This being Tax Day and all, I feel like I should repeat my occassional plea to make the tax system more complicated. In short, income tax brackets are a bad idea. The flat tax, of course, is a worse idea. What's needed is not a flat tax, but a curved tax, where rates are a smooth function of adjusted gross income. The total amount you owe could be calculated as the area beneath the curve -- an integral of the function. Back in the day, this was impractical because most people can't do calculus so the idea of a series of "brackets" was implemented as a mathematically tractable alternative. Thanks to computers, however, this is no longer a problem and calculating taxes owed according to a single function would be simple even if the function itself was very complicated.
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The Calculus Tax
16 Apr 2007 04:48 pm
Comments (90)
I pray to god that TOMORROW is Tax Day.
...and people would be able to debate about the higher derivatives... So, what's your view on the marginal gross jerk?
I think we should have a tax system in which every third line would force you to fill out a table in the associated publication in order to figure out whether you can take the full deduction or exemption, must pay an alternative tax, or ... oh, wait, we already have one of those.
Interesting...even conservative math geeks might get behind this.
Tax Day is, as Al says, tomorrow.
One's tax form is already a very lengthy agebraic calculation. Making the rate calculation incrementally more complex would barely be noticeable amidst the deductions.
Bad idea, because the tax code should not merely BE fair and understandable but should also APPEAR fair and understandable. If tax rates were based on a set of "black box" calculations that only mathematicians really understood, it would make popular distrust of the system go up (if that is possible).
This is the superficial appeal of the "flat tax" concept, even though it dishonestly ignores what really makes taxes complex, which is not progressive tax brackets but the mass of special interest tax breaks passed to please middle-class and corporate power groups.
Yup - just double checked - tax day is tomorrow. I have a couple of big checks to write, and Matthew just scared the bejezzus out of me that I was late.
Al, estimated tax is due today.
Isn't this similar to what Germany has? I don't remember a Democrat citing Germany's fiscal policies since... I think it was Bill Clinton, at the beginning of his administration. I could be wrong on that.
By the way, did anyone read Ari Fleischer's op/ed in today's WSJ on the tax code? Knock yourselves out with the ad hominem shots at Fleischer, but the numbers he cites demonstrate how progressive the federal income tax system is already. How much more progressive can you make it? What if some of the top 1% of earners -- who already pay more than a third of all income taxes -- decide to bail?
There are simpler, more efficient, and fairer ways to raise more revenues. One idea of mine would be to lower the exemption on the inheritance tax to, say, $10k, and lower the rate as well, to 10%. That would raise a huge amount of money over the next decade or two Gen Xers inherit real estate and securities from their boomer parents; keeping the tax rate low would reduce resentment, class warfare, and attempts at evasion. I would direct the proceeds of this into a real trust fund (i.e., not one invested in Treasury securities to be immediately spent by the government) to shore up Social Security, Medicare and Medicaid.
(a) You haven't said anything until you've told us what this function is.
(b) You seem to think that your idea differs qualitatively from the tax bracket idea. It doesn't - it only differs quantitatively, in how-many-and-how-narrow the tax brackets are. They'll never be zero-length - for the obvious reason that currency is discrete. All you want is a finer partition. Which is fine, but only differs numerically from the current structure, not in kind.
Dave-
Are you serious? This might sound revolutionary- but lowering the tax rate lowers tax revenue.
Of course right wingers love to focus on the only progressive tax ignoring the regressive taxes that more than offset the federal income tax. In the end the total percentage of taxes paid by the lowest income quintiles is pretty near the percentage paid by the top 20%.
Back in the day, this was impractical because most people can't do calculus
This seems wrong on several levels, although TW Andrews has a good point about the people writing the laws.
1: Most people don't do any mathematical calculations involving the tax rate. We figure out our taxable income and then look up the tax on a table. (If we're lucky and have qualified dividends, we go to p. 36 and get confused -- obviously part of it is that qualified dividends are taxed at 15% and everything else is taxed at the normal rate, but what are all the rest of those calculations doing? ostap is right here.) So this change wouldn't require the taxpayer to perform any more complicated calculations than before, it would require the people who print the tax table to do those calculations.
2: Anyone whose income is off the top of the tax table can afford to, and probably does, hire someone with as much math ability as they like to do their taxes.
3: The calculus involved isn't even very complicated; if you're talking a smooth function of adjusted gross income you're talking x^2/2 with a few scaling factors and cutoff points, right?
Lately I've been into the theoretical coolness of a 50/50 flat tax where the money you earn up to the median income isn't taxed and all remaining earnings are taxed at 50%.
It all boils down to looking up a number in a chart regardless of how simple or complex the rate is calculated, though. Simple is nice from the point of view of speachifying, though.
Dave: sure, the Federal income tax is progressive to some extent, but (a) it used to be more so, and (b) other than the Federal estate tax, it's pretty much the only progressive tax around. (It could be made a bit more progressive, without changing any tax rates, by the simple expedient of applying the AMT to dividend and capital gains income.)
The Social Security and Medicare payroll tax is regressive. State sales taxes are regressive. Most state income taxes are flat once you hit the beginning of their top bracket, which you generally hit at a pretty low level of income. Gasoline taxes are regressive.
I'm wondering, do you pay tax on a book advance when then money ($100,000, say) is, well, 'advanced'? What then if the royalties don't cover the advance (heaven forfend) and you need to return some of the money? Or does the publisher suck it up at that point?
James B. Shearer: No.
Please see the below list from the IRS website (url: http://www.irs.gov/publications/p553/ar01.html )
The April 17, 2007, due date will apply to the following.
*2006 federal individual income tax returns, whether filed electronically or on paper.
*Requests for an automatic six-month tax-filing extension, whether submitted electronically or on Form 4868.
*Tax year 2006 balance due payments, whether made electronically (direct debit or credit card) or by check.
*Individual estimated tax payments for the first quarter of 2007, whether made electronically or by check.
*Individual refund claims for tax year 2003, where the regular three-year statute of limitations is expiring.
*Calendar-year 2006 partnership returns (Form 1065 and Form 1065-B).
*Annual information returns (Form 990) and unrelated business income tax returns (Form 990-T) for tax-exempt organizations with a fiscal year ending on Nov. 30, 2006.
*Calendar-year Form 990-T for certain employee trusts, retirement plans, and education saving plans.
*2006 gift tax returns (Form 709).
*Extension requests for any return normally due April 15.
*The March tax deposit for employers (generally, small businesses) required to deposit withholding taxes on a monthly basis.
*Withholding-tax deposits for larger employers, subject to the next day deposit rule.
I don't even see why ANY calculus would be involved under this proposal--all you are proposing is a function of gross income to be continuous rather than discrete. There's no need to have a function that requires integrating. The function would just produce the amount of tax you would pay, and it would vary continuously over the full range of gross incomes. There would be a single input variable--your gross income--and a single output variable--tax owed. The equation would probably even be fairly transparent as to how it was increasing over the range of incomes.
Your "proposal" seems more like the suggestion of someone who wants to sound a bit more sophisticated mathematically than they really are....
Harsh!
I'm all in favor of a progressive tax on a smooth curve, but even if the great majority of people have access to computers capable of performing the necessary calclulations there will remain a segment of the population for which requiring a computer to calculate one's taxes is an unreasonable burden.
That said, we currently only have 6 tax brackets and there's no reason why we couldn't have several dozen at intervals of, say, $2,000, mapped approximately to the results of Matt's formula. You provide a table of the first 50 brackets, which gets you to $100,000, with the standard paperwork. For AGIs over $100K, you provide the formula for people who want to calculate it themselves, and provide a calculator at the IRS website, and of course most people making that much will either have an accountant or use TurboTax anyway, so there's no real burden.
Now what I'd be very curious to find out is how a change like this in the tax code would effect charitable giving, since we all know that one of the things people do is tune their AGI with tax deductions.
James B. Shearer: Al, estimated tax is due today.
James B. Shearer scares the bejeezus out of me AGAIN (thanks, Tax person). This thread is intended as payback for my "trolling", right?
Can I add that it is time for the Alternative Minimum Tax to go? I'm just sayin'.
Before this post I liked matthewyglesias.com. Now I love it!
Previous commenters are right:
1) Smooth function sounds good (tax bracket discontinuities are not so good-- the work done by citizens to avoid higher brackets is not useful work.)
2) Integrals aren't required. Forget about the marginal tax rate and just talk about the average tax rate. Poof, no integrals.
3) What's the shape of the curve? (This is a separate question, though: even a smoothed version of the current bracket structure would be OK)
Preston:
"Are you serious? This might sound revolutionary- but lowering the tax rate lowers tax revenue."
I suggested lowering the exemption on the estate tax as well as the rate. The current exemption is $2 million; my proposed exemption would be $10,000. The percentage of deceased people whose estates are subject to the estate tax now is less than 1% (according to this liberal tax policy organization).
Considering that 69% of Americans are homeowners, and over 50% own stock, I would estimate that the percentage who will have estates larger than $10k when they die would be well over 50%.
Can you see now how lowering the rate and the exemption significantly could result in higher estate tax revenue?
Many (perhaps most) people have a misconception about tax brackets that if you make a dollar more, suddenly you're paying a bunch more taxes. That's wrong, but it's awfully hard to explain to people that that's not the case. This misconception is part of why people think that tax brackets are unfair, and that in turn is part of why people think it's important to lower the marginal tax rates of the wealthy. Getting rid of the brackets would get rid of the misconception, which might be to our advantage.
Matt's idea lacks substance, but it might be psychologically helpful.
I think Matthew just revealed that he never did his own taxes before the advent of personal tax preparation software.
"back in the day" (i.e., the 90s and still today if you do your taxes by hand) you were presented with a tax table that had AGI ranges of $50 (where $50 is much smaller than each of the tax brackets). you matched your AGI to the range and then found your tax. there's no reason why the government couldn't have chosen a smooth marginal tax function and then used it to calculate the tax owed at the midpoint of each range. this would differ from the the "perfect" anwer by at most about +/- $10, and on average, by basically nothing. given that the typical federal tax bill is over $10,000, this would be an acceptable error. so the lack of a calculus based tax has
not been caused by the typical taxpayer's inability to calculate the tax or the lack of PC ownership, but more likely it was the result of something else. maybe a lack of creativity by legislators? or maybe the legislators were worried that the public wouldn't understand the taxation system? (Turbo Tax obviously doesn't fix this second
problem.)
Mark,
The AMT already applies to dividends from bond funds; applying it to capital gains would send investors fleeing from U.S. equity markets. There are plenty of other places to invest money these days. Government revenues from capital gains taxes have been booming over the last few years, even after (or, some might argue, partly because) the cap gain tax rate was lowered from 20% to 15% -- why choke this golden goose?
Regarding Social Security and Medicare taxes: These taxes may be regressive, but the benefits are progressive; in the case of Medicare, they are extremely progressive relative to taxes paid, since the Medicare part of FICA is uncapped. Also, those in the lowest income brackets get a government check that covers all their payroll taxes, and then some -- the EITC.
I think Matthew just revealed that he never did his own taxes before the advent of personal tax preparation software.
Well, he was twelve or so.
One idea I had was that taxes would be calculated by having after-taxed income be calculated as a downward concave function of before-tax income, say, a logarithm. So if your income were x, you'd take some log function of x, and keep that as your income, and pay (x - log function of x) as your taxes.
Admittedly, it's silly in practice, but it seemed like a kinda neat idea.
Al, sorry about that, I guess the directions on my forms were in error as Tax Person's link explains. Tax Person is this true for New York State also?
I want a tax rate that involves e!
Matt, this is what you're looking for:
http://en.wikipedia.org/wiki/Generalised_logistic_curve
Actually, the tax code isn't complicated enough. America is huge and there are huge disparities in terms of cost of living and lifestyle that a salary affords you. $45k a year in San Francisco gets you a lower standard of living than $45k a year in Topeka, Kansas. So, why are they taxed at the same rate? We should have a federal code that adjusts taxes to local living costs.
Um, Matt, any given function could be implemented as a table; you've forgotten the Fundamental Theorem of Calculus, which makes this post even funnier.
Matt, don't try to sell it as the calculus integral. Just say its a really, really, REALLY big number of brackets. (I love math humor.)
I am tired of such discrimination. Everyone is always so concerned about the area under the curve but no one ever stands up for the area above the curve. I think it is a matter of pure elitism. Real America is all about the area above the curve.
I don't even see why ANY calculus would be involved under this proposal--all you are proposing is a function of gross income to be continuous rather than discrete.
This depends on whether or not the function that defines the rate at which a given dollar should be taxed can be integrated symbolically or not. If so, then you're correct, you've got a function which takes your income (and potentially a few other variables besides) and spits out your tax owed.
If the rate function isn't amenable to symbolic integration, then you'd need to use numeric methods, and would probably need to be done for each individual.
Okay, I can see the theoretical appeal of this, but come on, now. I used software one year, but stopped using it because it took longer to navigate through the screens than it took me to do my taxes by hand (why spend money to waste my time on something unpleasant?). This just seems like a way to force everyone to get software or pay H&R Block, which is a complete loss to the economy.
Now, from the standpoint of those who want to disguise taxation, this would be a great way to keep everyone (except a select few) from ever knowing what their marginal tax rate is. Assuming the government publicized the taxes-owed function, one would have to differentiate the function to obtain the marginal function, and probably not one in a hundred could remember how to do that.
Kind of like the disappearing exemptions and deductions that insert arbitrary spikes into the marginal tax rates at various intervals.
Philosophy majors...
Looks like they don't teach the definition of a function to political science majors at Harvard.
If you don't mean to suggest that the function should be of the class C^1 or even C^0, and there is no reason for this to be so, even the current tax table is a function. A single function at that.
This just seems like a way to force everyone to get software or pay H&R Block, which is a complete loss to the economy.
I think the assumption that everyone who pays taxes has a computer or access to a computer reflects a forward-thinking but not quite realistic view of the U.S. population.
Matt,
No need for calculus all you need is to define the right function. So for example the following would work
T = I A (1 - exp[-b I]) where
T is the tax you pay
I is your income
A and b are selected to make the tax code as progressive as you want. Say you want the maximum tax paid on the highest possible income to be 50%, then A = 0.5. If you say that people earning $100,000 a year to pay at half that rate then b is (-ln(0.5))/100,000. The value of b is not obvious, but this would work. Something like this would meet your requirements.
I also don't see why you need calculus for this. That said, there is a good point buried somewhere in Matt's post.
To get a progressive tax, and it doesn't even have to be on income, you want to combine a debit that is a percentage, with a flat amount that is a credit. To get the most regressive tax possible, do the opposite.
Imagine if all income, and I mean ALL income (wages, gifts, inheritances, capital gains, perks) was taxed at 34%. However, everyone got a $17,000 deduction. You would get a perfectly progressive tax. A family making $17,000, the poverty wage, would owe 34% of $0, an effective tax rate of 0%. A family making the median income of $46,000 would owe 34% of $29,000, which translates into an effective tax rate of 23% or so. A family with an income of a million dollars would owe 34% of $983,000, which is pretty close to 34%.
Now imagine if everyone owed $17,000, but could deduct 34% of their income. You can see how large the tax credit would be for the millionaire, while the poor family would owe more than they make.
We, or actually the media, have allowed the "flat tax" label to be used for proposals to basically eliminate deductions that benefit poor and middle class people, and add deductions that benefit the wealthy. An actual flat tax (tax all income at the same percentage, give everyone a tax credit) is the most progressive tax imaginable. It can be combined with a negative income tax. It could work with a sales tax, just tax every transaction then mail a check for the same amount of money to everyone at the end of the year.
The standard personal deduction in the tax code is great, but there are tons of deductions for which you have to be a certain person or in certain circumstances to claim. The wealthy are better able to arrange their income to meet this complex criteria than the wage earner. Unfortuantely, the way the U.S. federal system works means we have to keep the deduction for state and local taxes (likewise any proposal to do away with this is not being made seriously), however progressives should be in favor of eliminating all deductions but that and the standard personal deduction, increasing the latter as much as is fiscally prudent, and making as much income as possible taxable. Two of these three things would also allow for much lower tax rates overall.
I think we should try to construct a tax system that uses infinite series, and divergent ones at that. Now that's progressive.
Speaking as a part-time publisher, advances on royalties ARE definitely taxed in the year they are paid. (There's a place on the 1099 form where you can put royalties.) If you have to return all or part of the advance, you get to redo your taxes (up to a certain number of years after--I think 5) and ask for a refund.
The German income tax system is formula-based, and the Italian system treats families with children in a way that is equivalent.
I think that the main problem with formulae-based income tax systems is that they reduce transparency for everyone who is not a mathematician - most of the population.
Otto, having worked in publishing for twenty five years I can tell you that authors are almost never asked to repay part of the advance, even if the book fails to earn it out. As a practical matter, the advance is non-refundable, even though many book contracts don't make this explicit.
Its easy to have a progressive flat tax. Have no tax on income below a certain level - say 30K. All income above that level is taxed at a flat rate. If you plot the percentage of income that is taxed as a function of income, you will see that the function is nice and curved.
What's really needed, of course, is to get rid of all the deductions. The question that really brought home the absurdity of the tax system was the one saying: if I was either born before 1942 or blind I should do X, otherwise I should do Y. Ridiculous. The whole slog probably took me about 8 hours.
I think we should do away with the math. Everyone should write an essay describing and justifying how much tax they should pay. These essays would be graded by committees of second tier liberal art school graduates, who will then decide how much you should pay.
Comments closed April 30, 2007.
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Heads in the Sand
I would love to hear the puditocracy argue tax policy after such a change:
"I really think that the first derivative of the tax function should be higher between the fourth and fifth inflection points, in order to "
It would mean that congress-folks would need to know some math, which pretty much makes this DOA.
Posted by TW Andrews | April 16, 2007 5:01 PM