I’ve been wanting to write an article entitled “Oatmeal Raisin: The Cookie Nobody Loves.” Unfortunately, although this title captures, I am convinced, a deep truth, I could not find a way to link it to tax law. So instead of describing why, if you leave out lots of plates of different kinds of cookies and come back a little while later there are always more oatmeal raisin cookies left than any other kind, but if you come back an hour later, all the cookies, including the oatmeal raisin cookies, are gone (nobody loves ‘em, but they do like ‘em), this post will describe the piece I wrote instead: Probably? Understanding Tax Law’s Uncertainty.
As I described in an earlier post, flipping a coin is risky, because while we do not know whether it will come up heads, we do know the probability that it will come up heads (50%). The presidential election is uncertain, because we do not know whether John McCain will be elected president, and we do not know the probability that he will be elected president. A.J. Sutter pointed out in a comment to that post that the distinction between risk and uncertainty (that is, between known probabilities and unknown probabilities) ties into the debate about the correct interpretation of probability statements. As it happens, that debate is precisely Probably?‘s topic.
We might say that the probability that an event will occur is the number of times that event will occur over the long run out of the number of times that it could occur. So when we say that a coin has a 50% chance of coming up heads, we mean that if we flip the coin a lot of times–a million, say–about half of those flips will come up heads. And the more times we flip, the closer the percentage of heads will get to 50%. This is a frequentist interpretation of a probability statement.
But this interpretation doesn’t work if the event we’re talking about is not risky, but is, rather, uncertain. As others have noted, tax law is uncertain–that is, that we do not, and cannot, know the probability that a court will uphold a particular tax position. Tax advisors make these sorts of probability statements all the time, because a taxpayer faces lower penalties if he can get a tax advisor to give an opinion that there is a certain level of probability that the taxpayer’s position will eventually be upheld by a court. But if we don’t and can’t know this probability, what does it mean to say that there is a, say, 90% chance that a particular tax position will be upheld?
It means, I think, that the speaker believes that there is a 90% chance the tax position will be upheld. Or, put another way, the speaker would pay 90 cents to play a game in which he would get a dollar if the position were upheld and get nothing if it were struck down. This is what’s known as a “subjectivist” interpretation of a probability statement.
So, who cares? Well, everyone should care, of course!
The IRS and tax advisors should care, because a subjectivist interpretation of tax probabilities could provide additional support for stringent and much-criticized laws that regulate the substance of tax advisors’ written opinions. If we think of tax probabilities of expressions of belief, we can see that these strict rules may actually help tax advisors arrive at less biased estimates of the chance that a tax position would be upheld by a court.
Lawmakers should care, because incorporating tax law’s uncertainty into economic models suggests that lawmakers should, perhaps counterintuitively, be cautious of reducing tax law’s uncertainty. Empirical work suggests that some taxpayers do not like uncertainty. So the uncertainty associated with whether certain questionable transactions are permitted (aside from any penalties imposed if transactions do turn out to be forbidden) might itself reduce the number of taxpayers who engage in those transactions.
And legal scholars who are working with economic models should care too, because these models can change if we acknowledge that neither taxpayers nor lawmakers have access to a “true” probability that a tax position will be struck down. For example, instead of just looking at the taxpayer’s estimation that his position will be struck down by a court, a subjectivist interpretation requires us to look at the relationship between the taxpayer’s estimation and the lawmaker’s estimation. (This last point–that legal scholars, as opposed to economists or statisticians or philosophers, should care about the subjectivist/frequentist distinction–is particularly interesting to me, but it is, I think, the subject for a different post.)