Rabin - Incorporating Limited Rationality Into Economics

8/10/2019 Rabin - Incorporating Limited Rationality Into Economics

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Journal of Economic Literature 2013, 51(2), 528543http://dx.doi.org/10.1257/jel.51.2.528

528

1. Introduction

In a thoughtful and well-hyphenatedarticle, Bounded-Rationality Models:Tasks to Become Intellectually Competitive,Harstad and Selten (this volume) lay outsome challenges to neoclassical economicsand a refreshingly serious challenge to thosetrying to improve it. I offer some thoughtson their article and their challenge. The setof topics I emphasize differs significantly

from theirs. This is due in part to differentinterests and knowledge. It is also becauseof division of labor: Crawfords contributionto this forum, Boundedly Rational versus

Optimization-Based Models of StrategicThinking and Learning in Games, offersperspectives on a set of strategic and mar-ket topics (e.g., asset bubbles) closer to thosetopics focused on by Harstad and Selten. Ifocus more on limits to rationality that mighthelp explain consumer and savings behavior,risky choice, and other classical problems ofindividual decision making.

In footnote 1, Harstad and Selten cor-rectly note that many researchers trying to

improve the psychological realism of eco-nomics do not necessarily see themselvesas bounded-rationality theorists outside therealm of neoclassical theory, broadly defined.Nor even do we all eschew optimizationmodels. Harstad and Selten themselves notethat there are virtues to optimization as amethodology. Instead, their article is explicitin understanding its virtues, and lays out thechallenge for those proposing alternatives to

Incorporating Limited Rationalityinto Economics

M R*

Harstad and Selten (this forum) raise interesting questions about the relative promise ofoptimization models and bounded-rationality models in making progress in economics.This article builds from their analysis by indicating the potential for using neoclassical(broadly defined) optimization models to integrate insights from psychology on thelimits to rationality into economics. I lay out an approach to making (imperfect and

incremental) improvements over previous economic theory by incorporating greaterrealism while attempting to maintain the breadth of application, the precision of

predictions, and the insights of neoclassical theory. I then discuss how many humanlimits to full rationality are, in fact, well understood in terms of optimization.(JEL B49, D01, D03, D81, D84)

*University of California, Berkeley. I thank TristanGagnon-Bartsch for valuable research assistance, and VinceCrawford, Janet Currie, Erik Eyster, Tristan Gagnon-Bartsch,and Ron Harstad for helpful comments.

Go tohttp://dx.doi.org/10.1257/jel.51.2.528to visit thearticle page and view author disclosure statement(s).


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529Rabin: Incorporating Limited Rationality into Economics

match some of those virtues. The articles byHarstad and Selten and by Crawford togetherprovide a very useful and thoughtful pre-sentation of the necessity and prospects fordeparting from optimization models in theset of topics they discuss. I agree with manyof their arguments. As such, my article is notso much a rejoinder to Harstad and Seltensarticle as it is an addendum listing some cur-rent and potential research incorporatinglimited rationality into a more neoclassicalframework. By discussing some principlesand examples of current research, I hope togive readers a richer sense of the benefitsand surprising possibilities for using opti-

mization models to understand the implica-tions of limits to rationality. In the process,my article will make more salient some typesof human errors that seem downplayed bythe community of scholars grappling withbounded-rationality models.

As the other articles in this forum note,much of the recent literature modifying neo-classical economics is about improving therealism of preferences by altering the util-ity function in ways that are fully compatible

with rationality, and hence quite obviouslyconducive to models that assume peopleoptimize.1This article outlines a perspectivethat may appear more surprising: that manylimits to rationality can be usefully studied

with optimization models. Some of the exam-ples are rather Procrustean: the underlyingpsychology does not have a very optimizingfeel to it, but can be crammed into the opti-mization framework to leverage the power of

1As Harstad and Selten note in the context of prefer-ence reversals, some of the psychologically inspired newmodels of preferences may have properties that econo-mists had previously associated with irrationality and whichmay require a somewhat different toolbox. Fully rationaltheories of belief-based utility, such as Koszegi (2010) andKoszegi and Rabin (2006, 2009), generate time inconsis-tencies and violations of other axioms that economists hadbeen in the habit of associating with rationality.

the neoclassical model.2But other examplesof human limits to rationality, I will argue,are genuinely best understood in terms ofoptimization models. As surely as optimiza-tion captures cases of fully rational behav-ior, it captures the psychology and resultingbehavior of some limits to rationality.

The case for optimization models of lim-ited rationality largely reflects an insightfrom psychology that is underappreciated byeconomists: not all limits to rationality arebased on computational unmanageability.Many of the ways humans are less than fullyrational are not because the right answersare so complex. They are instead because

the wrong answers are so enticing. Humanintuition leads us astray in all sorts of waysthat are simply not well described in termsof the difficulty or complexity of problemsthat bounded-rationality models seem bestsuited for. The pervasiveness of boundserrors where people are daunted by the taskof optimization, or are simply not geared toit, should not be doubted. But astray errors,as one might call them, likewise seem per-

vasive, and especially amenable to neoclas-sical modeling. We can capture many errorsin terms of systematic mistakes in the proxi-mate value function people maximize (quasi-maximization models) or where the beliefsincorporated into their maximizations aresystematically distorted (quasi-Bayesianmodels). The general sensibility and empha-sis of economic theorists, experimentaleconomists, and others lead them to neglectimportant examples of limited rationality

that are important for economics.

2The distinction between optimization models andbounded-rationality models is not so clear; at some level,they are probably isomorphic to the types of limits I dis-cuss in this article. Nor is the labeling important. But even

when they are distinct, we can still leave open the ques-tion of what models to use. And, especially in those cases

where we all agree that the optimization models are wrong,the different articles constituting this forum will help see arange of perspectives on the costs and benefits of movingforward with models that are wrong but useful.


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Journal of Economic Literature, Vol. LI (June 2013)530

Studying astray errors rather than boundserrors allows methodological advantagesthat facilitate meeting the challenges thatHarstad and Selten lay out. They directlysuggest that we should not be too eager tomove away from optimization models. Itis easier to study astray errors than bounderrors using optimization models becausethe former involve behavior that is richlypurposeful and driven by a logic that theeconomic agent finds compelling. Fullyrational investors who understand random-ness and who want to retire wealthy willmaximize their risk-adjusted expected sav-ings with investment strategies that are best

given their (correct) notion of randomness.But investors who believe in a false law ofaverages, expecting that good luck tendsto be followed by bad and bad luck tendsto be followed by good, will also maximizetheir risk-adjusted expected savings given

theirperceptions of randomness. Would-beexercisers who rationally forecast systematictaste change due to habit formation and dueto fluctuations in energy will plan to care-fully develop an exercise habit and will alsoknow that they should not radically changeplans in reaction to temporary fluctuationsin enthusiasm. But those who systematicallyunderappreciate taste change will not makeany plans based on inducing good habits butmay make unfortunate long-term plans (suchas joining a gym) based on falsely extrapo-lating temporary enthusiasm. Elaborate,goal-driven plans are the stuff of savvy maxi-mizers who correctly understand both the

laws of statistics and their own future utility.But elaborate, goal-driven plans are also thestuff of those who both misunderstand statis-tics and systematically mispredict their ownfuture behavior.

A second methodological advantage of thisapproach is that it embraces with enthusiasmHarstad and Seltens goal of making alterna-tive models competitive with the currentparadigm. These models use an approach

discussed in Rabin (forthcoming), which hasbeen employed in many papers: formulatemodels that offer complete mappings fromenvironment to outcome, using as much aspossible the same set of variables as in tra-ditional models, and embed both the earlier(neoclassical) model and the limited-ratio-nality model as parameter values. The com-petition between the old and new models isthen half doneweve shown the two mod-els to be structurally comparable in terms ofdegrees of freedom, applicability, etc. Andthe second half of the competition is put intomotion: the models can be compared and

judged, in a fair fight, by establishing point

estimates and confidence intervals on theparameter values.

Section 2 explains and illustrates thisapproach. I provide many examples of basicmodels that improve the realism of econom-ics in very structured, disciplinedcompeti-tiveways using optimization models thatclosely resemble existing models. And I layout concrete general criteria for realism-improving theories that make explicit theirpower and scopetheir ability to make pre-cise predictions and their general applicabil-ityand very explicit their relationship toexisting models.3I also discuss more gener-ally an orientation toward incremental prog-ress in improving models that can be used toimprove theoretical and empirical econom-ics. Section 3 turns to the methodologicaland substantive case for optimization-basedmodels of limited rationality, by briefly illus-trating human biases and limits that, by dint

of being driven by mistaken intuitions ratherthan automatic or rule-of-thumb behavior,are at their core optimization models. I con-clude in section 4 with a very brief discus-sion of the movement toward integrating

3Much of my discussion in this section reflectsarguments I have made elsewhere, especially Rabin(forthcoming).


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new models of limited rationality into main-stream empirical and theoretical economics.

2. Competitive Models

Since all models are wrong, and all para-digms have their limits, it is always a difficult

judgment call as to when and how to empha-size the severity of the shortfalls of prevailingapproachesand when to call for the devel-opment of a new paradigm. Nor is it evenclear what is inside a paradigm and what isoutside. And it certainly does not ultimatelymatter what labels we use. Especially in thedomain of rationality (and behavioral eco-

nomics), much unintentional harm and dis-traction and obfuscation has been caused byenthusiasm for categorizing models ratherthan elucidating specific empirical claims.Harstad and Selten thankfully avoid all that,and are thoughtful and balanced in theirapproach. But my own judgment is that theirassessment of the neoclassical research pro-gram is too dire. We all in this forum believe

working to reduce its shortcomings is worththe time of economistsmore timethan it isgetting. But part of the case for the approachI advocate perhaps comes from greater con-fidence that the core of microeconomic the-ory and empirical work has been a success,and is continuing as a success. And, mostimportantly in this context, that it is amena-ble to rapid improvements by incorporatinglimited-rationality models.

On the other hand, the entire premise oftheir article is to acknowledgethe merits of

the neoclassical optimization paradigm andthe burden on bounded-rationality modelsto add value to this approach. I am struck byHarstad and Seltens thoughtful observationthat generations of scholars have put effortinto bounded rationality without delivering aserious rival to the neoclassical model. Thehigh standard they hold new approaches to islaudable when applied to ones own researchapproach, as they are doing, but may also

bleed into underappreciation of progressin both their own and others research pro-grams. It is hard to know what counterfactu-als to compare a program to. But this articlecontributes to the forum by enumeratingsome of the current models of limited ratio-nality that are being introduced to improveeconomic theory and empirical economics.These models may still miss too much of thebounded in bounded rationality.

Rabin (forthcoming) proposes anapproach to improving the psychologicalrealism of economics while maintaining itsconventional techniques, of formal theo-retical and empirical analysis using tractable

models focused on prediction and estima-tion. The emphasis is on developing modelsimproving behavioral realism that can beused as inputs into economic theory by dintof their precision and broad applicability.4Striving for realism-improving theories to bemaximally useful to core economic researchsuggests a particular approach: portableextensions of existing models (PEEMs). Oneshould (a) extend the existing model by for-mulating a modification that embeds it as aconstellation of parameter values with the

4The desire for maximal precision of new theoriesdoes not come from confidence that the theories areright. Besides enhancing their usefulness, in fact, one

value of precision is that it highlights flaws to aid in fur-ther improvements. Indeed, in the context of this forum, I

would emphasize a macro version of this claim: it may bethat the most efficient and useful way to reach what mayeventually feel like a new paradigm is in incremental steps.In fact, with caution given the brilliance of the research-ers and research involved, it is my guess that the line of

research in the tradition of Simon (1955) and Newell andSimon (1972) generates too much emphasis on shortcom-ings of existing models andlargely as collateral damagefrom its wonderful emphasis on evidence and intuitionabout the way people behave in real-world problem-solv-ingis too oriented toward lists of specific shortcomings.The greater emphasis on generalizable alternative predic-tions in the approaches inspired by Kahneman and Tversky(2000), and discussed in reviews by Rabin (1998, 2002b)and DellaVigna (2009), may have a greater target chanceof both near-term improvements in workaday economicresearch and long-term improvements in the structure ofeconomics.


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new psychological assumptions as alterna-tive parameter values, and (b) make it por-table by defining it across domains using thesame independent variables as in existingresearch, or proposing measurable new vari-ables. To further their integration into main-stream economics, PEEMs lend themselvesto two types of comparative statics. The firstis to look within chosen environments athow predictions change with the parameter

values. This allows us to test their empiricalvalidity in comparison to existing theories byestimating those parameters, and to see theirpotential value added in comparison to exist-ing theories by seeing how those parameters

do and dont matter in important economiccontexts. The second type of comparativestatics is the more traditional one: fixingthe parameter values that accord with theimproved assumptions, how does changingthe environment affect economic outcomes?Applying this form of comparative staticsindicates that the improved psychologicalrealism is ready for economic primetime. Ifone views hypothesis testing and comparativestatics as empirical and theoretical competi-tions, then this approach sets up the compe-tition Harstad and Selten talk about. Rabin(forthcoming) argues that this competition isan important way forward for improvementsin economic models, disciplining both thoseproposing the theories and those doubtingthem in a way that pushes research towardconstructive, normal-science debates.

An early and successful example of thismethodology, in the domain of preferences

under uncertainty, is the literature provid-ing alternatives to classical expected utility.Beginning with Machina (1982), researchershave introduced realistic aspects of prefer-ences precluded from the expected-utilityformulation, ranging from nonlinear prob-ability weighting (Tversky and Kahneman1992 and Prelec 1998), to disappointment(Bell 1985, Loomes and Sugden 1986, andGul 1991), to ambiguity aversion (Gilboa and

Schmeidler 1989).5Although all these mod-els were developed with elegant generalityand formulated with axioms capturing basicprinciples, in the context of monetary riskthey have all lent themselves to providingprecise alternatives defined in the same setof situations to which classical wealth-basedexpected utility applies.

The model of reference-dependent pref-erences developed in Koszegi and Rabin(2006, 2007, 2009) likewise attempts tobring some of the insights from Kahnemanand Tverskys (1979) prospect theory towardgeneral applicability. In a simple linear formof the model, they take any classical eco-

nomic situation and make an alternative pre-diction based on the idea that people dontonly care about absolute consumption, butabout consumption relative to referencelevels. Under uncertainty or in determin-istic settings, when trading off consump-tion in different dimensions (quality versusprice on a given consumer item, or differ-ent items in a bundle of goods), people aremore bothered by losses relative to a refer-ence point than pleased by gains. A key tothe PEEMishness of the model is that refer-ence points are pinned down: they assumepeoples reference points are their expectedconsumption, and make a unique predictionin most settings. This is done by assuming aperson behaves according to preferred per-sonal equilibrium: she chooses her favoriteconsumption plan such that, if she has thereference point corresponding to expectingto follow the plan, she will do so. Koszegi and

Rabin (2006) show that, in static settingswith no uncertainty, the prediction of themodel corresponds to the classical predic-tions of consumer theory, but it makes pre-cise alternative predictions in settings witheither dynamic choice or where there isintrinsic uncertainty or surprise. The model

5See Harless and Camerer (1994) for an excellent con-ceptual and empirical review of these models.


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is parameterized by 0, the degree towhich one cares about news about gainsand losses, 1, the degree to which oneis more bothered by unexpected losses inconsumption relative to unexpected gains,and [0, 1], the degree to which peoplecare about news about future consumptionrelative to news about contemporaneousconsumption. (Classical reference-inde-pendent preferences correspond to =0.)

Perhaps the most active area of formulat-ing general alternatives to more traditionalneoclassical models is in departures fromnarrow self-interest. Following a long tradi-tion in economics, recent models building

from Bolton (1991) and Rabin (1993) havetried to study social preferences based onlaboratory data. Inspired by simple mod-els by Fehr and Schmidt (1999) and Boltonand Ockenfels (2000), Charness and Rabin(2002) specify a simple form where subjects

who get more money than others put weight> 0 on those others payoffs and 1 ontheir own payoff, and when behind the othersubject put weight >0 on those others and1 on their own payoff.6 These simplemodels ignore intentions-based reciproc-ity motives; theories such as the full modelcontained in Charness and Rabin (2002),Dufwenberg and Kirchsteiger (2004) andFalk and Fischbacher (2006) follow Rabin(1993) in formally modeling reciprocity con-cerns into the utility function.

Closer to the topic of this forum, modelshave been developed to capture departuresfrom full rationality. Crawford (this forum)

discusses various approaches; two mod-els that most closely fit the formal PEEM

6Although it is doubtful the parameters are very stableoutside the lab, in a broad class of games estimates areoften around = 0.4 and >0 is very close to zero.Notwithstanding a heavy emphasis in early literature onthe idea that subjects dislike getting less money than othersubjects, a small but positive value of is clearly morecommon once allocational preferences are disentangledfrom reciprocity.

framework in this domain are McKelvey andPalfreys (1996) quantal-response equilib-rium and Eyster and Rabins (2005) cursedequilibrium. In McKelvey and Palfrey, aparameter 0 captures the propensity ofplayers to make random mistakes, with anequilibrium assumption pinning down othersubjects beliefs; in Eyster and Rabins (2005)cursed equilibrium, parameter [0, 1]captures the degree to which players neglectthe informational content in other playersbehavior.7 Although, as with Nash equilib-rium, they do not always predict a uniqueequilibrium, they are defined in all gamessolely by the parameters and the structure

of the game. As such, they provide exactcompetitors to Bayesian Nash equilibriumand other classical game-theoretic solutionconcepts.8

Moving to limited-rationality models ofindividual choice, several formal modelsfall into the category of quasi-maximiza-tion models I discuss below. Loewenstein,ODonoghue, and Rabin (2003) develop amodel where economic actors underappre-ciate taste change. Relying on the timing ofutility and using a simple linear form, themodel predicts a particular form of peoplehaving irrational beliefs of their own futurebehavior: they believe their future tastes willbe more like their current tastes than theyare. The error is parameterized by 0 1,

where =1 means a person fully projects

7See also Esponda (2008) for a variant of cursed equi-librium. Although applied solely in simplified form to a

model of naive social learning, Eyster and Rabin (2008)define for all games a form of naive, face-value inference,parameterized by [0, 1].

8The alternative cognitive-hierarchy models discussedby Crawford (this forum), like Stahl and Wilson (1994),Camerer, Ho, and Chong (2004), Crawford and Iriberri(2007), and Crawford, Costas-Gomes, and Iriberri (2013)are not fully closed in the way I emphasize here insofar asthe level-0 play is not derived formulaically from the game.But they can be completed with any level 0, and also typi-cally provide unique, and hence more disciplined, predic-tions once a level-0 is chosen, than do cursed equilibriumand quantal-response equilibrium.


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her current tastes onto her future tastes, and=0 implies full rationality. These modelsshow that adding realistic systematic biasesin how we predict our future utility can com-pete on power and scope with the full-ratio-nality model. Barberis and Huang (2009)develop a formal parameterized model ofnarrow bracketing, following on the traditionof Benartzi and Thaler (1995), Kahnemanand Lovallo(1993), and Read, Loewenstein,and Rabin (1999), whereby agents maxi-mize prospect-theory preferences but failto consider how gains and losses across dif-ferent choices might cancel each other out.Barberis and Huang assume that people

partially maximize the normatively appro-priate combined outcomes from separatechoices, but erroneously partially maximizethe separate choices, parameterizing thedegree of narrow bracketing by the param-eter [0, 1]. Surely the most successfulPEEM to date is the simple model devel-oped by Strotz (1956) and rejuvenated byLaibson (1997), on what ODonoghue andRabin (1999) refer to as present bias: param-eter captures short-term impatience,and parameter captures misprediction offuture impatience. These models are applied

widely, improving economic research by anystandard that embraces the value of concep-tual and empirical insights on economicallyimportant topics.

Recent papers also develop formal mod-els of biases in statistical reasoning, althoughtypically in less general settings than themodels above. Grether (1980, 1992) models

base-rate neglect for the purposes of empiri-cal testing in a simple way, where decision-makers apply Bayes Rule in updating, but, inthe logarithmic form of Bayes Rule, weighthe base rate by only


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Models of social preferences likewise requirecardinal interpretations of material payoffs,such as money, before those models thatspecify exact parameters are pinned down.Likewise, models like Koszegi and Rabin(2006) that in principle pin down exact alter-native predictions in all situations require acardinal interpretation of the consumptionutility as it appears in economic models.In addition, an assumption of what aspectsof consumption constitute distinct hedonicdimensions must be specified in a way notdemanded of classical consumer theory. Yetthese too are rarely that ambiguous or sub-

ject to hidden specification mining in par-

ticular applications. Models of probabilityjudgment that depart from Bayesian reason-ing, on the other hand, often require evenmore ancillary assumptions specifying howdecisionmakers frame hypotheses. Modelsof narrow framing, like Barberis and Huang(2009), must make strong assumptions abouthow people separate their decisions.

In other cases, the parameters are likely tobe affected by factors outside the model tothe point where they are unstable. Care mustbe taken, however, not to invoke the insta-bility of specifications to favor worse stablemodels over better stable models simplybecause that is what earlier models assumed.For instance, the model that parameterizesinattentiveness to the information containedin others behavior, as formalized by Eysterand Rabin (2005), is clearly missing varia-tion due to factors missing from the model,such as experience of economic actors and

the salience of the information. This meansassuming the empirical average =0.5 (say)rather than a less-pinned-down [0, 1]may sacrifice too much realism for the sakeof precisionbut assuming a universal=0 as current game theory does sacrificeseven more.

Insofar as these new models leave openparameters, they will of course increasedegrees of freedom in making predictions.

Although research is necessarily still at thestage of estimating parameters (and, obvi-ously, building new models and modifyingprevious iterations), a theme of the literatureis that the improvements are coming fromprecise alternatives, not degrees of freedom.The variant of prospect theory in Koszegi andRabin (2006, 2007) corresponding to =1,=3, =0.88 probably fits large ranges ofdata better than classical reference-indepen-dent model corresponding to =0. Eysterand Rabin (2005) propose that estimating atype of information neglect by =0.5 fitsevidence across games better than the fullyrational =0. Models of present bias and

naivety specifying =0.7, =0.8 surelyfit most data better than the classical param-eters = = 1. Indeed, in this domain agood guess is that improved assumptions willfit behavior better while removinga degreeof freedom: instead of trying to fit data with

wildly varying values for the traditional dis-count factor, , once we use better values of and we can also restrict our models to themore reasonable yearly 0.95. Laboratorydata and early field estimates suggest that agood guess about the degree of underappre-ciation in taste predictions across settings asmodeled by Loewenstein, ODonoghue, andRabin (2003) is that a misprediction param-eter of =0.5 may generally fit better thanthe fully rational =0. Rabin and Vayanos(2010) and subsequent work estimate thatthe gamblers fallacy of (, ) =(0.2, 0.7) fitsbetter than the Bayesian =0. Benjamin,Rabin, and Raymond (2012) estimate the

degree of nonbelief in the law of large num-bers across a wide range of experiments at[7, 15] rather than the Bayesian modelof =. Such numbers will surely not holdup or be stable, and several are simply bestguesses I am listing here. But the effort todo so reflects an increasing standard in theliterature that some fixed parameterizationof alternative models ought to fit better thanthe rational model across settings, rather


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than performing well solely from degrees offreedom or selectivity of examples.

This standard, in turn, reflects a growingemphasis in this research program on makingpervasive improvements rather than findingparticular cases where new models do well.It is right to cut slack for new insights dur-ing early stages of developmentevidence-gathering and theory-forming under extremeand selective circumstances can be the best

way to understand the logic and potentialof new models. But if the long-run goal isfor newer models that explain things betterthan the traditional model, care should betaken to investigate whether the new models

improve insight on average.I believe that this is especially important

in the context of judging bounded-rationalitymodels. In my view, many new models andexplanations for experimental findings lookartificially good and artificially insightful inthe very limited domain to which they areapplied. Although this is a problem for allsorts of bounded-rationality and behavioral-economic theories, and a ubiquitous prob-lem for less formal theories people providefor their experimental results, it may be thatprocedurally rational models may be espe-cially susceptible to the illusion of explanatorypower. Roughly put, the models inherentlysteer us toward judging them solely in thespecific contexts where the procedures makebasic rational sense and seem intuitivelylikelyomitting all the cases where theypredict badly. In contrast, although (say)the tendency to infer too much from small

samples is centrally mediated by whether wepay attention to the data, in virtually everysituation where economists had previouslyapplied the Bayesian-updating model, thelaw-of-small-numbers inference model mayimprove our predictions. I am not as sanguineas others that bounded-rationality models ofthe sort emphasized in much of the litera-ture have the language or aspiration to applyso broadly. We are still likely to benefit from

having them as judiciously applied addendato rational models. My worry is that, short ofextremely tight empirical attention, applica-tions of the models as replacements for theneoclassical paradigm may worsen our pre-dictions in general.

To my mind, there is a simple and com-mon reason why some bounded-rationalitymodels are so unlikely to perform well acrosscontexts: too much realistic rationality isbeing left out. Many models of reinforce-ment learning, for instance, assume neithera priori rationality nor anything like Nashequilibrium. Yet virtually all applicationseither by design in the laboratory or by intu-

ition in thought experimentspresort theenvironment so that there is little scope forirrationality to lead people far astray. Of thethousands of disastrous things all of us coulddo in virtually every new situation we face inlifeincluding all situations economists careaboutbasic reason whittles away all but afew. That is, assumptions of rationality andNash equilibrium do much of the heavy lift-ing of restricting predictions, and only thendo other theories improve our predictionsfurther. It is good, practical science to focuson what the existing neoclassical modelsare missing. But when it comes to formu-lating the general models that are seriouscompetitors to full rationality, recognitionof the pervasive power of rationality andequilibrium suggests we need the new mod-els to be far closer to the old models thanoften proposed. Although in the interim itmakes sense to formulate models that make

improvements in specific contexts, one les-son from this perspective is that researchersought to imagine how they might eventuallycombine new theories with a core of strongrationality. I believe the types of models Idiscuss above and below are more orientedtoward that. Indeed, the PEEMs almost bystructure have the feature that they replicatethe rational model in all the ways that are notthe specific focus of the modifications.


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3. Optimal Models of Limited Rationality

I now turn to the case for modeling cer-tain types of economically relevant errors interms of optimization models, based on the

joint attractions of psychological realism andmethodological benefits.

Economists have an intuition and disposi-tion to model bounded rationality in terms ofcomplexity and inattention. The idea is oftenthat people are cognitive misers: we humans

wisely choose not to figure out all the exactright solutions to all the problems that faceus.9This intuition is often on target. But oneof the biggest lessons of some branches of

psychology is how many errors are simplynot in any useful sense conceptualized this

way. The degree to which attention to small-scale risks reflects rational maximization ofnews-utility preferences or reflects errors is adifficult question. But evidence suggests thatsmall-scale risk aversion is not only an error,but a rather effortful one: consumers wouldbe better off simply never buying small-scaleinsurance and extended warranties. Andthey would leave the store sooner. Amongthe many errors small investors make, theinability to see incredibly complicated arbi-trage opportunities in real time might becostly. Whether it is true and important thatarbitrage opportunities are left on the tableby those that dont see them, a far more per-

vasive error is that people tend to see pat-terns that are not there. Research on illusorycorrelation (e.g., Chapman and Chapman1969 and Hamilton and Gifford 1976), the

gamblers fallacy (see, e.g., Bar-Hillel and

9Economists are, I think, drawn to complexity explana-tions for limited rationality for several reasons. The mainand best reason is its realism: it is intuitive and it is truethat many of our limits come from the sheer impossibilityof attending to everything or fully maximizing when we dopay attention. But it also seems to have an appeal based onits affinity with computer science and math, rather thanpsychology, and its greater amenability to deriving assump-tions from first principles rather than empirical evidence.

Wagenaar 1991), and the hot-hand fallacy(see, e.g., Gilovich, Vallone, and Tversky1985) all concentrate on biased tendenciesto see imaginary patterns. The rational wayto do the familiar task of predicting the like-lihood that the next flip of a coin is tails hasa happy simplicity to it.10 But people havefar more complicated beliefs that differ-ent answers are needed for predictions fol-lowing HTHHHH versus HTTHTH versusTHTHTH.11 And traders appear not to askthe very simple question who in the marketis trading with me, and why?, or to come up

with the near inevitable and perspective-changing answer that it is somebody who is

himself trying to make money from differ-ent beliefs about an asset. The logic of real-izing that in the future youll have just thesame self-control problem as now is no morecomplicated than the belief that beginningtomorrow you will reform your ways; just lesspsychologically compelling. The logic that

you will crave food in the future when hun-gry, or (if addicted) crave a drug when youvegone too long without a hit, is cognitivelyavailable to all as a familiar fact of life; butit does not grab our attention at moments ofdecisionmaking when we are currently sated

with food or drug.Nor do all errors come from lack of effort

to overcome them, or intellectual or physicallaziness. People may not spend much effortpredicting coin flips, but many spend hugeamounts of time trying to see the patterns instocks that, for any plausible money-makingopportunities, are best approximated by

a random walk. Not only may we maintainnaivet about our self-control problems indefiance of any attentive learning rulewemay put a lot of intellectual energy into notlearning. The right explanation for misbehav-ior could eliminate convoluted, complicated,

10 0.5.11Subjects tend to predict lower and lower chances of

tails going from the first to the third sequence.


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and time-consuming stories; the 1,000 differ-ent reasons why you didnt start your diet ordissertation the previous 1,000 days could bereplaced with the simpler right answeryoudidnt have the willpower. Or you think youllnot drink or have unsafe sex or smoke when

you go out tonight, rather than think theequally simple (and truer) hypothesis that

youll likely do the same things you alwaysdo.12Such effortful errors are most strikinglyinconsistent with the bounded-rationalitymetaphor when they involve a great deal ofplanning and actions. If per DellaVigna andMalmendier (2006) we actively join gymsand make other long-term plans for virtuous

activities in irrational ways, it would appearthat there is a whole lot of optimization goingon. Just the wrong kind.

As noted earlier, one major class of opti-mization-based errors can be conceptualizedas very close to utility maximization: situationby situation, people have reasonably focusedgoals, and maximize those goals reasonably

well. We can model a person as engaging intraditional constrained maximization at eachmoment in time. But we specify the exactmistake the person is making in which func-tion she is maximizing, or in what choice

12There are two important caveats to this perspective.First, it is slightly misleading to frame things in terms ofhow simple an answer is. An answer can be simple withoutit being easy to figure out. But many of these errors seemrobust to simple communication of the right answer by atrustworthy person in a way that could happen only when aperson is enticed by a countervailing intuition. Second, weneed to be somewhat careful that the simplicity of a correct

answer in a particular class of situations doesnt require thecomplex and time-consuming task for people to identify

what situations they are in. Maybe the fact that we shouldnot extrapolate our current tastes in cases where ourtastes predictably change belies the fact that on averageour future tastes will be our current ones; simply assum-ing no change may be a simple rule of thumb. This tooseems wildly miscalibrated. Ignore current hunger seemsnot only a simpler rule of thumb than extrapolate currenthunger, but it also seems the mastering of improved ruleslike this is almost always employed in comparably impor-tant confrontations with binary variation in life that do notimplicate the hold that current cravings have on us.

set she is choosing from. The three mainclasses of such quasi-maximization errors are

what might be called (a) narrow bracketing,(b) present bias and hyperbolic discounting,and (c) projection bias in predicting futureutility. Narrow bracketing is where peoplemaximize their true utility functions amongeach choice set they focus on, but dont inte-grate others. Present bias is where, momentby moment, a person maximizes full inter-temporal utility, but at each moment tendsto overweight current utility. (And may mis-predict the propensity to do so in the future.)Projection bias is where, because of currenttastes or current focus, people (actively or

passively) mispredict the utility of futuresituations. Formally, all these errors can beconceptualized as follows. As a function ofa persons environment, the person makeschoices from a choice set, and maximizes aparticular goal: MaxxXv(x). But people mayeither focus on the wrong choice set (nar-row bracketing), overweight near-term util-ity (present bias) or mispredict future utility(projection bias).

Present bias and naivet about pres-ent bias as modeled by Laibson (1997) andODonoghue and Rabin (1999, 2001) is themost well known of these quasi-maximizationerrors. The third example, projection bias asmodeled by Loewenstein, ODonoghue, andRabin (2003), applies in situations wheretastes change over time, either due to tem-porary fluctuations (such as mood swings, orsatiation and deprivation of food or drugs),or due to longer term adaptation (such as

to our standard of living) or habit formation(such as exercise, or addiction to a drug).Changing tastes are a fact about utility, notan indication of irrationality. The error:people systematically underappreciate (even

very predictable) changes in their tastes, andhence falsely project their current tastesonto the future. Formally, Loewenstein,ODonoghue, and Rabin (2003) offer analternative to the rational-choice assumption


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that people maximize state-dependent utility,which can be represented (without dis-counting) by

Ut==t

T

u(c, s),

where u(c, s) is her instantaneous utilityin period , and c is the persons period-consumption vector which includes allperiod- behavior relevant for current orfuture instantaneous utilities. The vector sis the persons state in period , which incor-porates all factors that affect instantaneousutility besides current consumption. Theyassume that at timeta person maximizes

Ut==tT u(c, s|st),

where u(c, s| st) is the prediction at time tin state stofu(c, s). Whereas rational expec-tations posits that u(c, s| st) =u(c, s),Loewenstein, ODonoghue, and Rabin(2003) assume that a person may sufferfrom simple projection bias if there exists[0, 1] such that for all c, s, and s,

u (c, s | s) =(1 )u(c, s) +u(c, s).

This posits that at each moment in timepeople have well-defined perceived utilityfrom their courses of action, and take actionsto maximize their long-run happiness. Thisis right or wrong in all the ways the ratio-nal model can be right or wrong, differingsolely from this general principle of project-ing current tastes into the future. Projection

bias can help understand mispredictionsof food (Read and van Leeuwen 1998) anddrug (Badger et al. 2007) cravings, underap-preciation of long-run habit formation (Levy2010 and Acland and Levy 2011), catalogclothing purchases (Conlin, ODonoghue,and Vogelsang 2007), and demand for swim-ming pools and convertible car roofs basedon temporary weather fluctuations (Busse etal. 2012).

There are also now a class of models thatcapture errors in peoples statistical reason-ing that fully accord to neoclassical mod-els of preference optimization, but simplybuild in a systematic misunderstanding ofstatistics. In these quasi-Bayesian mod-els, people maximize expected utility (orany other appropriate utility function), butform their expectations based on wrongmodels of the world. Given prior probal-istic beliefs (h) about hypotheses hH,how does a person form updated beliefs,P(h|e), about the likelihood that a particu-lar hypothesis, hH, is true upon observ-ing evidence e? Proper Bayesian updating

implies that after observing informatione1, e2, a person forms posterior beliefs

B(h|e1, e2, ) =(e1, e2, |h

)(h)

__

hH

(e1, e2, |h)(h).

Some errors in statistical reasoning can beunderstood in terms of an alternative func-tional form of how people combine condi-tional probabilities and priors, by assumingthat people use some other functional form

P(h|e1, e2, ) =

f({(e1, e2, |h)}hH, {(h)}hH).

Most famously, people suffer from base-rate neglect: they underuse the priors{(h)}hH implying updated beliefs havefunctional form

P(h|e1, e2, ) = (e1, e2, |h)[(h

)]

__

hH

(e1, e2, |h)[(h)]

,

with 1.More interestingly, many errors can be

modeled as people engaging in putativelyproper Bayesian updating, but with a precise

way in which they either misobserve or mis-understand how that evidence relates to thehypotheses. Then researchers understand


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the implications of the error by studyinga form of Bayesian updating that embedsthe error. There are two categories of suchquasi-Bayesian updating that researchershave employed. Warped-model Bayesiansupdate according to

P(h|e1, e2, ) =(e1, e2, |h)(h)

__

hH

(e1, e2, |h)(h),

where (e1, e2, |h) is a false (but inter-nally consistent) model of how signals aregenerated. This approach was pioneered byBarberis, Shleifer, and Vishny (1998), andadopted by Rabin (2002a) and Rabin and

Vayanos (2010) to capture false overconfi-dence that small samples resemble under-lying proportions, and Benjamin, Rabin,and Raymond (2012) to capture the falsebelief that large samples might not resem-ble underlying proportions. Other errorsare captured by assuming that people areinformation-misreading Baye-sians, updat-ing according to

P(h

|e1, e2, ) =

(f (e1),f (e1, e2), ..), .. |h

)(h)

___

hH

(f (e1),f (e1, e2), ..), .. |h)(h),

wheref (e1), f (e1, e2) are misinterpreted sig-nals. Rabin and Schrag (1999) capture psy-chological evidence on confirmatory bias byassuming that people tend to misread signalsas supporting earlier hypotheses. Once a

teacher conjectures a student is smart ratherthan stupid, he may interpret complicatedanswers in class during the semester as subtlerather than confused. Mullainathan (2002)models naive memory problems by assumingpeople forget some signalsbut update as ifthe absence of signals contains information.A teacher may not remember all the goodanswers a student provides in class, but mayassess the student harshly because he thinks

a smart student should have given more goodanswers than he remembers her giving.

4. Conclusion

One welcome feature of the article byHarstad and Selten and the reply by Crawfordis the attempt to relate models of boundedrationality to important economic phenom-ena, such as asset-market bubbles. Although Iam not as optimistic as they are that the labo-ratory evidence they bring to bear provides theright building blocks for new models of behav-ior that drive real-world bubbles, the focuson the economic implications of new theories

of choice is an important step. This of coursecomes at a cost if it is too soon to try to applyour models, or if economists studying real-

world empirical applications are not the targetconsumers of our new models. Yet thinkingabout the implications of new models in work-aday applied-theory and empirical economicsis a tremendously important component of theprogram to improve psychological realism ineconomics. First, it should not be controver-sial that mainstream economic researchers arethe (eventual, downstream) target consumers.Second, it will provide guidance on which ofthe infinite ways we can improve the realismof economic assumptions are likely to be mostimportant. Third, it will provide some guid-ance on the methodology researchers shouldemploy to improve realism and the types ofmodels that will be most useful.

It is early days for the applications ofmany optimization models of limited ratio-

nality, but I do think the more intimate tiesbetween empirical economics and some ofthese models bodes well, in comparison tobounded-rationality models, for both theirapplicability and the speed at which themodels themselves can be improved.13 It

13But see Spiegler (2011) for an excellent exploration ofthe potential of both genres of models to provide insightsinto economic institutions and outcomes.


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would be bad judgment to bet confidentlyagainst the potential insights of a researchline that has generated so much excitementamong economic theorists. And it would alsobe bad empirical analysissince models ofbounded rationality have already inspirednew insights. But I think as we move forward

with economic implications, with theoreticalcomparative statics and empirical measure-ment, some of the abstract and intuitive argu-ments we have all provided in this forum willbe given more productive structure. Many ofthe new optimization models are being inte-grated rapidly into economic analysis to thebenefit of both economics and the new mod-

els. For models of present bias, Strotz (1956)and Laibson (1997) started with the impor-tant application to pared-down models ofsavings and consumption. But the literaturehas since expanded rapidly to applications intoo many domains of economics to list here.Angeletos et al. (2001) show how it can helpunderstand housing, credit-card, and othermarkets in the United States. And there isresearch now studying its implications fordefault effects and commitment devices insavings, as well as for smoking behavior, opti-mal taxation, etc. Models of the role of nar-row bracketing in loss aversion, from riskychoice (e.g., Benartzi and Thaler 1995) tolabor supply (e.g., Camerer et al. 1997 andCrawford and Meng 2011), are also surelygoing to improve empirical work. Analysisof the role of mispredicting future prefer-ences, now studied in the context of cloth-ing, car, and housing choices (see Conlin,

ODonoghue, and Vogelsang 2007 and Busseet al. 2012) are in earlier days. Little has yetbeen done to integrate statistical errors, ormodels of how people are neglectful andirrational in extracting information fromother economic actors in strategic and mar-ket contexts. But integrating the potential ofportable models of erroneous beliefse.g.,to form more realistic notions of the beliefsof small investors in asset marketsis clear.

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1. Ronald M. Harstad,, Reinhard Selten. 2013. Bounded-Rationality Models: Tasks to BecomeIntellectually Competitive. Journal of Economic Literature 51:2, 496-511. [Abstract] [View PDFarticle] [PDF with links]

2. Vincent P. Crawford. 2013. Boundedly Rational versus Optimization-Based Models of StrategicThinking and Learning in Games.Journal of Economic Literature51:2, 512-527. [Abstract] [ViewPDF article] [PDF with links]
http://pubs.aeaweb.org/doi/pdfplus/10.1257/jel.51.2.512http://pubs.aeaweb.org/doi/pdf/10.1257/jel.51.2.512http://pubs.aeaweb.org/doi/pdf/10.1257/jel.51.2.512http://dx.doi.org/10.1257/jel.51.2.512http://pubs.aeaweb.org/doi/pdfplus/10.1257/jel.51.2.496http://pubs.aeaweb.org/doi/pdf/10.1257/jel.51.2.496http://pubs.aeaweb.org/doi/pdf/10.1257/jel.51.2.496http://dx.doi.org/10.1257/jel.51.2.496

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