VIII Lecture

Time Preferences

Wrap up of the previous lecture

• Problem of distinguishing between biasing and shaping effect.

• Evidence for shaping effect in repeated median price selling auctions.

• If preferences form in the course of an interaction, can we intentionally manage them to avoid self-defeating behavior?

Normative theory and descriptive analysis

• Anomalous behavior of PR, coherent arbitrariness, shaping effect.

• Methodological implications: analysis of experimental methods; relationship between empirical regularities in behavior and the theoretical axiomatic core.

• Epistemological implications: intellectual integration of economic theory and cognitive sciences.

• Anomalous behavior of time preferences.

• Methodological implications: relationship between our actual discount rate of the future and the normative benchmark.

• Epistemological implications: integration between economics and cognitive sciences.

• Ontological implications: it is at issue the characterization of the economic agents.

Frame of the problem.Why people engage in self-defeating

behaviors?

• A behavior is self-defeating when people prefer a ready at hand utility yielding a long run dis-utility over a long run utility at a delayed point in time (i.e. drug or tobacco addiction).

• If we introduce timing then self-defeating behavior consists of preferring the delayed long run utility when the smaller one is far and reversing preferences when the small reward gets closer in time.

• People devaluate the future and the engagement in self-defeating behavior leads to devaluate it even more.

• Self-defeating behavior is a problem of the discount rate of the future: the more we discount the future the more likely we are to engage in a self-defeating behavior; time preferences is the logical structure of self-defeating behavior.

• RCT requires to subtract a constant proportion of the utility there would be at any given delay for every additional unit of delay.

• Formula: Value = “Objective” value × (1 − Discount rate) Delay.

• Exponential function of the discount rate: consistency preserving rule in inter-temporal choices.

Standard solution

Example of drinking

• Immediate utiles of 100; discount rate of 20% per day; costs of 120 utiles for the day after hangover.

• Drinking today: 100 − (120 × 80%) = 4 utiles

• Delay of a day for drinking: (100 × 80%) − 120 × (80%)2 = 3.2 utiles

Reason why the standard solution is misguided

• The standard solution is an action guiding rule but it does not explain the inconsistency of preferring a long run utility when the short run utility is far and the latter when it is ready at hand.

• Two cases: 1) The exponential discount rate of the future determines always a positive level of utility for a delayed action. 2) The discount rate determines always a negative utility.

• In both cases the standard solution does not explain why people engage self-defeating behaviors: no preferences reversal across time.

• I case: if I have a discount rate of 20%, then I always choose to drink because the level of utility never gets to be zero or negative.

• II case: if I have a discount rate of 10%, then if I choose not to drink from the point of view of some delay then I will not drink even when the occasion is ready at hand.

• Two days of delay: 100 × (90%)2 − 120 × (90%)3 = – 6.48

• Immediate occasion: 100 − 120 × 90% = - 8

Explanatory lack• The rule does not explain time reversal of preferences

between a short run reward and a long run one when the former is ready at hand.

• This reversal results in a long run disutility (self-defeating behavior).

• According to standard theory (that endorses the exponential discount rule) the explanation of self-defeating behaviors falls out of the economic domain.

Two alternatives

• I mistakenly calculate the discounted value of a prospect.

• Learning by bad consequences to implement the right calculation.

• My discount rate leads me to always drink.

• I probably need a doctor!

Relative limitations• Self-defeating behavior can be persistent even if I

learn from bad consequences.

• Time consistent behavior can be forestalled by self-defeating behavior even if I learn the benefits of my consistency.

• Pathological self-defeating behaviors (drug addiction) stand in a continuum relationship with normal ones.

Hyperbolic discount curve

• The devaluation of rewards is proportional to their delay.

• Ready-at-hand rewards and extremely delayed ones are discounted the same as with the exponential rule.

• The rewards in between the extremes are devaluated more: hyperbolic discount curves are more bowed than the exponential ones.

Illustration

Example of the coat• Ms Exponential could buy Ms Hyperbolic’s winter coat

each spring, when Ms H. devaluates it more.

• Ms. E could then sell the coat back to Ms. H every fall when the approach of winter sent Ms. H’s valuation of it into a high spike.

• Only an exponential discount curve will protect a person against exploitation: the hyperbolic discount curve is maladaptive within the economic environment.

Implications for markets

• An agent with hyperbolic discount curves will be exploited to the point that he will exit the market.

• From a normative point of view a hyperbolic discounter is not an economic agent.

• However hyperbolic discount curves are descriptively relevant.

Exponential discount curves. Predictive implications

• Offer a choice between a small reward at delay D and a larger reward available at delay D plus a constant lag L.

• Prediction of conventional theory: we consistently choose the larger reward at D + L (i.e. not drinking) even when the smaller reward gets closer in time (i.e. a beer just before me). This means that the respective discount curves stay proportional to each other.

Illustration of the standard theory prediction

Hyperbolic discount curves. Predictive implications

• Prediction of hyperbolic discounting: the original choice of the larger reward will be reverted when the smaller reward gets closer in time. This means that the two curves crosses.

Illustration of hyperbolic discount curves that cross

Behavioral regularity

• The reward is chosen in direct proportion to his size and in inverse proportion to his delay.

• Value = amount / [Constant 1 + (Constant 2 × Delay)]

• This rule explains how the evaluation of rewards is dependent on their delay such to allow the behavioral phenomenon of time inconsistent preferences.

Constants

• Constant 1 keeps the value from going to infinity when a reward is immediate; Constant 2 describes how steeply a subject discounts the future.

Normative theory and descriptive analysis

• We need to take in direct account how individuals assign real value to the prospect.

• We need to understand how much the real value departs from the cognitive benchmark.

• Can we naturalize the normative benchmark?

Conclusions• Problem of self-defeating behavior: we need to explaining its

occurrence and the possibility of its avoidance.

• Standard exponential discount curves are a normative benchmark not explaining why self-defeating behavior occurs.

• Hyperbolic discount curves are descriptive tools explaining why we engage in self-defeating behavior.

• How do we have to relate the normative and descriptive level?