What if the charitable deduction were larger?

Nov 3 JDN 2458791

Right now, the charitable tax deduction is really not all that significant. It makes donating to charity cheaper, but you still always end up with less money after donating than you had before. It might cause you to donate more than you otherwise would have, but you’ll still only give to a charity you already care about.

This is because the tax deduction applies to your income, rather than your taxes directly. So if you make $100,000 and donate $10,000, you pay taxes as if your income were $90,000. Say your tax rate is 25%; then you go from paying $25,000 and keeping $75,000 to paying $22,500 and keeping $67,500. The more you donate, the less money you will have to keep.

Many people don’t seem to understand this; they seem to think that rich people can actually get richer by donating to charity. That can’t be done in our current tax system, or at least not legally. (There are fraudulent ways to do so; but there are fraudulent ways to do lots of things.) Part of the confusion may be related to the fact that people don’t seem to understand how tax brackets work; they worry about being “pushed into a higher tax bracket” as though this could somehow reduce their after-tax income, but that doesn’t happen. That isn’t how tax brackets work.

Some welfare programs work that way—for instance, seeing your income rise high enough to lose Medicaid eligibility can be bad enough that you would prefer to have less income—but taxes themselves do not.

The graph below shows the actual average tax rate (red) and marginal tax rate (purple) of the current US federal income tax:

Average_tax_rate
From that graph alone, you might think that going to a higher tax bracket could result in lower after-tax income. But the next graph, of before-tax (blue) and after-tax (green) income shows otherwise:

After_tax_income

All that tax deductions can do is shift you left on the green line. Without the tax deduction, you would instead shift left on the blue line, and then read off your position on the green line. Thus the tax deduction benefits you if you were already donating, but never leaves you richer than you would have been without donating at all.

For example, if you have an income of $700,000, you would pay $223,000 in taxes and keep $477,000 in after-tax income. If you instead donate $100,000, your adjusted gross income will be reduced to $600,000, you will only pay $186,000 in taxes, and you will keep $414,000 in after-tax income. If there were no tax deduction, you would still have to pay $223,000 in taxes, and your after-tax income would be only $377,000. So you do benefit from the tax deduction; but there is no amount of donation which will actually increase your after-tax income to above $477,000.

But we wouldn’t have to do it this way. We could instead apply the deduction as a tax credit, which would make the effect of the deduction far larger.

Several years back, Miles Kimball (an economist who formerly worked at Michigan, now at UC Boulder) proposed a quite clever change to the tax system:

My proposal is to raise marginal tax rates above about $75,000 per person–or $150,000 per couple–by 10% (a dime on every extra dollar), but offer a 100% tax credit for public contributions up to the entire amount of the tax surcharge.

Kimball’s argument for the policy is mainly that this would make a tax increase more palatable, by giving people more control over where their money goes. This is surely true, and a worthwhile endeavor.

But the even larger benefit might come from the increased charitable donations. If we limited the tax credit to particularly high-impact charities, we would increase the donations to those charities. Whereas in the current system you get the same deduction regardless of where you give your money, even though we know that some charities are literally hundreds of times as cost-effective as others.

In fact, we might not even want to limit the tax credit to that 10% surcharge. If people want to donate more than 10% of their income to high-impact charities, perhaps we should let them. This would mean that the federal deficit could actually increase under this policy, but if so, there would have to be so much money donated that we’d most likely end world hunger. That’s a tradeoff I’m quite willing to make.

In principle, we could even introduce a tax credit that is greater than 100%—say for instance you get a 120% donation for the top-rated charities. This is not mathematically inconsistent, though it is surely a very bad idea. In that case, it absolutely would be possible to end up with more money than you started with, and the richer you are, the more you could get. There would effectively be a positive return on charitable donations, with the money paid for from the government budget. Bill Gates for instance could pay $10 billion a year to charity and the government would not only pay for it, but also have to give him an extra $2 billion. So even for the best charities—which probably are actually a good deal more cost-effective than the US government—we should cap the tax credit at 100%.

Obvious choices for high-impact charities include UNICEF, the Red Cross, GiveDirectly, and the Malaria Consortium. We would need some sort of criteria to decide which charities should get the benefits; I’m thinking we could have some sort of panel of experts who rate charities based on their cost-effectiveness.

It wouldn’t have to be all-or-nothing, either; charities with good but not top ratings could get an increased deduction but not a 100% deduction. The expert panel could rate charities on a scale from 0 to 10, and then anything above 5 gets an (X-5)*10% tax credit.

In effect, the current policy says, “If you give to charity, you don’t have to pay taxes on the money you gave; but all of your other taxes still apply.” The new policy would say, “You can give to a top-impact charity instead of paying taxes.”

Americans hate taxes and already give a lot to charity, but most of those donations are to relatively ineffective charities. This policy could incentivize people to give more or at least give to better places, probably without hurting the government budget—and if it does hurt the government budget, the benefits will be well worth the cost.

We are in a golden age of corporate profits

Sep 2 JDN 245836

Take a good look at this graph, from the Federal Reserve Economic Database:

corporate_profits
The red line is corporate profits before tax. It is, unsurprisingly, the largest. The purple line is corporate profits after tax, with the standard adjustments for inventory depletion and capital costs. The green line is revenue from the federal corporate tax. Finally, I added a dashed blue line which multiplies before-tax profits by 30% to compare more directly with tax revenues. All these figures are annual, inflation-adjusted using the GDP deflator. The units are hundreds of billions of 2012 dollars.

The first thing you should notice is that the red and purple lines are near the highest they have ever been. Before-tax profits are over $2 trillion. After-tax profits are over $1.6 trillion.

Yet, corporate tax revenues are not the highest they have ever been. In 2006, they were over $400 billion; yet this year they don’t even reach $300 billion. The obvious reason for this is that we have been cutting corporate taxes. The more important reason is that corporations have gotten very good at avoiding whatever corporate taxes we charge.

On the books, we used to have a corporate tax rate of about 35%, which Trump just cut to 21%. But if you look at my dashed line, you can see that corporations haven’t actually paid more than 30% of their profits in taxes since 1970—and back then, the rate on the books was almost 50%.

Corporations have always avoided taxes. The effective tax rate—tax revenue divided by profits—is always much lower than the rate on the books. In 1951, the statutory tax rate was 50.75%; the effective rate was 47%. In 1970, the statutory rate was 49.2%; the effective rate was 31%. In 1993, the statutory rate was 35%; the effective rate was 26%. On average, corporations paid about 2/3 to 3/4 of what the statutory rate said.

corporate_tax_rate

You can even see how the effective rate trended steadily downward, much faster than the statutory rate. Corporations got better and better at finding and creating loopholes to let them avoid taxes. In 1950, the statutory rate was 38%—and sure enough, the effective rate was… 38%. Under Truman, corporations actually paid what they said they paid. Compare that to 1987, under Reagan, when the statutory rate was 40%—but the effective rate was only 26%.

Yet even with that downward trend, something happened under George W. Bush that widened the gap even further. While the statutory rate remained fixed at 35%, the effective rate plummeted from 26% in 2000 to 16% in 2002. The effective rate never again rose above 19%, and in 2009 it hit a minimum of just over 10%—less than one-third the statutory tax rate. It was trending upward, making it as “high” as 15%, until Trump’s tax cuts hit; in 2017 it was 13%, and it is projected to be even lower this year.

This is why it has always been disingenuous to compare our corporate tax rates with other countries and complain that they are too high. Our effective corporate tax rates have been in line with most other highly-developed countries for a long time now. The idea of “cutting rates and removing loopholes” sounds good in principle—but never actually seems to happen. George W. Bush’s “tax reforms” which were supposed to do this added so many loopholes that the effective tax rate plummeted.

I’m actually fairly ambivalent about corporate taxes in general. Their incidence really isn’t well-understood, though as Krugman has pointed out, so much of corporate profit is now monopoly rent that we can reasonably expect most of the incidence to fall on shareholders. What I’d really like to see happen is a repeal of the corporate tax combined with an increase in capital gains taxes. But we haven’t been increasing capital gains taxes; we’ve just been cutting corporate taxes.

The result has been a golden age for corporate profits. Make higher profits than ever before, and keep almost all of them without paying taxes! Nevermind that the deficit is exploding and our infrastructure is falling apart. America was founded in part on a hatred of taxes, so I guess we’re still carrying on that proud tradition.

You know what? Let’s repeal Obamacare. Here’s my replacement.

Feb 18 JDN 2458168

By all reasonable measures, Obamacare has been a success. Healthcare costs are down but coverage rates are up. It reduced both the federal deficit and after-tax income inequality.

But Republicans have hated it the whole time, and in particular the individual mandate provision has always been unpopular. Under the Trump administration, the individual mandate has now been repealed.

By itself, this can only be disastrous. It threatens to undermine all the successes of the entire Obamacare system. Without the individual mandate, covering pre-existing conditions means that people can simply wait to get insurance until they need it—at which point it’s not insurance anymore. The risks stop being shared and end up concentrated on whoever gets sick, then we go back to people going bankrupt because they were unlucky enough to get cancer. The individual mandate was vital to making Obamacare work.

But I do actually understand why the individual mandate is unpopular: Nobody likes being forced into buying anything.

John Roberts ruled that the individual mandate was Constitutional on the grounds that it is economically equivalent to a tax. This is absolutely correct, and I applaud his sound reasoning.

That said, the individual mandate is not in fact psychologically equivalent to a tax.

Psychologically, being forced to specifically buy something or face punishment feels a lot more coercive than simply owing a certain amount of money that the government will use to buy something. Roberts is right; economically, these two things are equivalent. The same real goods get purchased, at the same people’s expense; the accounts balance in the same way. But it feels different.

And it would feel different to me too, if I were required to actually shop for that particular avionic component on that Apache helicopter my taxes paid for, or if I had to write a check for that particular section of Highway 405 that my taxes helped maintain. Yes, I know that I give the government a certain amount of money that they spent on salaries for US military personnel; but I’d find it pretty weird if they required me to actually hand over the money in cash to some specific Marine. (On the other hand, this sort of thing might actually give people a more visceral feel for the benefits of taxes, much as microfinance agencies like to show you the faces of particular people as you give them loans, whether or not those people are actually the ones getting your money.)

There’s another reason it feels different as well: We have framed the individual mandate as a penalty, as a loss. Human beings are loss averse; losing $10 feels about twice as bad as not getting $10. That makes the mandate more unpleasant, hence more unpopular.

What could we do instead? Well, obviously, we could implement a single-payer healthcare system like we already have in Medicare, like they have in Canada and the UK, or like they have in Scandinavia (#ScandinaviaIsBetter). And that’s really what we should do.

But since that doesn’t seem to be on the table right now, here’s my compromise proposal. Okay, yes, let’s repeal Obamacare. No more individual mandate. No fines for not having health insurance.

Here’s what we would do instead: You get a bonus refundable tax credit for having health insurance.

We top off the income tax rate to adjust so that revenue ends up the same.

Say goodbye to the “individual mandate” and welcome the “health care bonus rebate”.

Most of you reading this are economically savvy enough to realize that’s the same thing. If I tax you $100, then refund $100 if you have health insurance, that’s completely equivalent to charging you a fine of $100 if you don’t have health insurance.

But it doesn’t feel the same to most people. A fine feels like a punishment, like a loss. It hurts more than a mere foregone bonus, and it contains an element of disapproval and public shame.

Whereas, we forgo refundable tax credits all the time. You’ve probably forgone dozens of refundable tax credits you could have gotten, either because you didn’t know about them or because you realized they weren’t worth it to you.

Now instead of the government punishing you for such a petty crime as not having health insurance, the government is rewarding you for the responsible civic choice of having health insurance. We have replaced a mean, vindictive government with a friendly, supportive government.

Positive reinforcement is more reliable anyway. (Any child psychologist will tell you that while punishment is largely ineffective and corporal punishment is outright counterproductive, reward systems absolutely do work.) Uptake of health insurance should be at least as good as before, but the policy will be much more popular.

It’s a very simple change to make. It could be done in a single tax bill. Economically, it makes no difference at all. But psychologically—and politically—it could make all the difference in the world.

Why is redistribution of wealth so difficult to achieve in the US?

Jan 28 JDN 2458147

Income and wealth in equality is much higher in the US than in other First World countries. Within the OECD, only Mexico, Turkey, and Chile have higher income inequality than we do. Over 60% of Americans agree that the distribution of wealth in the US is unfair. Furthermore, the majority of Americans support the use of taxes and transfers to directly redistribute wealth from the rich to the poor.

Why, then, is it so hard to actually get any meaningful wealth redistribution in the United States?

Part of it is surely partisan differences: While about 70% of Democrats favor redistributive taxes, about 70% of Republicans oppose them. So one would not expect a move toward redistribution when Republicans control all three branches of government, and indeed we have seen quite the opposite. (Then again, one would also not expect a government shutdown under one-party rule, and yet that is what we have.)

But even most Republicans say they would like to see a much more equal distribution of wealth than the one we actually have. In fact, when I as an inequality economist look at the distribution of wealth people say they want, it looks a little too equal! Even Denmark and Sweden aren’t that egalitarian! I know more or less how to get from here to Denmark; but from here to “Equalden” looks like an awful long way. So if this is really the distribution of wealth people want, we need to be doing a huge amount of wealth redistribution—but we’re hardly doing any at all.

Indeed, we didn’t actually see all that much redistribution of wealth when Democrats more or less controlled all three branches in the period from 2008-2010. We may have seen a little bit shortly thereafter, and tax policy typically does come with a delay of a year or two. But as you can see in this graph, the Great Recession did more to reduce the top 1% income share than any tax policy changes:

US_top_income_share_1pct

The biggest changes made to our tax code under Obama were actually the handling of capital gains; the increase of the top rate on capital gains from 15% to 20%, plus the 3.8% capital surtax from the Affordable Care Act raised the tax bill for the top 0.1% by tens of billions of dollars. Surprisingly, Trump’s tax cuts don’t actually remove these provisions, though they did dramatically cut the corporate tax rate, which will probably have a similar effect on the income distribution.

To be honest, I’m not as disappointed with Trump’s tax cuts as I thought I would be. Some genuinely good ideas (like the reduction of the mortgage interest deduction, tighter restrictions on carried interest, and increase of the personal standard deduction) and some reasonable but debatable ideas (like cuts to the corporate tax rate, switching to a territorial corporate tax system, limits to deductions on corporate debt payments, removal of the deduction of state taxes, and extensions of 529 savings plans to private primary and secondary schools) were mixed in with the absolutely ludicrous and terrible ideas (like eliminating the Obamacare mandate, doubling the estate tax threshold, cutting the alcohol tax, and allowing offshore drilling in Alaska [One of these things is not like the other ones….]). Some of the terrible ideas, like ending the deduction of student loan interest and tuition waivers, were actually removed in the final version of the bill. Of course, you won’t be surprised when I tell you that the overall US tax system became a lot less progressive as a result of this bill. And even if cutting the corporate tax while raising the capital gains tax is probably a good idea (as I and many economists believe), cutting the corporate tax without raising the capital gains tax probably isn’t.

(An aside: For how much they claim to be “tough on crime”, it’s always kind of baffling to see how often Republicans like to cut alcohol taxes and pollution regulations, which are pretty much the only things that have ever been empirically shown to actually reduce crime. There is some evidence that maybe more policing also helps, but if so, it does so in a far less cost-effective way—indeed, the direct cost of alcohol taxes and pollution taxes is negative. Even if they didn’t work at all, they’d still be worth it just because they raise revenue. I begin to suspect that Republicans don’t actually want to reduce crime, because they know they can use the fear of crime to win votes; they simply want to appear tough on crime, and so they press as hard as they can for more policing and incarceration in the country that already has the highest incarceration rate in the world. This may be a more general phenomenon: While Democrats want to actually solve problems, Republicans want to appear to solve problems while actually exacerbating them, thus insuring their own job security. Compare how Bush kept talking about Osama bin laden while invading Iraq, and Obama actually killed Osama bin Laden. Is this too cynical? Can anything be too cynical in the era of Trump? There were 50,000 Russian bots on Twitter trying to tilt our election! Mueller’s FBI investigation is already implicating several of Trump’s top officials! Everything that seemed like paranoia or cynicism just a few years ago is turning out to be entirely true.)

This is what seems to happen: Year after year, we raise some taxes, then we cut some taxes. Then when raise some taxes, then we cut some taxes. The tax system gets a little more progressive for a few years and inequality begins to fall, and then those changes are removed and inequality begins to rise again. Back and forth and round and round we go.

Is there some way to lock in these tax changes for a longer period of time? The only way I can see would be a change in voter behavior: Keep voting in Democrats to all branches of government consistently for 20 years, and then maybe we would see a serious reduction in income and wealth inequality. Or at least stop voting in Republicans; aside from the Democrats, there are some third parties that would also support redistribution, like the Green Party. And yes, it really is about voting behavior: As prevalent as gerrymandering has become, as terrible as the Electoral College is, as widespread as voter suppression has gotten, Trump only won because 63 million Americans voted for him. Even after everything he’s done, Trumps’ approval rating is still about 39%. As long as there are enough people in this country whose partisan loyalty so strongly outweighs any rational assessment of policy, we are going to continue to see such travesties continue.

It would certainly help if our voting system were fairer, so that third parties had a better chance at taking seats. But it’s also difficult to see how that could happen any time soon. For now, the best I can come up with is trying to show people two things:

First, most Americans favor redistribution of wealth. You’re not alone in wanting that. It’s not some fringe opinion.

Second, there is a real difference between Democrats and Republicans on this issue. The canard “The two parties are the same” is the most untrue it has been in at least twenty years.

I would even understand if there are other issues you consider more important than wealth redistribution. Ecological sustainability is the most defensible—you can’t eat GNP—though that would push you even harder toward the left. Among things that might push you right, I can understand being concerned about higher taxes hurting economic growth, and while I think the view that abortion is murder is ludicrous, given that as your belief I can understand why you would want to prioritize fighting abortion. (If I thought we were murdering millions of babies every year, I’d be pretty mad too! Of course, you should be glad, then, that the US abortion rate has been falling. Right? You know about that, right?)

What I don’t get, however, is people who thought that voting for Donald Trump would help working people. I don’t understand how you can see someone who epitomizes everything that is wrong with the billionaire rentier class and think, “Yeah, he seems like he’s definitely a populist. That guy who was born insanely rich and made even more mind-boggling amounts of money by lying and screwing people over is definitely going to look out for folks like me.”

If I understood that, maybe I would know where to go from here. But people’s political beliefs can be astonishingly intransigent to evidence. Politics is the mind-killer.

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.

Tax plan possibilities

Mar 26, JDN 2457839

Recently President Trump (that phrase may never quite feel right) began presenting his new tax plan. To be honest, it’s not as ridiculous as I had imagined it might be. I mean, it’s still not very good, but it’s probably better than Reagan’s tax plan his last year in office, and it’s not nearly as absurd as the half-baked plan Trump originally proposed during the campaign.

But it got me thinking about the incredible untapped potential of our tax system—the things we could achieve as a nation, if we were willing to really commit to them and raise taxes accordingly.

A few years back I proposed a progressive tax system based upon logarithmic utility. I now have a catchy name for that tax proposal; I call it the logtax. It depends on two parameters—a poverty level, at which the tax rate goes to zero; and what I like to call a metarate—the fundamental rate that sets all the actual tax rates by the formula.

For the poverty level, I suggest we use the highest 2-household poverty level set by the Department of Health and Human Services: Because of Alaska’s high prices, that’s the Alaska poverty level, and the resulting figure is $20,290—let’s round to $20,000.

I would actually prefer to calculate taxes on an individual basis—I see no reason to incentivize particular household arrangements—but as current taxes are calculated on a household basis, I’m going to use that for now.

The metarate can be varied, and in the plans below I will compare different options for the metarate.

I will compare six different tax plans:

  1. Our existing tax plan, set under the Obama administration
  2. Trump’s proposed tax plan
  3. A flat rate of 30% with a basic income of $12,000, replacing welfare programs and Medicaid
  4. A flat rate of 40% with a basic income of $15,000, replacing welfare programs and Medicaid
  5. A logtax with a metarate of 20%, all spending intact
  6. A logtax with a metarate of 25% and a basic income of $12,000, replacing welfare programs and Medicaid
  7. A logtax with a metarate of 35% and a basic income of $15,000, cutting military spending by 50% and expanding Medicare to the entire population while eliminating Medicare payroll taxes

To do a proper comparison, I need estimates of the income distribution in the United States, in order to properly estimate the revenue from each type of tax. For that I used US Census data for most of the income data, supplementing with the World Top Incomes database for the very highest income brackets. The household data is broken up into brackets of $5,000 and only goes up to $250,000, so it’s a rough approximation to use the average household income for each bracket, but it’s all I’ve got.

The current brackets are 10%, 15%, 25%, 28%, 33%, 35%, and 39.6%. These are actually marginal rates, not average rates, which makes the calculation a lot more complicated. I did it properly though; for example, when you start paying the marginal rate of 28%, your average rate is really only 20.4%.

Worst of all, I used static scoring—that is, I ignored the Laffer Effect by which increasing taxes changes incentives and can change pre-tax incomes. To really do this analysis properly, one should use dynamic scoring, taking these effects into account—but proper dynamic scoring is an enormous undertaking, and this is a blog post, not my dissertation.

Still, I was able to get pretty close to the true figures. The actual federal budget shows total revenue net of payroll taxes to be $2.397 trillion, whereas I estimated $2.326 trillion; the true deficit is $608 billion and I estimated $682 billion.

Under Trump’s tax plan, almost all rates are cut. He also plans to remove some deductions, but all reports I could find on the plan were vague as to which ones, and with data this coarse it’s very hard to get any good figures on deduction amounts anyway. I also want to give him credit where it’s due: It was a lot easier to calculate the tax rates under Trump’s plan (but still harder than under mine…). But in general what I found was the following:

Almost everyone pays less income tax under Trump’s plan, by generally about 4-5% of their income. The poor benefit less or are slightly harmed; the rich benefit a bit more.

For example, a household in poverty making $12,300 would pay $1,384 currently, but $1,478 under Trump’s plan, losing $94 or 0.8% of their income. An average household making $52,000 would pay $8,768 currently but only $6,238 under Trump’s plan, saving $2,530 or about 4.8% of their income. A household making $152,000 would pay $35,580 currently but only $28,235 under Trump’s plan, saving $7,345 or again about 4.8%. A top 1% household making $781,000 would pay $265,625 currently, but only $230,158 under Trump’s plan, saving $35,467 or about 4.5%. A top 0.1% household making $2,037,000 would pay $762,656 currently, but only $644,350 under Trump’s plan, saving $118,306 or 5.8% of their income. A top 0.01% household making $9,936,000 would pay $3,890,736 currently, but only $3,251,083 under Trump’s plan, saving $639,653 or 6.4% of their income.

Because taxes are cut across the board, Trump’s plan would raise less revenue. My static scoring will exaggerate this effect, but only moderately; my estimate says we would lose over $470 billion in annual revenue, while the true figure might be $300 billion. In any case, Trump will definitely increase the deficit substantially unless he finds a way to cut an awful lot of spending elsewhere—and his pet $54 billion increase to the military isn’t helping in that regard. My estimate of the new deficit under Trump’s plan is $1.155 trillion—definitely not the sort of deficit you should be running during a peacetime economic expansion.

Let’s see what we might have done instead.

If we value simplicity and ease of calculation, it’s hard to beat a flat tax plus basic income. With a flat tax of 30% and a basic income of $12,000 per household, the poor do much better off because of the basic income, while the rich do a little better because of the flat tax, and the middle class feels about the same because the two effects largely cancel. Calculating your tax liability now couldn’t be easier; multiply your income by 3, remove a zero—that’s what you owe in taxes. And how much do you get in basic income? The same as everyone else, $12,000.

Using the same comparison households: The poor household making $12,300 would now receive $8,305—increasing their income by $9,689 or 78.8% relative to the current system. The middle-class household making $52,000 would pay $3,596, saving $5,172 or 10% of their income. The upper-middle-class household making $152,000 would now pay $33,582, saving only $1998 or 1.3% of their income. The top 1% household making $782,000 would pay $234,461, saving $31,164 or 4.0%. The top 0.1% household making $2,037,000 would pay $611,000, saving $151,656 or 7.4%. Finally, the top 0.01% household making $9,936,000 would pay $2,980,757, saving $910,000 or 9.1%.

Thus, like Trump’s plan, the tax cut almost across the board results in less revenue. However, because of the basic income, we can now justify cutting a lot of spending on social welfare programs. I estimated we could reasonably save about $630 billion by cutting Medicaid and other social welfare programs, while still not making poor people worse off because of the basic income. The resulting estimated deficit comes in at $1.085 trillion, which is still too large—but less than what Trump is proposing.

If I raise the flat rate to 40%—just as easy to calculate—I can bring that deficit down, even if I raise the basic income to $15,000 to compensate. The poverty household now receives $10,073, and the other representative households pay $5,974; $45,776; $297,615; $799,666; and $3,959,343 respectively. This means that the poor are again much better off, the middle class are about the same, and the rich are now substantially worse off. But what’s our deficit now? $180 billion—that’s about 1% of GDP, the sort of thing you can maintain indefinitely with a strong currency.

Can we do better than this? I think we can, with my logtax.

I confess that the logtax is not quite as easy to calculate as the flat tax. It does require taking exponents, and you can’t do it in your head. But it’s actually still easier than the current system, because there are no brackets to keep track of, no discontinuous shifts in the marginal rate. It is continuously progressive for all incomes, and the same formula can be used for all incomes from zero to infinity.
The simplest plan just replaces the income tax with a logtax of 20%. The poor household now receives $1,254, just from the automatic calculation of the tax—no basic income was added. The middle-class household pays $9,041, slightly more than what they are currently paying. Above that, people start paying more for sure: $50,655; $406,076; $1,228,795; and $7,065,274 respectively.

This system is obviously more progressive, but does it raise sufficient revenue? Why, as a matter of fact it removes the deficit entirely. The model estimates that the budget would now be at surplus of $110 billion. This is probably too optimistic; under dynamic scoring the distortions are probably going to cut the revenue a little. But it would almost certainly reduce the deficit, and very likely eliminate it altogether—without any changes in spending.

The next logtax plan adds a basic income of $12,000. To cover this, I raised the metarate to 25%. Now the poor household is receiving $11,413, the middle-class household is paying a mere $1,115, and the other households are paying $50,144; $458,140; $1,384,475; and $7,819,932 respectively. That top 0.01% household isn’t going to be happy, as they are now paying 78% of their income where in our current system they would pay only 39%. But their after-tax income is still over $2 million.

How does the budget look now? As with the flat tax plan, we can save about $630 billion by cutting redundant social welfare programs. So we are once again looking at a surplus, this time of about $63 billion. Again, the dynamic scoring might show some deficit, but definitely not a large one.

Finally, what if I raise the basic income to $15,000 and raise the metarate to 35%? The poor household now receives $14,186, while the median household pays $2,383. The richer households of course foot the bill, paying $64,180; $551,031; $1,618,703; and $8,790,124 respectively. Oh no, the top 0.01% household will have to make do with only $1.2 million; how will they survive!?

This raises enough revenue that it allows me to do some even more exciting things. With a $15,000 basic income, I can eliminate social welfare programs for sure. But then I can also cut military spending, say in half—still leaving us the largest military in the world. I can move funds around to give Medicare to every single American, an additional cost of about twice what we currently pay for Medicare. Then Medicaid doesn’t just get cut; it can be eliminated entirely, folded into Medicare. Assuming that the net effect on total spending is zero, the resulting deficit is estimated at only $168 billion, well within the range of what can be sustained indefinitely.

And really, that’s only the start. Once you consider all the savings on healthcare spending—an average of $4000 per person per year, if switching to single-payer brings us down to the average of other highly-developed countries. This is more than what the majority of the population would be paying in taxes under this plan—meaning that once you include the healthcare benefits, the majority of Americans would net receive money from the government. Compared to our current system, everyone making under about $80,000 would be better off. That is what we could be doing right now—free healthcare for everyone, a balanced budget (or close enough), and the majority of Americans receiving more from the government than they pay in taxes.

These results are summarized in the table below. (I also added several more rows of representative households—though still not all the brackets I used!) I’ve color-coded who would be paying less in tax in green and who would be more in tax in red under each plan, compared to our current system. This color-coding is overly generous to Trump’s plan and the 30% flat tax plan, because it doesn’t account for the increased government deficit (though I did color-code those as well, again relative to the current system). And yet, over 50% of households make less than $51,986, putting the poorest half of Americans in the green zone for every plan except Trump’s. For the last plan, I also color-coded those between $52,000 and $82,000 who would pay additional taxes, but less than they save on healthcare, thus net saving money in blue. Including those folks, we’re benefiting over 69% of Americans.

Household

pre-tax income

Current tax system Trump’s tax plan Flat 30% tax with $12k basic income Flat 40% tax with $15k basic income Logtax 20% Logtax 25% with $12k basic income Logtax 35% with $15k basic income, single-payer healthcare
$1,080 $108 $130 -$11,676 -$14,568 -$856 -$12,121 -$15,173
$12,317 $1,384 $1,478 -$8,305 -$10,073 -$1,254 -$11,413 -$14,186
$22,162 $2,861 $2,659 -$5,351 -$6,135 $450 -$9,224 -$11,213
$32,058 $4,345 $3,847 -$2,383 -$2,177 $2,887 -$6,256 -$7,258
$51,986 $8,768 $6,238 $3,596 $5,794 $9,041 $1,115 $2,383
$77,023 $15,027 $9,506 $11,107 $15,809 $18,206 $11,995 $16,350
$81,966 $16,263 $10,742 $12,590 $17,786 $20,148 $14,292 $17,786
$97,161 $20,242 $14,540 $17,148 $23,864 $26,334 $21,594 $28,516
$101,921 $21,575 $15,730 $18,576 $27,875 $30,571 $23,947 $31,482
$151,940 $35,580 $28,235 $33,582 $45,776 $50,655 $50,144 $64,180
$781,538 $265,625 $230,158 $222,461 $297,615 $406,076 $458,140 $551,031
$2,036,666 $762,656 $644,350 $599,000 $799,666 $1,228,795 $1,384,475 $1,618,703
$9,935,858 $3,890,736 $3,251,083 $2,968,757 $3,959,343 $7,065,274 $7,819,932 $8,790,124
Change in federal spending $0 $0 -$630 billion -$630 billion $0 -$630 billion $0
Estimated federal surplus -$682 billion -$1,155 billion -$822 billion -$180 billion $110 billion $63 billion -$168 billion