Econ 440: Lecture 10 PDF

Econ 440: Lecture 10 Prof. Ragan Petrie Texas A&M University September 26, 2024 Moblab Activities 4 & 5 - Results Motivation ▶ Individuals may appear relatively patient when all outcomes are in the future, but appear relatively impatient when trading off between right now and th...

Econ 440: Lecture 10 Prof. Ragan Petrie Texas A&M University September 26, 2024 Moblab Activities 4 & 5 - Results Motivation ▶ Individuals may appear relatively patient when all outcomes are in the future, but appear relatively impatient when trading off between right now and the future ▶ Standard exponential discounting model does not allow for this ▶ When trading off consumption between consecutive periods, discount factor is always δ ▶ Behavioral model treats the present differently than all future periods Time preference activities ▶ Time preference activity - Moblab Activity 4 Time (Lect 7) ▶ You chose between $100 today and $Y in a future period (95, 97, 99,...,115) ▶ Old Task 1: today and one month ▶ Old Task 2: one month and two months ▶ Time preference activity - Moblab Activity 5 Time and Risk (Lect 8) ▶ You chose a payment plan for $20/week for a number of weeks earlier and later ▶ Payment fixed and number of weeks for second option increases ▶ Task 1: first 26 weeks of year and second 26 weeks of year ▶ Task 2: first 13 weeks of year and second 13 weeks of year ▶ Task 3: third 13 weeks of year and last 13 weeks of year Correlations across tasks Table: Cross-correlation table Variables DF T1 (ML4) DF T2 (ML4) DF T1 DF T2 DF T3 Disc. Factor - T1 (ML4) 1.000 Disc. Factor - T2 (ML4) 0.857 1.000 Disc. Factor - T1 (ML5) 0.067 0.162 1.000 Disc. Factor - T2 (ML5) 0.043 0.076 0.680 1.000 Disc. Factor - T3 (ML5) -0.215 -0.165 0.548 0.446 1.000 Moblab - Activity 4 80 80 70 70 60 60 50 50 Percent Percent 40 40 30 30 20 20 10 10 0 0.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1 DF1old DF2old Today & 1 Month 1 Month & 2 Months Moblab - Activity 5 80 80 80 70 70 70 60 60 60 50 50 50 Percent Percent Percent 40 40 40 30 30 30 20 20 20 10 10 10 0 0 0.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1 DF1 DF2 DF3 1st v. 2nd half 1st Trim v. 2nd Trim 3rd Trim v. 4th Trim  80 80 70 70 60 60 50 50 Percent Percent 40 40 30 30 20 20 10 10 0 0.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1 DF1old DF2old Today & 1 Month 1 Month & 2 Months 80 80 80 70 70 70 60 60 60 50 50 50 Percent Percent Percent 40 40 40 30 30 30 20 20 20 10 10 10 0 0 0.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1.85.86.87.88.89.9.91.92.93.94.95.96.97.98.99 1 DF1 DF2 DF3 1st v. 2nd half 1st Trim v. 2nd Trim 3rd Trim v. 4th Trim Why are the two activities different? ▶ Discount factor calculation assumes exponential discounting ▶ The first calculation assumes people are risk-neutral ▶ The second calculation does not assume anything about risk preferences Moblab Activity 4 - is risk neutrality reasonable? ▶ Suppose u(c) = c and a person is indifferent between $105 in one month and $100 today ▶ Then, 100 = δ105 or δ = 100 105 = 0.95 ▶ Suppose u(c) = c 0.5 and a person is indifferent between $105 in one month and $100 today ▶ Then, 1000.5 = δ1050.5 or δ = 1000.5 1050.5 = 0.98 Moblab Activity 4 - is risk neutrality reasonable? ▶ Suppose δ = 0.95 and u(c) = c 0.5 ▶ How much does a person need to be paid to wait a month? ▶ 1000.5 = δY 0.5 ⇒ Y = 100 δ2 ▶ Y = 100 0.952 = 110.25 ▶ So, if you are risk averse, you will look more impatient when we use the old task ▶ Choices look more impatient in old task than new task – maybe this is risk aversion Why does second method not depend on risk preferences? ▶ Suppose you are indifferent between getting $20 each week the first 24 weeks of the year and getting $20 each of the last 28 weeks of the year. ▶ If you have exponential discounting preferences, then... P24 i−1 P52 ▶ i=1 δ u(c + 20) + i=25 δ i−1 u(c) = P24 i−1 P52 ▶ i=1 δ u(c) + i=25 δ i−1 u(c + 20) ▶ Re-arranging, the left-hand side of the expression is equal to: P24 ▶ i=1 δ i−1 (u(c + 20) − u(c)) ▶ Re-arranging, the right-hand side of the expression is equal to: P52 ▶ i=25 δ i−1 (u(c + 20) − u(c)) P24 i−1 P52 ▶ So, i=1 δ = i=25 δ i−1 ▶ Any term other than δ drops out. So, the measurement of δ does not depend on u(c). Evidence on Time Preferences Evidence on Time Preferences  Evidence on Time Preferences The Marshmallow Test: Mischel et al (1989) ▶ 35 preschoolers in lab, each given one marshmallow ▶ Told that if they can wait 15 minutes without eating marshmallow, they can get another one ▶ Measure how long they wait before eating marshmallow ▶ Video example ▶ 12 years later, those students take the SAT ▶ Results: ▶ Waiting time strongly positively correlated with SAT math and verbal scores ▶ Waiting for 5 more minutes predicts 40 points higher SAT math score ▶ What parameter is being measured here? β or δ? measuring beta (and implicitly, delta as well)  Evidence on Time Preferences Field Evidence: Meier and Sprenger (2010) ▶ Give multiple price list instrument to people coming in for tax advice in Boston ▶ Questions on MPL ask to choose between smaller sooner cash payment and larger later cash payment ▶ Did same procedure on same population in two different years: 2007 and 2008 ▶ 1500 observations, including 200 people who showed up both years ▶ Because of setting, had access to income data  Evidence on Time Preferences Meier and Sprenger (2010): Multiple Price Lists ▶ t is early period, τ is later period  Evidence on Time Preferences Meier and Sprenger (2010): Results ▶ When early reward is immediate, more likely to take early payment ▶ Estimates of β between 0.672 and 0.792 ▶ Estimates of monthly δ between 0.953 and 0.981 ▶ Estimates remarkably stable between years  Evidence on Time Preferences Potential Problems with the Standard MPL Approach ▶ Have assumed that transaction costs are same in all time periods ▶ But people may avoid getting money in a period if transaction cost is high that period ▶ What transaction costs might arise in an experiment over multiple time periods? ▶ Andreoni and Sprenger (2012) try to eliminate transaction costs ▶ Note we are trading off money, not consumption, in most of these experiments ▶ So subjects with access to bank accounts should be able to arbitrage if implicit interest rate in experiment is different than actual interest rate ▶ Augenblick, Niederle, and Sprenger (2015) have subjects trade off consumption good (namely leisure time)  Evidence on Time Preferences Convex Time Budgets: Andreoni and Sprenger (2012) ▶ Took extreme measures to address transaction cost issue ▶ All payments by check, delivered to student mailbox ▶ Thank you payment arrives as $5 today, $5 at later period ▶ Students self-address both envelopes ▶ Rather than make binary (sooner vs later) choice, introduce convex time budgets (CTB) ▶ Subject given budget of 100 tokens ▶ Tokens worth different amounts p1 , p2 in early and later periods, giving an implicit interest rate 1 + r = pp21 ▶ Allocate tokens as desired between periods ▶ Like price list, make decision for a variety of possible interest rates  Evidence on Time Preferences Andreoni and Sprenger (2012): Results ▶ Estimates of annual δ between 0.73 and 0.80 (δ = 1+r 1 ) ▶ Estimates of present-bias β very close to 1, i.e. no apparent aggregate time-inconsistency ▶ Note: t is earlier period, t + k is later period  Evidence on Time Preferences Money vs Consumption ▶ Andreoni and Sprenger use money as the main choice object ▶ Recall that time budgets imply interest rate r ▶ Compare to market interest rate rm ▶ If r < rm , student should put all tokens on sooner payoff, since they could invest all of that money and earn better return in the market ▶ If r > rm , student should put all tokens on later payoff, by similar argument ▶ This arbitrage argument shows that experiment is not really measuring time preferences for students with access to credit markets ▶ Ideally, subjects would be trading off actual consumption instead of money  Evidence on Time Preferences Working Over Time ▶ Lab experiment by Augenblick, Niederle, and Sprenger (2015) ▶ Real effort task: transcription of Greek characters OR Tetris ▶ Must do 50 tasks over course of experiment ▶ Occurs over several weeks ▶ Week 1: make plan to split work over weeks 2 and 3 ▶ Week 2: allowed to change plan with some probability; do week 2 work ▶ Week 3: do remaining work ▶ Must do at least 10 tasks in both weeks 2 and 3 (transaction costs) ▶ Transfer work tasks between weeks 2 and 3 at varying interest rates ▶ Only one interest rate actually implemented, much like price lists we have seen ▶ At same time, making sooner-smaller vs later-larger choices over cash  Evidence on Time Preferences The Tasks  Evidence on Time Preferences Different task interest rates  Evidence on Time Preferences Strong Present Bias in Effort Tasks  Evidence on Time Preferences No Present Bias in Monetary Decisions Evidence on Time Preferences Commitment Commitment  Evidence on Time Preferences Commitment Motivation ▶ We have seen lots of evidence that people have time-inconsistent preferences ▶ How do we know that they are sophisticated, i.e. aware of their time-inconsistency? ▶ One answer: allow people to commit themselves to an action ▶ This allows the present self to restrict the opportunity set of the future self ▶ With time-consistent preferences this would make them worse off ▶ But with present-biased preferences this restriction can be welfare improving  Evidence on Time Preferences Commitment Example From Last Lecture ▶ Recall the example writing your paper over the next four weeks ▶ We showed that a time-consistent student would do paper right away, missing only the really bad movie ▶ Sophisticated time-inconsistent student would procrastinate somewhat ▶ Go to really bad movie in first week ▶ Do paper in second week, missing OK movie ▶ Overall, they are worse-off than their time-consistent classmate, and they know this ▶ Should be willing to undertake costly commitment to force self to do paper in first week, e.g. by having friend take away movie tickets if they don’t do paper in first week ▶ Assuming they follow through, they are now as well-off as their time-consistent classmate  Evidence on Time Preferences Commitment Tying Odysseus to the Mast ▶ Ashraf et al (2006) design a commitment savings product for a bank in Philippines ▶ SEED: Save Early Enjoy Deposits ▶ Get 4% interest rate ▶ Can’t withdraw until either target month or target savings is reached ▶ Survey to collect hypothetical time preference questions of 1800 existing and former clients of bank ▶ Randomly offer commitment product to approximately half of sample ▶ Results: ▶ 28% of people uptake commitment device overall ▶ 16 percentage point (50%) increase in uptake among women if identified as time-inconsistent  Evidence on Time Preferences Commitment Commitment device in the wild Stickk.com ▶ Commitment contract is binding agreement with yourself ▶ Contracts that cannot be renegotiated ▶ Commit something (referee, financial stakes) that will be lost if do not achieve goal (loss aversion) ▶ “Make Your Dating Goals a Reality With This Science-Based Habit Tracker” 06/25/2024