Econ 440: Lecture 9 PDF

Econ 440: Lecture 9 Prof. Ragan Petrie Texas A&M University September 24, 2024 Present Bias Present Bias  Present Bias Procrastination  Present Bias Time inconsistency and present-bias ▶ For a time-consistent planner, all else equal, if...

Econ 440: Lecture 9 Prof. Ragan Petrie Texas A&M University September 24, 2024 Present Bias Present Bias  Present Bias Procrastination  Present Bias Time inconsistency and present-bias ▶ For a time-consistent planner, all else equal, if it is beneficial to do something next week/month, it is even more beneficial to do it now. Many do not act this way ▶ Familiar quotations you would never hear from a time consistent planner ▶ Next month, I’ll quit smoking ▶ Next week, I’ll catch up on the required reading ▶ Tomorrow morning, I’ll wake up early and exercise The Behavioral Model: Present-Bias The Behavioral Model: Present-Bias  The Behavioral Model: Present-Bias The β − δ Discounting Model ▶ First proposed by Strotz (1955) and popularized by Laibson (1997) ▶ Specifies a slight tweak to utility function: U(c) = u(c1 ) + βδu(c2 ) + βδ 2 u(c3 ) +... + βδ T −1 u(cT ) h i = u(c1 ) + β δu(c2 ) + δ 2 u(c3 ) +... + δ T −1 u(cT ) where ▶ 0≤β≤1 if beta = 1, then this model is the same as the exponential discounting model ▶ 0≤δ≤1 ▶ Model known as β-δ (beta-delta) discounting ▶ Embeds the standard exponential discounting model if β = 1 ▶ All periods that are not the present are additionally discounted by β, so present period utility gets a relative boost ▶ This kind of preference has present-bias  The Behavioral Model: Present-Bias Example: How Present-Bias Leads to Time-Inconsistency ▶ Three periods: t = 1, 2, 3 ▶ Two options: 1. Eat well: u2 = 5, u3 = 10 2. Eat poorly: u2 = 8, u3 = 6 ▶ Assume that DM has present-biased preferences with β = 21 , δ = 1 ▶ Decision in period 1: ▶ Eat well: U =.5 (5) +.5(10) = 7.5 ▶ Eat poorly: U =.5(8) +.5(6) = 7 ▶ Decision: eat well ▶ Decision in period 2: ▶ Eat well: U = 5 +.5(10) = 10 ▶ Eat poorly: U = 8 +.5(6) = 11 ▶ Decision: eat poorly  The Behavioral Model: Present-Bias Other Explanations of Time Inconsistency Other Explanations of Time Inconsistency  The Behavioral Model: Present-Bias Other Explanations of Time Inconsistency Non-Discounting Models of Time Inconsistency ▶ Dual self ▶ One thoughtful “planner” and many impulsive “doers” (one per period) ▶ If doer only cares about the present, can lead to time inconsistency ▶ Hot and cold decision states ▶ DM cannot control their cravings in hot states ▶ Time-inconsistency triggered by context clues (eg smelling food) ▶ Temptation preferences ▶ DM cares not just about consumption, but about consumption set ▶ Example: Feel differently consuming a sandwich when the menu included salad ▶ If we don’t consider menu, this can look like time-inconsistency The Behavioral Model: Examples The Behavioral Model: Examples  The Behavioral Model: Examples Procrastination ▶ In many economic problems, agent must do a task ▶ Task needs to be done exactly once ▶ Agent has several time periods to do task ▶ To analyze these types of decisions, use backwards induction: start analysis at the end of the process and work back to the first period ▶ Naive agent is time inconsistent, but assumes self will be time-consistent in future ▶ Sophisticated agent is time inconsistent, and knows self will be time-inconsistent in future remember, time inconsistent means beta < 1  The Behavioral Model: Examples Example: Paper writing ▶ Suppose student has a paper due in 4 weeks ▶ Can write the paper on weekend 1, 2, 3, or 4 ▶ Cost of writing paper is missing going to movies with friends: ▶ Weekend 1: bad movie, cost = 3 ▶ Weekend 2: OK movie, cost = 5 ▶ Weekend 3: good movie, cost = 8 ▶ Weekend 4: great movie, cost = 13 ▶ Benefit of writing the paper is v̄ > 0, received in week 5 when grades are given ▶ For all types of agents, assume δ = 1 in what follows ▶ For time-inconsistent types, assume β = 1 2  The Behavioral Model: Examples When Does Time-Consistent Agent Write Paper? ▶ Week 4: ▶ Have to do the paper at this point, so no real choice to be made ▶ Week 3: ▶ If do paper, utility is v̄ − 8 ▶ If wait till next week, utility is v̄ − 13 ▶ So, will do paper in week 3 (if not done already) ▶ Week 2: ▶ If do paper, utility is v̄ − 5 ▶ If don’t write paper, know will write next week for utility v̄ − 8 ▶ So, will do paper in week 2 (if not done already) ▶ Week 1: ▶ If do paper, utility is v̄ − 3 ▶ If don’t write paper, know will write next week for utility v̄ − 5 ▶ So, will do paper in week 1  The Behavioral Model: Examples Decision Tree ▶ Helpful to keep track of decisions of agent with a decision tree ▶ Note decision each period is whether to write or wait, not when to write Write v̄ − 3 Wait Write v̄ − 5 T =1 Wait Write v̄ − 8 T =2 Wait T =3 v̄ − 13  The Behavioral Model: Examples When Does Naive Time-Inconsistent Agent Write Paper? ▶ Naive agent is time inconsistent, but assumes will be time-consistent in future ▶ Week 4: ▶ Have to do the paper at this point, so no real choice to be made ▶ Week 3: ▶ If do paper, utility is 21 v̄ − 8 ▶ If wait till next week, utility is 12 v̄ − 12 13 = 12 v̄ − 6.5 ▶ So, will choose NOT to do paper in week 3 ▶ Week 2: ▶ If do paper, utility is 21 v̄ − 5 ▶ If don’t write paper: ▶ Remember, thinks future self is time-consistent ▶ So, thinks (incorrectly!) that will do paper in week 3 ▶ From perspective of week 2, utility of waiting is 1 v̄ − 1 8 = 1 v̄ − 4 2 2 2 ▶ So, will choose NOT to do paper in week 2  The Behavioral Model: Examples Naive Time-Inconsistent Agent, con’t ▶ Week 1: ▶ If do paper, utility is 21 v̄ − 3 ▶ If don’t write paper: ▶ Remember, thinks future self is time-consistent ▶ So, thinks (incorrectly!) that will do paper in week 2 ▶ From perspective of week 1, utility of waiting is 1 v̄ − 1 5 = 1 v̄ − 2.5 2 2 2 ▶ So, will choose NOT to do paper in week 1 ▶ Overall result: waits until week 4 to do paper, misses best movie  The Behavioral Model: Examples Decision Tree for Naive Agent Write v̄ − 3 Wait Write v̄ − 5 T =1 Wait Write v̄ − 8 T =2 Wait T =3 v̄ − 13  The Behavioral Model: Examples When Does Sophisticated Time-Inconsistent Agent Write Paper? ▶ Sophisticated agent is time inconsistent, and knows will be time-inconsistent in future ▶ Week 4: ▶ Have to do the paper at this point, so no real choice to be made ▶ Week 3: ▶ If do paper, utility is 21 v̄ − 8 ▶ If wait till next week, utility is 12 v̄ − 12 13 = 12 v̄ − 6.5 ▶ So, will choose NOT to do paper in week 3 ▶ Week 2: ▶ If do paper, utility is 21 v̄ − 5 ▶ If don’t write paper: ▶ Remember, knows future self is time-inconsistent ▶ So, thinks (correctly) that will NOT do paper in week 3 ▶ From perspective of week 2, utility of waiting is 1 v̄ − 6.5 2 ▶ So, will choose to DO paper in week 2  The Behavioral Model: Examples Sophisticated Time-Inconsistent Agent, con’t ▶ Week 1: ▶ If do paper, utility is 21 v̄ − 3 ▶ If don’t write paper: ▶ Remember, knows future self is time-inconsistent ▶ So, thinks (correct) that will do paper in week 2 ▶ From perspective of week 1, utility of waiting is 1 v̄ − 1 5 = 1 v̄ − 2.5 2 2 2 ▶ So, will choose NOT to do paper in week 1 ▶ Overall result: waits until week 2 to do paper, misses OK movie  The Behavioral Model: Examples Decision Tree for Sophisticated Agent Write v̄ − 3 Wait Write v̄ − 5 T =1 Wait Write v̄ − 8 T =2 Wait T =3 v̄ − 13  The Behavioral Model: Examples Measuring Time Preferences ▶ So far, evidence we have seen has not attempted to estimate either aggregate or individual time preference parameters (eg β or δ) ▶ General strategy in economics experiments ▶ Focus on tradeoffs two time periods, say t and t + k ▶ Try to find point where u(ct ) = β It>0 δ k u(ct+k ) ▶ By varying t, allows us to estimate β and δ separately ▶ Several experimental methods to go about doing this ▶ Willingness to pay: State the lowest amount you’d be willing to accept today instead of $ in one month ▶ Matching: I am indifferent between $ today and $X in one month ▶ Multiple Price Lists: Indicate which one you prefer: $X today or $Y in one month  The Behavioral Model: Examples Measuring β − δ Preferences ▶ Again, assume for simplicity that u(x) = x ▶ Suppose you say that you are indifferent between $100 in one month and $Y in two months ▶ Then we must have βδ100 = βδ 2 Y , which implies 100 δ= Y ▶ Suppose additionally you are indifferent between $100 today and $X in one month ▶ Then we must have 100 = βδX ▶ Together with the equation for δ above, this implies Y β= X  The Behavioral Model: Examples More Details on Multiple Price List Methodology ▶ Most commonly used experimental method to estimate individual time preferences ▶ Choices between a smaller, sooner reward and a later, larger reward ▶ Typically one option stays fixed while the other varies ▶ Point at which subject switches from smaller/sooner reward to larger/later reward helps estimate their time preference parameters ▶ Essential to have both delay = 0 and delay > 0 list to separately identify β and δ