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.

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  1. Dara says:

    Hidden due to low comment rating. Click here to see.

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    • brazzy says:

      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.

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      • dave says:

        I submit your premise is totally incorrect.
        commerce based economic activity is based on exchange. one exchanged ones time for a paycheck. one exchanges ones paycheck for food that someone else worked and exchanged for.

        income redistribution has no such exchange. It is taking from one without exchange or compensation.

        Hang this on your wall.

        reward production and penalize non-production and you will get production
        penalize production and reward non-production and you will get non-production.

        only production will generate taxes
        only production will feed the masses
        only production will create jobs

        do you need a study of inner city dealings to determine how much tax, food and jobs are created there ?

        When you take from those who have and give to those who have not tried, worked or helped, you have betrayed both.

        Let us get Congress to institute a new policy about taxes. no one gets a tax return. you paid it you lived without it, give it to those who do not work. let the individual check the box on their tax return. if more than half check that box, we voted with our wallets and there is no argument. that is democracy.

        as a note here strictly and only tax PAYERS would be involved. those who do not pay taxes would only benefit and not be otherwise involved.

        problem solved. no one can argue with the democratic voting with one’s own excess cash.

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    • Horatio says:

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    • Tom says:

      Dara, I’d consider myself very fiscally conservative, but when I look at this idea, I think of it like a stop-loss order to sell stock. If you understand that an extreme concentration of wealth (which we have not seen yet) is indeed a threat to any democracy (like a stock in your portfolio plunging is a threat to your wealth), then you must also see the value in a measure to prevent that scenario. It is a safety net – not for the needy, but for the integrity of our system that has worked (reasonably) well and in many ways has facilitated the process for many hard-working people to become very wealthy.

      Of course, all of the direct and indirect effects of this tax idea would need to be analyzed very thoroughly before I’ll fully buy into it; but if it can have the kind of focused, *preventative* effects that it’s purported to aim for, then I think that I could support it.

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      • dave says:

        I challenge you basic premise. the idea of freakenomics is to look at the result, the unintended outcome. take banks out of it, I cannot defend banks bonuses.
        but, if Steve Jobs were to get a job a the local microsoft store,he would be an employee. end of story.
        now, steve jobs has a idea, creates a business, employees builders, manufactures, truckers, architects, production line workers, and builds a multimillion dollar business that employees tens of thousands thru the existence of his product. the wealth he created for those tens of thousands is ??????? every executive lives VERY well, spends tens of thousands on cars boats, their lawn and pool.

        the very existence of the NEW 1%’s shows we as a country are on the RIGHT path.

        I cannot defend a banker who gets a 100mil bonus, or a stock broker who makes 100 mil in oil futures (that drive up the cost of oil) or an actor that makes 30 mil for 6 weeks on a movie shoot.

        Figure out how to reward the producer of wealth where it is spread around and then look at how that is why our economy grows !

        the premise that his fortune is not tied to a much larger fortune is overlooked.

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  2. rehajm says:

    “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?

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  3. Gary says:

    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.

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    • aepxc says:

      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?

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      • Gary says:

        I’m no expert in CL (still a novice student), but the key points of it are maximizing flow AND distributing the blockages so that they impede flow in the whole system at a minimum level. Remember too, that time is a factor as systems adjust. Economically we could be at a point where the global economy is so impeded that income inequity is a temporary condition that will free up the flow of capital by shifting it to people who are more likely to invest large sums (which is more efficient than collecting small sums from many). Over time as production/consumption rise and the economy again is growing sufficiently, the inequity returns to historical levels. That’s speculation, of course, but no matter where you look, nature never shows equality of the parts in a system. CL goes some distance to explain that.

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      • aepxc says:


        Thanks for your response. Have been reading more on CL and am increasingly impressed about just how elegant and revolutionary the idea is.

        Thinking further about its applicability to the economy, I am presently having trouble deciding whether human beings within the economy should be considered as vertices or as edges within the graph. For instance, there is a video of Prof. Bejan talking about the applicability of CL to basketball, in which case the players are clearly edges. The system is for the flow of the basketball from jump ball to the basket (the two nodes in the system), and the players serve as the ‘pipes’ for this flow (and so, as Bejan points out, the best players get the ball more often).

        When it comes to the economy, on the other hand, human beings look more like nodes to me (the source/creators of value and the capture/sink points of value), with economic transactions being the edges or ‘pipes’. As best as I can tell right now, CL does not much address anything about the setup of nodes, instead looking at the evolution of the most efficient flows between them. So we can look at money instead of barter (even though the trading of favours is still very important at lower scales), markets instead of planning (even though we still have firms when transaction costs need to be lowered), EFT instead of gold coins, etc. So the system is evolving in a way that eases the flow between the biggest generators of value and the biggest capturers of value, allowing the capturers to capture ever more. However, since we, as humans, periodically switch from capturer to producer roles, and since our capacity to produce is partly a function of the value we have previously captured (it lets us buy more/better tools), does this flow actually result in the system being able to create more in aggregate?

        If we are nodes, and if I am correct in my understanding that rules governing nodes are exogenous to CL, then I am not sure we can use it to say anything about income inequality.

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    • O S says:

      Inequality cannot be overcome, and the proposed tax is not trying to do that. It is trying to control or manage inequality.

      There remains, of course, a question of whether inequality needs to be controlled, or the system will settle at some (quasi-)steady state by itself. This is what seems to be debated here. Mechanisms for controlling inequality have been incorporated into our economic and social system for a long time. Are they still sufficient? Statistics seem to suggest that they are not sufficient any more, for whatever reason.

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  4. Ben says:

    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?

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    • rehajm says:

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

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    • Imad Qureshi says:

      Except that people are not working 3/4th of what they were working in 1980. And the fact that the income gap has increased more than 10 folds is not because top 1% is saving more. It’s lot more complex than you are pretending it is. That being said, I don’t think this income inequality tax will have intended consequences.

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      • Ben says:

        You’re missing the point. If the Brandeis ratio varies by hundreds of percent for a stylized community with perfect equality, how can it possibly be a good measure of real inequality?

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  5. Mike says:

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  6. MrAtoZ says:

    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).

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  7. Ben says:

    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)

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    • brazzy says:

      All that money in search of political influence would quickly find a way to bypass any such limit.

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      • Ben says:

        All that money in search of influential pockets would quickly find a way to bypass any such Brandeis tax.

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      • dave says:

        And you just said what we all know. Any tax will have little impact. those that can afford to bypass paying a tax will. The corollary is that no tax ever stays the same. once the tax is implemented, it will, with total certainty, be expanded until it effects all wage earners.

        The true formula is ‘how to collect taxes’ and not ‘how to be fair.’

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  8. William says:

    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?

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    • DaveyNC says:

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

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    • rehajm says:

      Compensation in Jaguars, houses and jewels is already considered taxable income. I suspect Brandeis proponents would keep it that way. Though to your point, a business owner subject to the Brandeis tax might be motivated to work for earnings up to the confiscatory tax rate, and once reached, lay off the staff and go play golf for the rest of the year…

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      • James says:

        Or might instead be motivated to move self and the entire business (except for the sales end, of course) to an offshore location.

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      • dave says:

        one can easily off-set income. first, incorporate yourself. now, expenses are fully deductible. you can lease a mansion (deductible) hire staff to run the leased property (deductible) have the mansion own a fleet of vehicles, complete with drivers (deductible)… etc…etc….etc…
        You can pay yourself $1.00 but live like Bill Gates.

        What we are counting on is that the excess is so great that the earner no longer cares about giving 100 million away when they make 500 million.

        The real bottom line is that too many are looking at the work of too few. Concentrate rather on getting 10%’ers to work and off hand-outs.
        if you had the opportunity to save 100 million, would you ?

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    • LOL says:

      I wonder how easy it would really be to tell that you’re making less money when you’re taking home $5 million instead of $11. What dramatic changes in lifestyle will you be forced to make!

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