Sample and attrition

In total, 2904 Norstat panelists logged onto the experiment web server with valid participation ids. Of these 230 were never randomized into treatment, either because they clicked the “no consent” button (169), or because they abandoned the study without signing out (61), and a total of 2674 participants were randomized into one of our four treatments. 2019 completed, giving us a post-randomization attrition rate of 24.5 percent, perhaps indicating that the experiment was more tedious or complicated than the Norstat panelists are used to. Fortunately, the attrition was not correlated with treatment assignment. Table 2 documents that more than half of the attrition was participants abandoning the experiment while reading instructions, about a third of the attrition was participants abandoning the experiment while in the process of making decisions about risk taking. Some participants kept a copy of the consent form open in their browser and revoked consent at some point after randomization. All these rates are very similar across treatments.

Even if attrition is not correlated with treatment assignment, attrition might cause the sam-ple of participants to become less representative. We do not have any information on the partici-pants that left before answering the background questions, but we can compare the final sample with the Norwegian population. Table 3 compares the distribution of participants across age and gender with official numbers from Statistics Norway; these are two characteristics in which there are unlikely to be much measurement error in, and for which official statistics of high quality are readily available. We see that our experimental sample is older than the population, particularly males 18–30 are underrepresented in our sample. Among women, the problem is not quite as severe as among the male in the younger age groups. Among the 60–80 year olds, we have oversampled both men and women to about the same extent. Overall, our sample has a slightly higher proportion of males than the Norwegian population, but not by much more than what could be expected due to random sampling.

Another concern that has been made about participants in online surveys and experiments is

Table 3: Representativeness of sample

Male Female

Sample Population Sample Population A. Share of age group – within gender

[18,20) 0.003 0.033 0.016 0.030

Note: The shares from the sample are coded from those that provided valid ages in the short survey after the decisions. The population numbers are taken from Statistics Norway’s 2019 numbers (Table 10211), https:

//www.ssb.no/statbank/table/10211/.

that they “speed” through the survey instrument without paying sufficient attention to the infor-mation presented to them (see, e.g., Greszki, Meyer, and Schoen (2014) and Zhang and Conrad (2014)). As mentioned in Section 3.3, this is a criterion that Norstat, our survey provider, at-tempts to screen out of the panel, but it is also something we can examine with the data we have collected. From entering the website to the first decisions, the median participant used 4 minutes and 5 seconds (with the 25th percentile spending 2 minutes and 57 seconds, the 75th percentile at 5 minutes and 47 seconds). Less than 1 percent of participants used less than a minute from start to the first decisions.⁵ The median time for the subsequent three decisions was 31 seconds (with the 25th percentile at 21 seconds and the 75th percentile at 46 seconds), with only 1.5 percent spending less than 10 seconds. We conclude that speeding is not a major concern in our data.

Table 4 provides descriptive statistics on the non-incentivized information we collected toward the end of the study. In addition to the age and gender variables we discussed above, comparing our sample to the Norwegian population, we see that most of our participants are parents, which means that they must have some experience making decisions on behalf of others. We see also that about a third of our participants have high school or less as their highest completed education, and fully 60 percent report to have higher education. Even if we might have some measurement error with the simplified categorization we used in the survey, it seems fair to conclude that our sample is better educated than the Norwegian population – of which 34 percent have attained higher education, and about 63 percent have high school or less.⁶

In Table 4 we can also see that on average our participants evaluate themselves as slightly

5The mean time to completion is not a useful statistic for detecting speeding, since the mean time to completion is dominated by a thin tail of participants who are likely to have taken long breaks before completing the survey.

6The education statistics for the full population are taken from Statistics Norway’s 2018 numbers (Table 11293),https://www.ssb.no/statbank/table/11293/, for the population 16 and above.

Table 4: Descriptive statistics

Self evaluation of risk willingness (1–7 scale) 3.593 1.357 (0.030) (0.021) Belief about others’ risk willingness (1–7 scale) 4.111 0.907

(0.020) (0.022) Own willingness for good works (1–7 scale) 4.889 1.274

(0.028) (0.021)

1There were 17 participants that did not provide an age.

Note: Descriptive statistics on the self-reported and non-incentivized data collected in the experiment. Standard errors in parentheses. Standard deviations are provided for the numerical variables only; the standard errors of the standard deviations are calculated with the jackknife.

cautious when it comes to risk taking, averaging 3.6 on a 1–7 scale. On average, they also believe other participants to be more risk taking than themselves, with an average of 4.1. It is also interesting that the standard deviation in what they believe about others is as much as 2/3 of the self-reported willingness to take risk, which might indicate that the population is not particularly well informed about the preferences of others. The correlation between own risk willingness and the belief about others risk willingness is 0.32. It is perhaps not surprising that this correlation is positive, but it is also not so large that it should be impossible to distinguish between them in trying to account for decision making. When it comes to evaluating their own willingness to support good works without expecting anything in return, the participants average almost a whole point above neutral on the 1–7 scale, this might reflect that those willing to take part in online research are positively selected on pro-social attitudes, but perhaps also a self serving bias.

The final group of variables in Table 4 concern the self reported affect during the exper-iment. Participants could check one out of five alternatives, and a bit more than half have indicated that they were either “excited” or “hopeful,” both of which can be classified as posi-tive anticipatory emotions. Only a small minority indicated the negaposi-tive anticipatory emotions (“anxious” or “worried”), while about a third did not find any of these categories to be a fit description of their emotional state.

4.2 Decisions

Figure 3 summarizes the choices in the experiment for each of the treatments in each of the ten different lotteries. A benchmark to keep in mind is that a risk neutral agent without any probability distortion would always choose the lottery for the first safe alternative, and never take the lottery for the last safe alternative. First, we can note that all lotteries provide evidence for both risk averse and risk seeking behavior, since the proportion that chose the lottery over the first (and smallest) safe alternative is well below unity, and the proportion that chose the lottery over the last (and largest) safe alternative is well above zero. Choice probabilities do not react as strongly to the value of the safe alternative as one would have believed. Consider the first safe amount in the first lottery. Participants evaluate a 1/6 probability of 240 NOK vs a safe amount of 10 NOK, and about 25 percent of participants chose the safe amount of 10 NOK. This seems risk averse in the extreme. Second, comparing each treatment (row) for a given lottery (column), it seems that choices do not differ much by treatment, at least not in any striking way.

Figure 4 provides a complementary view of the same data, focusing instead on the propor-tion of times each individual participant chose the lottery in the 28 decisions that they faced.

First, we can note that about 10 percent of participants never chose the lottery – slightly more in the now and short treatment, slightly less in the long and never treatments. In all treat-ments there are also a few percent of the participants who always chose the lottery over the safe alternative. Given the large range of safe outcome alternatives available (cf. the rightmost column of Table 1), this is a bit surprising. Second, only in thenowtreatment do the remaining participants center on a symmetric bell-shaped distribution. The three other treatments seem markedly non-symmetric, even if there are no differences in central tendency (the averages of the proportion of lottery choice are 0.440, 0.449,0.448, and 0.434, the differences are not significant). An Epps and Singleton (1986) test for equality of distribution, with the natural extension to 4 groups, reject that the four treatments generate the same distribution of average lottery choices at the 10% level (p<0.095).

The pictures of Figure 3 and Figure 4 hide some of the behavior by individuals with respect

12345678910

now short long never

1234567123456712345671234567123456712345671234567123456712345671234567

0.00

0.25

0.50

0.75 0.000.250.500.75 0.000.250.500.75 0.000.250.500.75 Safe alternative

Share that chose the lottery

Figure3:Distributionofchoices Note:Foreachofcombinationoflotteryandtreatment,thegraphshowstheproportionthatchosethelotteryforeachofthesevensafeoutcomealternatives.Thedienumbers andthesafeoutcomealternativesrefertothediceinTable1.

long never

now short

0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00

0.00 0.04 0.08 0.12

0.00 0.04 0.08 0.12

Fraction of situations the lottery was chosen

Fraction

Figure 4: Distribution of the proportion of lottery choices

Note: Each participant is represented by the proportion of situations in which they chose the lottery over the safe option.

to the dice they make decisions over. Examining the 8076 lotteries that our participants consid-ered, we find that in about 10 percent of the lotteries, participants chose the lottery regardless of the safe alternative, and in about 21 percent of the lotteries participants always chose the safe amount. In about 11 percent of the lotteries, participants made a switch from taking the safe amount to taking the lottery as the value of the safe alternative increased, this is inconsis-tent with reasonable interpretations of what altruistic behavior on behalf of the recipient would imply.

5 Results

In this section we first look at direct behavioral evidence for treatment effects on risk taking on behalf of others, before formulating an empirical counterpart of the choice model in Sec-tion 2. The empirical choice model is estimated with a hierarchical Bayes procedure before the evidence is summarized with respect to our registered hypotheses.