A Behavioral Study on Abandonment Decisions in
Multi-Stage Projects
Xiaoyang Long, Javad Nasiry
School of Business and Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong
Kong SAR., [email protected], [email protected]
Yaozhong Wu
National University of Singapore, Business School, Singapore 119245, [email protected]
In uncertain environments, project reviews provide an opportunity to make “continue or abandon” decisions
and thereby maximize a project’s expected payoff. We experimentally investigate continue/abandon decisions
in a multi-stage project under two conditions: when the project is reviewed at every stage and when review
opportunities are limited. Our results confirm findings in the literature that project abandonment tends to
be delayed, yet we also observe premature termination. Decisions are highly path dependent; in particular,
subjects are more likely to abandon after observing reduced project value, and abandonment rate is higher
near the middle—rather than near the beginning or end—of a project. Interestingly, when reviews are limited,
subjects are less likely to continue a project that should be abandoned. At the same time, subjects are more
inclined to review again after receiving negative (rather than positive) news. Our data are explained well
by a model that incorporates three behavioral concepts—gains or losses from comparing the project value
with an internal adaptive reference point, sunk cost bias, and status quo bias. Our work suggests that more
frequent reviews need not lead to better project performance, and it also identifies contexts in which outside
intervention is most valuable in project decision making.
Key words : project management, continue/abandon decisions, reference dependence, sunk cost effect,
status quo bias
1.
Introduction
In many projects, investments are allocated over time as uncertainties become resolved. For example, the manager of a new product development (NPD) project will monitor its progress and, at
each review, decide whether to continue investing in the project or abandon it. Such sequential
investment decision making enables decision makers to respond to new information, and it plays
an important role in managing project risk.
However, project managers often fail to make optimal decisions given the information available.
There is a tendency to delay termination of projects, often at considerable costs. For example,
Guler (2007) studies sequential investment decisions in the US venture capital industry and finds
1
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
2
that venture capitalists “tend to continue investing in companies even when prospects of success
are declining.” New products that fail in the market are often continued longer than is optimal
(Businessweek 1993, Simester and Zhang 2010). A similar tendency is observed in controlled experiments, where subjects who have made a previous investment in a project are more likely to continue
that project (Garland 1990, Staw and Ross 1989). This phenomenon is known as the sunk cost
effect.
Existing experimental research studies project termination delay primarily as a single-period
problem and does not investigate how the project manager (PM) makes continue/abandon decisions
over multiple stages. Real-world projects typically involve many stages and reviews, wherein the
PM’s decision may be affected by the project’s history, its performance trend and the time of
review.
The frequency and timing of project reviews are important in project management, and PMs
often “struggle to strike the right balance between excessive intervention and inadequate oversight”
(Krishnan and Ulrich 2001, p. 12). In NPD projects, the number of reviews can vary significantly
across different projects (Schmidt et al. 2009). It is widely recognized that the number of reviews
may be limited by transaction costs or resource constraints (Bergemann et al. 2009), yet little is
known about its effect on the PM’s continue/abandon decisions. Moreover, the PM’s willingness
to receive information can affect the timing of reviews. Assuming that investors derive utility from
information, Karlsson et al. (2009) show that they monitor their portfolios more frequently after
receiving good news than bad news. This tendency to avoid additional information after receiving
bad news is referred to as the “ostrich effect”; in a project management context, it would imply
that PMs prefer to delay future project reviews after observing a decrease in project value.
In this paper, we experimentally investigate continue/abandon decisions in a multi-stage project
under two conditions: when the project is reviewed at every stage and when review opportunities
are limited. We pose three research questions. First, do continue/abandon decisions systematically
deviate from normative predictions? Second, how do the project path and sunk cost affect the PM’s
continue/abandon decisions? Third, if review opportunities are limited and if the PM can decide
when to review, then how does previous information affect the review decision and what is the
effect of limited reviews on project outcome?
We formulate a dynamic programming model to capture the key characteristics of a sequential
investment project: (i) the expected project payoff evolves stochastically over time; (ii) a continuation cost is incurred at each stage; (iii) the PM may abandon the project before its completion;
and (iv) payoff is received only upon the project’s completion (Roberts and Weitzman 1981). A
review provides the PM with information on the project’s current value and an opportunity to
abandon the project. We consider two cases under this model: in the first case, every project stage
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
3
is reviewed; in the second case, review opportunities are limited and so the PM must decide when
to review. In both cases, a rational PM’s continue/abandon decision should depend only on the
project’s current value and the number of stages until completion. Moreover, if the continuation
cost is constant over time and the PM is rational, then the optimal continuation/abandonment
policy does not differ between the two cases.
After designing two experiments to test these normative predictions, we observe systematic
deviations from the optimal policy. Participants tend to delay termination, but there are also
cases of premature termination. We identify the conditions under which delayed or premature
termination occurs and find evidence of path dependence. In particular, participants are more likely
to abandon a project after its value decreases than after it increases. In a project whose value
continues to decrease, participants are more likely to abandon near the middle—rather than near
the beginning or end—of the project. We do not find support for the ostrich effect; to the contrary,
when review opportunities are limited and participants choose when to review, they review again
sooner after receiving bad news than after good news. Furthermore, comparing results from the
two experiments shows that participants are less likely to delay project termination when review
opportunities are limited.
To organize our data, we propose a behavioral model based on the utility of information (Karlsson
et al. 2009, Kőszegi and Rabin 2009). More specifically, we posit that if the project is continued
then the PM compares the observed project value with an internal reference point and, accordingly,
experiences a gain or loss in utility. We assume that the reference point reflects the PM’s expectation
of the project’s payoff and that it is updated (albeit imperfectly) over time. We also incorporate
two existing explanations for termination delay into our model: sunk cost bias and status quo
bias. The former describes the incentive to continue a project in order to recoup the sunk cost
(Thaler 1999), and the latter refers to a preference for following the “default” option (Samuelson
and Zeckhauser 1988). We capture these biases by assuming that a PM who abandons a project
experiences a constant negative utility (status quo bias) in addition to a negative utility that is
proportional to the amount of sunk cost.
Structural estimation results show that our behavioral model describes the data well. Simulations replicate the patterns of path dependence and a preference to review sooner after bad news.
The parameter estimates reveal that participants, when they anticipate utility from future information, are gain seeking rather than loss averse. This finding does not confirm the descriptions of
prospect theory (Kahneman and Tversky 1979), which could be a consequence of several differences
between our work and existing research (for a review, see Novemsky and Kahneman 2005). First,
we attribute perceptions of gains and losses to changes in information rather than final payoffs. We
believe that ours is the first work to investigates gain–loss preferences experimentally in contexts
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
4
that decouple the arrival time of information and monetary payoffs. The results suggest that gain–
loss preferences may differ for information versus actual payoffs. Second, the nature of the project
management task we study may induce a betting mindset that leads to gain-seeking behavior (Ert
and Erev 2013, Novemsky and Kahneman 2005).
Our estimation results show that termination delay can be mainly attributed to three factors:
sunk cost bias, status quo bias, and gain-seeking preference. The latter two factors induce the PM
to delay termination in a project’s early stages when sunk cost is small. Comparing the estimates
for the two experiments separately, we find that limiting the number of reviews results in more
gain-seeking behavior but also in smaller status quo bias and sunk cost bias, leading to an overall
greater willingness to abandon.
The behavioral study described in this paper complements current project management literature and helps develop a better understanding of the processes used by project managers to make
sequential decisions. We identify the situations under which PMs are more likely to wrongly continue/abandon a project—and thus the contexts in which an intervention is most valuable. Our
results also suggest that limiting the number of reviews need not compromise performance and
may even be effective in reducing project termination delay.
The paper proceeds as follows. After reviewing the literature in Section 2, in Section 3 we formulate the basic model and present the normative optimal policies. Section 4 describes our experiment
and hypotheses, and Section 5 reports the experimental results. In Section 6 we formulate the
behavioral model and present the structural estimation results. Section 7 concludes.
2.
Literature Review
Our work relates to the literature in four research domains: (i) investment decisions in research and
development projects, (ii) the sunk cost effect, (iii) utility of information and reference dependence,
and (iv) behavioral studies in project management.
Investment decisions in research and development projects. Our paper is closely related
to studies of investment decisions in research and development (R&D) projects. Such projects
typically involve accumulative costs, the opportunity to abandon the project before its completion, and benefits that are realized only after project completion (Roberts and Weitzman 1981).
Because resources are allocated over time as uncertainties about the outcomes are resolved, an
investor has the flexibility to take actions in response to new information. Hence it is important
to consider a project’s “option” value when making investment decisions (Dixit and Pindyck 1994,
Faulkner 1996, Luehrman 1997, Trigeorgis 1996). Roberts and Weitzman (1981) characterize the
optimal continue/abandon policy at each stage of a sequential development project based on newly
received information. Huchzermeier and Loch (2001) develop a dynamic programming model of
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
5
R&D investment to examine the effect of different kinds of uncertainty on project value; they find
that, although greater uncertainty about market payoffs increases project value, greater operational
uncertainty may not have the same effect. Santiago and Vakili (2005) adopt the same framework
to examine different sources of variability and their effects on project value. Our dynamic programming model is similar to that in Huchzermeier and Loch (2001) and Santiago and Vakili
(2005). Whereas previous research has studied investment decisions from a normative perspective,
we investigate experimentally whether (and in what way) PMs systematically deviate from the
optimal policy. This is a key question because flexibility in investment decisions is valuable only to
the extent that it helps investors make better decisions based on available information. Otherwise,
flexibility and information may hinder a project’s performance.
Sunk cost effect. There is extensive research in psychology and behavioral economics on the
sunk cost effect (for a review, see McCarthy et al. 1993) in various contexts: new product development (Boulding et al. 1997), venture capital investment (Guler 2007), and firms’ capital budgeting
(Denison 2009). Our study differs in three ways. First, we experimentally investigate the continue/
abandon decision in a dynamic setting, which allows us to identify path dependence effects. Second, our model clearly states the expected value and costs of the project, which enables rigorous
comparison between experimental observations and normative predictions. Heath (1995) points out
that expected payoffs, though seldom specified by previous experiments, play an important role in
PM decisions. Third, we consider the effect of limited review opportunities on the PM’s decision
and on the project’s outcome.
Our work complements existing research on policy recommendations to improve project decision
making. Boulding et al. (1997) design a two-stage experiment on product development (involving
one launch decision and one continue/abandon decision) and test the effectiveness of different
decision aids. They find that providing clearer information about project payoff to participants does
not render them more likely to decide correctly about terminating a project. Our study confirms
this result: we explicitly inform participants of the expected value and costs of the project and
still observe termination delay. Boulding et al. (1997) also find that termination delay is alleviated
by decision aids that mask the “history” factor (e.g., having different individuals make the first
and second decisions). Our results are consistent with this recommendation. In fact, decision aids
that shield project history from the decision maker may be even more beneficial than previously
believed because decision makers make path-dependent choices in a multi-stage project. Finally, we
suggest limiting the number of reviews as a new means to induce timely abandonment of projects.
Utility of information and reference dependence. Our behavioral model is based on the
work of Kőszegi and Rabin (2009), who propose that beliefs about future consumption are carriers
of utility and that gains (resp. losses) are felt in response to the positive (resp. negative) comparison
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
6
between new information and an internal reference point. These authors show that their belief-based
framework can provide the foundations for gain–loss utility with respect to wealth as proposed
by Kahneman and Tversky (1979). Kőszegi and Rabin (2009) assume that the reference point is
stochastic and that it coincides with rational expectations; but in this paper we adopt the adaptive
expectations framework (Nerlove 1958), which is widely used in the literature (Arkes et al. 2008,
Baucells et al. 2011, Gneezy 2005, Popescu and Wu 2007). Adaptive reference points have also
been used to study investment behavior. For example, Lee et al. (2008) propose that investors
dynamically adapt their neutral reference point as new information on stock performance arrives
and that this ‘adaptation’ affects investor decisions to hold or capitulate a losing investment.
Karlsson et al. (2009) likewise consider when information on the potential return from investment
has a “reference point–updating” effect.
Behavioral studies in project management. Researchers have paid scarce attention to
human behavior in the study of new product development and project management (Kavadias
2014, Sommer et al. 2008). This paper is an effort to bridge this gap. In a similar vein, Oraiopoulos
and Kavadias (2008) study the behavioral reasons behind delayed or premature termination of
innovation projects; they show analytically that diverse perspectives among group members, as
well as social conformity, may lead to systematically biased termination decisions. Wu et al. (2014)
analyze the optimal compensation scheme when project members are prone to procrastination.
Kavadias and Sommer (2009) consider behavioral issues in analyzing the effectiveness of different
team structures in creative processes. There are also several papers applying experimental methods
to topics in project management. For instance, Katok and Siemsen (2011) conduct experiments to
show that career concerns cause agents to choose more difficult tasks than necessary. Kagan et al.
(2016) find experimentally that teams perform worse when they can decide when to transition
from ideation to execution in NPD projects. Our paper contributes to this growing literature by
experimentally investigating project continue/abandon and review decisions.
3.
Model and Optimal Policies
The project has T stages. A project’s “state” at stage t is denoted xt , which is the expected value of
the project upon completion. The project state, or value, is stochastically evolving: xt+1 = xt + wt ,
where wt is independent and identically distributed (i.i.d.) for t = 1, 2, . . . , T − 1.
We consider two cases. In the first case, the PM observes xt at each stage t and decides whether
to continue or abandon the project. In the second case, review opportunities are limited and, at
every stage, the PM must first decide whether or not to review the project. If the PM does review
the project, then he learns its state xt and decides whether to continue or abandon the project. If
the PM decides not to review, then he does not learn the project value and the project continues
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
7
to the next stage. The cost of continuing the project at stage t is ct . Let the project payoff at time
T be xT ; this payoff is zero if the PM abandons the project before stage T .
We assume there is no time discounting. We assume also that wt = δ with probability p and
wt = −δ with probability 1 − p. The initial assessment of project value, x1 , is known to the PM. We
assume that projects exhibit no drift (p = 12 ) and have positive payoffs (x1 − (T − 1)δ ≥ 0). Figure
1 illustrates the model when T = 4.
Figure 1
3.1.
Example of a project with T = 4.
Optimal Policy
In this section we derive the normative solutions in the two cases, one with review at every stage
(“full review”, or FR) and one with limited review opportunities (“limited review”, or LR).
We first consider the PM’s continue/abandon decisions in FR. The value function in this case is
Vt (xt ) = max{−ct + EVt+1 (xt + wt ), 0},
for t = 1, . . . , T − 1, where EVt+1 (xt + wt ) is the expected value of Vt+1 with respect to wt , and
VT (x) = x. At stage t, the PM continues the project if and only if −ct + EVt+1 (xt + wt ) > 0.
Lemma 1. At stage t, there exists a threshold at such that the PM continues the project if and
only if xt > at .
All proofs are given in Appendix A. We can show that, if the continuation cost is the same at every
stage, then a PM who continues the project at stage t will also continue the project at stage t + 1.
Proposition 1. Assume ct = c. For t = 1, . . . , T − 2, if it is optimal to continue at xt in stage t,
then it is optimal to continue at xt+1 = xt ± δ in stage t + 1.
Proposition 1 implies that, for a constant continuation cost, if it is optimal to abandon at
xt+1 = xt − δ or xt+1 = xt + δ in stage t + 1 then it is optimal to abandon at xt in stage t. This
statement implies a simple optimal policy: the abandonment threshold at is equal to the total cost
of completing the project.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
8
Corollary 1. Assume that ct = c. For t = 1, . . . , T − 1, the PM continues the project if and
only if xt > (T − t)c.
Proposition 1 and Corollary 1 together imply that there are two types of projects. First, if
x1 > (T − 1)c, then the PM should start the project at stage 1 and continue until the project is
completed. Second, if x1 ≤ (T − 1)c, then the project should be abandoned at stage 1. We refer to
the first type as profitable projects and to the second as unprofitable; here profitability is viewed
from the PM’s perspective at the project’s initial stage (i.e., whether or not to start).
Now, we consider the LR case. Suppose there are at most M review opportunities for the project
(M < T − 2)—excluding the first stage, at which the PM learns the project’s initial value. Denote
the value function at stage t by Vt (xk , k, n), where xk is the most recently observed project value (in
stage k) and n represents the number of review opportunities left, 0 ≤ n ≤ M . Define Πit (xk , k, n) as
the expected profit from choosing action i at stage t, where i = C, A, R, NR stand for (respectively)
“continue”, “abandon”, “review”, and “no review”. Then, for t = 2, . . . , T − 1, we have
(
NR
max{ΠR
if n > 0;
t (xk , k, n), Πt (xk , k, n)}
Vt (xk , k, n) =
ΠNR
(x
,
k,
n)
otherwise.
k
t
A
The value function at stage 1 is V1 (x1 , 1, M ) = max{ΠC
1 (x1 , 1, M ), Π1 (x1 , 1, M )}. The value function
at stage T is VT (xk , k, n) = E[xT | xk , k], which is the expected project value upon completion (given
that the PM last observed xk at stage k). The expected profit if the PM does not review the project
at stage t is
ΠNR
t (xk , k, n) = −c + Vt+1 (xk , k, n).
The expected profit if the PM does review at stage t is
C
A
ΠR
t (xk , k, n) = E max{Πt (xt , t, n − 1), Πt (xt , t, n − 1)};
here the expectation is taken over xt (given that the PM last observed xk at stage k). The profits
from continuing/abandoning the project are, respectively,
ΠC
t (xt , t, n) = −c + Vt+1 (xt , t, n)
and
ΠA
t (xt , t, n) = 0.
It is easy to see that the optimal continuation policy in Corollary 1 applies to this case as well.
Corollary 2. Assume that ct = c. The optimal continuation/abandonment policy under LR is
the same as that under FR.
Regarding the optimal policy for review, we can show that earlier reviews are more valuable than
later reviews. Proposition 2 characterizes the optimal policy.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
9
Proposition 2. Let ct = c. Suppose that, at any stage t (t = 2, . . . , T − 1), the PM previously
reviewed at stage k (k < t) and has n ≥ 1 review opportunities left. (i) If xk > (T − k)c, then the
PM is indifferent between reviewing now or at any later stage. (ii) If xk ≤ (T − k)c, then the PM
prefers to review now.
In our stylized model, the normative threshold of abandonment is the same (at = (T − t)c)
irrespective of how many review opportunities are left. So overall, performance should be the same
under FR and LR (profitable projects are continued to completion and unprofitable projects are
abandoned in the first stage).
4.
Experimental Design and Hypotheses
In this section we detail the experimental design and our research hypotheses.
4.1.
Experimental Design
We designed two experiments corresponding to the cases described in Section 3. In both experiments, we ask participants to play the role of an investor in a series of projects. Each “project”
has an expected market value that evolves over time. The two experiments are identical except
for the review structure. In the first experiment, the participant observes the project value and
decides whether to continue or abandon the project at every stage. In the second experiment, the
number of review opportunities is limited. For example, the participant may be able to review
only twice in a 10-stage project; so at every stage, the participant must decide whether to review
the project. A review involves observing the current project value, after which the PM decides
whether to continue or abandon the project; in the absence of a review, the project is continued to
the next stage. At the start of a project, the participant is informed of: the project’s initial value;
its number of stages; the continuation cost, which is constant over time; and (if applicable) the
number of review opportunities. Once a project is either completed or abandoned, the participant
is informed of the payoff and moves on to the next project.
All participants are given the same 32 projects in random order. In all projects, we fix the
continuation cost at c = 11 and put δ = 10. The 32 project paths are shown in Table 1. We
choose projects with different number of stages (T = 4, 6, 8, 10) and different initial values. We
pre-determine the project paths to ensure that the expected total payoff is positive1 and that there
is sufficient variation—with some paths going up, some going down, and some staying around the
initial value. In the LR treatment, the number of review opportunities in a 4-stage project is 1;
1
We choose the project paths in such a way that those with positive returns more than compensate for those
with negative returns. Hence if one assumes that a participant chooses to continue any project on an upward path
and (randomly) either continues or abandons the other projects, then the average total payoff is positive. In the
experiment, only one participant received negative total payoff (excluding the participation fee).
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
10
the number of review opportunities in a 6-, 8-, or 10-stage project is 2. Participants are always
informed of the initial value of each project. In other words, they start to make review decisions
at stage 2.
Our design of the project paths has three key aspects. First, the projects differ in initial value,
x1 = (T − 1)δ or x1 = (T + 1)δ, to reflect that the PM should act differently depending on the initial
value (Corollary 1). So on the one hand, if the initial value is high (i.e., if x1 = (T + 1)δ) then the
project is profitable and should be started and continued at every subsequent stage. On the other
hand, if the initial value is low (x1 = (T − 1)δ) then the PM should abandon the project at stage 1
or at any subsequent stage that is on a strictly decreasing path (xt = (T − t)δ); he should continue
the project in all other cases.2 Figure 2 illustrates the optimal policy when x1 = 50 and T = 6. Of
Figure 2
Optimal abandonment policy—the PM should abandon a project at any of the states highlighted by a
box but should continue otherwise.
the 32 projects, 7 (22%) are profitable and 25 unprofitable with an optimal policy such as the one
illustrated in Figure 2.
Second, for projects with the same length (T ), project paths may overlap. This allows us to
study path dependence while keeping sunk cost constant. For example, compare projects 1 and 4
(see Table 1). They present the same decision problem at stage 3 with x3 = 30 and T = 4. So even
though their respective previous-stage values differ (x2 = 20 in project 1 and x2 = 40 in project 4),
the rational PM’s decision at stage 3 should be the same in both projects. Any observed difference
would reveal that a behavioral factor other than sunk cost affects the PM’s behavior.
Finally, paths may overlap also for projects of different lengths (i.e., number of stages). For
instance, the first two stages of project 1 are identical to the 3rd and 4th stages of project 16, to
the 5th and 6th stages of project 24, and to the 7th and 8th stages of project 30. A rational PM’s
decision at either of these two decision points should be independent of the project path observed
up to that stage.
2
The reason is that xt = (T − t)δ < (T − t)c for all t = 1, . . . , T − 1 if the project value keeps decreasing and that
xt ≥ (T − t + 2)δ > (T − t)c otherwise.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
Table 1
Project T
Path
11
Project paths.
Project
T
Path
1
2
3
4
5
6
7
8
4
4
4
4
4
4
4
4
30-20-30-20
50-40-50-60
30-20-10-20
30-40-30-20
50-60-70-80
30-40-50-60
30-40-30-40
30-20-30-40
9
10
11
12
13
14
15
16
6
6
6
6
6
6
6
6
50-40-30-40-50-40
50-60-70-80-90-100
50-40-50-40-50-60
50-60-70-60-70-80
70-80-70-80-90-100
70-60-50-40-50-60
50-60-50-40-50-60
50-40-30-20-30-40
17
18
19
20
21
22
23
24
8
8
8
8
8
8
8
8
70-80-70-80-90-100-110-120
70-80-90-100-110-100-90-80
90-80-70-80-70-80-90-100
90-80-70-60-50-60-70-80
70-60-50-60-70-60-70-80
70-60-50-40-50-40-50-60
90-100-90-80-90-80-90-100
70-60-50-40-30-20-30-40
25
26
27
28
29
30
31
32
10
10
10
10
10
10
10
10
90-80-70-60-50-60-70-60-70-80
90-100-90-100-110-120-130-140-150-160
90-100-90-80-90-100-90-100-90-100
90-80-70-80-90-100-110-100-90-80
90-80-90-100-110-120-130-140-150-140
90-80-70-60-50-40-30-20-30-40
90-100-110-100-90-100-110-120-110-120
90-100-90-100-90-100-110-100-110-120
We implemented the experiment via an online platform. When participants arrived at the lab,
each was assigned to a cubicle with a computer and then instructed to log into the experiment
platform. We read the instructions (which also appeared on the participant’s computer screen) out
loud and answered any questions privately. The participants then completed a short test to ensure
that they understood the instructions. After answering the test questions correctly, each participant
was given three practice projects before starting the actual experiment. All participants received a
cash payoff proportional to the sum of their respective earnings (project payoff minus total cost)
from the projects—in addition to a fixed participation fee. Payoffs were given to participants at the
end of the experiment. We also collected information about each participant’s gender and college
major, and we recorded the time taken to finish the 32 projects. The experiment’s instructions and
platform screenshots are presented in Appendix E.
Altogether, 75 undergraduate students at a large public university participated in the experiments: 37 in the FR experiment and 38 in the LR experiment. The experiments spanned four
sessions, with two sessions for each experiment and 18–20 participants in each session. All payments were made in the local currency. The average payment made to participants was equivalent
to $13.77 (US)—$13.21 for the FR experiment and $14.27 for the LR experiment. The average
time for participants to finish the experiment was 25 minutes for FR and 33 minutes for LR.
4.2.
Research Hypotheses
We are interested in whether participants make optimal decisions as described in Section 3. We
formulate three hypotheses to reflect normative predictions. The first hypothesis states that the
continuation policy is the same regardless of how many review opportunities are available (Corollary
2).
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
12
Hypothesis 1. Given xt = x and with T − t remaining stages, the continue/abandon decision
is the same in FR and LR as well as independent of the number of review opportunities left.
Because rational PMs are forward looking, their decisions depend not on past project states but
rather on its current state. In other words: given the same project value and number of remaining
stages, the decision should be the same and independent of the path through which that state was
reached. Therefore,
Hypothesis 2. Given xt = x and with T − t remaining stages, the continue/abandon decision
is independent of the project’s path.
Finally, we hypothesize that the review decision is also path independent. According to Proposition 2, if the optimal policy is to continue the project until completion then the PM is indifferent
about when to review. In particular, observing good news (increased value) or bad news (reduced
value) in the first review should not affect whether the PM prefers to review again sooner or later.
Hypothesis 3. The decision of when to review next is independent of the observed project’s
path.
5.
Experimental Results
Preliminary analysis shows no significant effect of age, gender, time spent, or treatment (FR or
LR) on a participant’s payoff.3 Notably, spending more time does not correlate with a higher or
lower payoff; and although the average payoff in FR is lower than that in LR, the difference is not
significant.
5.1.
Do Participants Make Optimal Continue/Abandon Decisions?
In this section, we investigate whether participants make optimal continue/abandon decisions. We
report their decisions in two cases: when the rational decision is to abandon or instead to continue.
We discuss separately the data from our FR and LR treatments.
Suppose the rational decision at a given stage is to abandon the project; in that case, a decision
to continue the project is a deviation from the rational decision. Table 2 presents the actual
abandonment rates in the FR experiment for those stages at which abandoning is the rational
decision. It is clear that participants are significantly less likely to abandon the project than would
be optimal. In fact, the proportion of abandonment never exceeds 25%. In total, of the 1,888
observations at decision points where the normative decision is to abandon the project, 87.76%
choose to continue. Figure 3 plots the FR participants’ abandonment decisions in a T = 10 project
3
Multiple regression with robust variance clustered by subject.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
13
as the project value decreases over time;4 we can see that the likelihood of the project being
wrongly continued for eight consecutive stages is approximately 40%. This result is in line with the
anecdotal and experimental evidence that PMs postpone termination even as project performance
deteriorates.
Table 2
T =4
x1 = 30
x2 = 20
x3 = 10
T =6
x1 = 50
x2 = 40
x3 = 30
x4 = 20
Abandonment rates under FR when the optimal decision is to abandon.
Abandonment
rate
N
14%
13%
3%
222
98
31
10%
6%
20%
19%
222
98
60
26
T =8
x1 = 70
x2 = 60
x3 = 50
x4 = 40
x5 = 30
x6 = 20
Abandonment
rate
N
11%
8%
18%
20%
23%
0%
185
99
91
50
22
17
Abandonment
rate
N
13%
7%
16%
18%
7%
10%
16%
0%
296
130
92
51
42
21
19
16
T = 10
x1 = 90
x2 = 80
x3 = 70
x4 = 60
x5 = 50
x6 = 40
x7 = 30
x8 = 20
Note: Reported values are based on data from the FR experiment. We use N to denote the number of observations,
which are grouped by the same path up to the current stage. At x4 = 60 and T = 10, for example, there are
51 observations of the continue/abandon decision (which consist of the observations from stage 4 of projects 25
and 30 being reached). Among these 51 observations, 18% are decisions to abandon the project.
Figure 3
Likelihood of continuing beyond stage t in T = 10 project with path
90 − 80 − 70 − 60 − 50 − 40 − 30 − 20 (according to FR data).
Conversely, at decision points where the rational decision is to continue the project, we observe
cases of abandonment. Table 3 shows the abandonment rate at each stage of a profitable project
whose value decreases over time. Of the 336 observations in total (excluding stage 1), 10% wrongly
abandon the project. In comparison, the abandonment error rate for the entire set of FR data is
4
The likelihood of continuing beyond stage t is the product of the likelihoods of continuing at stage 1, ...t. For instance,
the likelihood of continuing beyond stage 2 would be (1 − 13%) · (1 − 7%) = 81% (based on data from Table 2).
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
14
only 1.46%. This difference indicates that participants are more likely to abandon a project wrongly
when its value is decreasing than when it is increasing.
Table 3
Abandonment rates under FR when the optimal decision is to continue.
Abandonment
rate
N
T =4
x1 = 50
x2 = 40
T =6
x1 = 70
x2 = 60
x3 = 50
x4 = 40
4%
8%
74
36
3%
3%
6%
9%
74
36
35
33
Abandonment
rate
N
2%
6%
18%
13%
23%
111
72
68
30
26
T =8
x1 = 90
x2 = 80
x3 = 70
x4 = 60
x5 = 50
Note: Reported values are based on data from the FR experiment; N
denotes the number of observations, which are grouped by the same path
(of decreasing values) up to the current stage.
A similar pattern emerges for the continue/abandon decisions in the LR experiment (see Tables
4 and 5). Under LR, the continuation error rate is 86.35% and the abandonment error rate—given
a path of decreasing values—is 18% (the abandonment error rate is only 2.91% for the entire set
of LR data).
Overall, the results show that participants’ continue/abandon decisions deviate from the optimal
policy. In particular, we observe a strong tendency to delay termination of projects. Yet if value
decreases over time, then projects may also be terminated prematurely. This suggests that decisions
are path dependent, which we discuss extensively in Section 5.3.
Table 4
T =4
x1 = 30
x2 = 20
x3 = 10
T =6
x1 = 50
x2 = 40
x3 = 30
x4 = 20
Abandonment rates under LR when the optimal decision is to abandon.
Abandonment
rate
N
13%
37%
15%
228
62
13
5%
17%
33%
7%
228
59
45
15
Abandonment
rate
N
5%
23%
40%
23%
20%
38%
190
31
55
30
10
8
T =8
x1 = 70
x2 = 60
x3 = 50
x4 = 40
x5 = 30
x6 = 20
T = 10
x1 = 90
x2 = 80
x3 = 70
x4 = 60
x5 = 50
x6 = 40
x7 = 30
x8 = 20
Abandonment
rate
N
6%
17%
19%
36%
38%
28%
17%
25%
304
36
37
25
21
7
6
4
Notes. Reported values are based on data from the LR experiment; N denotes the number of observations, which
are grouped by the same path up to the current stage.
In stage 1, it is highly likely that a participant will start a project. An unprofitable project is
launched 87.7% of the time under FR and 92.9% of the time under LR; a profitable project is
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
Table 5
15
Abandonment rates under LR when the optimal decision is to continue.
Abandonment
rate
N
T =4
x1 = 50
x2 = 40
T =6
x1 = 70
x2 = 60
x3 = 50
x4 = 40
3%
25%
76
20
0%
5%
20%
9%
76
19
30
11
T =8
x1 = 90
x2 = 80
x3 = 70
x4 = 60
x5 = 50
Abandonment
rate
N
3%
18%
21%
25%
19%
114
17
34
12
16
Notes. Reported values are based on data from the LR experiment; N
denotes the number of observations, which are grouped by the same path
(of decreasing values) up to the current stage.
launched 97.3% of the time under FR and 98.1% of the time under LR. We estimate a logistic
regression model for the continuation decision at stage 1, in which the dependent variable is set
equal to 1 if the project is launched (and set to 0 otherwise). The independent variables are the
number of project stages (as indicator variables), whether the project is profitable (‘prof = 1’ if
profitable and ‘prof = 0’ otherwise) and whether the condition is FR or LR (‘FR = 1’ or ‘FR = 0’);
the robust variances are clustered by subject. All regression results are presented in Appendix B.
Our results (see Table 15 in Appendix B) show that the coefficient for ‘prof’ is positive and
significant (p < 0.01), while the coefficient for ‘FR’ is negative and not significant (p = 0.155). The
implication is that initial value does play a role in participants’ decisions, with a higher value
resulting in a greater willingness to start the project. Although participants in the LR experiment
are more likely (than those in the FR experiment) to start a project, the difference is not statistically
significant.
5.2.
Effect of Limited Reviews on Continue/Abandon Decisions
In this section we compare the error rates in FR and LR experiments. By Hypothesis 1, FR and
LR participants should make the same continue/abandon decisions because the optimal policies
do not differ between the two conditions, which implies that we should also observe no difference
between the error rates in the two experiments.
Table 6 reports the error rates under FR and LR. Upon a review at stage t > 1, an LR participant’s average likelihood of wrongly continuing the project is 72.84% as compared with 87.85% for
an FR participant. The difference is significant (p < 0.01) and suggests that limiting opportunities
to review increases the participant’s likelihood of abandoning an ongoing project. Similarly, the
LR participant’s likelihood of wrongly abandoning the project is significantly higher than that of
the FR participant.
Using observations at decision points where the rational decision is to abandon, we fit a logistic
regression model for the continuation decision on the binary variable ‘FR’ and the number of stages
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
16
Table 6
Comparison of error rates
Full review
Error of Continuing
Limited review
87.76% (N = 1,888) 86.35% (N = 1,414)
∗∗∗
Error of Continuing
(excluding stage 1)
Error of Abandoning∗∗∗
∗∗∗
Error of Abandoning
(excluding stage 1)
87.85% (N = 963)
72.84% (N = 464)
1.46% (N = 4,039)
2.91% (N = 1,686)
1.376% (N = 3,780) 3.098% (N = 1,420)
Notes. N = number of observations. The statistical test used is Fisher’s
exact test for comparing the error rates of FR versus LR.
∗
p < 0.1; ∗∗ p < 0.05; ∗∗∗ p < 0.01.
left,5 with robust variance clustered by subject (see Table 16 in Appendix B). We find that FR
participants are more likely than LR participants to continue a project once it has been launched
(p < 0.01); the predicted difference in the likelihood of continuing is 13%. This effect is no longer
significant if stage 1 is included (p = 0.556). As a further illustration of this point, Table 7 presents
a node-by-node comparison of abandonment rates in FR versus LR. At almost every node, LR
participants demonstrate a higher likelihood of abandonment. Therefore, Hypothesis 1 is rejected.
Table 7
Abandonment rates—under FR versus LR—when the optimal decision is to abandon.
Abandonment rate
FR
Abandonment rate
LR
T =4
x2 = 20
13%
37%
(N = 98) (N = 62)
x3 = 10
3%
15%
(N = 31) (N = 13)
T =8
x2 = 60
x3 = 50
x4 = 40
T =6
x2 = 40
6%
17%
(N = 98) (N = 59)
x3 = 30
20%
33%
(N = 60) (N = 45)
x4 = 20
19%
7%
(N = 26) (N = 15)
x5 = 30
x6 = 20
FR
LR
8%
(N = 99)
18%
(N = 91)
20%
(N = 50)
23%
(N = 22)
0%
(N = 17)
23%
(N = 31)
40%
(N = 55)
23%
(N = 30)
20%
(N = 10)
38%
(N = 8)
Abandonment rate
T = 10
x2 = 80
x3 = 70
x4 = 60
x5 = 50
x6 = 40
x7 = 30
x8 = 20
FR
LR
7%
(N = 130)
16%
(N = 92)
18%
(N = 51)
7%
(N = 42)
10%
(N = 21)
16%
(N = 19)
0%
(N = 16)
17%
(N = 36)
19%
(N = 37)
36%
(N = 25)
38%
(N = 21)
29%
(N = 7)
17%
(N = 6)
25%
(N = 4)
Notes. N = number of observations.
Although LR participants have fewer decision-making opportunities, they do not abandon their
projects later than do FR participants. Table 8 compares the average stopping stages for FR versus
LR participants. Excluding stage 1, LR participants stop at a slightly earlier stage than do FR
5
Because we focus on decision points at which the normative decision is to abandon (i.e., xt = (T − t)δ), controlling
for the number of stages left also controls for the project value.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
Table 8
17
Average stopping time—FR versus LR.
T = 4 T = 6 T = 8 T = 10
Including stage 1
FR
LR
Excluding stage 1
FR
LR
1.38
1.53
2.24
2.51
2.96
3.11
2.46∗
3.09
2.11
2.06
3.18
2.92
3.54
3.52
3.75
4.11
Notes. Reported values are the average stopping
stage of abandoned projects (completed projects
are excluded from this tabulation). The statistical
test used is two-sample Wilcoxon–Mann–Whitney
test for comparing the average stopping stages
under FR versus LR.
∗
p < 0.1; ∗∗ p < 0.05; ∗∗∗ p < 0.01.
participants in all cases except for T = 10. This shows that the LR participants’ higher likelihood
of abandoning a project counterbalances their reduced flexibility to act. Yet including stage 1
diminishes this effect owing to the higher launch rate under LR.
There are three possible reasons why LR participants are more likely than FR participants to
abandon an ongoing project. First, if participants value the flexibility that reviews bring—namely,
the chance to receive more information and abandon later—then they would be more likely to
continue a project with more future reviews. Second, limited reviews affect the information that
participants have received up to the decision point. It follows that, if participants’ decisions are path
dependent, then a difference in observed path may contribute to a difference in the continuation
decision. More specifically, observing a large decrease in project value may render participants
more likely to abandon than observing small but frequent decreases. Third, if reviews are limited
then participants may become more attentive to information and also more willing to abandon the
project.
Comparing the abandonment rates reported in Table 7 (for stage 2 only) using the Fisher’s exact
test reveals that, for all T , the differences between FR and LR abandonment rates are significant
(p < 0.1). Since the observed paths at stage 2 for FR and LR participants are identical, this
finding suggests that limited future review opportunities—that is, the first or third of our posited
reasons—play a part in driving the difference in abandonment rates.
5.3.
Path-dependent Continue/Abandon Decisions
To test Hypothesis 2, we consider whether and how project path affects continue/abandon decisions.
We focus on the FR data because this case abstracts from review decisions and their effect on
observed project path. Our results show that the path does indeed matter—in two ways. First,
we find that downward paths lead to a greater likelihood of project abandonment. Recall from
Section 5.1 that participants may wrongly abandon a profitable project when its value decreases.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
18
The abandonment rate is significantly lower at the same decision point given a different path. For
example, at stage 2 of a 4-stage project and with x2 = 40, the abandonment rate is 8% if that value
is lower than the initial value (x1 = 50), but is 0% if the (same) value is higher than the initial value
(x1 = 30). The difference is significant6 (p < 0.05). Similar comparisons can be made at all decision
points where the paths of different projects overlap. As another example, consider the abandonment
rates on decreasing paths presented in Table 3 and compare them with the abandonment rates
at the same decision points but given paths that do not strictly decrease (Table 9); the former
rates are higher in all cases. Using observations at the decision points presented in Table 9, we
estimate a logistic regression model for the continuation decision on path type (‘decpath = 1’ if
path is strictly decreasing, ‘decpath = 0’ otherwise) while controlling for project length T and stage
number.7 Our regression results (Table 17 in Appendix B) show that a decreasing path corresponds
to a significantly lower likelihood of continuing the project (coefficient < 0, p < 0.01). Finally, more
recent declines in project value induce a higher likelihood of abandonment. For instance, at decisionpoint x4 = 80 when T = 8, the abandonment rate given path (up to stage 4) 90-100-90-80 is 8%;
this is significantly higher than the 0% abandonment rate given path 70-80-70-80 or 90-80-70-80
(p < 0.05). The same pattern holds throughout the data.
Table 9
Abandonment rates corresponding to different paths.
Strictly decreasing path?
Yes
No
8%
(N = 36)
0%
(N = 92)
3%
(N = 36)
x3 = 50
6%
(N = 35)
x4 = 40
9%
(N = 33)
0%
(N = 101)
0%
(N = 66)
2%
(N = 88)
T =4
x2 = 40
T =6
x2 = 60
Strictly decreasing path?
Yes
T =8
x2 = 80
6%
(N = 72)
x3 = 70
18%
(N = 68)
x4 = 60
13%
(N = 30)
x5 = 50
23%
(N = 26)
No
0%
(N = 66)
6%
(N = 35)
0%
(N = 25)
0%
(N = 18)
Notes. Reported values are based on data from the FR experiment; N = number
of observations.
Second, project length has an inverted U-shaped effect on the abandonment rate when project
value decreases over time. Figure 4 shows the abandonment rates corresponding to different project
lengths for the same decision point. If the decision were path independent then, for a fixed project
value and fixed time to completion, the abandonment rate would be the same irrespective of T .
6
7
Fisher’s exact test.
Controlling for T and t effectively controls for the project value because the only decision points we use are xt =
(T − t + 2)δ for t > 1.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
19
Yet we consistently observe an inverted U-shaped pattern in Figure 4, where the likelihood of
abandonment is highest when the decision stage is near the middle of a project and is lower both
in earlier stages and in later stages. To test this observation rigorously, we separate the relevant
25%
20%
23%
20%
20%
19%
18%
18%
16%
15%
14%
16%
13%
10%
10%
10%
11%
8%
7%
6%
5%
0% 0%
0%
xT-3=30
xT-3=30
xxT-2=20
T-2=20
Figure 4
xT-4=40
xT-4=40
xT-5=50
xT-5=50
T=4
T=6
T=8
xT-7=70
xT-7=70
xT-6=60
xT-6=60
T=10
Proportion of abandonment in project on a decreasing-value path; T represents the total number of
project stages.
decision points8 into two parts depending on whether t is near the middle of a project. We define
“middle of a project” (‘mid = 1’) as t = 3, 4 for a T = 6 project and as t = 3, 4, 5 for a T = 8 or T = 10
project; these values are chosen based on the peaks observed in Figure 4.9 Let ‘mid = 0’ otherwise.
We fit a logistic regression for the decision to continue the project on ‘mid’ while controlling for both
the number of stages left and the project value (results are reported in Table 18 in Appendix B).
We find that the coefficient for ‘mid’ is negative and significant (p = 0.018 < 0.05), which confirms
that participants are less likely to abandon a project near its beginning or end.
Overall, we conclude that path does affect a participant’s decision to continue or abandon a
project and hence that Hypothesis 2 is rejected. Our data reveal two key results. First, given the
same project length, downward paths are associated with a higher likelihood of abandonment.
Second, when the project value is decreasing, participants are more likely to abandon the project
in its middle stages yet become less likely to abandon toward the beginning or end of a project.
5.4.
Do Participants Make Optimal Review Decisions?
In this section, we first examine whether participants make optimal review decisions. We then test
Hypothesis 3 by determining whether the review decision is affected by receiving good or bad news
in an earlier review. Lastly, we compare the abandonment rates at the first versus second review.
8
We use decision points in projects with decreasing values—that is, xt = (T − t)δ for unprofitable projects and
xt = (T − t + 2)δ for profitable projects.
9
In a T = 10 project, using t = 3, 4, 5, 6 or t = 4, 5, 6 for ‘mid = 1’ in the analysis yields similar significant results.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
20
Table 10
Project length
and initial value
T =4
x1 = 30
x1 = 50
T =6
x1 = 50
x1 = 70
T =8
x1 = 70
x1 = 90
T = 10
x1 = 90
Proportion of first review by stage.
Proportion of first review decision
N
Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 Stage 7 Stage 8 Stage 9
199
74
65%
61%
31%
32%
217
76
49%
50%
37%
41%
12%
9%
1%
0%
181
111
31%
23%
35%
36%
22%
26%
9%
13%
1%
0%
1%
0%
286
24%
26%
23%
13%
10%
2%
0%
0%
Notes. N = number of observations.
5.4.1.
Timing of Reviews Our results show that the participants’ review decisions do not
follow the predictions of the normative model in Section 3. Whereas the optimal policy is to review
an unprofitable project as early as possible (i.e., in stage 2), the observed proportion of participants
actually reviewing an unprofitable project at stage 2 is 65% for T = 4, 49% for T = 6, 31% for
T = 8, and 24% for T = 10. Participants distribute their reviews to span the duration of the project,
with a higher preference for early reviews. For example, of the 199 observations when a project
with T = 4 and x1 = 30 is launched, 65% review in stage 2, 31% in stage 3, and 4% do not review
at all. Table 10 shows the percentage of participants who decide to review the project for the
first time at a given stage. By comparing the first review decisions for projects with the same T
but different initial values, we find that the first review decisions for profitable versus unprofitable
projects are not significantly different.10 In other words, the initial value of the project does not
affect the timing of the first review.
However, the second review’s timing is significantly affected by the information received in the
first review. We segment the participants into those that observe an increase (or no change) in
project value in the first review and those that observe a decrease in project value; we then compare
the proportions that review again in the very next stage (provided the project is not abandoned).
A higher proportion of participants to review in the next stage indicates a preference for receiving
information sooner. The results are summarized in Table 11. In all cases where the difference
is statistically significant, a higher proportion reviews again in the next stage after observing a
decrease in project value. The proportions are not significantly different between those who observe
a strict increase in project value in the first review and those who observe no change in value. To rule
out the explanation that participants review sooner after observing a decrease in value because they
10
Fisher’s exact test.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
21
plan to abandon the project, we remove the data points corresponding to ultimately abandoned
projects and then fit an ordered logistic model for the number of stages between the first and the
second review on whether the news in the first review is good or bad (‘r1sign = 1’ if the value in
the first review is lower than the initial value; ‘r1sign = 0’ otherwise). The regression results (Table
19 in Appendix B) show that the coefficient for ‘r1sign’ is negative and significant (p < 0.01). We
therefore conclude that bad news make participants review sooner; hence Hypothesis 3 is rejected.
Table 11
Proportion that review again in the next stage.
xk − x1
≥0
T =6
k = 2∗∗∗
k=3
k = 4∗
xk − x1
<0
35%
63%
(N = 66) (N = 67)
42%
52%
(N = 69) (N = 33)
80%
100%
(N = 15) (N = 18)
T =8
k = 2∗∗∗
k = 3∗∗
k=4
k = 5∗∗
≥0
<0
27%
(N = 33)
23%
(N = 39)
18%
(N = 11)
0%
(N = 16)
63%
(N = 38)
44%
(N = 50)
22%
(N = 50)
36%
(N = 14)
xk − x1
T = 10
k=2
k = 3∗∗∗
k=4
k = 5∗
k=6
≥0
<0
44%
(N = 32)
12%
(N = 52)
5%
(N = 37)
0%
(N = 23)
5%
(N = 22)
63%
(N = 30)
52%
(N = 21)
13%
(N = 24)
20%
(N = 10)
25%
(N = 4)
Notes. N = number of observations; k = first review stage. The statistical test used is Fisher’s exact test.
∗
p < 0.1;
5.4.2.
∗∗
p < 0.05;
∗∗∗
p < 0.01.
Abandonment Rates at 1st versus 2nd Review For projects with two review
opportunities, the continuation error rate at the first review is 78.9% (versus 62.28% on the second
review). The abandonment error rate at the first (resp. second) review is 2.74% (resp. 3.38%). Our
comparisons suggest that the fewer review opportunities remaining, the greater the likelihood of
project abandonment.
Using LR data, we fit a logistic regression model for the continuation decision on the binary
variable ‘firstrev’ (set equal to 1 for the first review or to 0 for the second review) while controlling
for project value and number of remaining stages. Our results (Table 20 in Appendix B) show
that participants are more likely to abandon a project after its second than after its first review
(coefficient > 0, p = 0.015). The implication is that limiting opportunity for future action makes
participants more likely to abandon a project (similar to the discussion in Section 5.2).
6.
Behavioral Model
The experimental results show that participants’ decisions systematically deviate from the normative predictions. In this section we propose a behavioral model to describe the decision-making
process and explain these deviations.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
22
Several explanations have been given for why people delay termination. Thaler (1999) proposes
that an initial investment opens a “mental account” and that avoiding further investment would
feel as a “loss” proportional to the amount in the account (i.e., sunk cost). To avoid this loss,
people tend to continue the project—and more so as the sunk cost increases. Alternatively, the
preference to continue a project may be due to the status quo bias: the tendency to stick with the
default option or one’s “current or previous decision” (Samuelson and Zeckhauser 1988). Both the
sunk cost bias and the status quo bias are consistent with the continuation errors observed in our
experiments. The status quo bias can also explain why participants launch unprofitable projects
in the first stage (i.e., when the sunk cost is zero). Yet neither of these accounts can explain why,
even when sunk cost is the same (i.e., given the same stage number) and the project’s state is
the same, abandonment behavior still differs depending on the observed project path. Moreover,
although the sunk cost bias predicts that the participants are more likely to abandon a project in
its earlier stages, we find the abandonment rate to be highest not at a project’s beginning stages
but rather at its middle stages. Hence we conclude that, even though the sunk cost and status quo
biases may both affect participants’ decisions, they do not fully capture behavior.
As a benchmark, we also consider whether expected utility theory (EUT) explains our observations. When facing the choice between abandoning a project and gambling on the possibility
of a high return, risk-seeking participants may choose to continue. However, EUT is not able to
reconcile the continuation errors in unprofitable projects with the abandonment errors in profitable
projects—the former would suggest risk seeking; the latter, risk aversion. The framework is also
silent about how the path can affect decisions. In Appendix C we formulate an EUT model and
show that it does not describe our data as well as does a behavioral model.
6.1.
Reference-dependent Behavioral Model
To explain path dependence and late/premature terminations, we propose a reference-dependent
framework: the PM who decides to continue a project after observing its value experiences a “gain–
loss utility” by comparing the project value with an internal reference point. The PM experiences
a gain if the project value exceeds his expectation and experiences a loss otherwise. We express
this formally as m(xt − rt ), where rt denotes the PM’s reference point at time t. Specifically, let
m(x) = γx for x ≥ 0 and let m(x) = γλx for x < 0, where γ ≥ 0 is the weight of the referencedependent utility and λ is the loss aversion parameter. If λ 6= 1, then the PM perceives gains
and losses of the same size differently. Suppose his reference point is updated through exponential
smoothing. That is, let rt+1 = θrt + (1 − θ)xt if there is a review—and let rt+1 = rt if there is
no review—in stage t; the parameter θ ∈ [0, 1] captures the speed with which the PM assimilates
information. At the extremes, if θ = 1 then the PM’s reference point remains constant regardless
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
23
of incoming information, and if θ = 0 then the PM updates his reference point to fully reflect the
latest information. Let r1 = x1 .
We note that the gain–loss utility is experienced only if the PM receives information about the
project and the project is continued. This follows from the basic assumption that information
affects utility only when it represents immediate or future consumption (Kőszegi and Rabin 2009).
It is intuitive that, if the PM decides to abandon a project whose value is below his reference point,
then he will not incorporate that loss into his utility function because the project value no longer
represents his actual payoff. A PM would, analogously, experience no gain were the abandoned
project’s value above his reference point
The PM who abandons a project at stage t < T receives zero payoff from a total sunk cost of
(t − 1)c. In order to accommodate possible sunk cost or status quo biases, we assume that the
utility of abandoning is −A − B(t − 1)c for A, B ≥ 0. The parameter A captures the PM’s aversion
to abandoning the project given that continuing the project seems like the default option. The
parameter B is the sunk cost parameter that measures how strongly the sunk cost (t − 1)c affects
the PM.
The value function under FR is
Vt (xt , rt ) = max{UtC (xt , rt ), UtA (xt , rt )}
for t = 1, . . . , T − 1 and VT (x, r) = x + m(x − r). The expected utility from continuing the project is
UtC (xt , rt ) = −ct + m(xt − rt ) + EVt+1 (xt+1 , rt+1 );
here rt+1 = θrt + (1 − θ)xt and xt+1 = xt + wt , and EVt+1 (xt+1 , rt+1 ) is the expected value of
Vt+1 (xt+1 , rt+1 ) with respect to xt+1 . The utility from abandoning the project is UtA (xt , rt ) = −A −
B(t − 1). The PM continues the project at stage t if and only if UtC (xt , rt ) > UtA (xt , rt ).
In the LR case, suppose that xk and rk are (respectively) the project value and the reference
point from the PM’s most recent review stage (stage k). Let n be the number of reviews left. Then
the value function can be written as follows:
(
max{UtR (xk , rk , k, n), UtNR (xk , rk , k, n)} if n > 0,
Vt (xk , rk , k, n) =
UtNR (xk , rk , k, n)
otherwise
for t = 2, . . . , T − 1 and V1 (x1 , r1 , 1, M ) = max{U1C (x1 , r1 , 1, M ), UtA (x1 , r1 , 1, M )}. The value function at stage T is VT (xk , rk , k, n) = E[xT +m(xT − rT ) | xk , rk , k], which is the expected utility over xT
given that the PM last observed xk at stage k; the reference point is updated as rT = θrk + (1 − θ)xk .
The expected utility from not reviewing is UtNR (xk , rk , k, n) = −c + Vt+1 (xk , rk , k, n), whereas the
expected utility from reviewing is
UtR (xk , rk , k, n) = E max{UtC (xt , rt , t, n − 1), UtA (xt , rt , t, n − 1)};
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
24
here the expectation is with respect to xt (given that the PM last observed xk at stage k) and the
reference point is rt = θrk + (1 − θ)xk . The utilities from continuing or abandoning the project are,
respectively,
UtC (xt , rt , t, n − 1) = −ct +m(xt − rt )+Vt+1 (xt , rt , t, n − 1),
and UtA (xt , rt , t, n − 1) = −A − B(t − 1)c.
The reference-dependent PM’s continue/abandon decision depends not only on the project value
xt but also on his reference point rt . This case contrasts with that of the rational PM, who makes
decisions based on xt only.
Proposition 3. At stage t, (i) for a given rt , there exists a threshold āt such that the PM
continues if and only if xt > āt ; (ii) for a given xt , there exists a threshold r̄t such that the PM
continues if and only if rt < r̄t .
Proposition 3 states that, given xt , the PM’s continue/abandon decision depends on the reference
point rt . We can expand the reference point in the FR case as r2 = x1 and
rt = θ
t−2
x1 + (1 − θ)
t−1
X
θt−i−1 xi
for t > 2.
(1)
i=2
On the one hand, suppose that the PM observes a high initial value but that the project’s
value decreases over time. Then, by equation (1), the PM would have a reference point rt that is
higher than xt ; this entails a feeling of loss if he continues the project in stage t. And since the
PM’s current reference point is high, he is likely also to frame future outcomes as losses; that is,
Em(xt+1 − rt+1 ) is decreasing in rt . On the other hand, suppose the PM starts the project at a low
initial value but observes increasing values over time. Then the PM would have a low reference
point rt as compared with xt , which means that he experiences a gain from continuing the project
in stage t and also anticipates future gains. This example illustrates how, given xt , the path may
affect the likelihood of project abandonment.
Our model explains the two types of path dependence observed in the data. First: equation (1)
implies that, given xt and T , a PM who observes a downward (rather than an upward) history
will have a higher rt , which by Proposition 3 implies a greater likelihood of abandonment. Second:
Proposition 3 suggests that, all else constant, a longer history of decreasing values should make
the PM more likely to abandon the project owing to a higher rt ;11 yet a longer history also means
a larger sunk cost which makes the PM more likely to continue the project. Thus we may observe
a peak in abandonment rate as project length increases: in the early stages of a project, gain–
loss utility dominates and so makes the PM more likely to abandon a project as project length
11
A history of decreasing values means that xt−1 = xt − δ, xt−2 = xt − 2δ, . . . , x1 = xt − (t − 1)δ. It follows from
equation (1) that in this case, for a given xt = x, a larger t corresponds to a higher rt .
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
25
increases; in later project stages the sunk cost dominates, making the PM more likely to continue
the project. Our simulation results (see Section 6.4) confirm that this dynamic—between gain–loss
utility and sunk costs—explains the inverted U shape we observed in the abandonment rates as
project length increases.
For the rational PM, a review is valuable if it provides information that could lead to an abandonment decision. For the reference-dependent PM, however, a review can also affect his reference
point and hence the gain–loss utility. So even when the PM continues at every stage (i.e., when
reviews carry no decision-making value), he may still strictly prefer to review at an earlier or later
stage. We use an example to show that, if a review has no decision-making value, the PM may
prefer to review earlier or later depending on whether λ > 1 or λ < 1.
Example 1. Let T = 4, and let parameters A and B be sufficiently large such that the PM
always continues the project. Suppose there is only one review opportunity (M = 1). If λ > 1, then
reviewing at stage 3 is strictly preferred to reviewing at stage 2; if λ < 1, then reviewing at stage
2 is strictly preferred to reviewing at stage 3.
We also analyze the second review decision and find that it does not depend on whether the
PM observes an increase or a decrease in the first review. Although we have assumed that the
gain–loss utility is weighted the same at every stage, Kőszegi and Rabin (2009) argue that “news
about more imminent consumption is felt more strongly than news about distant consumption”
(p. 909). In our behavioral model, if this were the case then γ would increase as t becomes closer
to T . We explore this possibility in Appendix D, where we show that the news received by the PM
from the first review can affect the second review’s timing and, as we saw in the experiments, the
PM may prefer to review again sooner after receiving bad news.
6.2.
Maximum Likelihood Estimation
We estimate our behavioral model using the maximum likelihood estimation (MLE) method. In
this section we describe the estimation procedure.
At each stage t where participant j chooses whether to continue or abandon project i, the
participant continues if and only if
UtC − UtA + witj > 0,
where the noise term witj is an i.i.d., normally distributed random variable, with mean 0 and
variance 1/(s1 )2 , and where UtC and UtA are as given in Section 6.1 (we suppress the variables
to ease the exposition). It follows that the probability of the participant choosing to continue or
abandon is:
Pitj (continue | review) = Φ(s1 (UtC − UtA )),
Pitj (abandon | review) = Φ(s1 (UtA − UtC ));
(2)
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
26
where Φ(·) is the cumulative distribution function of a standard normal random variable. If there
is no review then Pitj (continue | no review) = 1 and Pitj (abandon | no review) = 0.
Similarly, the participant chooses to review at stage t of project i if and only if UitR − UitNR +vitj > 0;
here the noise term vitj is an i.i.d. normally distributed random variable with mean 0 and variance
1/(s2 )2 , and the terms UtR and UtNR are as given in Section 6.1. Therefore,
Pitj (review) = Φ(s2 (UtR − UtNR ));
and Pitj (no review) = Φ(s2 (UtNR − UtR )).
(3)
Given the probabilities in (2) and (3), the log-likelihood (LL) functions for FR and LR are:
LLFR =
Ti N1
32 X
X
X
aitj log Pitj (continue) + (1 − aitj ) log Pitj (abandon) ;
i=1 t=1 j=1
LLLR =
Ti N2
32 X
X
X
citj aitj bitj log Pitj (continue | review) + (1 − aitj )bitj log Pitj (abandon | review)
i=1 t=1 j=1
+ bitj log Pitj (review) + (1 − bitj ) log Pitj (no review) .
Here N1 = 37 is the number of participants in the FR experiment and N2 = 38 is the number
of participants in the LR experiment. Let aitj = 1 if participant j continues project i at stage t,
with aitj = 0 otherwise; similarly, bitj = 1 if participant j reviews project i at stage t (with bitj = 0
otherwise) and citj = 1 if the number of review opportunities left for participant j at stage t of
project i is positive (with citj = 0 otherwise).
We estimate our model using aggregate FR and LR data as well as using FR and LR data
separately. Specifically, the unknown parameters in our behavioral model (θ, γ, λ, A, B, s1 , s2 ) are
selected to maximize the respective log-likelihoods LLFR + LLLR , LLFR , and LLLR . To determine
whether our model describes behavior significantly better than either the rational model or the
behavioral model without gain–loss utility, we perform likelihood ratio tests.
6.3.
Estimation Results
Each of Tables 12–14 reports estimation results for the full model as well as for the nested model
with γ = 0 and the rational model with only noise parameters s1 and s2 . Table 12 presents the
estimation results using the aggregate data for FR and LR, while Tables 13 and 14 report results
for FR and LR data separately. The p-values from the likelihood ratio tests, which test the nested
models against the full model, are very small in all cases (p = 0.000). We conclude that the full
behavioral model provides the best fit to our data.
The parameter estimation in the full behavioral model yields some interesting insights. In all
three sets of estimates (FR+LR, FR, and LR) we find that the loss aversion parameter is less
than one (λ < 1), which means that the positive utility anticipated by participants upon receiving
good news is greater (in absolute value) than their anticipated negative utility.12 This result does
12
We also estimate the behavioral model using alternative formulations for the reference point and find that λ < 1 is
robust.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
Table 12
27
Estimation results for full behavioral model and nested models (FR+LR).
Behavioral parameters
Only noise
No gain–loss utility
θ
–
–
γ
–
–
λ
–
–
A
–
B
–
s1
52.12
(6.69)
0.00
(0.12)
0.025
(0.001)
0.50
(1.00)
0.06
(0.047)
0.00
(0.22)
s2
−LL
Likelihood ratio test
and p-value
6179.9
χ (5) = 3797.6
p = 0.000
2
4468.4
χ (3) = 374.6
p = 0.000
Full model
0.49
(0.03)
1.06
(0.05)
0.25
(0.05)
39.36
(3.18)
0.038
(0.06)
0.025
(0.001)
0.218
(0.026)
4281.1
2
Notes. Standard errors are reported in parentheses. The likelihood ratio test is against the full model.
Table 13
Behavioral parameters
Estimation results for full behavioral model and nested models (FR).
Only noise
No gain–loss utility
θ
–
–
γ
–
–
λ
–
–
A
–
B
–
s1
−LL
Likelihood ratio test
and p-value
0.065
(0.002)
2025.2
χ2 (5) = 2126.2
p = 0.000
49.39
(3.83)
0.00
(0.08)
0.027
(0.002)
993.4
χ2 (3) = 62.6
p = 0.000
Full model
0.54
(0.01)
1.30
(0.34)
0.73
(0.11)
73.28
(15.59)
0.64
(0.27)
0.017
(0.003)
962.1
Notes. Standard errors are reported in parentheses. The likelihood ratio test is against the full model.
not align with the descriptions of prospect theory (Kahneman and Tversky 1979), which may be
due to several differences that our work has with existing studies (for a review, see Novemsky and
Kahneman 2005).
The first main difference is that, whereas most existing research defines losses and gains in
relation to actual payoffs, in our model these utilities are associated with receiving information
about payoffs. We are interested in the extent to which bad (resp. good) news drives individuals to
abandon (resp. continue) a project. Experiments investigating gain–loss preferences in contexts of
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
28
Table 14
Behavioral parameters
Estimation results for full behavioral model and nested models (LR).
Only noise
No gain–loss utility
θ
–
–
γ
–
–
λ
–
–
A
–
B
–
s1
0.053
(0.003)
0.000
(0.021)
s2
−LL
Likelihood ratio test
and p-value
58.88
(74.36)
0.00
(0.99)
0.021
(0.006)
0.499
(1.582)
4146.4
χ (5) = 1765.6
p = 0.000
2
3469.9
χ (3) = 412.6
p = 0.000
Full model
0.46
(0.05)
2.41
(0.25)
0.024
(0.047)
18.09
(1.03)
0.00
(0.15)
0.026
(0.001)
0.089
(0.016)
3263.6
2
Notes. Standard errors are reported in parentheses. The likelihood ratio test is against the full model.
information utility are scarce, and theoretical discussions on the topic usually assume that λ ≥ 1
(Karlsson et al. 2009, Kőszegi and Rabin 2009). Our result challenges this assumption and suggests
that gain–loss preferences may be different for information versus monetary payoffs. According to
the hedonic principle (Higgins 1997, Thaler 1999), people are motivated to maximize pleasure and
minimize pain. Therefore, individuals may be motivated to treat positive news as a gain but to
trivialize negative news by believing that it does not necessarily reflect the final outcome. Harinck
et al. (2007) use a similar rationale to explain why people tend to be gain seeking over small
amounts of money (since small losses are easy to trivialize and ignore).
Second, it is instructive to compare our setting with those of existing works that report lossneutral or gain-seeking behavior. For example, Novemsky and Kahneman (2005) find that loss
aversion disappears when people intend to trade. Ert and Erev (2008) replicate well-known experiments testing preferences between mixed gambles and a safe option; these authors find that, if
context is abstracted away (i.e., if the safe option is no longer presented as the status quo), then
no loss aversion is evident. They conclude that context is a driver of asymmetric preferences with
regard to gains versus losses. Sonsino et al. (2001) find that participants are highly likely to participate in betting games even when the expected returns are negative. Erev et al. (2010) similarly
find that, in a market entry game, more participants choose entry over the safe option even when
expected profits are unspecified. It is possible that the nature of our project management task
induces a betting mindset that likewise leads to gain-seeking behavior (Ert and Erev 2013).
Our estimation results reveal that the status quo parameter A is large compared to the sunk
cost parameter B. In particular, the estimate for B is significantly different from zero only in the
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
29
FR case. The status quo parameter represents the part of utility from abandoning that does not
change over time, whereas a positive sunk cost parameter implies that the PM is more likely to
continue the project at later stages. One reason for not finding sunk cost bias in the LR experiment
could be that sunk cost is relatively less salient to LR participants because they do not make a
continue/abandon decision at every stage. Thus our results show the important role played by
status quo bias in termination delay during a project’s early stages or when reviews are limited.
Our estimates indicate that θ ∈ (0.46, 0.54), which implies that participants’ choices can be
affected by project values from as many as three previous observations. The estimate for θ is fairly
consistent across FR and LR data.
Comparing the estimates using FR versus LR data shows that λ, B, and A are all smaller in
LR. In fact, in the LR case neither the sunk cost parameter B nor the loss aversion parameter λ is
statistically different from zero. The smaller B and A reflect our observation that LR participants
are more likely to abandon an ongoing project than are FR participants, which suggests that
limiting the number of review opportunities may reduce both the status quo and sunk cost biases.
There are two possible explanations for the smaller λ in the LR estimates. First, γ and λ refer to
anticipated utilities; that is, participants are making decisions based on how they think they will
feel once a particular decision is made. Therefore, being optimistic, they may underestimate future
losses. This could be corrected by the experience of repeated losses, which are more likely to be
encountered in FR than in LR. Second, λ might simply vary with the frequency of potential losses;
that is, participants could be more averse to frequent small losses than to infrequent large ones
(Lambrecht and Skiera 2006).
6.4.
Simulation
In this section, we conduct numerical simulations using the parameter estimates from Section 6.3
to assess how well our model accounts for the observed behavioral patterns.
6.4.1.
Effect of Project Length on Continue/Abandon Decisions Using the estimates
from FR, we simulate the abandonment rates at a given decision point for different project lengths.
Figure 5 plots the rates for xT −4 = 40 and xT −2 = 20, respectively. As T increases, the abandonment
rate first increases and then decreases. This pattern reflects the experimental data and suggests
that such path-dependent behavior is well explained by our behavioral model. In studying further
the behavioral factors that may account for this pattern, we rerun the simulations with B = 0
(no sunk cost parameter), A = 0 (no status quo parameter), and γ = 0 (no gain–loss utility). The
results are presented in Figure 6.
Figure 6(a) shows that if the sunk cost parameter is zero (B = 0) then the abandonment rate
is strictly increasing in T . The reason is that a bigger T implies a longer history of decreasing
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
30
(a) xT −4 = 40
(b) xT −2 = 20
Proportion of abandonment for project on a path ofdecreasing value; T represents the project’s total
Figure 5
number of stages.
(a) B = 0.
(b) A = 0
(c) γ = 0
Figure 6
Proportion of abandonment at xT −4 = 40 for project on a path of decreasing value.
values (i.e., the observed path for T = 6 is 50-40 but for T = 10 it is 90-80-70-60-50-40), which in
turn corresponds to a higher reference point by equation (1). For a given project value, a higher
reference point enlarges the negative gain–loss utility and makes the PM more likely to abandon
the project. Figure 6(b) shows that putting A = 0 results in higher probabilities of abandonment
yet does not affect the pattern of abandonment as T changes. Finally, Figure 6(c) shows that if
γ = 0 (i.e., if there is no gain–loss utility) then the abandonment rate is strictly decreasing in T .
This is because a longer history corresponds to a larger sunk cost, which provides a bigger incentive
to continue the project. Overall, our simulation results establish that the gain–loss utility and sunk
cost combine to produce—under varying T —the abandonment rate’s inverted U shape at a given
decision point.
6.4.2.
Abandonment Rates When Reviews Are Limited In this section we simulate the
abandonment rates in LR—using the parameter estimates for LR—to probe the implications of
individual parameters.
Figure 7(a) compares abandonment rates in the FR and LR scenarios at each stage of a T = 10
project whose value decreases over time. The abandonment rate under LR is clearly lower for t = 1
but higher in later stages. Figure 7(b) plots the predicted abandonment rates in the LR scenario
when γ = 0; now the abandonment rate is decreasing in t. This reflects that, without gain–loss
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
31
utility, the benefit of continuing over abandoning increases over time. Yet a gain-seeking participant
is more likely to continue the project in early than in late stages because, as t increases and
project value declines, the prospect for large gains also diminishes. Finally, Figure 7(c) simulates
the abandonment rates for a higher value of the loss aversion parameter (λ = 0.5). We find that
this change leads to higher abandonment rates, which approach 100% in later stages of the project.
Overall, these simulations confirm our results that the loss parameter is small under LR because
the decrease in the value that participants observe has little effect on their abandonment decisions,
and gain-seeking makes the PM more likely to continue in early stages of the project.
(a) LR vs. FR
(b) LR abandonment: γ = 0
(c) LR abandonment: λ = 0.5
Figure 7
Proportion of abandonment at each stage of a T = 10 project with path
90-80-70-60-50-40-30-20-10-0; for LR, the abandonment rate is that upon the first review (for t > 1).
Simulation of the first review decision shows that it is unaffected by the project’s initial value.
The expected first review stage is 2.526, 2.857, 3.155, and 3.301 for T = 4, 6, 8, 10, respectively.
Simulation of the second review decision shows that the likelihood of reviewing again in the next
stage is unaffected by whether a positive or negative project value change is observed in the first
review. In Appendix D we consider an extension of our behavioral model in which the gain–loss
utility at stages closer to T carry more weight. We estimate this extended model and show, via
simulations, that such increasing weight explains the observation that participants are more likely
to review after observing bad news.
7.
Discussion and Conclusion
Sequential investment decision-making is a crucial component of managing projects in uncertain
environments. Project managers may make decisions that systematically deviate from the optimal
policy, and our study identifies several behavioral regularities in such decisions. First, we confirm
existing evidence that PMs have a strong tendency to delay termination even as project value
declines. Second, we find that participants’ decisions are affected by the project path. We observe
two types of path dependence: (i) keeping sunk cost fixed, a downward path is associated with a
greater likelihood of abandonment than is an upward path; (ii) if project value decreases over time,
then the likelihood of abandonment first increases and then decreases as project length increases.
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
32
The latter finding implies that, as a project develops and the PM continues to receive negative
feedback, he is less likely to abandon the project near the beginning or near the end of its duration.
Third, when review opportunities are limited, PMs reviews sooner after bad news. Moreover, a PM
is more likely to abandon an ongoing project when review opportunities are limited.
We build a behavioral model to organize our data and explain the regularities. We find that
reference dependence can explain the first type of path dependence (the effect of a downward versus
an upward path) and that reference dependence, together with sunk cost, can explain the second
type (the effect of shorter versus longer project length). Our structural estimation results show
that—in this particular decision context—participants are gain seeking rather than loss averse.
Although we find evidence for both sunk cost bias and status quo bias, the latter is especially
important in inducing termination delays at the early stages of a project or when reviews are
limited.
Our use of reference dependence to explain path-dependent behavior echoes Post et al. (2008),
who study the risky choices of contestants on the TV game show “Deal or No Deal”. These authors
find that risk attitudes are path dependent, with less risk aversion after both increases and decreases
in the game’s expected payoff. They also show that prospect theory with a lagged reference point
describes the contestants’ choices significantly better than does expected utility theory.
Our work helps to identify policies that might improve the quality of PM decisions. First, it may
be possible to counteract the effect of path dependence by periodically introducing new personnel
(e.g., outside experts)—who are not familiar with the project’s history—to assess its current situation. This type of outside intervention is especially useful when a project’s value has been steadily
increasing or decreasing, or when a project is near the beginning or the end of its duration. Second,
it is important to recognize the value of project abandonment in order to reduce the status quo
bias. Our experiments show that imposing a limit on review opportunities may help achieve this
goal, although a balance is necessary to ensure sufficient opportunity for action. Third, a flexible
review schedule facilitates responding to new information; yet PMs may benefit from also setting
a fixed review schedule that depends on the project’s initial estimated value (i.e., a sooner first
review for low valuation and a later first review for high valuation). This approach could prevent
project termination delays due to insufficient review.
There are several avenues for future research. First, we consider a simple sequential investment
setting and do not consider interactions among different parties. In reality, however, projects are
complex endeavors that involve multiple parties with different (and sometimes conflicting) incentives. It would be interesting to study the investment decisions in a principle–agent setting or
in a setting where the project is managed by multiple decision makers. Second, though we have
assumed a zero payoff for the project manager’s outside option, in reality the PM often has several
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
33
alternative options. For example, an investor may be investing in multiple projects at once, or a
manager who invests in the development of a new product may have the option of focusing instead
on an existing product. In these scenarios, it is unclear whether the behavioral patterns that we
have observed would still prevail.
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Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
36
Appendix A:
Proofs
Proof of Lemma 1.
It suffices to prove that Vt (x) is increasing in x for t = 1, 2, . . . , T − 1. First, observe
that VT (x) = x is increasing in x. Second, for t = 1, 2, . . . , T − 1, if Vt+1 (x) is increasing in x, then Vt (x) =
max{−ct + E[Vt+1 (x + wt )], 0} = max{−ct + 21 Vt+1 (x + δ) + 21 Vt+1 (x − δ), 0} is increasing in x. This completes
the proof.
Proof of Proposition 1.
The statement in the proposition is equivalent to: Given the project value xt
in stage t = 1, . . . , T − 2, if it is optimal to abandon either at xt+1 = xt − δ or at xt+1 = xt + δ in stage t + 1,
then it is optimal to abandon in stage t. We prove this in two possible cases.
Case 1: Suppose it is optimal in stage t + 1 to abandon at both xt+1 = xt + δ and xt+1 = xt − δ. This
implies zero value for the project in stage t + 1 (i.e., E[Vt+1 (xt + wt ) | xt ] = 0) and hence zero value for the
project at stage t (i.e., Vt (xt ) = max{−ct + E[Vt+1 (xt + wt )], 0} = max{−ct , 0} = 0). Therefore, it is optimal
to abandon the project at stage t.
Case 2: Suppose it is optimal in stage t + 1 to abandon at xt+1 = xt − δ but to continue at xt+1 = xt + δ.
In this case, we prove the result by induction.
First, we prove the result for t = T − 2. Thus: given xT −2 in stage T − 2, if it is optimal in stage T − 1 to
abandon the project at xT −1 = xT −2 − δ but to continue at xT −1 = xT −2 + δ, then it is optimal to abandon in
stage T − 2. Observe that xT −2 − δ − c ≤ 0 and δ ≤ c. The first inequality follows because (a) the PM abandons
the project at xT −1 = xT −2 − δ and (b) it is optimal to abandon in stage T − 1 if and only if xT −1 ≤ c.
The inequality δ ≤ c holds because project payoffs are non-negative—that is, xT −2 − 2δ ≥ 0—and this (when
combined with the first inequality) yields xT −2 − δ − c ≤ 0 ≤ xT −2 − 2δ or c ≥ δ. These two inequalities
together imply that VT −2 (xT −2 ) = max{−c + 21 (xT −2 + δ − c), 0} = max{ 21 (xT −2 − δ − c + 2δ − 2c), 0} = 0.
Second, we prove that if the result holds at stage k + 1 (k = 1, . . . , T − 3) then it holds also at stage k. If
the result holds at stage k + 1, . . . , T − 2, then Vk+1 (x) = max{x − (T − k − 1)c, 0}; that is, at stage k + 1 the
PM either abandons the project or continues until completion. From the conditions Vk+1 (xk + δ) > 0 and
Vk+1 (xk − δ) = 0 we then have
1
1
Vk (xk ) = max − c + (xk + δ − (T − k − 1)c), 0 = max
(xk − δ − (T − k − 1)c + 2δ − 2c), 0 = 0,
2
2
which follows from (i) xk − δ − (T − k − 1)c ≤ 0 and (ii) δ ≤ c. Inequality (i) follows from xk − δ − (T − k − 1)c ≤
Vt+1 (xk − δ) = 0; this statement holds because, at xk+1 = xk − δ, the expected profit from completing the
project (i.e., xk − δ − (T − k − 1)c) is by definition no greater than the project’s value Vt+1 (xk − δ). Inequality
(ii) follows because project payoffs are nonnegative (i.e., xk ≥ (T − k)δ), which—together with inequality
(i)—implies (T − k − 1)δ ≤ xk − δ ≤ (T − k − 1)c. This completes the proof.
Proof of Corollary 1.
This result follows directly from Lemma 1 and Proposition 1.
Proof of Corollary 2.
We denote the expected profits from continuing the project under FR and LR as
C
ΠC
t,FR (xt ) and Πt,LR (xt , t, n), respectively. First, at xt , if the optimal decision in FR is to abandon the project
C
(i.e., ΠC
t,FR (xt ) ≤ 0) then the optimal decision in LR is also to abandon the project because Πt,LR (xt , t, n) ≤
ΠC
t,FR (xt ) ≤ 0, where the first inequality holds because FR has no fewer review opportunities than does LR.
Next, at xt , if the optimal decision in FR is to continue the project (i.e., ΠC
t,FR (xt ) = xt − (T − t)c > 0;
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
37
see Proposition 1), then the optimal decision in LR is also to continue the project because ΠC
t,LR (xt , t, n) ≥
xt − (T − t)c—that is, the expected profit from continuing the project is no less than that from project
completion.
Proof of Proposition 2.
(i) If xk > (T − k)c, then it is optimal to continue the project until completion
(by Corollaries 1 and 2). The result then follows because a review neither changes the PM’s decisions nor
affects the expected profit.
(ii) If xk ≤ (T − k)c, then the PM may abandon the project upon review in stage t + κ, κ ≥ 0. More
specifically, he abandons the project if xt+κ ≤ (T − t − κ)c and continues otherwise (Corollaries 1 and 2).
We shall prove that the PM prefers to review now (in stage t) by showing that he prefers reviewing in stage
t + κ to reviewing in stage t + κ + 1. We consider two cases depending on the realized project value xt+κ in
stage t + κ.
In the first case, suppose it is optimal to continue the project at xt+κ in stage t + κ. Then, by Proposition 1,
it is also optimal to continue at stage t + κ + 1. So here the PM is indifferent between reviewing at either
stage.
In the second case, suppose it is optimal to abandon the project at xt+κ in stage t + κ. By Proposition 1
there are three possibilities if the PM reviews in stage t + κ + 1: [1] he abandons the project irrespective
of xt+κ+1 ; [2] he continues the project at xt+κ+1 = xt+k + δ but abandons at xt+k+1 = xt+κ − δ; or [3] he
continues the project irrespective of xt+κ+1 . If [1] applies, then the PM abandons at either stage and so
prefers to review early in order to save the continuation cost c. For [2], we can show that the expected profit
from reviewing in stage t + κ (which is zero because of abandonment) is higher than that from reviewing in
t + κ + 1. Formally, we have
1
1
(xt+κ + δ − (T − t − κ − 1)c) + (0) − c ≤ 0,
2
2
(4)
where xt+κ + δ − (T − t − κ − 1)c is the expected payoff from continuing the project at xt+κ+1 = xt+κ + δ in
stage t + κ + 1. We can rewrite (4) as xt+κ − (T − t − κ)c + δ − c ≤ 0, which holds because xt+κ − (T − t − κ)c ≤ 0
and δ ≤ c. The first of these inequalities holds because it is optimal to abandon the project at xt+κ in stage
t + κ, which by Proposition 1 implies xt+κ − (T − t − κ)c ≤ 0; that is, the expected profit from continuing
the project until completion is lower than the expected profit from abandonment. The inequality δ ≤ c holds
because project payoffs are positive (i.e, xt+κ − (T − t − κ)δ ≥ 0); when combined with the first inequality,
this gives δ ≤ c. Hence the PM prefers to review in stage t + κ rather than in stage t + κ + 1. For [3], again we
show that the expected profit from reviewing in stage t + κ is higher than that from reviewing in t + κ + 1,
or
1
1
(xt+κ + δ − (T − t − κ − 1)c) + (xt+κ − δ − (T − t − κ − 1)c) − c ≤ 0.
2
2
(5)
This expression simplifies to xt+κ − (T − t − κ)c ≤ 0, and it holds because it is optimal to abandon at xt+κ
in stage t + κ. This proves the second case for part (ii), completing our proof of the proposition.
Proof of Proposition 3.
We prove the results for the FR case; proofs for the LR case are similar. (i)
The proof is similar to that of Lemma 1 and so is omitted for brevity. (ii) We use backward induction to show
that Vt (xt , rt ) is decreasing in rt . First, observe that VT (xT , rT ) = xT + m(xT − rT ) is decreasing in rT . Next,
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
38
for t = 1, . . . , T − 1, if Vt+1 (xt+1 , rt+1 ) is decreasing in rt+1 then rt+1 = θrt + (1 − θ)xt implies Vt+1 (xt+1 , rt+1 )
is decreasing in rt , which in turn means that Vt (xt , rt ) = max{−ct + m(xt − rt ) + EVt+1 (xt+1 , rt+1 ), −A −
B(t − 1)c} is decreasing in rt . This completes the proof.
Appendix B:
Regression Results
This section documents the regression results mentioned in the paper.
Table 15
Logistic regression model for launching the project (Section 5.1)
Independent variable
Coefficient
−0.604
1.501∗∗∗
0.676∗∗∗
0.602∗
0.403
2.185∗∗∗
FR
prof
T=6
T=8
T=10
Constant
Observations
Clusters
∗
Table 16
Robust std. error
p < 0.10,
∗∗
(0.424)
(0.454)
(0.250)
(0.310)
(0.393)
(0.338)
2400
75
p < 0.05,
∗∗∗
p < 0.01
Logistic regression model for continue decision in FR vs. LR experiment (Section 5.2)
Model 1 (excluding stage 1)
Independent variable
Coefficient
FR
stageleft=2
stageleft=3
stageleft=4
stageleft=5
stageleft=6
stageleft=7
stageleft=8
stageleft=9
Constant
0.958∗∗∗
−1.104∗
−1.387∗∗
−0.743
−1.399∗∗
−1.006
−1.067∗
−0.400
(0.262)
(0.645)
(0.614)
(0.580)
(0.591)
(0.645)
(0.595)
(0.725)
2.028∗∗∗
(0.595)
Observations
Clusters
∗
p < 0.10,
∗∗
Robust std. error
1427
75
p < 0.05,
∗∗∗
p < 0.01
Model 2 (including stage 1)
Coefficient
Robust std. error
0.147
−1.136∗
−0.944
−0.787
−0.653
−0.962
−0.408
−0.318
−0.330
2.513∗∗∗
(0.250)
(0.634)
(0.625)
(0.579)
(0.614)
(0.640)
(0.625)
(0.720)
(0.724)
(0.615)
3302
75
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
Table 17
Logistic regression model for continue decision with different paths of same length (Section 5.3)
Independent variable
Coefficient
Observations
Clusters
∗
p < 0.10,
∗∗
Robust std. error
−2.397∗∗∗
1.156
0.285
0.341
−1.218∗
−0.636
−0.671
−1.336∗
5.034∗∗∗
decpath
(t=2)×(T=6)
(t=2)×(T=8)
(t=3)×(T=6)
(t=3)×(T=8)
(t=4)×(T=6)
(t=4)×(T=8)
(t=5)×(T=8)
Constant
Table 18
39
(0.485)
(0.843)
(0.957)
(0.737)
(0.715)
(0.540)
(0.560)
(0.776)
(0.747)
827
37
p < 0.05,
∗∗∗
p < 0.01
Logistic regression model for continue decision with different project lengths (Section 5.3)
Independent variable
mid
prof
stageleft=2
stageleft=3
stageleft=4
stageleft=5
stageleft=6
stageleft=7
stageleft=8
stageleft=9
(prof=1)×(stageleft=2)
(prof=1)×(stageleft=3)
(prof=1)×(stageleft=4)
(prof=1)×(stageleft=5)
(prof=1)×(stageleft=6)
Constant
Observations
Clusters
Coefficient
Robust std. error
∗∗
−0.706
1.788∗∗
−1.212
−1.538
−1.023
−1.083
−1.059
−1.191
−0.803
−1.516
−1.237
−0.857
−1.291
−1.505∗
−1.296
3.401∗∗∗
(0.298)
(0.769)
(1.102)
(1.106)
(0.984)
(1.074)
(1.124)
(1.048)
(1.197)
(1.153)
(0.904)
(0.800)
(0.851)
(0.776)
(1.046)
(1.031)
2483
37
Notes. We use the binary variable ‘prof’ which interacts with
the number of stages left as a proxy for project value.
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
40
Table 19
Ordered logistic regression model for interval between the first and second review (Section 5.4.1)
Model 1 (unprofitable projects)
Independent variable
Coefficient
Robust std. error
−0.819∗∗∗
−1.046∗∗∗
0.423∗∗∗
1.984∗∗∗
3.781∗∗∗
4.143∗∗∗
5.404∗∗∗
r1sign
cut1
cut2
cut3
cut4
cut5
cut6
Observations
Clusters
Model 2 (all projects)
Coefficient
Robust std. error
−0.766∗∗∗
−1.026∗∗∗
0.529∗∗∗
2.151∗∗∗
4.006∗∗∗
4.368∗∗∗
5.627∗∗∗
(0.156)
(0.197)
(0.146)
(0.224)
(0.528)
(0.731)
(0.989)
563
38
(0.148)
(0.200)
(0.138)
(0.214)
(0.524)
(0.728)
(0.987)
719
38
Notes. If no second review is undertaken, then the second review stage is set equal to the stage of
project completion (T ).
∗
p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
Table 20
Logistic regression model for continue decision at first vs. second review (Section 5.4.2)
Independent variable
Coefficient
firstrev
(stageleft=2)×(value=20)
(stageleft=2)×(value=40)
(stageleft=3)×(value=30)
(stageleft=3)×(value=50)
(stageleft=3)×(value=70)
(stageleft=4)×(value=40)
(stageleft=4)×(value=60)
(stageleft=4)×(value=80)
(stageleft=5)×(value=50)
(stageleft=5)×(value=70)
(stageleft=6)×(value=60)
(stageleft=6)×(value=80)
(stageleft=7)×(value=70)
(stageleft=7)×(value=90)
(stageleft=8)×(value=80)
Constant
0.682
−0.735
1.085
−0.463
0.915
1.601∗∗
−0.180
1.380
2.680∗∗∗
−1.053
0.345
−0.694
1.360
0.043
2.629∗∗
−0.095
1.023
Observations
Clusters
∗
p < 0.10,
∗∗
Robust std. error
∗∗
(0.279)
(0.870)
(0.803)
(0.755)
(0.813)
(0.789)
(0.790)
(0.911)
(0.753)
(0.835)
(0.892)
(0.843)
(0.948)
(0.918)
(1.253)
(0.911)
(0.814)
1221
38
p < 0.05,
∗∗∗
p < 0.01
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
Appendix C:
41
EUT Model
In this section we present a formulation for the EUT model in which participants may be either risk averse
or risk seeking. Define utility as U (x) = (1 − e−rx )/r, where r > 0 indicates risk aversion and r < 0 indicates
risk seeking. This exponential utility function implies constant absolute risk aversion and is widely used
(Kallberg and Ziemba 1983). The dynamic programming problem for FR is as follows.
The value function at stage T is VT (xT ) = U (xT ). Define CEt+1 as the certainty equivalent of the gamble
taken on the stage-(t + 1) outcome by a PM who decides, at stage t, to continue the project; that is,
U (CEt+1 ) ≡ EVt+1 (xt+1 ). Then
Vt (xt ) = max{U (−c + CEt+1 ), 0},
where U (−c + CEt+1 ) represents the utility of continuing the project and 0 is the utility of abandoning.
For the LR case, let U (CEt (xk , k, n)) = Vt (xk , k, n). Then
(
max{UtR (xk , k, n), UtNR (xk , k, n)}
Vt (xk , k, n) =
UtNR (xk , k, n)
if n > 0,
otherwise
for t = 2, . . . , T − 1, V1 (x1 , 1, M ) = max{U1C (x1 , 1, M ), U1A (x1 , 1, M )}, and VT (xk , k, n) = EU (xT | xk , k) is
the expected utility over project payoff xT given that the PM last observed xk in stage k. The expected
utility from not reviewing is UtNR (xk , k, n) = U (−c + CEt+1 (xk , k, n)); the expected utility from reviewing is
UtR (xk , k, n) = E max{UtC (xt , t, n − 1), UtA (xt , t, n − 1)}, where the expectation is over xt (given that the PM
last observed xk at stage k). The project’s continuation and abandonment utilities are (respectively)
UtC (xt , t, n) = U (−c + CEt+1 (xt , t, n))
and UtA (xt , t, n) = 0.
Table 21 reports the estimation results for the EUT model as compared with the full behavioral model.
The risk parameter is estimated to be negative, which means that participants are risk seeking. Comparing
the Akaike information criterion (AIC) values reveals that the full behavioral model consistently describes
the data better than does the EUT model.
Appendix D:
Gain–Loss Utility with Time-dependent Weights
We consider the possibility that information received closer to the completion stage carries greater weight
because it reflects more closely the project’s final value (Kőszegi and Rabin 2009). For this purpose we
replace γ in the gain–loss utility with γτ , where τ ≡ T − t represents how close the current stage is to the
stage of project completion and where γτ is decreasing in τ . For this term we assume a hyperbolic form:
γτ = γ/(1 + gτ ).13 Table 22 presents the MLE results.
Using the likelihood ratio test to compare this model with the one in Section 6.3, we find that g > 0 is
significant (p = 0.07 for FR, p = 0.0004 for LR, and p = 6 × 10−9 for FR+LR). The estimates for parameters
other than g are similar in the two models.
Using estimates from LR in Table 22, we now simulate the second review decision to show that sooner
reviews are preferred after receiving bad news (than after good news). Figure 8 compares the probabilities
of reviewing again in the next stage given that the first review happened at stage k, upon which an increase
13
We obtain similar results with the alternative formulations γτ = γ − gτ and γτ = γe−gτ .
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
42
Table 21
Estimation results for full behavioral model and EUT model
FR+LR
FR
Behavioral parameters Full model
EUT
r
−0.023
(0.001)
–
–
θ
0.49
(0.03)
1.06
(0.05)
0.25
(0.05)
39.36
(3.18)
0.038
(0.06)
0.025
(0.001)
0.218
(0.026)
γ
λ
A
B
s1
s2
−LL
AIC
4281.1
8576.2
–
–
–
–
0.04
(0.002)
0.49
(3.856)
5804.4
17015.8
Full model
–
0.54
(0.01)
1.30
(0.34)
0.73
(0.11)
73.28
(15.59)
0.64
(0.27)
0.017
(0.003)
–
962.1
1936.2
LR
EUT
Full model
−0.025
(0.001)
–
–
0.46
(0.05)
2.41
(0.25)
0.024
(0.047)
18.09
(1.03)
0.00
(0.15)
0.026
(0.001)
0.089
(0.016)
–
–
–
–
0.042
(0.002)
–
1782.9
3569.8
3263.6
6541.2
EUT
−0.0223
(0.004)
–
–
–
–
–
0.036
(0.009)
0.5
(1.00)
4007.7
8021.4
Notes. Standard errors are reported in parentheses.
Table 22
Estimation results—time dependency.
Behavioral parameters
g
θ
γ
λ
A
B
s1
s2
−LL
FR+LR
0.08
(0.02)
0.53
(0.00)
1.50
(0.10)
0.28
(0.04)
40.19
(3.65)
0.16
(0.09)
0.023
(0.001)
0.136
(0.033)
4264.2
FR
0.15
(0.11)
0.61
(0.09)
1.86
(0.59)
0.83
(0.16)
86.97
(23.9)
0.91
(0.48)
0.015
(0.004)
–
960.5
LR
0.02
(0.00)
0.43
(0.00)
2.65
(0.32)
0.05
(0.08)
18.86
(7.20)
0.02
(0.17)
0.025
(0.003)
0.089
(0.006)
3257.3
Notes. Standard errors are reported in parentheses.
or decrease from the initial project value was observed. We can see that, in all cases, a decrease in project
value makes a next-stage review more likely. Figure 9 plots the probability distributions of the second review
in a T = 10 project following a value increase or decrease in the first review stage (k = 3). The probabilities
for earlier second reviews (t = 4, 5) are higher following a value decrease in the first review. Note that the
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
43
probabilities do not add up to 1 because there is also a positive probability that the participant decides
not to undertake a second review. Suppose that having no second review is equivalent to the second review
occurring at stage T ; then the expected second review stage after observing a value decrease (resp. increase)
in the first review is 5.39 (resp. 5.67) in this 10-stage project.
50%
45%
46%
44%
42%
38%
38%
37%
40%
37%
35%
42%
39%
41%
37%
34%
33%
32%
30%
33%
27%
25%
20%
15%
10%
5%
0%
k=2 (T=6)
k=3 (T=6)
k=2 (T=8)
k=3 (T=8)
Value decrease
Figure 8
k=4 (T=8)
k=2 (T=10)
k=3 (T=10)
k=4 (T=10)
Value increase
Proportion that reviews again in the next stage; “value decrease” corresponds to xk − x1 = −(k − 1)δ,
and “value increase” corresponds to xk − x1 = (k − 1)δ.
40%
35%
34%
31%
30%
29%
27%
25%
22%
20%
15%
15%
16%
11%
10%
5%
5%
6%
8%
4%
0%
t=4
t=5
t=6
Value decrease
Figure 9
t=7
t=8
t=9
Value increase
Probability distribution of the second review; “value decrease” corresponds to observing
x3 − x1 = −20 in the first review, and “value increase” corresponds to x3 − x1 = 20.
44
Appendix E:
Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects
Experiment Instructions and Sample Screenshots
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Long, Nasiry and Wu: Abandonment Decisions in Multi-Stage Projects