Stephen Williamson on inequality and taxation

It is an excellent post.  The first part deals with Robert Frank, the second part deals with the recent Diamond and Saez paper, excerpt:

Finally, I have no idea where that “behavioral elasticity” is coming from, and I don’t trust it. My best guess is that it includes none of the factors that I think are important in addressing the problem. What we need here is a dynamic general equilibrium model that can take account of the short run and long run effects of a change in the income tax schedule. My best guess is that “behavioral elasticity” means that Diamond and Saez are measuring the effects of tax evasion and the intensive margin of labor supply, and that’s all. If so, I think they miss most of what is important:

1. There’s also an extensive margin. Tax people at a higher rate, and some drop out of the labor force.
2. Taxes affect occupational choice. Some work by Manuelli/Seshadri/Shin says that the effect of taxes on human capital is big time. Why do I want to undertake a costly and risky investment for a very small payoff?
3. Entepreneurial activity has to be very elastic with respect to tax rates at the top end. Why would I want to risk my own wealth or that of my close family for a very big payoff with very low probability, if that big payoff is taxed at 73%?
4. The United States is highly dependent on highly-skilled labor that migrates here from other countries. With a top tax rate of 73%, the Indian engineers might prefer to work in India, and the Canadian professors might prefer Canada.

Thus, I think it is likely that tax revenue is much more elastic with respect to the tax rate, particularly in the long run, than Diamond and Saez are letting on. To evaluate this properly, you need a serious model, and they have not provided one.


My pet issue, the discussion of taxes are always so bizarre. What are we getting for the price increase? Well, today what we are getting is the crap government bought with debt for the past 20 years. But in general, people don't usually get away with raising prices by berating the customer.

It's a fair question.

My vote is for less guns and better infrastructure.

You are not a customer in this relationship. Unless you usually buy things based mostly on other people's preferences.

I agree with Andrew. If I thought the money would be put to good use I would not mind paying more taxes but to me it seems like it would be easy to reduce SS by 30% without hurting the poor, cut defense 50% without hurting security, cut medicare 40% without hurting the elderly and slash education spending both local and federal by 50% and get the same output. So why increase texts? I outline my reasons at the link below:

Assuming all their assumptions are right, then 73% is the number they get, assuming that money is all that matters. But I assume one really big assumption is that we get something for that 73% collected in taxes. As of now, we are getting negative returns on much of what we send to D.C. That is not a libertarian take, that is this libertarian's objective view. What we get with $1 sent to government is them borrowing $2 to pay for unsustainable wars and transfer programs.

Our transfer programs were perfectly sustainable under Clinton, etc. We're charging rich people and corporations too little, they're not hiring because there's no incentive to invest, since it won't be taxed. And oh yes, we're subsidizing Oil directly and pharmas with medicare part d. That's your deficit.

If you're rich, you're getting more than your money out of this, because of stock buybacks and tax cuts for the corporations you benefit from.

Yes - a lot of people with million dollar incomes will ceartainly stop working.

Yes - with a 73 % tax rate the income of a indian engineer will be about the same as if he lived in the US (and of course the tax rate on the rich in one continent do not have an effect on the cost/benefit of tax rates in other countries)

"2 & 3."
Yes - because a safty net on the downside can´t possible more than make up for the axpected payoff on the upside. That is why e.g. Swedes are so hostile to changes.

And they say that there doesn´t exist any funny rightwing comedians.

PS: “4” And obviously brain drain is a no brainer as long as the US is benefiting.

Yes, let's enslave the smart people of developing countries to keep them where they were born.

What are you talking about?
My argument amounted to "why is it better that he makes the US rich instead of India"
Your argument is, i guess, that he should keep a bigger cut of his salary (beucase if he does not - he is a slave).

It is better that he makes the US rich because we are talking about tax policies of the US and not India.

As an aside this is also better because it makes him richer.

PS 2: For some unexplainable reason I followed the link and yes, Cowen, you are absolutely right – “excellent post” - and I will hereby declare Williamson as world champion in no rules straw man wrestling.

Say – do you think the positions Willamson is telling us that Frank have is somewhat resembling to those who Frank actually do hold?

But maybe you are rather referring to the many deep insights he is sharing with us thorough the post, such as: “Given mobility within the income distribution, we all care, for selfish reasons, about how the rich are treated, as we all could be rich some day, or our descendants could be rich.”
I do not even feel a need to argue against it – are you sure that it is Williamson and not Colbert who has written the post?

Also, are there fairies in the fictional rightwing universe?

Yes, there are fairies, but they can't get married.


Thread winner.


The people in million dollar homes generally already showed their tax avoiding hand, mortgage insurance and property tax deductions are much larger on a million dollar home than on a $300,000 home, but the utility difference is much more modest.

This post is silly. You don't need mortgage insurance if you put down 20%+ as most million dollar home buyers do.

And the utility function doesn't apply. The same exact house might cost $300K in suburban Houston and $1 million in Marin County (north of SF). People move to expensive areas and take out bigger mortgages to get a bigger deduction?

If the to tax rate is 73%, The indian engineer is still well ahead of his income in India. Besides, how much do you think Indian engineers make in the US? If all you did was raise the current top rate, most won't even be hit at all.

“If the to tax rate is 73%, The indian engineer is still well ahead of his income in India.”

Off course he is. My “yes” was Ironic. Williamsons (and Cowens by agreement?) positions were so stupid that I did not even fell the need to argue against them. Simply spelling them out was enough.


Why does everyone forget or not understand MARGINAL tax rates? When lefties call for rates to go back to the 1950s so the 'rich' get taxed at 70%+, they don't realize how rich you had to be to even see that rate, and it was only on the very upper part of your income, not the majority of it.

And when righties like Larry Kudlow say (quote): "Why don't we get rid of the 10% tax bracket, no one pays that anyway" are they so stupid they don't realize that EVERYONE with a higher income pays exactly that rate on their first $20,000 or so of income? Actually, I know the answer in Kudlow's case.


Income surveys often put Indians in the top ethnic brackets. So I bet they make a lot on average.

This is not a satirical question - who in today's America is paying a tax rate of 73% on anything? And i mean that literally literally, so to speak.

I'll admit to have not reading the article, in this case - 73% is such an obviously absurd number in an A merican context, however, I can't imagine that the article is worth my time.

Remember when Astrid Lindgren had to pay 103% of her income of her tax - yeah, me neither, but apparently it happened - once. depending on how you calculated the taxes in that year.

No one in today's America pays a 73% tax on anything (for that matter, I certainly don't pay anywhere near that much in the socialist Green hell that is Germany, even if I luckily earn less than the American level required for me to be double taxed (only the U.S. taxes such income twice, when it is earned outside of its boundaries - German tax office employees find this bizarre, by the way, according to my wife) But if necessary to make a point, I guess some people will do whatever is required to try to make their point.

Hell, 73% percent makes America look positively unattractivecompared to Germany, a trope that no one has bothered to advance until now.

I think it's a proposal.

Who is paying 73%. Why Greg Mankiw is. He did a post last year where he showed that the expiration of the Bush tax cut for the wealthiest eliminated all incentives for him to write a column. It was silly. He compounded interest, carried things forward till an estate tax captured some of the $500 payment, etc.

The truth is that with the Bush tax cuts--marginal rates, cap gains and ord dividend--the top .1%, which had been paying 28% of AGI in taxes, began paying 21% of AGI in taxes.

Merry Christmas.

Oh, if only he were rational and followed his incentives.

Nice. LOL.

I think most people agree that cap gains should be treated differently.

"It was silly. He compounded interest, carried things forward till an estate tax captured some of the $500 payment, etc." It's a math thing, Bill.

This thing lead by wrong decisions.

The Diamond and Saez paper is based on empirical evidence. Frank (based on the excerpt) is based on "best guess."

1) Some drop out of the labor force due to higher rates. Some work harder to earn the same after tax income as they did before. Some just work a normal schedule. Which effect predominates?

3) The US was booming in the post war years at very high marginal rates. That suggests Frank's "best guess" isn't supported.

4) The key phrase is "might prefer." Again, supposition rather than evidence.

When I see charts of US tax rates against GDP growth or other such macro variables, I see no consistent relation. Based on that alone, I find Frank's work (as reported here) implausible.

Substitute "Williamson" for "Frank" in my comment.

First of all, it's a really bizarre argument- if we tax the snot out of the bottom 10% we won't affect GDP much either. Anyway, you didn't see my comment about how ever increase in marginal rate was followed by a drop in GDP. This isn't a survey of the psychoanalyst usage by CEOs or sales of Atlas Shrugged, but GDP. Pretty remarkable that changes in one variable bubble all the way up to a noticeable blip in GDP at all. Zoom in on the chart.

Also, the above mention of Sweden is bizarre to me. They tax more and end up with lower GDP/capita. What's the problem? And that is a country that happens to be full of Swedes. Where would the inequality come from? In Sweden if someone ended up filthy rich then you might even justifiably wonder if it was luck. I don't get it. It's like Sweden muddling through proves that totalitarianism could never happen in Europe. Grabbing money from the top and handing it to the bottom isn't really central planning.

More Angry Bear:

"At 70% tax rates, there is more of an incentive to reinvest in the business, creating more growth in the business in subsequent years, and more economic growth thereafter. 70% tax rates are more likely to generate faster economic growth than 25% tax rates precisely because people are self-interested and the higher tax rates induce people to continue investing in things they do well."

The point is that you aren't actually getting the 70% when you tax at 70%. You are using the poor ROI of government to scare people into reinvesting. So, let's fix the whole "soak the 1%" that actually takes resources away from small business proprietors before instituting the high tax rate. Or, let's just call the whole thing off.

And "empirical," really? Observation or experiment? Not exactly.

Change "tax rates" to "taxes actually paid"- tax structure was much different when there were high marginal rates.


"The US was booming in the post war years at very high marginal rates."

That's because, by and large, nobody paid them. They sheltered income in trusts, claimed deductions, deferred compensation or snuck it into untaxable (or unreported) bennies, opened bank accounts in Switzerland or the Bahamas, etc. What do you think TFRA did in 1986? It was largely a wash

The utility of one's labor at 50+% tax rates flattens out very</i quickly, so people either 1) forego activities which would otherwise generate taxable income or 2) avoid taxation thru various means.

BTW, speaking of utility, the notion bandied about on this thread that high IQ Levantines, Asians and Indians will flock to the US to pay high taxes is pretty damn funny.

The whole tax argument misses the point. Many nations that have progressive social spending have what we would consider regressive taxation. Sweden depends a lot less of taxes from the wealthy than the U.S. (which is not to say they don't tax the wealthy heavily.) There aren't enough rich people to tax to fund social spending that could eleveate inequality.

I was wondering that. When we have no rich people we can tax the snot out of them too.

By the way, elevate should be eliminate. Sorry.

On close examination Williamson's argument boils down to personal incredulity/the evidence contradicting his 'common sense'.

'Tax people at a higher rate, and some drop out of the labor force.'

Unqualified assertion. He really does seem to believe the substitution theory of labour supply, as if peope don't *have* to work and they have control over their hours.

'Entepreneurial activity has to be very elastic with respect to tax rates at the top end. Why would I want to risk my own wealth or that of my close family for a very big payoff with very low probability, if that big payoff is taxed at 73%?'

More assertions. Somebody who actually lives in the real world (Buffet) has recently commented that he's never seen anybody not invest because of tax rates. And Williamson is completely ignoring the empirical data he is criticising here, which suggests effects like this aren't that big!

4. is, again, armchair reasoning with nothing to back it up.

‘Tax people at a higher rate, and some drop out of the labor force.’

This Republican talking point needs to be taken out behind the shed and beaten like a red-headed stepchild. My response: go effing ahead and drop out of the work force. Your little self-indulgent solo Occupy Wall Street-like "I'm makin' a moral stand to teach THE MAN a lesson" will go unnoticed by the remaining 180+ million who have to put food on the table.

And per above, who said anything about 73%?

It's not a moral stand at all, that would be ridiculous. It's a matter of practicality.

Buffet also thinks he gets taxed less than his secretary. Probably not a good example.

I don't think he thinks that. I think he thinks he's taxed at a higher tax rate than his secretary.

You mean lower? I think he pays his secretary like $200,000/yr strictly so that he can make that "argument"

No, I'm sure she has a higher tax rate. I'm also sure he offers health insurance and that she owns a home and she may even have children, so the tax rate is a moot point.

Yes, I meant lower. Screwed the pooch.

He's not trying to win a point, he's just noting how since he takes very little income as income and it's mostly cap gains and dividends, he pays a lower rate than a working stiff. And he's right. Anyone who gets all their income from cap gains and dividends does, it's simple math.

I would expect that being Warren Buffet's secretary is not something that anyone can do, and would require significant expense to replace because she already knows how to do things exactly the way she wants them.

There aren't many butlers any more, but people who get jobs as butlers make six figures, because people who hire butlers don't want to deal with the hassle of hiring new butlers.

Putting aside whether or not he does:

a) That wasn't my main point

b) It doesn't invalidate everything else he says if he's wrong about that

He really does seem to believe the substitution theory of labour supply, as if peope don’t *have* to work and they have control over their hours.

Many of the people who earn enough to be hit with the proposed new taxes, 1) don't *have* to work, and 2) do have control over their hours. Personally, my wife & I are more like 5-10 percenters (depending on the year) than 1-percenters, but having worked as an independent consultant for a couple of decades, I have earned, saved & invested enough that I could reduce my hours or even (at 50) retire, and, honestly, that is looking like an increasingly attractive option. Certainly in the face of a marginal rate north of 50%, cutting back on hours worked would be a no-brainer.

Not to deny that some have control over their hours but evidence suggests most of the 1% are high powered executives who have no less control over their hours than the average worker - investment bankers are well known to have long working hours for reasons beyond their control.

But high-income earners working more hours than low-income workers is a new economic/cultural phenomenon. It certainly wasn't that way back in the day of "bankers hours". It is very likely that a return to high marginal rates would lead companies to go back to a pattern of compensating top execs with rich, non-taxable perks and shorter, more relaxed working schedules.

More assertions. Somebody who actually lives in the real world (Buffet) has recently commented that he’s never seen anybody not invest because of tax rates. And Williamson is completely ignoring the empirical data he is criticizing here, which suggests effects like this aren’t that big!

Interestingly conservative lower spending people like Warren will have less money to spend.

> 4. The United States is highly dependent on highly-skilled labor that migrates here from other countries. With a top tax rate of 73%, the Indian engineers might prefer to work in India, and the Canadian professors might prefer Canada.

the top rate would pop in at an engineer's or professor's salary? can't imagine that

If 73% would keep Canadian professors in Canada, then hell yes, let's do it!

To be clear, there is much in Saez's research, probably more than in any other individual's, that deal with some of these questions. At least Williamson was upfront that he has "no idea where that “behavioral elasticity” is coming from."

There is always some healthy skepticism that you can read science with, esp. value judgments (though this argument did not have that many of those). But enlightened skepticism is a bit of an euphemism for ignorance...


A lot of people are mistaking Williamson's in-depth knowledge of the optimal taxation literature as his 'common sense.'

He doesn't really show any in-depth knowledge of anything; he just repeats the standard points about marginal tax rates that do not corroborate with empirical evidence.

What's with all the random assertions in the comments here about the labor supply elasticity, as if it's something we have zero evidence about? Are we living in a world in which Raj Chetty never existed? His forthcoming Econometrica paper on bounding what the elasticity is is well worth a read, for those interested in the topic.

What a joke, typical Tyler Cowen post - have some puppet repeat a bunch of Republican talking points and post it up as serious analysis.

Dunno about the Indian engineer's incentive to emigrate to face a 73% tax rate.

But I do know the effect on the Indian student of blogs such as this. Such Professors can Ben found in plenty in India, why cross the seven seas to do graduate work with such zeroes?

Why is everybody arguing over the labor supply elasticity of mere mortals when it is quite clear from the context that what really matters is that we do not stifle innovation by reducing the expected value of risky but socially beneficial projects? We get it, Joe Schmoe is not going to cut his hours to part time because of a 10 percentage point increase in his tax rate. This is about what projects get picked up and which ones don't. I mean this isn't a hard concept to grasp; the value of a project is multiplicative in the tax rate and success probability. If the tax rate goes up what happens to the minimum requirement for probability of success? What implications does that have for innovation and growth?

Ok. What exactly happens to the incentives of a company to do a risky projekt if their CEO is facing a higher tax on his personal income?

Will the number of risky projects that even is considered by affected by e.g. the founding of basic research and education?

Moving away from companies, what will generally make a person take higher risk. A improvement in the “bad” outcome or a similar improvement in the “good” outcome?

Economics 101 will tell you that the improvement of the bad outcome is making the risky bet more attractive, but maybe you have another theory.

I'm not even talking about the actual value of the reward and the bad outcome since they're both endogenous to the tax rate. The point is that if you think we need more innovation, increasing the top rate is not the way to get you there. It's a shame that given our current tax system we can't distinguish between the innovators and the fat cats.

Govt funding of fundamental research is necessary for technological innovation. Money for that comes from taxes. Higher taxes are needed if we are to sustain the existing level of investment.

No argument with sentences one or two--it's a basic function of government--but you're talking about a line item of $100Bn or so in a $3.7 Trillion budget. Far from clear to me that the only path to keeping the $100Bn is raising taxes, as opposed to reducing spending in other areas. As Tyler noted in TGS, you don't have to be rabidly anti-government to recognize that the last dollar of spending has a lot lower utility than the first dollar.

Yeah, it seems like some people are fixated on wage-earners, but there are issues more critical to economic growth like entrepreneurship, immigration/emigration, and, as you point out, risk.

I see that paper's authors offer many caveats to their information on elasticities, most notably "considerable uncertainty remains in the estimation of the long-run behavioral responses to top tax rates" and "we unfortunately have little compelling empirical evidence to assess whether taxes affect earnings through those long-run channels" (the channels being education and career choices). And they are candid on the weaknesses of using a one-period model. However, people quoting the paper seem much more sure of the empirical support for their assumptions.

Like the authors, I don't have empirical evidence for it, but it seems to me that offering a prospective entrepreneur the choice of "tails you lose, heads you become a 1/4 minority partner in the fruits of your marginal labor, ideas, investment, etc." would have a profoundly negative effect on capital formation.

Downside risk is severely restrained by limited liability laws. Look at what just happened with Frank McCourt. He bought the Dodgers with almost all debt, refinanced it with debt issued by the franchise, then proceeded to use the Dodgers as a credit card he never needed to pay back to fund all the other corporations he started to run the operations of the stadium and his family's own personal spending habits, and to give jobs to his family for doing nothing. What happens? The team goes bankrupt, yet he still manages to sell the franchise at no loss and be personally much richer than he was before.

Obviously, owning a pro sport franchise isn't much like owning a true startup, but even there, people severely overstate the risks. What happens to failed business owners? Are they living destitute on the streets? No, they're usually picking up and trying again until they find a way to finally make money, leaving a trail of pissed-off creditors and duped investors in their wake.

Limited liability laws restrain downside risk to 100% of invested capital--I'd hardly call that a "severe" restraint. I haven't followed the McCourt thing closely, but doubt that's a lesson with wide applications,
As to the fate of failed business owners, I know more than a few who have financed their startups on credit cards and 2nd mortgages...their downside? Personal bankruptcy, loss of savings, loss of home. That is, of course, their choice, but they'll be relieved to know that "people severely overstate the risks". Of course if we want actual data, that would be here:

Perhaps we have too many risky undertakings. There must be an optimal level of risk taking. Certainly professionals in finance got it wrong in asessing risk. Perhaps fewere risks should be taken in many areas. For instance, how much does society gain by the many restaurants and other small businesses that open and fail in less than a year?

That's like asking how much society gains by the many drugs that are developed and fail testing at one stage or another every year.

And the answer to that is?

Interesting. Per #3: If you find partners to spread the risk and reward between then the tax burden becomes much smaller. We now have excellent tools to distribute innovation and investment (a la and don't need to rely on singular individuals taking giant risks anymore.

Someone needs to read Daniel Kahneman's book. There are cognitive biases that provide force against the "rational" decisions in this case.

1. Status quo bias and loss aversion will make someone stay in the job market
2. "Why do I want to undertake a costly and risky investment for a very small payoff?" Because humans suffer from overconfidence bias and risk seeking at low probabilities of success. Humans are are also only sensitive to logarithmic changes in their income and even at a 90% marginal rate, log(0.1*x) = log(x) + log(0.1) ~ log(x) for large x.
3. Same as 2. Overconfidence bias and logarithmic sensitivity to income.
4. Affect heuristic will cause humans to move somewhere they like, regardless of a cost-benefit analysis. There is also a tendency to only see the benefits of something you are in favor of rather than the costs. Taken together, the US brand as a place where you can get ahead (even though there is a ~ 0.6 intergenerational wealth correlation) and the land of the free (even though we have a very high percentage of our people in prison) will dominate a decision to move here more than fiddly bits about relative marginal income tax rates.

At a certain rate, you push people into the black economy. At a 90% tax rate, it all goes underground. In Eastern Europe, where socialist era nominal tax rates could easily exceed 100%, most people made money in the cash economy, and that moral corruption (chronic tax evasion and the perpetual fear that accompanies it) continues to this day. People look for ways to keep income off the books.

At a certain rate r at a certain income x. Whenever the fractional difference in utility between untaxed and taxed amount (log(x) - log(r*x))/log(x) ~ log(r)/log(x) is large (say > 10%), then you will start to get evasion. Back of the envelope says this level is ~ $10 billion for a 90% marginal tax rate and ~$1 million for a 75% marginal tax rate. But it is only ~ $1000 at a 50% marginal rate meaning that most of us** would not notice the difference between our universe and a universe where there was a flat tax of 50%, given proper monetary policy with an NGDP target in both cases.

Basically in order for an amount of money to be large enough where a multi-billionaire would notice the difference, the difference between 10% and 90% of that amount is unimportant relative to the amount itself.

But I agree that 90% rates at $200k in the the 1950s (> $1 million today) are confiscatory and counterproductive. However a 90% rate on income above $10 billion would not be.

** Low income people would notice because the difference could be between earning 75% and 125% of the typical cost of living in the area. This is a fixed cost -- something like renting existence in a city. Above that income level, additional income is buying you retirement and niceties and the log sensitivity to income applies.

2. “Why do I want to undertake a costly and risky investment for a very small payoff?” Because humans suffer from overconfidence bias and risk seeking at low probabilities of success.

Yes but this is true already, in fact starting an entrepreneurial business is probably already a loosing proposition across the entire population. At some point as the odds get worse the most promising would be entrepreneurs will opt for easy safe Government work.

I agree -- at some point. The question here is: at what point? D & S are saying it could be a ~ 70%. At that rate, log(taxrate)/log(income) ~ 0.1 for about $160k, so you could ostensibly set the low end of the 70% tax bracket at that rough order of magnitude.

And government work only seems safe. Consider right now that you are more likely to lose your job if you have a government job. Private employment is growing at roughly the rate of population increase. Government employment is falling. I imagine "small government" forces and recessions could come along and be as devastating to one's government job as robots or other technological changes in other fields.

Well I finally found some proof that the US government creates terrorist. I even found a video of them doing it:

Whose side would you be on in a fight...the little boy or those imperial troopers?

Republicans and Democrats are both responsible for this. Anyone who supports the foreign policy of Hillary Clinton, George W Bush, Obama, Kissinger, McCain, Brezinski, David Brooks, Thomas Friedman, the Council on Foreign Relations.

The issue is not taxes, it's spending. If the government spends 42% of GDP, then at some point, you'll need high taxes. And as the European example shows, those tax rates will be high across the board. Hungary, for example, now has a 27% VAT rate. That's a big hit for the average consumer.

We know where high spending in the US will go: Social Security and Medicare. Thus, you will be taking funds from the productive sector and convert that into straight-forward consumption for retirees. There may be compassion and social responsibility here, but no investment. That in turn means that the productive sector will be stripped of some of its resources. In general, when money is tight, there is a natural tendency to restrain capital expenditures. So high spending may lead to low entrepreneurship and corporate innovation. That would be pretty consistent with the performance of Europe in recent decades, and I would consider something the US should avoid.

Indian engineers might prefer to work in India.

For a guy who questions the seriousness of someone else's research, I found this sentence particularly shocking in its not-backed-by-any-evidence candor: "Entepreneurial activity has to be very elastic with respect to tax rates at the top end."

same old question--why should we care? what evidence (across countries and across time) can you muster that the welfare and taxation of the 1% has any benefits for anyone else? none. you can muster no evidence.

Karl Smith at ModeledBehavior has the right take on this. Delightful.

I don't understand the criticism of behavioral elasticity. Isn't elasticity always a measure of behavior?

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