David R. Henderson  

DeLong vs. Feldstein on Romney Tax Cuts

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I know that there are not a lot of Brad DeLong fans who read this blog. I'm not one either. But when someone gives a good analysis, I tip my hat. If I understand the analysis of Marty Feldstein (my former boss at the Council of Economic Advisers) and of Brad DeLong correctly, Brad wins.

I could go into detail about why I say that, but there's no need. All you need do is check Martin Feldstein's article in today's Wall Street Journal and then read Brad's take-apart. Marty's article is titled, "Romney's Tax Plan Can Raise Revenue." He goes through and does a static analysis that purports to show that with reasonable assumptions about the dynamic feedback effect of cuts in marginal tax rates, Romney could keep his promise to cut all marginal tax rates by 20% (not 20 percentage points) and some other taxes, and, by ending itemized deductions, keep government revenue from the income tax constant without raising taxes on middle-income people.

But Marty makes a key error. When he goes to estimate the increased revenue from ending itemized deductions, he applies the old rates (25 to 35%) rather than the rates to which Romney would cut (20 to 28%). Brad catches it.

I know that some of you can't access the Journal, but on my reading, Brad does not pull a fast one and he does quote Marty correctly.

Interestingly, though, with Marty's assumptions and Brad's correction, the cut in marginal tax rates plus the other cuts Romney proposes would cut government revenue by only $34 billion annually.

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COMMENTS (38 to date)
Ted levy writes:

A back door around Journal-restricted articles that usually works is to Google the title and then click on the first link..

David R. Henderson writes:

@Ted Levy,

Frank Schober writes:

See also Burman in Forbes who notes many other more important problems with Feldstein's ridiculous analysis.

Bob Murphy writes:

Yep, I agree David, from what I can see, DeLong nailed him. I actually feel embarrassed for Feldstein. This isn't a little thing; it overturns the whole point of his op ed. Now he and the WSJ are in a really awkward position; it's not like they can just issue a little correction and fix a typo or something.

Incidentally I left a note congratulating DeLong at his blog, but he and I have such a history that I wonder if he'll think I'm being sarcastic and zap it?

txslr writes:

If the corrected analysis is only $34 billion in annual federal revenues of about $5 trillion, isn't Feldstein basically correct? That difference is rounding error.

Thomas writes:

DeLong's complaint about "high income taxpayers" is off base though. TPC uses cash income, not AGI.

Tracy W writes:

Surely Martin Feldstein wins too, by being corrected? Thus making this a win-win situation?
(The attitude I attempt to go through life with.)

Greg Rehmke writes:

Plus, it could be argued that raising total Federal revenue is as much a problem as a solution. Every dollar extracted from citizens and firms requires force or the threat of force.

Reforms that expand freedom through reducing tax rates, and result in reducing total Federal revenue some, still leave Federal tax revenue very large by any historical standard.

Reducing or eliminating deductions does raise tax rates in various ways, but could be justified as reducing the social engineering aspect of taxation.

Anthony Juan Bautista writes:

Yes, it's bad, but who cares? Make the correction, run the spreadsheet again, rinse, repeat.

I don't believe tax cuts pay for themselves in obvious ways, and I'm suspicious of supposed virtuous circles (there are too few of them).

But this is a few seconds in the life of the economist editorialist....fix the work and move on.

Joe Smith writes:

I have nothing but contempt for the economists who are blindly endorsing Romney/Ryan without even checking the math. If Feldstein made a mistake (as opposed to being deliberately misleading) then it was because he was blinded by partisanship.

Frank Schober writes:

But even with that one correction, as the Forbes piece points out Romney would have to eliminate ALL deductions (which he would clearly not do and has promised not to do) and he would STILL be $34 Billion short.

R Richard Schweitzer writes:

One can directly access the Feldstein NBER paper (pdf)
by going to Greg Manikew's blog and clicking on the link to MF's paper.

Ken B writes:

Hands up all those who really think that even if the numbers were right we'd *really* get to even with a hundred and thirty four billion once the rubber hit the road. Feldstein made an embarrassing boo-boo. I'm not sure that matters as to whether the Romney plan is a step in the right direction or not.

a Racoon writes:

those itemized deductions do not reduce revenue by the marginal rate, whether it be 35% or 20%, but some lesser amount because itemized deductions get picked up by AMT for most taxpayers who are taking itemized deductions instead of the standard deduction.

I left a note congratulating DeLong at his blog, but he and I have such a history that I wonder if he'll think I'm being sarcastic and zap it?

My experience is that if you slather enough praise on DeLong first, he'll allow your comment to go through. It's criticism he censors.

And now that I check at DeLong's blog, I see that I was correct. Bob Murphy's comment was allowed, and it began;

Very nice post, Prof. DeLong.

Let's think this through a little more. Feldstein's piece in the WSJ is hardly a model of clarity, but then neither are the rebuttals to it.

This from 'Vivian Darkbloom' is much better. The math is;

$1,000 of gross income less $200 in deductions, results in $800 of AGI taxed at 35%= $280 in income tax revenue to the govt.

And, $1,000 of gross income with zero deductions taxed at 28% = $280. Which is exactly the same revenue, but at tax rates which are 20% lower (Romney's proposal).

All the other stuff about whether to use AGI, or cash income, whether to score the 'loss' at the old or new rates applied to historical (2009 was an abnormally low year for incomes) levels of deductions just confuses things.

ChacoKevy writes:

I don't think I understand. In the assumptions of 1000 gross and 200 in deductions, aren't you simply pointing out the intersecting point of two lines?

Keeping $200 deductions constant at 35%, any income beyond 1,000 and you start to see the disparity between the two increase. If income were $2,000:

(2,000 - 200) * .35 = 630
2,000 * .28 = 560

I admit, though, I tried and could not understand Vivian's explanation.

Chaco, the criticism is that Romney's plan is 'mathematically impossible' (says so right in DeLong's title). Clearly it isn't.

But, it was unwise of Feldstein to go down the road he chose, especially using numbers from 2009, which is an abnormal year, to say the least.

Phil writes:

Raising the same amount of revenue by cutting marginal rates and eliminating exemptions is nothing but a income-redistribution program. And all this time I thought the GOP was opposed to redistribution.

Joe Smith writes:

The discussion about whether or not Romney's "plan" is even arithmetically possible is a completely ridiculous discussion to have to have. If Romney simply came out and said what deductions he is going to eliminate to broaden the tax base then we could have a proper principled discussion.

As it stands, I, for one, think Romney and Ryan both lack intelligence and integrity and that their alleged "plans" are simply confidence tricks but Romney and Ryan could alleviate some of my concerns about them by simply listing the deductions they would eliminate and the details of the calculation they rely on. They are going to have to disclose the details of their proposal at some point. Why not before the election?

Jack Davis writes:
Interestingly, though, with Marty's assumptions and Brad's correction, the cut in marginal tax rates plus the other cuts Romney proposes would cut government revenue by only $34 billion annually.

That $34 billion number is only plausible, though, if you accept the four other assumptions Feledstein made. DeLong argued, fairly convincingly (at least to me), that those were extremely unlikely to be true. The real number is much more likely to be around $50 billion.

David R. Henderson writes:

@Jack David,
That $34 billion number is only plausible, though, if you accept the four other assumptions Feledstein made. DeLong argued, fairly convincingly (at least to me), that those were extremely unlikely to be true. The real number is much more likely to be around $50 billion.
I think you can make a case for $50 billion. Even that, though, was a surprisingly small number compared to my prior. Get the U.S. government out of Afghanistan, as noted foreign policy analyst Clint Eastwood proposed last night, and you’ve made up the $50 billion loss.

Alan Morrison writes:

Yes, I see what DeLong is saying and there are many discussions on this on the internets. But I think he is wrong and Feldstein is correct. This similar to the Darkbloom reference above. To compare the Tax Revenues for both cases I wrote the simple equations for tax revenue and then subtracted them. The used both the Romney and Current tax rates and the information in Feldstein’s article for 2009 to get:

Difference in tax revenues between the Current and Romney tax proposal based on 2009 data:

(TRevC – TrevR) = AGI X (CTR – RTR) – (CTR X Ded9 – RTR X DedR)


TRevC = Tax Revenue using Current Rates

TRevR = Tax Revenue using Romney Rates

AGI = Adjusted Gross Income

CTR = Current Average High Income Tax Rate = 30%

RTR = Romney Average High Income Tax Rate = 24%

Ded9 = 2009 Tax Deductions for those with AGI over $100K (21% of filers)

DedR = Romney Tax Deductions for those with AGI over $100K = Zero

We know that the first term on the RHS of the equation after additions = $186 B. And we also know that the Ded9 = $636B.

(TRevC – TrevR) = $186B - $191B ~ Wash

The Romney revenue loss due to lost deductions is made up for the gain in taxable income due to the lower Romney rates.

This result is for the specific 2009 tax information, but you can see how the result would change for various other assumptions.

Eric writes:

@Greg Rehmke

A Libertarian starve the beast argument is not what's being offered here. Romney promised an revenue neutral reduction of rates by 20% without raising middle class taxes. It's not mathematically possible. If he promised a 20% reduction and actually explained which programs he would cut (and no NPR/NEA will not get you there) it would at least be an honest conversation.

That's just bad math. Start with your (implicit) start point TRevC = AGI x CTR. Do you not understand **marginal tax rates**? 0% of the income of somebody who makes 125k/year will be taxed at 30%. You can't just take two numbers that are part of a complex integral of income distribution and marginal tax rates and average them together and think your calculations will come out right.

2nd obvious point is the extension of the "rich" down to 100k to make the numbers "work". People who make 100k are engineers and primary care physicians. Unless you hit it big on internet stocks, you are not doing great after a decade of Bushonomics. I highly resent the attempt to take 4% of my gross income (yes I calculated it) in order to give executives and bankers another tax break.

Alan Morrison writes:


Yes, I do understand marginal tax rates. The terms are meant to link up with the arguments of Feldstein who states that using the 2009 data that $636 Billion come from the highest marginal earners. The argument by DeLong is that 24% (Romney avg rate) should be used instead of 30% (current avg rate) that Feldstein used. My thought process shows that Feldstein is correct when comparing the two methods for the same year.

Eric writes:


You and Feldstein just simply cannot use "average" marginal tax rates in this way. It is bad algebra. It does not work. You need to take into account the distribution of income and number of tax payers paying each rate. For example the top marginal rate in 1935 was 65%. However it only applied to one man. Adding that 65% into an "average" marginal rate of "rich" people isn't going to tell you anything about revenues generated unless you somehow weight it for the amount of income they have and the number of tax payers in the bracket.

Alan Morrison writes:


Yes, I'm fully aware of that simplification but that is not the point that DeLong is making which is that the new Romney average of 24% should have been used by Feldstein. IMO Feldstein was correct to use the 30% rate in his very simple analysis. As you point out a more detailed and accurate analysis would be to break down the $636 billion in deductions for the top 21% making over $100K AGI and look at it within each marginal tax bracket. Maybe Feldstein did indeed do that and showed to himself that the simplification was "accurate" and then simplified the explanation for the op ed - I don't know ??

eric writes:

186b is **not** agi(ctr-rtr). It is .2trevc. I will leave the rest as an exercise for you. (Hint the answer is not good for feldstien)

Alan Morrison writes:

AGI X (CTR – RTR) in the above equation represents the 20% reduction in rates then corrected for the dynamic effects of the tax cuts plus the added AMT and added taxes on dividends, cap gains, and interest. I tried to explain that in the wording underneath assuming that all we familiar with the op ed. This equals $186 billion from the Feldstein op ed in the WSJ. The term "AGI X (CTR – RTR)" is equal to a static loss of $181 billion. Dynamic effect reduce that to a dynamic loss of $148 billion and then losses of $23 billion of AMT and $15 billion of dividends, cap gains, and interest are added back in to make $186 billion.

But again the point that I'm making is that Feldstein is correct in using the 30% factor and not the 24% factor which DeLong suggests.

I'm not defending Feldstein's methods or approximations but the algebra involved in calculating the difference in revenues between the Romney and Bush tax rates for the 2009 data.

Eric writes:

Ok, I guess I can't leave this as an exercise for you.

Your assumed starting point:

TRev = TR(AGI - Ded)

(TRevC – TrevR) = AGI X (CTR – RTR) – (CTR X Ded9 – RTR X DedR)

But AGI = TrevC/CTR + Ded9

So (TRevC – TrevR) = (TrevC/CTR + Ded9) X (CTR – RTR) – (CTR X Ded9 – RTR X DedR)

TRevC = 904
CTR = .3
RTR = .24
Ded9 = 636
DedR = 0

Solve for (TRevC – TrevR)

X = (904/.3 + 636) x (.3 - .24) - (.3x636 - 0x.24)
= 3649 x .06 - 191
= 219 - 191 = 28b/year

This is just based on the algebra as you presented. Delong and I await your apology.

Alan Morrison writes:

Yes, I see what you have done. But the problem is that I’ve done a terrible job on the nomenclature, i.e. CTR and RTR mean different things in the first term (average tax rate) of the RHS than in the second term (max marginal rate). The $904 billion is tax revenue for all tax brackets so the average tax rate to be used is something much less than 0.30. The $636 billion in tax deductions is for the top 21%. Therefore when you substitute numbers in there is a mixing of baselines. Again what I was trying to do is to lump all the effects of the total tax rate changes into the first term of the RHS which results in the $186 billion and then subtract the loss of the 2009 tax deductions for the top 21% using an average tax rate of 30% which is what Feldstein did.

The equation should be changed as:

(TRevC – TrevR) = AGI X (ACTR – ARTR) – (MCTR X Ded9 – MRTR X DedR)

ACTR = average effective current tax rate
ARTR = average effective Romney tax rate
MCTR = Maximum average marginal current tax rate
MRTR = Maximum average marginal Romney tax rate

Eric writes:

[Comment removed pending confirmation of email address, for crude language, and policy violations. Email the webmaster@econlib.org to request restoring your comment privileges. A valid email address is required to post comments on EconLog and EconTalk.--Econlib Ed.]

Eric writes:

@ Alan

You are trying to save bad math, and it is unsavable. The Feldstien piece is sloppy, for more reasons then the algebraic errors. Stop trying to defend it, just stop. It is beyond redemption.

However that plea is unlikely to sway you. So here we go.

(TRevC – TrevR) = AGI X (ACTR – ARTR) – (MCTR X Ded9 – MRTR X DedR)

TrevC = AGI x ACTR - Ded9 x MCTR
AGI = (TrevC + Ded9xMCTR)/ACTR


LostRev = (TrevC + Ded9xMCTR)/ACTR X (.2ACTR) - MCTR X Ded9

LostRev = .2TrevC + .2Ded9xMCTR - Ded9xMCTR
LostRev = .2TrevC -.8MCTRxDed9
LostRev = 25-30bill$/year

Having defeated you (again!) I now insist you go far and wide across the internet forums and espouse my broader points about the Romney/Feldstien "plan"

A)it doesn't add up.
B)the very idea that you have a discontinuity at 100k is insane... I would probably take a strategic divorce rather then give up all (ALL!) of my deductions.
C)it is absolutely immoral to ask the engineers, school principals, primary care physicians, etc who are around 80% and have not seen a real dollar raise in 12 years to finance a tax cut for CEOs, Bankers, and senators who have piloted this economy into the crapper. Ask me to build roads, ask me to pay for college for some poor kid, even ask me to pay for the wars that W put on the credit card, OK. Asking me to buy Bob Nardelli or Carly Fiorina another yacht is not OK.
D)If you think some WSJ shill is better then Delong at math, it is probably time to rethink your position.

Alan Morrison writes:

Realizing that the initial equation I came up with was too simplified I went back and came up with hopefully a more complete and accurate description of the situation. Basically the tax revenue is split into segments below and above $100K of AGI. And to be accurate the splits of AGI and the effective tax rates for those splits must be known. Haven’t had a chance to pursue this data which may or may not be available and most likely will not do so – see below.

TRevC = ((AGI1 – DED1) X ACTR1 + (AGI2 - DED2C) X MCTR

TRevR = ((AGI1 – DED1) X ARTR1 + (AGI2 - DED2R) X MRTR

Then the metric is the difference (TRevC – TrevR)

1 = Adjusted gross income less than $100K

2 = Adjusted gross income greater than $100K

DED2C = $636 Billion

DED2R = $0

MCTR = 0.30

MRTR = 0.24

TRevC = $904

However I took a look at this from another angle.

TRevC = $904 Billion = (AGI – Ded) X (Effective Tax Rate)

Then TRevR1 = $721 Billion (20% reduction + dynamic gain – AMT – int/di/capgain)

But this TRevR1 includes Deductions for those making over $100K.

TRevR = $721 + ($636 X (MRTR = 0.24)) = $874

Diff = ($904 - $874) Billion = $30 Billion

So DeLong was indeed correct in his critique about using the Romney average max marginal tax rate and not the Current max marginal tax rate and Feldstein was wrong. The difference is small - ~ 3%. Small adjustments could be made in the tax reduction % or in the tax rate reduction for the upper brackets. If the tax cut is reduced to 18% across the board the Diff as calculated directly above is reduced to $8 Billion. Many details would have to be worked out including the transition from full deductions to zero deductions.

But why all the vitriol ?? I see one of your posts was taken down due to language. I proposed a simplified but flawed analysis which you helped debunk. Hopefully you and others who followed this are better informed – I know I am.

Eric writes:

The removed post was mostly due to a three letter acronym which is very common on the internet, which was not directed at you.

Here's why the vitriol:
A)people being published in the WSJ should not be able to misinform the public with terrible algebra. Make no mistake, the editorial is misleading even after the algebra is cleared up. Most people who saw the editorial didn't look skeptically at the numbers and probably wandered off thinking that the Romney plan is plausible. Probably less then 10% saw Feldstien cry uncle (on the algebra at least) on Mankiw's blog. Of course Feldstien corrected his error by doubling down his raid on my tax breaks - coming after my health care as well as my house.

B)30 billion/year isn't chicken feed. It's 20% of the sequester that has everybody worked up. It's sixty Solyndras, each year.

C)The first two times I pointed your algebra error out to you, it didn't stick.

D)I actually really like the idea of tax reform, and I find it really really aggravating that right wingers keep using it as a stalking horse to try and jack up my taxes and redistribute it up the ladder.

Alan Morrison writes:


My error was in overly simplifying the situation with respect to splitting AGI and tax rates. Your “algebra” actually played off those errors. Yes, it took a couple of days to realize the implications of the simplifications and develop the correct but more complicated expression requiring more data and then to come to the correct conclusion.

Actually if you apply a 30% recoup of static losses which is the estimated figure for the Reagan tax cuts then the very simple analysis works out. And if further modifications to the tax rates (reductions in the higher level tax reductions) and a smoother transition of the deductions with AGI the difference is reduced to a wash which indicates feasibility.

I did find the Feldstein article – he addresses the critics and again shows feasibility. Sure a lot of details and compromise is required but the only way out of this national debt situation is through growth and policy should address that fact.

Jack Davis writes:

David said:

Jack David, I think you can make a case for $50 billion. Even that, though, was a surprisingly small number compared to my prior. Get the U.S. government out of Afghanistan, (emphasis added) as noted foreign policy analyst Clint Eastwood proposed last night, and you’ve made up the $50 billion loss.

Two points: 1. Since Romney opposes withdrawng troops from Afghanistan, has hired a number of ex-Bush neocons who want a more aggressive foreign policy, and has called for more military spending, I don't see the relevance of this argument.

2. (Much less important point): My last name is Davis, not David.

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