An Inequality Tax Trigger: The Brandeis Ratio Explained

On Monday, Aaron Edlin and I published a cri de coeur op-ed in the New York Times calling for a Brandeis tax, an automatic tax that would put the brakes on income inequality.  This is the second in a series of posts (the first post is here) explaining more about our rationale and providing more details on how a Brandeis tax might be implemented.

An Inequality Tax Trigger
By Ian Ayres and Aaron Edlin

A central idea behind our Brandeis tax proposal was to have a tax that is triggered by increases in inequality. Our Brandeis tax does not target excessive income per se; it only caps inequality. Billionaires could double their current income without the tax kicking in — as long as the median income also doubles. The sky is the limit for the rich as long as the “rising tide lifts all boats.” Indeed, the tax gives job creators an extra reason to make sure that corporate wealth does in fact trickle down.

But in crafting an inequality trigger we might have chosen a more traditional measure of income inequality – such as the Gini coefficient or the Herfindahl-Hirschman Index (HHI).  Any standard of inequality would show a sharp increase over the last 25 years. 

In part, we choose the Brandeis ratio because we think it is more transparent. We could try to explain that the Gini number represents the ratio of two areas, including crucially the area above the Lorenz curve. The Lorenz curve is the inequality measure that Robert Shiller and coauthors use in their 2006 paper on this topic of inequality of tax triggers; they account for behavioral responses to such changes and consider how to optimally balance the benefits of lower risk and higher economic growth with the traditional negative incentive effects.  For those interested in the details, Shiller, one of the paper’s authors, has also written a compelling book on the costs of high risk finance and even proposed “inequality insurance.”  Shiller should get credit for coming up before us with the general idea of an inequality-contingent tax system.

Or alternatively, we might explain that a slight modification of the HHI represents the probability that two randomly selected items come from the same source.  For example, in antitrust analysis, if the modified HHI for the lawnmower market is equal to .43, that means there is a 43% chance that two randomly selected lawnmowers would have been produced by the same company.  A market is more concentrated if this probability approaches 100%. As applied to income concentration, the modified HHI would tell you the probability that two random dollars of income would be received by the same person (or possibly the probability that the two randomly selected dollars would have been earned by people of the same economic class).  But notwithstanding this nifty interpretation, it remains unclear why this probabilistic concentration measure is related to the Brandeis concern that excess inequality and democracy are incompatible.

In contrast, the Brandeis ratio as a measure of concentration is immediately graspable, and is more closely tied to the specific concern that a sliver of plutocrats with gargantuan wealth could distort the political process.  It doesn’t take a Ph.D in economics to understand that something seismic has occurred when the average one percenter goes from earning 12.5 medians to 36 median incomes.  It’s true that not all these measures of inequality are about income inequality; some might rightfully cite the Nobel Laureate Amartya Sen in arguing that income alone doesn’t capture human welfare, hence the multidimensional indices often used in global development.  Indeed, part of Brandeis’s concern was not income equality for its own sake but rather the consequences of income inequality on democracy.

More subtly, the Brandeis ratio intentionally ignores what is happening to two other parts of the income distribution.  Unlike the Gini coefficient, the Brandeis ratio does not take into account how many Americans are unemployed or living below the poverty line.  This is not a weakness.  The purpose of our inequality tax is not to respond to short- or even medium-term business cycle fluctuations.  We want the tax to respond to long-term structural shifts in inequality.  We consider it a strength of the measure that the denominator (the median household income) is relatively uninfluenced by the unemployment rate.  And using the Brandeis trigger similarly is independent of the impact of illegal immigration on the economy – so we don’t have to worry that in the shadow of a Brandeis tax that Congress would have particularly different incentives to include or exclude new lower paid households from entering the economy.  There are important debates and reforms needed to respond to the separate questions of structural unemployment and undocumented workers, but the Brandeis is geared toward another – to our minds – even more important policy issue. 

The Brandeis ratio as a measure of income inequality also doesn’t pay attention to the relative success of 2- or 3-percenters over time.  Focusing just on the relative income of the richest one percent is appropriate if we are concerned with the deleterious impacts of inequality on our democratic institutions because one-percenters (those currently making more than $330,000) disproportionately fund our political campaigns.  As emphasized by Lawrence Lessig in Republic, Lost (presaged somewhat in Ayres’ book with Bruce Ackerman, Voting With Dollars), the bulk of campaign finance dollars comes disproportionately from not just the 1% club, but the richest one-half of one-percenters.  Focusing on the average income of one-percenters is a good proxy for the rising political power of plutocrats.

But at the end of the day, we’re not wedded to the idea that there needs to be any single sufficient statistics.  We could imagine a world in which a Brandeis tax was contingent on a different inequality measure or even upon multiple measures.

For example, one might argue that rising wealth inequality could be an even worse problem for democracy than income inequality.  Accordingly, one could imagine a wealth tax or an estate tax that was contingent on some measure of wealth inequality.  But given the current political environment, an income-contingent wealth tax is bridge too far.

Steve Silberstein has been promoting an interesting way to make the corporate income tax for specific corporations contingent on an analogous inequality ratio.  As mentioned in the New Republic:

[A]nother proposal, put forward by investor Steve Silberstein, would adjust the corporate tax rate based on the ratio of CEO pay to the average worker. A company with a ratio at the 1980 level of 50:1 would pay tax at the current rate of 35 percent, with the rate rising
for companies with a higher ratio and lower for those with a narrower pay gap.

We had briefly thought about modifying our proposal to allow one percenters to avoid a trigger Brandeis tax if they could show that their income was less than 36 times the median income of workers who produced it, but concluded that personalized Brandeis ratios would be an administrative nightmare.  The Silberman corporate tax proposal is by comparison elegantly straightforward.

While we proposed a Brandeis tax based on the 2006 pretax Brandeis ratio of 36, it would be more natural to use a trigger based on an after-tax Brandeis ratio which went from something like 8 medians in 1980 to about 25 medians in 2006.1  Accordingly, the IRS might each year calculate the after-tax ratio and trigger the Brandeis tax if the ratio exceeds 25 medians.

Our proposal of a 36-median cap was doubly conservative.  The first reason is because the tax only asked that the after-tax ratio not exceed the pretax 2006 ratio and the second is because the tax used the 2006 year as a trigger, a year that probably had a higher Brandeis ratio than we would find today. The Brandeis ratio is likely to decline during a recession because the average income of one-percenters (think hedge-fund managers) is more sensitive to the recession than the median U.S. income.   Indeed, another debate which we would like to promote is about the question of the appropriate trigger size. 

Our proposal starts with an out-of-the-money status quo inequality trigger as a way to promote political common ground.  You can vote for a contingent Brandeis tax without voting to necessarily raise taxes.  Ours is a “tax more tomorrow” idea where the relevant tomorrow may never come.  Our trigger avoids the concern that we’re engaged in crude “class warfare.” It doesn’t take away any of existing inequality, it just tries to make sure that 99% share in prospective future gains of the 1%.  But reasonable people could argue for either higher or lower triggers – for example, returning to a simpler time when rich people only earned 20 medians.   Perhaps like with carbon emissions we could seek to lower inequality to 1990 levels by 2020. 

1 Our after-tax estimates of the Brandeis ratio are estimates, because we do not have comparable information on the after-tax median household income.  As a proxy, we used CBO after-tax data and divided the after-tax average income of one-percenters by the average income of the third quintile.


This is 'wealth redistribution' no matter what you try to call it! Pure Marxist garbage all dressed up is still Socialism/Communism.

We cannot tax our way back to prosperity! Personal responsiblity is what we need to get back to. Save our social/economic safety nets for the truly needy.

They were designed to help US citizens (note: not illegal aliens) who CAN'T work - not those who WON'T, due to extended dependence on Goverment handouts.

No one owes me or anyone else - a living!


All economic activity is wealth redistribution. The concern is that it has been distributed in an inceasingly unequal way, turning the USA into a mockery of its ideals. Call it all the nasty labels you want, but there are strong indicators that one *can*, in fact, tax one's way back to prosperity. You cannot have a healthy economy when the vast majority of people has problems meeting their basic needs and a small minority wallows in luxury.

This has absolutely nothing to do with government handouts. go take your strawmen elsewhere.


"Focusing just on the relative income of the richest one percent is appropriate if we are concerned with the deleterious impacts of inequality on our democratic institutions because one-percenters (those currently making more than $330,000) disproportionately fund our political campaigns."

It's curious then, if this is the concern, why your attention doesn't turn to examining how increased funds available for campaigns impacts elections or what can be done to neutralize it's effects if needed, but instead turns to how to redistribute wealth? Wealth redistribution always seems to be a bunt force sloution in search of a problem, doesn't it?


Why do you think inequality can be overcome? It's a fundamental result of the Constructal Law ( No matter what scheme is devised to circumvent them, CL forces will ultimately defeat it or the system itself will collapse.

I must admit at that endpoint equality will be achieved -- but everyone will be dead or so impoverished it won't matter.

It is so much wiser to design tax systems that give the least wealthy a comfortable, healthy life than to worry about inevitable disparities.


Absolutely fascinating link – thank you very much.

After my first dive into constructal theory, however, I am not quite clear about why it would necessitate the ever increasing levels of income inequality we see today. In fact, is it not quite the opposite? Most 'tree' structures are area-to-area (root and branch systems of trees, drainage basin and and delta systems of rivers, dense capillaries at both lungs/stomach and muscles, etc.), so if we visualise the economy as a flow of value, we would also expect the evolution of a many-to-many system, with value flowing too quickly along the major central trunks to be deposited/captured. In fact, it would take concerted, opposing actions to prevent such an evolution, instead capturing the value along the main trunk and leading, by the theory, to the end of the evolution of flow, and the death of the system – a prediction that seems well-inline with the strong economic malaise we are presently observing.

What am I missing?



Suppose there is a town with 100 people, all with perfectly equal abilities and opportunities, and all earning $50k/yr in 1980. Everyone except Bill spends everything they earn, but Bill invests half of what he earns. Since 1980, everyone's earning ability has doubled and 60 people decide to work only 3/4 as much to be with their families more. With an interest rate of 5%, the Brandeis ratio of this town will have more than tripled despite the fact that opportunity is perfectly equal. How is this a good basis for an "inequality" tax?


Because while people like you and I are concerned about equailty of opportunity, Brandeis professorss are apparently more concerned with equality of outcome.


Government waste, overspending, dependency, or corruption indices would be better IMHO.


I raised several questions about this proposal in Monday's blog. I'll return to the most relevant one, which is how does the increase in taxation on the 1% cohort help those in the 50th percentile? Just raising more revenue, by lowering the Brandies ratio, does nothing that I can see to help raise all the boats that aren't yachts (which is 99% of them).


If your concern really is "the deleterious impacts of inequality on our democratic institutions because one-percenters (those currently making more than $330,000) disproportionately fund our political campaigns," then why not simply limit the campaign contributions of the 1% to 36 times the campaign contributions of the median American? That would limit the political influence of the 1% much more than your proposal because the disposable income of the 1% is much higher than 36x the disposable income of the median American under your plan (even if one grants the dubious premise that campaign contributions have nearly as much influence as you assign them)


I like the idea, but I see unintended consequences. Say I'm a CEO being "held back" by the Brandeis ratio. Do I.....

1. Live with less money?

2. Work to raise median incomes?

3. Demand to be "paid" in Jaguars, houses, and jewelry?

Something tells me most CEOs would choose #3. What could be done to mitigate this?


Well, of course there would be a commission to handle that!


If history has proved one things it is that using the tax code for social engineering is doomed to failure.

caleb b

My wife always says how much she hates politics. She thinks it is stupid to even discuss taxes.

This is her first year in the workforce and her first "real" job.
She recieved a nice Christmas bonus of $1,000 - but only received $638. She was angry, "how can they take that much!?!?" I said, "Welcome to caring about politics."

Mike S

The reason this idea is particularly stupid is that rich people are easily able to avoid having taxable income. Most of the growth in their wealth comes from unrealized gains (appreciation in assets). In turn they can pay for their lavish lifestyles by borrowing against this appreciation, all without having any taxable income. Jack and Jill on the other hand, who come from middle class families, work and study very hard to become a big firm lawyer and a surgeon at a prestigious hospital and then continue to work grindingly long hours, will experience nearly all the growth in their wealth in the form of taxable income (likely W2 income or allocated partnership income). They in turn will take it in the shorts as a result of a tax like this. Meanwhile, the trust fund babies with the much larger homes down the street will not be touched by this tax.


I really have to question the fundamental assumption on which this tax scheme is based, which is that wealth inequality is a bad thing. On the contrary, it's a very good thing, and one of the basic foundations on which this country was built. There are plentiful examples, for instance (John Jacob Astor came to the US as a poor immigrant in 1784, and by his death had a fortune estimated at $110.1 billion in 2006 dollars), Cornelius Vanderbilt, Stephen Girard. All of these were richer, both in comparison to the average American and as a fraction of GNP, than most of today's 1%.


Rehajm makes some excellent points:
1. Reform in campaign finance rules are equally necessary to avoid the political distortions that go along with high concentrations of wealth and income. Unfortunately, since politicians write the rules and at the same time are the main bebeficiaries, asking them to cut off the tap is like asking the pigs to leave the trough;
2. Ben - yoir example of the town with 100 people ignores certain factors: what if some of the citizens began paying the mayor to assign the the best ocations in town; limiting access to the local schools to their children; ensuring their businesses received the lion's share of town funds; serving on each others oversight boards and voting for each others salaries? Would you still call it a purely meritorious outcome?
3. Mr.AtoZ - how can generating more revenue from the top percentile help the 50th percentile? Let's see: increased funding for Pell Grants and other needs-based educational loans; more money for poorer schools; increases to shamefully low teacher salaries; investments in relevant urban and rural infrastructure; increased funding for retraining and workforce education programs so the jobless can get back to work; or how about simply lowering taxes on the bottom 50%?
4. Scheinemann - history proves exactly the opposite. The history of the 19th and 20th centuries is one of growing empowerment and wealth, as a share of the total, for the poorest classes. The fact that there was strong economic growth AND greater equality of income makes rubbish of the arguments that you need income or wealth inequality to generate new jobs or economic growth. In fact, the opposite is true - extractive plutocracies are almost always net destroyers of national wealth.