A failure to think on the margin

In our textbook, Modern Principles, Tyler and I have “Thinking on the margin” as one of the “big ideas” in economics (I believe that other guy also mentions this concept.) USA Today, in a feature called Math tips for the rest of us, is sadly unclear on the concept of a marginal tax rate:

“That raise actually might not be as good as it looks. The extra money is nice, but it could very well bump you into the next tax bracket, possibly leaving you with less money than you had before the raise.”

As Dean Baker says:

Arghh!!!!!!!! ….No, no and 286,000 times no! The tax system brackets give marginal rates. This means that if the raise bumps you into a higher bracket then you pay more taxes only on the income in the higher bracket. Suppose that the tax bracket for income under $200k is 25 percent, and for income over $200k is 33 percent. If you get a raise that pushes your income from $195,000 to $205,000 then you only pay the higher 33 percent tax rate on the $5,000 that is above the $200k threshold not your whole income. Therefore, there is no (as in none, nada, not any) way that getting more money, and being pushed into a higher tax bracket will leave you with less money after taxes.


"USA Today." Need you say more?

Well, they fixed the article already.

You wouldn't catch a useless rag like the NYT correcting their errors so quickly. If, indeed, at all.

Except in Sweden where, at one time, the nighest marginal tax rates were above 100%.

Once in Britain too.

According to Greg Mankiw, if you add state and federal income taxes, taking care to fail to deduct state from federal, to undiscounted estate taxes, sales taxes, property taxes and corporate income taxes that you indirectly pay either as an investor or a consumer, the marginal tax rate is at least 90%. Surely, if you throw in other things that can be described as taxes such as inflation, you can push that well over 100%. So, when looked at with a little Mankiwian perspective, USA Today was not wrong at all.

Mankiw will get the prize for fiction for that one, but not the Nobel in Economics.

What do estate taxes and property taxes have to do with the marginal tax rate on income? As for sales and corporate income taxes, I suppose one could impute a value to these based on the average consumer's behavior and the relationship between income and different kinds of consumption but this is pretty slippery.

The point is "what would happen if you look at total taxes?" Yesterday I found a paper on a disease that affects about one out of a million people. I've tried looking for analyses of total taxes before for hours without too much luck. I guess the plus side is, do marginal rates matter for behavior if even PhDs in Economics can't get it anywhere near right (and Treasury Secretaries can't even do their taxes)?

Andrew'--Go back and look at the criticisms of Mankiws post and the economist who responded with a laugh at it. It was in the blogosphere for a while.

I believe that this is the case that people usually think of when they bring this up. http://en.wikipedia.org/wiki/Pomperipossa_in_Monismania

For tax year 2010 in the United States, if you make $33,400 while married filing jointly and put $2000 into an IRA, you get a $1000 tax credit on Form 8880.

If you make $34,000 -- $600 more -- that tax credit drops by $600. Plus you pay more FICA and income tax.

That's just one example. You can probably find more.

Of course it is true that our tax system operates on marginal principles in that higher tax rates apply only to income above the relevant threshold and deductions/credits phase out gradually, but there is no law of nature saying this has to be so. Without data to back it up, I suspect that for a number of reasons (simplicity of calculation, lack of forethought of perverse incentives, policymakers not really caring) there have been over time many instances of income tax regimes that apply above rates to earners above a given threshold and cover income both below and above the threshold, and therefore would have an effective rate of over 100% at least within certain ranges. I also suspect that such situations were more common in the past than they are now (if so, it would be a sadly isolated example of tax systems becoming less perverse over time)

Do you have any data on this?

further to that comment-
I recall reading about certain situations for entitlement beneficiaries where the combination of income tax and benefit abatement resulted in effective marginal rates of over 100%, but I don't remember any specifics.

I could give you a kiwi example of effective marginal tax rates over 100%. A friend of mine got sick of being a full-time house husband and took up 20 hours work earlier this year, leaving them worse off after losing the Working for Families credit.

Are the witholding tables structured so as to insure that this advice is sound? If your raise jumps you into a different bracket in the tables, while your actual tax bill at the end of the year would remain unchanged becasue of the weekly increase, the jump might result in less cash week-to-week (theoretically.)

It's been a long time since I've had to worry about such a thing- All apologies if I'm chasing a dead-end on this one.

Fed and State Withholdings are down payments on your current year tax liability. Changing the amount you withhold will not change the total amount of taxes you pay in a given year, but you may have to cut a bigger check to the IRS at the end (is that what you mean by tax bill?) because your taxable income went up but your W/H (down payments) did not adjust to compensate. At the end of the year, you pay the same total tax on your income either way, regardless of how much you withhold.

I agree with you and I assume I'm not explaining my scenario very well. I understand that withholdings have no substantive impact on your ultimate tax bill, but they do effect how much cash you get on payday. (Work with me here, I'm trying to defend the USAT.)

Consider only a single layer of taxation. Imagine the income tax rate goes from 28% to 32% starting at $52,001. A single male employee is our subject. I would assume (guess) that the bi-weekly tables for that employee making $51,500 per year set him up so that his bi-weekly withholdings get him close to the 28% (of the respective income- no tax until 12 K) that he must pay at the end of the year. If, on September 1, our employee gets a raise from $51,500 to X- a number which is slightly greater than $52,000- I would then assume (guess) that his biweekly checks after that raise would set him up to pay the proper share of that income. The tables would not (could not for practical reasons) understand that he in only making X for a part of the year- as opposed to making X for the whole year- and won't actually make it to $52,001 in that year. ( I recognize that the W/H tables will only be calculating 32% for a tiny sliver of income, but work with me here, I'm trying to defend the USAT.)

Ignoring all of the tax code ambiguities mentioned below, while gratuitously replacing the author's actual point with the random one I have created, and assuming this impossibly convoluted set of facts; is it not possible that there is some value for X at which the author's point- which he has subsequently abandoned and is universally regarded as erroneous- is, in fact, valid and, therefore, Mr. Tabarrok should be lashed repeatedly for having had the temerity to question it?

I don' t think there is, but my math-fu is only good enough so as to make me aware that my math-fu isn't very good- so I'll defer to the experts on this one.

Interestingly this is untrue in at least one (specific, unusual) case: if you're a Canadian studying in graduate school in the U.S. and receiving a stipend. If you make over $10,000 USD, you are subject to U.S. taxes on the entire amount, whereas if you make $9,999 you are completely exempt from U.S. taxes and pay only Canadian taxes. (And since you're a full-time student, you get lots of exemptions and deductions and pay almost no tax.) This is due to Article XV clause 2(a) of the Canada–U.S. tax treaty.

The way it worked out for me, if I was paid $9,999 USD, I would have taken home $9,999 USD but if I was paid $11,000 USD I would take home something like $9,000 USD.

I know, I know, not the point of the article…but an interesting case nevertheless.

Thanks -- exactly what I was looking for. I suspect your example isn't the only one in the entire US tax system.

There are others, particularly where phase-out of various exemptions, credits, etc., are involved. The worst case that I know of is with unemployment, where the benefit phaseout if you work at something low-paid enough to retain eligibility is equivalent to a 75% marginal tax rate. You also have to pay federal income tax on the benefits, though withholding for that is optional, and will have withholding (usually over 25%) on your earnings.

As an example, if you are eilgible for California's maximum benefit of $440, and you get a job which pays you $500 in one week, you will lose $375 of benefits, thus getting only $65 in benefits; your take-home pay from the job will likely be around $350-$400, leaving your take-home pay about the same as if you didn't work at all.

AMT comes to mind. Also, some deductions are phased out according to adjusted gross income. But these are (err...) marginal examples.

And the phase-out is marginal

Just because someone is not aware that marginal rates only applies to marginal increases in income doesn't necessarily mean that the concept of thinking on the margin is lost on them...it simply means they don't know how the tax system works. In fact, if the tax system did indeed work in the manner the USA Today author mistakenly believed it does, then that shows he DOES in fact think on the margin...

Personally I think that should be more offensive to accountants than economists.

It's not offensive, it's the reason I have a job.

If you've got a lot of things phasing out at the same time, your marginal rate can get very high. For instance, if you've got housing and child care assistance, EITC, and several other low-income programs the total phase out might push the effective rate over 100%. If your income is higher, and you've got a lot of kids, the child tax credit phases out simultaneously for each and every one of them and I think the phase out range is only 20k wide for a 1k credit, making it an effective 5% increase in marginal rate per child you have. NB, I know someone with 12 children--not sure where he is relative to that phase out point.

Six kids here, paid no income tax in 2009 and received a check for about $4k for EITC. That was money I didn't earn, so essentially a welfare payment. (And by the time I got it, I didn't need it.) In 2010 I earned plenty so no EITC, and even some of the child tax credit of $1k per kid phased out. So the year to year "tax increase" that I saw was tremendous.

While it's the simultaneous phaseout of multiple income tax benefits that penalize marginal earnings, when you apply income tests to other subsidies like utilities, school lunch programs, college tuition aid, etc., the penalty for earning a little more can be a lot.

Those high marginal tax rates are even more pronounced when you include different kinds of support at the state, county, and city level.

I'd imagine that for families at the poverty level and slightly above, that there is a big focus on obtaining forms of income that don't have to be reported or can be easily hidden from taxation.

Are you ****ing serious? Wow. Just Wow. USA Today is usually joked about and rightfully so, but this is some JUVENILE shit.

This is the newspaper that runs stories showing that 3 out of 4 people is 75%...

Thanks, that made me laugh.

BTW, this does happen to the poor -- it is quite possible to get a raise that pushes you into ineligibility for, say, an insulin subsidy.

(... in which the value of the raise could be less than the value of the subsidy. High MTRs for the poor are not good!)

Good point re insulin. Medicaid is probably the best example of >100% MTRs for poor people -- in some cases, it would result in MTRs of 1000s of %.

So making Medicaid universal amounts to a decrease in the tax rate?

Doing that would remove the sharp increase in MTR Medicaid recipients see. Of course, then someone would have to pay for it, which would require taxes somewhere...

We really need some way to provide medical service to those with low income without penalizing them for increasing their income. Perhaps a graduated benefits regime? Not the simplest problem.

I do think the better option is for the government to offer everyone the same choice: be in our free government-paid program, or take this (say) $1000 tax credit and get your own. At least poor people could make the decision for themselves when the free stuff is no longer enough.

And Medicaid and Medicare together have a budget of over $2000 for every man, woman, and child in America, which is around what other countries spend in total on their national health care. It's not a problem of not spending enough.

Mark twain, "if you don't read the papers you are uninformed. If you read the papers you are misinformed."

T. Shaw, that quote is the highlight of my day. Thank you.

> No, no and 286,000 times no!

Assuming the brackets are indexed for inflation.

It's when Reagan indexed the tax brackets that the left began to truly hate him.

Yeah, this part confused me. Wasn't the problem with "bracket creep" that people were being pushed into a higher bracket and therefore paying more in taxes than before simply because they were being paid inflated salaries? I'd appreciate an explanation; I genuinely want to know.

Yes, David, you have got it. People with a $50,000 income might earn $55,000 with the same purchasing power the next year because of a 10% inflation. But the tax code would charge them a higher marginal tax rate at their new higher income even though their new income makes them no wealthier because of the inflation. That is bracket creep.

There are a handful of non-marginal provisions in the tax code (e.g. more than a certain amount of investment income forfeits all of the EITC and a certain threshold of support can cause a loss of the head of household filing status), but they are few and far between, usually modest in amount, and certainly not applicable in the situation cited.

This discussion of marginal rates does not take into account composition of income.

Think about this: The top .1% paid 28% of Adjusted Gross Income in federal taxes in 2001, and only 21% of AGI in 2008.

Bush tax cuts and the cap gains and dividend tax rules got you there.

There is also geographic bracket creep, where people in high cost of living areas pay higher marginal tax rates on every dollar earned above the standard exemptions.
And as some have mentioned, there are phased out deductions and the AMT as well as the impact on state taxes. A person might probably never take home less from a pay increase, but it may affect employment decisions. Take, for example, someone who is offered a management position at substantially higher nominal pay. But that position is salaried and involves a lot of what would otherwise have been overtime. The job might also come with additional headaches. A rational and forward thinking person would consider, at the margin, whether the boost in nominal pay is worth uncertain prospects of career progression. Here, the "margin" isn't a few extra dollars at a higher marginal tax rate.

The general idea is correct, down in the EITC area (and in with several other credits rolled in there), you can face 100%+ marginal rates until they phase out.

USA today corrected the post

Technically, Dean Baker is only assessed on his final "no" since the first 285,999 are in a lower bracket.

Your fetish with "marginalism" is absurd. Yes, "marginalism" is a good and effective heuristic ... for the "opportunistic" personality, the hustler, the truck-and-barter man, the heroic survivor. It is a trivial strategem for the alive human.

What the hell are you talking about?

Most of the anomalies stem from accountants' fondness for brackets and tables. These step-changes lead to funky behavior at the discontinuity. If only we used smooth continuous functions for stuff like tax-rates, medicare eligibility etc.

A subsidy should not have to abruptly kick in at a arbitrary cutoff; a shaped taper is much better. With computers being ubiquitous I am puzzled why reams of lookup-tables keep getting printed for interest rates, annuities, tax brackets etc. where a simple formula would suffice.

A proportional tax would be even easier, Rahul. Tax every dollar of earned income at the same rate, less a generous standard deduction, and exemptions for retirement savings, capital gains, and health care savings.

Yeah, but now we enter moral territory about fairness etc. and the desirability (or not) of progressive taxation.

That isn't my point, I'm thinking do it flat, progressive, regressive, what ever you choose; just get rid of tables and artificial step changes.

Just to defend Mike's idea, a flat tax with a generous standard deduction *is* progressive. Especially if we consolidate payroll and income taxes (or extend them to all incomes).

I happen to think there are contexts in which it is "fair," too. In the most abstract sense, we can imagine that without the benefit of living in society, we'd be able to take care of some basic standards of living, but not much more. To what extent we can live as lavishly as we do -- compared to the arc of human history -- comes from living in society. That I think is a rationale for sparing some amount of income from any taxation -- the amount deemed to support some basic living standard -- and taxing the rest -- "the product of living in society," if you will -- at a flat rate.

If you did this for *all* taxes -- state, local, and all forms of federal: payroll, income, capital gains, etc. -- I suspect the resulting tax code would be more progressive than it is now.

In the short term, such a system would shift tax burden away from median income earners (and below) and toward the others. It *might* shift tax burden away from extremely wealthy and toward upper middle class, which wouldn't seem "fair" to me, but it's really hard to tell if this would be the result or not, and some might consider it worth it.

The writers at USA Today don't understand marginal tax rates. Would they and the average American understand T = (0.2+0.000001*x)*(x-6000)? As it is, it is tough to have a debate on the top marginal rate of 35% and whether it should be raised to 39.6%. I think it would be pretty tough to frame the issue to the general public about which coefficient in the tax equation should be changed and by how much.

I hope its all squared away now.

At least in Portugal, this is not totally wrong - in the global annual IRS, you indeed never receive less for earning more.

However, the monthly witholding taxes are not marginal, but apply to all income, than a small raise can make your receiving less in the end of the month (even if, in the net year, you will receive the rebate).

While USA Today is technically wrong about the higher bracket leaving you with less total take-home money, I made about 50 more than the limit for the child tax credit, so I would have been better off making 50 dollars less last year.

Ryan beat me to it (sort of). The tables are in $50 dollar increments, and you don't calculate any additional tax between, say, $50,000 and $50,049.99. At $50,050.00 you get the full (say) 25% on that $50, or $12.50. A one penny raise cost you $12.49.

If your AGI is $170,000 or greater, your Medicare premium (two years hence) is increased substantially. So an increase in income from $170,000 to $170,001 can be very expensive indeed. There are other thresholds at higher income levels that increase your premium even further. If you're close to one of these thresholds, it's important to refuse the raise (or take the maximum 401(k) deduction or take whatever other measures are available to you) in order to avoid crossing it.

Although I am a proponent of more progressive taxes, I don't think anyone should ever be worse off for making more money, and I think our current tax code and system of governance does this.

An example that comes immediately to mind is the ROTH IRA. I can avoid capital gains tax on $5k savings today, after paying taxes on it, which is a wonderful deal for a young person like myself. Limiting the program to $5k is, I think, a great idea to roughly even the benefit -- i.e. make sure rich people don't benefit much more than poor people. Except, on top of that, if one makes more than some amount, they're not allowed to participate at all! So they quite clearly get punished for making more money, and in a way that seems to me completely unnecessary, given the $5k cap that already exists.

There is a pretty simple solution to this problem. Make a nondeductible contribution of $5,000 to a traditional IRA and then immediately roll that over into your Roth IRA. Be sure to file a Form 8606 with your return. Problem solved.

In a year or two's time, eligibility for child benefit in the UK will cease for households where anyone pays tax at the higher rate (very roughly around $60,000). The marginal rates there become very screwy indeed (and also: two earners of $59,000 each get child benefit; one of $60,000 and one of none get none). The British tax system has piled on more and more perverse marginal rates in the last couple of years.

This is kind of orthogonal to the main point but there are a handful (probably a few million) right around the poverty line who do have marginal tax rates near or above 100%. Mankiw posted a story about a woman who went from earning $25,000 to $35,000 and it cost her $1600 in EITC, payroll taxes, state taxes, federal taxes, $3000 lost value on her housing voucher, lost child care benefits and it added up to more than $10,000 in lost services/higher taxes.


There is a similar mistaken idea where people will say "he needed the tax deduction." The idea that a rich guy can get more money by loosing money on some investment.

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