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Sunk Cost Fallacy in Driving the World’s Costliest Cars
Teck-Hua Ho*, I.P.L. Png†, and Sadat Reza†
January 15, 2013
Abstract
Do decision-makers suffer from the sunk cost fallacy in high-stakes situations? We develop
a behavioral model of usage of a durable good with mental accounting for sunk costs. The
model, which nests the conventionally rational model as a special case, predicts that usage
increases with the sunk cost and, conditional on the sunk cost, decreases with time.
We take the model to a panel of 6,474 cars between 2001-2011 in Singapore. During that
period, the sunk cost involved in a new car purchase varied substantially with continuing
government policy. We found robust evidence of sunk cost fallacy. The elasticity of usage
with respect to purchase price due to mental accounting for sunk costs was 0.037(±0.0038).
As a consequence, an increase in the purchase price by one standard deviation would have
been associated with an increase in driving by 0.57% or 9.48 kilometers per month, purely
due to increase in sunk cost. Our results were robust to various checks including alternative
controls for selection, differences in specification and model, and falsification.
*University of California, Berkeley and National University of Singapore; †National University of Singapore.
The authors contributed equally and are listed in alphabetical order. Direct correspondence to any of the
authors: Ho: [email protected]; Png: [email protected]; Reza: [email protected]. We thank audi-
ences at the Conference on Evidence-based Public Policy Using Administrative Data, Singapore Management
University, Nanyang Technological University, Workshop on “Behavioral Economics and Policy Design” and
the Singapore Economic Policy Forum at the Civil Service College for comments and advice, and Jia-An Tan,
Danny Liew, Chong Lee Kee, Dinh Hoang Phuong Thao, Chua Tziyuan, and above all, the Land Transport
Authority and an anonymous car dealer for assistance with data.
1 Introduction
“Customers who had initially paid more for a season subscription to a theater
series attended more plays during the next 6 months, presumably because of their
higher sunk cost in the season tickets” (Arkes and Blumer 1985: 124).
Economists and psychologists have long been interested in the effect of sunk costs on
consumer choice (Thaler 1980 and 1990). Sunk costs cannot be avoided regardless of future
actions. Since they are irreversible, they should not play any role in rational decision mak-
ing. Yet, sunk costs have been implicated in apparently irrational decisions across multiple
contexts.
In what Eyster (2002) described as the “most convincing single experiment”, Arkes and
Blumer (1985) gave unannounced price discounts at random to people buying season tickets
at a university theater. Over the first half of the season, individuals who paid full price
attended more shows than those who received discounts (4.1 versus 3.3 out of 5 shows).
In the second half of the season, however, there was no difference between the two groups.
In a related study, Gourville and Soman (1998) observed “payment depreciation”: among
consumers with one-year memberships at an athletic facility, attendance was highest in the
month in which the members paid their half-yearly installment, and then declined with time.1
However, in other settings, consumers appeared not to suffer from sunk cost fallacy. In
a large-scale Zambian field experiment, Ashraf et al. (2010) gave consumers unannounced
random discounts on sales of Clorin, a chemical to treat drinking water. Differences in the
amount paid did not affect the consumers’ use of the chemical to treat water. In laboratory
experiments, Phillips et al. (1991) and Friedman et al. (2007) did not find evidence of any
sunk cost fallacy.
Thus far, the unambiguously clear evidence on the sunk cost fallacy has been limited to
consumer situations of low stakes or low involvement. By contrast, when buying big-ticket
items such as cars, consumers might be more careful. Since the cost of mistakes would be
larger, they might invest more attention to correct irrational biases in decision-making. So,
1Strictly, the subscribers sunk their cost when buying the one-year membership, and not, when paying
the installments. The half-yearly installment payment however could have made the sunk cost salient and
triggered the increased usage.
1
we are motivated to ask whether consumers are subject to the sunk cost fallacy in situations
of high stakes.
In high-stakes contexts within organizations, several studies have pointed to the sunk cost
fallacy. Staw (1976) asked business students to decide funding of R&D over two stages of
a hypothetical case. At the second stage, students increased investment although financial
performance had deteriorated. Their “escalation of commitment” was interpreted as being
to rationalize their earlier choice. Similarly, National Basketball Association (NBA) teams
tended to field players whom they preferred at recruitment (lower draft picks) relatively
more, disregarding the player’s actual performance (Staw and Hoang 1995). Write downs
of bad loans and termination of operations were associated with changes in management,
suggesting that previous managers were influenced by their earlier commitments (Staw et
al. 1997; Barron et al. 2001). Entrepreneurs involved in founding businesses were more
likely than outside investors to increase investment despite poor performance (McCarthy et
al. 1993).
But, escalation of commitment could be the rational outcome of the decision maker’s
moral hazard. NBA team managers would rather field lower draft picks than admit choosing
players wrongly. Incumbent bank managers would rather postpone write downs, collect
their bonuses, and leave bad loans for their successors to handle. Founding entrepreneurs
would rather increase investment than admit errors in management. Further, the decision
maker might value a particular reputation and escalation of commitment would contribute
to building that reputation (Kanodia et al. 1989; Camerer and Weber 1999).2 Decision
making influenced by sunk costs might also be explained as rational investment in a real
option. By continuing to invest, the management preserves the option, which is valuable in
an uncertain environment (Friedman et al. 2007; McAfee et al. 2010). Yet another possible
rational explanation is that managers use the magnitude of the sunk cost as a reminder of
the project value in situations where they cannot recall the project details (Baliga and Ely
2011).
These alternative explanations can also account for the apparent impact of sunk costs on
decisions by politicians and government officials – the USA’s military escalation in Vietnam
2Camerer and Weber (1999) re-analyzed the Staw and Hoang (1995) data on the deployment of basketball
players. With accounting for the team managers’ incentive problem through two-stage estimation, draft order
had a significant but very small effect.
2
and Iraq, and continued government investment in developing the Concorde, the Space
Shuttle, and nuclear-powered generating plants. A politician would much rather continue
a high-profile project and preserve his reputation, than cancel the project and hurt his
prospects at the next election. Thus, we do not know whether sunk costs have an irrational
effect on high-stakes decision-making in the absence of confounding factors.
Here, we ask the question: Are decision-makers subject to the sunk cost fallacy in situ-
ations of high stakes? Based on structural estimation of a model of mental accounting for
sunk costs in the context of car usage in Singapore, our answer is an emphatic “yes”. This
suggests that individuals cannot self-correct (or cannot fully self-correct) decision bias even
when the cost of mistakes is large.
Car usage is an attractive setting for investigation of the effect of sunk costs because
ownership involves substantial monetary expenditure and usage is sustained over a period
of time. Moreover, the usage decision does not involve any of the confounds – moral hazard,
reputational concerns, real options, or imperfect information – that explain why decision-
making might rationally be influenced by sunk costs.
The Singapore context is particularly attractive because government policies to restrict
car ownership have resulted in substantial variation in the price and corresponding sunk
costs of new cars (and incidentally, caused Singapore cars to be the world’s most expensive).
The government policies are long-standing and are well publicized, and so, the sunk costs
are certainly salient to Singapore car buyers.
To test the effect of sunk costs on Singapore driver behavior, we first develop a behavioral
model of utility maximization to understand how sunk costs might influence consumer choice.
The model assumes that car buyers mentally account for the sunk cost of a new car by
amortizing the sunk cost relative to a target cumulative usage over the life of the car.3 The
model implies that car usage increases with the sunk cost, and, importantly, that the effect
of the sunk cost on usage attenuates over time. The behavioral model of mental accounting
nests conventionally rational behavior, where sunk costs do not affect decision making, as a
special case.
Second, we take the model to a panel of service records of 6,474 cars between 2001-2011.
3Gourville and Soman (1998) and Thaler (1999) provide behavioral justification.
3
During that period, the application of continuing government policies resulted in substantial
variation in the sunk costs associated with buying a new car. We exploit this variation in
structural estimation of the model of mental accounting.
Our empirical strategy explicitly addressed possible selection effects – that higher car
prices would screen out buyers who intend to drive less, and so, higher car prices would be
associated with more car usage – in three ways. One was the proposition that the sunk cost
effect would diminish over time (selection does not imply such attenuation). Another was
to estimate the model in terms of first differences of usage, rather than the levels of usage.
Differencing would wipe out any non-usage and non-time varying heterogeneity among car
buyers, such as that arising from selection. The third way was to explicitly model the
marginal benefit from usage as varying according to the retail price of the car.
Our structural estimates suggested that the elasticity of usage with respect to the re-
tail price of a car (which elasticity represents the mental accounting for sunk costs) was
0.037(±0.0038). An increase in the retail price by S$22,491 (the outcome of government
policy between 2009 and 2010) would have been associated with an increase in monthly us-
age by 0.49% or 8.1 kilometers. This effect is robust to various checks including alternative
controls for selection, differences in specification and model, and falsification.
In the remainder of this paper, Section 2 describes Singapore government policies towards
car ownership and usage and Section 3 presents a behavioral model of mental accounting for
sunk costs. Section 4 presents the empirical strategy, Section 5 introduces the data, Section
6 reports structural estimates of the behavioral model, and Section 7 presents an alternative
econometric model and estimates. Section 8 discusses implications of our findings for policy
and management, while Section 9 concludes.
2 Singapore Car Policies
Singapore is a small densely-populated city-state, which, like many other cities, faces the
challenge of managing traffic congestion. Since 1975, the Singapore government has ad-
dressed traffic congestion in two ways – pricing road usage and limiting the vehicle popula-
tion. While the government’s policies to limit the number of vehicles targeted all vehicles –
4
cars, buses, trucks, and motorcyles, we focus on cars in the discussion below.
Initially, the government sought to limit the car population through a hefty tax, the
“Additional Registration Fee” (ARF), on new car registrations. The ARF is based on the
wholesale cost or import price of the car, which is officially called the “open market value”
(OMV). (No cars are manufactured in Singapore, and since all are imported, the import
price equals the wholesale cost.) Besides the ARF, the purchase of a new car is also subject
to customs duty, and goods and services tax, both based on the OMV. At the time of writing,
the rates of the various taxes were: (i) ARF: 100% of OMV; (ii) customs duty: 20% of OMV;
and (iii) goods and services tax: 7% of OMV and customs duty, or, effectively 8.4% of OMV.
From 1990, the Singapore government explicitly limited the number of new car registra-
tions by imposing a monthly quota for “certificate of entitlement” (COE). A new car may be
registered only with a COE. The monthly quota was fixed by a formula in terms of a specified
growth rate of the overall car population and the number of cars that were de-registered in
the preceding time period. Twice a month, the government holds an auction for sale of the
COEs. The official name for the COE price is the “quota premium”, so-called because it
arises only if the number of bids for COEs exceeds the quota. There has always been excess
demand for the quota, giving rise to a non-negative COE premium.
Accordingly, in Singapore, the buyer of a new car pays:
Retail price = [1 + πARF + πDuty + πGST ] · OMV + COE premium + Retail mark-up, (1)
where πARF , πDuty, and πGST represent the rates of ARF, customs duty, and goods and
services tax respectively.4
As a result of Singapore’s government policy to limit car ownership , the retail prices
of cars in Singapore are the world’s highest. Further, the government’s policy had the
effect of vastly amplifying the differences in prices between the various brands of cars, and
within brands, between the various models. For instance, in October 2012, the dealer’s
wholesale cost of a Ford Focus (1.6 liters) was S$15,554 (US$12,749) while the retail price
was S$137,888 (US$113,023). Similarly, the dealer’s wholesale cost of a Toyota Camry (2.0
liters) was S$23,175 (US$18,996), while the retail price was S$165,888 (US$135,974).5
4For simplicity, we specify the rate of goods and services tax as a function of OMV.5Converted at US$1 = S$1.22. Source of car retail prices: “Cost (S$) For Cars Registered in Oct 2012”,
http://www.onemotoring.com.sg
5
Buyers of new cars incurred substantial policy-related sunk costs due to the rebate struc-
tures of the ARF and COE. Each COE is valid for ten years. Within our period of study,
the COE policy provided a rebate for de-registration of a car on the following terms. In the
first two years of ownership, the rebate was capped at 80% of the COE price, and so, 20%
of the COE price was sunk upon purchase of the car. Thereafter, the rebate was pro-rated
linearly by the days remaining until the car reached 10 years of age. The COE expired after
10 years, so, either the owner had to buy a new COE or remove the car from Singapore.
Within our period of study, the ARF policy provided a rebate for de-registration of a car
on the following terms. In the first five years of ownership, the rebate was capped at 75% of
the ARF, and so, 25% of the ARF was sunk upon purchase of the car. Thereafter, the rebate
was pro-rated, step-wise, by the number of years remaining until the car reached 10 years of
age.6 Figure 1 depicts the structure of COE and ARF rebates and the corresponding sunk
costs.
– Figure 1 here –
Consequently, in Singapore, the purchase of a new car involves two policy-related sunk
costs:7
• Within the first 24 months, 20% of the COE price would be sunk. This cost would not
vary with usage or time. From the day after the first 24 months, the car owner would
forego the pro-rated part of the COE price each day, a cost that would vary with time
but not usage.
• Within the first 60 months, 25% of ARF would be sunk. This cost would not vary
with usage or time. From the day after the first 60 months, the car owner would forego
the pro-rated part of the ARF each year, a cost that would vary with the year but not
within the year and not with usage.
Each of these sunk costs varies exogenously over time. Each month, the COE price
equilibrates the demand for new cars with the quota for new car registrations. Recall that
6Before July 2008, what we describe as a “rebate” – the Preferential Additional Registration Fee – was
only available as an offset against the ARF for a new car. In July 2008, the government allowed rebates of
the PARF in cash.7In the behavioral model, we also allow for a sunk cost on the car itself, unrelated to government policy.
6
the monthly quota is fixed according to a specific formula. With changes in demand and the
quota, the COE price would vary, and so, the COE-related sunk cost of a new car purchase
would vary.
The ARF, and the ARF-related sunk cost, also fluctuate over time. Since the ARF is
specified as a percentage of the OMV, any change in OMV due to changes in exchange rates
or the manufacturer’s wholesale pricing would affect the ARF, and so, the ARF-related sunk
cost. Moreover, within a single brand, the ARF on the various models would differ according
to the differences in their respective OMVs.
Figure 2 depicts the evolution of the retail price, ARF, COE premium, and policy-related
sunk costs (related to ARF and COE premium) for the two most popular models of car
in our sample from 2001 to 2011. Evidently, the retail price, ARF, COE premium, and
policy-related sunk costs varied considerably over time. For the smaller model, the standard
deviation of the policy-related sunk costs was S$3,800, compared with the mean retail price
of S$154,105. Similarly, for the larger model, the standard deviation of the policy-related
sunk costs was S$3,704, compared with the mean retail price of S$204,836. We exploit this
variation to identify the effect of sunk costs on car usage.
– Figure 2 here –
Besides limiting the number of vehicles, the Singapore government has also managed
traffic congestion by charging for road usage. The Land Transport Authority (LTA), which
is the government agency in charge of regulating car ownership and usage, has constructed
gates at entry points into the Central Business District and along major roads. Any vehicle
passing through the gate must pay a fee, which varies with the day of the week and time of
day, and also varies by the vehicle type.
3 Behavioral Model
To estimate the impact of sunk costs on car usage and appreciate the corresponding policy
implications, we develop a behavioral model of driver behavior for structural estimation. We
begin with a conventionally rational model, and then extend the model to include mental
7
accounting for sunk cost. Since the behavioral model nests the conventionally rational model
as a special case, we can empirically test whether the data would reject the rational model.
3.1 Conventionally Rational Behavior
Consider a driver who has just bought a car in period 0. (We focus on individuals who
have already bought a car and do not model the decision whether to buy a car (cf. de Jong
1990).) She must decide how many kilometers to drive, qt, in each month t over a planning
horizon, 1, . . . , T . In each month, t, let the driver’s utility be
U(qt, t) = B(qt, t)− C(qt, t)− D(t), (2)
where B(qt, t) is the benefit from usage, C(qt, t) is usage-related costs other than depreciation,
and D(t) is depreciation. Note that depreciation is independent of qt.
Let the benefit from usage,
B(qt) = θ0 + [θ1 − θ2t]qt − θ3q2t , (3)
or equivalently the marginal benefit from usage,
B ′(qt) = θ1 − θ2t − 2θ3qt. (4)
We assume that θ0, θ1, θ2, θ3 > 0, and are such that the marginal benefit, B ′(.) > 0, and the
marginal benefit diminishes with age and usage, B ′′(.) < 0.8
The coefficient, θ2, represents the effect of time on marginal benefit and is positive for
two reasons. One is a taste for novelty – newer cars provide more benefit. The other reason
is that older cars break down more frequently, and so, provide less benefit. Consequently,
the marginal benefit diminishes with time (or more precisely, age of the car).
With regard to the cost of usage other than depreciation, we suppose that it comprises the
cost of gasoline (petrol) and the cost of congestion. We assume both costs increase linearly
with usage. Specifically,
C(qt, t) = β1gtqt + β2ctqt, (5)
8The quadratic functional form, (3), may be interpreted as a Taylor series approximation of a more
general benefit function that exhibits diminishing marginal benefit.
8
where β1, β2 > 0, and β1gt is the cost of the gasoline per kilometer of usage and β2ct is the
cost of congestion per kilometer of usage.
With regard to depreciation, referring to the retail price of the car in (1), let
P = Retail price− ARF− COE = [1 + πduty + πGST ] · OMV + Retail mark-up, (6)
represent the “ex-policy price” of the car. Based on the rebate structure of the COE and
ARF (Section 2 above), we model the depreciation of the retail price as:
D(t) = δ0[P − s0] + δ1(t)[ARF − s1] · 1(t > 60) + δ2(t)[COE − s2] · 1(t > 24) (7)
where s0, s1, and s2 represent the sunk portions of the ex-policy price, ARF, and COE
premium, and δ0 is the depreciation rate of the ex-policy price, and δ1(t) and δ2(t) are the
depreciation functions of the ARF and COE premium with time.
Substituting above, the consumer’s utility is
U(qt, t) = θ0 + θ1qt − θ2qtt − θ3q2t − β1gtqt − β2ctqt − D(t). (8)
Assuming that the driver is forward-looking, in each month, t, she chooses usage, qt, to
maximize the cumulative utility of driving,∑T
τ=t U(qt, t). Proposition 1 characterizes the
optimal usage.
Proposition 1 With conventionally rational behavior, the optimal usage in month t =
1, . . . , T is
q∗t =1
2θ3
[θ1 − θ2t − β1gt − β2ct] . (9)
Proof. In each period t, the consumer chooses qt to maximize
T∑τ=t
Uτ =T∑
τ=t
[θ0 + θ1qt − θ2qtt − θ3q
2t − β1gtqt − β2ctqt −D(t)
]. (10)
Maximizing (10) with respect to qt, the optimal usage is
q∗t =θ1 − θ2t− β1gt − β2ct
2θ3, (11)
for all t.
By Proposition 1, the optimal usage is independent of the sunk costs, s0, s1, and s2,
related to the ex-policy price, ARF, and COE premium.
9
3.2 Mental Accounting for Sunk Costs
Next, we generalize the model to allow for the sunk cost fallacy. We suppose that the driver’s
utility is a function of both usage and mental accounting for the sunk cost. Specifically, the
consumer amortizes the sunk cost, S, by the actual cumulative usage, Qt, relative to some
target cumulative usage, Q, over the entire time horizon (Gourville and Soman 1998; Thaler
1999). Accordingly, we generalize the utility in month t as,
U(qt, t) = B(qt) − C(qt, t) − D(t) − max
{0, λS ·
[1 − Qt
Q
]}(12)
= θ0 + θ1qt − θ2qtt − θ3q2t − β1gtqt − β2ctqt − D(t) −max
{0, λS ·
[1 −
∑t1 qt
Q
]}.
The right-most term in the utility function, (12), represents the psychological disutility
of carrying a mental account of sunk cost, this disutility continues until the mental account
is closed by reaching the cumulative usage target, Q. Drivers may differ in their target
usage, Q. As we shall discuss below, our estimation procedure allows for this unobserved
heterogeneity. The parameter, λ, represents the driver’s sensitivity to sunk cost. We are
interested to test empirically the presence of the sunk cost fallacy, i.e., whether λ > 0.
As above, we assume that the driver is forward-looking, and, in each month, t, rationally
chooses usage, qt, to maximize∑T
τ=t Ut, where Ut ≡ U(qt, t). In this generalized model, the
driver takes account the effect of qt on future utility through the cumulative usage in month
t, Qt =∑t
τ=1 qt.
We calculate the driver’s usage by working backward, i.e., first q∗T , followed by q∗T−1, and
so on. Differentiating the cumulative expected utility for t = T ,
dUT
qT= θ1 − θ2T − 2θ3q
∗T − β1gT − β2cT +
λS
Q= 0,
and hence,
q∗T =1
2θ3
[θ1 − θ2T − β1gT − β2cT +
λS
Q
].
Similarly, differentiating the cumulative expected utility for t = T − 1,
dUT−1
qT−1= θ1 − θ2[T − 1] − 2θ3q
∗T−1 − β1gT−1 − β2cT−1 +
2λS
Q= 0,
10
and, so, we have
q∗T−1 =1
2θ3
[θ1 − θ2[T − 1] − β1gT−1 − β2cT−1 +
2λS
Q
].
Reasoning recursively, we can show that
Proposition 2 With mental accounting for sunk costs, the optimal usage in month t =
1, . . . , T is
q∗t =1
2θ3
{θ1 − θ2t− β1gt − β2ct + [T − t + 1]
λS
Q
}, (13)
which
(i) increases in the sunk cost, and
(ii) given any level of sunk cost, decreases in time.
Notice that, if λ = 0, then (13) simplifies to (9). Hence, the generalized model nests the
conventionally rational model as a special case. By (13), the optimal usage depends on time
(age of the car), price of gasoline, the unit cost of congestion, and the sunk cost.
– Figure 3 here –
Figure 3 illustrates the difference in the trajectory of usage with and without mental
accounting for sunk costs. Assume that the costs of gasoline and congestion are constant and
no novelty effect, i.e., gt, ct are time-invariant and θ2 = 0. Then, with conventionally rational
behavior, the monthly usage would be constant throughout the life of the car (assumed to
be 120 months).
By contrast, as Proposition 2 states, mental accounting for sunk costs would affect behav-
ior in two ways. One is that overall usage would be higher. Second, monthly usage would
attenuate with age of the car. As represented in Figure 3, the trajectory of usage would
begin at a higher vertical intercept, and slope downward with age of the car.
The rate of change of usage over the life of the car depends on the level of the sunk cost.
Figure 3 illustrates the trajectory for two levels of the sunk cost, S1 < S2. With a higher
11
sunk cost, the initial usage would be higher, but the usage would decline at a faster rate
(assuming that the cumulative usage target is the same).
The attenuation of the sunk cost effect over the life of the car is the essence of our empirical
strategy. The attenuation distinguishes the model of mental accounting for sunk costs from
the most obvious alternative explanation of any empirical relation between usage and sunk
costs, which is selection (which Ashraf et al. (2010) call a “screening effect”). When the
price of new cars is higher, people who plan to drive less would be less likely to buy cars, and
so, the population of car owners would comprise relatively more intensive drivers. Hence, a
higher retail price would be associated with higher usage, even absent any sunk cost fallacy.
An increase in usage with respect to the price of the car (higher vertical intercept) may
be attributed to mental accounting for sunk costs or to selection. However, there is no
reasonable explanation for why the effect of selection should attenuate over the life of the
car. By contrast, our behavioral model specifically implies that with mental accounting for
sunk costs, usage should decline over time.
Proposition 2(ii) – that the effect of the sunk cost attenuates with time – is consistent with
two previous studies. In the experiment by Arkes and Blumer (1985: 128), consumers who
paid a higher price for the season ticket attended more shows in the first half of the season,
but not in the second half. Gourville and Soman (1998: 169-172) monitored attendance
at an athletic facility by members who paid for a one-year membership in two semi-annual
instalments. Members visited the facility most during the month of paying the instalment,
and their visits declined with each succeeding month.
4 Empirical Strategy
Our data is monthly, and so, we organize it as an unbalanced panel by individual car and
time (in months). The model of mental accounting for sunk costs is cast in terms of time
from the purchase of the car to the end of ownership. However, our data set comprises cars
purchased at different dates, so, we must distinguish between calendar time and age of the
car. Hence, for purposes of structural estimation, we set up the econometric model as,
qit =1
2θ3
{θ1 − θ2t − β1gt − β2ct + [T − t + 1]
λSi
Qi
}+ εit, (14)
12
for individuals i = 1, . . . , N , and t = 1, . . . , 120, where t represents the age of the car, and
where εit is a composite error.
Referring to (14), with the available data, we cannot identify the parameter representing
the rate of change of marginal benefit, θ3. So, we normalize θ3 = 1/2. Substituting θ3 = 1/2
and from (16) in (14), the econometric model simplifies to
qit = θ1 − θ2t − β1gt − β2ct + [T − t + 1]λSi
Qi
+ εit. (15)
We assume that the error in (15) comprises two elements,
εit = νi + ξit, (16)
where νi is an individual fixed effect that represents personal taste for driving and captures
all unobervable time-invariant attributes of the individual that may influence usage, and
ξit is a pure idiosyncratic error. The individual fixed effect would control for individual
differences in driving intensity, and in particular, those arising from selection, as higher car
prices selectively screen out those who plan to drive less intensively. The individual fixed
effect would also control for differences between first and second cars. Households with two
cars would use each car less intensively than those with one car.9
With the available data, we cannot identify the individual fixed effect, νi. So, we cast
the econometric model in terms of the difference in the driver’s usage between consecutive
service visits,10
Δqit = qit − qit′ = −θ2Δt − β1Δgt − β2Δct − λSi
Qi
Δt + Δξit, (17)
where Δgt = gt −g′t, Δct = ct−c′t, Δt = t− t′, and Δξit = ξit−ξit′ . The differencing removes
all unobervable time-invariant attributes of the individual that may influence usage, and
leaves Δξit as a pure idiosyncratic error.
The essence of our empirical strategy is to identify the effect of sunk costs in two ways.
One is by differences in usage between drivers according to differences in their respective
9Empirically, the retail price of cars rose from 2001 to 2002, and then fell until 2009, and then rose again.
With lower prices, some households may have purchased a second car, and so, with two cars, would use each
car relatively less, thus, giving rise to correlation between lower car prices and less usage.10Note that the interval between service visits may vary.
13
sunk costs. The other is by the variation in each individual driver’s usage over the life of
their car.
Singapore government policy is very clear about the structure of the ARF and COE
rebates, and the policy has been long-standing. Nevertheless, just in case that drivers do
not understand the structure of the ARF and COE rebates, in the main specification, we
suppose that the sunk cost is a constant proportion of the retail price,
Si = ρ · Retail price. (18)
Substituting above, the econometric model becomes
Δqit = qit − qit′ = −θ2Δt − β1Δgt − β2Δct − λρ ·Retail price
Qi
Δt + Δξit. (19)
In this main specification, we can only estimate λρ, and cannot separately identify λ or ρ.
In a variant of the main specification, we model the sunk cost according to the structure
specified by government policy,
Si = 0.25 × ARFi + 0.2 × COEi + αPi, (20)
where Pi is the ex-policy price (wholesale cost, customs duty, GST, and retail mark-up) as
defined in (6) and α ≥ 0. This variant allows a fraction, α, of the ex-policy price to be sunk.
In this variant, the econometric model simplifies to
Δqit = −θ2Δt− β1Δgt − β2Δct − λ
Qi
[0.25 × ARFi + 0.2 × COEi + αPi]Δt + Δξit, (21)
and so, we can identify the driver’s sensitivity to sunk cost, λ, as well as the fraction of the
ex-policy price which is sunk, α.
The next issue is that we cannot observe the individual’s target cumulative usage, Qi.
So, we need to integrate out Qi from the econometric model. Accordingly, we estimated the
model using the method of simulated maximum likelihood (SML). SML involves randomly
drawing a large number of values from the distribution of the unobservable Qi to calculate
an average likelihood value. Gourieroux and Montfort (1990) show that the SML estimator
is consistent and asymptotically normal as the number of draws, M → ∞, and number of
individuals, N → ∞. 11
11See Gourieroux and Montfort (1996) for the use of simulation based models for statistical inference, and
also Lerman and Manski (1981), Pakes and Pollard (1989), Gourieroux and Montfort (1990), Hajivassiliou
and Ruud (1994), and Hajivassiliou and McFadden (1998).
14
Our behavioral model of mental accounting is silent on the distribution of the target
usage, Qi. Since Qi is a target quantity of driving (in kilometers) over the lifetime of the
car, its distribution must have positive support. Further, it seemed reasonable to assume
that the distribution of Qi is continuous. Specifically, we assumed that Qi follows a gamma
distribution with mean and variance equal to 120 times the sample mean and variance of
the monthly car usage.12
Since the ξit are independently and identically distributed, the differences, Δξit, are also
independently and identically distributed. Hence, we could pool the differenced data to
estimate (19). We further assumed that the Δξit are normally distributed with mean, 0, and
variance, σ2.
Therefore, the likelihood function is
Li(η) =
∫�i(η, Qi)Γ(Qi), (22)
where �i is the likelihood of a single observation as a function of the vector of parameters to
be estimated, η = (θ1, θ2, β1, β2, λρ), and the target usage, and Γ(·) is the gamma distribution
as explained above. We used SML to evaluate the likelihood function,
Li(η) ≈ 1
1000
1000∑j=1
�i(η, Qij), (23)
with 1000 independent draws of Qij for each individual i. Specifically, we conduct 1,000
draws of Q from the gamma distribution, evaluate the likelihood function at each of these
1000 draws, and then take the average to approximate the likelihood function in (20).13
5 Data
Our primary source of data was the authorized dealer for a premium brand of cars in Sin-
gapore. The dealer provided the complete service records of 8,997 new cars sold between
12If some variable has a gamma distribution, then the product of that variable with a constant also has
a gamma distribution. Assuming that, on average, drivers attain their target usage, the sample measures
seem to be a reasonable benchmark.13We also tried estimation with 500 and 750 draws, and obtained quite similar results, which, for brevity,
we do not report here.
15
2001-2011 under a non-disclosure agreement for the purposes of this study. The cars were
different models of the same brand.
Car owners make periodic visits to the authorized dealer for maintenance. The records
included the following information on each car: engine size, date of registration, service
dates, and odometer readings. The service records encompassed 15 models of the brand.
Sales of some models were very low with very few service observations. Accordingly, we
organized the models into four groups by engine size (which roughly correlated with price).
Consistent with our behavioral model of mental accounting, we limited the sample to cars
less than 120 months in age, which is the lifespan of a COE. Further, to exclude outliers,
we further limited the sample to cars with monthly usage between 480 and 4,365 kilometers
per month (the average usage in the entire population was 1,652 kilometers per month). As
the driving behavior of second-hand owners might differ from that of new car owners, we
excluded second-hand cars from the sample.
Our next source of data was the Land Transport Authority (LTA). The LTA collects
and publishes the retail price, OMV, ARF, and COE for each brand and model of car on a
monthly basis. We matched this information by model and month to the service records.
After cleaning for obvious recording errors (mainly cars with odometer readings that
decreased over time) and matching with the LTA data, we were left with records of 6,474
cars with 34,036 service visits. Owners perform maintenance at varying intervals, and, over
time, owners may switch from servicing their car at the authorized dealer to less expensive
third-party service facilities. Accordingly, the data constituted an unbalanced panel.
Finally, to represent the cost of gasoline, we used the Consumer Price Index of 98 octane
petrol. To represent traffic congestion, we used the number of cars (published monthly)
divided by the quantity of road space in kilometers (published annually).
Table 1 reports summary statistics of the data. Average monthly usage varied between
480 kilometers up to 4,370 kilometers, with a sample average of 1,652 kilometers. Retail
prices of the cars in our sample were within S$110,000 and S$263,181, with an average of
S$170,575, while the averages of the ARF and COE were S$46,708 and S$21,483 respec-
tively. So, the ARF and COE contributed to more than 40% of the retail price. The gasoline
price index increased sharply from high 60’s in late 2001 to over 120 in 2011. The level of
16
congestion also increased steadily from 86 cars per kilometer of road in 2001 to almost 108
cars per kilometer of road in 2011.
– Table 1 here –
For a first look at the data, Figure 4 depicts the retail price and average monthly usage
by vintage of car over the period of study for the two popular models. Evidently, people who
bought cars when prices were high tended to use them relatively more. This is consistent
with mental accounting for sunk costs. However, the correlation in Figure 4 could also be
explained by selection (people buying cars when prices are high tend to be those who want
to drive more).
– Figure 4 here –
Looking at the data from a different viewpoint, Figure 5 compares monthly usage over
the life of cars bought in 2002 and 2006.14 The retail price was higher in 2002 than 2006.
Consistent with Proposition 2, monthly usage was uniformly higher for the 2002 cars than
the 2006 cars, and usage declined with age of the car. Selection would not imply anything
about the trajectory of usage over the age of the car.
– Figure 5 here –
6 Results
Table 2 presents regressions of the difference in monthly usage by the method of SML, with
estimated standard errors clustered by car.15 First, as a baseline, Table 2, column (a), reports
14Figure 5 focuses on usage between months 7 and 60. We excluded the first 6 months when usage might
be affected by spurious factors, for instance, some cars were used for test drives and others were assigned to
international events before being sold to end-users. The ARF-related sunk costs end with the fifth year.15Following Wooldridge (2010: Chapter 13.8.2), we computed the standard errors allowing for autocorre-
lation within clusters as follows. The asymptotic variance of the parameters of interest, η, is A−10 B0A
−10 ,
where A0 is the expected Hessian and B0 is the expected outer product of gradients. With sit(η) as
the score for any individual i, the estimate of B0, allowing for clustering by i, is 1N
∑Ni=1
∑Tt=1 sits
′it +
1N
∑Ni=1
∑Tt=1
∑r �=t sir s
′it.
17
the estimate of a specification assuming that drivers behave according to the conventionally
rational model. The coefficient of the price of gasoline was negative but not precisely esti-
mated. The coefficient of the unit cost of congestion was positive and significant. Referring
to (19), this result suggests that usage decreased with more congestion. Finally, the coeffi-
cient of the age of the car was positive and precisely estimated. Apparently, owners drove
less as their car aged, which is consistent with the novelty effect.
– Table 2 here –
Next, Table 2, column (b), reports the estimate of the main specification, with the sunk
cost specified as a proportion of the retail price, (see equation (18)). Regarding our key
parameter, the coefficient of the mental accounting of sunk cost, λρ = 0.079(±0.004), was
positive and precisely estimated. To interpret this result, we computed the elasticity of
usage with respect to the retail price as being 0.037(±0.0038).16 The result is consistent
with Proposition 2(ii) that, conditional on the sunk cost, usage would decline with age of
the car. We emphasize, with (19), the dependent variable is the difference in monthly usage,
and hence the test of λρ > 0 is a test of Proposition 2(ii). Our model did not allow us to
test Proposition 2(i) separately.
To gauge the significance of our finding, consider an increase in the retail price by S$22,491
(or the equivalent of the increase in the COE premium from S$689 to S$23,180 between
February 2009 and February 2010). Relative to the average retail price, this would amount
to a 13.2% price increase, and using our estimate of the elasticity, would be associated with
an increase in usage by 0.49% or 8.1 kilometers a month.17
At first glance, the effect of sunk cost on car usage might seem modest. We believe the
estimate is not small for three reasons. First, most drivers may have little discretion in the
amount of driving. Discretionary driving may be a small proportion of monthly usage. For
16Consider an increase in the retail price by S$10,000. By the estimate in Table 2(b), this would increase
usage over the entire life of the car, with a larger effect in the earlier months and smaller effect in the later
months. The total increase in usage would be 430 kilometers over 120 months, which amounts to an average
of 3.58 kilometers a month. Dividing by the average monthly usage, 1652 kilometers, and multiplying by
the average price, S$170,575, we get the elasticity of 0.037.17Our estimates were based on the normalization θ3 = 1/2, and so, the estimated coefficients would
change with the normalization. However, the counterfactual effects would remain the same as the estimated
coefficients adjust accordingly.
18
example, if discretionary driving accounts only for 10% of monthly usage, then the effect due
to sunk cost would have been 5% of the discretionary driving. Second, we do not control
for income effects. An increase in the retail car price would reduce the buyer’s discretionary
income, and so, lead to a reduction in all consumption, including driving (Thaler 1980: 49-
50). Third, our regressions estimate the average effect over all drivers. But, not all people
engage in mental accounting (Shafir and Thaler 2006). So, the sunk cost effect among those
who do engage in mental accounting would be larger than the average effect that we have
estimated.
Below, we report multiple tests of robustness to check the sensitivity of our findings
to alternative specifications of the sunk costs, accounting for selection, differences between
smaller and larger cars, and a falsification exercise.
Alternative Specification of Sunk Cost
In (19), we framed the sunk cost very generally, as a proportion of the retail price. One
possible worry is that, while we interpret the positive relation between usage and retail
price as evidence of mental accounting for sunk costs, the effect might actually be related to
the retail price as such and not due to any sunk cost fallacy. To check this possibility, we
estimated a specification, (21), that explicitly modelled the structure of the sunk elements
of the ARF and COE premium as stipulated by Singapore government policy.
As reported in Table 2, column (c), the coefficient of the sunk cost, λ = 0.194(±0.097),
was positive and precisely estimated. Interestingly, the coefficient of the ex-policy price,
α = 0.475(±0.303), was weakly positive (p = 11.8%). These results suggest that car owners
did mentally account for the sunk elements of the ARF, COE premium, and the ex-policy
price.
Note that the fit of this variant and the main specification were quite similar, with the
log-likelihood of the variant being just 0.03% lower than that of the main specification. We
infer from this relatively good fit and the precision of the estimated coefficient of the sunk
cost, λ, that driver behavior was influenced by sunk costs, and not some other confounding
factor that was correlated with the retail price.
19
Marginal Benefit Scale Factor
In the main specification, we accounted for possible selection by testing whether the effect
of sunk costs diminished with age of the car and including an individual fixed effect. Besides
an individual fixed effect, selection might possibly affect usage if individuals differ in their
marginal benefit from usage by a scale factor. Since the obvious alternative explanation of
the empirical relation between usage and sunk costs is selection related to the retail price of
the car, we stipulate that the selection factor increases with the retail price. So, when the
retail price is higher, individual marginal benefits would be scaled up and car buyers would
choose higher usage.
To explore this possibility, we stipulated that the marginal benefit is
exp(μ0 + μ1Pi) · B ′(qt) = exp(μ0 + μ1Pi) · {[θ1 − θ2t] − 2θ3qt} , (24)
with μ1 > 0 in place of (4). After differencing, the econometric model simplifies to
Δqit = −θ2Δt− 1
exp(μ0 + μ1Pi)
{β1Δgt + β2Δct +
λρ · Retail price
Qi
Δt
}+ Δξit. (25)
Table 2, column (d), reports estimates of (25). The direction of effects of the various
covariates are consistent with those indicated by the main model estimates. However, the
magnitudes are not directly comparable. In order to compare the partial effects, we evaluate
the scale factor at the sample average price, we find that the adjusted λ to be 0.094, which
is close to the estimate, 0.079, from our main specification.18 Having accounted for the
selection effect in two different ways – through individual fixed effects and a scale factor on
the marginal benefit, we feel confident that our finding of the sunk cost fallacy is robust to
any selection effect.
Small vis-a-vis Large Cars
The cars in our sample broadly divided into two segments, with engine sizes less than 2500
c.c. (cubic centimeters) and between 2500 and 3000 c.c. To investigate possible differences in
18The variant implies that an increase in retail price by S$22,491 would be associated with monthly usage
being 9.6 kilometers higher. This is close to the counterfactual estimate of 8.1 kilometers from the main
specification.
20
the influence of sunk costs among buyers by size of car, we estimated the main specification
separately on the two segments.
Table 3, columns (e) and (f), report the estimates. According to these estimates, the sunk
cost effect was substantially larger among owners of smaller cars compare to owners of larger
cars. The estimated λρ was 0.198(±0.005) among smaller cars vis-a-vis and 0.056(±0.005)
among larger cars. Apparently, buyers of smaller cars were more sensitive to sunk costs.
The COE premium was the same and the ARF similar for the small and large cars (of the
brand in our study). Hence, the sunk costs related to the COE premium and ARF would
have been a larger proportion of the retail price for the small cars. To that extent, sunk costs
might have loomed proportionally larger to buyers of small cars. This finding is consistent
with Weber−Fechner law, which predicts that people’s sensitivity to sunk cost may also be
influenced by its share of the total purchase price.
The difference in sensitivity to sunk cost between the smaller and larger cars is surpris-
ing given that the usage was quite similar. The average monthly usage of smaller cars
(1, 681(±670) kilometers) was only slightly less than that of larger cars (1, 615(±682) kilo-
meters). The apparent similarity in average usage masked considerable heterogeneity in the
sensitivity to sunk costs.
The comparison between small and large cars also reveals that only large cars have a
significant novelty effect. This finding seems reasonable because large cars tend to be loaded
with the latest features and options, and hence may be inherently more novel initially. We
also notice an intriguing difference between sensitivity to congestion cost between small and
large cars. Perhaps large car drivers are preferred by certain segment of buyers (e.g., retirees)
who may be less sensitive to time delays.
Used Cars
Finally, in a falsification exercise, we estimated the main specification on the second-hand
cars. The sample was much smaller as there were relatively few second-hand cars in the data
(probably because most owners of second-hand cars service their cars at third party service
facilities rather than the authorized dealer). Table 3, column (g), reports the estimates. The
21
coefficient of the age of the car was precisely estimated and almost an order of magnitude
larger than in the estimate on original owner cars. The coefficient of sunk cost was miniscule
and insignificant. Subject to the limitation of a small sample, the result suggests that owners
of second-hand cars were not influenced by sunk costs in their car usage.
7 Inter-Service Time
By Proposition 2(ii), a car buyer’s mental accounting for sunk costs would cause her usage
to decline as the car gets older. If we assume that the owner brings the car for service
at regular mileage intervals, then a corollary of Proposition 2(ii) is that the time interval
between successive service visits would increase with the sunk cost.
This corollary motivates using a duration model as an alternative way of testing the sunk
cost fallacy. The empirical implication of the corollary is that, as the car gets older, the
expected time until the next service visit would increase with the sunk cost. Equivalently,
at each successive service visit, the hazard rate of continuing to drive the car (rather than
making a service visit) increases with the sunk cost.
The test in terms of the duration of inter-service times also distinguishes mental account-
ing for sunk costs from the alternative explanation of selection. There is no obvious reason
why the effect of selection would vary with the age of the car.19
Following Willet and Singer (1995), we set up a multiple spell extension of the single spell
discrete duration model (Baker and Melino 2000) with the dependent variable being the
probability that, in month, τ , following the last service visit, individual, i, continues to drive
rather than send the car for service. The first service visit may be fixed for administrative
reasons. So, we focus on the second to sixth visits, and, the corresponding four inter-service
time intervals (the second interval is that between the second and third visits, the third
interval is that between the third and fourth visits, etc).
19Sunk costs also have a different effect on inter-service time than diminution of novelty. The diminution
of novelty implies that, with each successive service visit, the hazard rate of the next service visit would
be lower. By contrast, mental accounting for sunk costs implies that, with each successive service visit, the
hazard rate of the next service visit decreases with the sunk cost.
22
We then estimate the effects of the covariates on the probability of continuation (of driving
rather than sending for service). If the coefficient of a covariate is positive, then, an increase
in that covariate would be associated with a higher continuation probability, which implies
a longer expected time until the next service.
In the duration model, we represent mental accounting for sunk costs by the interaction
between the sunk cost and the cumulative number of service visits. So, if the coefficient of the
interaction between the sunk cost and the cumulative number of service visits is positive,
then the length of time until the next service visit increases with the sunk cost and the
cumulative number of service visits.
We model the sunk costs by (18), and include, as other covariates, the elapsed time within
the inter-service interval, the cumulative number of service visits, j − 1, and the length of
the previous service interval. In constructing the sample, we suppose that cars whose last
service visit was in or after January 2011 to be censored as their next visit might fall outside
the period of study. Separately, we suppose that cars whose last service was more than 12
months before the end of the period of study to have ceased service at the authorized dealer.
Table 3, column (a), reports the estimates. The coefficient of the cumulative number of
service visits was positive and significant. This is consistent with the novelty effect. The
older is the car, the longer will be the time to the next service (because the owner uses the car
less). Importantly, the coefficient of the interaction between the retail price (representing the
sunk cost) and the cumulative number of service visits was positive and precisely estimated.
Hence, we infer that, the older is the car (larger cumulative number of service visits), the
likelihood of continuing to drive and the length of the time to the next service increases with
the sunk cost. This can happen only if usage of the car declines over time, and where the
rate of decline increases with the sunk cost.
So far, we have focused on the effect of sunk costs on car usage, either directly or indirectly
through the inter-service time interval. Sunk costs might affect other aspects of car buyer
behavior besides usage. In particular, car buyers might be influenced to spend more on
maintaining their car, and, in particular, servicing their car at the authorized dealer rather
than a cheaper third-party service facility. Another possibility is that buyers who incur larger
sunk costs may be influenced to keep their car longer and delay selling to the second-hand
23
market.
We can also test these possibilities with a duration model in which, in each month,
τ , individual, i, chooses between continuing to drive rather than ceasing service at the
authorized dealer or selling the car. Table 3(b) reports the results, with the sunk cost
represented by (18). The coefficient of the price (representing mental accounting for sunk
cost) was positive and marginally significant. This result was consistent with the hypothesis
that a larger sunk cost would influence the car owner to service their car their car at the
authorized dealer for a longer period of time or put off selling their car to the second-hand
market.
8 Implications for Public Policy and Pricing
Our findings of the sunk cost effect have implications for both public policy, particularly,
with respect to management of road congestion, and pricing of durable goods. Historically,
the Singapore government sought to manage traffic congestion through pricing of road usage
and discouraging car ownership. By design, the Additional Registration Fee (ARF) and
Certificates of Entitlement (COEs) embodied substantial sunk costs. Our results suggest
that these sunk costs resulted in the unintended consequence of stimulating driving (among
those who did buy a car).
Between February 2009 and February 2010, the quota of COEs in categories “B” and
“E” fell by one-third from 3818 to 2569.20 The quota reduction coupled with growth of the
Singapore economy resulted in the COE premium increasing sharply from S$689 to S$23,180.
Using our estimate of the main specification, an increase in the retail price by S$22,491 would
be associated with an increase in monthly usage by 8.1 kilometers a month.
Hence, absent any other policy changes, the reduction in the COE quota would have
affected road usage in two ways. Based on the average driving in our sample, the reduction
in the number of cars would have reduced car usage (as the government intended) by 2.06
million kilometers a month. On the other hand, based on our main estimate, the concomitant
20The Singapore government issues COEs in five categories. The two categories relevant to the brand of
cars in our data-set are categories “B” and “E”.
24
increase in the COE premium would have been associated with an increase in driving (as
the government did not intend) by 0.02 million kilometers a month. So, mental accounting
for sunk costs would give rise to a small countervailing effect.
Apparently, the Singapore government was aware of the effect of sunk costs on driver
behavior:
“because sunk costs matter, the high fixed cost of car ownership can be inimical
to our objective of restraining car usage. Thus, instead of simply relying on
high car ownership cost to manage congestion on the road, the Government has
been reducing vehicle taxes and shifting more towards usage charges (through
the ERP) to manage the demand for road space” (Leong and Lew 2009).21
However, in recent years, the fall in COE quotas has resulted in sharp increases in the COE
premium, which have outweighed reductions in vehicle taxes (ARF). Our estimated model
allows policy makers to systematically evaluate the net effect of the increase in COE premium
and the reduction in ARF.
To the extent that managers, being human, are also influenced by sunk costs, our results
have implications for the pricing of durable industrial goods such as enterprise software and
manufacturing equipment. For example, producers of enterprise software such as Oracle
sell systems and then also sell complementary post-sale services to their installed base of
customers. Similarly, manufacturers of equipment such as Tetrapak sell machinery and then
also sell consumables to buyers of their equipment.
Based on consumer psychology, the “razor-blade” model suggests setting a low price
for the platform to entice customers, and then setting higher prices on the complementary
consumable to earn profits. By contrast, our findings suggest that the vendor ought to price
the platform relatively high, so that the buyer will feel a need to mentally account for the
sunk cost of the purchase and hence step up purchases of the consumable (Thaler 1990:
49-50).
21Leong and Lew (2009) mistake “sunk costs” as being synonymous with “fixed costs”. See, for instance,
Png (2012: 119-120) for the distinction between sunk and fixed costs.
25
9 Concluding Remarks
In this paper, we investigated the effect of sunk costs on usage of a durable good. First,
we developed a behavioral model that incorporates mental accounting for sunk costs and
which nests the conventionally rational model as a special case. In the context of car usage,
we characterized optimal dynamic driving behavior and how sunk costs would affect driving
over time.
Then, we took the model to a proprietary panel data-set of 6,474 cars between 2001-2011
in Singapore, which is the world’s most expensive car market. Through structural estimates,
we found compelling evidence that usage was higher among buyers who incurred larger sunk
costs in purchasing their car and that the effect of the sunk cost on usage diminished with
age of the car. We also found evidence suggesting that the effect of the sunk cost increased
with the magnitude of the sunk cost relative to the price of the car. Our results were robust
to alternative explanations, the specification of sunk costs, and the type of car.
Our empirical finding suggests that individuals cannot self-correct the effect of sunk costs
on decision-making (or cannot fully self-correct) even in a situation of high stakes. The
empirical finding by Arkes and Blumer (1985) of a sunk cost fallacy in the context of smaller
purchases is consistent with this interpretation.
While our study was based on Singapore data, we believe that the same results apply
to car buyers in other countries, and more generally, the effect of sunk costs on usage in
other high-stakes situations. Our reason for so thinking is that, in the main specification,
we framed the sunk cost very generally, simply as a proportion of the retail price. Hence,
our estimates did not depend on the particular sunk-cost structure of the ARF and COE
premium. Based on our estimates, we expect that, in other markets, usage of durable goods
would increase with the sunk element of the price and the sunk cost effect to attenuate over
the life of the good.
By contrast to our results, in their large-scale field experiment on the pricing of a water-
purification chemical in Zambia, Ashraf et al. (2010) found no effect of sunk costs on
consumer behavior. The context of our study differed from theirs in several respects. We
focused on usage of a high-involvement durable that is quite expensive, so, given the high
stakes, consumers may pay more attention. Further, car usage is a continuing decision, and
26
not just a one-off experiment. The limitation of our study is that it was observational, being
based on actual behavior in response to changes in prices due to continuing government
policy. There was no random assignment of sunk costs to different individuals. Hence, we
could not absolutely rule out some unobserved factor accounting for the higher usage among
buyers who incurred larger sunk costs and the effect of the sunk cost diminishing with age
of the car.
In future research, it would be good to investigate the factors that influence the sunk
cost effect and how individuals differ in their sensitivity to sunk costs. Are consumers more
sensitive to sunk costs where the stakes are larger and in a repeated situation, as suggested
by the contrast between our results and those of Ashraf et al. (2010)? Besides the passage
of time, what other factors amplify or diminish the effect of sunk costs on decision-making?
What other factors affect an individual’s ability to overcome the effect of sunk costs? Are
people with training in management or economics less prone to the sunk cost fallacy?
The answers to these questions would help policy-makers, managers, and consumers to
correct sunk-cost bias and make more effective decisions across multiple contexts – public
policy, organizational management, and consumer choice.
27
References
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29
Figure 1. COE and ARF rebate structure
Car age (years)
Ex-policy
price
ARF
COE
premium
10 5 0
20% x COE premium
25% x ARF
Figure 2. Retail price, COE premium, ARF, and
policy-related sunk costs (Singapore dollars)
Note: Models A4 and C1 are the most popular ones in the sample.
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
Jun
-01
De
c-0
1
Jun
-02
De
c-0
2
Jun
-03
De
c-0
3
Jun
-04
De
c-0
4
Jun
-05
De
c-0
5
Jun
-06
De
c-0
6
Jun
-07
De
c-0
7
Jun
-08
De
c-0
8
Model A4
Retail price
ARF
COE premium
Policy-related sunk cost
0
50000
100000
150000
200000
250000
300000
De
c-0
2
Jul-
03
Feb
-04
Sep
-04
Ap
r-0
5
No
v-0
5
Jun
-06
Jan
-07
Au
g-0
7
Mar
-08
Oct
-08
May
-09
De
c-0
9
Jul-
10
Feb
-11
Model C1
Retail price
ARF
COE premium
Policy-related sunk cost
Figure 3. Effect of mental accounting for sunk cost
Car age (years)
Car usage
(km/month)
10 0
Optimal usage with mental accounting for sunk cost, S2 > S1
Optimal usage with mental accounting for sunk cost, S1
Optimal usage with conventionally rational behavior
Figure 4. Retail car price and monthly usage
Notes: Average retail price of car (in $10,000) on left-hand axis, and average monthly usage over
life of car (in kilometers) on right-hand axis.
Figure 5. Average monthly usage over life of car
1500
1550
1600
1650
1700
1750
1800
15
16
17
18
19
20
21
22
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Ave
rage
life
tim
e u
sage
- m
on
thly
(km
)
Ave
rage
ret
ail p
rice
(S$
00
00
)
Average retail price (S$0000) Average monthly usage (km)
0
500
1000
1500
2000
2500
7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
Ave
rage
mo
nth
ly u
sage
(km
)
Car age (month)
Model A4 (bought 2002) Model A4 (bought 2006)
Table 1. Summary statistics
Variable Unit Mean Standard
deviation
Min Max
Usage ‘000 kilometers per
month 1.65 0.68 0.48 4.37
Retail price S$10,000 17.06 2.64 11.00 26.32
ARF S$10,000 4.67 0.84 3.10 7.30
COE premium S$10,000 2.15 0.86 0.07 7.09
Gasoline price 2006 January = 100 94.80 16.30 69.10 126.60
Congestion Cars per kilometer 95.30 8.20 85.80 107.60
Table 2. Effect of sunk cost on usage
Variable (a)
Convent-
ionally
rational
(b)
Mental
accounting
(c)
Policy
structure
of sunk
cost
(d)
Marginal
benefit
scaled
(e)
Smaller
cars
(f)
Larger
cars
(g)
Falsifi-
cation:
Used
cars
Gasoline cost
-0.0004* -0.0004 -0.0004 -0.0002* -0.0007** -0.0001 -0.0204
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.015)
Congestion 0.006** 0.005** 0.004* 0.002* 0.010*** -0.002 -0.143
cost (0.002) (0.002) (0.002) (0.001) (0.003) (0.004) (0.229)
Age 0.215*** 0.118*** 0.126*** 0.100*** -0.002 0.167*** 0.796*
(0.009) (0.010) (0.010) (0.011) (0.012) (0.017) (0.450)
Sunk cost 0.079*** 0.046*** 0.198*** 0.056*** 0.001
(proportion of
retail price)
(0.004) (0.007) (0.005) (0.005) (0.313)
Sunk cost 0.194**
(policy
structure)
(0.097)
Ex-policy 0.475
price part of
sunk cost
(0.303)
No. of
observations 26983 26983 26983 26983 15110 11873 210
Mean log
likelihood -0.6720 -0.6709 -0.6711 -0.6694 -0.6424 -0.6987 -0.9939
Log likelihood -18133 -18102 -18108 -18062 -9707 -8296 -209
Notes: Estimated by simulated maximum likelihood regression; Dependent variable is first
difference of usage (kilometers per month). Column (a): Conventionally rational model; Column
(b): With mental accounting for sunk costs and sunk cost represented by proportion of retail
price; Column (c): Sunk cost according to COE and ARF policy; Column (d): Marginal benefit
inflated by scale factor depending on retail price; Column (e): Sub-sample of smaller cars;
Column (f): Sub-sample of larger cars; Column (g): Falsification with used cars. Estimated
standard errors clustered by car in parentheses (*** p<0.01, ** p<0.05, * p<0.1).
Table 3. Duration analyses
Variable Inter-service time Length of ownership
Price 0.087 0.285*
(0.060) (0.162)
Price x cumulative number of 0.212***
service visits (0.048)
Cumulative number of 4.768***
service visits (0.843)
Months since last service -6.535***
(0.354)
(Months since last service)2 2.118***
(0.169)
Length of last inter-service time 1.458***
(0.141)
Months since purchase -1.614***
(0.258)
(Months since purchase)2 0.110***
(0.028)
No. of observations 6474 7053
Mean log likelihood -0.2996 -0.0598
Log likelihood -1939 -422
Notes: Other control variables were cumulative mileage, gasoline cost, and fixed effects for
engine size, year, quarter. Estimated standard errors in parentheses (*** p<0.01, ** p<0.05, *
p<0.1).