’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

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1

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3

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7

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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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