May 08, 2006

 On discovering income tax

For 32 years, I was an international civil servant and didn't pay any income tax, or even file a tax return. It was like working in Antarctica, except for the Gewürztraminer. But this year I have to file, as it happens in France, and have discovered the unbelievable complexity of tax. The French do allow filing online, but you still have to work it out by hand like the subjects of the Pharaohs. The doubly lucky taxpayers of Geneva get in the mail, or can download, a complete tax filing program; a great step forward. While you can print, save and reexamine the return, you can't (that is, I don't know enough to) look under the hood and see what is going on. Why not use an ordinary multipage spreadsheet, with macros for the menus, and locking the formulae?

Another complication that strikes me as obsolete is the use of discontinuous tax bands.

Besides obscurity and a lot of busywork, these create economic distortions and encourage strategic behaviour at the margins. The sound part of the argument for a flat tax is transparency, but the real agenda is of course the loss of progressivity. The two can be reconciled. You can have a progressive but linear tax scale, as with British inheritance tax: the basic function is

inheritance tax = 40% times (estate - £240,000)
though naturally it's muddied by lifetime transfers, discretionary trusts and so on.

With universally available computers, there's no reason to limit yourself to linear functions. By advanced research techniques (poking around on Wikipedia and playing with Excel), I constructed a nice simple progressive tax function that increases smoothly from zero at €10k to an asymptote of 33%, reaching 30% at €100k. You can make my function more or less progressive by fiddling with the parameters.

Well, why not adopt tax rates as spreadsheet functions?
Tax function chart_rev_image002.gif
Oops, I've just realized that my formula is really the same form as the linear British inheritance tax function, so the example doesn't add anything. Still, my question stands.
Update 2
Label corrected in the chart. The graph is of the tax rate not total tax, so the function graphed is z=1/3 -10/3x .
Update 3
I've added to the chart below a genuinely non-linear tax function:
y = 0.2x + 0.006*((x-5)^1.7) - 4
In practice, you would need to set a maximum rate discontinuously.
Tax function chart rev2_24019_image004.gif

Posted at 07:26 AM | TrackBack (0) | |


There's something wrong with the math there. That equation wouldn't produce the graph shown. Was there maybe a superscript that got flattened into normal text?

Posted by: Zzedar at May 8, 2006 09:08 AM

Zzedar: It's because the equation is for the total tax payed, but the graph is showing the tax rate: i.e., it's actually a plot of y=(x-2/3(x+5))/x.

Posted by: micah at May 8, 2006 09:19 AM

IIRC, there was a paper which found no noticeable clumping effect in US individual tax returns. There are two possible functions which would produce some clumpiness: true cessation of income (i.e., work less to avoid moving up a band) and manipulation of taxable income (e.g., do I take a particular deduction on Dec 31 or Jan 1?). The fact that no clumping was found indicates that the effect of disontinuous bands was not of practical effect, at least for the US system at that time.

Posted by: at May 8, 2006 09:52 AM

I'll fix the label, but as it's embedded in the chart this will take a little while.

Posted by: James Wimberley at May 8, 2006 10:32 AM

Up to a reasonable level U.S. taxpayers just read their taxes off a table: If line X is n, your tax is m. Complexity is not a barrier at all; the tax rate could involve differential equations and it wouldn't be any more complex for the taxpayer to read the table.

Posted by: Matt Weiner at May 8, 2006 10:36 AM

"but the real agenda is of course the loss of progressivity"

The most common flat tax plans contain a large personal exemption, so they're still progressive (and not really flat), although somewhat less than current rates.

I think the REAL agenda is to remove tax from investment income. Proponents believe that this distorts investment decisions, punishes savings, and hurts growth.

Posted by: at May 8, 2006 11:22 AM

"to remove tax from investment income"

and from all other non-payroll sources including inheritances, and from corporate income, and to reduce progressivity. The scattering of the few crumbs that fall to those with modest non-payroll assets is a tolerable price to pay for the billions that will flow untaxed to those with real assets.

In the days before income taxes, Andrew Carnegie's best year was $5 million, and mostly dividends; at the time, families needed $400 a year to get by, and most full-time laborers didn't get quite that much for a six- or seven-day week, if they were healthy. Ah, wasn't that a time!

And these are the same people who denounce the use of tax policy for democratically-determined purposes as "social engineering" and "picking winners."


Posted by: Altoid at May 8, 2006 01:12 PM

Hmmm... it hasn't quite been pointed out yet that your "progressive but linear tax" is exactly a flat tax with an exemption. Steve Forbes: "Not one cent to the IRS on the first $36,000 [for a family of four]. Anything over that would be taxed at a flat, fair 17%." Granted, your tax has a lower exemption and a higher rate, but the principle is the same.

Posted by: anno-nymous at May 8, 2006 05:26 PM

Anonymous: I did admit the point in my first update.

Posted by: James Wimberley at May 9, 2006 12:32 AM
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