Read This Paper Later: Procrastination with Time-Consistent Preferences

Read This Paper Later:
Procrastination with
Time-Consistent Preferences
Carolyn Fischer
Discussion Paper 99-19
April 1999
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Read This Paper Later:
Procrastination with Time-Consistent Preferences1
CAROLYN FISCHER2
Resources for the Future
Abstract
A model of time-consistent procrastination is developed to assess the extent to
which the observed behavior is compatible with rational behavior. When a finite work
requirement must be completed by a deadline, the remaining time for leisure is an ex-
haustible resource. With a positive rate of time preference, the optimal allocation of
this resource results in more hours spent working (and fewer in leisure) the closer the
deadline. Key qualitative findings of psychological studies of academic procrastina-
tion are consistent with the standard natural resource management principles implied
by the model, when suitably adapted to task aversiveness, uncertainty, and multiple
deadlines. However, quantitatively, the fully rational model requires an extremely
high rate of time preference or elasticity of intertemporal substitution to generate seri-
ous procrastination; furthermore, it cannot explain undesired procrastination. A com-
panion paper, “Read This Paper Even Later: Procrastination with Time-Inconsistent
Preferences” analyzes the extent to which alternative time discounting preferences can
better explain such impatience and address the issue of self-control failures.
Keywords. procrastination, natural resource economics
JEL Classification No(s).: Q3, D9, J22, D81
1The author appreciates many useful comments from Steve Salant, Charles Fleischman, Miles Kimball,
Bob Barsky, Hal Varian, and seminar participants at the Universities of Michigan, Calgary, and Montr´eal,
Queen’s University, and Resources for the Future. Thanks to all my students and colleagues for inspiration.
This work has been supported financially by the University of Michigan and Resources for the Future.
2Resources for the Future, 1616 P St. NW, Washington, DC 20036. E-mail: fischer@rff.org

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Contents
1
Introduction
4
2
Stylized Facts
6
3
Model
7
3.1
Task Aversiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2
Procrastination under Uncertainty . . . . . . . . . . . . . . . . . . . . . . 13
3.3
Penalties and Multiple Deadlines . . . . . . . . . . . . . . . . . . . . . . . 22
3.4
Actual and Effective Discount Rates . . . . . . . . . . . . . . . . . . . . . 25
4
Conclusion
28
Appendix
29
References
30
List of Figures
1
Daily Labor Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2
Choke Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3
Capacity Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4
Task Aversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5
Value of the Last Stage Given I . . . . . . . . . . . . . . . . . . . . . . . . 17
6
Cumulative Work under Certainty . . . . . . . . . . . . . . . . . . . . . . 20
7
Expected Value of ψ
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
8
Multiple Deadlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
9
Setup Costs and the Path of Work
. . . . . . . . . . . . . . . . . . . . . . 27
2

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Table of Variables
In alphabetical order:
δ
daily discount factor
λ
multiplier for cumulative stock of work constraint
σ
rate of time preference
ψ(ω)
= u(1 − ω) + u(1 − ω)ω
ω
work rate
φ(·)
probability distribution function of ˜
N
a
marginal aversiveness of work
I
number of days taken to complete M
lt
leisure at time t
M
initial amount of work to be completed before uncertainty resolved
˜
N
uncertain remaining work requirement
N ∗
cutoff remaining work requirement for last stage beginning at I
I
P
penalty
R
required hours of work
t
time index
T
number of days until deadline (including day 0)
u(·)
utility of leisure
Ui(·)
discounted utility of leisure in stage i
Vi(·)
discounted value of stage i
wt
work at time t
3

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1
Introduction
It’s a familiar scene: the last day of classes and the day the term paper is due. Students
straggle in, some depositing papers only to turn around and head back to bed; some take
a seat but appear to mistake it for that other piece of furniture; and the rest struggle to
pay attention to the lecture, most offering up little more than a blank, red-eyed gaze to
the board. At these times, both students and professors must wonder, why do they put
themselves through it? (Of course, professors may not really ponder this question until the
morning the grade sheets are due.)
Procrastination, particularly in academics, has been the source of several psychological
studies, but few economic ones. Presumably, this dichotomy exists because psychologists
love to explore irrational behavior and economists usually restrict themselves to rational
conduct — and procrastination is perceived to be irrational. Freudians Blatt and Quinlan
(1967) attribute procrastination to an attempt to avoid “unconscious death anxiety”: “By
being continually late, the procrastinator is expressing rebellion at the finality of his or her
existence.”3 Missildine, another psychoanalyst of the 1960s, blames poor childrearing as
the cause: “an overindulgent parent encouraging underachievement, or an overdemanding
parent encouraging rebellious lassitude.”4 However, if not rational, the behavior is certainly
normal: Ellis and Knaus (1977) estimated that 95% of college students procrastinate. More
recently, empirical studies (such as Aitken (1982), Solomon and Rothblum (1984), and
McCown, Petzel and Rupert (1987)) have concentrated on the correlation between procras-
tination and certain psychological or personality traits, such as compulsiveness, anxiety,
and extraversion.
Some economists have also taken the perspective of irrational procrastination. Ak-
erlof (1991) studied procrastination when a task requires action at a single point in time.
Opportunity costs of time today are more salient than those tomorrow; that is, today’s op-
3McCown, Petzel, and Rupert (1987), p. 781.
4ibid.
4

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portunities are clear while tomorrow’s are vague, making the former seem more pressing.
With a “salience cost” to acting today, and none attributed to tomorrow, one always wants
to postpone action, even though the stream of benefits is maximized with immediate action.
But the dynamically inconsistent preferences generated by salience costs in his model are
not sufficient to produce indefinite procrastination: one must have irrational expectations
of the future. If a person realizes she will want to postpone again every day, the rational
expectations strategy is to perform the task at once. O’Donoghue and Rabin (1999) also
examine the decision to procrastinate a one-time task with Akerlof-style salience costs, al-
lowing for rewards or costs to be salient and expectations to be sophisticated (rational) or
na¨ıve.5
However, not all tasks require a one-time action. This paper considers a particular type
of task, distinct from Akerlof’s: work that can be divided into many (if not an infinite
number of) small actions to be completed over time, such as writing a term paper. Nor is
procrastination always characterized by missing deadlines or abandoning tasks; procrasti-
nation can exhibit itself in an increasing workload, as more of the task is performed the
closer the deadline.
Academic procrastination is a familiar example: assignments may be handed in on time
yet procrastination is deemed to have occurred since much of the work was accomplished
at the eleventh hour. But can delaying enough of the effort to such a point as the discomfort
of all-nighters really be rational?
Modeling time as an exhaustible resource, this paper shows that simple impatience of-
fers a reasonable theoretical explanation of dynamically consistent procrastination. The
next section overviews some of the observations psychologists have made regarding pro-
crastinating behavior. Section 3 develops the time allocation decision as an exhaustible
5They show that rational expectations can still allow for some procrastination. For example, in a four-
period model, if the task is worth performing in period 4, and knowing this the person in period 3 will
procrastinate, the person in period 2 may find waiting two more periods for the reward too costly and want to
perform it. Consequently, the person in the first period will procrastinate, confident the task will be performed
in the next period.
5

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resource utilization problem. Subsequent subsections draw on standard results from natu-
ral resource economics to explain key findings in the psychological studies: task aversion,
procrastination under uncertainty, and the effectiveness of multiple deadlines. A brief dis-
cussion of how to reconcile the high discount rates implicit in substantial procrastination
with standard concepts of discounting follows. Section 4 concludes.
2 Stylized Facts
In psychology as well as in economics, definitions of procrastination differ widely; perhaps
the one most closely corresponding to mine is presented by Solomon and Rothblum (1984):
“the act of needlessly delaying tasks to the point of experiencing subjective discomfort.”
I interpret “needless” to be in terms of feasibility and “subjective discomfort” to be sig-
nificant disutility of work near the deadline. A student could work at a steady pace, but a
procrastinator builds up her workload, putting off more work until near the deadline, even
at the cost of having little or no leisure left at that point.
Some stylized facts about procrastination observed by psychologists are summarized in
the box below.
6

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The Psychology of Procrastination: Some Stylized Facts
• Procrastination is pervasive.
95% of college students procrastinate. [5]
46% nearly always or always procrastinate n writing a term paper. [23]
• Major reasons cited for procrastination: [23]
1. Too many other things to do (61%)
2. Task is aversive (47+%)
3. Felt overwhelmed by the task (40%)
4. Fear of failure (14+%)
• Easier tasks are performed first. [17]
• Procrastinators are more likely to miss deadlines. [2]
• Extraverts procrastinate more. [17]
• Procrastination is perceived to be a problem. [23]
This paper will address each observation in turn, showing that almost every one can be
explained by a rational model of time allocation. The notable exception is the last obser-
vation, prompting discussion of modifications to the rational model to deal with problem
procrastination.
3
Model
Posing the problem succinctly, when the work requirement demands many units of effort
over a finite amount of time, when will that effort take place? The answer lies in the simple
idea that leisure time is an exhaustible resource. When a fixed amount of work must be done
by a distant deadline, leisure time in the interim is an exhaustible resource to be consumed
over time until the deadline, subject to a cumulative stock constraint. People like leisure
and prefer it sooner rather than later; time can be allocated between work and leisure, but
a certain amount of cumulative hours of work is required by some deadline. The person
thus weighs the gains from taking leisure now against the utility costs of having to do more
work later.
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Suppose a person gets utility u(lt) for l hours of leisure on any day t, and assume u(·) is
strictly increasing and concave. Let δ represent the daily discount factor. R hours of work
are required to write a paper, the deadline for which is T days from now. A maximum of
24 hours per day can be spent working on the paper;6 leisure thus equals the excess of 24
over wt hours of work: lt = 24 − wt. What is the optimal allocation of time into leisure
and work from now until the deadline?
We can think of leisure time as an exhaustible resource with a stock size of 24T − R
(assumed to be positive; i.e., the task is feasible). In addition, we have a maximum daily
extraction rate—a capacity constraint—of 24 hours. The student maximizes her utility
from leisure subject to the work requirement:
T −1
T −1
U (R, T ) = max
u(24 − wt)δt − λ R −
wt
.
(1)
wt∈[0,24] 0
0
The multiplier on the work constraint, λ represents the shadow value of another hour of
leisure. The resulting first-order conditions are really those found by Hotelling. One of the
following pairs must hold for all t:
(a) 0 < wt < 24, u (24 − wt)δt = λ;
(b)
wt = 0,
u (24)δt ≥ λ;
(c)
wt = 24,
u (0)δt ≤ λ;
(2)
These conditions imply that for any 0 < wt < 24, the marginal utility of leisure (MUL)
will be growing at the rate of time preference, which in turn implies that wt will rise mono-
tonically over time. Figure 1 shows the “daily labor supply” curve for a log utility function.
The student works until her discounted marginal utility of leisure equals the shadow value
of work.
6Those of less hardy stock who need a minimum of sleep may feel free to pick a smaller number.
8

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Figure 1: Daily Labor Supply
MUL
1
0.8
0.6
Shadow Value of Work
0.4
0.2
0 0
4
8
12
16
20
24
Hours of Work
In addition, one of these pairs must hold:
T −1
T −1
(a) λ > 0,
wt = R;
(b) λ = 0,
wt ≥ R.
(3)
0
0
That is, if λ is strictly positive, the work constraint is binding and cumulative hours of
work just equal the requirement; if the constraint does not bind (cumulative work hours ex-
ceed the requirement), then λ will be zero. But psychologists and economists alike should
recognize that doing more work than necessary is never rational, for if (3b) holds and u(·)
is strictly increasing, then (2b) implies that wt = 0 for all t ∈ [0, T − 1]. In other words, ex-
tra work requires leisure to be foregone and, in the context of this model, has no offsetting
benefit; thus, cumulative work hours must exactly equal the requirement.
If marginal utility at no leisure is finite, this value is essentially the “choke price.” Once
the MUL reaches this level, no leisure is consumed and the student works nonstop 24
hours per day. Suppose the choke price were reached at the last day of work. The student
works a little bit more each day until she spends the entire day before the deadline writing.
The cumulative hours of work implied by this path are unlikely to equal the requirement
except by pure chance. If the work requirement were less, the entire path would shift down
(lowering the MUL and wt for all t and thus lowering the cumulative hours of work until
they equalled the requirement), and the choke price would never be reached; in other words,
9

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