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: hoteck@haas.berkeley.edu; Png: ipng@nus.edu.sg; Reza: bizsadat@nus.edu.sg. 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

Arkes, Hal R., and Catherine Blumer, “The psychology of sunk cost”, Organizational Behaviourand Human Decision Processes, Vol. 35, No. 5, December 1985, 124-140.Ashraf, Nava, James Berry, and Jesse S. Shapiro, “Can Higher Prices Stimulate Product Use?Evidence from a Field Experiment in Zambia”, American Economic Review, Vol. 100 No. 5, 2010,2382-2413.Baker, Michael and Angelo Melino, “Duration dependence and nonparametric heterogeneity: AMonte Carlo study”, Journal of Econometrics, Vol. 96 No. 2, June 2000, 357-393.Baliga, Sanjeev, and Jeffrey. C. Ely, “Mnemonomics: The Sunk Cost Fallacy as a Memory Kludge”,American Economic Journal: Microeconomics, Vol. 3 No. 4, November 2011, 35-67.Barron, Jack M., Dmitry V. Chulkov, and Glen R. Waddell, “The escalation phenomenon andexecutive turnover: Theory and evidence”, Mimeo, Purdue University, 2001.Camerer, Colin F., and Robert A. Weber, “The econometrics and behavioral economics of escalationof commitment: a re-examination of Staw and Hoang’s NBA data”, Journal of Economic Behavior& Organization, Vol. 39, No. 1, 1999, 59-82.de Jong, G.C., “An Indirect Utility Model of Car Ownership and Private Car Use”, EuropeanEconomic Review, Vol. 34 No. 5, July 1990, 971-985. .Eyster, Erik, “Rationalizing the Past: A Taste for Consistency”, Nuffield College, Oxford, 15November 2002.Friedman, Daniel, Kai Pommerenke, Rajan Lukose, Garrett Milam, and Bernardo A. Huberman,“Searching for the sunk cost fallacy”, Experimental Economics, Vol 10, No 1, March 2007, 79-104.Gourieroux, Christian, and Alain Monfort, “Simulation Based Inference in Models with Hetero-geneity”, Annales dEconomie et de Statistique, Vol. 20/21, 1990, 69-107.Gourville, J. T. and Soman, D. “Payment Depreciation: The Behavioral Effects of TemporallySeparating Payments from Consumption”, Journal of Consumer Research, Vol. 25, September1998, 160-174.Gourieroux, Christian, and Alain Monfort, Simulation-Based Econometric Methods, Oxford, OxfordUniversity Press, 1996.Hajivassiliou, Vassilis A., and Daniel McFadden, “The Method of Simulated Scores for the Estima-tion of LDV Models”, Econometrica, Vol. 66, 1998, 863-896.Hajivassiliou, Vassilis A., and Paul A. Ruud, “Classical Estimation Methods for LDV ModelsUsing Simulation”, in R.F. Engle and D. L. McFadden, Eds., Handbook of Econometrics, Volume4, Amsterdam, North-Holland, 1994, 2384-2441.Hausman, Jerry A. and William E. Taylor, “Panel Data and Unobservable Individual Effects”,Econometrica, Vol. 49, 1981, 1377-1398.Heath, C. “Escalation and de-escalation of commitment in response to sunk costs: the role ofbudgeting in mental accounting”, Organizational Behavior and Human Decision Processes, Vol.62, 1995, 38-54.Kanodia, Chandra, Robert Bushman, and John Dickhaut, “Escalation Errors and the Sunk CostEffect: An Explanation Based on Reputation and Information Asymmetries”, Journal of AccountingResearch, Vol. 27 No. 1, Spring 1989, 59-77.Kahneman, D. and Tversky, A. “Choices, values, and frames”, The American Psychologist, Vol.39, 1984, 341-350.

28

Lerman, Steven R., and Charles F. Manski, “On the Use of Simulated Frequencies to ApproximateChoice Probabilities”, in C. F. Manski, and D. McFadden, Eds., Structural Analysis of DiscreteData with Econometric Applications, Cambridge, MA, MIT Press, 1981, 305-319.Lew, Yii Der, and Wai Yan Leong, “Managing Congestion in Singapore – A Behavioural EconomicsPerspective”, Journeys (Land Transport Authority, Singapore), May 2009, 15-22.McAfee, R. Preston, Hugo M. Mialon, and Sue H. Mialon, “Do Sunk Costs Matter?” EconomicInquiry, Vol. 48, No. 2, 2010, 323-36.McCarthy, Anne M., F. David Schoorman, and Arnold C. Cooper, “Reinvestment decisions byentrepreneurs: Rational decision-making or escalation of commitment?” Journal of Business Ven-turing, Vol. 8, No. 1, 1993, 9-24.Pakes, Ariel S., and David Pollard, “Simulation and the Asymptotics of Optimization Estimators”,Econometrica, Vol. 57, 1989, 1027-1057.Shafir, E. and Thaler, R. H. “Invest now, drink later, spend never: On the mental accounting ofdelayed consumption”, Journal of Economic Psychology, Vol. 27, 2006, 694-712.Staw, Barry M., “Knee-Deep in the Big Muddy: A Study of Escalating Commitment to a ChosenCourse of Action”, Organizational Behavior and Human Performance, Vol 16, No. 1, June 1976,27-44.Staw, Barry M., and Ha Hoang, “Sunk costs in the NBA: Why draft order affects playing timeand survival in professional basketball”, Administrative Science Quarterly, Vol. 40, No. 3, 1995,474-494.Staw, Barry M., Sigal G. Barsade, and Kenneth W. Koput, “Escalation at the credit window:A longitudinal study of bank executives’ recognition and write-off of problem loans”, Journal ofApplied Psychology, Vol. 82, No. 1, 1998, 130-142.Thaler, Richard, “Towards a Positive Theory of Consumer Choice”, Journal of Economic Behaviorand Organization, Vol. 1 No. 1, March 1980, 39-60.Thaler, Richard, “Saving, fungibility and mental accounts”, Journal of Economic Perspectives, Vol.4, 1990, 193-205.Thaler, Richard, “Mental Accounting Matters”, Journal of Behavioral Decision Making, Vol. 12No. 3, September 1999, 183-206.Willett, John B., and Judith D. Singer, “It’s Deja Vu All Over Again: Using Multiple-Spell Discrete-Time Survival Analysis”, Journal of Educational and Behavioral Statistics, Vol. 20 No. 1, March1995, 41-67.

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).