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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.
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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.
Standard solution • 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.
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.
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.
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.
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 1keeps 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?