David R. Henderson  

When Taxes are Cut, What Does Regressive Mean?

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How starting with a progressive tax system and cutting everyone's taxes by the same percent gives you a regressive tax cut.

We all know what a regressive tax is: it's one that takes a higher percentage of income from low-income people than from high-income people. So it seems straightforward to judge whether a tax cut is progressive or regressive. Is it?

Evan Soltas writes:

The Bush tax cuts were sharply regressive--that is, people with high incomes benefited far more as a percentage of their income.

And he gives a cite, to a 2008 Tax Policy Center study by Greg Leiserson and Jeffrey Rohaly. In it, they write:
In 2010, when the cuts are fully phased in, households in the middle fifth of the income distribution will receive an average tax reduction equal to 2.6 percent of after-tax income. Households in the top quintile--the 20 percent of the population with the highest incomes--will receive an average tax cut that is more than twice as large: 5.4 percent of income. Those in the bottom quintile will get an average cut equal to just 0.7 percent of income.

In the same piece, Leiserson and Rohaly explain why they think this is regressive:
A tax cut that gives all households the same percentage increase in after-tax income is distributionally neutral; it leaves the relative distribution of after-tax income unchanged. A tax cut that increases after-tax income proportionately more for lower-income households makes the tax system more progressive (or less regressive). One that increases after-tax income more for higher-income households makes the tax system less progressive (or more regressive).

By that standard, then, they show that all the Bush tax cuts combined were regressive.

But wait. Everyone, including Leiseron and Rohaly, recognizes that under the U.S. tax system, the higher your income, the higher a percentage of it you pay in federal taxes. In their Appendix, Table 1, for example, they show that average tax rate (including income taxes, payroll taxes, corporate income taxes, and estate taxes) is 5.3% of income for those in the bottom quintile, 13.0% of income for those in the second-from-bottom quintile, 19.1% for those in the middle quintile, 22.1% for the second-from-top quintile, and 28.6% for the top quintile. Within the top quintile, the average tax rate is 24.9% for the bottom of that top fifth, 26.0% for those in the 90th to 95th percentile, 28.1% for those in the 95th to 99th percentile, 32.8% for the top 1%, and 34.6% for the top 0.1%.

So . . . What would have happened had Bush come into office and got Congress to pass an across-the-board tax cut of 15%. That is, they add one provision to the law: calculate your taxes under the old tax system and subtract 15% to get your new liability. By Leiserson and Rohaly's measure, the tax system would have become more regressive. Why? Because when the high-income people pay a higher % of their income in taxes than the low-income people do, a given % cut in tax liability results (assuming no induced behavioral changes) in a higher increase in percent of income retained for the higher-income people than for the lower-income people. It's hard to cut taxes much for people who don't pay much.

To be sure, Bush figured out how to do that: Have a "refundable" tax credit of $1,000 per child. "Refundable" doesn't mean what you might think it means: it doesn't mean you get a refund. It means that even if your tax liability without the tax credit would be zero, you still get a check from the Feds for $1,000 per child. But even that credit, which essentially, for those who get such a check, turns the tax system into a direct-subsidy system, wasn't enough to make the tax cut "progressive" by Leiserson and Rohaly's measure.

I hasten to add that I'm not saying that Leiserson and Rohaly's measure is idiosyncratic. It may be widely used. Rather, I'm pointing out its pitfalls.

The bottom line is this: Start with any system of progressive taxation, cut everyone's taxes by the same percent, and you will have implemented, by their standard, a regressive tax cut.

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COMMENTS (24 to date)
John Fembup writes:

I thought that the Bush tax cuts were tax cuts for the rich. Isn't that what the administration has told us for four years?

So wouldn't eliminating the Bush tax cuts for the rich only affect the rich?

Why is the middle class any part of this discussion?

The point jumps out even more clearly (the math is easier) if we suppose an across-the-board 10% cut in income taxes. Those who were paying 19.1% of income get a tax cut of 1.9% of income; those who were paying 28.6% get a cut of 2.86%, etc.

Mordatar writes:

I don't see any contradiction or pitfall in the fact that cutting taxes at the same rate could be considered regressive.
I think that their classification is this: if a measure increases inequality of income, it is regressive, if it decreases it, it is progressive. If cutting tax rates equally increases inequality of income, then it is a regressive policy.

David R. Henderson writes:

@Lawrence H. White,
Well-stated. I should have run it by you first. :-)
I don't see a contradiction either. But I do see a pitfall: the one I stated in the post.

RPLong writes:

The first question I always ask when I see either the word "regressive" or the word "progressive" applied to taxes is, "With respect to what?" Personally, I think economists of all people should avoid these terms because they obfuscate more than they explain.

If you do a deep enough dive into the arithmetic of progressive versus regressive taxation, you start to realize that most of it involves choosing a clever denominator to make the case for one's preferred concept of social justice.

Bostonian writes:

The overall progressivity of goverment transfers and taxes should be considered, not just the progressivity of taxes. A situation where someone gets $18K of federal transfers and pays no tax is equivalent to one where he gets $20K of transfers and pays $2K in taxes. In both cases he is a net tax receiver, not a tax payer, and in the latter case I think it is misleading to say he faced a 10% tax rate.

I suggest that net tax payments (taxes paid - transfers received) divided by earned income be used as a measure of tax burden.

egd writes:
When Taxes are Cut, What Does Regressive Mean?
A simple answer: when the tax cuts are passed by a Republican.

Have you heard the Obama "tax cuts" on social security taxes described as "regressive"? Or AMT adjustment? Those with incomes in the top 10% get more out of these tax cuts than those not in the top 10%.

Doug writes:

If we have to cut the benefits of a single government employee for to keep taxes on the rich a single basis point below 90% than it is a travesty against social justice!

Henry writes:

I think you can counter this with a reducto ad absurdum: suppose there was a 100% income tax rate on the rich and 0% on everyone else. Any tax cut would necessarily solely accrue to rich people. Yet to call this "regressive" belies the fact that most people would have considered this state of affairs to have been far too progressive in the first place. You could argue that "regressive" is a value-free way of saying "less progressive" but the term is clearly negatively loaded.

Arthur_500 writes:
I don't see any contradiction or pitfall in the fact that cutting taxes at the same rate could be considered regressive. I think that their classification is this: if a measure increases inequality of income, it is regressive, if it decreases it, it is progressive. If cutting tax rates equally increases inequality of income, then it is a regressive policy.

If this is true than we are saying that we strive for a communist system in which everyone has an equal amount of money.

Hmmm, isn't this what people have been complaining about 'progressives' for years? In other words, Progressive is simply Liberal Communism.

Liberal Communism is where everyone is equal, except me.

Mark V Anderson writes:

Since the discussion includes corporate taxes, I am very curious what others think or have heard about the progressivity/regressivity of corporate taxes.

Here in Minnesota, the Dept. of Revenue regularly calculates the level of taxes by decile, and their calculation includes an assumption that corporate taxes are quite regressive. Because of this assumption, they calculate the total MN tax system as slightly regressive; without this assumption I think overall taxes would be progressive. They consider the taxes regressive because changes in such taxes are normally passed on to consumers (as higher prices) or employees (as lower wages), and only a small amount is paid by shareholders. (At least this is the theory)

Recently I was reading about how Federal taxes are calculated, and it is my understanding that the Federal corporate taxes are calculated as progressive taxes (mostly paid by shareholders). In both the MN and Federal case, there was no discussion about whether their assumptions were correct.

I really have no idea which one is correct, but I'd sure like to understand why different economists use such widely varying assumptions. I wold like to see the analysis where these decisions are made, although it is likely that I wouldn't understand the jargon and math used.

Jon writes:

A tax scheme is progressive whether the percentage of tax paid falls below the percentage of income earned. In a flat tax system, this is a line. In a regressive tax system it is a concave function above the flat-tax line and in a progressive tax system is a convex function below the flat-tax line. As this curve falls away from the flat-tax line it is more progressive or more regressive respectively.

I went here...

Then I plotted curves for the 2000 and 2007 tax years. The bush tax cuts made the tax-code slightly more progressive.

pyroseed13 writes:

Hmmm I'm confused. My understanding was that the Bush tax cuts actually made the tax system more progressive because the share of taxes paid by top fifth of earners increased and the share of taxes paid by bottom fifth decreased. Or is this in fact the point that you are trying to make, David?

Charlie writes:

This is a strange post. Why not just forcefully argue that you want the tax code to be more regressive? Why act like it's a word that is not well defined?

Joe Cushing writes:

I wondered if I was the only person who thought of tax cuts in terms of the percentage of the taxes that are paid that get cut instead of the percentage of income that is no longer taxed. In all these years, this is the first time somebody else has pointed this out. If a person has a marginal rate of 39% and another person has a marginal rate of 10%, then giving them both 4 percentage points off of their rate is a 40% marginal rate cut for one and a 10% marginal rate cut or the other. So naturally, the nominal percentage cut would have to be higher for the one paying 39% to be neither progressive nor regressive.

David R. Henderson writes:

Thanks very much.
Why not just forcefully argue that you want the tax code to be more regressive? Why act like it's a word that is not well defined?
I'm not acting like anything. I'm pointing out a weird implication. But see Jon above for a commonsensical pointing out that by one reasonable measure the tax cut was progressive.

Charlie writes:

@David H


"you will have implemented, by their standard, a regressive tax cut."

This isn't their standard. This is a well-defined word. They are using the standard definition in economics.

BMan writes:

Yes, Jon has it right. The whole notion of progressive/regressive makes sense only if one looks at the tax system as a whole. Adjustments to it -- the occasional cuts, increases, nips, and tucks -- cannot be usefully classified as pro/regressive in isolation, but only by looking at whether they increase or decrease the progressivity of the whole. Ideally, this is done using a good summary statistic like the Gini coefficient. By that measure the Bush tax cuts were progressive, meaning they increased the progressivity of the tax system.

But I think it is a mistake to go too far in the other direction (Mordatar) and apply the pro/regressive labels to the distribution of income itself. Even in the absence of any government at all, people will have a variety of incomes, and I don't know how we would decide what the "right" distribution would be. Properly used, progressivity is a value-neutral descriptive term, characterizing the relationship between the tax burden and income distribution.

Of course, as Bostonian points out, we need to think about transfers, too. When the tax system pays for public goods, progressivity is a straightforward concept. As we grow an increasingly redistributionist state, the whole concept begins to break down.

Ken B writes:
When taxes are cut, What does regressive mean?

The Leiserson and Rohaly definition of a regressive tax cut is biased towards calling tax cuts regressive.

I’ll give a quick example, then point out the characteristic that any definition of a regressive or progressive tax cut must have to be consistent.

Let’s examine a hypothetical tax code where the lower bracket is a 4% tax and the upper bracket a 40% tax. Imagine a tax cut of 2% for the lower tax bracket and 1.5% for the upper bracket, shifting the tax rates to 2% and 38.5%, respectively. Under their calculation, the lower tax bracket receives 2.1% more income (2/96) and the upper bracket receives 2.5% more income (1.5/40) – and thus the tax cut is regressive. One could argue back and forth for other definitions, for example, that one is a 50% tax cut and the other a 3.75% tax cut and so on.

Clearly, though, any definition must fit the requirement that if the tax cut is regressive, then reversing the tax cut must be progressive. Here is where the Leiserson and Rohaly definition fails laughably.

Consider the taxes in the “cut” state: a lower bracket of 2% and an upper bracket of 38.5%. Anyone who argued for raising taxes by 2% on the lower incomes and only 1.5% on the higher incomes would be clearly making the tax code less progressive. But the reverse – a cut – supposedly also makes the tax code less progressive.

I suppose I could be wrong and Leiserson and Rohaly would consider raising revenue by increasing the rates more on the poor and less on the well-off to be progressive since the rich are sacrificing a greater fraction of their remaining income. But I find that doubtful at best.

David R. Henderson writes:

@Robert Rounthwaite,
Under their calculation, the lower tax bracket receives 2.1% more income (2/96) and the upper bracket receives 2.5% more income (1.5/40) – and thus the tax cut is regressive.
That would not fit their use of the word "regressive."

Ken B writes:

Here is their definition of regressive:

[A tax cut] that increases after-tax income [prportionately] more for higher-income households makes the tax system less progressive

So why is Robert Roundthwaite wrong? He asserts
the lower tax bracket receives 2.1% more income [after tax] ... and the upper bracket receives 2.5% more income [after tax]
Why is that not regressive according to this definition?

David R. Henderson writes:

@Ken B,
I'm busy preparing my last lecture of the quarter and I like to tie things together and bring it to a crescendo. So I don't have time to answer. But here's a hint: Go back to the first quote I have above from Greg Leiserson and Jeffrey Rohaly in which they explain their concept. I think you will see that it is not the same criterion as Robert Rounthwaite's. When you figure it out--which I know, from past experience, that you will--please post your answer so that others can see.

Ken B writes:

@DRH: Ahh the appeal to ego. You know me too well.

I've looked and it still seems to me he's right because of this definition I quoted:

"[A tax cut] that increases after-tax income [proportionately] more for higher-income households makes the tax system" regressive.

Proportions are measured in terms of after tax income. That implies a comparison of ratios, whose denominators are the post tax income.Let's look at some.

For any taxpayer, let I be untaxed income, ti the intital tax and tf the final tax.
For RR's example I take
Poor: I = 100, ti = 4, tf = 2
Rich: I = 1000, ti = 400, tf = 385

Define the post tax income effect ratio Q for each tax payer as (I - tf)/(I - ti).
If tf 1.

The L&S criterion is (in my reading) that a tax is regressive when Qj > Qk for taxpayers j and k having Ij > Ik
(That is, the rich gain more proportionally from a cut as a fraction of their prior after-tax income).

For RR's example I make
Qp = 98/98 = 1.021
Qr = 615/600 = 1.025
So Qr > Qp with Ir > Ip.

The tax is by the L&S definition regressive.

We might be interpreting the implied ratio differently, but as long as the denominator is post-tax income, then for this example all measures agree.

Comparing the increased post-tax income directly,
(I - tf) - (I - ti) = ti - tf.
This is the net gain in income.

Define Z as (ti - tf)/(I-ti)
Proportional net gain relative to prior taxes.
I get Zp = .021, Zr = .025

Define G as (ti - tf)/(I-tf)
Proprortional net gain relative to new taxes.

I get Gp = .020, Gr = .024

It's very different with just Ik as the denominator for each k. I believe this is RR's point.

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