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 Taxes require some paternalism that privileges the current smoker over his future incarnations, or alternatively, privileges the young smoker over the older person who has already borne all the costs of past smoking.

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

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

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

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

Strictly better off (because Period Three self is 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

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 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 Maximum level of phi rises with the degree of time-inconsistency, the future health harms of smoking, and the extent of under-saving by the period 2 individual.

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

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

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 Other biomarkers are available: hair nicotine

Serum and salivary cotinine have R-squared of 0.996

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

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: Essentially, we use average income across ages as a proxy for actual lifetime income. Inconsistency in this estimator will be due solely to the use of the proxy variable.

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