A. Deference to individual judgment

In standard welfare economics, why do we proceed from the premise that each of us is the best judge of our own well-being? As I see it, the argument has two components. The first consists of justifications for individualism and self-determination in the tradition of classical liberalism: my views about my life are paramount because it is, after all, my life. The second entails the central Cartesian principle that subjective experience is inherently private and not directly observable.Footnote ⁵ This state of affairs renders each of us uniquely qualified to assess our own well-being. We know how we feel; others can only make educated guesses. These considerations create a strong presumption in favor of deference to our judgments.

According to one argument, behavioral economics overturns this presumption, and thereby challenges the validity of the first premise, by showing that people do not reliably exercise good judgment. As I explain below, that argument is faulty because it conflates what I will call direct and indirect judgments. A direct judgment pertains to outcomes we care about for their own sake – our “ultimate objectives” – whereas an indirect judgment involves alternatives that lead to those outcomes. Behavioral economics impugns various indirect judgments, but not direct ones.

A simple example serves to illustrate the issue. Suppose Norma must choose between two closed boxes, a red one containing apples, and a yellow one containing pears. For the moment, to keep the example as transparent as possible, assume her ultimate goal is to obtain a particular type of fruit rather than to achieve particular mental states such as satiation and satisfaction. On an earlier occasion she looked inside both boxes, but her memory is faulty and she now thinks the yellow box contains bananas. She chooses the yellow box because she likes bananas more than apples. However, if she peered inside the boxes once again, she would choose the red one because she likes apples better than pears.

In this example, a choice between the red and yellow boxes involves an indirect judgment. Norma does not care about the boxes; each one is simply a means to an end. In contrast, under our assumptions, her choices among different types of fruit involve direct judgments. Clearly, when Norma’s poor memory causes her to choose the yellow box over the red one, she is exercising poor indirect judgment. However, there is nothing wrong with her direct judgment. Indeed, we consider her indirect judgment faulty precisely between her direct and indirect judgments diverge.

Now let us add a wrinkle: assume Norma’s ultimate goal is to achieve certain mental states (“internal goods”). From that perspective, all consumption items (“external goods”) are means to ends, and choices among them always involve indirect judgments.Footnote ⁶ Moreover, just as Norma may misjudge the contents of a box, she may also misapprehend the relationships between consumption goods and mental states. However, assuming she is sufficiently familiar with apples, pears, and bananas to understand the consequences of eating each, her indirect judgments among open boxes will be correctly informed, and hence will faithfully reflect her direct judgments.

Behavioral economics and psychology provide us with ample reason to question certain types of indirect judgments. No doubt some would claim there is also evidence that people exercise poor direct judgment – for example, that they like certain goods or experiences “too much” and others “not enough.” Let us be clear, however: existing economic research demonstrates nothing of the sort.Footnote ⁷ Specific claims concerning instances of poor judgment usually turn out upon close examination to involve indirect evaluations. The occasional objection to a direct judgment entails nothing more than a difference of opinion between the analyst and the consumer as to what constitutes a good or fulfilling life. If Norma thinks she is better off with apples than with pears knowing full well the consequences of consuming each, an analyst who weighs the various dimensions of experience differently can certainly disagree, but there is no objective foundation for overturning the presumption articulated at the start of this section and declaring the analyst’s perspective superior.

A determined critic might argue that (1) observed judgments are generally indirect, and (2) defects in human reasoning are so pervasive that they taint all indirect judgments. In that case, the first premise is useless: as analysts, we may aspire to respect each person’s direct judgments, but we lack the information required to do so. Some form of paternalism then becomes unavoidable. For the most part, however, behavioral economists do not credit the view that human decision making is universally defective, and indeed our research generally points to concerns that arise within limited domains.

Thus, despite initial appearances, behavioral economics does not overturn the first premise of standard welfare economics. It does, however, potentially qualify that premise. Each of us may be the best judge of our own well-being, but all our indirect judgments are not created equal.

B. Preferences versus contextual aggregation

Choice anomalies are the bread and butter of behavioral economics. Some economists try to rationalize them while preserving the assumption of stable, coherent preferences, either by creatively redefining the objects of choice, or by positing imperfect decision-making processes that project preferences into choices with distortions. According to this view, “true preferences” actually exist inside our heads, and we access them (perhaps imperfectly) each time we are called upon to make a choice. When formulating models, economists usually posit the existence of a utility function, $U$, that embodies these preferences. Sometimes behavioral economists also assume that, upon receiving a particular alternative, call it $x$, we actually experience $U(x)$ as a subjective sensation, which some would call “experienced utility.”Footnote ⁸

An alternative perspective on choice anomalies assumes that each of us acts on the basis of multiple objective functions, which we harmonize inconsistently. This view likewise holds that true preferences actually exist inside our heads, but it allows for the possibility that different versions of those preferences may either coexist or successively replace each other. I tend to equate this view with the hypothesis that we all suffer from a mild form of multiple personality disorder, and indeed behavioral economists often describe these theories as envisioning “multiple selves.”

The concepts of preferences and utility are so ingrained among economists that we naturally gravitate to one of the two preceding alternatives. However, there is a third possibility, one derived from psychologists’ notion of “constructed preference,” that for me has the greater ring of truth. According to this view, I aggregate the many diverse aspects of my experience only when called upon to do so for a given purpose, such as making a choice or answering a question about my well-being.Footnote ⁹ For instance, at a given point in time, I may be troubled by a financial setback, happy about some recent professional success, worried about a conflict with a family member, pleased by the taste of a good wine, and irritated by the itch of a mosquito bite, but nevertheless experience no comprehensive sensation of well-being.Footnote ¹⁰ To answer a question about my overall welfare, or to choose between alternatives without deploying a previously constructed rule of thumb,Footnote ¹¹ I must weigh the positives against the negatives and construct an answer de novo. I cannot simply access an aggregate sensation that is already part of my subjective experience, or consult an overall preference ordering that already resides inside my head, because neither of these aggregates exist until I am called upon to deliberate and aggregate. From this perspective, the concepts of “true preferences” and “experienced utility” are fictions; they may play useful roles in “as-if” representations of behavior, but we should not take them literally.

This third perspective potentially attributes particular choice anomalies to the vagaries of aggregation. In particular, when I deliberate and aggregate, the weights I attach to the various dimensions of my subjective experience may be sensitive to context. For example, circumstances may render one aspect of experience more psychologically salient than another. In that case, even my direct judgments may be context-dependent. To be sure, each time I aggregate, I may well deploy similar principles and criteria, and come to conclusions that are at least roughly consistent, in which case an analyst may be tempted to infer that I actually have well-defined preferences that imperfectly govern my choices. However, under this third view, my consistency simply means that I use similar aggregation procedures in different contexts, not that my aggregation procedures are all derived from my “true preferences.”

In light of the foregoing, I find the second premise of conventional welfare economics untenable. Fortunately, it is also unnecessary. The first (modified) premise instructs us to defer to consumer’s direct judgments and correctly informed indirect judgments.Footnote ¹² The preceding discussion alerts us to the fact that those judgments may not be monolithic. In deferring to the individual, we may simply have to live with the possibility that some evaluations will be inconclusive.Footnote ¹³

C. Why choice?

As explained in the previous section, there are sound reasons for skepticism concerning a literal interpretation of the hypothesis that “preferences guide our choices.” Even so, a behavioral economist can comfortably endorse the principle that “when we choose, we seek to benefit ourselves.” Accordingly, while the third premise of conventional welfare economics does not emerge unscathed from this discussion, we can still treat consumers’ choices as shedding useful light on their judgments.

To be sure, as emphasized in Section 2.A, a judgment is not worth respecting if it is based on a misunderstanding. Choices are often susceptible to misunderstandings because they generally involve indirect judgments, for instance about physical goods we value for the mental states they deliver, rather than direct ones. It follows that there may be valid reasons for deferring to the judgments behind some but not all of our choices.

The question remains, why should we draw the line at choices? Why not accord equal status to other types of judgments, such as evaluations of happiness and life satisfaction? Alternatively, why not try to build an even better welfare framework around self-reported well-being (henceforth abbreviated SRWB)?Footnote ¹⁴ Obviously one cannot assert the primacy of choice based on a presumed connection with “true preference” if the latter does not actually exist. If choice is simply a constructed judgment, one could argue that other types of constructed judgments should be equally admissible for the purpose of evaluating welfare.

Traditionally, economists have been dismissive of SRWB. As a group, we derive this perspective from the revealed preference tradition, which holds that choice is observable and measurable, while well-being is inherently unobservable and not directly measurable.Footnote ¹⁵ Proponents of SRWB view this position as overly simplistic and easily refuted.Footnote ¹⁶ Certainly, self-reported well-being is no less observable or measurable than choice.Footnote ¹⁷ Moreover, the purported premises for a welfare framework based on SRWB – that people tend to know how they feel and are generally willing to say – strike its devotees as no less reasonable than those justifying a choice-based approach. Indeed, some would argue that SRWB elicits evaluations of actual subjective experience more directly than choice. Many economists have become increasingly sympathetic to this view and, as a result, SRWB has made significant inroads into economic research.

While choice and SRWB may both entail judgments that the individual constructs without referencing “true preferences,” this state of affairs does not necessarily place them on an equal footing. When conducting normative analysis, deference to a constructed judgment is warranted only if the purposes of the analysis and the judgment are conformable.

Naturally, different people may have different purposes in mind when they make normative evaluations. That said, in my experience, economists typically see normative analysis as a tool for guiding policy makers when they select among alternatives, under the assumption that the objective is to promote the well-being of those affected by the selection. Significantly, when people make choices for themselves, they aggregate over the many dimensions of their experience for precisely the same purpose – that is, to make a selection that promotes their well-being. Thus, the purposes of constructing judgments for normative analysis on the one hand, and for making choices on the other, are conformable. When advising policy makers on the selection of an alternative that affects Norma, we defer to Norma’s choices because they reveal the alternatives that, in her judgment, would provide her with the greatest overall benefit if selected.

Critically, other types of constructed judgments aggregate experience for entirely different purposes. Granted, if we interpreted the purpose of normative economic analysis differently, we might construe it as sharing those objectives – for example, we might say that its purpose is to aid the selection of alternatives that induce people to report the highest level well-being in response to survey questions. However, on close examination such positions prove difficult to defend. To make this point more concrete, in the next subsection I evaluate the conceptual case for building a welfare framework around SRWB instead of choice.Footnote ¹⁸

D. A closer look at self-reported well-being

E. Strategies for integration

A fan of SRWB might react to the preceding observations by pointing out that choice is no picnic either. I could not agree more: practical problems crop up in both contexts. One problem with a choice-oriented approach is that we cannot always observe choices within the pertinent domain. Consider the problem of evaluating the welfare impact of policies that reduce the likelihood of oil spills. The typical individual makes no choices that directly and measurably impact that probability. Another concern mentioned above and discussed at length in Section 5 below is that some choices are faulty, for example because people misunderstand or ignore the connections between options and outcomes.

Sometimes we can “fill in” the missing choices and/or “correct” the faulty ones by extrapolating from observed decisions or by conducting experiments, but in other cases the decision of interest is too far removed from prior experience and too costly to implement. That is when measures of SRWB, as well as other types of subjective evaluations and even biometrics (including facial expression, skin conductance, blood pressure, brain activity, and the like), may be particularly helpful. Because they are highly correlated with behavior, we can use them to predict the choices people would make if they had the opportunity in settings where no actual choices are observed. In addition, because we can measure reactions to actual outcomes, we can also in principle predict the selections people would have made had they understood the consequences of their actions correctly in settings where they were actually confused.

Consider the following examples.

• ∙ By estimating functions relating SRWB to environmental conditions, income, and other covariates, we may be able to predict the average willingness to pay for environmental goods, even though no individual makes choices that meaningfully influence the levels of those goods (see Frey, Luechinger & Stutzer, Reference Frey, Luechinger and Stutzer2009).

• ∙ If we have reason to believe that people systematically misunderstand how they will feel about lengthy commutes and consequently make faulty decisions about where to live, we may be able to infer their fully informed choices from the corresponding levels of SRWB (see Stutzer & Frey, Reference Stutzer and Frey2008).

• ∙ Even if we are interested in completely novel choice settings, so that there is no opportunity to observe hedonic reactions to the outcomes of interest, we can use assessments of anticipated well-being for particular outcomes, along with other prospective subjective evaluations and biometric reactions, to predict the choices people would make in those settings (see Bernheim, Fradkin & Popov, Reference Bernheim, Fradkin and Popov2015).

Most existing research on SRWB fits easily into a unified choice-oriented welfare framework, but it requires a different interpretation. Instead of taking SRWB at face value as a generally reliable measure of overall well-being, we construe it as an indicator of what people would likely choose. This distinction has important practical implications because it recasts the object of the exercise as accurate prediction (of choice) rather than accurate measurement (of well-being).

To illustrate the advantages of this alternative interpretation, suppose we want to know whether a particular policy improves welfare. Imagine that some jurisdictions have implemented the policy while others have not, and that we can survey residents of both. To perform SRWB-oriented welfare analysis, we must ask the “right” question about aggregate well-being. If different questions (for instance, about “happiness” versus “life satisfaction”) yield different answers, we have to select one, despite having no objective basis for doing so.

In contrast, within a choice-oriented welfare framework, we view the answers to those same questions as predicting which policy regime people would choose, assuming they correctly anticipate the consequences. One option is to proceed exactly as in the SRWB-oriented approach: try to settle on the “right” question, and assume people would choose the alternative that delivers the greatest SRWB. This strategy involves the same analytic steps as the SRWB-oriented approach; we simply reinterpret the findings. While it may on occasion yield reasonably accurate predictions, it is also simplistic and in many contexts demonstrably biased. A better option is to treat the problem as one of optimal statistical prediction, and deploy the various tools that economists and statisticians have developed for this purpose. With this approach, there is no need to resolve which of two SRWB measures is “correct,” because one can use them as co-predictors of choice. Indeed, to obtain even greater accuracy, one can expand the set of co-predictors to include other types of subjective evaluations, and possibly even biometric reactions.Footnote ²⁸ Experimental evidence indicates that this strategy can substantially improve upon the practice of taking measures of SRWB at face value, in the sense that it dramatically reduces both average prediction error and bias; see Bernheim et al. (Reference Bernheim, Fradkin and Popov2015).

D. Summary

The preceding discussion leaves us with two revised premises that survive the various challenges from behavioral economics and provide us with a foundation for the choice-oriented welfare framework outlined in Sections 4 through 6. They are:

Premise A: With respect to matters involving either direct judgment or correctly informed indirect judgment, each of us is the best arbiter of our own well-being.

Premise B: When we choose, we seek to benefit ourselves by selecting the alternative that, in our judgment, is most conducive to our well-being.

Notice that, in stating these premises, I refer to “judgments” rather than “preferences.” My object is to avoid confusion among multiple distinct interpretations of “preference,” including: (i) the notion that every choice tautologically expresses a preference; (ii) the notion that every choice derived from a direct or correctly informed indirect judgment tautologically expresses a preference, and (iii) the (in my view problematic) assumption that we choose by consulting our “true preferences,” the supposed existence of which does not depend on the act of choice or the construction of judgment.Footnote ²⁹ Henceforth, whenever I refer to “preference” rather than “true preference,” I intend the second interpretation.

To formulate a welfare framework based on our revised premises, we must grapple with two main issues. First, how do we distinguish between choices that reflect correctly and incorrectly informed judgments? Second, how do we accommodate inconsistencies among the judgments that merit deference? In the next section, I discuss an approach that has gained some traction among behavioral economists, but that often requires a more complete understanding of decision processes than we currently possess, or perhaps are ever likely to achieve. However, careful consideration of the challenges presented by that approach leads us to a tractable alternative, which I describe in subsequent sections.

A. Building a BRP model

Building a BRP model requires one to make strong assumptions. Broadly, they fall into the following three categories.

• ∙ First, one must take a stand on the aspects of experience that contribute to well-being. Formally, by specifying the domain of preferences, which is implicit in the dimensions of the consumption set, $\boldsymbol{X}$, we implicitly provide an answer to the question, what do people care about?

• ∙ Second, one must take a stand on whether the decision maker has unitary or conglomerate preferences over the consumption set. Are her direct and correctly informed indirect judgments always mutually consistent? Alternatively, does she arrive at different conclusions under different conditions? Does she hold conflicting views simultaneously?

• ∙ Third, one must take a stand on the nature of the apparatus that maps our direct judgments into decisions. Are those judgments expressed directly into choices, or are they distorted by limited cognition, biases, and other psychological phenomena? Does the answer depend on context, and if so, how? If we assume the decision maker has conglomerate preferences, does the context determine which judgments are “in charge,” or is there a process through which conflicts between objectives play out?

B. Challenges

The idealized “recipe” for BRP analysis follows standard scientific practice. We formulate theories, then evaluate and refine them by confronting them with new data and testing their implications. For successful theories, we recover unknown parameters including preferences, and use the parameterized models to conduct both positive and normative analysis.

The intellectual appeal of this approach is undeniable, and there are certainly contexts in which its application is compelling. Consequently, a unified normative framework should incorporate it. At the same time, an application of the BRP framework demands a thorough structural understanding of choice processes. Unfortunately, our understanding of many (perhaps most) choice phenomena remains partial and imperfect. The uncomfortable aspect of this approach is that it requires us to take strong stands concerning the nature of preferences and decision processes, even when – if we are honest with ourselves – we must acknowledge that we have very little basis for doing so.

Advocates of the BRP approach respond that its successful application will become less challenging over time because the state of our knowledge will steadily improve. While I hope that rosy prognosis turns out to be accurate, I also recognize that it might not. The associated challenges may prove surmountable, but they are nonetheless daunting.

The first challenge is that behavioral models often have multiple normative interpretations. Consequently, even if we can satisfy ourselves that we have arrived at the right positive model, welfare analysis may remain problematic. For example, suppose we become convinced that people make their choices according to the following model:

$$\begin{eqnarray}\max _{x\in X}s(x)~\text{s.t.}~u(x)\geqslant t(X)\end{eqnarray}$$

where $x$ is a consumption bundle, $X$ is an opportunity set, and $s,u$, and $t$ are functions. Norman (who by now has completed his Ph.D. in economics) offers the following interpretation: $s$ measures the salience of an alternative, $u$ measures the utility it delivers, and $t$ establishes a threshold. In other words, people “satisfice” by selecting the most salient alternative from among those that clear some utility hurdle. Norma (similarly credentialed) disagrees. She believes Norman has mislabeled the model, and offers an alternative interpretation: $u$ measures the salience of an alternative, and $s$ measures the utility it delivers. In other words, people select their preferred alternative from among those that are sufficiently salient. Their daughter Felicity (who is unschooled but precociously clever) insists that they are both mistaken. She asserts that people have conglomerate preferences (both $u$ and $s$) which they struggle to reconcile. Even though Norman, Norma, and Felicity agree about the positive model, they disagree about welfare.

To be fair, there may be ways to resolve this disagreement. For example, Norma and Norman may agree that SRWB is at least a rough proxy for the quality of subjective experience. If they find that it is highly correlated with $u(x)$ and uncorrelated with $s(x)$, Norman would declare victory, and Norma might acquiesce. However, they are more likely to discover that SRWB is positively correlated with both, because more attractive alternatives tend to be more salient. In that case, they may spend the rest of their careers writing a succession of journal articles that debate the merits of alternative SRWB measures, without resolving much of anything.

In some cases, many economists appear to think that the correct normative interpretation of a positive behavioral model is obvious. Consider, for instance, the familiar formulation of quasi-hyperbolic discounting (also known as ${\it\beta}{\it\delta}$ preferences), popularized by Laibson (Reference Laibson1997). Discussions of this model often employ heavily value-laden language, including phrases such as “present bias” and “self-control problems.” Consistent with the judgments implied by this language, they frequently assume people have unitary preferences and equate welfare with${\it\delta}$-discounted utility (“the long-run criterion”). And yet, as I have explained elsewhere (Bernheim, Reference Bernheim2009a), this model admits a large number of disparate normative interpretations. For example, one could take the position that true happiness is achieved by living in the moment, and that we suffer from a tendency to over-intellectualize when making decisions about the future.

Advocates of the long-run criterion have been known on occasion to scoff at this objection. They ask incredulously whether I reject the medical and psychiatric consensus that substance addiction is a problem. To be absolutely clear, I accept that consensus, because in that context there is a reasoned, evidence-based foundation for the normative conclusion (see Bernheim & Rangel, Reference Bernheim and Rangel2004, and Section 5 below). That said, substance addiction is a distinctive neurobiological phenomenon. Consequently, the foundation is narrow, and does not justify the same normative judgment in all contexts where time inconsistency is observed.

Nor can one dismiss my reservation concerning the general application of the long-run criterion as an abstract philosophical issue. Many cultures emphasize the importance of living in the moment. Moreover, according to popular wisdom, no one wishes on their deathbed that they had put in more hours at the office. On the contrary, people tend to regret having worked too hard and spent too little time with their families. Thus, when economists advocate the long-run criterion as a general normative principle, one has to wonder whether this is simply a case of successful workaholics believing that everyone else ought to be more like them.

The second challenge is that, as a general rule, many distinct nonstandard positive models can account for the same choice mapping. Practitioners of the BRP approach face a difficult dilemma. On the one hand, to rationalize nonstandard behavior, they have to broaden the class of potential explanations. On the other hand, to identify preferences, they have to limit that class. Once one steps away from the standard framework, it is difficult to know where to place those limits, or how to justify them. Thus, the problem becomes one of having too many degrees of freedom.

The practical implications of this observation are readily evident in the pertinent literature. Over the past decade or so, we have seen a growing proliferation of theories purporting to explain classic anomalies such as behavior in the ultimatum game or the endowment effect. In principle, the proliferation of theories could be scientifically healthy, but only if there is also a winnowing. Unfortunately, precious little winnowing occurs. In behavioral economics, theories are hard to kill.

In some cases, different theories about decision processes have observationally equivalent implications for choice patterns. Consequently, there is no hope of distinguishing one from another unless we find ways to incorporate rigorous analysis of nonchoice data into formal tests. So far, that agenda has met with only limited success (see Bernheim, Reference Bernheim2009b).

Of course, in many cases, competing theoretical explanations for the same anomaly have distinctive implications for other choices, and consequently we could in principle distinguish between them. Yet even then, theories rarely die, due to the third challenge: human behavior is extraordinarily complex.

One of the main lessons I take from the empirical literature in behavioral economics concerns the prevalence and complexity of context-dependent choice patterns. There is growing evidence that the details of decision problems not only matter, but do so in ways that are difficult to systematize outside of limited domains. Even choice patterns that behavioral economists consider “well established” appear to be context-dependent.Footnote ³² As a result, our theories often perform rather poorly when we test their predictions in contexts that do not closely resemble those in which they are calibrated.Footnote ³³

Poor predictive performance sounds like a good justification for some winnowing. And yet the theories in question usually survive, for two reasons. First, given the acknowledged complexity of human behavior, all models are regarded as parsimonious approximations. The theorist aims to capture an important and systematic aspect of the decision process, but never pretends to describe that process comprehensively. Consequently, one can always construe a “failure” as an indication that something else is also going on in a given setting, rather than as proof that the model is fundamentally wrong-headed. Because we implicitly or explicitly allow for the possibility that special contextual details can bring other mechanisms into play, proponents of different theories can find themselves arguing endlessly and unproductively over which experimental setting most effectively illuminates the “fundamental” mechanisms.Footnote ³⁴ Second, with limitless degrees of freedom, models are easily tweaked. Instead of vanishing in favor of their competitors, they morph.Footnote ³⁵ The impetus to winnow is thereby once again defeated.

To make matters even more challenging, some theories are formulated in ways that make them virtually impossible to falsify. To take an example, the theory of reference-dependent preferences can rationalize virtually any choice pattern. Many of its vaunted successes largely consist of showing that, by making fortuitous assumptions about reference points, one can “account” for otherwise anomalous patterns. Consider the oft-repeated claim that reference dependence successfully predicts daily income targeting by taxicab drivers (Camerer et al., Reference Camerer, Babcock, Loewenstein and Thaler1997). This “prediction” hinges on two additional assumptions: first, the reference point applies to income rather than to leisure (or both); second, drivers evaluate each day’s earnings separately relative to the referent (“narrow framing”). With respect to the first assumption, one can show that, if the reference point applies to leisure instead of income, the within-day labor supply elasticity will typically be positive rather than negative. This is of course convenient for fans of reference dependence, given that the findings of Camerer et al. (Reference Camerer, Babcock, Loewenstein and Thaler1997) are now disputed (see, for example, Farber, Reference Farber2008).

Will we eventually discover ways to overcome these challenges? I certainly hope so. For my own part, I continue to conduct research concerning structural models of decision making, and I would expect a unified normative framework to accommodate progress along these lines. However, we are not yet at the point where we can always comfortably hang our hats on particular structural models with clear normative interpretations, and we may not arrive at that point any time soon. Therefore, a unified normative framework should also offer us an alternative.

A. A useful reinterpretation of BRP analysis

What is “the general spirit of the choice-oriented BRP paradigm”? Some might say that it involves the process of understanding preferences and choices through structural models. I take a somewhat different view. When we perform welfare analysis within the BRP framework, we implicitly accomplish two tasks:

• ∙ First, we identify collections of decision problems for which choices express preferences (that is, direct or correctly informed indirect judgments) without distortion.

• ∙ Second, we construct a welfare criterion by conducting standard revealed preference analysis on those restricted domains.

In most cases, it is easy to see how one unpacks BRP analyses into these two components. To illustrate, take the case of quasi-hyperbolic discounting (the ${\it\beta}{\it\delta}$ model). As I have noted, a common normative interpretation of this model is that ${\it\delta}$-discounting governs true preferences, and that ${\it\beta}$ reflects a bias. In that case, decisions made at the earliest possible date with full commitment express preferences without distortion. One can therefore recover that ordering directly from those choices.Footnote ³⁷

In some cases, this point is less obvious. For certain models, it may appear that choices always distort preferences. However, I would argue that this appearance reflects a failure to envision the entire choice domain.

As an example, consider decisions involving ordered lists of options, such as candidates enumerated on a ballot. Various studies document a tendency to pick the alternatives listed first (Miller & Krosnick, Reference Miller and Krosnick1998)). Rubinstein and Salant (Reference Rubinstein and Salant2006) formulate a theoretical BRP model of this phenomenon in which choice problems consist of ordered lists. Here, the ordering defines the decision frame, and all orderings potentially distort the expression of “true preferences.” At first this may appear contrary to what I have written above, but the explanation is simple: as formulated, the theory only pertains to the limited choice domain within which the distortion occurs.

The nub of this theory is that cognitive limitations lead people to simplify certain choices by applying a heuristic. It is relatively easy to envision other decision frames engineered so that they do not trigger this simplification. I can imagine a number of testable possibilities. The bias might not apply to sufficiently short lists, such as pairs of alternatives, or to settings where the decision maker is not permitted either to rush or to skip over descriptions of particular options. Alternatively, one could simply avoid presenting the menu in list form. Imagine, for example, making a choice between two options that appear on a screen, one to the northeast of the other. Presumably one can adjust the positions so that there is demonstrably no bias toward one or the other. Each of these possibilities points to a set of decision problems that could reveal preferences without distortion.

As a purely logical matter, one can of course imagine environments in which choice mechanisms always distort preferences. However, we cannot accept such formulations without implicitly licensing all manner of mischief. Consider the following illustration. Upon learning that Norman never orders salad, an economist theorizes that he actually prefers salad, but is consistently governed by habit. If there is truly no setting that would overturn the purported habit, are we really prepared to accept the proposition that Norman is better off, according to his own judgment, with a salad? I am not. Absent any setting that is free from an alleged distortion, we ought to question whether the associated conception of preference is merely a contrivance.

B. Overall structure of the Unified Framework

The reinterpretation of the BRP framework discussed in the previous section is useful because it motivates the two core tasks of the Unified Framework:

• ∙ Step 1: We identify all decisions that merit deference (the welfare-relevant domain).

• ∙ Step 2: We construct a welfare criterion based (at least in part) on the properties of choices within that domain.

The BRP approach entails serious challenges because it places demanding restrictions on the inputs for the second step: we cannot “recover preferences” unless choices are consistent. This requirement is what forces us, in the first step, to take the strong stands on the nature of direct judgments and the apparatus that maps them into choices, as discussed in Section 3A. Consequently, to avoid the need for those stands, we must dispense with the consistency requirement.

A key feature of the Unified Framework is that the second step flexibly accommodates inconsistencies among the choices that merit deference. As we will see, we derive the criterion used in that step from the unambiguous choice relation: we say that one alternative is unambiguously superior to another if and only if the second is never chosen when the first is available. Intuitively, this criterion instructs us to respect choice whenever it provides clear normative guidance, and to live with whatever ambiguity remains. Thus, it allows us to exploit the coherent aspects of behavior, which feature prominently in virtually all behavioral theories, while embracing the normative ambiguity implied by any lack of coherence. Significantly, when all choices are mutually consistent, the criterion specializes to the standard notion of revealed preference.

This alternative approach to the second task fundamentally alters the nature of the first task. In Step 1 of the Unified Framework, we can in principle identify choices that reflect direct or correctly informed indirect judgments by entertaining the same evidence, arguments, and modeling strategies as in the BRP framework. However, we are not compelled to settle on welfare-relevant domains (or, in the case of compound preferences, broad subdomains) within which all choices are internally consistent. Consequently, unlike the BRP approach, the Unified Framework does not force us to go out on a limb and take strong stands concerning the nature of preferences and decision processes when we lack an adequate foundation for doing so, or to ignore the important possibility that the construction of direct judgments may be highly context-dependent. Instead, we can set objective and appropriate criteria for evaluating whether a choice merits deference. If, after applying those criteria, we fail to arrive at an internally consistent set of choices, we are not compelled to “try harder”; instead, the Unified Framework lets us proceed. In contrast to the BRP approach, it also allows us to perform welfare analysis provisionally under different views of which choices do and do not merit deference, and thereby provide a better understanding of the assumptions upon which particular normative conclusions depend.

I turn next to the details of the Unified Framework. First, I discuss the types of data that will play a role (Section 4.C). Then I explain how one might arrive at the welfare-relevant domain (Section 5). Finally, I describe the derivation and application of the welfare criterion (Section 6).

C. Data inputs

The main data input for a choice-oriented normative framework is the choice mapping $C(X,f)$, which tells us the alternative(s) selected from the opportunity set $X$ when frame $f$ prevails. Economists typically learn about the choice mapping by observing certain choices and statistically interpolating or extrapolating others, sometimes using structural models. Often these methods suffice, but sometimes they do not. In any given setting, it is entirely possible that one will take a stand on the domain of preferences, only to discover that observed decisions shed inadequate light on choices within that domain.Footnote ³⁸

To understand the problem, consider an example. When Norman has lunch at a restaurant, his subjective enjoyment naturally depends on what he eats. Suppose it also depends on the entire menu, including the items he does not order. That might make sense if he is on a diet and becomes irritated when he has to turn down tempting but fattening alternatives. In that case, a properly defined consumption bundle is a pair, $(X,x)$, where $X$ is the menu and $x$ is the selected item (as in Gul & Pesendorfer, Reference Gul and Pesendorfer2001). If Norman lives in an area with a wide variety of restaurants, we can in principle observe his choices among these bundles. If instead he lives in a small town with a single restaurant that changes its menu from day to day, we can observe choices among bundles involving the same menu – for instance, ({pasta, salad}, pasta) versus ({pasta, salad}, salad) – but not among bundles involving different menus, such as ({pasta, salad}, pasta) versus ({pizza, salad}, pizza). To see why that is a problem, suppose a “planner” has to select Norman’s lunch for him. When the planner picks $x$, Norman “chooses” from the degenerate menu $\{x\}$, which means he ends up with the bundle $(\{x\},x)$. Unfortunately, Norman never has the opportunity to choose between ({pasta}, pasta) and ({salad}, salad), so the planner cannot take guidance from his choices.

What can economic analysts do in such situations? One possibility is to adopt restrictive structural assumptions that allow us to extrapolate from the choices we do observe. If our object is to avoid taking strong stands for which we have little foundation, that may well be an unattractive alternative. A second possibility is to fill in the missing choices through experiments. Sometimes that is an excellent strategy, but it can also be logistically complicated and/or prohibitively expensive. Thus, when allowing for the possibility that people have nonstandard concerns, we will likely encounter settings in which we need to learn about the choice mapping at least in part through nonstandard methods. As noted at the end of Section 2.C, a third (nonstandard) possibility is to draw inferences from nonchoice data, including SRWB, stated preferences, and biometrics. For example, even if Norman lives in a small town, we can elicit SRWB when the menu is limited to pasta, and when the menu is limited to salad, and on that basis perhaps make a reasonable inference about his choice between ({pasta}, pasta) and ({salad}, salad). It is worth reiterating that those inferences do not need to be simplistic, as they are when one takes SRWB responses at face value. Instead, we can treat the problem as one of optimal statistical prediction, using a variety of subjective responses as predictors, as in Bernheim et al. (Reference Bernheim, Fradkin and Popov2015).

The third possibility mentioned in the previous paragraph defines one important role for nonchoice data, including SRWB, within a unified normative framework. I discuss other roles below. Accordingly, the potential inputs for this framework are not limited to choice mappings. As a general matter, we will allow for the use of all other information about decisions and the processes that generate them, including anything one might employ, even qualitatively, in the course of BRP analysis to arrive at the correct model of choice. Any well-reasoned inference one might make in the BRP framework bearing on the scope of the welfare-relevant domain will also be permitted in this one.

A. Principles

The Unified Framework allows the analyst to offer any evidence-based justification for limiting the welfare-relevant domain, provided it is made explicit so others can evaluate it for themselves. If, for example, the foundation for a BRP model is compelling, then the welfare-relevant domain implied by the model will be equally compelling within the Unified Framework once one spells out the reasoning that supports it.

That said, the structure of the BRP framework does not inherently focus attention on the identification of the welfare-relevant domain. As explained in Section 4, the issue is often implicit – sometimes even buried – rather than explicit, and little thought has been given to systematizing the principles and criteria used for this purpose. It is therefore natural to wonder whether the restricted domains implied by some BRP models would withstand open scrutiny.

B. An empirical application

Putting the concepts discussed in the preceding subsection into practice can be reasonably straightforward. To illustrate, I will describe a recent empirical application involving financial education due to Ambuehl, Bernheim and Lusardi (Reference Ambuehl, Bernheim and Lusardi2015).

Low levels of financial literacy have raised concerns about the quality of financial decision making. Financial education seeks to improve decisions by helping consumers understand the principles governing the connections between choices and consequences. Traditionally, evaluations of financial education focus on measured literacy, self-reported decision strategies, and directional effects on behavior. Normative claims are generally based on strong preconceptions (“literacy must help”) or paternalism (“people ought to save more”), rather than rigorous welfare analysis. In fact, the effects of financial education on the quality of decision making are far from obvious, given that it may influence behavior through mechanisms involving indoctrination, deference to authority, social pressure, and the like.

Plainly, one cannot evaluate the welfare effects of financial education within the standard revealed preference paradigm, because all choices tautologically serve the objectives they reveal. A more nuanced view holds that characterization failures occur whenever the relationships between choices and outcomes hinge on principles the individual does not understand. To evaluate the welfare loss from characterization failure, we need to construct a normative criterion based on choices in settings where such failures do not occur. It would of course be circular to assume that educated choices are free of these failures. How then can we proceed?

One way forward is to identify decisions that do not hinge on the principles one suspects the individual misunderstands. Within the BRP framework, one can recover preferences from those choices, and use them to evaluate the quality of more complex and potentially problematic decisions. For example, Song (Reference Song2015) parameterizes a life-cycle model based on risk and time preferences elicited from subjects through simple choice experiments, and then uses it to evaluate retirement saving. This strategy involves some heroic assumptions: one must believe the chosen model of risk and time preference is the right one in radically different types of tasks. The strength of these assumptions points to a more general concern: the BRP approach to evaluating financial education requires a better understanding of decisions involving risk and time than we actually possess.

In Ambuehl et al. (Reference Ambuehl, Bernheim and Lusardi2015), we adopt a different approach derived from the Unified Framework that allows us to measure the effects of financial education on the quality of decision making without adopting a particular structural model of choice. The easiest way to understand our approach is through a simple illustration.

Say we are concerned that people poorly understand the concept of compound interest, and that this limitation causes them to make suboptimal investment decisions. To evaluate this possibility, we have to specify a decision context. Accordingly, suppose Norman has an opportunity to buy one of two financial assets. Asset A represents a $10 investment that promises a return of 6% per day, compounded daily for 15 days. Asset B simply promises $24 in 15 days. To make matters simple, assume Norman is liquidity constrained (so that his decision does not depend on market interest rates), and that he only cares about the time path of his consumption. Ordinarily he will be willing to purchase each asset if and only if its price does not exceed some threshold value, call it $p^{\ast }$ for the first asset and $q^{\ast }$ for the second. A quick calculation reveals that the two assets are equivalent, subject to rounding. Thus, swapping out one for the other in a decision problem changes framing while leaving opportunities intact. If we find that $q^{\ast }\,\neq \,p^{\ast }$, we would conclude that Norman’s decisions are frame-dependent.

A discrepancy between $p^{\ast }$ and $q^{\ast }$ raises the possibility that Norman errs when making decisions involving one or both of the assets. If we are correct in assuming that he evaluates assets by trying to figure out their implications for future cash flows, then the description of asset B is transparent whereas the description of asset A is not. That observation tells us that characterization failure is more likely in decisions involving asset A, but it does not by itself imply that such failures occur. After all, the alternative frames could simply trigger different processes for constructing direct judgments, for example by rendering salient different aspects of anticipated experience. To exclude choices from the welfare-relevant domain, we need to provide evidence that frame dependence goes hand in hand with a failure to appreciate the relationship between choices and outcomes in a particular frame. In this instance, we can administer a test to evaluate Norman’s command of the principles governing compound interest. Assuming he fails it, we would then have a foundation for inferring that he mischaracterizes his opportunity sets in decision problems involving asset A, and hence for excluding those choices from the welfare-relevant domain, but not for excluding decision problems involving asset B.

Having reduced the welfare-relevant domain to decision problems involving asset B, and assuming those choices are internally consistent, welfare calculations are straightforward. The greatest welfare loss Norman can sustain when deciding whether to purchase asset A is $|q^{\ast }-p^{\ast }|$. For example, if $q^{\ast }>p^{\ast }$, he may fail to purchase the asset at price $p^{\ast }+{\it\varepsilon}$, even though it is actually worth $q^{\ast }$ to him. In an environment where the price of asset A is drawn from a uniform distribution, Norman’s expected welfare loss is proportional to $(q^{\ast }-p^{\ast })^{2}$, and this formula remains valid to a second-order approximation for other distributions.

One might object that I have outlined a framework for evaluating welfare losses in a somewhat artificial class of decision problems rather than, for example, actual decisions involving retirement saving. The interest here is not, however, in the magnitude of the welfare loss, but rather in a comparative static: how does financial education effect that magnitude? Unless it improves the quality of decision making in simple contexts to which the pertinent principles are easily applied, there is little hope that it will do so in more complex settings, except by accident.

In Ambuehl et al. (Reference Ambuehl, Bernheim and Lusardi2015), we implement these ideas by presenting consumers with pairs of equivalent valuation problems involving “simply framed” and “complexly framed” assets, and comparing performance across groups receiving different educational interventions, including a control. We find that the main intervention substantially improves subjects’ knowledge and conceptual understanding of compound interest. Subjects report using the newly gained knowledge in their decisions without displacing other potentially reliable methods. Directionally, effects on valuations of complexly framed investments counteract a widely suspected bias (underestimation of compounding). Yet despite these indications of apparent success, the intervention does not increase aggregate welfare. While improvements in knowledge result from the substantive elements of instruction, it turns out that behavior is responsive only to rhetorical elements aimed at motivation. Consequently, while the behavioral response is directionally appropriate, it is also indiscriminate, and ultimate unconstructive.

C. Reinterpreting the literature

The perspective on welfare outlined in this paper is unifying because it encompasses, rationalizes, and usefully refines a wide variety of ideas and analyses that appear in the literature. In this section, I offer some examples pertaining to the identification of welfare-relevant choices.

A. Settling on a normative criterion

Let us start with a more basic question: What, exactly, is a normative criterion? As I use the term, it is a rule that tells us whether one outcome is better than another. Mathematically, that means it is a binary relation. If $W$ is the welfare relation, and if $x$ and $y$ are outcomes, the statement “$xWy$” means that $x$ is a better outcome than $y$.Footnote ⁴⁶

In principle, we could arrive at a welfare relation by enumerating and comparing a multitude of alternatives. Instead, let us first narrow down the possibilities by establishing the minimal requirements for a sensible criterion.

The first requirement is that $W$ should be coherent. Operationally, I take coherence to mean that we can identify at least one best element within any opportunity set.Footnote ⁴⁷ In standard consumer theory, we ensure coherence by assuming completeness and transitivity of the preference ordering. However, weaker conditions will also suffice. In the spirit of setting minimal requirements, I will insist instead on the weakest possible property that delivers coherence:

Property #1 (coherence):$W$ is acyclic.Footnote ⁴⁸

Acyclicity simply rules out cycles – for example, it tells us that, if an apple is better than a pear and a pear is better than a banana, a banana cannot be better than an apple.Footnote ⁴⁹

The welfare relation also ought to depend on choices in a reasonable way. Certainly, if Norma consistently chooses an apple over a pear, and never chooses a pear when an apple is available, the only reasonable conclusion one can draw in a choice-oriented framework is that she is better off with an apple than a pear. Thus, we also require:

Finally, there ought to be a degree of consistency between Step 2, which generates the welfare relation, and Step 1, which yields the welfare-relevant domain. Specifically, we require:

To declare $x$ improvable within $X$ would mean that choosing $x$ in the choice problem $(X,f)$ is a mistake. But a central purpose of Step 1 was to weed out all identifiable mistakes, and no data or inferential methods admitted in Step 2 were excluded from Step 1. Therefore, if one can legitimately classify the selection of $x$ as a mistake in Step 2, one should already have deleted it from the welfare-relevant domain in Step 1.

Fortunately, it is possible to satisfy all three of these requirements simultaneously. Consider, for example, the unambiguous choice relation, denoted $P^{\ast }$. Formally, $xP^{\ast }y$ if and only if the welfare-relevant domain contains no decision problem in which $x$ is available but $y$ is chosen. Obviously, $P^{\ast }$ satisfies Property #2 by construction. The other two properties are easily checked.Footnote ⁵¹

What other possibilities besides $P^{\ast }$ might we consider in our search for a welfare relation? The following theorem tells us that there are no others.Footnote ⁵² As long as we want our welfare criterion to satisfy Properties 1–3, $P^{\ast }$ is the only game in town.

This theorem makes our lives fairly simple. It means, for example, that although we have not explicitly ruled out the possibility of using nonchoice information about well-being, choice processes, and the like in Step 2, there is in fact no room for it. Once we arrive at Step 2 of this choice-oriented framework, choice necessarily dictates the normative criterion.

Having reached this conclusion, it is reassuring to note that the Unified Framework nests the BRP approach, as we intended. To see why this is so, note that $P^{\ast }$ coincides with the usual revealed preference relation in the special case where choice is fully consistent within the welfare-relevant domain. In fact, the definition of $P^{\ast }$ generalizes that relation to nonstandard settings in an intuitive and transparent way.

What happens when there are inconsistencies within the welfare-relevant domain? Mathematically, the answer is that $P^{\ast }$ becomes incomplete. Speaking practically, that means we treat certain comparisons as normatively ambiguous. Suppose, for example, that Norma never chooses a pear, banana, or orange when an apple is available, and never chooses an orange when an apple, pear, or banana is available. However, depending on the decision frame, she sometimes chooses a pear and sometimes chooses a banana when both are available. In that case, we can draw a number of potentially useful conclusions about her welfare. For example, if she initially has an orange and we replace it with any of the other three alternatives, we can say that she is better off. However, if she initially has a pear and we replace it with a banana, the effect on her well-being is ambiguous.

In settings where choice inconsistencies are pervasive, $P^{\ast }$ may not be very discerning. Whether the resulting ambiguity undermines our ability to draw useful welfare conclusions depends on the context. As noted in Section 5.C, I have discovered that it is sometimes possible to reach sharp conclusions about important policy questions even when $P^{\ast }$ entails a great deal of normative ambiguity. That said, a lack of discernment will certainly prove problematic in some instances. When that occurs, it is important to acknowledge that our inability to make precise normative statements reflects the limits of our knowledge. Admitting this ambiguity is intellectually honest. If we wish to sharpen our conclusions, the Unified Framework appropriately directs us back to Step 1, and focuses our attention on the empirical issues we need to resolve.

B. Applying the criterion

So far, this discussion of normative criteria has been more than a little abstract. How would the typical applied economist, who probably has not thought much about binary relations since his or her first year of graduate school, implement these ideas?

Fortunately, implementation is neither complex nor mysterious. To illustrate, suppose Norman has two tickets to a college football game, and is wondering whether he should use them or sell them. His willingness to accept differs across decision frames, but is never less than $50 and never more than $60. In that case, we can say that having and using the tickets improves his welfare by $50 to $60. That range reflects the ambiguity implied by his choices.

Now consider a more elaborate example that has the look and feel of familiar applied economics. Suppose consumers care about a bundle of goods, $\boldsymbol{z}$. Our object is to evaluate the welfare effects of policies that change that bundle. As in classical economics, we measure welfare in units of a numeraire good, $y$, and use $\boldsymbol{x}$ to denote the rest of the bundle (so that $\boldsymbol{z}=(\boldsymbol{x},y)$).

Imagine first that, after studying data on consumers’ choices, we conclude that they behave as if they maximize a standard utility function of the form $y+U(\boldsymbol{x})$. To measure the welfare effects of a policy that ends up switching a consumer from an initial bundle $(\boldsymbol{x}_{\mathbf{0}},y_{0})$ to an alternative $(\boldsymbol{x}_{\mathbf{1}},y_{1})$, we can calculate the amount of the numeraire we would need to remove from the alternative bundle, call it $c$, to make the consumer indifferent between $(\boldsymbol{x}_{\mathbf{0}},y_{0})$ and $(\boldsymbol{x}_{\mathbf{1}},y_{1}-c)$:

(1)$$\begin{eqnarray}c=(y_{1}-y_{0})+[U(\boldsymbol{x}_{\mathbf{1}})-U(\boldsymbol{x}_{\mathbf{0}})].\end{eqnarray}$$

Now imagine instead that we conclude consumers behave as if they maximize a function of the form $y+U(\boldsymbol{x},f)$, where $f$, the decision frame, belongs to some set $F$.Footnote ⁵³ While we are comfortable assuming that consumers do not actually care about the frame, our understanding of the mechanism through which it affects their choices is poor. Consequently, we treat all of the frames as equally relevant for normative analysis, and avoid interpreting the as-if objective function literally as “utility.”

The unambiguous choice relation, $P^{\ast }$, provides us with two ways to measure the welfare effect of replacing $(\boldsymbol{x}_{\mathbf{0}},y_{0})$ with $(\boldsymbol{x}_{\mathbf{1}},y_{1})$. First, we can calculate the smallest (infimum) amount of the numeraire good we could remove from the new bundle, call it $c_{A}$, such that the consumer would unambiguously choose the initial bundle:

$$\begin{eqnarray}c_{A}=\inf \{c\mid (x_{0},y_{0})P^{\ast }(x_{1},y_{1}-c)\}.\end{eqnarray}$$

Second, we can calculate the largest (supremum) amount of the numeraire good we could remove from the new bundle (call it $c_{B}$) such that the consumer would unambiguously choose that bundle:

$$\begin{eqnarray}c_{B}=\sup \{c\mid (x_{1},y_{1}-c)P^{\ast }(x_{0},y_{0})\}.\end{eqnarray}$$

Critically, because we have specified an as-if objective function, we can easily translate these conditions into analytic expressions for $c_{A}$ and $c_{B}$:

(2)$$\begin{eqnarray}c_{A}=\max _{f\in F}[(y_{1}-y_{0})+[U(\boldsymbol{x}_{\mathbf{1}},f)-U(\boldsymbol{x}_{\mathbf{0}},f)]]\end{eqnarray}$$

and

(3)$$\begin{eqnarray}c_{B}=\min _{f\in F}[(y_{1}-y_{0})+[U(\boldsymbol{x}_{\mathbf{1}},f)-U(\boldsymbol{x}_{\mathbf{0}},f)]].\end{eqnarray}$$

Clearly, $c_{A}\geqslant c_{B}$.

Once we solve for $c_{A}$ and $c_{B}$, we can make a variety of discerning welfare statements. For example, we can say that the policy is definitely more valuable than $c_{B}$ units of the numeraire and definitely less valuable than $c_{A}$ units. If it turns out that the implementation costs (in units of the numeraire) are less than $c_{B}$, it is definitely beneficial, and if they are greater than $c_{A}$, it is definitely harmful. However, if those costs lie between $c_{A}$ and $c_{B}$, we must acknowledge ambiguity as to whether the policy is helpful or harmful.

What if we gather additional information about choice processes that justifies restricting the welfare-relevant domain to some smaller set $F^{\ast }\subset F$? The only change is that we replace $F$ with $F^{\ast }$ in equations (1) and (2). As result, $c_{A}$ falls while $c_{B}$ rises (weakly in both cases), shrinking the region of ambiguity.

The striking similarity between equations (2) and (3) on the one hand and equation (1) on the other highlights the fact that applied welfare analysis within the Unified Framework closely resembles its familiar counterpart within the standard framework. Indeed, the standard tools of applied welfare analysis, including equivalent and compensating variation, consumer surplus, aggregate consumer surplus, the Pareto criteria, Pareto efficiency, and methods of making interpersonal comparisons, all have close counterparts within the Unified Framework. A complete discussion of these issues would consume many pages; I refer the reader to Bernheim and Rangel (Reference Bernheim and Rangel2009), Bernheim et al. (Reference Bernheim, Fradkin and Popov2015), and Fluerbaey and Schokkaert (Reference Fluerbaey and Schokkaert2013).

C. An empirical application

Abstract discussions of economic welfare are all well and good, but a useful framework also lends itself to empirical applications. Here I summarize a recent study that exemplifies Step 2 of the Unified Framework.

Starting with Madrian and Shea (Reference Madrian and Shea2001), a number of studies have found that changing the default contribution rate for a 401(k) pension plan, for example from 0% to 3%, has a powerful effect on employees’ contributions, particularly compared with conventional policy instruments such as capital income taxes. Indeed, increases in these default rates are often cited as highly successful examples of nudges.

Formal normative analysis of 401(k) default options is tricky. Due to its magnitude, the default effect is generally regarded as a nonstandard behavioral phenomenon (Della Vigna, Reference Della Vigna2009). Possible explanations include a tendency to procrastinate 401(k) elections due to time inconsistency (either sophisticated or naive), inattention, and psychological anchoring on the default as a target.

The BRP approach requires the analyst to adopt one of these models, parameterize it, and take a stand on which decisions reveal “true preferences.” For example Carroll et al. (Reference Carroll, Choi, Laibson, Madrian and Metrick2009) analyze the welfare effects of 401(k) default options using a model of sophisticated time inconsistency. They also assume that true preferences are revealed only by full-commitment choices with no immediate consequences. For the reasons discussed in Section 3, even if that model is correct, this “long-run” welfare standard may not be compelling. Unfortunately, any alternative standard may seem equally arbitrary, and the BRP approach does not allow us to acknowledge that ambiguity. Similar concerns arise with respect to other potential explanations for the default effect. For example, interventions that are intended to focus attention on 401(k) elections may simply browbeat workers into making choices they would prefer to avoid.

Bernheim et al. (Reference Bernheim, Fradkin and Popov2015) evaluate the welfare effects of 401(k) default options empirically using the Unified Framework. Observed behavior illuminates the choice mapping in a “naturally occurring” decision frame, and each potential theory of default effects extends the mapping to additional decision frames that have not yet been observed – for example, in the case of sophisticated time inconsistency, day-in-advance commitments to making 401(k) elections. Using these choice mappings as inputs, the paper analyzes the welfare effects of setting particular defaults, and evaluates optimal defaults, under various assumptions about which decisions frames are welfare-relevant. When the welfare-relevant domain encompasses conflicting choices, the analysis identifies the range of normative ambiguity.

A complete summary and explanation of the various findings in Bernheim et al. (Reference Bernheim, Fradkin and Popov2015) is beyond the scope of this paper. Instead I will focus on a single finding that illustrates an important point. According to the empirical analysis, in the naturally occurring frame workers act as if the average cost of making 401(k) elections is extremely high. Most of the behavioral explanations for default effects envision alternative frames in which the as-if opt-out cost would be very small. One would therefore tend to think that welfare conclusions would be highly dependent on the choice of the welfare-relevant domain, in which case the analysis would only be discerning and useful if one took a stand on “true preferences,” as in the BRP approach. As it turns out, that is not the case. Whether we evaluate welfare from the perspective of decisions made in the naturally occurring frame or an alternative frame, we subtract opt-out costs only for those people who actually opt out, and not for those who stay with the default. Those who do opt out in the naturally occurring frame have much lower as-if opt-out costs, on average, than those who do not. Whether we count those incurred as-if opt-out costs in full (to respect decisions made in the naturally occurring frame) or discount them heavily (to respect decisions made in an alternative frame) therefore makes surprisingly little difference. Welfare calculations and optimal defaults are not entirely independent of the evaluation frame, but the region of ambiguity turns out to be surprisingly small. Thus, to reach useful conclusions, one simply does not need to take the strong stands required by the BRP approach.