Procrastination, Self-Imposed Deadlines and Other Commitment Devices: Theory and Experiment

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1 Procrastination, Self-Imposed Deadlines and Other Commitment Devices: Theory and Experiment Alberto Bisin 1 Kyle Hyndman 2 1 New York University 2 Southern Methodist University University of Maryland College Park, MD (Procrastination & Deadlines) Kyle Hyndman Maryland 1 / 46

2 Some Humour To Begin (Procrastination & Deadlines) Kyle Hyndman Maryland 2 / 46

3 Motivation The study of procrastination needs almost no motivation everyone procrastinates: Academics put off doing referee reports. Students put off homework and/or studying for exams. Workers delay making retirement savings contributions. We put off going to the gym or starting a diet. Alberto and I have procrastinated on this paper. (Procrastination & Deadlines) Kyle Hyndman Maryland 3 / 46

4 May 2006: Started project Motivation Timeline of This Paper March 2008: Derived main theoretical results August 2008: Work on software for experiment began March-April 2010: First experiments conducted March-April 2011: Second experiments to be conducted?? (Procrastination & Deadlines) Kyle Hyndman Maryland 4 / 46

5 Motivation Why Do People Delay? 1. Time Consistent Procrastination (Fischer 2001): If the cost of completing a task (e.g., cost of effort) is stochastic, it is natural to delay working on a task until later because the cost might be lower in the future. Suppose that T = 2, δ = 1, V = 1. Suppose also that c 1 = 0.5 and c 2 {0.25, 0.5} (with equal probability). Value of completing the task today: π 1 = V c 1 = 0.5. Value of completing the task tomorrow: π 2 = V E[c 2 ] = (Procrastination & Deadlines) Kyle Hyndman Maryland 5 / 46

6 Motivation Why Do People Delay? 2. Time Inconsistent Procrastination (O Donoghue & Rabin): Because of hyperbolic discounting, decision makers think that they are more likely to exert effort in the next period and will, therefore, delay. Distinction between naive & sophisticated decision makers: Naifs are unaware of their self-control problems and, therefore, might delay forever, or start but not finish. Sophisticates are aware of their proclivities for procrastination, and because of their awareness they are more disciplined than naifs. (Procrastination & Deadlines) Kyle Hyndman Maryland 6 / 46

7 Overcoming Procrastination People often seek ways to commit themselves to doing a particular task or achieving a particular goal. Common/interesting techniques: Pre-paid gym memberships Christmas clubs Social pressure (e.g., the Twitter diet) Deadlines (Procrastination & Deadlines) Kyle Hyndman Maryland 7 / 46

8 Overcoming Procrastination Deadlines & Commitment (Procrastination & Deadlines) Kyle Hyndman Maryland 8 / 46

9 Overcoming Procrastination Deadlines Deadlines have been suggested by many (e.g., Ariely and Wertembroch (2002)) as a way to overcome one s tendency towards procrastination. Cost of deadlines: Destroys the option value of waiting for a lower cost realisation. Benefit of deadlines: Focuses attention on present and may help decision makers allocate their time more effectively. (Procrastination & Deadlines) Kyle Hyndman Maryland 9 / 46

10 Experimental Evidence on Deadlines The Case in Favour Ariely and Wertembroch (2002): subjects must complete three tasks by the end of the semester. Study 1 (writing 3 papers for a course) had two treatments: 1. Tasks exogenously and evenly spaced throughout the semester 2. Subjects can set their own deadlines. Study 2 (finding grammatical errors in 3 nonsense texts) had three treatments: 1. No intermediate deadlines. 2. Tasks exogenously and evenly spaced over 3 weeks 3. Subjects can set their own deadlines. (Procrastination & Deadlines) Kyle Hyndman Maryland 10 / 46

11 Ariely and Wertembroch (2002) Results In the endogenous deadlines treatment, most set binding deadlines. For Study 1, among those setting deadlines: Average deadline for task 1: 42 days before the last day of class. Average deadline for task 2: 26 days before the last day of class. Average deadline for task 3: 10 days before the last day of class.. Subjects in the exogenous deadline treatment do best, followed by subjects in the endogenous deadline treatment, and subjects with no deadlines did the worst. Subjects liked the task the most in the no deadlines treatment, followed by endogenous deadlines, followed by exogenous deadlines. Time spent on task also goes in the predicted direction across treatments. (Procrastination & Deadlines) Kyle Hyndman Maryland 11 / 46

12 Experimental Evidence on Deadlines The Case Against Burger, Charness and Lynham (2009): Subjects must complete 75 hours of studying at a monitored location over a five-week period. Two treatments: 1. No intermediate study deadlines. 2. Subjects must complete 15 hours during the first week, at least 30 by the end of the second week, etc. Subjects in the no deadlines treatment were substantially more likely to complete the task. Subjects studied a lot Monday Thursday and very little Friday Sunday. (Procrastination & Deadlines) Kyle Hyndman Maryland 12 / 46

13 Personal Evidence on Deadlines The Case Against In an effort to commit, I have made (or plan to make) the following conference / seminar presentations: June 2008 May 2010 August 2010 November 2010 March 2011 April 2011 May 2011 Yet the paper is still not finished! (Procrastination & Deadlines) Kyle Hyndman Maryland 13 / 46

14 Personal Evidence on Deadlines The Case Against In an effort to commit, I have made (or plan to make) the following conference / seminar presentations: June 2008 May 2010 August 2010 November 2010 March 2011 April 2011 May 2011 Yet the paper is still not finished! Problem: These deadlines had a commitment effect on me, but not on our programmer! (Procrastination & Deadlines) Kyle Hyndman Maryland 13 / 46

15 Our Goals To study both theoretically and experimentally the implications of self-imposed deadlines. What kind of people self-impose deadlines? When do they do it? Do self-imposed deadlines aid in task completion? (Procrastination & Deadlines) Kyle Hyndman Maryland 14 / 46

16 Model The Basics A single task needs to be completed before T. If task is completed at time t T, a reward of V is paid at time t +. The cost of completing the task, x, evolves according to a geometric Brownian motion dx = σx dz The decision maker has exponential discount function e ρt, where ρ > 0 captures the rate of time preference. (Procrastination & Deadlines) Kyle Hyndman Maryland 15 / 46

17 The Exponential Case Formally, this is equivalent to an American put option: W (x, t) = sup 0 τ T t E x,t (e ρτ max{ V x, 0}) The solution is a threshold, x(t), such that if x(t) x(t), the decision maker completes the task, otherwise she delays. Characterised by: ρw (x, t) = 1 2 σ2 x 2 W xx (x, t) + W t (x, t) W ( x(t), t) = V x(t) W x ( x(t), t) = 1 W (x, 0) = max{ V x, 0} (Procrastination & Deadlines) Kyle Hyndman Maryland 16 / 46

18 Proposition The Exponential Case Self-Imposed Deadlines An exponential discounter prefers later to earlier deadlines. Same intuition as for the American put option: a longer deadline increases the option value of waiting for a lower cost to complete the task. Since discounting is exponential, there is no extra pressure to delay; therefore, best not to destroy this option value by setting a deadline. (Procrastination & Deadlines) Kyle Hyndman Maryland 17 / 46

19 Hyperbolic Discounting Much experimental evidence that people are not exponential discounters. Instead, people become more impatient as rewards get closer. We use Harris and Laibson s (2004) model of quasi-hyperbolic discounting in continuous time: A decision maker is divided into two selves: current & future. Current self exercises control from time t to t + ˆt. Future self lasts from t + ˆt to. ˆt follows a Poisson process with arrival rate λ. { γ t if t [0, ˆt) D(t) = βγ t if t [ˆt, ) where 0 < β < 1. (Procrastination & Deadlines) Kyle Hyndman Maryland 18 / 46

20 Hyperbolic Discounters Naïfs Naïfs think that their future selves are exponential. They solve: W n (x, t) = max {U(λ) x, e ρdt E [ e λdt W n (x + dx, t + dt) +(1 e λdt )βw e (x + dx, t + dt) ]} Can re-write the problem as: ρw n (x, t) = 1 2 σ2 x 2 W n xx(x, t) + W n t (x, t) + λ[βw e (x, t) W n (x, t)] along with the following optimality conditions: W n ( x n (t), t) = U(λ) x n (t) W n x ( x n (t), t) = 1 W n (x, T ) = max{u(λ) x, 0} (Procrastination & Deadlines) Kyle Hyndman Maryland 19 / 46

21 Hyperbolic Discounters Naïfs Taking λ, so that the current self lasts only an instant, in the waiting region, we obtain: W n (x, t) = βw e (x, t). Proposition Unless x(t) = 0, the naïve decision maker will complete the task only at time T and only if x(t ) β V. (Procrastination & Deadlines) Kyle Hyndman Maryland 20 / 46

22 Proposition Hyperbolic Discounters Naïfs Unless x(t) = 0, the naïve decision maker will complete the task only at time T and only if x(t ) β V. 1. If 0 < x(t) < x(t), so that W e (x(t), t) = V x(t) meaning that an exponential DM would complete the task then since W n (x, t) = max{β V x, βw e (x, t)} the naïve hyperbolic agent completes the task if x(t) β[ V ( V x(t))] = βx(t). 2. This is impossible since β < 1. (Procrastination & Deadlines) Kyle Hyndman Maryland 20 / 46

23 Hyperbolic Discounters Sophisticates Sophisticates know that they have a tendency to procrastinate. They solve: W s (x, t) = max {U(λ) x, e ρdt E [ e λdt W s (x + dx, t + dt) +(1 e λdt )βw c (x + dx, t + dt) ]} Can re-write the problem as: ρw s (x, t) = 1 2 σ2 x 2 W s xx(x, t) + W s t (x, t) + λ[βw c (x, t) W s (x, t)] along with the following optimality conditions: W s ( x s (t), t) = U(λ) x s (t) W s x ( x s (t), t) = 1 W s (x, T ) = max{u(λ) x, 0} (Procrastination & Deadlines) Kyle Hyndman Maryland 21 / 46

24 Hyperbolic Discounters Sophisticates Taking λ, so that the current self lasts only an instant, we obtain: W s (x, t) = βw c (x, t). Proposition In the limit as λ, the sophisticated hyperbolic discounter behaves as if he were an exponential discounter in which the reward for completing the task is β V. The PDE and boundary conditions for the sophisticated hyperbolic decision maker are the same as that of an exponential decision maker with value β V of completing the task. (Procrastination & Deadlines) Kyle Hyndman Maryland 22 / 46

25 Proposition Optimal Deadline For Sophisticates It is sometimes optimal for sophisticated decision makers to set a binding deadline. If they do, they set either an immediate deadline or a sufficiently strict deadline so that they immediately complete the task. E x [βw c (x, 0; τ)] = x s (0,τ) 0 β( V x)df (x) + W s (x, 0; τ)df (x) x s (0,τ) W s (x, t) is increasing in t, but for costs near x s (t), W s (x, t) β V x s (t) < β( V x s (t)). Therefore, there is a discontinuous benefit from immediately completing the task. (Procrastination & Deadlines) Kyle Hyndman Maryland 23 / 46

26 Numerical Exercise Initial Cost Known x 10-4 b = 0.1; r = 0.01; s = b = 0.2; r = 0.01; s = b = 0.3; r = 0.01; s = b = 0.4; r = 0.01; s = b = 0.5; r = 0.01; s = b = 0.6; r = 0.01; s = b = 0.7; r = 0.01; s = b = 0.8; r = 0.01; s = b = 0.9; r = 0.01; s = (Procrastination & Deadlines) Kyle Hyndman Maryland 24 / 46

27 Numerical Exercise Initial Cost Unknown Uniformly Distributed on [0, 1] 1 b = 0.1; r = 0.05; s = b = 0.2; r = 0.05; s = b = 0.3; r = 0.05; s = b = 0.4; r = 0.05; s = b = 0.5; r = 0.05; s = b = 0.6; r = 0.05; s = b = 0.7; r = 0.05; s = b = 0.8; r = 0.05; s = b = 0.9; r = 0.05; s = (Procrastination & Deadlines) Kyle Hyndman Maryland 25 / 46

28 The Experiment Subjects have to complete 3 tasks over a two-week period. Each task is to alphabetize a list of 150 words. Payment of $15 for each task completed by the deadline. Pre-experiment survey in order to elicit: How busy they are with school, family, work and social obligations in order to capture the perceived opportunity cost of time & anticipated cost shocks ; Personality traits (e.g., dependability, punctuality, self-control problems) Their perceptions of how likely they are to complete the tasks. We can observe the time at which they logon, as well as task submission attempts and new task issuance. (Procrastination & Deadlines) Kyle Hyndman Maryland 26 / 46

29 The Experiment The List of Words (Procrastination & Deadlines) Kyle Hyndman Maryland 27 / 46

30 The Experiment The List of Words (Procrastination & Deadlines) Kyle Hyndman Maryland 28 / 46

31 The Experiment In order to simulate a stopping time problem as closely as possible: Once a task was issued to a subject, he/she would have to complete it by the earlier of 2 hours and the actual deadline. Subjects could not save their work and come back later. If subjects refreshed the screen or logged back in later, they would be given a new list. We also told subjects in the instructions how they should do the tasks. This was done so as to put everyone on a more level playing field. (Procrastination & Deadlines) Kyle Hyndman Maryland 29 / 46

32 The Experiment Treatments Basic treatments: No Intermediate Deadlines Exogenous (and evenly spaced) Deadlines Self-Imposed Deadlines One session of each treatment in the middle of the semester (65 subjects). One session of each treatment at the end of the semester (72 subjects). (Procrastination & Deadlines) Kyle Hyndman Maryland 30 / 46

33 Remarks & Hypotheses If a subject sets a non-trivial deadline, it is evidence of that subject being a sophisticated hyperbolic discounter. Subjects setting no deadlines, could be any of the three types. Naifs wait until the last moment to do the task, if at all. Exponential discounters may complete the task at any time up to the deadline. Sophisticates are somewhere between naifs and exponential types. Exogenously set deadlines: make it less likely that exponential type completes the tasks. make it no more or less likely that a naif completes the tasks. have an ambiguous effect on sophisticated types. Busier subjects are less likely to set deadlines and less likely to complete tasks. (Procrastination & Deadlines) Kyle Hyndman Maryland 31 / 46

34 Results: Beliefs We asked subjects to report their beliefs about how likely they were to complete 0, 1, 2, or 3 tasks. (Procrastination & Deadlines) Kyle Hyndman Maryland 32 / 46

35 Results: Beliefs We asked subjects to report their beliefs about how likely they were to complete 0, 1, 2, or 3 tasks. Session 1: Not Busy Endogenous Evenly Spaced No Deadlines 0 Tasks 0.7% 2.3% 5.6% 3 Tasks 89.5% 79.5% 91.2% Session 2: Busy Endogenous Evenly Spaced No Deadlines 0 Tasks 1.8% 0% 5.4% 3 Tasks 86.0% 87.3% 88.8% (Procrastination & Deadlines) Kyle Hyndman Maryland 32 / 46

36 Results: Tasks Completed Endogenous Evenly Spaced No Deadlines Session 1 (Not Busy) 44.4% 44.4% 59.4% Session 2 (Busy) 36.1% 26.4% 31.9% Overall 40.0% 34.8% 45.4% Distribution of Tasks Completed (Pooled) Endogenous Evenly Spaced No Deadlines 0 Tasks 51.1% 51.1% 44.7% 1 Task 8.9% 11.1% 10.6% 2 Tasks 8.9% 20.0% 8.5% 3 Tasks 31.1% 18.8% 36.2% (Procrastination & Deadlines) Kyle Hyndman Maryland 33 / 46

37 Results: On Which Day Are Tasks Completed? 1: Not Busy Session Session 1: Not Busy.3382 Session 2: Busy : Not Busy Session 2: Busy Fraction Day Task Completed Fraction Day Task Completed (Procrastination & Deadlines) Kyle Hyndman Maryland 34 / 46

38 Results: Endogenous Deadlines Session 1: Not Busy Task 1 Task 2 Task 3 Days Before (Unconditional) Days Before (Conditional) % Setting Deadlines Session 2: Busy Task 1 Task 2 Task 3 Days Before (Unconditional) Days Before (Conditional) % Setting Deadlines (Procrastination & Deadlines) Kyle Hyndman Maryland 35 / 46

39 Who Sets Deadlines? Subjects who self-imposed deadlines are (two-sided tests): less conscientious (p = 0.016), spend more time socializing with friends (p = 0.032), have more major assignments due (p = 0.043), enrolled in fewer courses (p = 0.085), more frequently on-time (p = 0.091), and less likely to follow a schedule (p = 0.12) than subjects who did not self-impose deadlines. (Procrastination & Deadlines) Kyle Hyndman Maryland 36 / 46

40 Results: Are Deadlines Valuable? Endogenous deadlines do not appear to aid in task completion: No deadline set: 43.6% of tasks completed. Deadline set: 35.1% of tasks completed. Subjects who set a deadline were much more likely to run up against it. The closer that subjects run up against the deadline (in terms of task issuance), the less likely they are to complete the task. (Procrastination & Deadlines) Kyle Hyndman Maryland 37 / 46

41 Results: Are Deadlines Valuable? (deadline) Endogenous Endogenous (deadline) Endogenous (no deadline) (deadline) Endogenous (no Even No Deadlines Fraction Difference Between Task Issuance Time & Deadline Fraction Even No Deadlines Difference Between Task Issuance Time & Deadline 15 (Procrastination & Deadlines) Kyle Hyndman Maryland 38 / 46

42 When Do Tasks Get Completed? Number of Days Before Deadline (Session 1) Endogenous Evenly Spaced No Deadlines Task Task Task Number of Days Before Deadline (Session 2) Endogenous Evenly Spaced No Deadlines Task Task Task (Procrastination & Deadlines) Kyle Hyndman Maryland 39 / 46

43 Other Results Subjects who finished 0 tasks are (two-sided tests): less organised (p = 0.002), in more clubs/social organisations (p = 0.064), spend less time with their family (p = 0.097), place more weight on probability of completing 0 tasks (p = 0.107), place less weight on probability of completing 3 tasks (p = 0.131), less likely to follow a schedule (p = 0.158), and are less frequently punctual (p = 0.172) than subjects who finished all 3 tasks. (Procrastination & Deadlines) Kyle Hyndman Maryland 40 / 46

44 Other Results 79% of subjects who completed 0 tasks logged on at least once and 70% had at least one submission failure. Maybe not procrastination? Perhaps they found the task harder than expected and quit? (Procrastination & Deadlines) Kyle Hyndman Maryland 41 / 46

45 Future Plans Theory One undesirable feature of our model is that, if a decision maker self-imposes a deadline, he sets it in order to ensure immediate task completion. We observe a lot of intermediate deadlines and task completion. How can we incorporate this into our model? Brunnermeier et al (2008) present a model of the planning fallacy in which people self-impose intermediate deadlines (though deadlines here represent an amount of work to be completed in each period). (Procrastination & Deadlines) Kyle Hyndman Maryland 42 / 46

46 Future Plans Experiment Increase the number of words (i.e., make the task more difficult). Allow subjects to request reminders. Change deadlines from a strict cut-off to a per-period penalty to lessen the severity of deadlines (à la Ariely and Wertembroch). (Procrastination & Deadlines) Kyle Hyndman Maryland 43 / 46

47 Some Humour To End (Procrastination & Deadlines) Kyle Hyndman Maryland 44 / 46

Some Humour To End IDIIIJ 13... SCDTT r-idr-ims YOUR PROJECT DEAD- LINE 1& NEXT MONTH.

48 Some Humour To End IDIIIJ SCDTT r-idr-ims YOUR PROJECT DEAD- LINE 1& NEXT MONTH. AND I CAN"T IMAGINE YOU FINI&HING ON TIME. Mothering Sunday (UK) sunday (Procrastination & Deadlines) Kyle Hyndman Maryland 45 / 46

49 Some Humour To End (Procrastination & Deadlines) Kyle Hyndman Maryland 46 / 46

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