This essay examines how field subjects perceive the risk of delay that is uncertain in a
driving simulator. Specifically, are field subjects able to form estimates of the risk of delay that
vary with the underlying objective congestion probability? Furthermore, under an endogenous
9 Note that Chapters 1 and 2 both examine route choices in a setting where arrival time is continuous (following the model of Noland and Small (1995). Chapter 1 examines route choices where the late penalty is fixed, whereas Chapter 2 examines route choices where the late penalty is continuous.
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information environment, do they adjust their beliefs in the direction of the objective congestion
probability? Does the adjustment of beliefs differ depending on the underlying objective
congestion probability?
The probability of delay depends partly on the probability of congestion, which is
unknown to the subjects. When there is a bus, subjects could be late to work; but when there is
not a bus, subjects could still be late to work. In other words, the perceived risk of delay depends
on the following factors: (1) the probability of congestion, (2) the probability of delay
conditional on the presence of congestion, and (3) the probability of delay conditional on the
absence of congestion.
Once the subject selects 9th Avenue and finds out if a bus appears or not, the uncertainty
about congestion is resolved, thus the conditional probabilities of delay in (2) and (3) is
independent of the congestion probability in (1). To illustrate, supposed Subjects X and Y are
two subjects from this essay. Subject X is assigned to a treatment where the probability of a bus
is 0.2 on 9th Avenue (i.e., low congestion risk), whereas Subject Y is assigned to a treatment
where the probability of a bus is 0.8 on 9th Avenue (i.e., high congestion risk), ceteris paribus. If
Subject X decides to choose 9th Avenue and the bus appears, the chance of her arriving late is
high. On a separate and independent choice task, if subject Y decides to choose 9th Avenue and
the bus appears, the chance of him arriving late is high. In other words, any subject who chooses
9th Avenue and encounters a bus has a high chance of arriving late. This is true whether the
subject is assigned to a low risk scenario or a high risk scenario. In other words, the probability
of delay conditional on a bus is theoretically expected to be similar for all subjects; the same
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Recall that the perceived risk of delay depends on (1), (2) and (3). Since (2) and (3) are
theoretically expected to be constant regardless of (1), it follows that the perceived risk of delay
should follow the same rank-ordering as (1). In this essay, the perceived risk of delay is
estimated without decomposing it into (1), (2) and (3).
The following two hypotheses are tested:
Hypothesis I – Subjects are able to form estimates of the risk of delay, and the perceived risk of
delay will be ranked in the order of the congestion probabilities.
Hypothesis II – Subjects who start with a lower belief of delay will experience more belief
adjustment than those who start with a higher belief. In an endogenous information
environment, subjects who perceive that a route has a higher risk of delay also perceive
collecting information to be riskier, therefore they are less like to drive on the route or to collect
information. Since little or no information is gathered, it leads to limited or no belief adjustment.
Subjects are assumed to have a subjective belief of late arrival on each route. Conditional
on their subjective beliefs and risk attitudes, they compare the utilities across routes and choose
the one with a higher subjective expected utility.
1.4.3 Simulator Route Choice Task
Subjects are presented with a binary route choice: 7th Avenue is a risk-free route with no
congestion and 9th Avenue is a risky route with an unknown probability of congestion. Subjects’
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Relative Risk Aversion (CRRA) utility function. The subjective expected utility of the risk-free
route, 7th Avenue, is:
𝑆𝐸𝑈7 = (𝑚7(1−𝑟)
(1−𝑟) ) (1)
where 𝑟 is the coefficient of relative risk aversion,
𝑚7 = 𝑤 − 𝑡 is money payoff,
𝑤 is wage, and
𝑡 is the toll charge on 7th Avenue.
Similarly, the subjective expected utility of the risky route, 9th Avenue, is:
𝑆𝐸𝑈9 = 𝑝 ∗ (𝑚9𝑙𝑎𝑡𝑒(1−𝑟)
(1−𝑟) ) + (1 – 𝑝) ∗ (
𝑚9𝑛𝑜𝑡𝑙𝑎𝑡𝑒(1−𝑟)
(1−𝑟) ) (2) where 𝑝 is the subjective probability of late arrival when taking 9th Avenue,
𝑚9𝑙𝑎𝑡𝑒 = 𝑤 − 𝑙 is the money payoff when subject takes 9th Avenue and arrives late, where 𝑙 is the late penalty for arriving late, and
𝑚9𝑛𝑜𝑡𝑙𝑎𝑡𝑒 = 𝑤 is the money payoff when subject takes 9th Avenue and arrives on time. Next, subjects are assumed to behave as if they compare the two subjective expected
utilities and choose the one with the higher SEU.10
10 In the maximum likelihood estimation, the estimated belief of late arrival for 7th Avenue is zero and is implicit in (1).
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This approach can easily be extended to Rank Dependent Utility (Quiggin (1982)). To
illustrate, assume a simple power weighting function. The rank dependent utility of the risk-free
route, 7th Avenue, is:
𝑅𝐷𝑈7 = (𝑚7 (1−𝑟)
(1−𝑟) ) (1’)
The rank dependent utility of the risky route, 9th Avenue, is:
𝑅𝐷𝑈9 = 𝑝𝛾 ∗ (𝑚9𝑙𝑎𝑡𝑒 (1−𝑟)
(1−𝑟) ) + (1 – 𝑝𝛾) ∗ (
𝑚9𝑛𝑜𝑡𝑙𝑎𝑡𝑒(1−𝑟)
(1−𝑟) ) (2’)
where 𝛾 is the probability weighting parameter.
Next, subjects are assumed to behave as if they compare the two rank dependent utilities
and choose the one with the higher RDU. This simple power weighting function can be given a
nice behavioral interpretation. If 𝛾 < 1, then 𝑝𝛾> 𝑝 and the function is everywhere concave. This means that the subjects puts more weight on the likelihood of late arrival than what is
otherwise implied by 𝑝, and the subjective belief is effectively pessimistic. Vice versa, if 𝛾 > 1, then 𝑝𝛾< 𝑝 and the function is everywhere convex. This means that the subjects puts less weight on the likelihood of late arrival than what is otherwise implied by 𝑝, and the subjective belief is effectively optimistic.
1.4.4 Binary Lottery Task
Subjects are presented with four binary lottery tasks with known probabilities that elicit
their risk attitudes. In each task a decision is made between a relatively safe lottery and a
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and a Constant Relative Risk Aversion (CRRA) utility function. The expected utility of the safe
option (EUS) is:
𝐸𝑈𝑆 = 𝑝 ∗ (𝑥𝐿(1−𝑟)
(1−𝑟)) + (1 – 𝑝) ∗ ( 𝑥𝐻(1−𝑟)
(1−𝑟) ) (3) where p is the probability of a low prize, xL,
(1-p) is the probability of a higher prize, xH, and
𝑟 is the coefficient of relative risk aversion.
Similarly, the expected utility of the risky option is:
𝐸𝑈𝑅 = 𝑝 ∗ (𝑦𝐿 (1−𝑟)
(1−𝑟)) + (1 – 𝑝) ∗ ( 𝑦𝐻(1−𝑟)
(1−𝑟) ) (4) where p, is the probability of a low prize, yL, and
(1-p) is the probability of a high prize, yH.
This approach can be extended to RDU. If RDU is assumed for the route choice task,
then the essentially same specification follows for the lottery task as with EUT. The rank
dependent utility of the safe option is:
𝑅𝐷𝑈𝑆 = 𝑝𝛾 ∗ (𝑥𝐿(1−𝑟)
(1−𝑟)) + (1 – 𝑝𝛾) ∗ ( 𝑥𝐻(1−𝑟)
(1−𝑟)) (3’)
where p is the probability of a low prize, xL,
(1-p) is the probability of a higher prize, xH,
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𝛾 is the probability weighting parameter that weights the probability of the low prize. Similarly, the rank dependent utility of the risky option is:
𝑅𝐷𝑈𝑅 = 𝑝𝛾 ∗ (𝑦𝐿(1−𝑟)
(1−𝑟)) + (1 – 𝑝𝛾) ∗ ( 𝑦𝐻(1−𝑟)
(1−𝑟) ) (4’)
with the same probability, p, for a low prizes, yL, and
(1-p) for a high prize, yH.