Tax compliance and the neuroeconomics of intertemporal substitution.

INTRODUCTION

It is well understood that human decisions are more complicated than standard economic models assume. Indeed, the reason for modeling a problem is to simplify it in such a way that we can understand some portion of the problem and, from this understanding, obtain some degree of predictive power. A model that incorporates all of the complexities of the real world might be useless because it may be too complicated for us to understand. (1)

There have been a variety of methods by which social scientists have attempted to address the problem of the complexity of decision-making. In general, economists have attempted to adopt assumptions about individual behavior that allow one to make predictions of the behavior of groups of individuals. These simplifications have been made in part because we do not truly understand how individuals make decisions and in part because complicated models often are intractable when confronted with anything but the simplest situations.

When the basic models currently used in economics were developed, it was assumed that it was not possible to understand the actual physical processes that occur within the brain (Camerer, 2007). As a result, economists were forced to make assumptions about these processes or, more accurately, about how decisions are made, and what affects these decisions. However, more than a century has transpired since the development of these basic neoclassical models and neurological research has advanced significantly in that time. While one cannot say that we fully understand all of the relevant processes, neuroscience has advanced to the point where it can give significant insights into the nature of the processes we utilize in making various types of decisions. A relatively new discipline referred to as neuroeconomics seeks to understand the physical processes in the brain that are involved in decision-making in order for us to develop more accurate models of human behavior. Once one considers that there are limits to the ability of humans to process information, and that these limits are the result of particular neuromechanisms, then one can see the potential importance of understanding these neuromechanisms. That is, if we understand the cognitive abilities of individuals to comprehend the world and respond to it, then we can better understand the actions they take in response, and possibly how to influence them if we so choose.

The most important question for the study of tax compliance is what causes people to pay taxes. (2) The standard models assume that at least some element of this decision is based on the level of benefits that follow from artificially reducing reported taxable income as compared to the penalties for so doing, discounted by the probability of detection (Allingham and Sandmo, 1972). (3) Scholars have long understood that while standard models based on simple microeconomic assumptions are useful in many ways, they do not fully capture all aspects of the decision concerning the payment of taxes. This article will attempt to demonstrate how recent research in neuroeconomics can help to illuminate at least one aspect of this decision, namely how individuals discount for time.

The discussion begins by examining the traditional Allingham-Sandmo model of taxpayer compliance and discusses both its assumptions and its predictions about behavior (Allingham and Sandmo, 1972). The first section of the article also discusses some of the extensions and problems with the application of this model. (4) The second section of the article discusses the implications of various models of intertemporal discounting for issues of tax compliance, in particular the effect of the timing of the payment of tax or refunds as well as the payment of penalties for underpayment of tax. It examines some of the more prominent models of intertemporal discounting and their effects under the Allingham-Sandmo model of tax compliance. In particular, it explores the implications of exponential discounting, the quasi-hyperbolic model of discounting, as well as a model developed by Benhabib and Bisin (2005), which considers the notion of the cost of cognitive control and how this impacts the nature of intertemporal discounting. It also considers an alternative model proposed by Rubinstein (2003), which posits that individuals make intertemporal decisions based on the similarities and differences of salient features of the available choices. A more extensive discussion of the reasonably large literature on the subject is beyond the scope of a short article such as this.

The article goes on to discuss the manner in which neuroeconomic research can help Us to select between various models of intertemporal discounting, which we can then apply to better understand taxpayer compliance behavior. The article applies various models of temporal discounting to an Allingham-Sandmo framework to discuss how the timing of the payment of taxes and refunds can affect the level of compliance. It particular, it argues that, under hyperbolic or quasi-hyperbolic models of temporal discounting, one would expect to observe a lower level of compliance if the benefits of cheating are experienced immediately while the penalties are only experienced in the future, as compared to a system where both the benefits and the penalties will occur in the future. One prediction of the quasi-hyperbolic or [beta]-[delta] model would be that allowing individuals to obtain essentially immediate refunds would decrease the level of compliance. This may or may not be the case with the cognitive control models, depending on the relative costs and benefits. Under exponential discounting models, the effect of accelerating refunds by a matter of weeks should have relatively little marginal effect on compliance, and any effect would likely be too small to measure.

This article will not try to establish a particular theory of human behavior. While the article introduces some evidence concerning different models of behavior, this article does not come to any definite conclusions. There is a simple reason for this; the research that has occurred to date does not allow for such conclusions. The purpose of this article is merely to introduce this research and to discuss its possible implications for tax compliance policy.

THE STANDARD MODEL OF TAXPAYER COMPLIANCE

The standard models of taxpayer compliance are derived from basic microeconomic models of behavior. Because the assumptions of such models are relatively simple, one can add a fair level of institutional complexity to these models without making them unwieldy. This is one the great strengths of these models--their ability to be adapted to a large variety of circumstances. This section reviews the most prominent of these models--the Allingham-Sandmo-Yitzhaki model.

The Allingham-Sandmo-Yitzhaki Model

The seminal work in the area of tax compliance is a paper by Allingham and Sandmo (1972) in which they propose a model of the tax compliance decision based on standard microeconomic assumptions such as the notions that individuals are utility maximizers, utility increases with increasing wealth, and individuals conceive of probability in linear fashion. (5) The model addresses the decision by individuals to comply with the tax laws. Under the Allingham-Sandmo model, the analysis of the compliance decision is based on a simple expected utility function. Under standard expected utility theory, (6) the utility of some contingent payoff in the future is given by

[delta][summation over (i)][p.sub.i]u([x.sub.i]),

where [x.sub.i] represents the ith of state of the world in the next period, u([x.sub.i]) is the utility in that state of the world, [p.sub.i] is the probability of that state of the world, and [delta] is used to discount for the fact that the payoff will occur in the future. (7) In the simplest version of the Allingham-Sandmo model, the decision of whether or not to cheat on one's taxes is based on the probability of detection and the likely fine if detected.

While the standard version of the Allingham-Sandmo model only discusses this decision in connection with income taxes, this framework can be and has been applied to other types of taxes as well. Under the Allingham-Sandmo model, the decision can be framed as maximizing expected utility, where expected utility is equal to

(1- p)U(y(1 - t) + t(y - x)) + pU(y(1 - t) - f(y - x)),

where p is the probability of detection, y is pre-tax income, y(1 - t) is true after-tax income, x is the amount of income reported to the government, y - x is, therefore, unreported income, and U represents a standard utility function. The model states that the individual's expected utility is the utility of the individual if an audit occurs multiplied by the probability of being audited, plus the individual's utility if they are not audited multiplied by the probability of not being audited (which is to say, essentially, the expected value of the taxpayer's utility).

The predictions of the Allingham-Sandmo model depend crucially upon the probability of detection, p, and the amount of the penalty, f. Under standard optimizing assumptions, the taxpayer will choose to report income such that

U'([y.sub.A])/U'([y.sub.B]) = t(1 - p)/pf,