Time-Inconsistency and Welfare

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Time-Inconsistency and WelfareTime-Inconsistency and Welfare

Jay BhattacharyaStanford University

Darius LakdawallaRAND Corporation

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Problems for Welfare AnalysisProblems for Welfare Analysis

•Behavioral economics has argued that people are time-inconsistent: preference orderings change over time

Relative to neoclassical consumers, overconsume goods with future costs

•If a person “disagrees with himself” about welfare, how can he be made better off?

•Hard to avoid paternalism, where government chooses a single preference ordering

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Are Sin Taxes A Solution?Are Sin Taxes A Solution?

•Time-inconsistency is a type of market failure to be solved with Pigou-style taxes

Suggests taxation for goods like cigarettes, alcohol, or food

•But sin taxes suffer from the inconsistency of preferences

Taxes often help current “selves” at expense of future selves

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Research QuestionsResearch Questions

1. How should we think about welfare for time-inconsistent people?

2. Do sin taxes improve welfare according to this view?

3. If not, what policies improve welfare? When are they feasible?

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Key IdeasKey Ideas

•Time-Inconsistency calls for a Pareto self-improvement criterion: welfare must go up (weakly) at every point in time

•A welfare-improvement involves transfers from the current self (who benefits) to the future self

Couple taxes with up-front payments, like license fees or “buy-in” fees

Future selves receive lump-sum payments for facing the tax

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Background: Rational AddictionBackground: Rational Addiction

Economic framework for a rational individual making decisions about the consumption of addictive goods: Individuals maximize a stream of discounted utility

over a lifetime, given prices and income Period utility depends upon the consumption of:

Traditional goods (which increases utility) Addictive goods (which increases utility) Addiction “stock” (which decreases utility)

High levels of consumption of the addictive good today leads to increases in addiction stock

The stock deteriorates over time

Becker and Murphy (1988)

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Rational Addiction: ImplicationsRational Addiction: Implications

The model makes testable predictions: Increase in the future price of the addictive

good decrease in the demand for it today. People are time-consistent: plans made

today are followed in the future

Normative implications: Individuals anticipate the future costs of

addiction, and evaluate these costs appropriately.

The optimal tax on the addictive good is zero.

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OutlineOutline

I. Thinking about Welfare Criteria

II. The Economics of Sin Taxes

III. Designing Welfare-improving policies

IV. Enforcement and Feasibility

V. Empirical Application

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The Pareto CriterionThe Pareto Criterion

A time-inconsistent individual is a collection of selves with opposed interests

Usual approach to a collection of opposed selves (a society) is the Pareto criterion

Welfare improvement requires that everyone is made (weakly) better off

Analogous Pareto self-improvement criterion applies: an individual must be made (weakly) better off at all points in time

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Alternative ApproachesAlternative Approaches

“Dictatorship of the Present”

Privilege preferences of current self

Gruber/Koszegi, Cropper/Laibson

“Long-Run Preferences”

Weight all selves equally

O’Donoghue/Rabin

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OutlineOutline


II. The Economics of Time Inconsistency




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Time-Inconsistent AddictionTime-Inconsistent Addiction

Addicts are time-inconsistent and have a self-control problem (Gruber and Koszegi)

Positive implications

1) Respond to future price increases

2) Addicts demand self-control devices

Normative Implication Government should provide self-control devices (like taxes)

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Taxes and Time-InconsistencyTaxes and Time-Inconsistency

Time-inconsistent addicts want a policy that lowers future smoking

Taxes lower present and future smoking

Inconsistent smoker compares cost of current tax to benefit of future tax

For a sufficiently old smoker, cost outweighs benefits

Later in the talk, we show this with a numerical empirical application

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Costs of TaxationCosts of Taxation

1. Taxes benefit younger smokers at the expense of older smokers

2. For a single individual, taxes benefit him at younger ages, at the expense of his desires at older ages

Taxes are redistributive rather than strictly welfare-improving

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OutlineOutline






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An Alternative Taxation SchemeAn Alternative Taxation Scheme

Need to lower future smoking but shift the cost onto the current smoker who is willing to pay

Structure of a policy solution:

1. Young smokers purchase a smoking “license”

2. License commits the smoker to future cigarette taxes, but also a compensating lump-sum transfer

3. License fee funds the lump-sum transfer

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Effects of the PolicyEffects of the Policy

1. Future smoking falls—improves welfare of the current smoker

2. Utility of future smoker held fixed, by means of the compensating transfer

Smoker is made (weakly) better off at all ages

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Modeling Time-InconsistencyModeling Time-Inconsistency

Hyperbolic discounting: Individual discounts next period at rate

Discounts period t at rate

Creates unstable intertemporal rates of substitution

t

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Effects of Time-InconsistencyEffects of Time-Inconsistency

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Effects of Time-InconsistencyEffects of Time-Inconsistency

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Types of Time-InconsistencyTypes of Time-Inconsistency

“Naïve” time-inconsistent agents fail to recognize their self-control problem

Zero demand for self-control devices or government intervention

Sophisticated time-inconsistent agents recognize their self-control problem but cannot eradicate it

Demand for self-control, publicly or privately provided

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Time-Inconsistent Decision MakingTime-Inconsistent Decision Making

Sophisticated agents understand that they cannot commit to future consumption path

Instead they incorporate the decision rules of their future selves

Mechanically, solve the model via backwards induction

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Properties of Our ModelProperties of Our Model

Three periods of life

Cigarette consumption builds up a stock of addiction which:

Lowers utility (e.g., poor health)

Makes smoking more enjoyable

Allow borrowing and lending across time

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Properties of Time-InconsistencyProperties of Time-Inconsistency

Compared to time-consistent agents, inconsistent agents may cut back their consumption to discipline future selves

Agents undertake costly investments to influence future selves

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Licensing StructureLicensing Structure(Zero Interest Rate Case)(Zero Interest Rate Case)

Period OnePay license fee

Period TwoPay per-cigarette tax

Receive lump-sum transfer q(q exactly offsets utility lost from taxes)

Period ThreeReceive tiny refund

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Welfare ImplicationsWelfare Implications




Period ThreeStrictly better off

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Period TwoStrictly better off (because

Period Three self is better off)


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Period OneStrictly better off with some

(Time-Inconsistent agent)




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Maximum fee rises with

1. Degree of time-inconsistency

2. Future harms of smoking

3. Tax responsiveness

4. Extent of under-saving

License FeeLicense Fee

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ddv

dcdU

dda

dSdU

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Period OneWelfare-Neutral with (Time-consistent agent)




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Two Views of Two Views of

1. can be used to recover administrative costs, leaving surplus to consumer

2. can be set to extract all consumer surplus, raising revenue for government at no cost to welfare

Time-inconsistent agents are “money pumps”

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Voluntary TaxationVoluntary Taxation

•Sin taxes are usually thought of as mandatory

Affect even time-consistent agents

•In theory, a Pareto-improving tax scheme could be voluntary

IF adverse selection and enforcement problems can be solved

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OutlineOutline






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Enforcement ProblemsEnforcement Problems

•A voluntary version of this scheme requires tax-discrimination

•Resale of cigarettes by untaxed people to taxed people can destroy the scheme

•Implementation would be aided by monitoring of sales and consumption

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Consumption MonitoringConsumption MonitoringSalivary cotinine is a reliable smoking measure

Several studies show relationship between cotinine levels and cigarette intake

Haley et al (1983, AJPH) show relationship between salivary cotinine variation and daily smoking

Huge literature on salivary cotinine levels and exposure to secondhand smoke

Studies show salivary cotinine predicts negative health impacts of smoking better than self-reports

Kendrick et al (1995) show smoking cessation programs verified with salivary cotinine are much more successful than programs without verification

Greeley et al (1992) show salivary samples can be transported by mail without affecting results

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OutlineOutline






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Objective of Empirical ApplicationObjective of Empirical Application

Calibrate a model of the demand for cigarettes by a time-inconsistent individual who lives 55 periods (ages 25-80)

Calculate the optimal flat tax imposed on all selves from the point of view of each self

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DataData

Cigarette Price Series are from Tax Burden on Tobacco

We use NHIS (Sample Adult Files, 1998-2000) for nationally representative data on smoking behavior

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Optimal Smoking PathsOptimal Smoking Paths

We assume period utility is quadratic in smoking, consumption, and smoking stock

Solving rational addiction model involves straightforward Euler equations

Time-inconsistent model must be solved via backwards induction

There must be strategic equilibrium among all “time t selves”

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Estimation MethodEstimation Method

We calibrate models to observed smoking patterns

For every set of parameters , lifetime income stream {It}, and cigarette price {qt}, there is an optimal smoking path ct(,{It},{qt})

The estimated parameters minimize the squared distance between a representative individual’s optimal smoking path, and her mean smoking

We minimize the loss function:

2*1 1

1

min ( ,{ } ,{ } )T

T Tt j j j j t

t

c I q c

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Predicted vs. Actual Budget Share on CigarettesMales, 1998

0

0.01

0.02

0.03

0.04

0.05

0.06

25 35 45 55 65 75

Age

Bu

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et s

har

e

actual budget share

predicted budget share

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0

.5

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2

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Tax

as

a p

erce

nt o

f pric

e

20 40 60 80age

Males 1998Optimal Tax Decreases as End of Life Approaches

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ConclusionsConclusions

Time-inconsistency does not produce an incontrovertible case for sin taxes

Pareto welfare-improvement requires time-invariant policies involving transfers across time

These could be voluntary

Time-inconsistent agents can be exploited for welfare-neutral revenue-raising, or revenue-neutral welfare-improvement

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Malfeasance in Taxation ChoiceMalfeasance in Taxation Choice

Consider a world with “heavy” smokers and “light” smokers

The optimal tax and transfer differs across groups

An agent who chooses the “wrong” bundle can destroy the scheme

There are incentives to choose the wrong bundle

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Incentives to CheatIncentives to Cheat

Period 1 agent has two different incentives

Misreporting a high level of smoking to secure a higher period 2 transfer

Misreporting a low level of smoking to punish period 2 agent

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SafeguardsSafeguards

Cheating is easily observed ex post, by examining tax payments

Two mechanisms can be used to prevent the discussed forms of cheating:

1. Period 3 fines

2. Allowing period 2 agents to opt out for a small fee

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Deterring MisrepresentationDeterring Misrepresentation

Period 3 fines against people whose transfers exceed their tax payments

Deters agents from misrepresenting themselves as “high” consumers

Allowing opt-out in period 2

Deters agents from mispresenting themselves as low consumers to punish period 2 agent

Time-Inconsistency and Welfare

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