Discussion Papers In Economics
And Business

The effect of risk attitudes on search behavior:
A laboratory search experiment
Takahiro Miura, Keigo Inukai and Masaru Sasaki

Discussion Paper 17-17

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe effect of risk attitudes on search behavior:
A laboratory search experiment
Takahiro Miura, Keigo Inukai and Masaru Sasaki

Discussion Paper 17-17

June 2017

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANThe effect of risk attitudes on search behavior:
A laboratory search experiment
Takahiro Miura ∗Keigo Inukai †Masaru Sasaki ‡§Abstract
This paper tests the effect of risk preferences on search activities by using a laboratory experiment. We used an infinite-horizon sequential search model with no recall
in which an individual gains over search. We elicit the risk preferences from observed
search activities of participants and from the multiple price list (MPL) method. We
found the statistically significant effect of risk preferences elicited from the MPL methodon the duration of search. The search duration is on average shorter for a risk averse
individual than for risk loving one, which is consistent with the theoretical prediction.
The significant effect of risk preferences on search activities has not been observed in theprevious literature that used search model with recall in which an individual pays fromthe initial endowment over search (Schunk 2009, Schunk and Winter 2009). Therefore,
the correlation between risk preferences and search activities depends on the type ofsearch models.
JEL Classification: D81, D83
Keywords: Risk preference, Sequential search, MPL∗

Graduate School of Economics, Osaka University, 1-7, Machikaneyama, Toyonaka, Osaka, 560-0042,
Japan, E-mail: u304898i@ecs.osaka-u.ac.jp†
Osaka University, ISER, E-mail: inukai@iser.osaka-u.ac.jp‡
Graduate School of Economics, Osaka University, E-mail: sasaki@econ.osaka-u.ac.jp
§
IZA

1

Introduction

In this paper, we study the effect of risk preferences on search behavior by using a laboratory
experiment that embodying labor search. Search behavior is risky. Consider a fundamental
sequential labor search model in Lippman and McCall (1976). An individual draws a wage
offer from a given wage offer distribution. If the drawn wage offer is equal to or higher thanher or his reservation wage, the individual accepts the offer, but otherwise, the individual
rejects the offer and draw a new wage offer from the same wage offer distribution. However,rejecting a wage offer have a risk: There is no guarantee to get a new offer. Even if she or
he draws a new offer, additionally, there is no guarantee that the new offered wage is higher
than the one that the individual rejected before. Individual search behavior, therefore, differs
by the extent of risk aversion: A risk averse individual has a lower reservation wage than arisk loving individual, and therefore, the search duration is on average shorter for the former
than the latter.
Schunk (2009), Schunk and Winter (2009) studied the relationship between search behavior and risk preferences by using laboratory experiments. They cannot observe any significant
correlation between search behavior and risk preferences that elicited from the multiple pricelist (MPL) method (Holt and Laury 2002), the certainty-equivalent method (Wakker and
Deneffe 1996), and the trade-off method (Abdellaoui 2000). Instead, they observe a significant correlation between search behavior and the extent of loss aversions.
The potential reason why they found a significant correlation between the extent of loss
aversion and search activities but not between the extent of risk preferences and search
activities is that they design a sequential search model with recall in which individual pays
from the initial endowment. This embodies “consumer search”. In the consumer searchmodel, a good is sold at many locations, but the price of good is different at each location.
An individual does not know the price of good at a location ex ante. Therefore, he or
she searches sequentially for a lower price among locations. However, he or she has to pay
the fixed cost as she or he visits a new location for an additional search activity. Schunk1

(2009) and Schunk and Winter (2009) designed the consumer search model: Participants are
exogenously given an initial endowment as the value of good. They have to pay the fixed
cost when they draw a new point. In addition, a recall option is incorporated into theirexperimental design, which means that the participants are allowed to recall previous draws.
Therefore, if the participants decide to finish search activity, they can choose the good at thelowest point among the previous draws. In this design, participants tend to consider search
activity into which the loss frame is embodied: The participants set the initial endowment asa reference point, and they are inclined to avoid to lose own endowment by paying the fixed
cost of additional search. Moreover, risk preferences may not affect search behavior because
the recall option is allowed. Even if a new draw is higher than the one that they rejected
before, they can purchase a good at the one that they rejected before.
We instead consider the sequential search model developed by (Lippman and McCall
1976) with no recall and no initial endowment. We focus attention on search activity into
which the gain frame is embodied. This is “labor search” in contrast to consumer search.
Therefore, it seems that risk preferences are more important than loss aversion in labor searchmodel. In this paper, we study the effect of risk preferences on search behavior by using alaboratory experiment that embodying labor search. As our best knowledge, this is the first
paper that focuses on differences between the two search models in terms of the effect of risk
preferences. A growing literature uses a laboratory search experiment to test the theoreticalprediction obtained from a sequential search model (Asano et al. 2015, Boone et al. 2009,
Cox and Oaxaca 1989, 1992). Our study is also in line with the past literature.
Our findings are summarized below. First, we found the statistically significant effect ofrisk preferences elicited from the MPL method (Holt and Laury 2002) on search behavior.
Secondly, the search duration is on average shorter for a risk averse individual than for arisk loving one, which is consistent with the theoretical prediction in (Lippman and McCall
1976). Thirdly, there is no upward or downward bias between risk preferences elicited fromsearch activities and that from the MPL method. Finally, our search model is susceptible to2

probability weighting but not gambler’s fallacy or the decreasing reservation point by search
duration.
The rest of our paper is organized below. The next section develops an infinite-horizon
sequential search model used in our experiments. Section 3 explains the experimental design,
and Section 4 shows the result. We discuss the result in Section 5. The conclusion is provided
in Section 6.

2

Model

In this section, we explain an infinite-horizon sequential search model developed by Lippman
and McCall (1976). We then derive the reservation point and the expected duration of search.
Moreover, we explain how to elicit risk attitudes from observed search activities.
A representative individual i engages in search activity. Individual i draws a point from a
uniform distribution, where the lower bound is m − a and the upper bound is m + a. Becausea point follows the uniform distribution, the expected draw is m. The individual decides
whether to accept or reject the point. If the individual accepts the point, then the searchbehavior is ended, and the point becomes the individual’s payoff. If the individual rejects
the point, then the individual decides to continue the search behavior and moves to the next
round to draw a new point from the same uniform distribution. However, the individual
who rejects a point and decides to move to the next round is forced to end search activity
with the probability λ, in a case of which the payoff of the individual is zero. Therefore, theindividual continues to search to obtain a higher point, facing a risk of forced terminationof search behavior. In addition, we assume in our laboratory experiment that the discountrate is zero for simplicity because the search behavior is conducted only at a laboratory.
The individual can search as long as possible unless she/he stops searching or is forced to
end search activity. Therefore, this model describes the essence of infinite-horizon sequential
search activity.

3

The value function of individual i is given:

Vi = Emax[ui (Cx), (1 − λ)Vi ],(1)

where Vi is the present value for individual i, ui (Cx) is the utility function, and x is theaccepted point. C represents the conversion rate between the accepted point and JPY.
Equation (1) can be rewritten below:
Z m+a
[ui (Cx) − (1 − λ)Vi ]

λVi =
Ri

1
2a


dx,

(2)

where Ri represents individual i reservation point.
Assuming that individual i is risk neutral, then her or his utility function can be rewritten
as ui (Cx) = pi Cx, where pi is the individualistic parameter that decides the utility from anaccepted point. According to the reservation point property, the reservation point Ri is thevalue that satisfies ui (CRi ) = pi CRi . Substituting the utility function into equation (2)yields:(1 − λ)pi CRi= pi CλZ m+a[x − Ri ]

Ri

1
2a


dx.

(3)

Note that individualistic parameters pi and the conversion rate C are at the both sides.
Because pi can be canceled out, then the equation determining the reservation point is:
Z m+a(1 − λ)R = λ
[x − R]

R

1
2a


dx.

(4)

Risk neutral individuals share the same reservation point, regardless of the level of the individualistic parameter. Therefore, the lower subscript i can be eliminated. The right handside of equation (4) represents the expected marginal gain of an additional search behavior,and the left hand side indicates the marginal cost of an additional search behavior. Note thatthe reservation point does not vary with the search duration in the infinite-horizon sequential
4

search model.
Because the duration of search of individual i follows the Geometric distribution, theexpected duration of search, S, can be calculated as:

S=

2a
.
(m + a) − R(5)

We set the expected value of point distribution, m as 500, and the scale of range of point
distribution, a as 500. We prepare two types of probability of termination of search behavior,
λ as 5% and 2%. Under each probability, the reservation point for a risk neutral agent canbe calculated by using equation (4), and the expected search duration can be calculated byusing equation (5) and the reservation point.
Table 1: The reservation point and the expected search duration for risk neutral agent
m = 500, a = 500
Large(λ = 5%) Small (λ = 2%)
Reservation point
Expected search duration

724
3.62

817
5.46

In the direct response method, an individual’s reservation point cannot be observed directly, but her/his search duration can be observed. According to te reservation point property, the reservation point is lower for risk averse individual than for risk neutral individuals,
and the expected search duration is shorter for the former than for the latter, which is reported at the second row of Table 1. Therefore, in the direct response method, we use anindividual’s average search duration as a proxy of her or his expected search duration, thenwe measure the extent of risk attitude, varying by the probabilities of termination of search
activity.

5

3

Experimental Design and Measuring Risk Attitudes

Our experiment consisted of two parts, Part 1 and 2. The order of Part 1 and Part 2 was
randomly determined in each session.
In Part 1, participants conducted a search experiment. We prepared two conditions (Large
and Small). The probability of termination of search activity was different between two typesof games. We set λ as 5% in Large condition and as 2% in Small condition. Participants
played search activities in Large and Small conditions ten times for each. Note that the orderof two conditions was random to control for the order bias.
We have so far assumed that a representative individual i is risk neutral. We explain theway of eliciting the degree of risk attitudes, using data from laboratory search experiments.
1−θ

We assume that an individual’s utility exhibits CRRA, u(x) = x1−θ if θ 6= 1 and u(x) =ln(x) if θ = 1. θ represents the parameter of risk aversion: θ = 0 means that the individual isrisk neutral, θ > 0 means that individual is risk averse, and θ < 0 means that the individualis risk loving.
By substituting the CRRA utility function into equation (2), the reservation point canbe obtained as the function of θ, R(θ). The expected search period can be written as thefunction of θ, that is,S(θ) =

2a.
(m + a) − R(θ)(6)

As we mentioned above, we cannot observe the reservation point directly. Hence, by using
an average search duration, we estimate the parameter of risk aversion for individual i, θi ,by minimizing the following objective function of the sum of squared sum:

SSE(θi ; Si ) = S L (θi ) − S̄iL2

+ S S (θi ) − S̄iS

2

,

(7)

where SiL (θi ), SiS (θi ) are the calculated expected search duration for θi in Large and Small6conditions, respectively. S̄iL , S̄iS are the average search duration for individual i in Large andSmall conditions, respectively.
In Part 2, participants answered a monetary incentivized questionnaire concerning risk
preference. We used the multiple price list (MPL) method developed by Holt and Laury(2002). Table 2 displays an example of contents of the questionnaire. Participants chose apreferred one between lottery A and lottery B for each row. If the participants choose lottery
A, they receive xA with probability p or yA with probability 1 − p. On the other hand, if
the participants choose lottery B, they receive xB with probability p or yB with probability
1 − p. Noting that xA > yA , xB > yB , xA < xB , and yA > yB . We prepared four patterns ofoutcomes: (xA , yA ) versus (xB , yB ) as (1500,1300) versus (2000,0), (1050,900) versus (2000,0),(1200,950) versus (1400,700), and (1050,900) versus (1400,700). The order of outcomes was
randomly determined in each session. As the row does down, p increases by 10 percentage
points and the increasing rate of the expected value is larger in the column of lottery B thanin the column of lottery A. According to their risk preferences, some participants switch
their choices from lottery A to lottery B. Similarly to the way of measuring risk attitudes
from observed search activities, we assume that the utility exhibits CRRA. From the lottery
choices, we can infer the interval of the degree of risk aversion. For example, if the number oflottery B chosen by individual i for k type of outocme, rik is 5, then we can infer the intervalof degree of risk attitudes for individual i for k type of outcomes, θ5k < θik ≤ θ6k . Nothingthat we dropped samples who chose lottery B at all rows (i.e. rik = 10). The log likelihoodfor individual i for k type of outcome is as follows:
 

 
 

θ2k − µ
θ1k − µ
θ1k − µ+ 1[rik = 1]log Φ− Φlik (µ, σ) = 1[rik = 0]log Φ
σ
σ
σ



θ10k − µ+ · · · + 1[rik = 9]log 1 − Φ, (θ1k < ... < θ10k )(8)σ
We run the interval regression to find the expected degree of risk aversion for individual i foreach type of outcomes. In this paper, we define the degree of risk aversion elicited from the7

MPL method for individual i is the mean of the expected degree of risk averse elicited from
the MPL method by using the interval regression.
Table 2: An example of contents of questionnaire concerning risk preference
Choice Number

Lottery A

Lottery B

1
2
3
4
5
6
7
8
9
10

1,500 (10%), 1,300 (90%)
1,500 (20%), 1,300 (80%)
1,500 (30%), 1,300 (70%)
1,500 (40%), 1,300 (60%)
1,500 (50%), 1,300 (50%)
1,500 (60%), 1,300 (40%)
1,500 (70%), 1,300 (30%)
1,500 (80%), 1,300 (20%)
1,500 (90%), 1,300 (10%)
1,500 (100%), 1,300 (0%)

2,000 (10%), 0 (90%)
2,000 (20%), 0 (80%)
2,000 (30%), 0 (70%)
2,000 (40%), 0 (60%)
2,000 (50%), 0 (50%)
2,000 (60%), 0 (40%)
2,000 (70%), 0 (30%)
2,000 (80%), 0 (20%)
2,000 (90%), 0 (10%)
2,000 (100%), 0 (0%)

After finishing Part 1 and Part 2, we randomly choose one decision that determines the
reward of experiments, based on the payoffs among 60 times decision making ( 10 × 2 trials
in Part 1 and 10 × 4 choices in Part 2). If a decision in Part 1 is chosen, we conveted 1
point to JPY 2. And if a decision in Part 2 is chosen, then we drew a lottery to determine
the outcome according to the choice. In addition, we paid all participants JPY 1000 as ashow-up fee.

4

Result4.1

Summary Statistics

The participants of our experiment consist of students at Osaka University, Japan. The
experiments were conducted in December 2016. We recruited the participants by using
ORSEE(Greiner et al. 2004) and run the experiments by using z-Tree (Fischbacher 2007).
The number of participants was 59, 26 of which was male. We dropped 3 participants because
they made a inconsistent choice in the MPL method: Choosing lottery A although lottery B
8

at a lower expected value is chosen or choosing lottery A at probability p = 1 although they
can get the higher outcome certainly by choosing lottery B.
Table 3 shows the summary statistics. Because participants played ten trials of search
activities for each condition, we show the average search durations in the result. The average
search duration in Small condition is longer than that in Large condition. Therefore, thesmaller termination of probability is, the longer average search duration is. This is consistent
with the theoretical prediction in Pissarides (2000). We show risk attitudes elicited from
the MPL method, which is the average number of individual who choose lottery B at eachtype of outcomes. As the number of lottery B chosen by an individual is larger, she or heis more risk loving. The proportions of risk aversion by using the MPL method has not so
far been in the previous literature (Crosetto and Filippin 2016, Holt and Laury 2002, 2005).
The proportions of risk aversion from average search duration are larger than that from the
MPL method.
Figure 1 displays the histogram of the average search duration in Large and Small conditions. In total, the average search duration is shorter than the expected duration of search
for a risk neutral individual predicted by the theoretical search model. This implies that theparticipants were overall risk averse in our experiment.
Table 3: Summary statistics

Large (λ = 5%)
Small (λ = 2%)
Risk Attitudes (MPL)
Male
N

Mean

S.D.

% Risk averse

2.90
3.82
3.33
0.46
56.00

2.48
4.01
1.23
0.5

76.79
83.93
73.21

Note: Large and Small show the average search duration among ten trials at eachcondition, respectively.
Risk attitudes (MPL) shows the average number of individuals that choose lottery B ateach type of outcomes. Noting that as the number of lottery B chosen by an individualis larger, she or he is more risk loving.

9

Figure 1: The histogram of average search duration

Note: The vertical lines in figure represent the expected search durations for risk neutral agent

4.2

Regression Analysis

We run regressions to estimate the effect of the degree of risk aversion elicited from the
MPL method on the average search duration and the correlation between the two estimateddegrees of risk aversion from the sequential search model and the MPL method. Table 4shows the result. The degree of risk aversion, θ elicited from the MPL method significantly
affected the average search duration and the degree of risk averse, θ elicited from observed
search activities using Equation 7. These results are in contrast to the result from laboratory
search experiment in Schunk (2009), Schunk and Winter (2009). They cannot observe thesignificant correlation between observed search behavior and risk attitudes elicited from the
MPL method. Although the constant term is statistically significant in column (4), theconstant term is not statistically significant when the degree of risk aversion elicited from
the MPL method is controlled for (Columns 5 and 6). This implies that there is no upward
or downward bias between two risk preference parameters. The average search duration islonger and the degree of risk aversion is smaller for male. This is consistent with the resultthat male is more risk loving than female (Crosetto and Filippin 2013). However, thesegender differences are statistically insignificant.
10Table 4: OLS result
Dependent variable
Small
Male
θ(MPL)
Constant

Observations
R-squared

Average search duration
(1)
(2)
(3)

(4)

θ(Search)(5)(6)

0.847∗∗∗ 0.847∗∗∗ 0.847∗∗∗(0.204)(0.204) (0.205)
0.587
0.513 −0.349−0.313(0.438)(0.389)(0.237)(0.211)
∗∗∗
∗∗∗
∗∗
∗∗
−0.657 −0.642
0.326
0.317
(0.226) (0.221)(0.140)(0.135)
∗∗∗
∗∗∗
∗∗∗
∗∗∗
2.711
3.717
3.462
0.579
0.05230.208(0.185)(0.384) (0.309)(0.0733) (0.251)(0.179)
112
0.091

112
0.155

112
0.176

56
0.053

56
0.114

56
0.152

Cluster robust standard errors by individuals in parenthesis.
∗ p < 0.10, ∗∗ p < 0.05, and ∗∗∗ p < 0.01.

5Discussion

In this section, we test the robustness of our search model and discuss the result.
First, we test the gambler’s fallacy. People become obsessed with an idea that sequential
events are conditionally dependent even thought those are conditionally independent. Hence,
they underestimate the probability that an outcome that occurred before occurs again. The
gambler’s fallacy is observed in many situations (Chen et al. 2016). In search activities,
two potential gambler’s fallacies exist: Participants do not consider that the termination
risk is conditionally independent among (1) trials or (2) rounds. (1) If the participants do
not consider the termination risks among trials are not conditionally independent, they thenunderestimate the termination risk after a termination. In this case, the participants who
were terminated before are more likely to search longer afterward. Therefore, the degreeof risk aversion will be underestimated. (2) If participants do not consider the termination
risks among rounds are not conditionally independent, then participants who move to thenext round consider that the termination risk is higher than that at the last round. Then,they overestimate the termination risks by rounds. In this case, the participants decrease11

reservation point by rounds, then the payoffs decrease by the accepted rounds.
To test these hypotheses, we run the regression using the fixed effect model to observe achange of the average search duration between before and after termination within a participant, and a change of the average payoff among accepted rounds within a participant. Table
5 shows the result. The dependent variables in columns (1) and (2) are the search duration,
and After termination shows the difference of average search duration between before andafter termination. We cannot observe any significant effect of termination on the average
search duration when the samples are restricted to those were terminated more than or equal
to one (column 1) or once (column 2). Moreover, the dependent variable in column (3) isthe payoff, and Large×Accepted round, Small×Accepted round show the difference of average
payoff among the accepted rounds in Large and Small conditions, respectively. Those arestatistically insignificant in Table 5 in column (3). Therefore, the gambler’s fallacy does notplay a critical role in our search model.
Table 5: Gambler’s Fallacy
Dependent variable

Search duration(1)(2)

Payoff(3)

Small

0.84∗∗∗
0.66∗∗∗(0.20)(0.34)
0.02−0.30(0.27)(0.40)

85.15∗∗∗(20.15)After termination
Large × Accepted round
Small × Accepted round2.89∗∗∗(0.19)
≥1
Yes
998
0.091

Constant
Number of termination
Fixed effectObservations
R-squared

3.00∗∗∗(0.30)
=1
Yes
323
0.155

8.34
(5.23)
4.81(3.23)
694.14∗∗∗(17.76)
Yes
1120
0.176

Cluster robust standard errors by individuals in parenthesis.
∗ p < 0.10, ∗∗ p < 0.05, and ∗∗∗ p < 0.01.

Other concern is about the reservation point property. In infinite-horizon sequential
12search model, the reservation point is constant among search duration. However, Brown
et al. (2011) showed reservation point decrease by search duration. If participants decrease
their reservation point by search duration, then the degree of risk aversion is overestimated.
We can test the possibility by comparing the payoffs among accepted point, and we cannot
observe such a possibility (Table 5 in column 3). 1
Second, we test the probability weighting. The previous literature found that probability
weighting function is an inverse S-shaped; people tend to overestimate small probability andunderestimate large probability. In our experimental design, the termination risk is small (5%in Large and 2% in Small conditions). If participants overestimate the termination risk, thenthe degree of risk averse is overestimated. To check the possibility, we compare with the degreeof risk averse between elicited from Large condition and that from Small condition. Because
the probability weighting function is inverse S-shaped according to previous literature, theoverestimation of termination risk in Small condition is larger than that in Large condition.
Therefore, the degree of risk averse in Small condition is larger than that in Large condition.
We estimate the degree of risk averse by rearranging Equation 7 to aggregate level. Consistent
with our hypothesis, in total, the degree of risk averse in Small condition is larger than thatin Large condition. When we separated our samples by gender, the bias is not observed
fro male subsample but observed for female subsample. Therefore, our search model issusceptible from probability weighting. It should be noted when we interpret the result of
our search model.
1

Brown et al. (2011) found that the key determinants of decreasing reservation point are elapsed time andaccumulated cost of search. In the experimental design in Brown et al. (2011), they set an arrival rate ofpoint, which is the probability that a new point is offered in a second. Therefore, participants have to wait
until a new point is offered if they decide to continue to search activity. In addition, participants have to pay a
fixed search cost during waiting for a new offer. However, in our experimental design, if participants continue
to search activity, then a new point will be proposed immediately if they are not terminated. Moreover, thecost of additional search is zero. Therefore, we consider the problem of decreasing reservation point by search
duration is not severe in our experimental design as that in Brown et al. (2011).

13

Table 6: Probability weighting
Total
Small (λ=2%)
Constant
N

Male

Female0.20∗∗∗ 0.17
(0.07) (0.11)
0.35∗∗∗ 0.23
(0.09) (0.17)11252

0.22∗∗∗(0.08)
0.43∗∗∗(0.08)
60

Cluster robust standard errors by individuals in parenthesis.
∗ p < 0.10, ∗∗ p < 0.05, and ∗∗∗ p < 0.01.

6Conclusion

In this paper, we tested the effect of risk preferences on search behavior by using a laboratory
experiment that embodying labor search.
We found the statistically significant effect of risk preferences elicited from the MPL
method (Holt and Laury 2002) on search behavior. Consistent with the theoretical predictionin (Lippman and McCall 1976), the search duration for risk averse individual is on average
shorter than that of a risk loving individual. The significant effect of risk preferences on search
activities is not observed in Schunk (2009), Schunk and Winter (2009), which used searchmodel embodying consumer search. Therefore, the extent of the effect of risk preferences
on search activities depends on search model. Moreover, there is no upward or downward
bias between risk preferences elicited from search activities and that from the MPL method.
Our search model is susceptible to probability weighting but not gambler’s fallacy or thedecreasing reservation point by search duration.
Our research has several limitations. First, we do not see the correlation between therisk preference that is elicited from a laboratory search experiment and the behavior in thereal world such as wage and unemployment spells. Second, we do not see the correlation
between search behavior and personal preferences except for risk preference. Future researchis needed to tackle these limitations.

14

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