2.1 Experimental context

We conducted a laboratory experiment at the Busara Center of Behavioral Economics in Nairobi, Kenya. The centre provides a state-of-the-art lab infrastructure, including up to 25 computer-supported workplaces. It maintains a subject pool with currently around 12,000 registered individuals, many of them recruited from the Nairobi informal settlement Kibera. The living situation in this slum community is characterized by extreme poverty and insecurity due to the lack of property rights and high criminality. Housing and hygiene conditions are very poor since the government does not provide water, electricity, sanitation systems or other infrastructure (The Economist Reference Economist2012). Most of the slum residents work as small-scale entrepreneurs and casual workers in the informal sector, therefore relying on uncertain and irregular income streams. Related to the lack of formal employment, most of the slum dwellers have no formal risk protection such as health insurance (Kimani et al. Reference Kimani, Ettarh, Kyobutungi, Mberu and Muindi2012). Many households are, however, member in some kind of social network, such as merry-go-rounds, which allow saving and borrowing and implicitly provide an informal safety net (Amendah et al. Reference Amendah, Buigut and Mohamed2014).

In Kenya, in general, there is a strong spirit of harambee (the Swahili term for ’pulling together’) which encloses ideas of mutual support, self-help and cooperative effort. Harambee takes various forms, such as local fundraising activities to help persons in need or the joint implementation of community projects (e.g. building schools or health centers). While being an indigenous tradition in many Kenyan communities, the concept became a national movement since Kenya’s first president Komo Kenyatta used it as slogan for mobilizing local participation in the country’s development (Ngau Reference Ngau1987; Mathauer et al. Reference Mathauer, Schmidt and Wenyaa2008; Jakiela and Ozier Reference Jakiela and Ozier2016). In the light of this strong tradition of solidarity and seemingly well-established informal security nets it is therefore particular interesting and important to understand which behavioural mechanisms drive willingness to support others.

2.2 Experimental design

2.2.1 Risk solidarity game

The core game of the study aims at measuring solidarity behaviour in situations where subjects either can choose or are exogenously assigned to a certain risk exposure. Figure 1 gives an overview on the sequence of steps in the game. At the beginning, two projects were presented to each subject: a safe option offering 500 KSh and a risky alternative yielding either 1000 or 0 KSh with equal probability. Depending on the treatment, subjects could either choose (treatment CHOICE) or were randomly assigned with probability 0.5 (treatment RANDOM) to one of these two options (step 1). After having chosen one project or being informed about the randomly received option, each subject was randomly and anonymously paired with another person in the room, who followed the same experimental procedure and was hence in the same treatment condition as the subject herself (step 2).Footnote ⁶

Fig. 1 Sequence of steps in the risk solidarity game

Before informing the subjects about their own realized payoff and their matched partner’s project and earnings, we elicited their conditional transfers using the strategy method (step 3). Thereby, all subjects were asked how much of their project income they wanted to transfer to the partner if the partner earned (1) 500 KSh from the safe project, (2) 1000 KSh from the risky project, or (3) 0 KSh from the risky project. Subjects with the safe project made these three transfer decisions based on their sure income of 500 KSh, while subjects with the risky project stated their three gifts in case of winning the high project payoff of 1000 KSh. Risky project holders could not make any transfer in case of earning the zero payoff of their option. Although we are interested in solidarity from better-off to worse-off persons and will exclusively evaluate these transfers in the following analyses, we nevertheless elicited transfers for all three possible payoffs of the partner (including situations where the partner is equally well or better off than the donor) in order to keep the decision task neutral and symmetric across project holders.

After the transfer statements, subjects were asked in a similar way which monetary amount they expected to receive from their partner if the partner earned (1) 500 KSh from the safe option, or (2) 1000 KSh from the risky option (step 4). Subjects with the safe project stated their expectations based on their sure earnings of 500 KSh, and subjects in the risky option stated their beliefs in case of winning zero shillings, respectively.Footnote ⁷ At the end of the experiment, the lottery outcomes of all participants were individually determined (step 5). Subjects had been informed at the beginning of the game that their own and the partner’s payoffs would be established by two different random draws. Transfers between the partners were then effected according to the actually realizing states. The stakes of the game represented considerable amounts for the mainly very poor participants who reported an average daily income of 160 KSh ( $\sim$ 1.50 USD).

The design implies that in the RANDOM treatment, subject’s income is determined purely by chance, while in the other treatment, it can be influenced by the participant’s choice. In particular, becoming a needy person, i.e. earning the zero income from the lottery, is just bad luck in RANDOM but involves a voluntary decision for the risky lottery in CHOICE. The imposed trade-off between a safe and a risky option thereby ensures that risk taking is salient to the participants. Moreover, since the payoffs of the two alternatives both equal 500 KSh in expectation, the risky option reflects a mean-preserving spread of the safe alternative implying that taking the risk is not compensated by higher expected income. Hence, choosing the lottery is not utility maximizing for risk averse individuals and possibly unnecessary in the risk-sharing partner’s view since avoiding the risk is not costly. This case has also been studied in the related experimental literature (e.g. Trhal and Radermacher Reference Trhal and Radermacher2009; Bolle and Costard Reference Bolle and Costard2015; Cettolin and Tausch Reference Cettolin, Riedl and Tran2015). It provides an important benchmark for the effect of risk exposure choice on solidarity in alternative scenarios in which risk taking is either beneficial or even unfavorable in terms of expected income. Moreover, it allows us to distinguish subjects with distinct risk preferences (risk averse or not) without having to make assumptions about the underlying utility function.

The design as an anonymous one-shot game deviates from conditions of real-world solidarity in developing countries, which typically takes place among persons within the family or neighbourhood in repeated exchanges. Keeping subjects’ identity confidential is, however, necessary in order to avoid that possible real-life relationships or fear of sanctions outside the lab bias behaviour of participants. Further, by restricting the game to one single round we implicitly rule out that subjects base their risk-taking and sharing decisions on strategic considerations induced by repeated interactions. This isolates the effect of risk taking on giving behaviour motivated by (social) preferences, such as altruism or distributive preferences (cf. Charness and Genicot Reference Charness and Genicot2009). It represents an important reference case since it avoids that possibly interacting intrinsic and extrinsic motivations blur the measured impact. Overall, since our design excludes issues of social pressure and reciprocity considerations that probably would have reduced the participants’ incentives to punish a risk-taking partner, our experiment is likely to measure an upper bound of the behavioural effect of risky choices on solidarity.

2.2.3 Procedures

For recruitment, subjects were randomly chosen from the Kibera subject pool registered at Busara and then invited by SMS. A precondition for being selected was an education level of at least primary school (8 years) to ensure some familiarity with numerical values as is necessary for our study. Using a between-subject design, the recruited persons were randomly assigned to one of the two treatments. The core experiment was run within 13 sessions in December 2017. Six sessions were conducted of the RANDOM treatment and seven of the CHOICE treatment. As a result, all subjects in the same session are also in the same treatment.Footnote ¹⁰ Moreover, subjects in a given treatment were not aware of the existence of the other treatment. Hence, we can rule out that within-session dynamics explain differences across treatments. In total, 238 subjects participated in our study, thereof 120 in RANDOM and 118 in CHOICE. 33% of our subjects are male and 47% are married. On average, the participants are 31 years old and have a schooling level of 11 years. Table 1 gives an overview on selected basic characteristics of the participants by treatment and project. In addition, we ran 5 sessions of the auxiliary treatment in January 2018 where, in total, 111 subjects participated.

Table 1 Basic characteristics of participants by treatment and project

	All			Random			Choice
	Random	Choice	Difference	Safe	Risky	Difference	Safe	Risky	Difference
	(1)	(2)	(2–1)	(3)	(4)	(4–3)	(5)	(6)	(6–5)
Age	30.48	31.36	0.88	30.12	30.83	0.72	31.18	32.09	0.91
Male	0.33	0.35	0.02	0.30	0.35	0.05	0.32	0.48	0.16
Schooling	11.53	11.25	−0.28	11.20	11.85	0.65	11.26	11.17	−0.09
Married	0.45	0.48	0.03	0.43	0.47	0.03	0.46	0.57	0.10
Occupational status
Employed	0.13	0.14	0.01	0.15	0.10	−0.05	0.13	0.17	0.05
Self-employed	0.19	0.27	0.08	0.15	0.23	0.08	0.25	0.35	0.10
Unemployed	0.50	0.45	−0.05	0.50	0.50	0.00	0.46	0.39	−0.07
Other	0.18	0.14	−0.04	0.20	0.17	−0.03	0.16	0.09	−0.07
Social preferences
Inequality aversion 1 (disadv.)	0.18	0.20	0.03	0.23	0.12	−0.12*	0.19	0.26	0.07
Inequality aversion 2 (adv.)	0.24	0.32	0.08	0.30	0.18	−0.12	0.31	0.39	0.09
Fairness	0.32	0.34	0.02	0.32	0.32	0.00	0.35	0.30	−0.04
Trust	0.13	0.19	0.07	0.15	0.10	−0.05	0.21	0.13	−0.08
Risk preference	3.42	3.59	0.18	3.47	3.37	−0.10	2.99	6.09	3.10***
Observations	120	118		60	60		95	23

*, **, *** indicates significance on the 10/5/1% level

Upon arrival, subjects were identified by fingerprint and randomly assigned to a computer station. The instructions were then read out in Swahili by a research assistant, while simultaneously, some corresponding illustrations and screenshots were displayed on the computer screens (see online Appendix F for an English version of the instructions, exemplarily for CHOICE).Footnote ¹¹ For the entire experiment the z-Tree software code (Fischbacher Reference Fischbacher2007) was programmed to enable an operation per touchscreen which eases the use for subjects with limited literacy or computer experience. Subsequently, some test questions verified the participants’ comprehension of the game rules. In case of a wrong answer, the subject was blocked to proceed to the following question. A research assistant then unlocked the program and gave some clarifying explanations if needed. This procedure aimed at increasing the likelihood that all participants fully understood the games. After the comprehension test, the participants performed the actual experimental task. The experiment involved, firstly, a risk preference game which aimed at measuring subjects risk attitudes (see online Appendix E for details) and, secondly, the risk solidarity game explained in detail in the previous section.Footnote ¹² Importantly, the subjects completed the decisions in these two games without learning the realized payoff in the precedent game. Moreover, after randomly determining the game payoffs at the end of the experiment, only the result of one randomly selected game was relevant for real payment. These two design features avoid that results are biased due to any strategic behaviour, expectation forming or income effects across games.

At the end of the session, participants completed a questionnaire covering important individual and household characteristics. After the session, subjects received 200 KSh in cash as show-up fee which compensated mainly for the travel costs to the center. Moreover, subjects earned a minimum of 250 KSh in the experiment in order to guarantee an appropriate compensation for the time spent. However, participants were not informed about this minimum compensation before the end of the game. In total, average earnings amounted to 447 KSh per person. They were transferred cashless to the respondents’ MPesa accounts.Footnote ¹³

2.3 Supplementary data collected within the experiment

In the post-experimental survey we collected all individual and household characteristics that are important drivers of risk taking and solidarity. We use this information to assess whether subjects with the same stated preferences for the risky or the safe project, respectively, do not differ in these important characteristics across treatments because they differ in the way these preferences are measured (hypothetical question in RANDOM versus incentivized decision in CHOICE and in the auxiliary experiment).

Besides basic demographics, subjects’ risk attitudes are an important determinant of risk taking. Therefore, we elicitated an experimental measure of risk preferences which is comparable across all treatments. Prior to the risk solidarity game we ran a risk preference game which was incentivized and designed as an ordered lottery selection procedure (Harrison and Rutstroem Reference Harrison, Rutstroem, Cox and Harrison2008).Footnote ¹⁴ The details of this game are described in online Appendix E. Besides risk preferences, background risk theory (e.g. Gollier and Pratt Reference Gollier and Pratt1996) suggests that individuals reduce financial risk taking in the presence of other, even independent risks. Therefore, subjects’ risk exposure in their real life might influence their decisions in the lab (Harrison et al. Reference Harrison, Humphrey and Verschoor2010). Moreover, individuals may also be less willing to make transfers in the presence of other risks because they want to preserve a certain capacity to cope with negative shocks with their own resources. We have collected a broad range of variables reflecting exposure to the main sources of risk, such as income risk (occupation in paid employment, type of main occupation) and health and health expenditure risk (past and expected future health shocks, health insurance enrolment). Additionally, we have measures of the capacity to cope with negative shocks (wealth, household composition). Proxies for social capital and inequality aversion may also be relevant for predicting both project choice and transfers. Higher levels of trust and cooperation as well as inequality aversion in a society can encourage greater informal risk-sharing among community members and therefore provide better risk coping possibilities (Narayan and Pritchett Reference Narayan and Pritchett1999). Moreover, higher social capital is found to promote financial risk-taking (Guiso et al. Reference Guiso, Sapienza and Zingales2004). We observe five variables which are typically used to measure these factors (e.g. Giné et al. Reference Giné, Jakiela, Karlan and Morduch2010; Karlan Reference Karlan2005): fairness, trust, helpfulness and two measures of inequality aversion.Footnote ¹⁵ Table 10 in online Appendix A provides an overview of all variables.

3.1 A simple model of optimal transfers

In the experiment, subjects make transfer decisions once they know in which project they are for all possible situations of the partner where the assigned partner is worse off. This has two implications. Firstly, all payoff combinations for which transfer decisions have to be made are known. Secondly, transfer decisions are independent of expected transfers from the assigned partner because subjects only receive transfers if the are worse off than their partner, in which case they do not have to make a transfer themselves.

Let $x_i$ denote the payoff subject i receives from the assigned or chosen project, and let $T_i$ denote the transfer made to partner j with $0\le T_i\le x_i$ . Subjects only make transfer decisions if $x_i>x_j$ . Hence, the net payoff of subject i is given by ${\pi }_i=x_i-T_i$ , whereas the net payoff of the matched partner j is ${\pi }_j=x_j+T_i$ . In the following, we formulate a simple model of donor i’s preferences that is inspired by Charness and Rabin (Reference Charness and Rabin2002). It allows for a variety of different preferences for and determinants of redistribution including pure self-interest. We assume that utility takes the following form:

(1) $\begin{array}{c}{U}_i=u({\mu }_i[{\pi }_j-{\rho }_i{({\pi }_i-{\pi }_j)}^2]+(1-{\mu }_i){\pi }_i)\end{array}$

where ${\mu }_i$ is the weight given to the net payoff of the assigned partner j in subject i’s utility function and where ${\rho }_i\ge 0$ allows for inequality aversion. If subject i only cares about his own payoff we have ${\mu }_i=0$ . If, instead, ${\mu }_i>0$ , then partner j’s income matters to subject i. If, additionally, ${\rho }_i>0$ , then subject i is inequality averse. Optimal transfers can be derived by maximizing $U_i$ . A purely self-interested subject with ${\mu }_i=0$ chooses $T_i=0$ . A subject who cares about the partner’s income ( ${\mu }_i>0$ ) but not about inequality ( ${\rho }_i=0$ ) minimizes transfers to $T_i=0$ if ${\mu }_i<\frac{1}{2}$ and maximizes transfers to $T_i=x_i$ if ${\mu }_i>\frac{1}{2}$ . If subject i cares about his own income as much as about his partner’s income such that ${\mu }_i=\frac{1}{2}$ , then transfers are irrelevant if the subject is not inequality averse, ${\rho }_i=0$ . If a subject cares about the partner’s payoff and is inequality averse such that ${\mu }_i,{\rho }_i>0$ , optimal transfers are given by

(2) $\begin{array}{c}{T}_i^{\ast }=\frac{1}{2}\left(x_i,-,x_j,+,\frac{1}{2{\rho }_i},-,\frac{1}{4{\mu }_i{\rho }_i}\right)\equiv T(x_i-x_j,{\rho }_i,{\mu }_i).\end{array}$

They increase in the payoff difference $x_i-x_j$ , which is exogenously given and fully determined by the combination of donor’s and partner’s project. They also increase with the weight given to the partner’s net payoff in subject i’s utility function, ${\mu }_i$ . An inequality averse subject who cares about his own income as much as about his partner’s income such that ${\mu }_i=\frac{1}{2}$ , will equalize his and his partner’s income by splitting the payoff difference equally independent of the degree of inequality aversion, ${\rho }_i$ . If, instead, he cares more about his own income, he will lower his transfer compared to this benchmark, and he will increase it if he cares more about his partner’s income. However, with increasing degree of inequality aversion ${\rho }_i$ , optimal transfers will approach equal splitting asymptotically independent of ${\mu }_i$ , either from above if ${\mu }_i>\frac{1}{2}$ or from below if ${\mu }_i<\frac{1}{2}$ . The results for optimal transfers are summarized in Table 2. Optimal transfers $T_i^{\ast }$ are unique except for the case where the subject i is not inequality averse ( ${\rho }_i=0$ ) and cares about his own income as much as about his partner’s income ( ${\mu }_i=\frac{1}{2}$ ).

Table 2 Optimal transfers as a function of ${\mu }_i$ and ${\rho }_i$

Share of partner’s income	Inequality aversion
	${\rho }_i=0$	${\rho }_i>0$
${\mu }_i=0$	$T_i^{\ast }=0$	$T_i^{\ast }=0$
${\mu }_i<0.5$	$T_i^{\ast }=0$	$T_i^{\ast }=0.5(x_i-x_j)-{\epsilon }_i$
${\mu }_i=0.5$	$T_i^{\ast }\in [0,x_i]$	$T_i^{\ast }=0.5(x_i-x_j)$
${\mu }_i>0.5$	$T_i^{\ast }=x_i$	$T_i^{\ast }=0.5(x_i-x_j)+{\epsilon }_i$

For ${\rho }_i>0$ and ${\mu }_i\ne 0.5$ we have ${\epsilon }_i>0$ with ${lim}_{\rho \to \infty }{\epsilon }_i=0$

It is plausible to assume that subjects’ degree of inequality aversion is exogenous to the project’s payoffs and the experimental treatments, which is in line with our data.Footnote ¹⁶ For a given payoff difference and degree of inequality aversion, optimal transfers will depend on the weight of the partner’s income in the donor’s utility function, ${\mu }_i$ . Therefore, we model differences in other-regarding preferences across projects and treatments in terms of ${\mu }_i$ . Table 3 summarizes all possible constellations that we observe in the experiment. Let $C_i=0$ indicate subjects in RANDOM and $C_i=1$ subjects in CHOICE. Moreover, let $R_i$ denote donor’s project where $R_i=0$ for the safe project and $R_i=1$ for the risky project. Correspondingly, we denote partner’s project by $R_j$ . The combination of donor’s and partner’s project determines payoff levels and payoff differences.

For each treatment $C_i$ there are three combinations of donor’s project $R_i$ and partner’s project $R_j$ where the partner is worse off that correspond to three different combinations of donor’s and partner’s payoffs $x_i$ and $x_j$ . Moreover, a unique feature of the RANDOM treatment is that, due to randomization of projects, some subjects will unavoidably end up in a project that they would not choose for themselves. Let $R_i^{\ast }$ denote donor’s preferred project. In CHOICE, all subjects chose their preferred project such that actual and preferred project always coincide ( $R_i=R_i^{\ast }$ ). Yet in RANDOM, there will always be a positive share of subjects where actual and preferred project differ ( $R_i\ne R_i^{\ast }$ ). As a result, there are nine distinct groups in Table 3 that may differ in their other-regarding preferences ${\mu }_i$ . Therefore, we model ${\mu }_i$ flexibly as a function of all of these features: ${\mu }_i\equiv \mu (x_i,x_j,C_i,R_i^{\ast })$ .

Table 3 Observed groups and optimal transfers when ${\mu }_i,{\rho }_i>0$

	Project of donor		Project of partner	Donor’s earnings	Partner’s earnings	Payoff difference
	Actual	Preferred
	$R_i$	$R_i^{\ast }$	$R_j$	$x_i$	$x_j$	$x_i-x_j$
RANDOM not in preferred project ( $C_i=0,R_i\ne R_i^{\ast }$ )
(1)	SAFE	RISKY	RISKY	500	0	500
(2)	RISKY	SAFE	SAFE	1000	500	500
(3)	RISKY	SAFE	RISKY	1000	0	1000
RANDOM in preferred project ( $C_i=0,R_i=R_i^{\ast }$ )
(4)	SAFE	SAFE	RISKY	500	0	500
(5)	RISKY	RISKY	SAFE	1000	500	500
(6)	RISKY	RISKY	RISKY	1000	0	1000
CHOICE always in preferred project ( $C_i=1,R_i=R_i^{\ast }$ )
(7)	SAFE	SAFE	RISKY	500	0	500
(8)	RISKY	RISKY	SAFE	1000	500	500
(9)	RISKY	RISKY	RISKY	1000	0	1000

For given inequality aversion ${\rho }_i>0$ , it follows from equation (2) that optimal transfers increase with the payoff difference, $x_i-x_j$ , and the partner’s share in the utility function, ${\mu }_i$ . Thus, differences in transfers that we measure in the experiment are informative about differences in ${\mu }_i$ . Carpenter et al. (Reference Carpenter, Verhoogen and Burks2005) and Korenok et al. (Reference Korenok, Millner and Razzolini2012) show that transfers increase with the donor’s endowment, suggesting that $\partial {\mu }_i/\partial x_i>0$ . Moreover, Korenok et al. (Reference Korenok, Millner and Razzolini2012) show that the willingness to share income depends negatively on beneficiary’s income, for example because donors perceive individuals with higher income as less needy, suggesting that $\partial {\mu }_i/\partial x_j<0$ .

With our experiment we aim to test whether CHOICE of risk exposure affects the willingness to give compared to RANDOM assignment of risk exposure, i.e. whether $\mu (x_i,x_j,1,R_i^{\ast })-\mu (x_i,x_j,0,R_i^{\ast })\ne 0$ . In particular, we hypothesize that this difference is negative. The notation already suggests that testing this hypothesis requires comparing subjects with the same preferred project. This is because the willingness to share income may also depend on risk preferences. For example, Cettolin and Riedl (Reference Cettolin and Riedl2017) and Cettolin et al. (Reference Cettolin and Tausch2017) show that risk preferences correlate with other-regarding preferences. Moreover, the subjects in RANDOM who end up in a project that they would not choose for themselves ( $R_i\ne R_i^{\ast }$ ) face a utility loss compared to assignment to their preferred project. Hence, they may find it optimal to lower transfers to compensate for this utility loss.

If transfers indeed depend on preferred projects, then comparing average transfers across treatments no longer provides a valid test of the hypothesis that CHOICE reduces transfers compared to RANDOM. This is because for subjects in RANDOM who are not in their preferred project there are no comparable subjects in CHOICE as all subjects are in their preferred project in CHOICE. We can exploit, though, that whether or not a subject in RANDOM ends up in his or her preferred project is random. As a result, we can compare transfers across treatments conditional on being in one’s preferred project to obtain a valid test of the hypothesis that CHOICE reduces transfers compared to RANDOM. This, however, requires eliciting subjects preferred project in RANDOM, which we do in our experiment.

Another advantage of conditioning on being in one’s preferred project is that it enables us to compare the effect of CHOICE for different combinations of donor’s and partner’s project. This, in turn, allows us to discriminate between different possible explanations for reduced transfers, as we discuss in the next section. Without the ability to align project preferences across treatments, comparing transfers of subjects with the same project across treatments is flawed by selection bias that results from the fact that subjects who chose a given project in CHOICE systematically differ from the subjects randomly assigned to the same project in RANDOM.

3.2 Hypotheses

Table 4 Hypotheses

Donor’s project		ALL	SAFE	RISKY	RISKY
Partner’s project		ALL	RISKY	SAFE	RISKY
Comparison of subjects in preferred vs. not in preferred project within RANDOM
H1	Assignment to unwanted projects in RANDOM matters for transfers	$\Delta T_i\ne 0$	$\Delta T_i\ne 0$	$\Delta T_i\ne 0$	$\Delta T_i\ne 0$
Comparison of subjects in CHOICE with subjects in preferred project in RANDOM
H2	CHOICE reduces transfers	$\Delta T_i<0$	–	–	–
H3	Attributions of responsibility	$\Delta T_i<0$	$\Delta T_i<0$	$\Delta T_i\ge 0$	$\Delta T_i<0$
H4	Ex-ante choice egalitarianism	$\Delta T_i<0$	$\Delta T_i<0$	$\Delta T_i<0$	$\Delta T_i<0$
H5	Ex-post choice egalitarianism	$\Delta T_i<0$	$\Delta T_i<0$	$\Delta T_i<0$	$\Delta T_i=0$

4.1 Did randomization work?

To obtain unbiased estimates we need to make sure that randomization into treatments and into projects within RANDOM created comparable groups. In Table 10 in online Appendix A, we report the means of all variables in our data by treatment and by project within treatment. Randomization of treatments worked very well. The majority of means is very similar. For only 2 out of 50 variables we find differences that are significant on the 10% level. The randomization of projects within RANDOM also succeeded in creating comparable groups with only 3 out of 50 differences in means being significant on the 10% level. For CHOICE, Table 10 in online Appendix A shows the selectivity of project choice. Subjects who choose the risky project have a much stronger preference for risk as expected, higher income, fewer other earners in the household, and they are more likely to be the household head, where the latter is explained by a higher share of males.

4.2 Do we correctly measure preferred projects in RANDOM?

Given that randomization worked very well, the most crucial part of our experiment is whether we correctly measure preferred projects for subjects in RANDOM. One major concern could be that subjects in RANDOM only answer a hypothetical question without any monetary consequences, whereas the subjects in CHOICE have to face the consequences of their choice. Another concern is that we elicit preferences ex post after transfer decisions have been made. There are several ways to assess whether there are any systematic differences in the preferences stated by the subjects in RANDOM compared to those in CHOICE. As a first check, we compare the share of subjects preferring the risky project in CHOICE and RANDOM. In CHOICE, 19.5% of subjects choose the risky project whereas in RANDOM 24.2% prefer it. The difference is not statistically significant with a p-value of .38 (see Table 5).

Table 5 Distribution of projects by treatment

	RANDOM				CHOICE		Auxiliary		Differences
	Actual		Preferred
	(1)		(2)		(3)		(4)		(3–2)	(4–2)
	N	%	N	%	N	%	N	%
Safe project	60	50.0	91	75.8	95	80.5	86	77.5	4.7	1.6
Risky project	60	50.0	29	24.2	23	19.5	25	22.5	(0.38)	(0.77)
Observations	120		120		118		111

P-values in parentheses

As a second check, we test whether subjects rationalize the project they have been assigned to in RANDOM when stating their preferred project ex post. To do so, we firstly, check for a statistically significant difference in the share being assigned to and preferring the risky project in RANDOM in line (1) of Table 6. The difference is 25.8 percentage points and highly statistically significant. Secondly, we test for a positive correlation between assigned and preferred project in RANDOM in line (2) of Table 6. The correlations are positive but small and not statistically significant with p-values around 30%. Hence, we cannot reject the hypothesis that assigned and preferred projects are uncorrelated in RANDOM.

Table 6 Relation between assigned and preferred projects in RANDOM

	Assigned	Preferred	Difference	P-value
(1) RISKY	0.500	0.242	0.258	0.000
(2) Correlation	Pearson	P-value	Spearman	P-value	Tetrachoric	P-value
	0.097	0.290	0.097	0.290	0.167	0.394

The third check compares the characteristics of the subjects preferring the same project across the two treatments. These should not differ systematically because subjects with the same characteristics should on average state the same preference in CHOICE as in RANDOM if preferences are measured correctly. In Table 10 in online Appendix A we report the means of all variables by chosen project in CHOICE and by preferred project in RANDOM, and we test for statistically significant differences between the two. For subjects who prefer the safe project, only 3 out of 50 differences in means are significant on the 10% level and 2 of them correspond to the ones for which we find small sample imbalances between RANDOM and CHOICE in general. For subjects who prefer the risky project, there are only 2 statistically significant differences in means on the 5% level which is to be expected with 50 variables tested. In Table 11 in online Appendix A we additionally report the same statistics conditional on assigned project in RANDOM. Specifically, we compare subjects with the safe project in CHOICE with the subgroup of subjects assigned to the safe project in RANDOM that also prefers the safe project and correspondingly for the risky project. These are the groups that will be used for the estimation. For both the safe and the risky project we only find one variable with a difference in means that is significant on the 10% level. Thus, we can conclude that subjects in CHOICE and RANDOM who state to prefer the same project do not differ systematically in the large number of observed drivers of project choice and willingness to give.

The fourth check makes use of the auxiliary experiment, where all subjects choose between the safe and the risky project as in CHOICE but without running the solidarity game. This addresses two possible concerns. Firstly, we can assess whether real monetary consequences matter for stated preferences. In the auxiliary experiment but not in RANDOM, project choice is incentivized as it determines subjects’ payoff from the experiment. Secondly, we can address the issue that subjects may choose projects strategically in CHOICE because they know that they have to make a decision on transfers to worse-off partners after having chosen a project. This is because the probability to face a partner who is worse off differs by project.Footnote ¹⁷ This would imply that project choice is determined by other factors than risk preferences in CHOICE. If we find no systematic differences between the distributions of stated preferences and the characteristics of subjects with the same stated preference between the auxiliary experiment and each of the two treatment groups in the main experiment, then this is supporting evidence for the validity of our experimental design.

In Table 12 in online Appendix A, we report the means of all variables for the subjects in RANDOM and in the auxiliary experiment, as well as in the subgroups that state to prefer the safe and the risky project, respectively. The subjects we sampled for the auxiliary experiment are somewhat better educated than the ones we sampled for the main experiment, which results in lower rates of unemployment and higher wealth, and which is correlated with ethnicity. Other than that, there are 3 more statistically significant means which do not show a systematic pattern, though. Apart from these small sample imbalances we do not find any systematic differences between subjects with the same stated preferences, though. The share of subjects preferring the risky project in the auxiliary experiment is 22%, which is 1.6 percentage points lower than in RANDOM with the difference being not statistically different from zero at a p-value of .77 (see Table 5). Differences in mean characteristics of safety choosers between the main and the auxiliary experiment only mirror the sample imbalances. The findings for risk takers are similar with only few statistically significant differences in means that mostly mirror the sample imbalances. There are only 2 out of 50 variables with significant difference that are not directly related to the sample imbalances. Thus, the auxiliary experiment does not provide any evidence for systematic differences in stated preferences to subjects in RANDOM, and for them, we do not find systematic differences compared to CHOICE. This, together with the other evidence presented above, makes us very confident that we correctly measure preferred projects for all subjects and that project choices reflect risk preferences.