When a behavioral response is illegal, it is called tax evasion. Today's article is a classic in the public finance literature, and it focuses on a particular type of evasion: misreporting income.
The basic idea is that people choose how much income to report to the tax authority based on their income, the tax rate, the probability of being caught misreporting, and the penalty if they are caught. The paper concludes that people will misreport less when the probability of being caught is high and the penalty is severe, and that increasing the probability of being caught is more or less interchangeable with increasing the severity of the penalty.
There is not an obvious relationship between true income and the extent of misreporting. This is related to the idea that misreporting is like taking a gamble. You "lose" if you evade and get caught and "win" if you evade without getting caught. Are rich people more likely to gamble? Not necessarily. They might be more willing to part with money, but the lure of a successful gamble is also weaker. So the paper does not draw strong conclusions about the relationship between income and the extent of evasion.
What if the probability of detection depends on the extent of misreporting? The paper derives some technical conditions for optimal behavior, but concludes only by echoing the idea that people misreport less when they are more likely to be caught.
What if, when an audit takes place, it discovers not only current cheating but also past cheating? The paper notes that this can be interpreted as a relatively more severe penalty for misreporting, which it has already been noted reduces misreporting. Again there are a few technical results.
This paper comes with caveats. Most employers report income to the IRS, so misreporting is for many employees not a realistic option because it would be so easy to catch them. Some people feel a moral obligation to report truthfully, so they are not tempted by the gamble. For these and other reasons, the paper is not a complete analysis of tax evasion, but it sets up a clean framework.
Allingham Sandmo JPE 1972 Income tax evasion: a theoretical analysis
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