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Dynamic Goal Attainment – A Formal Model and
Experimental Evidence
by Anastasia Danilov
a
, Bernd Irlenbusch
b
and Dirk Sliwka
c
This paper examines the effect of externally assigned goals on dynamic effort provision. First,
we develop a formal economic model to examine the timing of optimal effort provision when
an agent receives a bonus for the attainment of the goal in a multiple period context. Dynamic
optimization gives a precise prediction on the optimal effort levels for any given goal and
bonus, conditional on the goal-attainment progress and deadline closeness. In a second step,
we test the theoretical prediction in a laboratory experiment. In line with a pattern predicted
by the theoretical model, subjects exert low effort in the beginning and gradually increase
effort as long as the goal attainment probability is high, and decrease effort otherwise.
However, we find evidence for a systematic effort overprovision which is (i) decreasing if the
noise in the output process is positive and (ii) increasing with the costs already invested.
JEL Classification: A12, C91, D03, D81, J01, J30, J31, M52
Keywords: Goal attainment; Performance targets; Self-regulation
a
Corresponding author: Department of Corporate Development and Business Ethics, University of Cologne, Albertus-Magnus-Platz, 50923
Cologne, Germany, Email: danilov@wiso.uni-koeln.de, Telephone: +49 (0) 221 470 6313.
b
Department of Corporate Development and Business Ethics, University of Cologne, Albertus-Magnus-Platz, 50923 Cologne, Germany.
c
Department of Personnel Economics and Human Resource Management, University of Cologne, Albertus-Magnus-Platz, 50923 Cologne,
Germany.
2
“Briefly to illustrate some of the other elements which go to make
up the science of shoveling, thousands of stop-watch observations
were made to study just how quickly a labourer […] can push his
shovel into the pile of materials […] With data of this sort before
him […] it is evident that the man who is directing shovelers can
[…] assign them daily tasks which are so just that the workman
can each day be sure of earning the large bonus which is paid
whenever he successfully performs this task.”
Frederick Winslow Taylor (1911, pp. 32-33)
1. Introduction
Since the origins of scientific management dating back to Frederick W. Taylor’s (1911) famous
performance studies of shovelers, linking pay to performance has become a powerful tool for
motivating employees in organizations. As illustrated by Taylor, a prominent way to link pay to
performance is to assign goals to employees and to promise a substantial bonus if they reach the
performance standard, but provide no bonus if they do not. A key aspect of many performance targets
is that they involve a dynamic decision sequence, i.e., several effort moves are required over a period
of time to attain a goal. It is often at the discretion of the agents to adapt their efforts over time. Think
of Taylor’s shovelers, who are promised a bonus if their daily output reaches a certain performance
standard. As long as they meet their targets, it is up to the shovelers whether they work with a constant
effort or, for instance, provide high efforts in the morning in order to be able to relax their care during
the afternoon. Other examples of dynamic goal attainment include yearly profit targets for investment
bankers, quarterly sales targets for insurance sellers, or monthly targets for consultants’ billable
project hours. The purpose of this paper is to investigate optimal effort provision in such situations.
This paper explores to what extent a dynamic optimization model, assuming strict rationality, can
contribute to understand the behavior of real decision makers. In the formal model – where an
individual target is linked to a monetary bonus – we study the behavior of a rational agent who
sequentially works during several periods. Within each period, the agents can advance one step
towards the goal, where the probability of progress is a function of individual effort. The effort is
costly, and therefore the agents constantly update their expected net utility evaluating the difference
between the expected bonus and the cost of effort. The recursive solution of this dynamic optimization
problem leads to precise path-dependent effort predictions. Our model suggests that balancing convex
costs against the expected monetary returns, rational agents choose rather low efforts when sufficient
amount of time left. As time passes, the agents will have an incentive to work more in order to achieve
a desirable goal and will increase their efforts when less time remains. However, the efforts will drop
when chance of reaching the performance threshold becomes low.
We then conducted a laboratory experiment to test the numeric predictions derived from our
model. In each of 12 periods, participants had to choose a costly effort. This effort choice determined
the probability of advancing towards the assigned goal. We systematically varied the goal size
3
between treatments. In order to allow subjects to gain experience they repeatedly had to work on 8
identical goal attainment tasks. In the following we will refer to these consecutive tasks as runs.
In general, the experimental data come close to the theoretical benchmark. However, we also find
systematic deviations. First, there is excessive effort provision, i.e., frequently the chosen efforts
exceed the predicted efforts. Such effort overprovision is particularly strong in early periods when the
deadline is remote. Having experienced task progress more often, the subjects learn to reduce their
effort overprovision in the subsequent period and try to achieve successful results by working less.
While those who were out of luck, increase their efforts. In addition, we find evidence for an
escalation of commitment, as agents increase their effort to a stronger extent when they have already
invested higher efforts for attaining the goal.
An economic literature on goals and their potential effects on employees’ behavior has only
recently started to emerge. Wu et al. (2004) and Heath et al. (1999) use prospect theory to explain how
not-incentivized goals affect performance. Hsiaw (2011), Koch and Nafziger (2011) and Jain (2009)
study the effect of intrinsic goals in the context of self-control problems and procrastination. In a
randomized field experiment, Goerg and Kube (2012) find that especially self-assigned goals lead to a
significant performance increase compared to a piece-rate incentive scheme. Whereas most of these
studies consider personal or self-chosen goals rather than externally imposed ones (see also Crawford
and Meng, 2011; Farber, 2008; Fehr and Götte, 2007; Camerer et al., 1997), some other works explore
to what extent the assigned targets influence performance. For example, Murphy (2000) discussed
contracts with external performance standards. In an empirical study with navy recruiters, Asch (1990)
observes a significant performance increase before the goal attainment deadline and postponement of
new achievements into the next period. Kivetz et al. (2006) observe increased frequency in customers’
purchases when the threshold for receiving a free consumption reward is near.
In addition to motivational effects, other severe negative side effects of performance targets have
been reported. Engaging in illegal and/or immoral activities to manipulate performance measures in
order to meet the goals is a pertinent example of undesired behavior that seems to be fostered by goal
setting. Jensen (2003), for example, emphasizes that the discontinuities of compensation schemes that
promise a bonus when a goal is met create high incentives to game the system if one is close to the
target. Ordonez et al. (2009) and Schweitzer et al. (2007) argue that “goals have gone wild” and
emphasize the detrimental effect of goal setting.
This discussion about goal-setting on the one hand being a powerful tool to motivate employees
and on the other hand a potential to harm an organization if not appropriately applied, makes it
necessary to better understand how exactly individuals respond to goals and to what extent a rational
model of goal attainment can predict behavior.
The remainder of the paper proceeds as follows. The next session outlines a simple model on
effort provision within a dynamic context with an exogenously set target. Section 3 introduces the
4
experimental treatments. The experimental design and procedures are described in Session 4. Section 5
presents and discusses the experimental results. Section 6 concludes.
2. Theoretical Analysis
2.1 The Model
We consider a rational agent who works on a certain task during T periods. The agent is assumed
to be risk neutral and to discount future payoffs with a factor . In each period the agent
chooses how much effort
to invest in the task. The performance
in period is either
with probability
or otherwise. Hence, in each period the agent can advance one step
towards the goal, and the effort determines the probability of such advancement. The agent has to bear
costs of the effort. We assume a convex cost function of effort, i.e.,
. If the goal
is met or exceeded at the end of the last period , the agent receives a bonus payment .
1
We denote the distance between the target and accumulated output with and the remaining
number of periods with (where
). In the last period, before choosing an effort, the agent
maximizes her expected utility
which is given by
!
"
#
$%&'$$()*)$+,*$-&./$,.0$1**2$.++.(2*3
$%&'$$()*)$+,*$-&./$4.22&+$1*$.++.(2*3$.256&'*
$%&'$$()*)$+,*$-&./$(0$0+(//$.++.(2.1/*
By backward induction we derive the agent’s value function and characterize a recursive
solution to the dynamic optimization problem. Let 76.8
9
be the optimal effort
chosen by an agent when the distance to the goal is and periods remain. The agent’s expected
utility : is given by
;
"<"##=>#?"#@#
A"
$ %&'$
%&'$
%&'$BC
Solving the optimization problem we obtain the following recursive characterization of optimal effort
and utility levels:
Proposition: The agent’s optimal effort level as a function of D and
τ
is given by
;
"####E$ %&'$
%&'$
%&'$BC
1
For a related structure with only two periods see Lizzeri et al. (2002).
5
and the agent’s expected utility is
;
A"####E
="#$ %&'$
%&'$
%&'$BC
Proof: The objective function is strictly concave. The optimal effort is zero if either (as
###) or if
τ
(as in this case it is impossible to attain the goal and
###). From the first order condition of the optimization problem we
obtain the optimal effort level as a function of the expected utility in the subsequent period. By
inserting these optimal efforts into the objective function we obtain expected utility as a function of
and
τ
.
One of the main features of our mechanism is that the optimal choice only depends on the current
distance to the goal and the remaining time while past progress and sunk effort costs are irrelevant for
a rational decision maker. In other words, the same level of effort should be exerted by an agent who
was assigned a goal of and achieved already a positive number of output units but still misses
steps to the target, as by some other agent who just started to work and was assigned a goal of F.
2.2 Dynamics in Effort Provision
Using the proposition, we compute point predictions for the optimal effort levels as a function of
and
τ
for any bonus B and cost parameter a. Assuming
δ
, Figure 1 shows the optimal effort levels
for the main parameter constellation investigated in our experiment
2
as a function of the remaining
time
τ
for five different goal distance values G. To understand this pattern, first consider a
situation in which agent’s effort remains without success, i.e., remains unchanged between periods.
To assess the agent’s reaction we track his effort by proceeding along a respective curve in Figure 1.
For example, we consider the curve, with the goal distance equal to one. In this case, the
optimal effort levels gradually increase from 0.13 effort units in the beginning to 0.99 in the very last
period. Also for AHI the efforts increase monotonically up to certain periods but then fall. The
intuition for this pattern is the following: Due to the convex cost function, the agent has a basic
interest to distribute the effort rather evenly across periods. However, incentives change as the
remaining time decreases. As long as the goal is easy (i.e., is relatively small compared to
τ
), the
agent should gradually increase effort in order to achieve the goal. If, however, is relatively large
compared to
τ
the achievement probability becomes smaller, and as the expected probability that the
goal will be attained drops the agent rationally begins to reduce effort.
2
The parameter values that we employ in the experiment and in the figure are G, A, ,
and δ.
6
F
IGURE
1:
O
PTIMAL
E
FFORT
L
EVELS AS A
F
UNCTION OF THE
G
OAL
D
ISTANCE AND
R
EMAINING
T
IME
Note: For , and
δ
.
When an agent is successful in a certain period, is reduced by one unit. In Figure 1, this means
that the optimal behavior of the agent moves from the curve to the curve #. As can be seen from
Figure 1, this move may lead either to an increase in effort (when the curve # is above the curve
) or to a drop in effort (when the curve # lies below the curve ). For instance, consider the
curve H (marked with squares) when 10 periods remain. When the agent advances towards the
goal by one step, this will result in a move from the curve H to A (marked with diamonds). If,
for instance J$the new effort on the A curve lies below the H effort: the progress towards
the goal results in reduced effort during the next period as the risk of not attaining the goal has become
smaller and the costs of effort to attain the goal can be distributed on a sufficiently large number of
remaining periods (“The agent can relax a bit”). But when, for example, 5 periods or fewer remain,
progress from H to A leads to a substantial increase in effort: In this case, a reduction in
increases the chances of attaining the goal and thus the marginal returns of advancing one step have
increased while at the same time less time remains to attain the goal which makes it more important to
advance towards the goal.
2.3 Incentive Effect of Goals
The point predictions for the dynamic optimal effort choices allow us to compute the expected
total effort exerted across all periods. Figure 2 illustrates total effort depending on the size of the
123456789101112
Periods left
g=1 g=2 g=3 g=4 g=5
Distance to the target:
0 10.2 0.6 0.80.4
Optimal effort
(
τ
)
7
bonus (which is either 750 or 1,000 ), goal size (which varies from 1 to 5 on the x-axis) and number of
available periods (varies from 5 to 12 between the panels).
F
IGURE
2:
T
OTAL
B
ENCHMARK
E
FFORT AS A
F
UNCTION OF
G
OAL
,
T
IME AND
B
ONUS
As we see, the total effort naturally increases with the bonus, as a higher bonus makes goal
attainment more attractive. The total optimal effort peaks in the areas where the goal size is
moderately large. The total efforts are also, ceteris paribus, higher when there are more remaining
periods. When the agent has more time (and therefore trials), it is more likely that her effort will lead
to successful goal attainment and thus she has in incentive to invest more. Additionally, having more
periods available allows the agent to keep the effort costs low by spreading costs across several
periods. Hence, the expected net payoff increases.
3. Experimental Design
To collect experimental evidence on the theoretical predictions derived above and to investigate
the impact of goal size and bonus on dynamic goal achievement, we run a laboratory experiment. Our
core setting comprises 3 treatments where we vary the goal size while keeping the time frame
12
T
=
and bonus size
000,1B
=
constant. The cost parameter a and discount factor
δ
were set to 1,001 and 1
respectively. An overview of parameter combinations used in each treatment is given in Table 1. In
particular, we conduct treatments with a Low Goal (
3G
=
), Medium Goal (
4G
=
) and High Goal
(
5G
=
). In addition, a Medium Goal Low Bonus treatment was designed to test the impact of the
lower bonus of 750.
0 100 200 3000 100 200 300
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
5678
9 10 11 12
Bonus750
1000
Total effort
Goal
8
T
ABLE
1:
P
ARAMETER VALUES AND THEORETICAL PREDICTIONS FOR A
= 1,001
AND
δ = 1
Treatment Goal (G)
Available
periods of
time (T) Bonus (B)
Theoretical predictions regarding optimal
behavior
Total effort
Probability of
goal
achievement Agent’s net
payoff
Low Goal 3 12 1,000 283.98 0.94 430.47
Medium Goal 4 12 1,000 289.23 0.68 160.36
High Goal 5 12 1,000 85.16 0.13 12.87
Medium Goal Low
Bonus 4 12 750 147.68 0.30 37.34
Table 1 lists the predictions for the total expected effort, probability of goal attainment and agent’s
net payoff derived from the formal model. These values are computed by backward induction applying
Proposition 1 in Section 2.
3
The theoretical benchmark shows that the highest level of total effort is
achieved in the Medium Goal treatment as indeed, the goal size has a non-monotonic effect on the
total optimal effort. The probability of goal attainment, when following the utility maximizing effort
pattern, decreases substantially from 0.94 in the Low Goal treatment to 0.13 in the High Goal
treatment.
The impact of the bonus reduction is in line with incentive theory. Overall, a 25% reduction in the
bonus in Medium Goal Low Bonus reduces the total effort by almost one half. The lower effort results
in a reduced probability of goal attainment. Also the expected net payoff is lower when the bonus is
low.
4. Experimental Procedures
We ran the experiment in the Cologne Laboratory for Economic Research at the University of
Cologne using the experimental software zTree (Fischbacher, 2007). In total, 4 sessions were
conducted with 120 participants (46% females), who were recruited with ORSEE (Greiner, 2004).
Each subject was assigned to one treatment and participated in the experiment only once. Instructions
were shown on the screen and handed out on paper at the beginning of the experiment. Each
participant received a one-time endowment of 5,000 experimental currency units (ECU), equivalent to
€15.
In every period participants had to choose an effort level from the set {0; …; 99}, which
determined the costs of effort to be subtracted from their experimental account.
4
Immediately after
each effort choice a random device decided with probability equal to the effort (divided by 100)
3
Note that the predicted effort patterns illustrated in Figure 1 are unaffected by
G
. Therefore, the prediction is
relevant for all core treatments with
.000,1B
=
The Medium Goal Low Bonus treatment is the only one in which
effort allocation comprises different values but qualitatively follows a similar pattern (for comparison see Figure
A1 in Appendix).
4
Participants learned their goal, bonus size and number of periods at the beginning of the experiment. For
information about values of these parameters see Table 1.
9
whether the performance output was increased by 1 or not. The participants precisely knew the
remaining distance to the goal and the incurred costs. If the total output met or exceeded the goal G at
the end of the last period T, a bonus B was awarded. The identical goal-attainment task was repeated 8
times.
At the end of the experiment the subjects took part in two lottery choice experiments for loss and
risk preferences (Gächter et al., 2007; Holt and Laury, 2002). Additionally, they had to answer a 10-
items Big Five Inventory (Rammstedt and John, 2007), as well as general questions concerning their
motivation. The participants earned on average €17.50, plus a show-up fee of €2.50. They were paid
anonymously at the end of the experiment. The sessions lasted for about 1 hour and 20 minutes. The
total sample size was 120 subjects, i.e., 30 independent observations per treatment.
5. Results
5.1 Goal Attainment and Effort
Observation 1: The goal attainment frequency decreases with the goal size.
First, we focus on the goal attainment rates – defined as relative frequency of successfully
achieved goals. Figure 3 demonstrates the average goal attainment rate per run, standard errors,
theoretical benchmark and total average. The higher the goal the less frequently it is attained. The
difference in individual goal-attainment rates (individual average over 8 runs) is statistically highly
significant between the three treatments (p-value < 0.001, Jonckheere-Terpstra test for descending
alternatives) - see also the regression analysis reported in Table 2.
5
The relative goal attainment
frequencies come very close to the predicted rates of the optimal effort path in the Low Goal (0.95 vs
the benchmark of 0.94) and the Medium Goal (0.72 vs. the benchmark of 0.68) treatments (p-
values > 0.55, two-sided Fisher-Pitman permutation test for paired replicates
6
). In the High Goal
treatment, participants achieve the performance standard substantially more often than a utility
maximizing agent would (0.39 vs. the benchmark 0.13, p-value < 0.001). However, there are
substantial learning effects as attainment frequencies converge towards the prediction. As the goal
attainment naturally depends on the amount of the exerted effort, we look in the next step at the effort
provision in details.
5
For all non-parametric tests, unless something different is mentioned, we calculate one average value per
subject.
6
See Kaiser (2007) for more details.
10
F
IGURE
3:
G
OAL ATTAINMENT
T
ABLE
2:
G
OAL
S
IZE AND
G
OAL
A
TTAINMENT
(1) (2)
Probit marginal effects Random effects panel regression
Coef. SE Coef. SE
Low goal 0.32
***
(0.05) 0.25*** (0.05)
High goal -0.26
***
(0.08) -0.30*** (0.08)
Run 1 0.15
***
(0.04) 0.14*** (0.05)
Run 2 0.08 (0.06) 0.08 (0.06)
Run 4 0.04 (0.05) 0.03 (0.05)
Run 5 0.04 (0.05) 0.03 (0.04)
Run 6 -0.05 (0.06) -0.04 (0.05)
Run 7 -0.03 (0.05) -0.02 (0.04)
Run 8 -0.11
*
(0.06) -0.09* (0.05)
Constant 0.34 (0.20) 0.55*** (0.20)
R
2
0.25 0.05
N of obs. 719 719
N of subjects 90 90
Note: The dependent variable in both specifications is goal attainment (0/1). The reference group is the Medium
Goal treatment. Controls are gender and age and are not significant. Standard errors in parentheses;
*
p < 0.1,
**
p < 0.05,
***
p < 0.01
Observation 2: Subjects exert less effort when the goal is high.
Figure 4 demonstrates the average total effort per run, standard errors and theoretical benchmark.
In line with the theoretical prediction, we observe a non-monotonic relation between the goal size and
overall contributions: While working on average 280.09 units per run in the Low Goal treatment, the
subjects provide on average total effort of 309.74 units in the Medium Goal and of 244.38 in the High
Goal treatments. Testing the difference in means of goal-attainment efforts (individual average over 8
runs) between treatments with a two-sided Fisher-Pitman permutation test for independent samples
reveals that subjects work significantly more in the Medium Goal than in the High Goal (p-
0
.95
1
0
.68
.72
1
0
.13
.39
1
0
.2
.4
.6
.8
1
0
.2
.4
.6
.8
1
0
.2
.4
.6
.8
1
12345678 12345678 12345678
Low goal Medium goal High goal
Low goal Medium goal High goal
Standard errors Benchmarks Average values
Relative frequency of goal attainment
Run
11
value = 0.059). Especially in the last 4 rounds, the detrimental effect of the high goal becomes clear:
With 177.22 units the average effort in the High Goal treatment is significantly smaller compared to
the Medium Goal treatment (287.18, p-value = 0.012) and to the Low Goal treatment (268.78, p-
value = 0.015). The average total effort in the Low Goal does not significantly differ from the Medium
Goal treatment (p-values > 0.15). The regression reported in Table 3 supports these observations.
F
IGURE
4:
T
OTAL EFFORT PER RUN
T
ABLE
3:
G
OAL
S
IZE AND
E
FFORT
(1) (2)
Random effects panel regression (All runs) Random effects panel regression (last 4
runs)
Coef. SE Coef. SE
Low goal -27.87 (20.31) -16.14 (26.18)
High goal -58.78* (35.05) -104.25** (43.99)
Run 1 72.43*** (19.33)
Run 2 70.47*** (17.65)
Run 4 -8.16 (15.92)
Run 5 -33.16* (17.27)
Run 6 -25.29* (14.50) 7.87 (14.04)
Run 7 -20.70 (17.12) 12.46 (17.90)
Run 8 -55.61*** (16.29) -22.46 (17.10)
Constant 265.50*** (87.10) 298.46*** (101.07)
R
2
0.13 0.02
N of obs. 720 360
N of subjects 90 90
Note: The dependent variable in both specifications is the total level per run. The reference group is the Medium
Goal treatment. Controls are gender and age and are not significant. Standard errors in parentheses;
*
p < 0.1,
**
p < 0.05,
***
p < 0.01
0
280
450
0
289
310
450
0
85
244
450
0
50
100
150
200
250
300
350
400
450
0
50
100
150
200
250
300
350
400
450
0
50
100
150
200
250
300
350
400
450
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Low goal Medium goal High goal
Low goal Medium goal High goal
Standard errors Benchmarks Average values
Total effort per run
Run
12
Observation 3: When the goal is high the total effort is significantly higher than would be expected
from the theoretical benchmark.
Although the comparison between treatments delivers results consistent with the theoretical
prediction discussed in section 3, we observe some significant deviations from the benchmark in the
High Goal treatment. Here, participants provide significantly more total effort than predicted by the
theory in all except the last run (p-values ≤ 0.018, two-sided Fisher-Pitman permutation test).
The subjects thereby exert an inefficiently large amount of effort to achieve the high target. A
potential explanation for this rests on the idea that the subjects have a desire to attain the goal beyond
the pure monetary considerations. As in the High Goal treatment the goal attainment probability based
on the benchmark effort is low, subjects invest too much effort at the cost of their payoff while
striving to meet a performance standard and to avoid failure. Hence, the results indicate that overly
ambitious targets may lead to inefficient self-exploitation at least in the short run.
In the Low and Medium Goal treatment it is very likely that subjects reach the goal by remaining
on the payoff-maximizing effort path In the Low (Medium) Goal treatments, effort overprovision
occurs only in the first (first 2) run(-s) (p-values ≤ 0.096) and vanishes afterwards.
5.2 Determinants of Effort Overprovision
More insightful evidence can be found when examining the effort overprovision on a more
detailed level within a single period. In every period subjects face particular (g,
τ
)-constellations when
making their decisions. Whereas the parameter
τ
(the number periods left) diminishes from period to
period at an equal pace for all subjects, the change in the parameter g (the actual distance to the target)
depends on individual effort and exogenous luck. According to our framework, for any fixed bonus
only the remaining goal distance and the number of remaining periods affect the effort size. In other
words, rational agents who face identical (g,
τ
)-combinations should exert the same amount of effort
regardless their initial goal and previous progress. To detect systematic deviations from the predicted
path we now bring all data points with the respective (g,
τ
)-combinations together and compare them
between treatments.
Observation 4: The theoretical benchmark explains the observed average behavior quite well, with
one exception: Efforts systematically exceed the predictions when the number of remaining periods is
large.
Figure 5 is divided into 5 panels, one for each value of g∈{1, 2, ..., 5}, and shows the average
effort contributions exerted for any particular (g,
τ
)-combination, where g is fixed within every panel
and
τ
varies along the x-axis. The dashed lines depict the benchmark effort derived from our model
(recall that these are identical for all three treatments). The connected lines show the average effort
levels chosen by subjects who are in a particular (g,
τ
)-constellation. As only subjects in the High Goal
treatment can be in a constellation where g = 5, the respective panel presents only one line. Similarly,
13
g = 4 can be experienced either in the High Goal or Medium Goal treatments but not in the Low Goal
treatment. Therefore there is no line representing the Low Goal treatment in the panel g = 4. On the
other hand, in the High Goal treatment no subject can be confronted with (g,
τ
)- constellation such as
(4,12), (3,12), (3,11), (2,12), (2,11), (2,10) etc. as it is impossible to attain this level of progress toward
the goal in such a limited number of periods.
F
IGURE
5:
E
FFORT FOR DIFFERENT DISTANCES FROM THE GOAL
Figure 5 reveals that the pattern of behavior is qualitatively similar to the theoretical prediction,
especially for values of g ≥ 3 and when the number of remaining periods is rather small. But it appears
to be different from the prediction for g ≤ 2 if the number of remaining periods is large, indicating that
subjects exert too much effort when they have many periods remaining to achieve only one or two
more goal steps. When g is large (see panels for g = 4 and g = 5) effort decreases as the number of
remaining periods decreases, which is in line with the theoretical prediction. For g = 3 the effort
remains almost stable when
τ
≥ 6 and then slowly approaches zero. Thus, the most notable deviations
from theory is observed when g = 1 and g = 2 for large values of
τ
, in which a strong overprovision of
effort occurs. The non-parametric statistical analysis confirms in all three treatments that the effort is
indeed often significantly higher than in the theoretical prediction, especially when many periods
remain (for p-values see Table A1 in Appendix).
7
7
Nevertheless, the situation for g = 1 and
τ
= 1 appears different: In our setting it is possible to attain the goal
with near certainty when it is only one step away, and in the core treatments it is always worthwhile to make the
investment of 99.9 units to guarantee that the goal is attained. However, agents do not exert enough effort in this
respect and provide on average not more than 69.35% of the required effort. This difference is significant at the
0.1% level in all three treatments. This might be due to a ceiling-effect, as the optimal effort for g = 1 and
τ
= 1
was also the highest possible input in the experiment. However, this effect is also pronounced in the Medium
0 20 40 60 80 1000 20 40 60 80 100
123456789101112
123456789101112 123456789101112
g=1 g=2 g=3
g=4 g=5
Low goal
Medium goal
High goal
Benchmark
Average effort
Periods left
14
In all three treatments we observe a reduction in the deviations from the prediction with the
progress of periods. So why is there effort overprovision especially at the beginning of a run? It might
partially result from a selection issue: The data points with low g and high τ represent subjects that
come close to the target in very early periods.
8
Some subjects might systematically try to attain the
goal early on and therefore exert excessively high efforts in early periods, while it would be optimal to
smooth out the costs of effort and start with lower effort levels. Indeed, out of the 34 cases observed in
the Low Goal treatment where subjects arrived at g = 1 in the earliest possible period (here
τ
= 10),
91.18% exert above median effort in the very first period of the respective run. In the Medium Goal
and High Goal treatments, this measure amounts to 83.33% (out of in total 18 cases) and 100% (from
4 cases), respectively. Similarly, in the Low Goal (Medium Goal, High Goal) treatment when g = 2
and
τ
= 11 (10, 9), the share of the initial above-median contributors is 62.70% (66.67% and 92.31%)
respectively. Hence, a large share of participants who tend to overprovide efforts is reflected in the
means of early periods with low g. In other words, subjects who spread their efforts more evenly, and
thus behave more in line with our theory, are much less likely to come close to the goal at such an
early point. Indeed, considering only those observations where subjects provide not more than the 50th
percentile of effort in the very first period of a run, we observe efforts that are more in line with the
theory (see Figure A2 in Appendix).
The observation that also in the Low Goal treatment the effort choices are significantly higher than
the benchmark values may at first look seem contradictory to observation 3. However, this results
from subjects exerting more effort early on instead of distributing it more equally over several periods.
As a result, the goal is reached within a shorter time, and effort is reduced afterwards to zero.
Therefore there is no significant difference between the total effort and the theoretical prediction, but
there is a significant effort overprovision in the early periods of a run at inefficiently high costs.
To gain a deeper understanding of the reasons for potential deviations from the benchmark we
investigate the following regressions. The dependent variable is the actual effort minus the theoretical
effort in the respective (g,
τ
)-constellation. The predicted effort for a particular (g,
τ
)-combination is the
same in all three treatments. Thus, the dependent variable can also be interpreted as a ceteris paribus
increase in effort. As the optimal (and in the majority of cases the actual) efforts in situations when the
goal is either attained or cannot be attained anymore are equal to 0, we exclude these (g,
τ
)-
combinations from our analysis. We also include dummy variables for each possible (g,
τ
)-
combination. We cluster the data on the individual level and control for gender and age.
Observation 5: Above-average luck leads to a decrease in effort (relative to the benchmark effort).
Our first explanatory variable of interest is defined as a ratio of successfully attained performance
units and cumulative effort exerted in the past periods (henceforth referred as “experienced luck”).
Goal Low Bonus treatment (see below), where the optimal choice is 75 but the observed mean effort 54.11 (p-
value<0.01).
8
There is a lower number of observations behind each data point.
15
Recall that the probability of receiving one additional performance unit is equal to chosen effort
divided by 100. Therefore, on average the expected return to effort is equal to the effort itself, and the
ratio equals one. However, actually realized returns differ because of the random draw and thus there
is exogenous variation in past “success”. When the realized performance lies above the exerted effort,
the “experienced luck” variable is above one and the subject can be considered as “lucky”. To the
contrary, an “experienced luck” below one means that the subject received fewer units than the
expected value of the invested efforts would predict. By definition, on average the “experienced luck”
is equal to 1. Indeed, the mean value of this variable in the very last period is 0.97.
A rational decision maker would not condition the decision on past luck but only on the
current (g,
τ
)-constellation. Any systematic deviation thus represents a behavioral bias. As
Table 4 reports, “experienced luck” indeed has a significantly negative effect on effort. A
rough interpretation is that subjects who are rewarded with twice as much performance units
than they should have received according to their efforts reduce effort by 6.46 units compared
to those individuals who progressed along the expected performance given their efforts.
9
One
potential explanation is due to a systematic attribution error. To explore this further we
estimate in model (2) whether subjects react symmetrically to being “lucky” or “unlucky”,
i.e., achieving a performance above or below its expected value given the exerted efforts. The
variable “luck” is equal to KLMNOP7LMQ$RST and “no luck” to
KONOP7LMQ$RST. Interestingly, agents reduce their efforts when having
experienced above average luck but do not increase them when being unlucky. A potential
explanation is related to the fundamental attribution bias: potentially subjects understand than
below average luck is just a result of the randomization process, while they (erroneously)
attribute above average successes to their own efforts and thus reduce these efforts.
9
Consider as example two agents provide in three consequent periods 33 effort units. One agent succeeded in
two out of three periods and his “luck”-measure is equal to 2*100/(3*33) ≈ 2. Another agent experienced success
only in one period and his “luck” measure equals to 1*100/(3*33) ≈ 3.
16
T
ABLE
4:
P
AST SUCCESS AND EFFORT OVERPROVISION
(1) (2)
Coef. SE Coef. SE
Experienced luck in previous periods -6.46*** (1.91)
Luck -8.38*** (2.77)
No luck -1.70 (3.51)
Low goal -0.34 (2.43) -0.62 (2.34)
High goal -0.90 (2.50) -0.52 (2.38)
Constant -37.48*** (8.94) -33.13*** (9.42)
Runs yes yes
Dummies for (g,
τ
)-combinations yes yes
R
2
0.29 0.29
N of obs. 5970 6060
N of subjects 90 90
Note: The dependent variable in both specifications is ∆=e(g,
τ
) - e
opt
(g,
τ
). The reference group is the Medium
Goal treatment. Controls are gender and age and are not significant. The observations are restricted to data points
where g > 0 and g ≤ τ. Standard errors in parentheses;
*
p < 0.1,
**
p < 0.05,
***
p < 0.01
A final conjecture is that we may see an escalation of commitment effect as a further reason for
the overprovision of effort. To explore this possibility, we investigate to what extent the costs already
invested in the goal attainment affect efforts in a given run. Again we run regressions with the
difference between actual and theoretical effort as the dependent variable. We include individual fixed
effects to account for heterogeneity in the general propensity to exert effort. We conduct separate
regressions for each τ, as cumulative costs naturally increase from period to period. In this case, our
main independent variable of interest is the costs per period accrued in the current run. In other words,
we control for average incurred goal attainment expenditures.
Observation 6: Efforts increase with the costs already invested in the goal attainment.
For a rational decision maker previously invested costs are irrelevant for the effort and goal
attainment since only the (g,
τ
)-constellation should matter for the optimal effort choice. This would
imply that the estimated coefficient of the invested costs should be zero. However, we find positive
and, in a vast majority of cases, highly significant coefficients of the costs invested. The results are
reported in Tables A2 and A3 in the Appendix. Thus agents’ effort on average increases with the
previous monetary investment in the goal attainment. Hence, sunk costs significantly affect behavior,
and participants indeed show behavior that can be interpreted as an escalation of commitment.
5.3 Payoffs
Observation 7: Actual payoffs are in general lower than predicted because participants exert
inefficiently large efforts. However, payoffs increase over rounds as the agents’ choices converge
towards the predicted efforts.
By definition an overprovision of effort must lead to lower expected payoffs, as the marginal
effort costs exceed the marginal monetary benefit. Indeed, as can be seen in Figure 6, in every
treatment the average net payoffs in all 8 runs lie below the predicted values, which are depicted with
17
dashed lines. Interestingly, the average net payoffs are negative in the High Goal treatment: In this
treatment payoffs are significantly lower than predicted in all runs but 4, 5 and 7 (p-values < 0.1, two-
sided Fisher-Pitman test). The average net payoff in the Medium Goal treatment is only positive after
run 4, and payoffs are significantly lower than the predicted value of 160.36 (p-values < 0.1 in all but
run 5 and 6). The Low Goal treatment is the only one in which the net payoffs remain positive during
the whole experiment, but also here in runs 1, 2, 3 and 7 the payoffs are significantly lower than
predicted (p-values < 0.1).
F
IGURE
6:
A
VERAGE NET PAYOFFS AND
95%
CONFIDENCE INTERVALS
Note: Dashed lines are a-priori expected net payoffs conditional on optimal effort.
5.4 “Goal Acceptance” and Drop-Outs
While the dynamic optimization model would predict that agents should always exert some effort
early on (and as long as the goal is in principle attainable), Locke and Latham (1990) have stressed
that a goal has to be “accepted” beforehand, as otherwise individuals will not work towards the goal.
According to goal-setting theory, the more difficult the goal, the lower the number of subjects that will
accept it. Also in our setting one could expect that the acceptance rate falls with the goal difficulty,
especially because of the strongly decreasing expected net payoffs. If subjects have not provided any
effort in a particular run, we characterize them as “not accepted the goal” in this run. We classify those
subjects who have exerted any positive effort at least in one period of a run, as “accepted the goal” in
this particular run. Figure 7 shows the number of participants in the group “not accepted the goal”. In
the Low Goal treatment the agents almost always work towards the goal. In the High Goal treatment
the picture looks different. In the first three runs, the vast majority of the participants provide some
295
430
160
-22 13
-176
-500
-400
-300
-200
-100
0
100
200
300
400
500
-500
-400
-300
-200
-100
0
100
200
300
400
500
-500
-400
-300
-200
-100
0
100
200
300
400
500
12345678 12345678 12345678
Low goal Medium goal High goal
Low goal Medium goal High goal
Standard errors Benchmarks Average values
Net payoff
Run
18
positive effort, while in the runs 5 to 8 approximately 40% of subjects choose no effort at all.
Although the expected net payoff from goal attainment in the High Goal treatment is very low (ECU
12.86 = €0.04), approximately two thirds of subjects work toward the goal. Taken together, this
suggests that the goal attainment is not driven merely by monetary incentives but also by some
intrinsic goal achievement drive or feelings of obligation which is reduced only in later runs as
individuals experienced losses.
Observation 8: The more difficult the goal and the lower the expected payoff, the more likely
participants are to drop out from the goal attainment task and exert no effort at all. Even though the
expected net utility from attaining the goal is very low in the High Goal treatment, more than 50% of
subjects work to reach it.
F
IGURE
7:
N
UMBER OF
“
NOT ACCEPTED
”
GOALS
Note: The number of independent observations in each treatment is N=30.
Table 6 reports Probit regressions clustered on the level individuals, which aim to study the
determinants of “goal acceptance”. Taking the treatment Medium Goal as a reference group and
controlling for the average costs per run, we observe a significantly positive coefficient of the Low
Goal treatment dummy on the goal attainment and a significantly negative coefficient of the High
Goal treatment dummy on the goal acceptance. However, when we control for the experienced goal
attainment success, the treatments’ coefficients become insignificant. On the one hand, the goal size is
highly correlated with achievement, as the low goal could be easily achieved (it was attained in 94%
of cases), whereas goal achievement in the high goal treatment was rather rare (13% of cases).
Nonetheless, goal acceptance depends on previous individual experience. Hence, the lack of goal
acceptance is indeed mainly driven by reactions to the past experience of failing to reach the goal.
Observation 9: Not only the goal difficulty, but also previous success affects the goal acceptance.
0 5 10 15 20 25 30
Number of subjects who did not accept the goal
12345678
Run
Low goal Medium goal High goal
19
T
ABLE
5:
P
AST SUCCESSES AND GOAL ACCEPTANCE
(1) (2)
Coef. SE Coef. SE
Low goal 0.079*** (0.03) -0.00 (0.12)
High goal -0.067** (0.04) -0.004 (0.01)
Average costs per run 0.0001*** (0.00) -0.00 (0.00)
# Achieved goals / # Played runs 0.06*** (0.04)
Dummies for sequences
Controls
Pseudo R
2
0.42 0.56
N of obs. 623 623
N of subjects 89 89
Note: The dependent variable is goal acceptance (Yes=1, No=0). Marginal effects orobit regression estimates. Clustered by
individuals. Robust standard errors are reported in parentheses. The reference group is the Medium Goal treatment. . Controls
are gender and age and are not significant. Significance levels based on the Probit estimationa are denoted by * p < 0.1,
** p < 0.05, *** p < 0.01
5.5 Effect of the Bonus
We have focused so far only on the core treatments in which the goal difficulty was varied. In this
section, we discuss an additional treatment where we lowered the bonus paid for goal attainment.
Observation 10: The average individual effort is significantly smaller when the bonus for goal
attainment is low. Nevertheless, there is also a significant amount of effort overprovision in the
Medium Goal Low Bonus treatment.
Table 2 shows the descriptive statistics of the key outcome variables in this Medium Goal Low
Bonus treatment. The model predicts an average total effort of 147.68 for the Low Bonus, as opposed
to 289.23 for the High Bonus treatment. Indeed, the difference in the expected total effort is
significant: The participants provide on average 32% less effort in the treatment Medium Goal Low
Bonus (p-value = 0.015, two-sided Fisher-Pitman test for independent samples).
It is, however, interesting to note that the overprovision of effort is also significant in the Medium
Goal Low Bonus treatment. This again supports the conjecture laid out above that the agents have an
intrinsic motivation or feel an obligation to attain the goal, which in turn leads to overprovision of
effort. Indeed, recall that under the high bonus the probability of attaining the goal is, with about 72%
across all rounds, very close to the prediction. But under the low bonus this probability is, at 46%, by
far higher than the prediction of 30% (p-values < 0.10 for runs 2-4 and 6, p-values < 0.05 for runs 1, 5
and 7-8, one-sided Binomial test, N = 30).
5.6 Personal Characteristics and Effort Overprovision
In Tables A3 and A4 in the Appendix we replicate the regression models presented above,
including personal characteristics such as gender, the Big Five personality dimension measures, risk
and loss aversion measures and running regression estimations with individual clusters pooled over
treatments. The Big Five personality traits were measured with a 10-item scale introduced by
Rammstedt and John (2007). The risk aversion measure was derived from the lottery choices
20
suggested by Holt and Laury (2002) and varies from 0 to 10. The loss aversion was measured on the
scale from 0 to 6 (Gächter et al., 2007).
These personal characteristics are not significant in any of the models.
6. Conclusion
We investigated a stylized formal model of dynamic goal attainment in which agents receive a
bonus payment when attaining a predetermined goal within a given time frame. Dynamic optimization
provides a precise prediction regarding optimal effort choices. We have tested this setting in a
laboratory experiment, and we find that the dynamic optimization model qualitatively explains
patterns of the experimental data quite well. According to our prediction, the relationship between goal
size and the amount of provided effort is non-monotonic, as subjects exert the most effort when facing
medium challenging goals. But we also find evidence for systematic deviations from the rational
prediction. For instance, participants provide too much effort as compared to the prediction in
treatments where the goal is hard to attain without making losses. This indicates that participants to
some extent feel an intrinsic motivation or obligation to attain the goal, even when it is too costly from
a purely economic perspective.
Moreover, we find that past luck affects effort provision and also observe substantial evidence for
an escalation of commitment, as agents increase their effort to a stronger extent when they have
already invested higher amounts of money in attaining the goal.
We conclude that the investigation of dynamic optimization models indeed helps to understand the
intertemporal behavior of agents faced with a goal. However, behavioral phenomena lead to
systematic deviations from the optimal effort path that yield interesting challenges for future research
on optimal goal setting.
21
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23
Appendix
F
IGURE
A1:
O
PTIMAL EFFORT FOR
B=1,000
COMPARED TO
B=750
F
IGURE
A2:
B
EHAVIOR IF THE EFFORT IN THE FIRST PERIOD OF A RUN WAS EQUAL OR BELOW MEDIAN
0 10.2 0.6 0.80.4
Optimal effort
123456789101112131415 Periods left
g=1 g=2 g=3 g=4 g=5
Distance to the target:
Optimal effort for bonus 1,000
0 10.2 0.60.4 0.8
Optimal effort
123456789101112131415 Periods left
g=1 g=2 g=3 g=4 g=5
Distance to the target:
Optimal effort for bonus 750
0 20 40 60 80 1000 20 40 60 80 100
123456789101112
123456789101112 123456789101112
g=1 g=2 g=3
g=4 g=5
Low goal
Medium goal
High goal
Benchmark
Average effort
Periods left
Exerted effort in the first period of a run is equal or below median
24
T
ABLE
A1:
E
FFORT OVERPROVISION
Low Goal
τ
g 12 11 10 9 8 7 6 5 4 3 2 1
1 ***° ***° ***° ***° ***° ** * (***°)
2 ***° ***° ***° *** ** (**)
3 ***° ***
Medium Goal
τ
g 12 11 10 9 8 7 6 5 4 3 2 1
1 *** ***° ***° ***° *** ** (***°)
2 ***° ***° *** *** ***°
3 ***° ***° *** *** ** *
4 ***° ** *** ** * *
High Goal
τ
g 12 11 10 9 8 7 6 5 4 3 2 1
1 *** ***° ***° ** (***) (***°)
2 ** ***° *** ***
3 ** ***° ***° ** *
4 ***° ***° *** ***° ***° *** ** *
5 ***° ***° ***° ***° ** ** ***
Note: The table denotes for any (g,
τ
)-combination the significance levels for rejecting the null hypothesis that effort is equal
to the benchmark as tested with the two-sided Fisher-Pitman permutation test for paired replicates. We average efforts for
each (g,
τ
)-combination of each agent across all runs for this agent. Through this approach we generate a data set with
statistically independent observations for the different (g,
τ
)-combinations, which correspond to economically identical
choice problems. Possible parameter constellations are highlighted in grey; Significant discrepancies are indicated with
***°p < 0.001; *** p < 0.01, ** p < 0.05, * p < 0.1; The parenthesis indicate that the observed effort level is significantly
lower than the predicted; The number of indipendent observations varies between 7 and 31 per cell.
25
T
ABLE
A2:
P
AST COSTS AND EFFORTS IN THE MAIN TREATMENTS
Low Goal
τ 1 2 3 4 5 6 7 8 9 10 11
Average costs spent per period -0.12 -0.30 -0.10 0.09 0.17*** 0.18*** 0.17*** 0.19*** 0.20*** 0.14*** 0.10***
(1.01) (0.67) (0.30) (0.09) (0.04) (0.04) (0.05) (0.03) (0.03) (0.02) (0.02)
Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
g dummies - Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
R2 0.956 0.520 0.803 0.470 0.710 0.721 0.693 0.732 0.727 0.808 0.696
Adj. R2 0.129 -0.441 0.566 0.079 0.559 0.609 0.600 0.663 0.669 0.771 0.639
N of subjects 16 22 26 28 28 29 30 30 30 30 30
N of obs.
21 46 65 88 109 134 168 193 222 240 240
Medium Goal
τ 1 2 3 4 5 6 7 8 9 10 11
Average costs spent per period 0.27** 0.11 0.07 0.17** 0.14** 0.18*** 0.13** 0.17*** 0.19*** 0.16*** 0.13***
(0.12) (0.13) (0.08) (0.07) (0.06) (0.04) (0.05) (0.04) (0.03) (0.03) (0.02)
Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
g dummies - Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
R
2
0.987 0.777 0.651 0.506 0.397 0.542 0.565 0.695 0.684 0.653 0.687
Adj. R
2
0.941 0.561 0.417 0.319 0.208 0.418 0.462 0.631 0.621 0.585 0.627
N of subjects 17 25 26 29 29 30 30 30 30 30 30
N of obs.
32 68 88 143 164 189 209 230 240 240 240
High Goal
τ 1 2 3 4 5 6 7 8 9 10 11
Average costs spent per period -0.05 0.21* 0.28*** 0.23*** 0.15*** 0.11** 0.11*** 0.04 0.06 0.20*** 0.22***
(0.06) (0.11) (0.04) (0.06) (0.04) (0.05) (0.04) (0.04) (0.04) (0.04) (0.03)
Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
g dummies - Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
R
2
0.998 0.790 0.671 0.615 0.480 0.427 0.528 0.453 0.534 0.646 0.683
Adj. R
2
0.989 0.573 0.455 0.425 0.367 0.306 0.429 0.340 0.440 0.577 0.623
N of subjects 18 23 27 29 30 30 30 30 30 30 30
N of obs.
32 62 92 119 231 236 239 240 240 240 240
Note: Dependent variable: ∆=e(g, τ) - e
opt
(g, τ); Fixed effects regression clustered by individualswith robust standard errors in paranthesis; Controlled for runs (with dummies); The observations are
restricted to data points where g>0 and g≤τ; Significance levels denoted by * p < 0.1, ** p < 0.05, *** p < 0.01
26
T
ABLE
A2:
P
AST COSTS AND EFFORTS IN THE
M
EDIUM
G
OAL
L
OW
B
ONUS TREATMENT
Medium Goal Low Bonus
τ 1 2 3 4 5 6 7 8 9 10 11
Average spentcosts -0.0785 0.3876** 0.22 0.0851 0.1313** 0.1524*** 0.1818*** 0.2078*** 0.1673*** 0.1979*** 0.1633***
(0.1307) (0.1403) (0.1484) (0.0672) (0.0538) (0.0567) (0.0471) (0.0297) (0.0336) (0.0357) (0.0228)
Constant Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
g dummies - Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
R
2
0.952 0.7544 0.598 0.4468 0.368 0.4899 0.5153 0.6698 0.6613 0.6167 0.6395
Adj. R
2
0.8938 0.5986 0.4073 0.2858 0.2136 0.3813 0.424 0.6142 0.607 0.5575 0.5858
N of obs.
32 68 88 143 164 189 209 230 240 240 240
Note: Dependent variable: ∆=e(g, τ) - e
opt
(g, τ); Fixed effects regression with robust standard errors in paranthesis; The observations are restricted to data points where g>0 and g≤τ; Significance
levels denoted by * p < 0.1, ** p < 0.05, *** p < 0.01
27
T
ABLE
A3:
E
FFECT OF PERSONALITY TRAITS ON EFFORT OVERPROVISION
(1) (2) (3) (4)
Total effort Total effort
∆=e(g,
τ
) - e
opt
(g,
τ
).
∆=e(g,
τ
) - e
opt
(g,
τ
).
Low goal -27.17 (21.66) -12.57 (25.96) -0.38 (2.39) -0.52 (2.33)
High goal -62.10
*
(37.55) -105.79
**
(46.60) -2.26 (2.73) -1.97 (2.62)
Experienced luck in previous periods -6.51
***
(1.91)
Luck -8.18
***
(2.77)
No luck -2.22 (3.45)
Female dummy 0.68 (2.54) 0.95 (3.31) 2.95 (2.69) 2.90 (2.59)
Age 0.19 (0.30) 0.10 (0.36) 0.23 (0.31) 0.22 (0.30)
Risk aversion 0.00 (0.50) -0.27 (0.62) -0.07 (0.51) -0.08 (0.48)
Loss aversion -0.45 (0.78) 0.09 (1.00) -0.10 (0.74) -0.08 (0.72)
Extroversion 0.38 (0.75) 0.11 (0.91) 0.51 (0.70) 0.44 (0.68)
Agreeableness -0.20 (0.72) -0.53 (1.05) 0.11 (0.67) 0.13 (0.64)
Neuroticism 0.58 (0.57) 0.77 (0.76) 0.97 (0.61) 0.95 (0.60)
Conscientiousness -0.38 (0.59) -0.73 (0.80) -0.70 (0.63) -0.68 (0.60)
Openness -0.92
*
(0.51) -1.36
*
(0.69) -0.77 (0.54) -0.75 (0.52)
R
2
0.13 0.02 0.29 0.29
N of obs. 720 360 5970 6060
N of subjects 90 90 90 90
Note: The reference group is the Medium Goal treatment. Controls are gender and age and are not significant. The observations are restricted to data points where g > 0 and g ≤ τ. Standard errors in
parentheses; * p < 0.1, ** p < 0.05, *** p < 0.01.
28
T
ABLE
A4:
G
OAL ATTAINMENT
,
GOAL ACCEPTANCE AND PERSONALITY TRAITS
(1) (2) (3)
Bonus received (0/1) Goal accepted (0/1) Goal accepted (0/1)
Low goal 1.19
***
(0.24) 1.46
***
(0.54) -1.18 (0.72)
High goal -0.87
***
(0.26) -1.06
***
(0.36) -0.97
*
(0.52)
Average costs per run 0.00
***
(0.00) -0.00 (0.00)
# Achieved goals / # Played runs 5.48
***
(0.73)
Female dummy 0.10 (0.24) 0.24 (0.37) 0.30 (0.42)
Age 0.04 (0.03) 0.03 (0.06) 0.03 (0.06)
Risk aversion -0.04 (0.05) 0.05 (0.07) 0.10 (0.09)
Loss aversion -0.11 (0.08) 0.01 (0.15) 0.20 (0.17)
Extroversion 0.06 (0.07) 0.05 (0.09) 0.12 (0.11)
Agreeableness -0.04 (0.07) -0.22
*
(0.13) -0.23
*
(0.12)
Neuroticism 0.08 (0.06) 0.09 (0.10) 0.11 (0.13)
Conscientiousness -0.04 (0.07) -0.16 (0.11) -0.28
**
(0.12)
Openness -0.09 (0.05) 0.03 (0.08) 0.12 (0.10)
R
2
N of obs. 719 623 623
N of subjects 90 89 89
Note: Probit regression estimates. Clustered by individuals. Robust standard errors are reported in parentheses. The reference group is the Medium Goal treatment. Significance levels denoted by
* p < 0.1, ** p < 0.05, *** p < 0.01
29
SUPPLEMENTARY MATERIALS FOR MANUSCRIPT
‘DYNAMIC GOAL ATTAINMENT – A FORMAL MODEL AND EXPERIMENTAL
EVIDENCE’
Instructions
Translation from German:
General information
At the beginning of the experiment, for every participant receives an endowment of 5.000 tokens.
The experiment consists of 8 parts. In no part of the experiment your income depends on the decisions
of another participant. Each part consists of 12 periods.
Decision in each period
In each part you can win a bonus of 1.000 tokens. You get this bonus if your result is at least as high
as the objective. This amounts to 5 units in every part.
At the beginning of the first period of a part your result is zero.
In each period your result can go up by exactly one unit or remain unchanged. To do so, you can
choose an effort from the set [0, …, 99]. This effort causes you costs that will be subtracted from your
account. The exact amount of costs is presented in the attached table and can be computed with the
“costs calculator” on the screen.
After you choose your effort, the computer will determine if your result is raised by one unit. The
probability that your result will be raised by 1 unit equals your input (in %).
At the end of each period you learn whether your result went up by one unit or not, and the updated
score.
Bonus at the end of a part
If your result is at least as high as the objective of 5 units you receive a bonus of 1.000 tokens.
Otherwise you do not receive any bonus.
Information at the end of a part
At the end of a part you will receive a message whether you met the objective, how many tokens are
left on your account, and an overview on the calculation of your income.
Total income
Your total income from the experiment results as follows:
Endowment of 5.000 tokens
minus accumulated cost for the provided efforts
plus bonuses received in each of the 8 parts.
At the end of the 8th part your earnings will be paid to you at an exchange rate of € 0.30 for 100
tokens.
Please note
After the experiment another very short experiment will take place. Subsequent to this we will ask you
to answer a few questions concerning your own person.
During the whole experiment no communication is permitted. If you have a question, raise your hand
out of the cabinet. All decisions are taken anonymously, i.e., none of the other participants will come
to know the identity of anyone having taken a particular decision. The disbursement will also be
carried out anonymously, i.e., no participant will come to know which amount is paid to another
participant.
30
Original instructions in German:
Allgemeine Informationen
Zu Beginn des Experiments bekommt jeder Teilnehmer ein Startkapital von 5000 Talern auf seinem
Konto gutgeschrieben.
Das Experiment besteht aus 8 Teilen. In keinem Teil ist Ihr Einkommen von den Entscheidungen
eines anderen Teilnehmers abhängig.
Jeder Teil besteht aus 12 Perioden.
Entscheidung in jeder Periode
In jedem Teil können Sie einen Bonus in Höhe von 1000 Talern gewinnen. Diesen Bonus bekommen
Sie, wenn Ihr Ergebnis mindestens so hoch wie das Ziel ist. Das Ziel beträgt in jedem Teil 3
Einheiten.
Zu Beginn der ersten Periode eines Teils ist Ihr Ergebnis Null.
In jeder Periode eines Teils kann sich Ihr Ergebnis um genau eine Einheit erhöhen oder unverändert
bleiben.
Hierzu wählen Sie in jeder Periode einen ganzzahligen Einsatz aus der Menge [0, ..., 99].
Der gewählte Einsatz verursacht Ihnen Kosten, welche Ihnen von Ihrem Konto abgezogen werden.
Die Kosten für jeden Einsatz können Sie der beigelegten Tabelle entnehmen oder mit Hilfe eines
Kostenrechners ausrechnen, den Sie unten auf dem Bildschirm finden.
Nachdem Sie einen Einsatz gewählt haben, bestimmt ein Zufallszug, ob sich Ihr Ergebnis um eine
Einheit erhöht. Die Wahrscheinlichkeit, dass Ihr Ergebnis sich um 1 Einheit erhöht, ist gleich Ihrem
Einsatz (in %).
Am Ende einer Periode erfahren Sie, ob sich Ihr Ergebnis um eine Einheit erhöht hat oder nicht, sowie
das aktuelle Ergebnis am Ende dieser Periode.
Bonus am Ende eines Teils
Ist Ihr Ergebnis am Ende eines Teils mindestens so hoch wie das Ziel von 3 Einheiten, erhalten Sie
den Bonus in Höhe von 1000 Talern. Ansonsten erhalten Sie keinen Bonus.
Information am Ende eines Teils
Nach einem Teil erhalten Sie eine Mitteilung, ob Sie das Ziel erreicht haben, wie hoch Ihr
Gesamtkontostand im Experiment ist, sowie eine Übersicht über die Berechnung Ihres Einkommens.
Gesamteinkommen
Das Gesamteinkommen aus dem Experiment ergibt sich wie folgt:
Startkapital in Höhe von 5000 Talern
minus Summe der angefallenen Kosten für die geleisteten Einsätze
plus Summe der Boni aus jedem der 8 Teile.
Am Ende der 8 Teile wird Ihnen Ihr Gesamteinkommen zu einem Wechselkurs von €0.30 pro 100
Taler ausgezahlt.
Bitte beachten Sie
Nach diesem Experiment findet noch ein anderes sehr kurzes Experiment statt. Im Anschluss daran
werden wir Sie bitten, einige Fragen zu Ihrer Person zu beantworten.
Während des gesamten Experiments ist keine Kommunikation gestattet. Wenn Sie eine Frage haben,
strecken Sie bitte die Hand aus der Kabine. Sämtliche Entscheidungen erfolgen anonym, d.h. keiner
der anderen Teilnehmer erfährt die Identität desjenigen, der eine bestimmte Entscheidung getroffen
hat. Auch die Auszahlung erfolgt anonym, d.h. kein Teilnehmer erfährt, wie hoch die Auszahlung eines
anderen Teilnehmers ist.
