United, but Not Uniform. Experimental Evidence About Risk Taking in the Family

Christoph Engel | PASS Academician

United, but Not Uniform. Experimental Evidence About Risk Taking in the Family

In his Encyclical Letter Laudato Si’, the Pope writes

“I would stress the great importance of the family, which is ‘the place in which life – the gift of God – can be properly welcomed and protected against the many attacks to which it is exposed, and can develop in accordance with what constitutes authentic human growth. In the face of the so-called culture of death, the family is the heart of the culture of life’. In the family we first learn how to show love and respect for life; we are taught the proper use of things, order and cleanliness, respect for the local ecosystem and care for all creatures. In the family we receive an integral education, which enables us to grow harmoniously in personal maturity. In the family we learn to ask without demanding, to say ‘thank you’ as an expression of genuine gratitude for what we have been given, to control our aggressivity and greed, and to ask forgiveness when we have caused harm. These simple gestures of heartfelt courtesy help to create a culture of shared life and respect for our surroundings”.[1]

In this paper, I read the statement as an empirical claim: families have a formative influence. In children, at least in those children who have the good fortune to grow up in their family of origin, the “enculturation” (Collins 1989) channel is isolated. They did not choose their family. If a family member joins later in life, enculturation is still at work. But it competes with selection. Sometimes selection is unidirectional, as in parents adopting a child. More often, selection is reciprocal as, quintessentially, in mating (Bacon, Conte et al. 2014). Husband and wife seek out each other: for many reasons, but arguably also because they are a good fit in terms of their attitudes.

There is a large literature on family influences, on matters as mundane as healthy eating (Gross, Pollock et al. 2010), but also considerably more consequential behavior, like implementing a therapy plan (Edelstein and Linn 1985), engaging in premarital sexual relations (Thornton and Camburn 1987), or in crime and delinquency (Derzon 2010). In this paper, I focus on one feature of the decision problem that is characteristic for many, arguably even most choices: the decision-maker faces uncertainty. I investigate in which ways families affect risky choice.

With observational data, it has been shown that married individuals take less risk than singles (Dohmen, Falk et al. 2011), but that married women take more risk than females who are single parents (Halek and Eisenhauer 2001), and that the risk attitudes of couples tend to correlate (Brown, Dickerson et al. 2012, Bacon, Conte et al. 2014). There is a small number of risk-taking experiments with households (Bateman and Munro 2005, De Palma, Picard et al. 2011, Abdellaoui and Paraschiv 2013). But they are interested in how much risk the household, i.e. a more aggregate unit, is happy to take. I, by contrast, investigate the impact of the family on risks an individual family member is taking. In which ways is risk taking shaped by one’s family?

I present empirical evidence from an experiment that Alexandra Fedorets, Olga Gorelkina and myself have run on the German Socio-Economic Panel SOEP (Goebel, Grabka et al. 2019). Details about the design of the experiment, hypotheses derived from a formal model, more elaborate statistical analysis of the data, and heterogeneity analysis with the help of a machine learning algorithm will be published elsewhere (Engel, Fedorets et al. 2022). In this paper, I only report descriptive statistics, along with run of the mill regressions, and focus on implications for the theme of the Plenary.

I proceed in five steps. In Section 2, I report to which degree family membership leads to an alignment of risk preferences. For this purpose, I use choices of family members that only affect their own payment. In Section 3 I contrast these choices with four choices that affect the payoff of a second family member. In Section 4 I turn from motivation to cognition, and test whether family members are aware of differences in risk preferences in their family. In Section 5 I turn to key demographic features: how is the attitude towards exposing another family member to risk moderated by enculturation vs. selection; how do parents thus differ from children? Which is the influence of household and of individual income, employment, education, gender, and membership in a religious community? Section 6 ties the findings back to the theme of the Plenary.

2.     Alignment

In its most straightforward reading, the opening quote from Laudato Si’ is a claim about preferences: the preferences of two members of the same household are more aligned than the preferences of two persons randomly drawn from the same population. I use data from my experiment with Alexandra Fedorets and Olga Gorelkina to test this claim.

All the many safeguards in the design of the experiment are discussed in a more technical paper (Engel, Fedorets et al. 2022). In the present context, the following suffices. Participants choose one of 11 lotteries. Each lottery has a high and a low outcome. Both outcomes are equally probable. The first lottery is actually a safe choice, as both outcomes are the same. Participants gain 10€ with certainty. All other lotteries expose participants to true risk. But there is a catch. Risk-taking is profitable. The good outcome increases twice as fast as the bad outcome deteriorates. Hence in the second lottery, the good outcome is 12, while the bad outcome is 9. The gap between the good and bad outcome increases in steps of 2 for the good and in steps of 1 for the bad outcome. In the final lottery, the good outcome is 30 while the bad outcome is 0. Hence the more a participant is averse to risk the smaller the spread between the good and the bad outcome.

We had the good fortune to run our experiment on the complete intervention sample of the German socio-economic panel SOEP. In 494 households, interviewers randomly selected 2 household members. Theoretically this could have been one of the parents and one of the children. But effectively we have only very few (48) parent-child pairs, but 177 parent-parent pairs, and 269 child-child pairs. Due to concerns about prior consent, we only tested children who were 18 years old or older (but still live in the household of their parents). In this section, I report data from the first part of the experiment. In this part, participants decide on their own. They do not know what the second part of the experiment will be about.

The left panel of Figure 1 plots a participant’s own choice against the choice of the other household member. If risk preferences were perfectly aligned, all bubbles should be on the diagonal: if one household member is not willing to accept any risk, the other household member should not do so as well. The choice should be at 0,0. If one household member is happy to tolerate a medium size of risk and is willing to lose at most half of the sure gain, the choice should be at 5,5. And if one household member is attracted by the possibility to gain as much as 30, both choices should be at 10,10. As the figure shows, there are some choices on the diagonal. But the majority of choices are not. Even the bubbles in the extreme 0,10 and 10,0 corners are large. Risk preferences in households are clearly not anything close to perfectly aligned.

Still the regression in Table 1 finds a highly significant association between the choice of the other household member and the participant’s own choice. The coefficient is positive. The more risk the other household member is happy to accept, the more risk the regression predicts this household member to accept. However, the coefficient is small. If the other household member is accepting the risk of losing one more € in exchange for the possibility of gaining two more €, this household member is 11% more likely to do so as well.

The right-hand panel explains what drives this overall effect. It looks at the difference between a participant’s own choice and the independent choice of the other household member. If this difference is zero, risk preferences have been perfectly aligned. Both participants have made the same choice. For 16% of all participants this is indeed the case. Apparently, the midpoint and the extremes have been prominent numbers, which is why we find peaks at differences of +5 and -5 and +10 and -10. With this qualification, the distribution of differences is shaped like a pyramid. Household members are not just the same when it comes to risk preferences. But living together with a very risk averse person makes it less likely to be very risk seeking oneself, and vice versa. We thus find an alignment effect, but the size of the effect is small.

3.     Respect

a)     Free Respect

In the second part of the experiment, participants again chose one of the 11 lotteries. But in this part of the experiment, their choice has an effect for the other household member. In the interest of eliciting these choices from every participant, we used what experimental economists call the strategy method (Selten 1967). We thus asked each participant to make all choices, and only after the experiment was finished we randomly determined which choice, from which household member, would be implemented.

In the first condition of the second part of the experiment the active participant is choosing on behalf of the other, passive household member. Hence her choice has no material consequences for herself, and only affects the outcome of the other household member. The left panel of Figure 2 is the equivalent of the right panel of Figure 1. I thus report the difference between the participant’s choice and the choice that the other participant has made when deciding on her own. I call the condition “free respect” as, in this condition, paying respect to what the other household member wants is completely free of charge. Still only 16% of these rulers do exactly what the family member wants for whom the decision matters. Participants pay respect to the wishes of other family members, but only to a rather limited degree.

The right-hand panel isolates the difference between deciding on one’s own and deciding on behalf of another family member. It is a graphical representation of the “difference in differences”. The figure thus compares by how much, and in which direction, the decision of the participant deviates from the decision of her counterpart when both are alone, compared with the decision when one participant decides on behalf of the other. There is again a peek at zero. For 37% of our participants, it does not make a difference whether they decide on behalf of themselves or on behalf of the other family member. This null effect does, however, not imply that participants simply impose their own risk preference on the other household member. The more their risk preferences have been aligned in the first place (the closer they have been to 0 in the left panel of Figure 1) the less there is a need for adjustment if participants now decide on behalf of the other household member. Yet about two thirds of the participants make a difference between deciding on their own and deciding on behalf of the other household member. When deciding on behalf of the other family member they become more risk seeking than when deciding on their own, or they become more risk averse. Actually, there is a clear asymmetry. When their decision matters for the other household member, participants are considerably more likely to reduce the exposure to risk, rather than increasing it. This suggests that participants shy away from being responsible for a bad outcome more than they shy away from depriving the other participant of an even higher gain.

The regression in Table 2 fully supports the visual impression. If participants decide on behalf of another household member (free respect), on average their choices are considerably more risk averse. But, through the interaction effect, this dampening effect is reduced the more the other household member has a taste for risk. The first effect shows that participants become more cautious when they are responsible for an outcome that exclusively affects another family member. However, the second effect shows that family members are not blindly protective. If they know that the other family member is more risk tolerant, they are (at least partly) sensitive to this.

b)    Costly Respect

In the next condition, there is still one active and one passive household member. But now the choice of the active household member affects the payoff of both household members. Hence if the risk materializes, both of them receive a lower payoff. But both of them also receive a higher payoff if the active participant has accepted a higher degree of risk and the risk has not materialized. In this condition, the active participant is thus in the position of a (risk) dictator.

The left panel of Figure 3 shows that only about 14% of dictators perfectly implement the risk preference of the other household member. Comparing the left panel of Figure 3 with the left panel of Figure 2, we also see that the asymmetry has disappeared. Descriptively, dictators are even slightly more likely to expose the other household member to a bit more risk, compared to less risk. This does also become visible in the right-hand panel of Figure 3. It again displays the difference in differences, between the first and this part of the experiment.

The regression of Table 3 further nuances the picture. If the other participant is highly averse to risk (chooses the lottery that gives her a sure gain of 10, other’s choice is then coded as 0) the dictator reduces risk exposure by 78 of 100 points. Yet the interaction effect shows that, for any point the passive household member is more willing to take risk, the active member increases joint risk exposure by about .2 points. All main and interaction effects are highly significant. This demonstrates that dictators strike a balance between respect for the risk preferences of the other family member and their own risk attitude.

c)     Joint Decision

In the following condition, both household members participate in decision-making. But they have to make one decision that affects both of them; technically, the average of both decisions is implemented. As Figure 4 shows, many more participants make the same choice as when deciding on their own. About 35% of the bars are at zero. This is about twice as frequent as in the other two conditions (see Figure 2 and Figure 3). In particular the comparison with the costly respect condition is interesting. In both conditions, the outcome affects both household members equally. But in the present condition, the other household member may fend for herself. Participants are clearly sensitive to this. Yet if a participant is also willing to consider the well-being of the other household member, she is more likely to reduce, rather than increase the exposure to risk, compared with the decision she has taken when alone (the bars left of 0 are higher than right of 0). The differences in differences (right panel) are very similar to the left panel, except for the bar at 0 being much lower: participants are more likely to choose their individually preferred risk level, rather than the level preferred by the other family member. All visual impressions are supported by statistical analysis (Table 4).

d)    Veto

In the final condition, the decisions of both household members are checked, but only the more conservative of the two choices is implemented. This design effectively gives the more risk-averse participant a veto. Interestingly, comparing Figure 5 with Figure 4 one sees that, in this condition, less participants repeat the choice they have made when on their own. Deviations in the direction of a higher exposure to risk are considerably more frequent. This suggests that some of the more risk-averse family members move in the direction of the preferences of their counterpart. Arguably they realize that it is very likely that their choice will be implemented, and they strike a balance with the more pronounced taste for risk of the other family member. However, as the right panel of Figure 5 shows, in the veto condition many participants do not repeat the choice they have made when they alone were deciding on behalf of the other family member (the bar at 0 is relatively low). There are about as many deviations into the direction of higher and of lower exposure to risk. This is in line with at least some of the more risk averse participants moving into the direction of the preferences of their counterpart.

The regression in Table 5 establishes a significant negative main effect of this condition. If the other family member is unwilling to accept any risk, even in this condition more risk-seeking participants move into the direction of her preferences. This pattern might result from them expecting a movement of their counterpart into the opposite direction, and playing it safe.

4.     Knowledge

Earlier sections have investigated the motivational effect of living in a family, and of deciding on behalf of other family members. In the experiment, we are free to neutralize the cognitive dimension, by explicitly informing participants in the second part of the experiment about the choice of their experimental counterpart in the first part of the experiment. This is what we did for half of our participants. For the randomly determined other half we withheld this information. Figure 6 is an alternative way of representing the left panel of Figure 2. The figure thus reports the distribution of the difference between the choice a participant makes when deciding on behalf of the other participant, and the choice when exclusively deciding for herself. Yet in this figure, the distributions are separately reported when the counterpart’s decision in the first part of the experiment is revealed (dotted) and when it is concealed (dashed). Distributions are strikingly similar. In a regression, we also do not find any significant differences.[2] Obviously, family members need no information about the risk preferences of each other. They just know them, and exhibit the same (heterogeneous) sensitivity towards the risk preference of another family member.

5.     Demographic Moderators

a)     Selection vs. Enculturation

Conceptually, in child pairs the channel through which their risk preferences can be aligned must be enculturation. In parent pairs, selective mating is an alternative channel. Yet as Figure 7 shows, distributions look very similar. Descriptively, children are a bit more likely to make no difference between deciding on their own and deciding on behalf of another child. But this difference is far from significance.[3] With our data we cannot say whether the lack of a significant difference is due to the fact that enculturation over time overshadows selection effects, or whether the competing mental mechanisms converge to a comparable outcome.

b)    Income

Descriptively, personal income has a bigger effect than household income (Figure 8). Those who fully rely on the income of the breadwinner, hence have a personal income of 0, are least sensitive to differences in risk preferences between themselves and the other family member with whom they have been paired. Participants living in a household with a monthly income above 5000€ are a bit more sensitive than those living in households with a lower income.

Yet despite the fact that effects are not big, the regressions of Table 6 show that they are discernible. The main effect of household income in model 1 implies that the higher the income the more risk the individual takes when deciding on her own. Yet the interaction with being responsible for the risk exposure of another family member is more than six times as large and clearly significant. Hence the higher the household income, the more pronounced the reticence to inflict a bad outcome on a passive family member. The interaction between household income and the other family member’s risk preference is significantly negative: when the participant decides on her own, she is less influenced by the risk preference of the other family member the higher the income of the household. Yet the three-way interaction is again significantly positive. It neutralizes the dampening effect of household income on the sensitivity towards the wishes of the passive participant when deciding on her behalf.

The three-way interaction is not significant in model 2, which investigates the moderating effect of the participant’s own income. All other effects are however significant, have the same sign as with household income, and approximately the same size. Statistically we do thus find a moderating effect of income, but the effect is small.

c)     Employment

Descriptively, employment status has a more pronounced effect on sensitivity towards the risk preferences of other family members. If the active family member is unemployed, she is most likely to impose the same choice on the other family member that she had made herself when alone. This is different for those with a regular employment relation, and even more so for those who work part-time.

The regression reported in Table 7 first shows that controlling for employment status does not substantially change the effects reported in Table 2: when they decide on behalf of another family member, participants reduce the risk exposure. They are influenced by the risk preferences of the other participant. But this effect is almost twice as big if they decide on this person’s behalf. Statistically, irregular employment has essentially no effect. By contrast those regularly employed take substantially more risk when deciding for themselves. But they reduce the exposure substantially when they decide on behalf of the other person. And they are less influenced by the other person’s risk preferences, both when deciding on their own and on behalf of this other family member (the three-way interaction is insignificant).

d)    Education

Education has visibly no discernible effect (Figure 10). Statistical analysis also finds no effect that is significant at conventional levels.[4]

e)    Gender

Descriptively, there is a clear gender effect (Figure 11). Male participants are considerably more likely to impose their own risk assessment on the other family member (many more differences are at or near 0). Female participants are also more likely to become more cautious when deciding on behalf of the other family member, rather than more risk-seeking.

In the regression of Table 8, the interaction between free respect and the other family member’s choice when alone is only weakly significant, and much smaller than in Table 2. This shows that, indeed, male participants are less sensitive to a gap between their own risk attitude and the risk attitude of the family member on whose behalf they decide: as the regression controls for active participants being female, this interaction effect captures the sensitivity of male participants. By contrast, the three-way interaction is large and significant. While male participants exhibit little deference to the risk preference of other family members, female participants are sensitive.

f)      Religion

In the general survey that we are allowed to match with our data, participants were asked whether they are a member of a religious community. Descriptively, reporting to be religious in this sense has little effect (Figure 12). Yet the regression of Table 9 finds a significant three-way interaction: religious participants are substantially more sensitive to the risk preferences of another family member on whose behalf they decide.

6.     Tentative Lessons

Experiments are not descriptions. They are tools for isolating causes. In a strict sense, the present experiment does not generate evidence about the cause that is the topic of this plenary. The experiment is not randomly assigning some participants to a family, while it withholds family life from others. This would require a cohort of Kaspar Hausers. No review board would approve such a cruel research design. One could of course exploit the vagaries of life and compare individuals who had the good fortune to grow up in a well-functioning family with others who had to live in a foster home or an institution. But such evidence would at best be suggestive, as these two groups of individuals are bound to differ in many more respects.

The evidence reported in section 2 of this paper tries to parry the methodological challenge in an indirect way. The households that we had a chance to study come from all parts of Germany, and from all walks of life. We find that the risk preferences of two independently tested family members are correlated. The correlation is far from perfect. But the distributions of choices are also far from uniform. The statement, of course, does not hold for all households. But the risk preferences of household members are likely not to be strongly dissimilar. We find a small degree of alignment. To this extent, the experimental evidence supports the empirical claim that (risk) preferences are shaped by families.

In the opening quote, claims about process and claims about outcome go hand-in-hand. In the experiment, one process channel is isolated. Actually, in this dimension the experiment benefits from random assignment (of the one situation that is payoff relevant) and therefore generates strictly causal evidence. This process channel is respect. The experiment again shows that it is not perfect. Even if one family member decides on behalf of the other, with no material consequences for the decision-maker, choices frequently deviate from the preferences of the addressee. But choices participants make in this role are about twice as intensely influenced by the risk preferences of the addressee, compared with the choice the decision-maker has made when deciding on her own. Living together in a family makes one sensitive towards the interests of other family members. This also holds if paying respect is costly, in that the well-being of the decision-maker is also at stake. Respect is also visible if two family members have to agree on the level of risk exposure, and even if the choice of the more risk-averse family member is implemented by design.

Family life is not only formative, it is also informative. In this respect, the finding does benefit from random assignment to treatment. It makes virtually no difference whether the active participant receives explicit information about the degree of risk the passive participant has accepted when deciding on her own, or not. This is remarkable since measuring risk preferences is not a task family members routinely undertake. Their sense of acceptable risk exposure must result from intuitively aggregating over multiple observations in the past. As the data shows, these intuitive estimates are very precise.

Families are defined by an asymmetry. The parents have chosen each other, and voluntarily agreed to be married. By contrast, children are born into their families. Against this backdrop, it remains remarkable how comparable the choices of parent-parent and child-child pairs turn out to be. Apparently, it makes no visible difference for both alignment and respect whether the bond is freely chosen, or results from upbringing.

Demographic variables can only be observed. They are not exogenously assigned. One may therefore not be sure that a significant effect is causal. Still, it is interesting that both household income and personal income make more risk-seeking when alone, but the effect is significantly reduced when deciding on behalf of another family member. Moreover, the higher the household income, the less pronounced the effect of the other household member’s risk attitude when deciding alone, but the more pronounced the effect when deciding on behalf the other family member. The bottom line is: members of wealthy families are happy to accept more risk when deciding in isolation, but they become more cautious when deciding on behalf of another family member. Wealthy households are more likely to care about each other. The same pattern is found if the decision-maker earns a regular outcome, compared with participants who have no personal income, or who only work part-time. Female participants are more responsive towards the risk preferences of the other household member. The same holds for participants who report belonging to a religious community.

Are we our families? Evidence from this experiment is nuanced. When it comes to accepting risk, family members are not all the same. Living together for decades does not regularly lead to the alignment of risk preferences. But if risk preferences vary within a family, family members know that, and have a fairly good sense how much risk other members of the family are willing to tolerate. And to a remarkable degree, they are willing to act upon this knowledge. They pay respect to each other. Family members tend to be united, but not uniform.



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[1] Encyclical Letter of May 24, 2015, https://www.vatican.va/content/francesco/en/encyclicals/documents/papa-francesco_20150524_enciclica-laudato-si.html, R 213.

[2] The regression is available upon request.

[3] The regression is available upon request.

[4] The regression is available upon request.