Policy and Choice: Public Finance through the Lens of Behavioral Economics

Appendix A: Preference, Choice, and Welfare

201 A Preference, Choice, and Welfare As an additional step in integrating insights from psychology into public finance along the lines described in chapter 2, we introduce a highly simplified model for thinking through what those insights imply for preference and choice and, by extension, for public finance. Note that the purpose of this appendix is to clarify this relationship for the interested reader; the text itself, with the exception of appendix B, does not employ the notation developed here. There are two components to this model. The first includes the implications of behavioral tendencies for preference and choice. Imperfect optimization, bounded self-control, and nonstandard preferences mean that choice no longer reveals preference. The second includes the implications of choice behavior for how we think about welfare. The possibility that choice does not consistently reveal preference poses a challenge for evaluating welfare. Preference and Choice Perhaps the core insight of economics with respect to choice is that when the standard assumptions about individual choice hold, choice reveals preference. Findings from behavioral economics suggest that those assumptions often do not hold and that as a result choice may not reveal preference. We present a way to capture that aspect of choice and to compare how individuals make choices in the behavioral and in the standard model. Appendix 08-0498-0 appendixes.indd 201 1/3/11 3:30 PM 202 appendix a Setup Let x = an action (such as consuming a good) that individuals choose to engage in or not. Let b = the subjective valuation of x; in other words b = u(x). Let c = the objective costs associated with x, denominated in the same units as b. Standard Model In the standard model, individuals choose x when the benefits outweigh the costs: b > c. Different individuals value actions differently, so b is distributed f(b). For example, if x is consumption of donuts, high b individuals are those who love donuts. Furthermore, individuals optimize perfectly, have unbounded selfcontrol , and hold standard preferences. The key implication of this is that choice reveals preference: x iff b > c. Behavioral Model In a behavioral model, people are imperfect optimizers, have bounded selfcontrol , and hold nonstandard preferences. We can represent those tendencies by saying that the choice of x now reflects the following decision criterion: β(b) > c, where β(·) is a transformation of the benefits, b, due to behavioral tendencies. So, for example, overconfidence about likely good outcomes might lead individuals to choose as though b were higher than its true value or procrastination might lead individuals to choose as though b were lower than its true value. When we make the simplifying assumption that c (the costs of x) are perceived without error, even by behavioral agents, then β(b) > b when behavioral tendencies lead individuals to overvalue x β(b) c. 08-0498-0 appendixes.indd 202 1/3/11 3:30 PM appendix a 203 Because, in general, β(b) ≠ b, it may be the case that individuals choose x when b c. There is some true b that represents welfare, but in general it cannot be inferred from observable patterns of choice. Moreover, notice that markets under these conditions operate on β(b), not b. We can allow in this model that choice can be sensitive to features that do not matter in the standard model, such as framing or presentation effects. We call them nudges, following Thaler and Sunstein.1 In general, nudges affect the form of β(·). But to reflect their importance, we can write that slightly less generally as β(b, n), where n are nudges. Written that way, we get: Choice of x occurs where β(b, n) > c, where different nudges—default rules, framing effects, appeals to social norms, and so on—can affect the choice of x, even when they do not alter the underlying costs and benefits of that choice. Choice and Welfare The failure of choice to reveal preference can create difficulties for public finance as well as for economic analysis more generally. What can we infer about welfare when choice does not reveal preference? That is, how do we infer b when people choose according to β(b)? Or, if under different nudges we observe different revealed preferences β(b, n), what do we take to be the true value of b? In considering social welfare, what b do we put in the social welfare function for people? One way to model this indeterminacy that is useful for...