addiction and cue-triggered decision processes...$300 billion per year. on average over 500,000...

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Addiction and Cue-Triggered Decision Processes By B. DOUGLAS BERNHEIM AND ANTONIO RANGEL* We propose a model of addiction based on three premises: (i) use among addicts is frequently a mistake; (ii) experience sensitizes an individual to environmental cues that trigger mistaken usage; (iii) addicts understand and manage their susceptibil- ities. We argue that these premises find support in evidence from psychology, neuroscience, and clinical practice. The model is tractable and generates a plau- sible mapping between behavior and the characteristics of the user, substance, and environment. It accounts for a number of important patterns associated with addiction, gives rise to a clear welfare standard, and has novel implications for policy. (JEL D01, D11, H20, H21, H23, H31, I12, I18, K32) According to clinical definitions, substance addiction occurs when, after significant expo- sure, users find themselves engaging in compul- sive, repeated, and unwanted use despite clearly harmful consequences, and often despite a strong desire to quit unconditionally (see, e.g., the American Psychiatric Association’s Diag- nostic and Statistical Manual of Mental Disor- ders, known as DSM-IV). There is widespread agreement that certain substances have addic- tive properties, 1 and there is some debate as to whether formal definitions of addiction should be expanded to include other substances (such as fats and sugars) and activities (such as shop- ping, shoplifting, sex, television viewing, and internet use). The consumption of addictive substances raises important social issues affecting mem- bers of all socioeconomic strata. 2 Tens of mil- lions of Americans use addictive substances. Nearly 25 million adults have a history of alco- hol dependence, and more than five million qualify as “hard-core” chronic drug users. Esti- mates for 1999 place total U.S. expenditures on tobacco products, alcoholic beverages, cocaine, heroin, marijuana, and methamphetamines at more than $150 billion, with still more spent on caffeine and addictive prescription drugs. Esti- mated social costs (health care, impaired pro- ductivity, crime, and so forth) total more than * Bernheim: Department of Economics, Stanford Uni- versity, Stanford, CA 94305-6072, and NBER (e-mail: [email protected]); Rangel: Department of Economics, Stanford University, Stanford, CA 94305, and NBER (e-mail: [email protected]). We thank George Akerlof, Gadi Barlevy, Michele Boldrin, Kim Bor- der, Samuel Bowles, Colin Camerer, Luis Corchon, David Cutler, Alan Durell, Dorit Eliou, Victor Fuchs, Ed Glaeser, Steven Grant, Jonathan Gruber, Justine Hastings, Jim Hines, Matthew Jackson, Chad Jones, Patrick Kehoe, Narayana Kocherlakota, Botond Koszegi, David Laibson, Darius Lak- dawalla, Ricky Lam, John Ledyard, George Loewenstein, Rob Malenka, Ted O’Donahue, David Pearce, Christopher Phelan, Wolfgang Psendorfer, Edward Prescott, Matthew Rabin, Paul Romer, Pablo Ruiz-Verdu, Andrew Samwick, Ilya Segal, Jonathan Skinner, Stephano de la Vigna, Andrew Weiss, Bob Wilson, Leeat Yariv, Jeff Zwiebel, seminar participants at UC–Berkeley, Caltech, Carlos III, Darmouth, Harvard, Hoover Institution, Instituto the Analysis Eco- nomico, LSE, Michigan, NBER, Northwestern, UCSD, Yale, Wisconsin, SITE, Federal Reserve Bank of Minneap- olis, and the McArthur Preferences Network for useful comments and discussions. We also thank Luis Rayo, Daniel Quint, and John Hatfiled for outstanding research assistance. Rangel gratefully acknowledges financial sup- port from the NSF (SES-0134618) and thanks the Hoover Institution for its financial support and stimulating research environment. This paper was prepared in part while B. Douglas Bernheim was a Fellow at the Center for Advanced Study in the Behavioral Sciences (CASBS), where he was supported in part by funds from the William and Flora Hewlett Foundation (Grant No. 2000-5633). 1 Eliot Gardner and James David (1999) provide the following list of 11 addictive substances: alcohol, barbitu- rates, amphetamines, cocaine, caffeine and related methyl- xanthine stimulants, cannabis, hallucinogenics, nicotine, opioids, dissociative anasthetics, and volatile solvents. 2 The statistics in this paragraph were obtained from the following sources: Center for Disease Control (1993), Na- tional Institute on Drug Abuse (1998), National Institute on Alcohol Abuse and Alcoholism (2001), Office of National Drug Control Policy (2001a, b), and U.S. Census Bureau (2001). There is, of course, disagreement as to many of the reported figures. 1558

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Page 1: Addiction and Cue-Triggered Decision Processes...$300 billion per year. On average over 500,000 deaths each year are attributed directly to ciga-rettes and alcohol. Public policies

Addiction and Cue-Triggered Decision Processes

By B. DOUGLAS BERNHEIM AND ANTONIO RANGEL*

We propose a model of addiction based on three premises: (i) use among addicts isfrequently a mistake; (ii) experience sensitizes an individual to environmental cuesthat trigger mistaken usage; (iii) addicts understand and manage their susceptibil-ities. We argue that these premises find support in evidence from psychology,neuroscience, and clinical practice. The model is tractable and generates a plau-sible mapping between behavior and the characteristics of the user, substance, andenvironment. It accounts for a number of important patterns associated withaddiction, gives rise to a clear welfare standard, and has novel implications forpolicy. (JEL D01, D11, H20, H21, H23, H31, I12, I18, K32)

According to clinical definitions, substanceaddiction occurs when, after significant expo-sure, users find themselves engaging in compul-sive, repeated, and unwanted use despite clearlyharmful consequences, and often despite astrong desire to quit unconditionally (see, e.g.,the American Psychiatric Association’s Diag-

nostic and Statistical Manual of Mental Disor-ders, known as DSM-IV). There is widespreadagreement that certain substances have addic-tive properties,1 and there is some debate as towhether formal definitions of addiction shouldbe expanded to include other substances (suchas fats and sugars) and activities (such as shop-ping, shoplifting, sex, television viewing, andinternet use).

The consumption of addictive substancesraises important social issues affecting mem-bers of all socioeconomic strata.2 Tens of mil-lions of Americans use addictive substances.Nearly 25 million adults have a history of alco-hol dependence, and more than five millionqualify as “hard-core” chronic drug users. Esti-mates for 1999 place total U.S. expenditures ontobacco products, alcoholic beverages, cocaine,heroin, marijuana, and methamphetamines atmore than $150 billion, with still more spent oncaffeine and addictive prescription drugs. Esti-mated social costs (health care, impaired pro-ductivity, crime, and so forth) total more than

* Bernheim: Department of Economics, Stanford Uni-versity, Stanford, CA 94305-6072, and NBER (e-mail:[email protected]); Rangel: Department ofEconomics, Stanford University, Stanford, CA 94305, andNBER (e-mail: [email protected]). We thankGeorge Akerlof, Gadi Barlevy, Michele Boldrin, Kim Bor-der, Samuel Bowles, Colin Camerer, Luis Corchon, DavidCutler, Alan Durell, Dorit Eliou, Victor Fuchs, Ed Glaeser,Steven Grant, Jonathan Gruber, Justine Hastings, Jim Hines,Matthew Jackson, Chad Jones, Patrick Kehoe, NarayanaKocherlakota, Botond Koszegi, David Laibson, Darius Lak-dawalla, Ricky Lam, John Ledyard, George Loewenstein,Rob Malenka, Ted O’Donahue, David Pearce, ChristopherPhelan, Wolfgang Psendorfer, Edward Prescott, MatthewRabin, Paul Romer, Pablo Ruiz-Verdu, Andrew Samwick,Ilya Segal, Jonathan Skinner, Stephano de la Vigna, AndrewWeiss, Bob Wilson, Leeat Yariv, Jeff Zwiebel, seminarparticipants at UC–Berkeley, Caltech, Carlos III, Darmouth,Harvard, Hoover Institution, Instituto the Analysis Eco-nomico, LSE, Michigan, NBER, Northwestern, UCSD,Yale, Wisconsin, SITE, Federal Reserve Bank of Minneap-olis, and the McArthur Preferences Network for usefulcomments and discussions. We also thank Luis Rayo,Daniel Quint, and John Hatfiled for outstanding researchassistance. Rangel gratefully acknowledges financial sup-port from the NSF (SES-0134618) and thanks the HooverInstitution for its financial support and stimulating researchenvironment. This paper was prepared in part while B.Douglas Bernheim was a Fellow at the Center for AdvancedStudy in the Behavioral Sciences (CASBS), where he wassupported in part by funds from the William and FloraHewlett Foundation (Grant No. 2000-5633).

1 Eliot Gardner and James David (1999) provide thefollowing list of 11 addictive substances: alcohol, barbitu-rates, amphetamines, cocaine, caffeine and related methyl-xanthine stimulants, cannabis, hallucinogenics, nicotine,opioids, dissociative anasthetics, and volatile solvents.

2 The statistics in this paragraph were obtained from thefollowing sources: Center for Disease Control (1993), Na-tional Institute on Drug Abuse (1998), National Institute onAlcohol Abuse and Alcoholism (2001), Office of NationalDrug Control Policy (2001a, b), and U.S. Census Bureau(2001). There is, of course, disagreement as to many of thereported figures.

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$300 billion per year. On average over 500,000deaths each year are attributed directly to ciga-rettes and alcohol.

Public policies regarding addictive sub-stances run the gamut from laissez-faire to tax-ation, subsidization (e.g., of rehabilitationprograms), regulated dispensation, criminaliza-tion, product liability, and public health cam-paigns. Each alternative policy approach haspassionate advocates and detractors. Economicanalysis can potentially inform this debate, butit requires a sound theory of addiction.

This paper presents a new theory of addictionbased on three central premises: first, useamong addicts is frequently a mistake; second,experience with an addictive substance sensi-tizes an individual to environmental cues thattrigger mistaken usage; third, addicts under-stand their susceptibility to cue-triggered mis-takes and attempt to manage the process withsome degree of sophistication. We argue thatthese premises find strong support in evidencefrom psychology, neuroscience, and clinicalpractice. In particular, research has shown thataddictive substances systematically interferewith the proper operation of an important classof processes which the brain uses to forecastnear-term hedonic rewards (pleasure), and thisleads to strong, misguided, cue-conditioned im-pulses that often defeat higher cognitive control.

We provide a parsimonious representation ofthis phenomenon in an otherwise standardmodel of intertemporal decision-making. Spe-cifically, we allow for the possibility that, uponexposure to environmental cues, the individualmay enter a “hot” decision-making mode inwhich he always consumes the substance irre-spective of underlying preferences, and we as-sume that sensitivity to cues is related to pastexperiences. The individual may also operate ina “cold” mode, wherein he considers all alter-natives and contemplates all consequences, in-cluding the effects of current choices on thelikelihood of entering the hot mode in thefuture.3

As a matter of formal mathematics, ourmodel involves a small departure from the stan-dard framework. Behavior corresponds to thesolution of a dynamic programming problemwith stochastic state-dependent mistakes. Ourapproach therefore harmonizes economic the-ory with evidence on the biological foundationsof addiction without sacrificing analytic tracta-bility. We underscore this point by providingresults that illuminate the relationships betweenbehavior and the characteristics of the user,substance, and environment. For example, wefind that, when one substance is more addictivethan another, then ceteris paribus the more ad-dictive substance is associated with less con-sumption among relatively new users, but withmore consumption (both intentional and acci-dental) among highly experienced users.

The theory can account for a number of im-portant patterns associated with addiction. Italso gives rise to a clear welfare standard andhas novel implications for public policy. Ourpolicy analysis focuses on consumer welfareand therefore ignores supply-side effects andexternalities. It emphasizes the role of policy inaverting mistakes and in either ameliorating ormagnifying significant, uninsurable monetaryrisks indirectly caused by exposure to stochasticenvironmental cues. We show that a beneficialpolicy intervention potentially exists if and onlyif there are circumstances in which users unsuc-cessfully attempt to abstain. In that case, theoptimal policy depends on usage patterns. In anatural benchmark case, it is optimal to subsi-dize an addictive substance when the likelihoodof use rises with the level of past experience. Incontrast, provided the substance is sufficientlyinexpensive, it is optimal to tax the substancewhen the likelihood of use declines with thelevel of past experience. Under weak condi-tions, a small subsidy for rehabilitation is ben-eficial, and a small tax is harmful. When substancetaxation is optimal, under some conditions crimi-nalization can perform even better. Programs thatmake addictive substances available on a prescrip-tion basis have potentially large benefits. Restric-tions on advertising and public consumption, and

3 Our analysis is related to work by George Loewenstein(1996, 1999), who considers simple models in which anindividual can operate either in a hot or cold decision-making mode. Notably, Loewenstein assumes that behaviorin the hot mode reflects the application of a “false” utilityfunction, rather than a breakdown of the processes by which

a utility function is maximized. He also argues, contrary tothe findings of this paper, that imperfect self-understandingis necessary for addiction-like behaviors.

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statutes requiring counter-cues on packaging, arealso potentially beneficial.

The remainder of the paper is organized asfollows. Section I describes some important be-havioral patterns associated with addiction thatrequire explanation. Section II lays out and jus-tifies, with particular reference to evidence frompsychology and neuroscience, the central pre-mises of our theory. Section III presents theformal model. Section IV explores the model’spositive implications, including its ability togenerate observed behavioral patterns. SectionV concerns policy analysis. Section VI clarifiesthe relationships between our theory of addic-tion and others that appear in the literature,including the standard model of rational addic-tion (Gary Becker and Kevin Murphy, 1988),various extensions of this model (AthanasiosOrphanides and David Zervos, 1995; AngelaHung, 2000; David Laibson, 2001), and a num-ber of behavioral alternatives (Loewenstein,1996, 1999; Ted O’Donoghue and MatthewRabin, 1999, 2000; Jonathan Gruber andBotond Koszegi, 2001; Loewenstein et al., Fa-ruk Gul and Wolfgang Pesendorfer, 2001a, b).Section VII concludes and discusses directionsfor future research. The appendices provide ad-ditional technical details and proofs; in somecases we sketch proofs to conserve space.

I. Patterns of Addictive Behavior

What makes addiction a distinctive phenom-enon? From the extensive body of research onaddiction in neuroscience, psychology, andclinical practice, we have distilled five impor-tant behavioral patterns requiring explanation.

1. Unsuccessful Attempts to Quit.—Addictsoften express a desire to stop using a substancepermanently and unconditionally but are unableto follow through. Short-term abstention iscommon while long-term recidivism rates arehigh. For example, during 2000, 70 percent ofcurrent smokers expressed a desire to quit com-pletely, and 41 percent stopped smoking for atleast one day in an attempt to quit, but only 4.7percent successfully abstained for more thanthree months (see J. E. Harris, 1993; Y. I. Hseret al., 1993; C. O’Brien, 1997; A. Goldstein,2001; A. Trosclair et al., 2002). This pattern isparticularly striking because regular users ini-

tially experience painful withdrawal symptomswhen they attempt to quit, and these symptomsdecline over time with successful abstention.Thus, recidivism often occurs after users haveborne the most significant costs of quitting,sometimes following years of determinedabstention.

2. Cue-Triggered Recidivism.—Recidivismrates are especially high when addicts are ex-posed to cues related to past drug consumption.Long-term usage is considerably lower amongthose who experience significant changes ofenvironment (see O’Brien, 1975, 1997; Gold-stein and H. Kalant, 1990; Hser et al., 1993,2001; Goldstein, 2001).4 Treatment programsoften advise recovering addicts to move to newlocations and to avoid the places where previousconsumption took place. Stress and “priming”(exposure to a small taste of the substance) havealso been shown to trigger recidivism (seeGoldstein, 2001; Terry Robinson and Kent Ber-ridge, 2003).

3. Self-Described Mistakes.—Addicts oftendescribe past use as a mistake in a very strongsense: they think that they would have beenbetter off in the past as well as the present hadthey acted differently. They recognize that theyare likely to make similar errors in the future,and that this will undermine their desire to ab-stain. When they succumb to cravings, theysometimes characterize choices as mistakeseven while in the act of consumption.5 It isinstructive that the 12-step program of Alco-holic Anonymous begins: “We admit we arepowerless over alcohol—that our lives have be-come unmanageable.”

4 L. Robins (1974) and Robins et al. (1974) found thatVietnam veterans who were addicted to heroin and/oropium at the end of the war experienced much lower relapserates than other young male addicts during the same period.A plausible explanation is that veterans encountered fewerenvironmental triggers (familiar circumstances associatedwith drug use) upon returning to the United States.

5 Goldstein (2001, p. 249) describes this phenomenon asfollows: the addict had been “suddenly overwhelmed by anirresistible craving, and he had rushed out of his house tofind some heroin. ... it was as though he were driven bysome external force he was powerless to resist, even thoughhe knew while it was happening that it was a disastrouscourse of action for him” (italics added).

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4. Self-Control through Precommitment.—Recovering users often manage their tendencyto make mistakes by voluntarily removing ordegrading future options. They voluntarily ad-mit themselves into “lock-up” rehabilitationfacilities, often not to avoid cravings, but pre-cisely because they expect to experience crav-ings and wish to control their actions. They alsoconsume medications that either generate un-pleasant side effects, or reduce pleasurablesensations, if the substance is subsequently con-sumed.6 Severe addicts sometimes enlist othersto assist with physical confinement to assureabstinence through the withdrawal process.

5. Self-Control through Behavioral and Cog-nitive Therapy.—Recovering addicts attempt tominimize the probability of relapse through be-havioral and cognitive therapies. Successful be-havioral therapies teach cue-avoidance, often byencouraging the adoption of new lifestyles andthe development of new interests. Successfulcognitive therapies teach cue-management,which entails refocusing attention on alternativeconsequences and objectives, often with the as-sistance of a mentor or trusted friend or througha meditative activity such as prayer. Notably,these therapeutic strategies affect addicts’choices without providing new information.7

While consumption patterns for addictivesubstances are distinctive in some respects, it isimportant to bear in mind that they are ordinaryin other respects. A number of studies haveshown that aggregate drug use responds both to

prices and to information about the effects ofaddictive substances. For example, an aggres-sive U.S. public health campaign is widely cred-ited with reduction in smoking rates. There isalso evidence that users engage in sophisticatedforward-looking deliberation, reducing currentconsumption in response to anticipated priceincreases.8

It is important to remember that consumptionpatterns for the typical addictive substance varyconsiderably from person to person.9 Some peo-ple never use it. Some use it in a controlled way,either periodically or for a short time period.Some experience occasional episodes wherethey appear to “lose control” (binge) but sufferno significant ongoing impairment and have nodesire to quit permanently. Some fit theDSM-IV definition of addiction. In the rest ofthe paper the term addict is reserved for thethird and fourth groups, whereas the term useris applied to everyone.

II. Central Premises

The theory developed in this paper is basedon three premises: (i) use among addicts isfrequently a mistake—that is, a pathologicaldivergence between choice and preference; (ii)experience with an addictive substance sensi-tizes an individual to environmental cues thattrigger mistaken usage; and (iii) addicts under-stand their susceptibility to cue-triggered mis-takes and attempt to manage the process withsome degree of sophistication. The thirdpremise is consistent with observed behavioralpatterns involving cue-avoidance and/or pre-commitments, and should be relatively uncon-troversial. In contrast, the notion that choicesand preferences can diverge is contrary to thestandard doctrine of revealed preference andtherefore requires thorough justification.

There are plainly circumstances in which itmakes no sense to infer preferences fromchoices. For example, American visitors to the

6 Disulfiram interferes with the liver’s ability to metab-olize alcohol; as a result, ingestion of alcohol produces ahighly unpleasant physical reaction for a period of time.Methadone, an agonist, activates the same opioid receptorsas heroin, and thus produces a mild high, but has a slowonset and a long-lasting effect, and it reduces the highproduced by heroin. Naltrexone, an antagonist, blocks spe-cific brain receptors and thereby diminishes the high pro-duced by opioids. All of these treatments reduce thefrequency of relapse (see O’Brien, 1997; Goldstein, 2001).

7 Goldstein (2001, p. 149) reports that there is a sharedimpression among the professional community that 12-stepprograms such as AA “are effective for many (if not most)alcohol addicts.” However, given the nature of these pro-grams, objective performance tests are not available. TheAA treatment philosophy is based on “keeping it simple byputting the focus on not drinking, on attending meetings,and on reaching out to other alcoholics.”

8 See F. Chaloupka and K. Warner (2001), Gruber andKoszegi (2001), and R. MacCoun and P. Reuter (2001) fora review of the evidence.

9 Even for a substance such as cocaine, which is consid-ered highly addictive, only 15–16 percent of people becomeaddicted within 10 years of first use (F. A. Wagner and J. C.Anthony, 2002).

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United Kingdom suffer numerous injuries andfatalities because they often look only to the leftbefore stepping into streets, even though theyknow traffic approaches from the right. Onecannot reasonably attribute this to the pleasureof looking left or to masochistic preferences. Thepedestrian’s objectives—to cross the street safely—are clear, and the decision is plainly a mistake.The source of this systematic error is traceable tofeatures of the human brain. Habituated, semi-automatic responses beneficially increase thespeed of decision-making in some circumstancesbut lead to systematic mistakes in others.

Recent research on the neuroscience of addic-tion has identified specific features of the brainthat appear to produce systematic errors with re-spect to decisions involving the consumption ofaddictive substances. The key process involves amechanism (henceforth called the “hedonic fore-casting mechanism” or HFM) that is responsiblefor associating environmental cues with forecastsof short-term hedonic (pleasure/pain) responses.10

Normally, the HFM learns through feedbackfrom the hedonic system: with experience, itassociates a situation and action with an antic-ipatory biochemical response, the magnitude ofwhich reflects the intensity of expected plea-sure. Addictive substances interfere with thenormal operation of the HFM by acting directly(i.e., independent of the pleasure experienced)on the learning process that teaches the HFM togenerate the anticipatory response. With re-peated use of a substance, cues associated withpast consumption cause the HFM to forecastgrossly exaggerated pleasure responses, creat-ing a powerful (and disproportionate) impulseto use. When this happens, a portion of theuser’s decision processes functions as if it hassystematically skewed information, which leadsto mistakes in decision-making.

Next we describe some of the key evidencethat leads to these conclusions. We organize ourdiscussion around four points.

1. Brain Processes Include a Hedonic Fore-casting Mechanism (HFM) Which, with Experi-ence, Produces a Biochemical Response to

Situations and Opportunities, the Magnitude ofWhich Constitutes a Forecast of Near-TermPleasure.—Neuroscientists have long recog-nized that the mesolimbic dopamine system(MDS) is a basic component of human deci-sion processes.11 A large body of recent re-search indicates that the MDS functions, atleast in part, as an HFM. In a series of exper-iments, subjects (often monkeys) are pre-sented with a cue that is associated with areward delivered a few seconds later (seeWolfram Schultz et al., 1997; Schultz, 1998,2000). Initially, the MDS fires in response tothe delivery of the reward and not in responseto the cue. However, as time passes, the MDSfires with the presentation of the cue and notwith the delivery of the reward. Moreover, thelevel of cue-triggered MDS activity is propor-tional to the size of the eventual reward. If,after a number of trials, the experimenterincreases the magnitude of the reward, theMDS fires twice: with the presentation of thecue (at a level proportional to the originalanticipated reward), and with the delivery ofthe reward (at a level reflecting the differencebetween the anticipated and actual rewards).After repeated trials with the new reward, theMDS fires more intensely upon presentationof the cue and, once again, does not respondto the delivery of the reward. Thus, withexperience, the MDS generates a cue-condi-tioned dopamine response that anticipates themagnitude of the eventual reward.

2. Activation of the HFM Does Not Neces-sarily Create Hedonic Sensation, and HedonicSensation Can be Experienced without HFMActivation.—Since the MDS produces a dopa-mine response prior to an anticipated experienceand no response during the experience, it isnatural to conjecture that this mechanism isneither a source nor a manifestation of pleasure.

10 The phrase “hedonic forecasting mechanism” summarizesthe role of this process in economic terms; this terminology is notused in the existing behavioral neuroscience literature.

11 The MDS originates in the ventral tegmentalarea, near the base of the brain, and sends projectionsto multiple regions of the frontal lobe, especially to the nu-cleus accumbens. The MDS also connects with the amyg-dala, basal forebrain, and other areas of the prefrontal lobe.These connections are believed to serve as an interfacebetween the MDS and attentional, learning, and cognitiveprocesses (Robinson and Berridge, 2003).

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Indeed, the human brain appears to contain aseparate hedonic system that is responsible forproducing sensations of “well-being.”12 In aseries of papers, neuroscientists Kent Berridgeand Terry Robinson have argued that two sep-arate processes are at work in decision making:a “wanting” process, which encompasses theimpulse created by a positive MDS forecast,and a “liking” process, which refers to a hedo-nic response (see Robinson and Berridge, 1993,2000, 2003; Berridge, 1996, 1999; Berridgeand Robinson, 1998, 2003).13 Their hypothesisemerges from numerous experimental studies,including the following. Using measures of“liking” based on rats’ facial expressions whenresponding to sweet and sour tastes, severalexperiments have shown that neither the directactivation of the MDS nor its suppression af-fects liking (S. Pecina et al., 1997; H. J. Kacz-marek and S. W. Kiefer, 2000; C. L. Wyvell andBerridge, 2000). Others have demonstrated thatthe “liking” system functions well even withmassive lesions to the MDS (see Berridge andRobinson, 1998). Direct activation of the MDSthrough microinjections of amphetamine in thenucleus accumbens (NAc) increases wantingbut fails to increase liking (Wyvell and Ber-ridge, 2000). Finally, blocking the MDS withdopamine antagonists does not have an impacton the level of pleasure obtained from using adrug reported by amphetamine and nicotine us-ers (L. H. Brauer et al., 1997, 2001; S. R.Wachtel et al., 2002).

3. HFM-Generated Forecasts InfluenceChoices.—A series of classic experiments by J.Olds and P. Milner (1954) demonstrated thatrats learn to return to locations where they havereceived direct electrical stimulation to the

MDS. When provided with opportunities toself-administer by pressing a lever, the rats rap-idly became addicted, giving themselves ap-proximately 5,000–10,000 “hits” during eachone-hour daily session, ignoring food, water,and opportunities to mate. These rats are willingto endure painful electric shocks to reach thelever (see Gardner and David, 1999 for a sum-mary of these experiments). Complementaryevidence shows that rats given drugs that blockdopamine receptors, thereby impeding the ap-propriate operation of the MDS, eventually stopfeeding (Berridge, 1999).

Notably, the MDS activates “seeking be-haviors” as well as immediate consumptionchoices. That is, it learns to make associationsnot just between consumption opportunities andhedonic payoffs, but also between environmen-tal cues and activities that tend to produce theseconsumption opportunities. For example, thesight of food may create a powerful impulse toeat, while an odor may create a powerful im-pulse to seek food. The size of the set of envi-ronmental cues that trigger an associatedseeking behavior increases with the strength ofthe hedonic forecast (see Robinson and Ber-ridge, 1993, 2000, 2003; Berridge and Robin-son, 1998, 2003).

While the MDS plays a key role in determin-ing choices, it is not the only process at work. Inan organism with a sufficiently developed fron-tal cortex, higher cognitive mechanisms canoverride HFM-generated impulses. Though thespecific mechanisms are not yet fully under-stood, structures in the frontal cortex appear toactivate competing “cognitive incentives” (Ber-ridge and Robinson, 2003), for example, byidentifying alternative courses of action or pro-jecting the future consequences of choices. Theoutcome depends on the intensity of the HFMforecast and on the ability of the frontal cortexto engage the necessary cognitive operations.14

Thus, a more attractive HFM-generated forecastmakes cognitive override less likely. In addi-tion, the MDS seems to affect which stimuli thebrain attends to, which cognitive operations it

12 The existing evidence suggests that the hedonic sys-tem is modulated by a distributed network, separate fromthe structures involved in the HFM, that includes GABAer-gic neurons in the shell of the NAc, the ventral palladium,and the brainstem parachial nucleus (see Berridge and Rob-inson, 2003).

13 For decades, neuroscientists and psychologists haveused the term “reward” to describe both liking and wanting.In most experimental settings, the distinction is immaterialsince outcomes that are liked are also wanted, and viceversa. However, as we will see, this distinction is critical tounderstanding why repeated exposure to drugs leads tomistaken usage.

14 The activation of the cognitive operations required forcognitive control depends on neocortical structures such asthe insula and the orbitofrontal cortex (see e.g., J. D. Cohenand K. I. Blum, 2002; D. C. Krawczyk, 2002; E. T. Rolls,2002; Masataka Watanabe et al., 2002).

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activates (what it thinks about), and whichmemories it preserves, and this may make itmore difficult to engage the cognitive opera-tions required to override the HFM.15

We emphasize that the HFM and higher cog-nitive processes are not two different sets of“preferences” or “selves” competing for controlof decisions. Hedonic experiences are generatedseparately, and an individual maximizes thequality of these experiences by appropriatelydeploying both forecasting processes to antici-pate outcomes. The HFM’s main advantage isthat it can produce rapid decisions with gener-ally beneficial near-term outcomes, providedthe environment is stable. It cannot, however,anticipate sufficiently delayed consequences,and when the environment changes, it canneither ignore irrelevant past experiences noradjust forecasts prior to acquiring further expe-rience. The competing cognitive forecastingsystem addresses these shortcomings (albeit im-perfectly) but is comparatively slow. Balancedcompetition between these two processes appar-ently emerged as evolution’s best compromise.

4. Addictive Substances Act Directly on theHFM, Disrupting Its Ability to Construct Accu-rate Hedonic Forecasts and Exaggerating theAnticipated Hedonic Benefits of Consump-tion.—Although addictive substances differconsiderably in their chemical and psychologi-cal properties, there is a large and growingconsensus in neuroscience that they share anability to activate the firing of dopamine into theNAc with much greater intensity and persis-tence than other substances. They do this eitherby activating the MDS directly, or by activatingother networks that have a similar effect on theNAc (see Ingrid Wickelgren, 1997; Steven Hy-man and Robert Malenka, 2001; E. J. Nestler,2001; Robinson and Berridge, 2003; Nestlerand Robert Malenka, 2004).16

For nonaddictive substances, the MDS learnsto assign a hedonic forecast that bears somenormal relation to the subsequent hedonic ex-perience. For addictive substances, consump-tion activates dopamine firing directly, so theMDS learns to assign a hedonic forecast that isout of proportion to the subsequent hedonicexperience. This not only creates a strong (andmisleading) impulse to seek and use the sub-stance, but also undermines the potential forcognitive override.17 Cognitive override still oc-curs, but in a limited range of circumstances.18,19

Our central premises have two implicationsthat are worth emphasizing because they are atodds with some of the alternative models ofaddiction discussed in Section VI. First, theprocesses that produce systematic mistakes aretriggered by stochastic environmental cues andare not always operative. Second, cue-triggered

15 Notably, more educated individuals are far more likelyto quit smoking successfully, even though education bearslittle relation either to the desire to quit or to the frequencywith which smokers attempt to quit (Trosclair et al., 2002).

16 Of the addictive substances listed in footnote 1, onlyhallucinogenics (or psychedelics) do not appear to produceintense stimulation of the MDS. Instead, they act on a“subtype of serotonin receptor which is widely distributedin areas of the brain that process sensory inputs” (Goldstein,2001 p. 231). There is some disagreement as to whether

hallucinogens are properly classified as addictive substances(see Goldstein, 2001, Ch. 14). Notably, laboratory animalsand humans learn to self-administer the same set of sub-stances, with the possible exception of hallucinogenics(Gardner and David, 1999, pp. 97–98).

17 A stronger MDS-generated impulse is more likely toovercome competing cognitive incentives of any givenmagnitude. In addition, the MDS-generated impulse maymake it more difficult to engage the cognitive operationsrequired to override the HFM. For example, recoveringaddicts may pay too much attention to drugs, activate andmaintain thoughts about the drug too easily, and retainparticularly vivid memories of the high. Consistent withthis, S. Vorel et al. (2001) have shown that the stimulationof memory centers can trigger strong cravings and recidi-vism among rats that have previously self-administeredcocaine (J. P. Berke et al., 2001, and C. Holden, 2001a, b,provide nontechnical discussions).

18 The importance of cognitive override is evident fromcomparisons of rats and humans. When rats are allowed toself-administer cocaine, after a short period of exposurethey begin to ignore hunger, reproductive urges, and allother drives, consuming the substance until they die (R.Pickens and W. C. Harris, 1968; E. Gardner and David,1999). In contrast, even severely addicted humans some-times resist cravings and abstain for long periods of time.The difference is that rats rely solely on the HFM.

19 Several studies (see J. I. Bolla et al., 1998; J. D.Jentsch and J. R. Taylor, 1999; T. W. Robbins and B. J.Everitt, 1999; A. Behara and H. Damasio, 2002; Behara, S.Dolan, and A. Hindes, 2002) have shown that addicts sharepsychological disorders with patients who have damagedfrontal lobes affecting functions related to cognitive control.In addition, some of these studies have argued that drug useis partly responsible for this impairment. Thus, use mayincrease the likelihood of subsequent use by crippling cog-nitive control mechanisms.

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mistakes are specific to narrow domains. Thatis, they adhere to particular activities in partic-ular circumstances and do not reflect a generalbias toward immediate gratification. Since poorcognitive control increases the likelihood of be-coming addicted, it should not be surprising thatthe typical addict exhibits other self-controlproblems. However, it does not follow that ageneral deficit in cognitive control is necessaryfor addiction.

In emphasizing the effects of addictive sub-stances on decision process, we do not mean todiscount the significance of their hedonic ef-fects. The typical user is initially drawn to anaddictive substance because it produces a hedo-nic “high.” Over time, regular use leads to he-donic and physical tolerance. That is, the drugloses its ability to produce a high unless the userabstains for a while,20 and any attempt to dis-continue the drug may have unpleasant sideeffects (withdrawal). Cue-conditioned “crav-ings” may have hedonic implications as well asnon-hedonic causes (i.e., HFM-generated im-pulses). All of these effects are clearly impor-tant, and with one exception discussed in thenext section, our model subsumes them. How-ever, there is an emerging consensus in neuro-science and psychology that decision-processeffects, rather than hedonic effects, provide thekey to understanding addictive behavior (seeRoy Wise, 1989; G. Di Chiara, 1999; A. E.Kelley, 1999; Robbins and Everitt, 1999; Rob-inson and Berridge, 2000; Hyman and Malenka,2001; Berridge and Robinson, 2003; Nestlerand Malenka, 2004).

III. The Model

We consider a decision-maker (DM) who canoperate in either of two modes: a “cold” modein which he selects his most preferred alterna-tive (by imposing cognitive control), and a dys-functional “hot” mode in which decisions and

preferences may diverge (because he respondsto distorted HFM-generated forecasts). He livesfor an infinite number of discrete periods. Ineach period, he makes two decisions in succes-sion. First he selects a “lifestyle” activity (a);then he allocates resources between an addictivesubstance (x � {0, 1}) and a nonaddictive sub-stance (e � 0). He enters each period in the coldmode and chooses his lifestyle activity ratio-nally. This choice, along with his history of useand other environmental factors, determines theprobability with which he encounters cues thattrigger the hot mode. If triggered, he alwaysuses the substance, even if this is not his bestchoice. If he is not triggered, he rationally de-cides whether to indulge or abstain.

The intensity (or volume) of substance-related cues encountered, c(a, �), depends onthe activity a and an exogenous state of nature,�, drawn randomly from a state space � ac-cording to some probability measure �. Thefunction M(c, s, a, �) denotes the attractivenessassigned to the drug by the HFM-generatedforecast; this depends on the intensity of cues,the chosen activity, the state of nature, and avariable s summarizing the DM’s history of use(his addictive state). The impulse from thisforecast defeats cognitive control and places theindividual in the “hot” mode when its strengthexceeds some threshold, MT.

There are S � 1 addictive states labeled s �0, 1, ... , S. Usage in state s leads to state min{S,s � 1} in the next period. No use leads to statemax{1, s � 1} from state s � 1, and to state 0from state 0. Note that it is impossible to reachstate 0 from any state s � 1. The state s � 0represents a “virgin state” in which the DM hashad no contact with the substance. Since peoplebecome sensitized to cues through repeated use,we assume M(c, s�, �, a) � M(c, s�, a, �) fors� � s�, with M(c, 0, a, �) � MT.

The lifestyle activity a is chosen from the set{E, A, R}. Activity E (“exposure”) entails a highlikelihood that the DM will encounter a largenumber of substance-related cues. Examples in-clude attending parties at which the substance isreadily available. Activity A (“avoidance”) isless intrinsically enjoyable than E, but exposesthe DM to fewer substance-related cues [c(E,�) � c(A, �)] and potentially reduces sensitiv-ity to cues [M(c, s, A, �) � M(c, s, E, �)].Examples include staying at home to read or

20 According to one user-oriented Web site, tolerance tomarijuana “builds up rapidly after a few doses and disap-pears rapidly after a couple of days of abstinence. Heavyusers need as much as eight times higher doses to achievethe same psychoactive effects as regular users using smalleramounts. They still get stoned but not as powerfully” (seehttp://www.thegooddrugsguide.com/cannabis/addiction.htm).

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attending AA meetings. Activity R (“rehabilita-tion”) entails a commitment to clinical treat-ment at a residential center during the currentperiod. It is even less intrinsically enjoyablethan A, it may further reduce exposure andsensitivity to substance-related cues [c(A, �) �c(R, �) and M(c, s, R, �) � M(c, s, A, �)], andmost importantly, it guarantees abstention (x �0) during the current period.

Let T(s, a) � {� � ��M(c(a, �), s, a, �) �MT}. The DM enters the hot state if and only if� � T(s, a). Let ps

a � �(T(s, a)) denote theprobability of entering the hot mode in addic-tive state s after selecting lifestyle activity a.Our assumptions on the functions c and M im-ply the following.

ASSUMPTION 1: ps�1a � ps

a, p0a � 0, and

psE � ps

A � psR.

In state s, the DM receives an immediatehedonic payoff, ws(e, x, a) (recall that e denoteshis consumption of nonaddictive goods). Thedependence of the payoff function on the addic-tive state incorporates the effect of past usageon current well-being (tolerance, deteriorationof health, and so forth). When evaluating thedesirability of any possible set of current andfuture outcomes, the DM discounts future he-donic payoffs at a constant rate �.

Notice that we do not allow the hedonic pay-off to depend on the state of nature, �. This is incontrast to the more conventional assumptionthat cravings reflect cue-triggered taste shocks(Laibson, 2001). As indicated in the previoussection, we recognize that cravings have hedo-nic implications. We abstract from this possi-bility to focus more narrowly on the novelaspects of our theory, which involve cue-triggered mistakes. Allowing for dependence ofws on � is straightforward, but our model canaccount for the key features of addictive behav-ior without this extension.

With ws independent of �, rehabilitation servesonly as a precommitment to abstain.21 Since the

DM’s hedonic payoff from abstention is the sameregardless of whether he is hot or cold, he neverenters rehabilitation with the object of reducingthe likelihood of cravings.22 As a result, the prob-abilities ps

R are irrelevant parameters.In state s the DM has access to resources ys

(“income”). In many cases, it is natural to as-sume that ys declines with s due to deterioratinghealth, reduced productivity (e.g., through ab-senteeism), and increased out-of-pocket medi-cal expenses. The price of the addictivesubstance is q, the cost of rehabilitation is rs(which potentially depends on the addictivestate), and the price of the nonaddictive sub-stance is normalized to unity. For simplicity, weassume that the DM cannot borrow or save.

The following notation simplifies our discus-sion. Let us

a � ws(ys, 0, a) and bsa � ws(ys � q,

1, a) � usa for a � {E, A}; and let us

R � ws(ys �rs, 0, R). Intuitively, us

a represents the baselinepayoff associated with successful abstention instate s and activity a, and bs

a represents themarginal instantaneous benefit from use the in-dividual receives in state s after taking activitya. Thus, us

a � bsa is the payoff for usage. Let

ps � (psE, ps

A, psR), us � (us

E, usA, us

R), bs � (bsE,

bsA), �s � (ps, us, bs), and � � (�0 , ... , �S). The

vector � specifies all pertinent “derivative” pa-rameters. It reflects the properties of the sub-stance, the method of administration, thecharacteristics of the individual user, and thepublic policy environment. We make the fol-lowing assumption (the latter part of which is inkeeping with our earlier discussion).

ASSUMPTION 2: The payoff function ws isincreasing, unbounded, strictly concave, andtwice differentiable with bounded second deriv-ative in the variable e (consumption of the non-addictive good). Moreover, us

E � usA � us

R, andus

E � bsE � us

A � bsA.

For each state s, the DM follows one of fivecontingent plans: engage in activity E and then

21 Though we assume that the DM can commit to reha-bilitation only one period at a time, this is without loss ofgenerality since he starts each period in the cold mode. Inpractice, rehabilitation programs may also teach self-management skills and desensitize addicts to cues. One canmodel these possibilities by assuming that ps

a (for a given

state or states) declines subsequent to rehabilitation or ther-apy. Since the evidence suggests that these treatments arenot completely effective (Goldstein, 2001, p. 188), the forcesdescribed here would still come into play after treatment.

22 When ws depends on � and psA � ps

R, rehabilitation canserve as a strategy for avoiding cues that trigger reductionsin hedonic payoffs (through cravings).

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use the substance when in the cold mode [(a,x) � (E, 1)], engage in E and refrain from usewhen in the cold mode [(a, x) � (E, 0), hence-forth “half-hearted abstention”], engage in Aand use when in the cold mode [(a, x) � (A, 1)],engage in A and refrain from use when in thecold mode [(a, x) � (A, 0), henceforth “con-certed abstention”], or enter rehabilitation [(a,x) � (R, 0)]. From Assumption 2, it follows that(E, 1) always dominates (A, 1), so there are inpractice only four pertinent choices.

The cold-mode DM is sophisticated in thesense that he correctly anticipates his futurechoices in either decision mode, and he under-stands the process triggering the hot mode. Ac-cordingly, his choices in the cold modecorrespond to the solution of a simple dynamicstochastic programming problem with a valuefunction Vs(� ) (evaluated as of the beginning ofa period) satisfying

(1) Vs �� � max�a,x ���E,1 ,�E,0 ,�A,0 ,�R,0 �

usa � s

a,xbsa

� ���1 sa,x Vmax�1,s � 1� �� � s

a,xVmin�S,s � 1� �� �

for s � 1,23 where sa,x represents the probabil-

ity of consuming the substance in state s withcontingent plan (a, x) (so s

E,1 � 1, sE,0 � ps

E,s

A,0 � psA, and s

R,0 � 0). Existence, unique-ness, and continuity of Vs(� ) in � follow fromstandard arguments.

We close this section with several remarks.First, though simple and stylized, our modeladheres closely to the three key premises de-scribed in Section II. Specifically, use amongaddicts is potentially a mistake; experience withan addictive substance sensitizes the user toenvironmental cues that subsequently triggermistaken use; and the awareness of this possi-bility leads users to manage their susceptibilities.

Second, our model reduces to the standard“rational addiction” framework when ps

a � 0 forall s and a. Thus, the novelty of our approachinvolves the introduction of stochastic shocks(occurring with probability ps

a � 0) that poten-tially cause decisions to diverge from prefer-ences. This possibility is a central feature of our

model since, without it, the DM would neverchoose to avoid cues or enter rehabilitation(with ps

E � 0, (E, 0) dominates both (A, 0) and(R, 0)). For the same reason, a naive DM whoincorrectly believes he does not suffer froma self-control problem (that is, who acts as ifps

a � 0) will never choose cue-avoidance orrehabilitation.

Third, even though our model allows for thepossibility that choices and preferences maydiverge, with careful use of appropriate data itshould still be possible to recover preferencesand other critical parameters (such as hot-modeprobabilities) empirically. Since we assume thatpreferences and choices are sometimes aligned,the most obvious approach involves the selec-tive application of the revealed preference prin-ciple. The empirical challenge is to identifyinstances of alignment. One cannot make thisdetermination using only information on choices.We contend, however, that other evidence, suchas the research results summarized in Section II,justifies treating the central assumptions of ourmodel as maintained hypotheses. This meansthat we can use choice data involving precom-mitments and cue-avoidance to infer hot-modeprobabilities and the utility costs of unintendeduse (recall the discussion in the preceding para-graph). Furthermore, measures of physiologi-cal arousal and/or self-reported affective statescould be used to differentiate “cold” choicesfrom “hot” choices in experimental settings. Fora more general discussion of preference mea-surement when choices and preferences system-atically diverge, see Bernheim and Rangel(2005).

Fourth, unlike other economic theories of ad-diction, ours does not necessarily assume thatpresent use increases the marginal benefit offuture use (bs�1 � bs). We show that, contraryto some claims in the literature, it is possible toexplain the central features of addiction withoutinvoking intertemporal preference complemen-tarities (provided the probability of cue-triggered mistakes increases with s). This isimportant because intertemporal complementa-rities do not appear to drive some distinctiveaddictive behaviors,24 and these behaviors are

23 The associated expression for s � 0 is virtually iden-tical, except that V0(�) replaces Vmax{1,s�1}(�).

24 The phenomenon of withdrawal is often interpretedas the key manifestation of intertemporal comple-

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observed in contexts where such complementa-rities are probably not present (e.g., compulsiveshopping and kleptomania).

Fifth, though one could incorporate the re-alistic possibility that some individuals arepartially myopic with respect to the likelihoodand effects of becoming addicted, we assumethat the DM is sophisticated in the cold mode.If, as we argue, counterproductive addictivebehaviors can arise even with sophisticateddecision-makers, efforts to eradicate addic-tion solely through education and information aremisguided.

IV. Positive Analysis

A. Comparative Dynamics

Our comparative dynamic results concern theintensity with which the DM voluntarily usesthe addictive substance. We study two notionsof intensity. We say that the disposition to use isgreatest for (E, 1), followed in order by (E, 0),(A, 0), and (R, 0). Thus, for example, the dis-position to use increases when the DM’s choiceshifts from (A, 0) to (E, 1). We judge theintensity of intentional use by asking whetherthe DM plans to consume the substance. Thus,intentional use is highest for (E, 1), and equiv-alent for (E, 0), (A, 0), and (R, 0).25 An increasein intentional use implies an increase in thedisposition to use, but not vice versa. Bothdefinitions permit us to compare the intensity ofvoluntary use both within states and acrossstates.

We study comparative dynamics with re-

spect to the elements of the parameter vector�. Since some of these are simple functions ofprices and income (q, rs, and ys), comparativedynamics with respect to the latter variablesfollow immediately. We are particularly in-terested in the effects of the parameters ps

E

and psA, since these are directly tied to the

novel aspects of our framework (stochasticevents that create pathological discrepanciesbetween preferences and choice). We are alsointerested in the effects of us

A, bsA, and us

R,since these parameters are relevant only if thenovel components of our model are opera-tional ( ps

E � 0).

1. Changes in Individual Parameters.—Inpractice, we are rarely interested in phenomenathat affect only one state-specific parameter.However, examining these effects in isolationlays the groundwork for subsequent results in-volving changes in groups of parameters.

PROPOSITION 1: (i) The disposition to use instate j is:

(i-a) weakly increasing in bka and uk

a, andweakly decreasing in pk

a, for k � j;(i-b) weakly decreasing in bk

a and uka, and

weakly increasing in pka, for k � j;

(i-c) weakly decreasing in pjE and uj

R andweakly increasing in bj

E.

(ii) Intentional use in state j is invariant withrespect to pj

E, pjA, uj

A, bjA, and uj

R.

Parts (i-a) and (i-b) establish the intuitiveproperty that beneficial changes in parametersfor more (less) advanced states of addictionincrease (decrease) the disposition to use in thecurrent state. Thus, an increase in the likelihoodor severity of a cue-triggered mistake in state sinduces the DM to make choices that reduce thelikelihood of reaching state s. Part (i-c) is alsointuitive: the disposition to use in the currentstate rises with the benefits to current use andfalls with both the desirability of rehabilitationand the likelihood that the exposure activitytriggers the hot mode (since this increases theattractiveness of concerted abstention and reha-bilitation relative to half-hearted abstention).Part (ii) is perhaps less transparent. A change inparameters can affect intentional use only if it

mentarities. Notably, W. E. McAuliffe (1982) showedthat only 27.5 percent of heroin addicts experiencedcue-triggered withdrawal symptoms, and only 5 percentof these felt these symptoms were responsible for recid-ivism.

25 For some parameter values, the DM may be indif-ferent between two (but never more than two) choices inany particular addictive state. When this occurs, the set ofoptimal choices is always {(E, 1), (E, 0)}, {(E, 0), ( A,0)}, {(E, 0), (R, 0)}, or {( A, 0), (R, 0)}. We say thata change in parameters from �� to �� weakly increases thedisposition to use (intentional use) if it leads to a weakincrease in both the minimum and maximum dispositionto use (intentional use) among optimal choices, andstrictly increases the disposition to use (intentional use) ifeither the minimum or the maximum strictly increasesand neither declines.

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tips the balance between (E, 1) and (E, 0).26

Clearly, this comparison does not implicate pjA, uj

A,bj

A, or ujR; neither does it depend on pj

E.27

The characterization of directional effects inProposition 1 is not quite complete. This isbecause the effects of bj

A, ujA, and uj

E on thedisposition to use in state j can be positive ornegative, depending on the parameter values.

2. Changes in Groups of Parameters.—Toexamine the effects of policy and environmentalchanges, and to make comparisons between op-timal decision rules for different substances, wemust typically consider the effects of varyingmany parameters simultaneously. For example,a general reduction in the cost of rehabilitation(due perhaps to the development of a new thera-peutic drug) raises us

R for all s. Likewise, whenone substance is more addictive than another, it isnatural to assume that ps

a is higher at every state s.For any state-indexed variable zs, we say that

a change from (z�s)s�0S to (z�s)s�0

S represents ageneral increase (decrease) if z�s � z�s (z�s � z�s)for all s, with strict inequality for some s. Prop-osition 1 suggests that compound parameterchanges of this type often have ambiguous ef-fects on use. For example, a general increase inus

R or a general decrease in psa can reduce the

disposition to use in state j by making lowerstates (weakly) more attractive but can alsoincrease this disposition by making higherstates (weakly) more attractive.

It is nevertheless possible to reach a numberof conclusions without imposing additionalstructure. Public policy discussions often em-phasize initial use, choices among casual userswho are at risk of becoming addicted, and pat-

terns of behavior among hard-core addicts. Toshed light on initial use, we study behavior instate 0. To shed light on the choices of casualusers, we examine behavior in state 1, the lengthof the first intentional use interval (defined as{1, ... , s1 � 1} where s1 is the largest integersuch that (E, 1) is chosen for all s � {1, ... , s1 �1} but not for s1), and the length of the initialresistance interval (defined as {1, ... , s2 � 1}where s2 is the largest integer such that (R, 0) ischosen for all s � {1, ... , s2 � 1} but not fors2).28 To shed light on the behavior of thosewith substantial cumulative exposure, we focuson choices in state S, as well as the length of thefinal resignation interval (defined as {s3 �1, ... , S} where s3 is the smallest integer suchthat (E, 1) is chosen for all s � {s3 � 1, ... , S}but not for s3). While these aspects of behaviorrespond ambiguously to general changes in someparameters, other effects are unambiguous.29

PROPOSITION 2: (i) A general increase in psE

or psA, or a general reduction in us

A or bsA, weakly

decreases the disposition to use in state 0 (andstate 1 for ps

E), weakly shortens the first inten-tional use interval, weakly lengthens the initialresistance interval, and weakly lengthens thefinal resignation interval.

(ii) A general increase in usR weakly increases

the disposition to use in all states (includingstate 0) up to (but not including) the first state inwhich rehabilitation is an optimal choice afterthe increase. It also weakly lengthens the firstintentional use interval, weakly reduces the dis-position to use in state S, and weakly shortensthe final resignation interval.

(iii) A general increase in usE or bs

E weaklyshortens the initial resistance interval. In addi-tion, a general increase in bs

E weakly increasesthe disposition to use in states 0 and 1.

How do patterns of use compare for two sub-stances that are the same in all respects, except

26 If (E, 0) yields a higher expected discounted payoffthan (E, 1), then (E, 1) is obviously not the DM’s bestchoice. Conversely, if (E, 1) yields a weakly higher ex-pected discounted payoff than (E, 0), then (E, 1) is neces-sarily preferred to both (A, 0) and (R, 0). To understandwhy, note that (a) us

E � bsE � �Vmin{S,s�1}(�) � us

E ��Vmax{1,s�1}(�) � us

a � �Vmax{1,s�1}(�) for a � A, R[where the first inequality follows because the DM weaklyprefers (E, 1) to (E, 0), and the second inequality followsfrom Assumption 2], and (b) us

E � bsE � �Vmin{S,s�1}(�) �

usA � bs

A � �Vmin{S,s�1}(�) (by Assumption 2). For (R, 0),the desired conclusion follows from (a); for (A, 0), it fol-lows from (a) and (b).

27 The DM prefers (E, 1) to (E, 0) if and only if heprefers it to E with the certainty of abstention. The proba-bility pj

E does not enter this comparison.

28 At least one of these intervals is always empty. Thelength of the initial resistance interval is relevant only if pa-rameters change after the DM starts using the substance (oth-erwise he would never advance beyond state 1). In that case, itsheds light on the DM’s ability to achieve permanent recovery.

29 To allow for multiple optima, we say that a parameterchange weakly shortens (lengthens) an interval if it weaklyreduces (increases) both the minimum and maximum lengthof the interval.

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that one is more addictive than the other (highervalues of ps

E and psA for all s)? Part (i) of the

proposition provides a partial answer. Not surpris-ingly, an increase in addictiveness discourages useamong new users (reducing the disposition to usein state 0, shortening the first intentional use in-terval, and lengthening the initial resistance inter-val). Strikingly, it always has the opposite effecton hard-core addicts, producing longer resignationintervals. One might think that an increase inaddictiveness might discourage a relatively ad-vanced user from taking actions likely to placehim in an even more highly addicted state, but thiseffect never materializes in the final resignationinterval. Instead, the DM is influenced by theincreased futility of resisting use at lower states.He resigns himself to severe addiction because herecognizes his powerlessness to control his subse-quent behavior adequately at lower states, despiteintentions to abstain. According to part (i), generalchanges in the parameters governing payoffs fromthe avoidance activity (us

A and bsA) have similar

effects.How does an improvement in rehabilitation

technology (higher values of usR for all s) affect

patterns of use? According to part (ii) of theproposition, use among those with low cumula-tive exposure increases in a strong sense (thedisposition to use rising in all states up to thepoint where the DM enters rehabilitation). Sincerehabilitation cushions the negative effects ofaddiction, this is not surprising. As in part (i),this development has the opposite effect onhard-core addicts, shortening the resignation in-terval. Notably, increasing us

R only for states inthe resignation interval would have no effect onbehavior. Thus, for a general increase in us

R, theDM turns away from intentional use in theresignation interval because rehabilitation be-comes a more attractive option in lower states.

Part (ii) of Proposition 2 also implies that animprovement in rehabilitation technology canhave the perverse effect of shifting the entirepopulation distribution to more addicted states.Provided that all members of the populationstart out at s � 0, this occurs when a generalincrease in us

R raises the lowest state at whichthe DM selects rehabilitation.30

Part (iii) of the proposition concerns usE and

bsE. These parameters do not relate to the novel

features of our model, but we have includedtheir effects for completeness.

Proposition 2 underscores the fact thatchanges in the environment have complex ef-fects on use, often driving consumption amongnew users and hard-core addicts in oppositedirections. It is natural to wonder whether thereare any general parameter changes that alwayshave the same directional effect on the disposi-tion to use in every addictive state. Our nextresult provides an example: if baseline well-being deteriorates more rapidly as the addictivestate rises, then the disposition to use is lower inevery state. This property holds in the standardrational addiction framework (ps

a � 0) and ispreserved in the presence of cue-triggeredmistakes.

PROPOSITION 3: Consider �� and �� derived,respectively, from w� s(e, x, a) and w� s(e, x, a) �w� s(e, x, a) � ds (with the same values of ys, rs,q, and ps

a). If ds is weakly increasing in s, thedisposition to use is weakly higher with �� thanwith �� for all s.

Propositions 2 and 3 shed light on the rela-tionship between income and the consumptionof addictive substances. While an increase inincome raises the inclination to experiment rec-reationally, it can reduce the inclination to useat higher addictive states; accordingly, themodel can generate higher rates of addictionamong the poor. To see why, suppose the utilityfunction has the following separable form: ws(e,x, a) � u(e) � vs(x, a). What happens when weadd a fixed increment, �, to income in all states?The parameters us

E and usA all rise by u(ys �

�) � u(ys), which is weakly increasing in s(assuming ys is weakly decreasing in s). Theparameters us

R increase by u(ys � rs � �) �u(ys � �) � u(ys � �) � u(ys), and theparameters bs

a increase by [u(ys � q � �) �u(ys � �)] � [u(ys � q) � u(ys)] � 0. Thus, wecan decompose the effect into three pieces: (a) afixed increase in us

a equal to u(ys � �) � u(ys)for each s and a � E, A, R; (b) a general

30 From simulations, we know that a general increase inus

R increases the lowest state at which the DM selectsrehabilitation for some parameter values and decreases it forothers.

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increase in usR, and (c) a general increase in bs

a

for a � E, A. Proposition 3 tells us that theeffect of the first piece is to weakly increase thedisposition to use in every state. Part (ii) ofProposition 2 tells us that the second pieceincreases the disposition to use in state 0, andparts (i) and (iii) tell us the same thing for thethird piece. Thus, the addictive substance isnormal in state 0. Note, however, that the sec-ond and third pieces have ambiguous effects onthe disposition to use in more advanced states ofaddiction, which is why the income effect canchange signs.

B. Patterns of Consumption

According to our theory, the particular pat-tern of consumption that emerges in anyinstance depends systematically on the charac-teristics of the individual (including aptitude forcognitive control), the substance, and the envi-ronment. For reasonable parameter values, themodel generates a wide variety of observedconsumption patterns.31

Consider a highly addictive substance (psa

large). If baseline well-being declines rapidlywith consumption, the DM may choose never touse [(E, 0) at s � 0]. For most people, crackcocaine appears to be a good example of this(see Goldstein, 2001). In contrast, if the declinein baseline well-being is initially gradual butaccelerates from one state to the next, the modelcan produce a pattern of progressive resistance.That is, the DM may begin using the substanceintentionally, engage in half-hearted abstention(and therefore use intermittently) after reachingan intermediate addictive state, and shift to con-certed abstention after a string of bad luck. Ifbad luck continues, precommitment to absten-tion through rehabilitation may follow with sub-sequent probabilistic recidivism. If baselinewell-being flattens out for sufficiently advancedaddictive states (the DM “hits bottom”), themodel can also produce resignation. That is, aDM may give up, opting for (E, 1) once hereaches a highly addicted state after an unsuc-cessful battle to abstain.

Now consider an enjoyable substance forwhich baseline well-being declines slowly withconsumption. Irrespective of whether the prob-ability of entering the hot mode is high or low,constant use often emerges. Caffeine potentiallyfits this description.

Finally, a sufficiently sharp drop in the plea-sure generated by the substance from one ad-dictive state to the next can produce intentionalrecidivism. That is, the DM may choose (E, 1)in one state and (R, 0) in the next, in which casehe oscillates between the two. He enters reha-bilitation in each instance without any desire tostay clean; he knows that he will resume usingthe substance upon release from rehabilitation,and fully expects to enter rehabilitation onceagain. This pattern is in fact observed amongserious heroin users when repeated use dilutesthe “high” (see Michael Massing, 2000). It isevidence of fairly sophisticated, forward think-ing among junkies whose objective is to renewthe high by temporarily getting clean, and whoknow that rehabilitation accomplishes this morereliably than abstention.

C. Explaining the Distinctive Features ofAddiction

In Section I we argued that addiction is as-sociated with five distinctive behavioral pat-terns. Our theory generates each of thesepatterns.

1. Unsuccessful Attempts to Quit.—Supposelife circumstances change over time, graduallyshifting the parameters of the DM’s problemfrom �� to ��. Suppose the DM’s best choice forstate 0 is (E, 1) if �� prevails forever, but thatthe optimal decision rule prescribes either (E,0), (A, 0), or (R, 0) for all s if �� prevailsforever. If the shift from �� to �� is eitherunanticipated or anticipated and sufficientlyslow, the DM starts using the substance butsubsequently decides to quit unconditionally.With p1

a � 0, the attempt is unsuccessful wheneither (E, 0) or (A, 0) is chosen in state 1.

2. Cue-Triggered Recidivism.—For the set-ting described in the previous paragraph, unsuc-cessful attempts to quit are associated with highrealizations of c(a, �) (that is, exposure to rel-atively intense cues).

31 We have generated each of the patterns described inthis section through numerical simulations, which we omitto conserve space.

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3. Self-Described Mistakes.—In our model,choices and preferences diverge whenever theDM selects (E, 0) or (A, 0) and then enters the hotmode. This constitutes a recognizable mistake.32

4. Self-Control through Precommitment.—The choice (R, 0) is a costly precommitment;under our assumptions, its only purpose is toremove the option of consuming the substance.

5. Self-Control through Behavioral and Cog-nitive Therapy.—The choice (A, 0) involvescostly cue-avoidance. Its only purpose is to re-duce the probability of encountering cues thattrigger mistaken usage. Though not modeledexplicitly, cognitive therapy would influencebehavior in our setting by increasing MT (that is,raising the threshold impulse required to defeatcognitive control).

Our three central premises play critical rolesin accounting for each pattern. We can removecue-triggered mistakes by setting MT � ��, sothat the DM always exercises cognitive control.With this change, ps

a � 0 for all a and s, and theDM always choose either (E, 1) or (E, 0). Allattempts to quit are successful, and there is norecidivism. Preferences and choices never di-verge, so there are no mistakes. The DM neverexercises self-control through precommitmentby choosing (R, 0), or through cue-managementby choosing (A, 0). Some sophistication is alsoessential; otherwise the DM would ignore hissusceptibility to cue-triggered errors and makechoices based on the mistaken assumption thatps

a � 0 for all a and s.We also observed in Section I that aggregate

consumption of addictive substances respondsto prices and information in the usual way. Thistoo is consistent with our theory, as users some-times make decisions in the cold mode.

V. Demand-Side Policy Analysis

In this section we study the welfare effects ofvarious public policies concerning addictive

substances. In keeping with the focus of thepreceding sections, we restrict attention to “de-mand side” welfare effects, ignoring “supplyside” consequences associated with the devel-opment of black markets, the spread of corrup-tion, and enforcement costs.33

A. The Welfare Criterion

In formulating our model, we retain thestandard assumption that each individual hasa single coherent set of preferences. Our de-parture, which is grounded in the evidencefrom neuroscience presented in Section II, isto assume that there are imperfections in theprocess by which the brain makes choices,and that these imperfections give rise to mis-takes in identifiable circumstances. Since theindividual has only one set of preferences,discounted experiential utility, ¥t�0

� �twst(et,

xt, at), accurately measures his well-being,and is unambiguously the appropriate welfarestandard.34

It may be tempting to reinterpret our model asone with multiple selves, “hot” and “cold,”where the preferences of the hot self can beinferred from choices in the hot mode. Underthat interpretation, our use of cold preferencesas a welfare standard is arbitrary. In our view,this interpretation commits a fallacy. By assum-ing that choices are always consistent with un-derlying preferences, it assumes away thepossibility that individuals make systematicmistakes. This possibility is a central premise ofour analysis and is justified based on the state ofknowledge concerning the neuroscience of ad-diction. One can certainly dispute the validity ofthis premise. However, given the premise andour adherence to the standard formulation ofpreferences, the correct welfare criterion isunambiguous.

32 When the HFM-generated forecast is sufficiently posi-tive, cognitive override may not occur even when higher cog-nition forecasts undesirable consequences. Thus, an individualmay use a substance while simultaneously recognizing (interms of higher cognitive judgment) that this is a mistake.

33 Supply-side effects are discussed elsewhere (see,e.g., MacCoun and Reuter, 2001; J. Miron and J.Zwiebel, 1995).

34 This is in contrast with a number of the behavioraltheories discussed in Section VI, for which one must eitheruse a weak welfare standard such as the Pareto criterion(applied to multiple selves or multiple perspectives), orselect a particular method of resolving conflicting prefer-ences, for example, by respecting the tastes of only one selfor perspective.

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B. Policy Objectives

What might society hope to accomplishthrough public policies regarding addictive sub-stances? Possible objectives include protectingthird parties from externalities (e.g., second-hand smoke), combatting misinformation andignorance, moderating the consequences of un-insurable risks, and helping consumers avoidmistakes. Both externalities and informationalproblems provide well-understood rationalesfor government intervention, and neither is in-trinsically linked to the novel aspects of ourframework. We therefore focus primarily on thelast two sets of objectives.

1. Amelioration of Uninsurable Risks.—Riskand uncertainty relating to the effects of envi-ronmental cues on decision processes are cen-tral to our model. The DM’s lack of knowledgeconcerning future states of nature, �t, preventshim from perfectly forecasting future decisionmodes and choices in states for which he plansto select either (E, 0) or (A, 0) and therebycreates uncertainty about subsequent addictivestates. This translates into monetary risk be-cause his resources depend on his addictivestate, and because variation in expenditures onthe addictive substance and rehabilitation implyvariation in consumption of the nonaddictivegood. Since the financial consequences of ad-diction—its effects on job retention, productiv-ity, out-of-pocket medical costs (includingrehabilitation), and, for some substances (e.g.,cocaine, heroin), direct expenditures—are oftensubstantial, this risk is quantitatively significant.35

From the perspective of risk (ignoring otherconsiderations), policies that create actuariallyfair redistributions over realizations of futurestates of nature are beneficial (harmful) whenthey distribute resources toward (away from)outcomes for which the marginal utility of non-addictive consumption is relatively high. In sub-sequent sections, we initially impose theassumption that ws(e, x, a) � u(e) � vs(x, a),which implies that the marginal utility derivedfrom nonaddictive consumption depends only

(and inversely) on the level of nonaddictiveconsumption. We focus on this case because weregard it as a natural benchmark, but we alsodiscuss the implications of relaxing separability.

We assume throughout that private insurancemarkets fail completely. As is well known, thewelfare effects of public policies that redistrib-ute resources across states of nature can dependon the specific factors that cause markets to fail(see, e.g., Mark V. Pauly, 1974). It is thereforeimportant to specify the source of the marketfailure and to explain how it interacts with thepolicies considered.

We assume that private insurance companiesare unable either to observe or to verify the stateof nature �t, cues, the DM’s decision mode, theaddictive state, lifestyle activities, or consump-tion of the addictive substance.36 The govern-ment is similarly handicapped. However, unlikeprivate companies, it can observe transactionsinvolving legal addictive substances (typicallywithout identifying purchasers), and it can ma-nipulate the prices of these commoditiesthrough taxation and subsidization.

Private companies can observe aspects oftreatment (rehabilitation and medical costs), butwe assume that treatment insurance is unavail-able because (i) practical considerations pre-clude ex ante contracting at age zero when risksare homogeneous (e.g., before teen or even pre-teen exposure), and (ii) adverse selection arisingfrom ex post heterogeneity precludes ex postcontracting.37 The government is similarlyhandicapped by the second problem but canavoid the first by imposing a universal policy onall consumers ex ante.

2. Mistake Avoidance.—Public policy canpotentially improve welfare by creating con-ditions that reduce the frequency with whichindividuals experience decision process mal-functions or by forcing them to make alternative

35 Among chronic users, average annual expenditures oncocaine and heroin exceeded $10,000 in 1999 (Office ofNational Drug Control Policy, 2001a).

36 With respect to the addictive state, clinical diagnosisof addiction is both costly and imprecise. Consumption ispotentially observable when the substance is dispensed as aprescription medicine, but in that case the same problemsarise as for treatment (discussed in the next paragraph).

37 In practice, private health insurance policies do pro-vide some coverage for the treatment of addiction. Yetmany people are not insured, and coverage is typicallyincomplete.

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choices when malfunctions occur. In our model,these possibilities correspond, respectively, toreducing the probability of entering the hot modeand to ensuring abstention when appropriate.

In solving the DM’s optimization problem,we treated the probabilities of entering the hotmode, ps

a, as fixed parameters. Many of thepolicies considered below potentially changethese parameters; for example, one can model aban on advertising as a reduction in the volumeof cues encountered. For some portions of ouranalysis, we also allow for the possibility that ps

a

depends on the price of the addictive good, q,and/or the DM’s income, y. We reason that thefrontal cortex is more likely to generate strongercognitive incentives and override cues when theimmediate consequences of use are more se-vere.38 Accordingly, we assume that MT weaklydecreases with y, weakly increases with q, andweakly increases with an equal increase in y andq.39 It is useful to state these assumptions morecompactly in terms of ps

a (with the added tech-nical requirement of differentiability).

ASSUMPTION 3: The probability of enteringthe hot mode, ps

a, is differentiable in q and ywith

��

�qps

a ��

�yps

a � 0.

C. When Is Government InterventionJustified?

When do the objectives discussed in Sec-tion V B potentially justify government inter-

vention? The following result provides aninitial answer. Here and elsewhere, we saythat use is continual if the DM selects (E, 1)in every state.

PROPOSITION 4: (i) Continual use solves theDM’s choice problem if and only if it is first best(in the sense that it solves the maximizationproblem when ps

a � 0 for all a and s). (ii)Suppose there is some state s� with ps�

E � 0 suchthat (E, 1) is not a best choice in s�. Then theDM’s choices are not first best (in the sense thatsetting ps

a � 0 for all a and s and reoptimizingstrictly increases the value function for somestates).

Part (i) tells us that noncontinual use isnecessary for the existence of a beneficialpolicy intervention. Laissez-faire is thereforethe best policy for substance users who makeno serious attempt to abstain (e.g., contentedsmokers or coffee drinkers). Notably, thisconclusion follows even when the substancein question is highly addictive ( ps

a risessharply with s) and well-being declines sig-nificantly with long-term use. The intuition isthe same as for the final portion of Proposi-tion 1.

Part (ii) tells us that noncontinual use is suf-ficient for the existence of a theoretical policyintervention that benefits the DM, provided thedeparture from continual use occurs in a statefor which the DM is susceptible to cue-triggeredmistakes. Of course, this intervention may beimpractical given the government’s informationconstraints.

D. A Framework for Tax Policy Analysis

The formal results below concern the de-sirability of various types of tax policies. Fol-lowing standard practice, we evaluate thesepolicies by embedding our decision-maker ina simple economy and studying effects onequilibrium allocations. Here we outline thestructure of the economic environment. Nota-tion and some additional formal details ap-pear in Appendix A.

The economy consists of an infinite sequenceof generations. In the absence of governmentintervention, every member of every generationis identical and confronts the decision problem

38 Since cognitive control often must be asserted quicklyif at all, and since extrapolation of future consequences istime consuming, we implicitly assume that the deploymentof cognitive control responds to variation in immediatecircumstance-specific consequences, but not to variation infuture circumstance-specific consequences.

39 When q is higher or y is lower, the immediate negativeconsequences of use are plainly greater, and potentiallymore likely to occupy the DM’s awareness. When q and yrise by equal amounts, the immediate hedonic payoff fromabstention rises while the immediate hedonic payoff fromuse is unchanged, so the immediate negative consequence ofuse is again more severe. It would also be natural to assumethat cue exposure, c(a, �), weakly declines in q (since useamong social contacts declines), and this would reinforceAssumption 3. In principle, c(a, �) could rise or fall withincome.

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described in Section III. We interpret the DM’sdiscount factor � as the product of a pure rate oftime preference and a constant single-periodsurvival probability. We assume that the size ofeach new generation is just sufficient to keep thetotal population constant. The total populationis very large, and realization of hot and coldstates are independent across DMs, so there isessentially no aggregate uncertainty. Income ar-rives in the form of the nonaddictive good, andthe addictive good is produced under competi-tive conditions with constant-returns-to-scaletechnology, as are rehabilitation services. Thus,q and rs are fixed and equal to unit productioncosts (where the costs of rehabilitation servicespotentially vary with the addictive state).

In each period, the government can tax (orsubsidize) either the addictive substance or re-habilitation (we consider these instruments oneat a time). There is no revenue requirement;taxes are purely corrective. By assumption, thegovernment cannot condition the associated taxrates on either the DM’s age or his addictivestate. This could reflect either the practical dif-ficulties associated with tailoring these taxesand subsidies to an individual’s conditions (in-cluding the need for clinical diagnosis) or pri-vacy concerns. Imagine in particular that thetax/subsidy for the addictive substance is eitherapplied to anonymous transactions (like a salestax) or imposed on producers (like a value-added tax), while the rehabilitation tax/subsidynominally falls on service providers (again, likea value-added tax). The government can also useage-specific (equivalently, generation-specific)lump-sum instruments. An intertemporal policyspecifies values for all available tax/subsidy in-struments in every period.

Since there is no borrowing or lending in ourmodel, and since we do not wish to advantagethe government artificially, we assume that pol-icies cannot redistribute resources across peri-ods. We say that an intertemporal policy isfeasible if there is, for each generation, an op-timal decision rule such that the government’sbudget is balanced in every period. Feasiblepolicies permit within-period transfers acrossgenerations, which can mimic borrowing andlending, thereby leaving the government in anartificially advantageous position. One couldtherefore argue for a stronger restriction requir-ing government budget balance for each gener-

ation within each period. While we impose theweaker requirement, our results also hold forthe stronger requirement.40

A steady-state policy prescribes a constanttax rate and constant age-specific lump-sumtaxes. Notably, each individual’s problem ispotentially nonstationary because steady-statelump-sum tax/subsidies may change with age.The set of feasible steady-state policies includesthe zero-tax alternative, henceforth denoted �,for which all tax/subsidy instruments are set tozero.

In the next two sections, we focus on thesteady-state welfare effects of steady-statepolicies (often dropping the modifier “steady-state” for brevity). For any steady-state pol-icy, we use the lifetime expected discountedhedonic payoff for the representative individ-ual as our welfare measure. An optimalsteady-state policy maximizes this payoffamong all feasible steady-state policies. Thisobjective function respects each individual’stime preference over his own lifetime but isinfinitely patient with regard to intergenera-tional comparisons, in effect placing equalweight on all generations. Since the DM’schoice set is discrete, best choices are ofteninsensitive to small parameter changes, so theoptimal policy is typically not unique.

E. Taxation and Subsidization of AddictiveSubstances

Addictive substances are often heavily taxed(e.g. nicotine and alcohol) and occasionallysubsidized (see, e.g., the description of a Swissheroin prescription program in MacCoun andReuter, 2001). Some policy analysts argue fortaxation of addictive substances on the groundsthat this discourages excessive use (e.g., Gruberand Koszegi, 2001). Others suggest that, in theabsence of externalities, use is voluntary solaissez-faire is best (e.g., Becker and Murphy,1988). Our theory of addiction suggests a morenuanced view.

Proposition 5 below relates the sign of theoptimal tax rate on the addictive substance to

40 In fact, the proof of Proposition 5 requires only minoradjustments when we impose the strong requirement; Prop-osition 6 holds as stated under either restriction.

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observable patterns of consumption. Notably,the consumption patterns that determine opti-mal tax rates are endogenous, and the proposi-tion requires us to assess them at the optimal taxrates.41 This feature is common to many well-known optimal-tax results. For example, theRamsey rule relates optimal commodity taxrates to compensated demand elasticities evalu-ated at the optimal tax rates (though the rule isfrequently stated in a way that disguises thisdependency).

The proposition refers to the following twopossible patterns involving the likelihood ofuse.42

Condition A: For every age t, the likelihood ofuse is weakly increasing in s over states reachedwith positive probability at that age, and theDM does not enter rehabilitation in the lowestsuch state.43 Moreover, at some age t, at leasttwo addictive states are reached with positiveprobability.

Condition B: For every age t, the likelihood ofuse is weakly decreasing in s over states reachedwith positive probability at that age.44 More-over, at some age t, at least two addictive statesare reached with positive probability, with nei-ther expected use nor ys constant over suchstates.

For each condition, the requirement “for all t”is less demanding than it might initially appear.Remember that, in the absence of taxes andsubsidies, each DM’s problem is stationary, andthe best choices at each state are independent ofage. In a steady state for the economy, agematters only because it affects the lump-sum tax(or subsidy). If the lump sums are relativelysmall, the general pattern of use will tend to besimilar at different ages provided it is not toosensitive to small changes in income.

PROPOSITION 5: Suppose that ws(e, x, a) �u(e) � vs(x, a), that ys is weakly decreasing ins, and that ps

a does not depend on prices orincome.

(i) Consider an optimal steady-state policy forwhich all budget-balancing optimal deci-sion rules satisfy Condition A. The taxrate on the addictive substance is strictlynegative.

(ii) Consider an optimal steady-state policy forwhich all budget-balancing optimal deci-sion rules satisfy Condition B. If q is suffi-ciently small, the tax rate on the addictivesubstance is strictly positive.

To develop intuition for this result, note thattaxation (or subsidization) potentially affectswelfare through three channels. First, it canchange decisions in the cold mode. Second, itcan redistribute resources across uncertain out-comes. Third, it can alter the effects of environ-mental cues on operational decision modes(through the trigger mapping T). With ps

a inde-pendent of prices and income, the third channelvanishes (we discuss the implications of rein-stating it below). Effects involving the secondchannel dominate welfare calculations for smalltaxes and subsidies because they are generallyfirst order, while effects involving the first chan-nel are not.45 Accordingly, starting from a sit-uation with no taxes, one can determine whethera small tax or subsidy improves welfare byfocusing on the correlation between the taxed

41 Alternatively, one can make statements about welfare-improving changes, assessing usage patterns at arbitrarystarting points. For example, from the proof of Proposition5, we also have the following results: eliminating a positivetax is beneficial if initially Condition A holds; eliminating apositive subsidy is beneficial if initially Condition B holdsand q is small; if Condition A holds with the no-tax policy�, a small subsidy is welfare improving; if Condition Bholds with � and q is small, a small tax is welfare improving.

42 In Appendix A, we define st( ) as the probability of

use in state s at age t given a decision rule , accounting forthe possibility of entering the hot mode. Here, the “likeli-hood of use” refers to s

t( ). Note that the likelihood of useis necessarily weakly increasing in s when the disposition touse is weakly increasing in s.

43 Since the DM’s decision problem is potentially non-stationary, it is possible for him to find himself in a statebeyond the lowest one in which he would select rehabilita-tion during the same period.

44 This occurs, for example, if best choices are unique,the disposition to use is weakly decreasing in s, the firstintentional use interval is nonempty, and ps

a is constantoutside of this interval (i.e., the DM is fully addicted by thetime he attempts to refrain from consuming the substance).

45 With continuous decision variables and interior solu-tions, the first channel would be second order for small taxesand subsidies. With discrete decision variables (as in ourcurrent model), it is literally zero for sufficiently small taxesand subsidies.

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activity and the marginal utility of nonaddictiveconsumption.46 This helps to build intuitionconcerning the signs of optimal tax rates. Oneshould bear in mind, however, that the optimal-tax problem is more complex because, at theoptimum, welfare effects involving the firstchannel (incentive effects) are also first order.

A policy provides de facto insurance if itredistributes age-t resources toward outcomesin which the marginal utility of nonaddictiveconsumption is relatively high, which in thebenchmark case [ws(e, x, a) � u(e) � vs(x, a)]means that the level of nonaddictive consump-tion is relatively low. This occurs when otherexpenditures are high and when the state is itselfhigh (since ys weakly declines with s).47 Asubsidy necessarily redistributes resources to-ward outcomes with relatively high expendi-tures on addictive substances. Moreover, if thelikelihood of use increases with the addictivestate (Condition A), it also redistributes re-sources toward outcomes for which income isrelatively low. Since both effects are beneficial,a subsidy is desirable [part (i)]. Conversely, ifthe likelihood of use declines with the addictivestate (Condition B), a positive tax (with abudget-balancing lump-sum payout) redistrib-utes resources toward outcomes for which in-come is relatively low and rehabilitationexpenditures are relatively high. It also redis-tributes resources away from outcomes withrelatively high expenditures on addictive sub-stances, but this effect is secondary when q issmall, rendering the tax beneficial [part (ii)].

Proposition 5 underscores the fact that differ-ent policies are appropriate for different addic-tive substances, and that the characteristics ofgood policies are related to usage patterns. As

we have seen in Section IV, usage patterns arein turn systematically related to aspects of thesubstance, the user, and the environment.

Part (i) suggests that a subsidy may be wel-fare improving in the case of a substance forwhich initial use tends to be “spur of the mo-ment,” but where an intention to use becomesincreasingly predominant as the individual be-comes more addicted. The argument for subsi-dization is stronger when the substance inquestion is more expensive. The apparent im-plication that the government might beneficiallysubsidize substances such as cocaine and heroinis provocative to say the least, and it should betempered by several considerations, includingthe likely existence of externalities, the poten-tial effects of price and income on the triggermechanism (discussed below), and the fact thatCondition A apparently does not hold univer-sally, as many addicts seek treatment. Still, ouranalysis adds a potentially important cautionarynote to existing discussions of the benefits of sintaxes (e.g., Gruber and Koszegi, 2001; TedO’Donoghue and Matthew Rabin, 2004), whichcan violate social insurance principles by penal-izing those who have experienced bad luck. Italso provides a framework for understandingthe potential benefits of somewhat more refinedapproaches, such as the Swiss policy of provid-ing cheap heroin to users who cross some diag-nostic threshold of addiction, and who are notinterested in rehabilitation.

Part (ii) suggests that a tax may be welfareimproving in the case of an inexpensive sub-stance that people initially use regularly, forwhich attempts to abstain begin only after cuetriggers are well established and stable (so thatthey change little with further use). Coffee, cig-arettes, and alcohol arguably fall into thiscategory.

How robust are these findings? Complemen-tarity between addictive and nonaddictive con-sumption would raise the marginal utility ofnonaddictive consumption whenever the DMuses the addictive good, strengthening the ad-vantages of a subsidy, thereby reinforcing part(i) but potentially reversing part (ii). Substitut-ability would reduce the marginal utility of non-addictive consumption whenever the DM usesthe addictive good, strengthening the advan-tages of a tax, thereby reinforcing part (ii) butpotentially reversing part (i).

46 There are some subtleties here. A small tax or subsidythat changes cold-mode decisions can alter the correlationbetween a taxed activity and the marginal utility of nonad-dictive consumption, thereby changing effects through thesecond channel. With discrete choice sets, the pertinentcorrelation can change dramatically even for tiny taxes andsubsidies.

47 In principle, the government could also redistributeresources through an income tax. Implicitly, we take theincome-tax system as exogenously given. This is reasonableas long as addiction is not one of the primary factorsinfluencing income distribution and the equity–efficiencytrade-offs that an optimal income tax system is intended toaddress.

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We can also relax the assumption that psa is

invariant with respect to taxation and subsidi-zation. A tax of � per unit increases price by �and, from individuals of age t, raises less than �in per capita revenues. Suppose the governmentdistributes the revenue raised from each agegroup back to the same age group as a lumpsum. Since the amount received by each indi-vidual is less than the price increase, Assump-tion 3 implies that ps

a falls in every state. Anypolicy that reduces ps

a weakly increases welfarethrough the third channel [strictly if the state isreached with positive probability and the DMselects (a, 0)]. This strengthens the advantagesof a tax, reinforcing part (ii) of the proposition,and potentially reversing part (i).48

F. Harm-Reduction Policies

Subsidization of rehabilitation is relativelycommon. Popular justifications appeal to thenotion that treatment should be affordable anduniversally available, though sometimes posi-tive externalities are invoked.

In the context of our model, there are at leasttwo reasons to subsidize rehabilitation. First,this provides de facto insurance for a large,uncertain expense. Second, under Assumption3, the DM is less prone to make cue-triggeredmistakes when he receives resources in kind(through a rehabilitation subsidy) rather than incash.

There is, however, an additional consider-ation arising from the correlation between reha-bilitation and income. If rehabilitation is morelikely at advanced stages of addiction, then asubsidy beneficially redistributes resources to-ward low-income states. Since this reinforcesthe considerations discussed in the previousparagraph, subsidized rehabilitation is unambig-uously desirable. If, however, rehabilitation isless likely at advanced stages of addiction, thena subsidy detrimentally redistributes resourcestoward high-income states, offsetting the con-siderations discussed in the previous paragraph.Formally, one can prove a result analogous toProposition 5, relating the optimal tax/subsidy

treatment of rehabilitation to rehabilitationpatterns.

Our next result deals instead with the welfareeffects of small rehabilitation taxes and subsi-dies. It shows that a small rehabilitation subsidyis beneficial, and a small tax harmful, underextremely general conditions: at the no-tax al-ternative �, rehabilitation must be chosen insome state, and there must be some random-ness.49 Here, we allow from the outset for thepossibility that ps

a depends on ys and q.

PROPOSITION 6: Suppose that ws(e, x, a) �u(e) � vs(x, a), that ys is weakly decreasing ins, and that rs � q for all s. Suppose also that, inthe absence of taxes and subsidies (that is, withpolicy �), the following conditions hold: first,there is at least one state in which rehabilitationis a best choice; second, rehabilitation is theunique best choice in the earliest of these; third,for some earlier state (other than 0), (E, 1) isnot a best choice. Then, within the class ofpolicies that do not create net inter-cohorttransfers, a small steady-state subsidy for reha-bilitation is beneficial, and a small steady-statetax is harmful.

Since Proposition 6 holds even when the costof rehabilitation is very small, it is not primarilyabout the desirability of insuring a large, uncer-tain expense. For the correct intuition, note thatwith the no-tax alternative �, each DM’s prob-lem is stationary, so best choices for each stateare independent of age. This implies that theDM can never advance beyond the first state inwhich (R, 0) is the best choice. Consequently,the likelihood of rehabilitation is positively cor-related with the addictive state and negativelycorrelated with income, so the three effects dis-cussed at the outset of this section work in thesame direction, in favor of subsidization. Thepractical lesson is simple: if addiction is rela-tively unlikely to advance beyond the pointwhere people start to seek rehabilitation, thensubsidies are unambiguously desirable.

An appropriately modified version of ourmodel could address the effects of other harm-

48 The proof of Proposition 6 formally demonstrates aclosely related point in the context of a subsidy for rehabil-itation services.

49 The assumption that (E, 1) is not a best choice in everystate up to the first in which rehabilitation is selected en-sures some randomness.

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reduction policies such as needle exchanges.We leave this for future work.

G. Criminalization

Historically, criminalization has been the cor-nerstone of U.S. drug policy, with more than600,000 citizens incarcerated for drug-relatedoffenses in 1999 (Office of National Drug Con-trol Policy, 2001b). It affects users through twodistinct channels: a price effect and a rationingeffect. The price effect refers to changes in themarginal cost of using the substance resultingfrom penalties and other costs imposed on usersand suppliers. The rationing effect refers to in-terference with the process of matching buyersand sellers: since criminalization forces buyersand sellers to carry out transactions secretively,buyers sometimes have difficulty locatingsupply.50

It is instructive to consider the price andrationing effects separately. The price effect isequivalent to a tax policy in which the revenueraised by the tax is destroyed. If criminalizationonly created a price effect, taxation would dom-inate it.

Now consider the rationing effect. Disrupt-ing access to supply is potentially beneficialwhen the DM chooses (E, 0) or ( A, 0), andpotentially detrimental when he chooses (E,1). However, the impact of the rationing ef-fect on consumption may be smaller when theDM chooses (E, 1). An individual who in-tends to consume an illegal substance can setabout locating supply deliberately and sys-tematically and can maintain stocks in antic-ipation of transitory difficulties. In theextreme case where the rationing effect hasno impact on consumption when the DM se-lects (E, 1), it is unambiguously beneficial.This conclusion is obviously weakened, oreven reversed, if unsuccessful search activityis costly (e.g., because it exposes the DM tophysical harm).51

It follows that, in some circumstances, crimi-nalization may be superior to taxation and tolaissez-faire. This result deserves emphasis,since it is difficult to justify a policy of crimi-nalization based on demand-side welfare con-siderations without adopting the nonstandardperspective that supply disruptions can avertmistakes.52 Since it is better not to disruptplanned consumption, the case for criminaliza-tion is, ironically, strongest when enforcementis imperfect.

H. Selective Legalization with ControlledDistribution

Some policies permit transactions involvingaddictive substances in certain circumstancesbut not in others. Examples include a 1998Swiss law legalizing the prescription of heroinfor severe addicts and “blue laws” prohibitingalcohol sales on Sundays.

Policies of selective legalization with con-trolled distribution often make deliberateplanning a prerequisite for availability, selec-tively disrupting impulsive use without dis-turbing planned use (assuming the hot modeonly activates behaviors that target immediateconsumption). This effect is potentially ben-eficial, if unintended. For example, with bluelaws, alcoholics can make themselves lessvulnerable to compulsive drinking on Sun-days by choosing not to stock up in advance.These laws appear to reduce impulsive use inpractice (Peter T. Kilborn, 2003; T. Norstromand O. J. Skog, 2003).

A prescription requirement can play a similarrole, provided prescriptions are filled with a lag.To represent this possibility formally, we mod-ify our model as follows. Imagine that, in eachperiod m, the DM must decide whether to “callin” a prescription for the substance. Taking thisaction makes the substance available in periodm � 1; otherwise it is unavailable, and con-sumption is impossible.

With this option, the DM can alwaysachieve the first-best outcome. Solving the

50 Probabilistic consumption following the choice (E, 1)changes the value function somewhat, but the results fromSection IV extend to this case. See Goldstein and Kalant(1990) for evidence that drug usage declines as substancesbecome less available.

51 The costs of a successful search are part of the priceeffect.

52 Though the mechanisms considered in this paper in-volve stochastic mistakes, the same conclusion would fol-low in a model with deterministic mistakes, for example,one in which the DM always errs by placing too muchweight on the immediate hedonic reward.

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dynamic programming problem with ps � 0for all s yields a deterministic consumptionpath. The DM can mimic this outcome bycalling in his prescription in period m if andonly if he consumes the substance in periodm � 1 on the first-best path. In this way, heprecommits to the first-best choice by opti-mally rationing himself.53

If the hot mode also activates behaviors thattarget future consumption, the preceding policyis ineffective. However, a small modificationrestores the first-best outcome: allow the DM tocancel irrevocably, at any point in period m, hisprescription for m � 1. It is then optimal forhim to cancel during period m while in the coldmode if and only if he does not wish to consumethe substance in period m � 1.54

In more realistic settings, these policiesmight not permit consumers to achieve first-best outcomes. If, for example, the desirabil-ity of using a substance in period m dependsupon conditions (e.g., mood) that are not re-solved until the period is underway, the indi-vidual may sometimes regret failing to call ina prescription. However, the policy stillweakly benefits consumers because it pro-vides them with a tool for self-regulationwithout mandating its use.

Heterogeneity across individuals makes se-lective legalization with controlled distributioneven more attractive relative to other policies. Aprescription program accommodates heteroge-neity by providing consumers with discretion:intentional users can continue to indulge with-out impediment, while unintentional users nev-ertheless benefit from improved self-control. Incontrast, any feasible tax, subsidy, or criminalstatute may be inappropriate—even harmful—for large subsets of consumers.

The policies considered in this section wouldbe advantageous in any model where the DMmakes similar types of mistakes and where he

understands this proclivity. The particular sto-chastic mechanism discussed in this paper is notessential. Our conclusions do depend on theassumption that the government can limit resaleof the substance (e.g., by requiring on-site ad-ministration) and can suppress illicit supply.Notably, selective legalization impairs blackmarkets by siphoning off demand.

I. Policies Affecting Cue-Triggered DecisionProcesses

In our model, public policy can potentiallyhelp consumers by attenuating either exposureor sensitivity to cues (i.e., reducing c(a, �) orM(c, s, a, �) or raising MT). Arguably, theproducers of addictive substances raise the like-lihood of triggering hot modes by exposingconsumers to ubiquitous cues through billboards,television advertisements, product placement instores, and so forth. Advertising and marketingrestrictions of the type imposed on tobacco andalcohol may eliminate a cause of compulsive use.Restrictions on public consumption may havesimilar effects.

Other public policies may reduce cue-sensitivity by creating counter-cues. Braziland Canada require every pack of cigarettes todisplay a prominent viscerally charged imagedepicting some deleterious consequence ofsmoking, such as erectile dysfunction, lung dis-ease, or neonatal morbidity.55 These counter-cues are designed to activate the cognitivecontrol process described in Section II.

In our model, policies that reduce the likeli-hood of cue-triggered mistakes by removingproblematic cues or establishing counter-cuesunambiguously increase welfare. As with selec-tive legalization, these policies are attractivebecause they are noncoercive, because theyaccommodate individual heterogeneity, andbecause they have the potential to reduce unin-tended use without distorting choice in the colddecision mode. Though individuals may havesome ability to avoid problematic cues and cre-ate their own counter-cues, the government isarguably better positioned to do this.

53 In a related analysis, Loewenstein et al. (2000) em-phasize the role of “mandatory waiting periods” in a modelwhere agents systematically overconsume durable goods.

54 Alternatively, if the hot mode has a greater tendencyto activate behaviors targeting future consumption when theplanning horizon is short, one could restore (or at leastenhance) the policy’s efficacy simply by lengthening the lagbetween prescription requests and availability (e.g., callingin a prescription in period m makes the substance availablein m � k, with k � 1).

55 See http://www.hc-sc.gc.ca/hecs-sesc/tobacco/research/archive/ for a description and some preliminaryevidence on the effectiveness of the Canadian program.

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VI. Related Literature

Existing economic theories of addiction in-clude (i) variations on the standard model ofintertemporal decision making (Becker andMurphy, 1988; Orphanides and Zervos, 1995),including generalizations that allow for randomshocks and state-contingent utility (Hung, 2000;Laibson, 2001), (ii) models with “projectionbias” wherein agents mistakenly assume thatfuture tastes will resemble current tastes, butwhich otherwise conform to the standard model(Loewenstein, 1996, 1999; Loewenstein et al.,2001), (iii) models with present-biased prefer-ences and either naive or sophisticated expecta-tions (O’Donoghue and Rabin, 1999, 2000;Gruber and Koszegi, 2001), and (iv) models of“temptation” wherein well-being depends notonly upon the chosen action, but also on actionsnot chosen (Gul and Pesendorfer, 2001a, b;Laibson, 2001). While all of these theories con-tribute to our understanding of addiction andshare some important features with our model,none adheres to all of the central premises setforth and justified in Section II. In particular,none of these models depicts addiction as aprogressive susceptibility to stochastic environ-mental cues that can trigger mistaken usage.

All models of rational addiction (beginningwith Becker and Murphy, 1988) presupposecomplete alignment of choices and time-consistent preferences, thereby denying the pos-sibility of mistakes. Precommitments are neverstrictly beneficial, and a user would never statea sincere, unconditional intention to quit with-out following through. Stochastic environmen-tal cues play a role in Laibson’s (2001)extension, but the mechanism involves hedoniceffects (cues trigger a change in taste for thesubstance) rather than mistakes. Laibson’sframework can account for voluntary admissionto rehabilitation clinics and related behaviorsprovided that these activities reduce the likeli-hood of experiencing cravings. However, itcannot account for the observation that manyaddicts seek in-patient treatment not becausethey expect to avoid cravings, but rather pre-cisely because they anticipate cravings and wishto control their reactions. Furthermore, even ininstances where entering a rehabilitation facilitydoes reduce the likelihood of cravings (e.g., byremoving environmental cues), the standard

framework implies counterfactually that the ad-dict would find the facility’s program more at-tractive if it made the substance available upondemand (in case of cravings).

Adding projection bias to the standard modelintroduces the possibility that users may regardpast actions as mistakes. For example, an addictmay blame his initial drug use on a failure toanticipate the escalating difficulty of abstention.Coupled with state-contingent utility shocks (asin Laibson’s model), projection bias could ac-count both for the high frequency of attemptedquitting (when not triggered, users underesti-mate the future difficulty of abstention), and thehigh frequency of failure (once triggered, usersoverestimate the future difficulty of continuedabstention). However, even with projectionbias, an otherwise standard decision-makerwould never anticipate making mistakes in thefuture and sees no need for precommitments.

In models with present-biased decision-makers, choice is always aligned with the pref-erences prevailing at the moment when thechoice is made. Even so, one can interpretpresent-bias as shorthand for considerations thatlead to systematic mistakes in favor of imme-diate gratification, contrary to true (long-run)preferences (see, e.g., Gruber and Koszegi,2001). As a model of addiction, this frameworksuffers from two main shortcomings. First, thedecision-making bias is not domain-specific. Apresent-biased decision-maker mistakenly con-sumes all pleasurable commodities excessively;in this respect, there is nothing special aboutaddictive substances. Second, the bias is alwaysoperative—it is not cue-conditioned.

In principle, one could formulate a modelwith a powerful, narrow-domain, cue-triggeredpresent-bias. The resulting model (which doesnot appear in the literature) would conform toour premises; indeed, it would be nearly equiv-alent to our approach. Our model is somewhatsimpler and more tractable than this alternativebecause we treat behavior in the hot mode asmechanical, whereas this present-bias approachwould portray even triggered choices as optimalgiven well-behaved preferences. Naturally, forour model, one can say that the triggered decision-maker acts as if he optimizes subject to well-behaved preferences that attach enormousimportance to consuming the addictive sub-stance, but we think this “as if” representation is

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unenlightening. Since the decision-maker is as-sumed always to consume the substance in thehot mode, and since we regard this as a mistakewhenever he would behave differently in thecold mode, the representation illuminates nei-ther choices nor welfare.

Finally, Gul and Pesendorfer (2001a, b) modeladdictive behaviors by defining preferences overboth the chosen action and actions not chosen,thereby providing a potential role for “temptation”and a rationale for precommitment. Their axiom-atic approach embraces the doctrine of revealedpreference and therefore presupposes an align-ment of choices and preferences, ruling out thepossibility of mistakes. In addition, their model, asformulated, does not examine the role of stochas-tic cues in stimulating use.

VII. Final Remarks

This paper develops an economic model ofaddiction based on three premises: (i) useamong addicts is frequently a mistake (a patho-logical divergence between choice and pref-erence); (ii) experience with an addictive sub-stance sensitizes an individual to environmentalcues that trigger mistaken usage; and (iii) ad-dicts understand their susceptibility to cue-trig-gered mistakes and act with some degree ofsophistication. We argue that these premisesfind strong support in evidence from psychol-ogy, neuroscience, and clinical practice. Re-search indicates that addictive substancessystematically interfere with the proper opera-tion of an important process which the brainuses to forecast near-term hedonic rewards(pleasure), and this leads to strong, misguided,cue-triggered impulses that often defeat highercognitive control. As a matter of formal math-ematics, our model is tractable and involves asmall departure from the standard framework. Itgenerates a plausible mapping from the charac-teristics of the user, substance, and environmentto dynamic behavior. It accounts for a numberof important patterns associated with addiction,gives rise to a clear welfare standard, and hasnovel implications for public policy.

Our theory also has potentially important im-plications for empirical studies of addiction. Itsuggests that users of addictive substances mayrespond very differently to changes in prices,with dramatically different implications for

welfare, depending on whether decisions reflect“hot” impulses or “cold” deliberation. In con-trast, existing studies treat data on consumptionas if it were generated by a single process.

The model could be extended in a variety ofways to improve realism and predictive power.Possibilities include: developing a more com-plete model of cognitive control in which futureconsequences may influence the likelihood ofoverriding HFM-generated impulses (throughthe threshold MT); adding stochastic taste shocksrealized at the outset of each period (to producevariation in the contingent plan chosen for eachstate); allowing payoffs (ws) to depend directlyon � (to reflect the hedonic effects of cravings);allowing for imperfect information concerningan individual’s susceptibility to cue-triggeredmistakes; introducing partial, rather than full,self-understanding; modeling life-cycle changes(either anticipated or unanticipated) in prefer-ences and susceptibilities resulting from agingand changes in circumstances; and modeling thelong-term effects of early-life experiences.

It is natural to wonder whether the modelapplies not just to addictive substances, but alsoto other problematic behaviors such as overeat-ing or compulsive shopping. These questionsare currently the subject of study among neuro-scientists and psychologists, and it is too earlyto say whether similar brain processes are atwork.56 Notably, people who suffer from patho-logical gambling, overeating, compulsive shop-ping, and kleptomania describe their experienceas involving strong and often overwhelmingcravings, they respond to cues such as stress andadvertisements, and they exhibit cycles ofbinges and abstention.

APPENDIX A: THE DYNAMIC ECONOMY

This appendix contains additional technicaldetails concerning the economy described in

56 Some preliminary evidence suggests that there may besome connection. For example, compulsive gamblers andkleptomaniacs respond to drugs such as naltrexone whichblock the brain’s ability to experience euphoric states; com-pulsive gamblers and bulimics experience sudden relapse evenafter many years of abstinence. See Holden (2001a) for adiscussion of recent research concerning the commonalitiesbetween various behavioral pathologies and substanceaddiction.

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Section V D and referenced in Propositions 5and 6.

Let g denote generation, t denote age, and mdenote time. Members of generation g are bornin period m � g, and reach age t in period m �g � t. Let � denote the pure rate of time pref-erence, and let � denote the constant single-period survival probability, so that � � ��. Thesize of each new generation at age t � 0 is (1 ��)N, where N is the constant size of the totalpopulation.

Let �m denote the taxes/subsidies applied inperiod m, including either a tax on the addictivesubstance, �m, or a tax on rehabilitation, �m, aswell as age-specific lump-sum instruments, T tm.The period-m policy determines tax-inclusiveprices and incomes, from which we can com-pute (as described in Section III), for each gen-eration g � m, a parameter vector �g,t �(�1

g,t, ... , �Sg,t) with t � m � g applicable in

period m. An intertemporal policy � assigns apolicy �m to each period m, and induces, foreach generation, an infinite sequence of param-eter vectors, �g � (�g0, �g1, ...). Since �gt canvary over t (in contrast to the case treated insections III and IV), we must allow choice tovary with age as well as the addictive state. Adecision rule maps age t and state s into aprobability distribution over {(E, 1), (E, 0), (A,0), (R, 0)} (note that we allow for randomiza-tions) and implies a probability s

t( ) of use instate s at age t. We use g to denote the decisionrule of generation g. The optimized value func-tion Vs

t(�g) depends on the particular sequenceof parameters confronted by generation g, andvaries with age t. Since decisions are discrete,an optimal decision rule need not be unique and,indeed, is definitely not unique when it involvesrandomizations.

The optimized usage probabilities generate astate-transition probability matrix �t( g). For alarge population of DMs starting in state 0 atage 0 and following decision rule g, the pop-ulation distribution across addictive states atage t is zt( g) � [�k�0

t�1 �k( g)] z0, where z0 isan S-dimensional vector with a 1 in the firstposition and zeros elsewhere.

We say that an intertemporal policy � isfeasible if there is, for each generation g, somedecision rule g solving the DM’s choice prob-lem given �g induced by �, such that thegovernment’s budget is balanced in every pe-

riod. A steady-state policy � prescribes aconstant tax rate, either � or �, and constantage-specific lump-sum taxes, T t. Each genera-tion faces the same sequence of parameters,� � (�0, �1, ...), and V0

0(�) is the lifetimediscounted expected hedonic payoff for the rep-resentative individual.

APPENDIX B: PROOFS

Here we prove Propositions 3 and 4, andsketch the proofs of Propositions 1, 2, 5, and 6to conserve space. Complete proofs are avail-able on the AER’s web site.

SKETCH OF PROOF FOR PROPOSITION 1:Sketch for parts (i-a) and (i-b).—The proof

involves three steps.Step 1: Consider �� and �� such that: (1)

��k � ��k, (2) ��i � ��i for i � k, and (3) Vs(��) �Vs(��) for all s. Then (a) for all j � k, Vj(��) �Vj(��) � Vj�1(��) � Vj�1(��), and (b) for allj � k, Vj(��) � Vj(��) � Vj�1(��) � Vj�1(��).The argument, omitted, involves inductionstarting with j � 1 for part (a), and with j � Sfor part (b).

Step 2: Consider �� and �� such that: (1)��k � ��k, (2) ��i � ��i for i � k, and (3) Vs(��) �Vs(��) for all s. Then (a) for j � k, the disposi-tion to use in state j is weakly higher with ��than with ��, and (b) for j � k, the disposition touse in state j is weakly lower with �� than with��. These conclusions follow from step 1, whichimplies that, for j � k ( j � k), the difference incontinuation values following abstention anduse, and hence the disincentive to use, is weaklygreater (smaller) with �� than with ��.

Step 3: It is easy to verify that Vs(�) isweakly increasing in uk

a and bka, and weakly

decreasing in pka. Combining this with step 2

completes the proof of parts (i-a) and (i-b).

Sketch for part (i-c).—Consider two param-eter vectors, �� and �� , such that b� j

E � b� jE with all

other components equal, or p� jE � �pj

E with allother components equal. We argue, in twosteps, that the disposition to use in state j isweakly higher with �� than with �� .

Step 1: (a) If (E, 1) is optimal in state j with�� , then it is optimal in state j with �� , and (b) if(E, 1) is the unique optimal choice in state j with�� , then it is the unique optimal choice in state j

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with �� . When p� jE � �pj

E and all other componentsof �� and �� are equal, (a) and (b) follow frompart (ii) of the proposition. When b� j

E � b� jE and

all other components of �� and �� are equal, onecan show that the difference in discounted con-tinuation values following abstention and use instate j, and hence the disincentive to use, isstrictly less than the increase in the immediatebenefits of use, b� j

E � b� jE. If the DM weakly

prefers use to abstention with �� , he must there-fore strictly prefer it with �� .

Step 2: (a) If neither (E, 1) nor (E, 0) areoptimal choices in state j for �� , then the sets ofoptimal state j choices are identical with �� and�� ; (b) if either (A, 0) or (R, 0) is optimal in statej with �� , it is also optimal with �� . In each case,the result follows from the easily verified factthat the same value function, Vs(�� ), continues tosatisfy the valuation equation (1) when the pa-rameter vector is changed from �� to �� .

From part (a) of step 1 and part (a) of step 2,the maximum disposition to use in state j isweakly greater with �� than with �� . From part (b)of step 1 and part (b) of step 2, the minimumdisposition to use in state j is weakly greaterwith �� than with �� .

Now consider two parameter vectors, �� and�� , such that u� j

R � u� jR with all other components

equal. We claim that if something other than (R,0) is optimal in state j with �� , then it is alsooptimal in state j with �� (from which it followsthat the maximum disposition to use cannot behigher with �� ); moreover, if (R, 0) is not optimalin state j with �� , then the sets of optimal state jchoices are identical with �� and �� (from whichit follows that the minimum disposition to usecannot be higher with �� ). Analogously to step 2,these conclusions follow from the easily veri-fied fact that the same value function, Vs(�� ),continues to satisfy the valuation equation (1)when the parameter vector is changed from ��to �� .

Sketch for part (ii).—Suppose �� coincideswith �� except for pj

E, pjA, uj

A, ujR, and/or bj

A

(subject to the restrictions imposed by Assump-tions 1 and 2). We claim that, if (E, 1) is optimalin state j for �� , it is also optimal in state j for �� ;moreover, if (E, 1) is the unique optimum in thefirst instance, it is also the unique optimum inthe second instance. Analogously to step 2 ofpart (i-c), these conclusions follow from the

easily verified fact that the same value function,Vs(�� ), continues to satisfy the valuation equa-tion (1) when the parameter vector is changedfrom �� to �� . Part (ii) follows directly.

SKETCH OF PROOF FOR PROPOSITION 2:The proposition is proved by breaking each

change into components, where the effect ofeach component is either neutral or described byProposition 1.

To illustrate, we consider the effect of chang-ing ps

E on the length of the final resignationinterval. Consider �� and �� with �ps

E � p�sE for all

s (and all other parameters fixed). With �� , let s�3

denote the first state (working backward from S)in which (E, 1) is not an optimal choice; thisdefines the longest possible resignation interval.Let s�0

3 � s�3 denote the first state (working back-ward from S) in which something other than (E,1) is an optimal choice; this defines the shortestpossible resignation interval. Remember that s�3

and s�03 may differ because the optimal choice in

each state is not necessarily unique. Considermoving from �� to �� in two steps. (1) Changefrom �ps

E to p�sE for s � s�3. Since (E, 1) is initially

optimal for all such states, this leaves all opti-mal choices unchanged [Proposition 1, part (ii),coupled with the observation that, when (E, 1) isoptimal, neither (A, 0) nor (R, 0) is ever opti-mal]. (2) Change from �ps

E to p�sE for s � s�3. This

weakly increases the disposition to use in statess�3 � 1 through S [Proposition 1, part (i-b)].Thus, the disposition to use in all states s � s�3

is weakly lower with �� than with �� . It followsthat (E, 1) continues to be an optimal choice instates s � s�3 with �� , so the maximum finalresignation interval is weakly longer with �� thanwith �� . Since nothing other than (E, 1) is opti-mal in states s � s�0

3 with �� , nothing other than(E, 1) can be optimal in states s � s�0

3 with �� , sothe minimum final resignation interval isweakly longer with �� than with �� .

PROOF OF PROPOSITION 3:Select any state s�. We can decompose the

change from �� to �� into two components: (i) achange from �� to �� derived from ws(e, x, a) �w� s(e, x, a) � ds�, and (ii) a change from �� to �� .The first change reduces us

a by ds� for all statess and actions a. This is simply a renormaliza-tion, and has no effect on choices. The secondchange weakly increases us

a by ds� � ds for all

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s � s�, which weakly reduces the disposition touse in state s� by Proposition 1 part (i-b), andweakly decreases us

a by ds � ds� for all s � s�,which also weakly reduces the disposition touse in state s� by Proposition 1 part (i-a). Thus,the disposition to use in state s� weaklydecreases.

PROOF OF PROPOSITION 4:Part (i).—Consider some parameter vector �� ,

and let �� denote the parameter vector obtained bysetting �ps

a � 0 for all a and s, leaving all otherelements of �� unchanged. By part (ii) of Proposi-tion 1, continual use solves the DM’s choice prob-lem for �� if and only if it does so for �� .

Part (ii).—Consider some parameter vector�� , and suppose there is some state s� with ps�

E �0 such that (E, 1) is not a best choice in s�.Applying (1) for � � �� and using the fact that(E, 1) is not a best choice in s�, we have

Vs� ��� � max��1 p� s�E �u� s�

E � �Vmax�1,s� � 1� ���

� p� s�E�u� s�

E � b� s�E � �Vmin�S,s� � 1� ��� , �1 p� s�

A

� �u� s�A � �Vmax�1,s� � 1� ���

� p� s�A �u� s�

A � b� s�A � �Vmin�S,s� � 1� ��� , u� j

R

� �Vmax�1,s� � 1� ��� }.

Since (E, 1) is not a best choice in s�, the firstterm in braces is strictly less than u�s�

E ��Vmax{1,s��1}(�� ); given Assumption 2, so arethe other two terms. Thus, Vs�(�� ) � u�s�

E ��Vmax{1,s��1}(�� ). Let �� denote the parametervector obtained by setting �ps

a � 0 for all a ands, leaving all other parameters unchanged. Sincethe DM could select (E, 0) in s�, we haveVs�(�� ) � u�s�

E � �Vmax{1,s��1}(�� ) � u�s�E �

�Vmax{1,s��1}(�� ), so Vs�(�� ) � Vs�(�� ).

SKETCH OF PROOF FOR PROPOSITION 5:Without loss of generality, we can proceed as if,

for the optimal policy, the net transfer to eachcohort is zero in each period. If this is not the case,simply redefine income in state s at age t as yst �ys � Lt, where Lt is the net transfer received at aget; the original policy remains optimal.

Sketch for part (i).—We prove this in two steps.Step 1: An optimal tax rate must be weakly

negative. To prove this, we assume that there isa strictly positive optimal tax rate and establisha contradiction by showing that this policy mustbe strictly inferior to � (the no-tax policy).

Consider a decision rule (where we dropthe generational superscript g because we areexamining steady states) that is optimal andsatisfies budget balance with the optimal policy,and any age t� at which neither use nor nonuseis a certainty from the perspective of period 0(under the stated assumptions, there is always atleast one such age). Now suppose that policy �prevails but that the DM nevertheless continuesto follow . Through a series of algebraic steps,one can show that E0[u�(et�)�xt� � 1] �E0[u�(et�)�xt� � 0]. That is, the expectation, as ofage zero, of the marginal utility of nonaddictiveconsumption in t� is greater when conditionedon use than when conditioned on nonuse. Intu-itively, use tends to occur when income islower, and it also entails a cost.

Suppose we switch from the optimal policyto �. Assume for the moment the DM continuesto follow . From the perspective of age 0, theresult is an actuarially fair redistribution acrossage-t realizations of (s, �), from realizationsin which the DM does not use the substanceto realizations in which he does. SinceE0[u�(et)�xt � 1] � E0[u�(et)�xt � 0] for the lastdollar redistributed, and since u is strictly con-cave, the transfer makes him strictly better off.Thus, his discounted expected hedonic payoffweakly increases for every age t and strictlyincreases for some. Reoptimizing the decisionrule given � reinforces this conclusion.

Step 2: The no-tax policy, �, is not optimal.Intuitively, for the same reasons as in step 1, asmall subsidy coupled with lump-sum transfersthat achieve budget balance within each cohortand period should generate a first-order welfareimprovement by creating an actuarially fair re-distribution from realizations in which the DMdoes not use the substance to realizations inwhich he does. Formally, this reasoning en-counters two technical issues. First, we mustestablish that policies with small tax rates andbudget balance within each cohort and periodare feasible. Allowing for randomized choices,this is accomplished through standard argu-ments and a routine application of the KakutaniFixed Point Theorem. Second, any such redis-

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tribution must be actuarially fair relative toprobabilities associated with a decision rule thatis optimal with the new policy, not with �.

To deal with this second issue, we consider asequence of tax rates, associated age-specificlump-sum taxes, and optimal decision ruleswith budget balance within each cohort andperiod, (�j, Tj, j), with �j, Tj 3 0, and jconverging to some limit �. By standard argu-ments, � is optimal with �. Let b�

t denote thelikelihood of use at age t with �. Fixing thechoice rule at �, a small tax � generates percapita revenue b�

t � from a cohort of age �.Distributing this back to the same cohort as alump sum, and taking the derivative of the ex-pected age-t payoff with respect to �, we obtain(1 � b�

t )b�t (E0[u�(et)�xt � 0] � E0[u�(et)�xt �

1]). This is zero when b�t is 0 or 1, and by the

same arguments as in step 1, is strictly positivefor intermediate values. For large j, j is arbi-trarily close to �, so holding the choice rulefixed at �, a switch from � to (�j, Tj) creates aredistribution that is almost actuarially fair forthe probabilities implicit in �. We thereforeknow that redistribution is almost neutral for tsuch that b�

t � {0, 1}, and strictly beneficial fort such that b�

t � (0, 1). Accordingly, there existsj sufficiently large such that the expectedpresent value of the DM’s payoff is higher with(�j, Tj) than with �, assuming he chooses �.Reoptimizing for (�j, Tj) reinforces thisconclusion.

Sketch for part (ii).—The argument parallelsthat given for part (i), except we use the fact thatE0[u�(et�)�xt� � 0] � E0[u�(et�)�xt� � 1] when q issufficiently small.

SKETCH OF PROOF FOR PROPOSITION 6:First consider small subsidies. The argument

generally parallels step 2 of the sketch for Prop-osition 5, part (i). Take any sequence of reha-bilitation tax rates, associated age-specificlump-sum taxes, and optimal decision ruleswith budget balance within each cohort andperiod, (�j, Tj, j), with �j � 0, �j 3 0, Tj 30, and j converging to some limit �. Let B�

t

denote the likelihood of rehabilitation at age twith �. Fixing the choice rule at �, a small tax� generates per capita revenue B�

t � froma cohort of age t. Distributing this back tothe same cohort as a lump sum, and taking

the derivative of the expected age-t payoffwith respect to �, we obtain (1 �B�

t )B�t (E0[u�(et)�at � R] � E0[u�(et)�at � R]).

This equals zero when B�t � {0, 1}, and it is

strictly negative for B�t � (0, 1) (under the

conditions stated in the proposition, the DMchooses R only in the highest state reached withpositive probability in t; rehabilitation thereforeoccurs when income is lower, and it entails acost greater than q, so the expected marginalutility of nonaddictive consumption must begreater when conditioned on rehabilitation thanwhen conditioned on no rehabilitation).

We evaluate the change from (�, �) to (�j,Tj, j) in three steps. First, change the hot-modeprobabilities to those prevailing under (�j, Tj),leaving everything else constant. Second,change the policy from � to (�j, Tj), still hold-ing the choice rule fixed at �. Third, reopti-mize, changing the choice rule to j. The thirdchange is obviously weakly beneficial, as is thefirst (with �j � 0, the lump-sum transfers arenegative, so, under Assumption 3, the hot-modeprobabilities fall). Now consider the secondstep. For large j, (�j, Tj, j) is arbitrarily close to(�, �), so the hot-mode probabilities are al-most unchanged, and we compute expected util-ity using almost the same probabilities as with(�, �); moreover, holding the choice rule fixedat �, a switch from � to (�j, Tj) creates aredistribution that is almost actuarially fair forthe probabilities implicit in (�, �). Thus,�j(1 � B�

t ) B�t (E0[u�(et)�at � 0] � E0[u�(et)�at �

R]) approximates the period-t welfare effect. Fromthe concluding sentence of the previous para-graph, we therefore know that the second stepimproves the DM’s expected discounted payofffor sufficiently large j.

Now consider small taxes. For policy �, lets* denote the earliest state in which rehabilita-tion is an optimal choice (recall that it is theunique optimal choice in s*), and let s� �{1, ... , s* � 1} denote a state in which (E, 1) isnot a best choice (both states are referenced inthe proposition). For sufficiently small � � 0,one can show that, for all t, s* is also the earlieststate in which rehabilitation is an optimal choice(and that it is the unique optimal choice in s*),and (E, 1) is not a best choice in s�. This meansthat, for any budget-balancing optimal deci-sion rule �, there is at least one t in whichboth rehabilitation and no rehabilitation occur

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with strictly positive probability; for any such t,the same considerations as above implyE0[u�(et)�at � R] � E0[u�(et)�at � R], where wetake expectations assuming the policy � is inplace, but the hot-mode probabilities associatedwith � prevail, and the DM continues to fol-low �.

We evaluate the elimination of a small tax inthree steps. First, eliminate the tax (and associ-ated lump-sum transfers) without changing thehot-mode probabilities, and keeping the choicerule fixed at �. This is strictly beneficial (itcreates an actuarially fair redistribution fromrealizations with no rehabilitation to realiza-tions with rehabilitation; from the precedingparagraph, we know this is strictly beneficial forthe t at which both types of realizations occurwith positive probabilities, and neutral other-wise). Second, reoptimize the decision rule; thisis weakly beneficial. Third, change the hot-mode probabilities to those prevailing with thepolicy � and reoptimize the decision rule; underAssumption 3, this is also weakly beneficial.

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