1 5/21/2015 time-inconsistency and welfare jay bhattacharya stanford university darius lakdawalla...
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1 04/18/23
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
I. Thinking about Welfare Criteria
II. The Economics of Time Inconsistency
III. Designing Welfare-improving policies
IV. Enforcement and Feasibility
V. Empirical Application
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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
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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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 OnePay license fee
Period TwoPay per-cigarette tax
Receive lump-sum transfer q(q exactly offsets utility lost from taxes)
Period ThreeStrictly better off
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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 OnePay license fee
Period TwoStrictly better off (because
Period Three self is better off)
Period ThreeReceive tiny refund
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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 OneStrictly better off with some
(Time-Inconsistent agent)
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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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
dcdU
ddv
dcdU
dda
dSdU
1
232232 )1()1(
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Welfare ImplicationsWelfare Implications
Period OneWelfare-Neutral with (Time-consistent agent)
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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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
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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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
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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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
dg
et s
har
e
actual budget share
predicted budget share
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0
.5
1
1.5
2
2.5
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