The Relationship Between Shocks and Higher-Order Risk Attitudes

We use a controlled economic experiment to assess the relationship between shocks and higher-order risk attitudes. Particularly, we study if previous apparent discrepancies are generated by the impossibility of field data separating the effects of the income shocks on wealth from those with risk attitudes. To do so, we propose a between-subjects experiment in which we vary the amount of initial experimental endowments (wealth) that subjects receive and the occurrence or not of the shock. To capture these relationships from a broader set of subjects than college students, the experiment is implemented via Forthright Access, an online platform with a representative sample of the U.S. population. We exogenously isolate shocks from wealth to assess their independent effect on higher-order risk preferences.
We implement an experiment with seven randomly assigned treatments between subjects, as described in Table 1.




Table 1. Treatments
Endowment\Shock Deterministic Shock
$2 Deterministic-$2 Negative Shock-$2 (Negative shock from a 50% chance of a ($2, $6) bundle)
$6 Deterministic-$6 Positive Shock-$6 (Positive shock from a 50% chance of a ($2, $6) bundle)
Negative Shock-$6 (Negative shock from a 50% chance of a ($6, $10) bundle)
$10 Deterministic-$10 Positive Shock-$10 (Positive shock from a 50% chance of a ($6, $10) bundle)

In Stage I, subjects learn their endowment and the source of it.
In Stage II, subjects will perform an investment task to measure their risk aversion (Gneezy & Potters 1997). This tool has previously been employed to assess risk tolerance for economic shocks (Cohn et al., 2015; Holden & Tilahun, 2021). In this simple risk elicitation task, participants will be asked how much of their initial endowment based on the random treatment assignment in Stage I ($2, $6, $10) they wish to invest in a risky option and how much to keep. The invested amount yields a dividend of 2.5 for 4 rounds and a dividend of 5 for the other four rounds with a 50% probability. The decision maker keeps the money not invested.
In Stage III, subjects will perform an additional lottery selection task to measure attitudes toward risk (Eckel and Grossman, 2008). More specifically, subjects select a lottery of their preference from six available options (Eckel and Grossman, 2008). Each lottery has the same outcome probabilities but varies the payments of the low and high outcomes. Subsequently, subjects complete 17 binary selection lotteries designed to capture higher-order risk attitudes following Noussair et al. (2014). Table 2 describes the 17 lottery decisions presented in are grouped into four parts: five choices to assess risk aversion by comparing a sure payoff with a risky lottery; five choices to measure prudence, defined as the preference to assign unavoidable risks to higher income states rather than lower ones; five choices to assess temperance, reflecting the preference to spread independent risks across states rather than concentrating them; and two additional choices to test relative risk aversion and prudence under expected utility theory. The choice of the left lottery indicates risk aversion, prudence, and temperance.
Left Lottery Right Lottery
Risk Aversion 1 20 [65_5]
Risk Aversion 2 25 [65_5]
Risk Aversion 3 30 [65_5]
Risk Aversion 4 35 [65_5]
Risk Aversion 5 40 [65_5]
Prudence 1 [(90+ [20_-20]) _60] [(90_ (60+ [20_-20])]
Prudence 2 [(90+ [10_-10]) _60] [(90_ (60+ [10_-10])]
Prudence 3 [(90+ [40_-40]) _60] [(90_ (60+ [40_-40])]
Prudence 4 [(135+ [30_-30]) _90] [(135_ (90+ [30_-30])]
Prudence 5 [(65+ [20_-20]) _35] [(65_ (35+ [20_-20])]
Temperance 1 [(90+ [30_-30]) _ (90+ [30_-30])] [(90_ (90+ [30_-30] + [30_-30])]
Temperance 2 [(90+ [30_-30]) _ (90+ [10_-10])] [(90_ (90+ [30_-30] + [10_-10])]
Temperance 3 [(90+ [30_-30])_(90+[50_-50])] [(90_ (90+ [30_-30] + [50_-50])]
Temperance 4 [(30+ [10_-10]) _ (30+ [10_-10])] [(30_ (30+ [10_-10] + [10_-10])]
Temperance 5 [(70+ [30_-30]) _ (70+ [30_-30])] [(70_ (70+ [30_-30] + [30_-30])]
Ra_EU1 [40_30] [50_24]
Prud_EU2 [(50+ [25_-25]) _30] [(50_ (30+ [15_-15])]

Finally, participants complete a short questionnaire to assess sociodemographic and personality dimensions relevant to risk and shock behavior. Table 3 briefly provides a chronology of the tasks with the number of choices or questions per task and source.



Table 3. Chronology of tasks
Task Observed choices per subject Source
Task 1 Risk Aversion 8 Gneezy & Potters (1997)
Task 2 RA Simple 1 Eckel and Grossman 2008
Task 2 Risk Aversion 5 Noussair et al., (2014)
Task 2 Prudence 5 Noussair et al., (2014)
Task 2 Temperance 5 Noussair et al., (2014)
Task 2 RA EU1 1 Noussair et al., (2014)
Task 2 PRudEU2 1 Noussair et al., (2014)
Questionnaire (Ten-Item Personal Information) 10 Gosling, S. D., Rentfrow, P. J., & Swann, W. B., Jr. (2003).

Further descriptions of our experimental tasks can be found in Eckel & Grossman (2008), Gneezy & Potters (1997), and Noussair et al. (2014). The Forthright Access panel provides additional socio-demographics, including age, nationality, residency, education, ethnicity, employment, gender, income, marital status, political ideology, religion, sexual orientation, etc.

2025-04-21

2025-06-21

1. Risky Investments Choices
2. Lottery choice
3. Risk Aversion Measure
4. Prudence Measure
5. Temperance Measure

1. Risky Investment Task (Gneezy and Potters, 1997): The primary outcome is the proportion of the endowment invested in the risky asset, where a higher proportion indicates greater risk tolerance, while a lower proportion shows higher risk aversion. Do we differentiate between the 2.5 and 5?
2. Eckel and Grossman Gamble Task (2008): The primary outcome is the choice of a gamble from six ordered lotteries, where higher numbers indicate lower risk aversion.
3. Risk Aversion Measure (Noussair et al., 2014): Risk aversion will be measured as the number of safe choices made among the five decisions involving a sure payoff and a risky lottery.
4. Prudence Measure (Noussair et al., 2014): Prudence will be measured as the number of prudent choices made among the five decisions for prudence.
5. Temperance Measure (Noussair et al., 2014): Temperance will be measured as the number of temperate choices made among the five decisions for temperance.
Following previous literature (Deck & Schlesinger, 2010; Ebert & Wiesen, 2014; Noussair et al., 2014; Xu et al., 2024), the number of risk-averse, prudent, and temperate choices will be interpreted as a measure of the strength of these higher-order risk attitudes.

Correlation between risk aversion, prudence, and temperance

We use a controlled economic experiment to assess the relationship between shocks and higher-order risk attitudes. We study whether previous apparent discrepancies are generated by the impossibility of field data separating the effects of income shocks on wealth from those with risk attitudes. To do so, we propose a between-subjects experiment in which we vary the amount of initial experimental endowments (wealth) that subjects receive and the occurrence or not of the shock.

Table 1. Treatments
Endowment\Shock Deterministic Shock
$2 Deterministic-$2 Negative Shock-$2 (Negative shock from a 50% chance of a ($2, $6) bundle)
$6 Deterministic-$6 Positive Shock-$6 (Positive shock from a 50% chance of a ($2, $6) bundle)
Negative Shock-$6 (Negative shock from a 50% chance of a ($6, $10) bundle)
$10 Deterministic-$10 Positive Shock-$10 (Positive shock from a 50% chance of a ($6, $10) bundle)

In Stage I, subjects learn their endowment and the source of it.
In Stage II, subjects will perform an investment task to measure their risk aversion (Gneezy & Potters 1997). This tool was previously employed to assess risk tolerance for economic shocks (Cohn et al., 2015; Holden & Tilahun, 2021). In this simple risk elicitation task, participants will be asked how much of their initial endowment based on the random treatment assignment in Stage I ($2, $6, $10) they wish to invest in a risky option and how much to keep. The invested amount yields a dividend of 2.5 for 4 rounds and a dividend of 5 for the other four rounds with a 50% probability. The decision maker keeps the money not invested.
In Stage III, subjects will perform an additional lottery selection task to measure attitudes toward risk (Eckel and Grossman, 2008). More specifically, subjects select a lottery of their preference from six available options (Eckel and Grossman, 2008). Each lottery has the same outcome probabilities but varies the payments of the low and high outcomes. Subsequently, subjects complete 17 binary selection lotteries designed to capture higher-order risk attitudes following Noussair et al. (2014). Table 2 describes the 17 lottery decisions presented are grouped into four parts: five choices to assess risk aversion by comparing a sure payoff with a risky lottery; five choices to measure prudence, defined as the preference to assign unavoidable risks to higher income states rather than lower ones; five choices to assess temperance, reflecting the preference to spread independent risks across states rather than concentrating them; and two additional choices to test relative risk aversion and prudence under expected utility theory. The choice of the left lottery indicates risk aversion, prudence, and temperance.
Left Lottery Right Lottery
Risk Aversion 1 20 [65_5]
Risk Aversion 2 25 [65_5]
Risk Aversion 3 30 [65_5]
Risk Aversion 4 35 [65_5]
Risk Aversion 5 40 [65_5]
Prudence 1 [(90+ [20_-20]) _60] [(90_ (60+ [20_-20])]
Prudence 2 [(90+ [10_-10]) _60] [(90_ (60+ [10_-10])]
Prudence 3 [(90+ [40_-40]) _60] [(90_ (60+ [40_-40])]
Prudence 4 [(135+ [30_-30]) _90] [(135_ (90+ [30_-30])]
Prudence 5 [(65+ [20_-20]) _35] [(65_ (35+ [20_-20])]
Temperance 1 [(90+ [30_-30]) _ (90+ [30_-30])] [(90_ (90+ [30_-30] + [30_-30])]
Temperance 2 [(90+ [30_-30]) _ (90+ [10_-10])] [(90_ (90+ [30_-30] + [10_-10])]
Temperance 3 [(90+ [30_-30])_(90+[50_-50])] [(90_ (90+ [30_-30] + [50_-50])]
Temperance 4 [(30+ [10_-10]) _ (30+ [10_-10])] [(30_ (30+ [10_-10] + [10_-10])]
Temperance 5 [(70+ [30_-30]) _ (70+ [30_-30])] [(70_ (70+ [30_-30] + [30_-30])]
Ra_EU1 [40_30] [50_24]
Prud_EU2 [(50+ [25_-25]) _30] [(50_ (30+ [15_-15])]

Finally, participants complete a short questionnaire to assess sociodemographic and personality dimensions relevant to risk and shock behavior. Table 3 briefly provides a chronology of the tasks with the number of choices or questions per task and source.



Table 3. Chronology of tasks
Task Observed choices per subject Source
Task 1 Risk Aversion 8 Gneezy & Potters (1997)
Task 2 RA Simple 1 Eckel and Grossman 2008
Task 2 Risk Aversion 5 Noussair et al., (2014)
Task 2 Prudence 5 Noussair et al., (2014)
Task 2 Temperance 5 Noussair et al., (2014)
Task 2 RA EU1 1 Noussair et al., (2014)
Task 2 PRudEU2 1 Noussair et al., (2014)
Questionnaire (Ten-Item Personal Information) 10 Gosling, S. D., Rentfrow, P. J., & Swann, W. B., Jr. (2003).

Further descriptions of our experimental tasks can be found in Eckel & Grossman (2008), Gneezy & Potters (1997), and Noussair et al. (2014). The Forthright Access panel provides additional socio-demographics, including age, nationality, residency, education, ethnicity, employment, gender, income, marital status, political ideology, religion, sexual orientation, etc.

The computer will do randomization.
. The randomization will be conducted within the Otree experimental platform; each individual will be randomly assigned to a different treatment with equal probability.

individual

No

as many clusters as individuals observations

1,050 individuals

1,050 individuals, 150 subjects per treatment

Based on power calculations and previous studies (Cohn et al., 2015), which found an effect size of d=0.42, we estimate we will need 100 participants per cell to detect a slightly smaller effect size (d=0.35), considering that our conditions and experimental design differ. Since online participants often fail standard attention checks, we will over-sample to account for dropouts and incomplete session studies.

AP_The Relationship Between Shocks and Higher.docx