only need to aggressively enforce laws that have been on the books for a century. It doesn’t even seem like it should be politically unpopular, as you’re basically giving a check for tens of thousands of dollars to each voting resident in the city.

Of course, it won’t happen. As usual, I’m imagining more justice in the world than there actually has ever been.