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# Modeling Uncertainty in Tax Law

By: Lawsky, Sarah B. | Stanford Law Review, February 2013 | Article details

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# Modeling Uncertainty in Tax Law

Lawsky, Sarah B., Stanford Law Review

```INTRODUCTION
I.   THREE MODELS OF TAX COMPLIANCE
A. Simple Costs and Benefits
1. The model
2. Evaluating the model
B. Expected Value
1. The model
2. Evaluating the model
C. Expected Utility
1. The model
2. Evaluating the model
II.  THE UNCERTAINTY MODEL OF TAX COMPLIANCE
A. Motivating the Uncertainty Model
B. The Uncertainty Model
1. The certainty component
2. The uncertainty component
3. Combining the components
4. Weighing outcomes
5. A tax compliance example
III. THE UNCERTAINTY MODEL'S USEFULNESS FOR TAX LAW
A. Attitudes Toward Uncertainty
B. Manipulating Uncertainty
D. Future Research: Identifying Attitudes Toward Uncertainty
E. The Simplicity Objection
CONCLUSION
```

The most rational man I ever met, whom I shall call Ysidro, determined his own ... preference[s].... When told that he did not satisfy all of the ... axioms [of game theory], he replied that he thought it more rational to satisfy his preferences and let the axioms satisfy themselves.

--Paul Samuelson (1)

INTRODUCTION

Imagine you are offered a choice between, on the one hand, \$100, or, on the other hand, the opportunity to bet on a coin flip, where you will get \$50 if the coin comes up heads and \$150 if it comes up tails. If you are like most people, you prefer the certain \$100, even though the risky choice has the same expected value. (2) Now imagine another choice: the coin flip game, which gives you an even chance at \$50 or \$150, or a different game, which will give you an unknown chance at \$50 and an unknown chance at \$150. Most people pick the coin flip, the game that features a known probability (that is, an even chance of winning), over the second game, which presents an unknown probability. (3) The first choice, between \$100 and a coin flip, tests how you feel about risk, that is, a known probability. The second choice, between the coin flip and the other game, tests how you feel about uncertainty, an unknown probability.

A taxpayer trying to decide whether to comply with the tax law faces uncertainty, not risk. He does not know whether he will be audited by the Internal Revenue Service (IRS), and perhaps he does not even know whether his tax position is correct as a matter of law. And he also does not know the chance that he will be audited, or the chance that his tax position is correct. If the IRS were rolling dice to determine whether to audit the taxpayer, the taxpayer would know the chance that he would be audited (assuming he knew that the IRS's dice were not weighted). If, for example, rolling a pair of sixes would trigger an audit, the taxpayer would know that he had a 1 in 36 chance of being audited. He would not know how the roll of the dice would turn out, but he would know the chance that the roll would go against him. If a roll of the dice determined whether a taxpayer would be audited, and the taxpayer knew that, the taxpayer would be making a decision under risk--an unknown outcome with known probabilities.

Rather, when the taxpayer decides whether to comply, he grapples with a decision more like the decision of how much to bet on the outcome of a football game. Not only does the taxpayer not know who is going to win the football game, but he also does not know with certainty the chance that a given team will win. And when the taxpayer decides whether to comply with the tax law, not only does he not know whether he will be audited and his position will be disallowed; he also does not know the chance that he will be audited and his position will be disallowed. The taxpayer's decision whether to comply is thus a decision under uncertainty, an unknown outcome with unknown probabilities.

Many people are averse to uncertainty, both in general (4) and in the tax compliance context. For example, one experiment found that taxpayers are so uncertainty averse that "when low fines were combined with vague information about the probability of audits, the average percentage of reported income was quite close to that obtained when high fines were employed." (5) Low fines and uncertainty, that is, deterred cheating almost as much as high fines alone. Brain imaging studies show that different parts of the human brain activate when considering risk as opposed to uncertainty. (6) Indeed, even apes (7) and monkeys (8) have been shown to distinguish between risk and uncertainty, and to prefer risk to uncertainty.

But while legal scholarship's existing economic models of tax compliance can take risk and attitudes toward risk into account, they cannot incorporate attitudes toward uncertainty. By "model," I mean a deductive argument from exactly specified premises that deliberately simplify and omit facts about the world. (9) To say that the models of tax compliance cannot take uncertainty into account is to say that nothing in the models can be adjusted to represent increased (or decreased) uncertainty about the probability that a fine will be imposed, or to represent taxpayers' attitudes toward uncertainty. It is not just that the models do not take uncertainty into account; rather, the models cannot take uncertainty into account. (10)

This Article, in contrast, offers a formal model of tax compliance--what I call the uncertainty model--which takes into account both the taxpayer's degree of uncertainty and the taxpayer's attitude toward uncertainty. The uncertainty model imagines that taxpayers determine whether to comply with tax law based not only on the fine that could be imposed, the probability of that fine, and the taxpayer's feelings about risk (unknown outcomes), but also based on how sure the taxpayer is about the probabilities he assigns to various outcomes, and how the taxpayer feels about unknown probabilities. The model provides new insights into a variety of contentious problems in tax law and policy, including how the government should reveal information about its approach to audits, whether the government should use anti-abuse rules to attack tax shelters, and whether tax professionals should be subject to penalties for providing unsupported tax advice.

Several scholars outside the legal academy have empirically studied taxpayer attitudes toward uncertainty, (11) but only a few legal scholars even take into account that the decision whether to comply with the tax law is a decision under uncertainty. (12) In other areas of the law, especially criminal law and tort law, some legal scholars have begun to investigate uncertainty and uncertainty aversion using a combination of theoretical, empirical, and doctrinal approaches. (13) (The recent financial crisis may have piqued general interest in unknown probabilities, as some believe that the crisis was due in part to mistaking uncertainty for risk, unknown for known probabilities.) (14) Unlike most legal scholarship that addresses uncertainty, however, this Article focuses on formal modeling, rather than empirical studies or a more intuitive (which is not to say any less valuable) analysis.

Only three pieces of legal scholarship have incorporated any of the significant amount of scholarship outside of legal academia on formal modeling of uncertainty. First, Daniel Farber has applied formal modeling of uncertainty to propose a new approach to environmental policymaking. (15) Second, Eric Talley has investigated material adverse event clauses in contracts using an uncertainty modeling framework. (16) The current Article takes a different approach to modeling uncertainty than either Farber or Talley. (17) Finally, Joshua Teitelbaum has modeled uncertainty in tort law using the same approach as this Article: Choquet expected utility with neoadditive capacities. (18)

After this Introduction, Part I describes three approaches to modeling tax compliance and how scholars have used these models. Part II proposes a new model for tax compliance--the uncertainty model--that, unlike any other model of tax compliance in legal scholarship, takes uncertainty into account. Part III explores the benefits and practical consequences of the new model: the information it gives us that we can incorporate into our understanding of the law, the questions it raises that might lead to useful empirical work, and problems with translating the model directly into law.

I. THREE MODELS OF TAX COMPLIANCE

This Part considers three models that scholars and policymakers use to understand why taxpayers comply with the tax law and how to increase tax compliance. The first model, the simple cost-benefit model, posits a taxpayer who weighs the cost in dollars of complying (tax owed) against the cost in dollars of not complying (tax owed plus fine owed). This model is not generally used in scholarship, though it might be used by unsophisticated individuals who are deciding whether to take a particular tax position. The second model, the expected value model, is the most common model in tax legal scholarship. It also imagines that each taxpayer compares costs in dollars, but discounts each possible dollar outcome by the probability of that outcome. The third model, the expected utility model, is common in economic scholarship and has been incorporated into some policy documents. It posits a taxpayer who compares the expected utility of various outcomes, not the expected dollar amount; this model, unlike the expected value model, can take into account taxpayers' attitudes towards risk.

One cannot, of course, determine in the abstract how useful a given model is to legal scholars and policymakers. A particular model may be useful for one sort of question but not for another. Nonetheless, better to understand when a given model may be useful, this Part evaluates each model on three criteria: the model's accuracy, the extent to which it directs legal scholarship, and its simplicity. (19)

First, a model may be more useful to legal scholars for certain purposes the more accurately it describes the world. For example, a more accurate model might help policymakers calibrate penalty and audit levels. One way to demonstrate the accuracy of a model is to show that an element of the model corresponds to a fact in the world--for example, that people's behavior in reality corresponds to the model's assumptions about behavior. Another way to show that a model is accurate is to show that it correctly predicts outcomes--in our case, predicts the extent to which people comply with the tax law. Second, a model can be useful if it focuses scholars' attention on factors that are susceptible to change, or suggests areas that should be further studied. Such a model is not somehow intrinsically better than a model that focuses on immutable or unreachable factors; it is more useful to legal scholars, however, to the extent that legal scholars are interested in critiquing or amending the law. Finally, a simpler model is, all else equal, better for legal scholars and policymakers, because it is easier to understand and to use. (20)

These three criteria do not, of course, always point in the same direction. For example, a model that reflects many facts in the world and is therefore very accurate would also be complex, perhaps to the point of being unworkable. And there is no particular weight one can assign to each factor to determine that one model is somehow "better" than another in the abstract; the correct balance among the factors depends on, among other things, how the model is to be used. But these factors are nonetheless useful as a framework for comparing different models.

A. Simple Costs and Benefits

1. The model

Perhaps the simplest way to think about the taxpayer's choice whether to comply is to think of him as comparing dollars to dollars, comparing what the law says the taxpayer will pay if he complies to what the law says he will pay if he does not comply. I call this the simple cost-benefit model. Take, for example, a taxpayer, Henry, who has pretax income (I) of \$100 and is trying to decide whether to pay a \$40 tax (T). If he does not pay the tax and is caught, he will owe the tax plus a \$10 fine (F). In the simple cost-benefit model, Henry compares \$40, the tax he will owe, with the number of dollars the law tells him he will have to pay if he does not comply--in our example, \$50, the tax plus the fine. (21) Henry would prefer to pay as little to the government as possible, so he will choose to pay his tax. In the simple cost-benefit model, any fine will be enough to get a taxpayer to comply.

Symbolically, Henry will comply whenever he will have more money after paying the tax than after paying the tax together with the fine. That is, he will comply whenever

I - T > I - T - F (1)

Obviously, this implies that a taxpayer will comply whenever F > 0.

2. Evaluating the model

The simple cost-benefit model (represented in Equation 1) may be useful in some contexts. Law enforcement, for example, sometimes encourages people to make decisions without discounting penalties by probabilities. An ad that used to play over the speakers in Washington, D.C., Metro stations asked whether eating a candy bar on the subway was worth \$100, the fine for eating on the subway. Of course, the ex ante cost of eating the candy bar was better considered to be \$100 discounted by the (extremely low) probability of the fine being imposed.

Notwithstanding its potential use as a device to encourage compliance through misinformation, the simple cost-benefit model is limited in a number of ways. This model is not terribly accurate: it does not describe how taxpayers actually make decisions because, in general, taxpayers do discount outcomes by probabilities, at least to some extent. (22) The simple cost-benefit model also does not accurately predict when people will comply with the tax law, because it predicts that everyone will comply whenever penalties are greater than zero, which is clearly false.

The simple cost-benefit model does capture the important idea that taxpayers weigh costs and benefits when determining whether to comply, but aside from that, the simple cost-benefit model focuses one's attention only on whether the fine is nonzero. That is, although the size of the fine is susceptible to change, the only change this model suggests is that penalties should be greater than zero.

Finally, the simple cost-benefit model is, as its name suggests, simple, but perhaps too simple. It is nearly useless for those who wish to improve tax compliance, because it gives so little information about how to structure penalties and shape detection efforts and does not direct researchers' efforts.

B. Expected Value

1. The model

A more sophisticated model envisions a taxpayer who not only weighs costs and benefits, but also weights each possible outcome by the probability of that outcome. Consider a taxpayer who is weighing a tax position that would allow him to avoid paying a particular tax. If the taxpayer does not take this tax position, he will, under the expected value model, pay the tax (T) which reduces his pretax income (I) so that after tax, he has total income of I - T. If he does take the position, he might be audited or he might not be audited; if he is audited, his position might or might not be detected by the authorities; and, if the position is detected, it might or might not be upheld. Call the probability of the bad outcome p (bad from the taxpayer's perspective), where p combines all the relevant probabilities, including the chance that the IRS will audit the taxpayer, the chance that if the IRS audits the taxpayer, it will detect and challenge his position, and the chance that if the IRS detects and challenges his position, a court will ultimately strike down the position. (23)

If the IRS detects and successfully challenges his position, the taxpayer must pay not only the correct amount of tax (T) but also a fine (F). If the position is successful--is not struck down--he will pay no tax at all. That is, if he takes the position, he expects to have income equal to p(I - T - F) + (1 - p)(I), because he weights each possible outcome by the probability of that outcome. The taxpayer will therefore comply when

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