Tuesday, April 15, 2008

Complexity of Income Tax

Its INCOME TAX TIME in the USA. Which country has the most complicated Income Tax System? How can you measure the complexity of an Income Tax System? Some factors:
  • The number of pages in the tax code.
  • The length of the form you hand in.
  • The percent of tax payers who hire someone to do their taxes for them. (This may also be affected by the computer literacy of the country.)
  • The number of changes in the tax law from year to year.
  • The minimum amount you have to declare. (Do I need to declare my 25 cents that I won from Justin, my 8 year old great nephew, on a math game? Can he use the -25 cents as a deduction? He can use it to offset gambling gains.
  • The number of items you can deduct.

There is a problem with all of these measures. What if the tax code is 100,000 pages long but 99.9% of the people only need the first page? One solution is to do some sort of weighted sum.

Deciding whether a tax system is complicated is a hard problem; however, deciding if its fair is a much harder problem.


  1. Oh, come on, Bill, what kind of computer scientist are you? The only reasonable measure is the complexity class of the following decision problem:

    Instance: A set of n financial transactions.

    Problem: Do I owe the IRS any money?

    Most likely, this problem is undecidable.

  2. > some sort of weighted sum.

    hardcore math, man.

  3. anon 1:

    It can be decided in constant time -- its a trivial language.

  4. The weighted average idea isn't bad. My concern is for the rules that affect how you interpret all the other rules and amounts. So maybe take the expected value of c^X, where X is the number of rules that apply? Probably 1 < c < 2.

  5. I see it as "how often do I have to invoke(and calculate) exceptions?

    For instance, IRA contibutions lose dedectability abouve a certain income, and theres a formula.

    Or how about the "do I need to file AMT?" calcualtion? That's a time consuming stumper.

  6. Come on...buy some software for $25 that will handle all your needs almost painlessly. I agree that in theory one should not have to pay anything in order to fill out a return (for that matter, I refuse to use e-filing until they make it free), but in practice it is worth spending the money and forgetting about it.

  7. There are two numbers associated with each US tax form: How much time should be required for record-keeping and how much time for filling out the form. Even with a tax program all you save is the latter and the former is often considerable. I've rarely found that the forms overestimate the record-keeping time, either.

    In some years the tax law is set so late that the forms aren't right. A couple of years ago the sales tax deduction was not even passed until after the beginning of the next year so if you ran your tax program too early then you would have missed it. This year, the exemption for the alternative minimum tax wasn't set early enough so the main forms reflect too low a value. The AMT form had the right exemption - which was more than $20K larger - but not a revised worksheet.; so, if you fell in that gap, to figure out that you didn't need to file the form you had to fill it out first. This is still better than the time in the 1970's when the earned income exemption for Americans living abroad wasn't decided on until June of the following year!

  8. http://www.cs.amherst.edu/~djv/irs.pdf