Exemptions and deductions

The tax is dependent on income, but what exactly is the income used in the tax equation?

Well, this is where the difficulties begin. Tax laws come from Congress that cannot resist its urge at pleasing specific parts of the population by introducing tweaks, normally in the form of deductions linked to specific conditions like marriage, house ownership, children, .... The base principle becomes the tax law that is then formalized in specific rules by the IRS, i.e. what is the definition of a kid.

Because the world is not as regular as can be expressed in a law, the IRS rules are complex, full of details that apply probably only to a very small percentage of cases but still must be detailed in the instructions booklets written by the IRS.

The income used in the tax equation is known as the adjusted gross income, it is essentially calculated as follows for your workpay:
* start with your nominal salary
* remove a number of special items: social security, 401k contributions, ... and you get your taxable income
* remove the exemptions, these are usually amounts that are not directly related to any real expenses
* remove deductions, these are usually amounts that correspond to specific expenses that are considered useful for the society, at least as seen by Congress
* presto, you have your adjusted gross income.

Of course, this is where the pain starts, you as a taxpayer, have to assemble all the information needed to correctly assess your taxable income, but also to substantiate your deductions. The IRS estimates are that filling a 1040 form requires 30.3 hours of which 19 hours are for record keeping. If you can take 2 hours a day after work, this requires two full weeks of work.

The IRS also estimates the average cost at $269, but this probably assumes your time is free. No surprise this is called a burden. Of course, the IRS is part of the problem as the rules are at best complex. Just an example, line 42, Exemptions has special treatment for persons displaced by Hurricane Katrina. This probably comes from a good intention, but a first obvious remark is that this is only a very small part of the population, but it impacts all taxpayers (you have to read the instructions).

Then there are the exact rules, with no less than 6 small details that you have to check if you happen to be housing a displaced person, the first one reads "The person displaced lived in your main home for a period of at least 60 consecutive days ending in 2006". The definition appears rigorous, but this is a nice example of how arbitrary the process can be, note the following:
* main home, what if you have contributed a cottage that is on the same piece of land as your main home?
* 60 consecutive days, what if the displaced person traveled for one week, say to New Orleans, is it still consecutive. If you remember that the displaced person was there in January and February, can you positively remember that he or she was there for 60 days?

This is not directly a critic of the IRS, but of the whole process of trying to carve out special cases. Every special case comes with a set of rules and all these rules will probably raise a number of secondary questions that may end up as more rules and the cycle never ends. After a few years of this, you need 30 hours to fill your tax form and everybody hates filling the form.

But this derails us from the goal, a mathematical treatment of the tax equation. Mathematically, deductions and exemptions correspond to an offset. Essentially pushing the tax curves to the right when using the taxable income for the x axis. This will be further discussed and illustrated in a next article.