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

2. 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

3. 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

4. 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?

5. 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

6. 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)

7. 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.

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

9. 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

10. 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

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

12. 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)

13. 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

14. 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.

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

16. 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

17. 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

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

19. Effects of Time-Inconsistency

20. Effects of Time-Inconsistency

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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.

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

32. 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

33. 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”

34. 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

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

36. 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

37. 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

38. Serum and salivary cotinine have R-squared of 0.996

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

40. Objective of Empirical Application
Calibrate a model of the demand for cigarettes by a time-inconsistent individual who lives 55 periods (ages )
Calculate the optimal flat tax imposed on all selves from the point of view of each self

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

42. 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”

43. 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.

46. 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

47. 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

48. 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

49. 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

50. 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