Time-Inconsistency and Welfare

Time-Inconsistency and Welfare Jay Bhattacharya Stanford University Darius Lakdawalla RAND Corporation

Problems 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

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

Research Questions • How should we think about welfare for time-inconsistent people? • Do sin taxes improve welfare according to this view? • If not, what policies improve welfare? When are they feasible?

Key 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

Background: 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)

Rational 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.

Outline • Thinking about Welfare Criteria • The Economics of Sin Taxes • Designing Welfare-improving policies • Enforcement and Feasibility • Empirical Application

The 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

Alternative Approaches • “Dictatorship of the Present” • Privilege preferences of current self • Gruber/Koszegi, Cropper/Laibson • “Long-Run Preferences” • Weight all selves equally • O’Donoghue/Rabin

Outline • Thinking about Welfare Criteria • The Economics of Time Inconsistency • Designing Welfare-improving policies • Enforcement and Feasibility • Empirical Application

Time-Inconsistent Addiction • Addicts are time-inconsistent and have a self-control problem (Gruber and Koszegi) • Positive implications • Respond to future price increases • Addicts demand self-control devices • Normative Implication Government should provide self-control devices (like taxes)

Taxes 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

Costs of Taxation • Taxes benefit younger smokers at the expense of older smokers • 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

An 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: • Young smokers purchase a smoking “license” • License commits the smoker to future cigarette taxes, but also a compensating lump-sum transfer • License fee funds the lump-sum transfer

Effects of the Policy • Future smoking falls—improves welfare of the current smoker • Utility of future smoker held fixed, by means of the compensating transfer • Smoker is made (weakly) better off at all ages

Modeling Time-Inconsistency • Hyperbolic discounting: Individual discounts next period at rate • Discounts period t at rate • Creates unstable intertemporal rates of substitution

Effects of Time-Inconsistency

Types 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

Time-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

Properties 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

Properties 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

Licensing Structure(Zero Interest Rate Case) • Period One • Pay license fee f • Period Two • Pay per-cigarette tax  • Receive lump-sum transfer q • (q exactly offsets utility lost from taxes) • Period Three • Receive tiny refund e

Welfare Implications • Period One • Pay license fee f • Period Two • Pay per-cigarette tax  • Receive lump-sum transfer q • (q exactly offsets utility lost from taxes) • Period Three • Strictly better off

Welfare Implications • Period One • Pay license fee f • Period Two • Strictly better off (because • Period Three self is better off) • Period Three • Receive tiny refund e

Welfare Implications • Period One • Strictly better off with some f>0 • (Time-Inconsistent agent) • Period Two • Pay per-cigarette tax  • Receive lump-sum transfer q • (q exactly offsets utility lost from taxes) • Period Three • Receive tiny refund e

License Fee • Maximum fee rises with • Degree of time-inconsistency • Future harms of smoking • Tax responsiveness • Extent of under-saving

Welfare Implications • Period One • Welfare-Neutral with f=0 • (Time-consistent agent) • Period Two • Pay per-cigarette tax  • Receive lump-sum transfer q • (q exactly offsets utility lost from taxes) • Period Three • Receive tiny refund e

Two Views of f • f can be used to recover administrative costs, leaving surplus to consumer • f can be set to extract all consumer surplus, raising revenue for government at no cost to welfare • Time-inconsistent agents are “money pumps”

Voluntary 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

Enforcement 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

Consumption Monitoring • Salivary 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

Objective 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

Data • Cigarette Price Series are from Tax Burden on Tobacco • We use NHIS (Sample Adult Files, 1998-2000) for nationally representative data on smoking behavior

Optimal 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”

Estimation Method • We calibrate models to observed smoking patterns • For every set of parameters G, lifetime income stream {It}, and cigarette price {qt}, there is an optimal smoking path ct(G,{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:

Conclusions • 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

Malfeasance 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

Incentives 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

Safeguards • Cheating is easily observed ex post, by examining tax payments • Two mechanisms can be used to prevent the discussed forms of cheating: • Period 3 fines • Allowing period 2 agents to opt out for a small fee

Deterring 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