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’O Sole MioAn Experimental Analysis of Weather and Risk Attitudes
in Financial Decisions
– ONLINE APPENDIX –
1 Additional Details on the Experimental procedures
Each experimental session consisted of six rounds of tasks performed by subjects who
enrolled in the e-recruit subject pool. Subjects joined the subject pool voluntarily by
completing a form on line indicating their interest in participating in experiments.
When a student enrolled for participation in the experiment, she was told only that
she would participate in an experiment about decision making under uncertainty and
that “You will be offered at least $15 for your participation. You may be able to make
up to $50 (or even more) by participating. On average, participants will earn around
$25, though you may earn less. The total amount of time you will spend in the study
will be less than one hour.”
When a subject entered the laboratory, she was given a card with a unique subject
number, which identified the subject during the experiment, and they were given a
consent form. After signing the consent form, subjects were given six tables. Each
table consisted of 10 different pair of lotteries with monetary payoffs attached to every
lottery. The subject needed to choose a lottery out of each pair, thus making a total of
60 decisions. Along with the tables, the subjects were given written instructions that
were read aloud to induce common knowledge that every subject was participating in
1
the same experiment. The instructions included specific examples to clarify the use
of the tables. The instructions given to the subjects are displayed in the Appendix.
After reading the instructions, subjects were given an opportunity to ask questions.
There was no time limit for the experiment and subjects had the opportunity to ask
additional questions during the experiment in private. A monitor was present to
answer questions and to ensure that subjects did not communicate with each other.
After all subjects made their decisions, subjects were asked to complete a question-
naire to report their mood (PANAS-X). When all subjects had finished completing the
questionnaire, experimental personnel went to each subject to randomly determine
their payoffs. After the determination of the payoffs, subjects were asked to complete
a mathematical quiz. Subjects were awarded a compensation for each correct answer.
After the completion of the mathematical quiz, subjects were given a questionnaire
about biographical information and socio-economic attitudes. As soon as a subject
had answered the questionnaire, he/she was paid privately and could leave the room
where the experiment was taking place.
2 Additional Results on the Risk Aversion Treatment
Extended tables with additional control variables. Table 1 and Table 2 extend
the analysis of Table 1 and Table 2 in the paper by including additional control vari-
ables. Specifically, they report the regressions of the number of A choices (the safer
lottery) on a dummy variable which is equal to 1 when the weather is bad, to -1
when the weather is good, and to 0 when the weather is neither good nor bad. All
regressions also include an intercept, and the following control variables: income, re-
ligiousness, political leaning, gender (a dummy which equals 1 for male and -1 for
female), race, play lotteries (a dummy which equals 1 if the subject plays lotteries at
least once a year), and economy concerned (a dummy that equals 1, if the subject re-
sponded “yes” to the question “Are you concerned about the economy?”). The results
document that the inclusion of these additional control variables does not alter our
2
Table 1Risk Aversion (baseline - extended)
Precipitation Overcast-Clear Subjective WeatherIntercept 5.875 5.554 5.611
(0.234) (0.220) (0.208)
Bad-Good Weather 0.347 0.234 0.239(0.082) (0.120) (0.097)
Income 0.001 0.001 0.001(0.001) (0.001) (0.001)
Religious −0.339 −0.301 −0.294(Yes-No) (0.295) (0.307) (0.299)
Political Leaning 0.203 0.201 0.224(Liberal-Conservative) (0.219) (0.217) (0.212)
Gender 0.121 0.067 0.129(0.260) (0.270) (0.262)
Race (white) −0.331 −0.227 −0.242(0.269) (0.257) (0.281)
Race (asian) −0.297 −0.206 −0.237(0.392) (0.356) (0.372)
Play Lotteries −0.146 −0.131 −0.104(once a month or more) (0.062) (0.067) (0.062)
Concerned about economy −0.176 −0.182 −0.189(0.147) (0.124) (0.123)
Notes - The table reports the estimated coefficients of the regressions of the number of Achoices (the safer lottery) on a dummy variable which is equal to 1 when the weather is bad,to -1 when the weather is good, and to 0 when the weather is neither good nor bad. All re-gressions also include an intercept, and the following control variables: income, religiousness,political leaning, gender (a dummy which equals 1 for male and -1 for female), race, playlotteries (a dummy which equals 1 if the subject plays lotteries at least once a year), andeconomy concerned (a dummy that equals 1, if the subject responded yes to the question Areyou concerned about the economy?). The numbers in parenthese are the standard errors ofthe estimated coefficients.
main conclusion about the significant impact of weather on risk taking behavior.
Logit Analysis. We perform an econometric analysis to estimate the marginal
effect of each of our weather measures on the probability of selecting the safer Option
A, after controlling for other personal characteristics that may have an impact on risk
taking behavior. We use a logit regression to estimate the effect of each of our weather
measures on the probability of selecting the safer Option A. Specifically, we set:
Prob (Y = A) =eβ
′x·lottery
1 + eβ′x·lottery = Λ (β′x · lottery) ,
where A is the safer choice, x is a vector of explanatory variables (which always in-
3
Table 2Risk Aversion (High Payoffs - extended)
Precipitation Overcast-Clear Subjective WeatherIntercept 7.005 6.419 6.594
(0.215) (0.284) (0.222)
Bad-Good Weather 0.508 0.490 0.298(0.068) (0.083) (0.169)
Income 0.002 0.004 0.005(0.001) (0.000) (0.000)
Religious 0.080 0.123 0.118(Yes-No) (0.129) (0.130) (0.127)
Political Leaning 0.193 0.103 0.186(Liberal-Conservative) (0.147) (0.126) (0.131)
Gender 0.190 0.134 0.220(0.155) (0.147) (0.180)
Race (white) −0.191 0.018 −0.059(0.222) (0.214) (0.220)
Race (asian) −0.630 −0.414 −0.495(0.281) (0.232) (0.297)
Play Lotteries −0.169 −0.200 −0.141(once a month or more) (0.120) (0.117) (0.125)
Concerned about economy −0.282 −0.357 −0.333(0.095) (0.089) (0.080)
Notes - The table reports the estimated coefficients of the regressions of the number of Achoices (the safer lottery) on a dummy variable which is equal to 1 when the weather is badand -1 when the weather is good. All regressions also include an intercept, and the followingcontrol variables: income, religiousness, political leaning, gender (a dummy which equals1 for male and -1 for female), race, play lotteries (a dummy which equals 1 if the subjectplays lotteries at least once a year), and economy concerned (a dummy that equals 1, if thesubject responded yes to the question Are you concerned about the economy?). The numbersin parenthese are the standard errors of the estimated coefficients.
cludes a constant), lottery is the decision number, and Λ stands for logistic function.
Interacting the regressors with the decision number is a parsimonious way of includ-
ing fixed effects for the decision number. We chose this econometric specification in
order to maximize the statistical power of the regression. Alternatively, we could
have estimated different intercepts and, possibly, different explanatory variables co-
efficients for each lottery, but at the cost of reducing the significance of our coefficient
estimates.
To account for the possible dependence in individual choices, we block-bootstrapped
the confidence intervals of the estimated parameters. Specifically, the bootstrap was
implemented by block sampling the sequence of decisions at an individual level with
4
replacement. For example, if subject j was randomly selected, then the entire se-
quence of subject j’s decisions was added to the bootstrap sample. The bootstrap
distribution of the vector of coefficients was computed using the estimates on 10,000
random samples of the same size of the actual dataset. The added benefit of boot-
strapping is that the resulting confidence intervals take into account the sample size
of the population of subjects. For more details on block-bootstrap with serially depen-
dent data see Horowitz (2006).
In Figure 1 we report the results when Decisions 1- 9 are used for the estimates
(we exclude Decision 10, which is set to be always equal to 0, because this decision
compares two safe lotteries where Option B is strictly better than Option A). Figure 1
reports the estimated probabilities of choosing the safer option for our three main
weather variables. The three panels also include the 95% confidence intervals. Fig-
ure 1 highlights that bad weather leads to a larger probability of choosing Option A,
that is the safer option. This is particularly evident by looking at Decisions 5 and 6,
which are the ones for which a non risk-neutral decision maker would start consider-
ing switching from the safer to the riskier option.
In Figure 2 we conduct the same analysis featured in Figure 1, but we focus only
on Decisions 4-7. We restrict the analysis to this subset of decisions because the
multiple price list method of Holt and Laury is designed, by construction, to measure
risk aversion by observation of the decision at which a subject switches from Option A
to Option B. Thus, the inclusion the treatment effect on the first few and the last few
decisions is not informative from an experimental point of view since these decisions
are only used to anchor subjects choices to Option A (at the beginning of the payoff
table) and to Option B (at the end of the payoff table). This implies that by excluding
from the estimation process Decisions 1-3 and Decisions 8 and 9, we would be able to
obtain a more accurate estimate of the average increase in the probability of choosing
Option A that is due to weather. As expected, the estimates displayed in table 2
show that the effect of weather is more pronounced when we focus only on the set of
decisions around which subjects are likely to switch from Option A to Option B. In
other words, since the effect of weather is by design relevant only in middle range
5
of the Decision set (where the switching point from Option A to Option B is likely
occur), the inclusion of the other decisions determines, by construction, a reduction of
the estimated average increase in the probability of choosing Option A.
Figure 3 and Figure 4 report the estimated probabilities of choosing the safer
option for our three main weather variables in the case of high payoffs and the 95%
confidence intervals. The logit regression follows the same procedure as in the low-
payoffs case. We perform again the estimation by using both the Decions 1-9 (we
exclude again Decision 10 for the same reason discussed above) - reported in Figure 3
- and for the restricted sample - reported in 4. In the restricted estimation we now
include Decisions 5 through 9, since risk aversion is on average higher for higher
payoffs as documented in Holt and Laury (2002). By direct comparison of Figure 3
and Figure 4, it is easy to see that in the case of high payoffs the impact of weather
is so pronounced that the results are still strongly statistically significant even after
taking into account the dampening effect determined by the inclusion of the initial
“anchoring” Decisions 1-4. Just as in the case of low payoff, bad weather induces
greater risk aversion when any of our three measures of bad weather is used.
3 Additional Robustness checks
Skewness Aversion. During our experimental sessions, we also conducted a robust-
ness check to test the effect of weather on the willingness to accept gambles with
varying levels of skewness. The top panel of Table 3 reports the paired lotteries be-
tween which the subjects were asked to choose in the case of low payoffs (denoted as
the low-payoff skewness treatment). Additionally, subjects were also faced with an
additional treatment in which all payoffs displayed in Table 3 were multiplied by 10
(high payoffs skewness treatment).
Panel B of Table 3 documents that “Option A” and “Option B” were identical in
terms of even moments, but differed for expected values and skewness. Equivalently,
we use this treatment to assess the amount of average return that the subjects are
6
0102030405060708090100
12
34
56
78
910
Estimated probability of choosing Option A
Pane
l A: T
he E
ffect
of C
lear
/Ove
rcas
t on
Risk
Ave
rsio
n
Dire
ctio
n of
incr
easin
g
Risk
Ave
rsio
n
0102030405060708090100
12
34
56
78
910
Estimated probability of choosing Option A
Pane
l B: T
he E
ffect
of P
reci
pita
tion
on R
isk
Aver
sion
Dire
ctio
n of
incr
easin
g
Risk
Ave
rsio
n
0102030405060708090100
12
34
56
78
910
Estimated probability of choosing Option A
Pane
l C: T
he E
ffect
of S
ubje
ctiv
e W
eath
er A
sses
smen
t on
Risk
Ave
rsio
n
Dire
ctio
n of
incr
easin
g
Risk
Ave
rsio
n
FIG
UR
E1
-The
effe
ctof
Wea
ther
onR
isk
Ave
rsio
n:es
tim
ated
data
(Dec
isio
ns1-
9),b
asel
ine
case
.T
heve
rtic
alax
isre
port
sth
ees
tim
ated
prob
abili
tyof
choo
sing
Opt
ion
“A”,
the
safe
rlo
tter
y.T
heho
rizo
ntal
axis
repo
rts
the
deci
sion
num
ber.
Inea
chpa
nel,
the
line
wit
hth
e“s
uns”
refe
rsto
the
case
ofgo
odw
eath
er,w
hile
the
othe
rlin
ere
fers
toth
eca
seof
bad
wea
ther
.In
the
top
two
pane
ls,o
bser
vati
ons
are
grou
ped
acco
rdin
gto
the
obje
ctiv
em
easu
res
ofw
eath
er.T
hebo
ttom
pane
lref
ers
toth
esu
bjec
tive
wea
ther
asse
ssm
ent.
7
0
10
20
30
40
50
60
70
80
90
10
0
1
2
3
4
5
6
7
8
9
10
Estimated probability of choosing Option A
Pan
el A
: Th
e E
ffe
ct o
f C
lear
/Ove
rcas
t o
n R
isk
Ave
rsio
n
Dir
ecti
on
of
incr
easi
ng
R
isk
Ave
rsio
n
0
10
20
30
40
50
60
70
80
90
10
0
1
2
3
4
5
6
7
8
9
10
Estimated probability of choosing Option A
Pan
el B
: Th
e E
ffe
ct o
f P
reci
pit
atio
n o
n R
isk
Ave
rsio
n
Dir
ecti
on
of
incr
easi
ng
R
isk
Ave
rsio
n
0
10
20
30
40
50
60
70
80
90
10
0
1
2
3
4
5
6
7
8
9
10
Estimated probability of choosing Option A
Pan
el C
: Th
e E
ffe
ct o
f Su
bje
ctiv
e W
eat
he
r A
sse
ssm
en
t o
n R
isk
Ave
rsio
n
Dir
ecti
on
of
incr
easi
ng
R
isk
Ave
rsio
n
FIG
UR
E2
-The
effe
ctof
Wea
ther
onR
isk
Ave
rsio
n:es
tim
ated
data
(Dec
isio
ns4-
7),b
asel
ine
case
.T
heve
rtic
alax
isre
port
sth
ees
tim
ated
prob
abili
tyof
choo
sing
Opt
ion
“A”,
the
safe
rlo
tter
y.T
heho
rizo
ntal
axis
repo
rts
the
deci
sion
num
ber.
Inea
chpa
nel,
the
line
wit
hth
e“s
uns”
refe
rsto
the
case
ofgo
odw
eath
er,w
hile
the
othe
rlin
ere
fers
toth
eca
seof
bad
wea
ther
.In
the
top
two
pane
ls,o
bser
vati
ons
are
grou
ped
acco
rdin
gto
the
obje
ctiv
em
easu
res
ofw
eath
er.T
hebo
ttom
pane
lref
ers
toth
esu
bjec
tive
wea
ther
asse
ssm
ent.
8
0102030405060708090100
12
34
56
78
910
Estimated probability of choosing Option A
Pane
l A: T
he E
ffect
of C
lear
/Ove
rcas
t on
Risk
Ave
rsio
n (H
igh
Payo
ffs)
Dire
ctio
n of
incr
easin
g
Risk
Ave
rsio
n
0102030405060708090100
12
34
56
78
910
Estimated probability of choosing Option A
Pane
l B: T
he E
ffect
of P
reci
pita
tion
on R
isk
Aver
sion
(H
igh
Payo
ffs)
Dire
ctio
n of
incr
easin
g
Risk
Ave
rsio
n
0102030405060708090100
12
34
56
78
910
Estimated probability of choosing Option A
Pane
l C: T
he E
ffect
of S
ubje
ctiv
e W
eath
er A
sses
smen
t on
Risk
Ave
rsio
n (H
igh
Payo
ffs)
Dire
ctio
n of
incr
easin
g
Risk
Ave
rsio
n
FIG
UR
E3
-The
effe
ctof
Wea
ther
onR
isk
Ave
rsio
n:es
tim
ated
data
(Dec
isio
ns1-
9),h
igh
payo
ffs.
The
vert
ical
axis
repo
rts
the
esti
mat
edpr
obab
ility
ofch
oosi
ngO
ptio
n“A
”,th
esa
fer
lott
ery.
The
hori
zont
alax
isre
port
sth
ede
cisi
onnu
mbe
r.In
each
pane
l,th
elin
ew
ith
the
“sun
s”re
fers
toth
eca
seof
good
wea
ther
,whi
leth
eot
her
line
refe
rsto
the
case
ofba
dw
eath
er.
Inth
eto
ptw
opa
nels
,obs
erva
tion
sar
egr
oupe
dac
cord
ing
toth
eob
ject
ive
mea
sure
sof
wea
ther
.The
bott
ompa
nelr
efer
sto
the
subj
ecti
vew
eath
eras
sess
men
t.
9
0
10
20
30
40
50
60
70
80
90
10
0
1
2
3
4
5
6
7
8
9
10
Estimated probability of choosing Option A
Pan
el A
: Th
e E
ffe
ct o
f C
lear
/Ove
rcas
t o
n R
isk
Ave
rsio
n
(Hig
h P
ayo
ffs)
Dir
ecti
on
of
incr
easi
ng
R
isk
Ave
rsio
n
0
10
20
30
40
50
60
70
80
90
10
0
1
2
3
4
5
6
7
8
9
10
Estimated probability of choosing Option A
Pan
el B
: Th
e E
ffe
ct o
f P
reci
pit
atio
n o
n R
isk
Ave
rsio
n
(Hig
h P
ayo
ffs)
Dir
ecti
on
of
incr
easi
ng
R
isk
Ave
rsio
n
0
10
20
30
40
50
60
70
80
90
10
0
1
2
3
4
5
6
7
8
9
10
Estimated probability of choosing Option A
Pan
el C
: Th
e E
ffe
ct o
f Su
bje
ctiv
e W
eat
he
r A
sse
ssm
en
t o
n R
isk
Ave
rsio
n
(Hig
h P
ayo
ffs)
Dir
ecti
on
of
incr
easi
ng
R
isk
Ave
rsio
n
FIG
UR
E4
-The
effe
ctof
Wea
ther
onR
isk
Ave
rsio
n:es
tim
ated
data
(Dec
isio
ns5-
9),h
igh
payo
ffs.
The
vert
ical
axis
repo
rts
the
esti
mat
edpr
obab
ility
ofch
oosi
ngO
ptio
n“A
”,th
esa
fer
lott
ery.
The
hori
zont
alax
isre
port
sth
ede
cisi
onnu
mbe
r.In
each
pane
l,th
elin
ew
ith
the
“sun
s”re
fers
toth
eca
seof
good
wea
ther
,whi
leth
eot
her
line
refe
rsto
the
case
ofba
dw
eath
er.
Inth
eto
ptw
opa
nels
,obs
erva
tion
sar
egr
oupe
dac
cord
ing
toth
eob
ject
ive
mea
sure
sof
wea
ther
.The
bott
ompa
nelr
efer
sto
the
subj
ecti
vew
eath
eras
sess
men
t.
10
willing to give up in order to achieve a reduction in the negative skewness of the
lottery. The choices at Decisions 6, 7, and 8 are the most interesting ones, given that
expected values are almost identical and one option is positively skewed, while the
other is negatively skewed. Indeed, up to Decision 5 more than 90% of our subjects
chose “Option A” (see Bassi, Colacito, and Fulghieri (2012) for a more comprehensive
analysis of preference for skewness in this environment).
We perform then the same regression analysis as in the other treatments, and we
report the results in panels C and D of Table 3. The numbers document that bad
weather increases the likelihood of the subjects choosing “Option A”, despite this op-
tion being the one with the lower expected value from Decision 8 onwards. This result
holds for both low and high payoffs. We interpret these results as suggesting that
weather increases individuals’ aversion to negatively skewed gambles. The effect,
however, is not always large enough to claim statistical significance. This is possibly
due to the subjects’ difficulties in analytically assessing the differences between the
skewnesses of the two options.
Risk and Skew Aversion. We have also performed a series of treatments in
which the riskier lottery is also positively skewed, for each paired assignment. Con-
sistently with our earlier findings, we did not find any statistically significant differ-
ence related to the weather condition. We conjecture that this finding is due to the
offsetting effects of weather on risk- and skewness-aversion.
11
Table 3Skewness Treatment
Panel A: Payoffs TableOption A Option B
Decision 1 : $1.00 w.p 10% , $3.00 w.p 90% $0.20 w.p 90% , $2.20 w.p 10%Decision 2 : $1.00 w.p 20% , $3.00 w.p 80% $0.20 w.p 80% , $2.20 w.p 20%Decision 3 : $1.00 w.p 30% , $3.00 w.p 70% $0.20 w.p 70% , $2.20 w.p 30%Decision 4 : $1.00 w.p 40% , $3.00 w.p 60% $0.20 w.p 60% , $2.20 w.p 40%Decision 5 : $1.00 w.p 50% , $3.00 w.p 50% $0.20 w.p 50% , $2.20 w.p 50%Decision 6 : $1.00 w.p 60% , $3.00 w.p 40% $0.20 w.p 40% , $2.20 w.p 60%Decision 7 : $1.00 w.p 70% , $3.00 w.p 30% $0.20 w.p 30% , $2.20 w.p 70%Decision 8 : $1.00 w.p 80% , $3.00 w.p 20% $0.20 w.p 20% , $2.20 w.p 80%Decision 9 : $1.00 w.p 90% , $3.00 w.p 10% $0.20 w.p 10% , $2.20 w.p 90%Decision 10 : $1.00 w.p 100% , $3.00 w.p 0% $0.20 w.p 0% , $2.20 w.p 100%
Panel B: Distribution of LotteriesOption A Option B
Exp Var Skew Kurt Exp Var Skew KurtDecision 1 : 2.80 0.36 -2.67 8.11 0.40 0.36 2.67 8.11Decision 2 : 2.60 0.64 -1.50 3.25 0.60 0.64 1.50 3.25Decision 3 : 2.40 0.84 -0.87 1.76 0.80 0.84 0.87 1.76Decision 4 : 2.20 0.96 -0.41 1.17 1.00 0.96 0.41 1.17Decision 5 : 2.00 1.00 0.00 1.00 1.20 1.00 0.00 1.00Decision 6 : 1.80 0.96 0.41 1.17 1.40 0.96 -0.41 1.17Decision 7 : 1.60 0.84 0.87 1.76 1.60 0.84 -0.87 1.76Decision 8 : 1.40 0.64 1.50 3.25 1.80 0.64 -1.50 3.25Decision 9 : 1.20 0.36 2.67 8.11 2.00 0.36 -2.67 8.11Decision 10 : 1.00 0.00 - - 2.20 0.00 - -
Panel C: Low Payoffs TreatmentPrecipitation Overcast-Clear Subjective Weather
Bad-Good Weather 0.228 0.148 0.300(0.100) (0.145) (0.119)
Panel D: High Payoffs TreatmentPrecipitation Overcast-Clear Subjective Weather
Bad-Good Weather 0.250 0.129 0.112(0.054) (0.080) (0.127)
Notes - Panel A reports the table of payoffs for the low payoffs treatment. In the high payoffstreatment (not reported) all payoffs are multiplied by 10. Panel B reports mean, variance,skewness, and kurtosis for each lottery. Panels C and D report the estimated coefficientsof the regressions of A choices on the dummies for the weather conditions. All regressionsinclude an intercept, a lottery number indicator, and Income, Religious, and Political Leaningas controls. These parameters are not reported in table in the interest of space, but they areavailable upon request. The numbers in parentheses are the standard errors of the estimatedcoefficients.
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ReferencesBassi, A., Riccardo Colacito, and Paolo Fulghieri (2012). “Someone Likes it Skewed:
an Experimental Analysis of Skewness and Risk Aversion,” University of North CarolinaWorking Paper.
Holt Charles A., and Susan K. Laury (2002). “Risk Aversion and Incentive Effects,”The American Economic Review, 92(5), 1644—1655.
Horowitz, J. L. (2006) “The bootstrap,” Chapter 1 in The Handbook of Econometrics,vol.5, pp. 3159—3228 , edited by Heckman, James J. and Leamer, Edward E., published byElsevier.
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