Redistribution, Risk-taking and Implicit Punishment

Transcription

1 Redistribution, Risk-taking and Implicit Punishment Experimental Evidence from Risk-taking Decisions of Farmers in Ethiopia Karlijn Morsink August 2015 Please do not cite without the authors permission Abstract The functioning of welfare systems depends heavily on the willingness of individuals to help members of society who experience financial losses. Empirical evidence shows that some people are willing to redistribute some of their income to peers who experience losses as a result of bad luck. The willingness to assist others, however, is also influenced by the extent to which losses of peers are the result of their risk-taking behaviour. I use data from framed-field experiments with 1536 farmers from informal risk-sharing arrangements in rural Ethiopia to investigate how redistribution decisions of farmers are influenced by the decisions of their peers to reduce or increase risk. I explain these redistribution decisions with a model of social preferences in which individuals can have distributional preferences and implicitly punish their peers for reducing or increasing their risk. My results show that implicit punishment of peers for their decisions to increase or reduce risk ex ante can be explained by the risk preferences of the individual making redistribution decisions. Risk averse individuals are more likely to implicitly punish peers when they decide to refrain from reducing Centre for the Study of African Economies, Department of Economics, University of Oxford. karlijn.morsink@economics.ox.ac.uk. I am indebted to Tagel Gebrehiwot Gidey and Qhelile Nyathi for research assistance. I am grateful for comments and suggestions from Abhijit Banerjee, Abigail Barr, Veronika Bertram-Mueller, Stefano Caria, Jeffrey Carpenter, James Cox, Daniel Clarke, Avinash Dixit, Marcel Fafchamps, James Fenske, Eliana la Ferrara, Andrew Foster, Simon Gaechter, Glenn Harrison, Friederike Lenel, Sujoy Mukerji, Gosia Poplawska, Elisabet Rutström and seminar participants at the 15 AEA Annual Meeting, 2015 CSAE conference and CSAE, Nottingham and Nuffield seminars. This document is an output from research funding by the UK Department for International Development (DFID) as part of the iig, a research programme to study how to improve institutions for pro-poor growth in Africa and South-Asia. The views expressed are not necessarily those of DFID. Karlijn Morsink greatly acknowledges financial support from the British Academy, UK. 1

2 their risk or take on additional risk ex ante. Risk loving individuals implicitly punish peers for not taking ex ante opportunities to increase their risk exposure. Keywords: Social preferences, Risk-taking, Implicit Punishment, Framed-field experiments, Ethiopia JEL classification: C93 D03 D81 O17 2

3 1 Introduction The functioning of welfare systems depends heavily on the willingness of individuals to help members of society who experience financial losses. Empirical evidence shows that some people are willing to redistribute some of their own income to peers who experience losses as a result of misfortune (Charness and Rabin, 2002). However, it is largely unknown how the willingness of individuals to assist peers is influenced by ex-ante opportunities which allow them to increase or reduce risk. Understanding how the responsibility of peers for their own risk exposure and consequential losses influences the willingness of individuals to redistribute income is important in many settings. For instance, in publicly funded health-care systems in which individuals may choose unhealthy behaviors and expose themselves to risk, thereby generating a relatively larger part of the financial burden of the system. Another example is when governments choose to use public money to bail out banks that have taken an exorbitant risk. Finally, in informal support systems, such as mutuals, cooperatives and informal risk-sharing arrangements (IRSAs) where individuals may protect themselves against risk by purchasing formal insurance, which is the specific focus here. Understanding what drives people s redistribution decisions is relevant as policy increasingly focuses on economic inequality and redistribution of income. It is especially relevant in developing countries where a shift can be observed from local and informal redistribution to largerscale, formalized systems. I investigate how the willingness to redistribute income to peers with losses is influenced by the decisions of these peers to increase or reduce their risk exposure ex-ante. I do so by conducting framed-field experiments with 1536 farmers from pre-existing IR- SAs in rural Ethiopia. I develop a social preference model where individuals may behave conditionally altruistic based on their peers decision to increase or reduce risk. I then structurally estimate parameters of this model to investigate individuals motives to make transfers under different treatment conditions. I use data from Ethiopian farmers which are members of risk-sharing arrangements in which it is common for individuals to redistribute income after gains and losses from risk are realized. There is some evidence 3

4 from experimental economics that shows that willingness to redistribute income to anonymous others in laboratory experiments depends both on ex-post outcomes and on ex-ante opportunities to affect outcomes (Cappelen et al., 2013). In this paper I add to this literature by explaining why and how peers responsibility for losses affects individuals willingness to redistribute their own income and how this can be explained by individuals social preferences. I am particularly interested in studying these questions in a context where decisions about risk-taking, mitigating risk and redistribution are salient features of the relationship between individuals and occur naturally. I conduct a novel framed-field experiment with 1536 farmers from pre-existing IRSA s, known as Iddir, in rural Ethiopia. Farmers are randomly assigned to be farmer i or farmer j in a two-person group. In the benchmark game, farmers play dictator games after one farmer (j) experiences a shock. Farmer i is the dictator and makes a strategic transfer decision to j, conditional on j experiencing a loss, before the realization of the shock (Selten,1967). In the treatment games, j gets an offer to take up actuarially fair indemnity or index insurance before the shock. Indemnity insurance provides a pay-out to farmer j in case she experiences losses and hence reduces variance in outcomes. Index insurance provides a pay-out based on an index which is correlated, but imperfectly so, with farmer j s losses. Under the index insurance treatment farmer j may either pay a premium, experience losses but not receive a pay-out; this is known as downside basis risk. She may also pay a premium, not experience losses but still receive a pay-out; this is known as upside basis risk. As such, index insurance thus increases the expected variance in outcomes and hence increases the risk exposure of farmer j. Farmer i, the dictator, makes a strategic conditional transfer decision for the state where j experiences losses and decided to take insurance and for the state where j experiences losses and decided not to take insurance. Even though there are a number of important research questions relevant to understanding the willingness of individuals to redistribute income to peers who choose to increase or reduce risk, this particular research design enables me to focus on two specific questions. First, to what extent do individuals redistribute income when losses of peers are the result of bad luck, decisions to protect themselves, or decisions to take on 4

5 additional risk? I do this by comparing transfers of the dictator in the treatment games (where recipients get an offer to increase or reduce their risk ex-ante), to the dictators transfers in the benchmark game (where recipients do not get this ex-ante opportunity). Second, to what extent can these redistribution decisions be explained by the social preferences of individuals? I do this by developing a social preference model which allows me to distinguish individuals with self-interested preferences from individuals with pure distributional preferences over ex-post outcomes, and individuals who care about the exante decisions of peers and may implicitly punish their peers for these decisions. I then structurally estimate the parameters of this social preference model with a mixture model, which allows me to understand to what extent redistribution decisions that individuals make are motivated by self-interest, distributional preferences over ex-post outcomes, or if individuals also implicitly punish their peers ex-ante decisions to increase or decrease their exposure to risk. Finally, I investigate if the ex-ante decision of peers effects the dictators transfer decision based on a universal norm about risk-taking decisions or if the dictator evaluates it based on their own attitudes towards risk. I do this by conducting additional incentivized risk preference elicitation experiments and structurally estimating to what extent the parameters of the social preference model can be explained by the dictators risk preferences as a covariate. I show that the willingness of individuals to redistribute income to peers with losses is influenced by the ex-ante decision of their peers to increase or decrease their risk exposure. If peers reduce risk exposure by taking indemnity insurance ex-ante, transfers by the dictator ex-post are less than when peers don t get an ex-ante opportunity to protect themselves (benchmark). This can be explained by individuals being more likely to behave according to self-interested preferences when losses of their peers are protected by insurance, suggesting crowding out of redistribution. If peers increase their risk exposure ex-ante by taking index-insurance but end up experiencing severe losses, individuals do redistribute some of their own income but significantly less than when losses are purely caused my misfortune. This significant reduction in the dictators ex-post transfers can be explained by risk averse dictators implicitly punishing recipients for increasing their risk exposure ex-ante. As such implicit punishment is not driven by a universal norm 5

6 which dictates appropriate risk-taking behavior but rather by an individual norm, based on the risk preferences of the dictator, e.g. if individuals are risk averse (risk-loving) they implicitly punish peers for increasing (decreasing) their risk exposure. This research contributes to three strands of literature. First, I contribute to a literature on redistribution norms and beliefs about people s responsibility for economic losses and successes (Harsanyi, 1955; Konow, 2000; Rutström and Williams, 2000; Krawczyk, 2010; Cappelen et al., 2007; 2013). Most of this literature has focused on people s willingness to redistribute income to peers when their income is a consequence of their own effort rather than windfall income. I complement this literature by investigating a new dimension, willingness to redistribute income to peers when peers have ex-ante opportunities to increase or decrease the risk they are exposed to. Second, I contribute to a closely related literature on factors that shape social preferences outside of the experimental laboratory such as effort in the workplace or ethnic and hierarchical identities (Bandiera, Barankay and Rasul, 2005; Chen and Li, 2009; Jakiela, 2011; Kosfeld and Rustagi, 2015). I add to this literature by investigating the effect of risk-taking choices on redistribution decisions of farmers that are members of Iddir in Ethiopia. Iddir are informal or semi-formal risk-sharing groups of approximately 85 members in which members redistribute income to other members in case they experience losses (Pankhurst, 2000). Iddir typically insure against funeral expenses or agricultural losses. It is common practice in the Iddir in my sample for a committee of Iddir-members to monitor other members effort and agricultural risk mitigating activities. As such decisions to increase or decrease risk exposure and redistribution are salient features of the lives of Iddir-members. I further exploit this characteristic of Iddirs in my research design by anonymously teaming-up half of the dictators in my sample with a recipient that is a member of their own Iddir and half of the dictators with a anonymous other. This allows me to compare the extent to which social preferences differ according to the identity of recipients. Finally, this research contributes to a literature on crowding-out of solidarity and informal institutions when formal insurance is introduced (Attanasio and Rios-Rull, 2000; Albaran and Attanasio, 2003; Mobarak and Rosenzweig, 2012; DeJanvry, Dequiedt and 6

7 Sadoulet, 2013; Dercon et al., 2014). This literature has demonstrated that, in dynamic settings allowing for weak reciprocity, indemnity insurance can crowd out informal risksharing while index-insurance has the potential for complementing informal risk-sharing. The theoretical foundations of this literature are based on models assuming agents have self-interested preferences. I add to this literature by showing that, even in one-shot settings, the introduction of both indemnity and index insurance to people in IRSAs can crowd out redistribution if individuals implicitly punish their peers for increasing or decreasing risk exposure. The paper is organized as follows. In Section 2 I present the sample and the experimental design and in Section 3 I present the results of the effects of treatments on transfers. In Section 4 I proceed by presenting the conceptual framework with the social preference model and the predictions of transfer decisions. In Section 5 I present the results of the structural estimation of the social preferences parameters and discuss how social preferences explain the transfers observed in Section 3. In Section 6 I conclude. 2 Experimental Design To construct the sample I recruited 1536 farmers from pre-existing Iddir in rural Ethiopia, out of which 1152 farmers were from 16 focal Iddir and 384 farmers were from a random selection of non-focal Iddir. The distinction between focal and non-focal Iddir allowed variation as to whether farmers were teamed up in two-person groups with another farmer from their own IRSA or with a completely anonymous other farmer, not from their own IRSA. Out of the total sample two-thirds of the 1152 farmers were assigned to be farmer i and one-third were assigned to be farmer j while all 384 farmers from non-focal Iddir were assigned to be farmer j. Farmers i were then randomly assigned to farmers j, leading to 384 two-person groups consisting of members from the same pre-existing risksharing group and 384 two-person groups consisting of members from a different risksharing group. The 16 Iddir were randomly selected from seven villages spanning three administrative regions in Tigray, one of the Northern provinces of Ethiopia and comprised of between 75 and 150 farmers. Four sessions with 24 farmers per session were played per 7

8 randomly selected Iddir. In total 64 different sessions were played. In each session eight farmers i were anonymously teamed up with a farmer j from their own Iddir and eight farmers i were teamed up with a farmer j who was not from their own Iddir. Farmers were seated in private portable cubicles for a maximum period of three hours. During the recruitment phase farmers were informed that they were eligible to participate in a survey and an experiment in which they would be teamed up with another farmer and would be asked to make decisions about risk-taking and transfers. They were informed that they would be randomly matched with either a farmer from their own Iddir or an anonymous other farmer. Even if the farmer they were teamed-up with was from their own Iddir, the identity of the farmer was never revealed and farmers remained anonymous during and after the game. They were informed that they would receive a base-payment of 50 Ethiopian Birr (50 ETB; 2.5 USD) irrespective of the outcomes of their own or other farmers decisions in the experiments. They were also informed that they would be able to win an additional 0 to 110 ETB depending on the decisions they and others would make in the games. Farmers were also informed that the total participation time including the experiment, the survey and the payment would not be more than three hours. The incentives in the experiments reflected a daily wage for unskilled labour, ranging between 50 and 150 ETB during the timing of the experiments. 2.1 The experiments Farmers were informed that they were randomly assigned to play a role of dictator, which I call farmer i, and receiver, which I call farmer j. They were informed that the income of farmer j was exposed to risk. In the experiment farmer i and j have initial wealth of 0 ETB. Farmer i earns income of 100 ETB with certainty. Farmer j s income is subject to a shock {S j = 0, 1} with binary loss. If j experiences no loss her income takes a value of 100 ETB, if j experiences a loss her income takes a value of 28 ETB. The probability of j losing income is determined by the realization of a first-stage shock {A j = 0, 1} in period t = 1. The first-stage shock A takes a value of 1 with probability one-fourth and value of 0 with probability three-fourths. The state of A determines the probability of the state-dependent shock to j s income, S j. In period t = 2 the loss to j s income is realized. 8

9 If A = 0 the probability of loss to j s income is one-third and if A = 1 the probability of loss is two-thirds. If j experiences a loss she receives an income of 28 ETB and if she has no loss she receives an income of 100 ETB. The expected outcome of the experiment, µ, is 70 ETB and the variance of outcomes, σ 2, is 1260 ETB. The shocks, probabilities and payoffs of farmer i, x i, and farmer j, x j are displayed in Figure 1. Figure 1: Payoffs in autarky The experiments were explained to farmers by making reference to agricultural production. The realization of the first-stage shock was explained in terms of local weather conditions. In the game this was simulated by a draw from an envelope which contained four tokens, three blue tokens, representing rainfall and one yellow token representing drought. Losses to income were explained in terms of crop losses. The conditional probabilities of losses to income were simulated by two different colored dice (red and white) with different probabilities of second-stage losses, simulating the conditionality on the first-stage shock. If a blue token was drawn (A = 0) farmers would play the red dice (p = 1/3) which had four blue sides, representing no loss to income (100 ETB), and two yellow sides, representing loss to income (28 ETB). If a yellow token was drawn (A = 1) farmers would play the white dice (p = 2/3) which had two blue sides and four yellow sides. Before starting the actual game farmers received a central explanation and an individual explanation by their enumerator with a schematic representation of the game tree, 9

10 Figure 2, which was used to show farmers the possible realizations of shocks and payoffs in the game. Before actual play farmers answered ten questions about the game to test their understanding. Figure 2: Game tree explained to farmers Farmer i0 s potential payoffs are presented in rows; farmer j 0 s potential payoffs in columns The benchmark treatment In the benchmark game, farmer i makes a strategic conditional transfer decision in the case j experiences losses, before shocks are realized. In period t = 3, after the shocks are realized, the actual transfer τ from i to j is implemented leading to an income of xj + τ for farmer j and income of xi τ for farmer i. The game tree is shown in Figure 3. 10

11 Figure 3: Benchmark treatment The indemnity insurance treatment In the indemnity insurance treatment, before the realization of the first-stage shock, farmer j receives a private offer to take up actuarially fair indemnity insurance at t = 0. The insurance can be characterized as: m Im = 5/12 P Im (1) where m Im is the insurance premium which is set at 30 ETB and P Im is the pay out, which is set at 72 ETB. The expected outcome, µ Im, is 70 ETB and the expected variance of outcomes, (σ 2 ) Im, is 0 ETB. As such, the indemnity insurance experiment has the same expected outcome as the benchmark experiment but reduces the variance of j s outcomes to zero. The endowment which is given to j before the experiment starts is chosen such that subjects with the insurance treatment have the same expected income as subjects in the benchmark treatment if they choose not to take up insurance. The endowment provided reflects the insurance premium of 30 ETB. Care was taken to explain to farmers that if they chose to take up insurance, the premium would be deducted from their income, while if they chose not to take up the insurance the premium would not be deducted. Farmer j s insurance decisions were made privately. Before S j is realized, and 11

12 without knowing j s insurance decision, farmer i makes a conditional strategic decision about transfers to j. The conditions are the state in which farmer j experiences a loss and decided to take insurance and the state in which farmer j experiences a loss and decided not to take insurance. After the realization of the loss to j s income actual transfers are made based on the actual insurance decision by j, the relevant strategic decision by i and the actual realization of the shock to j s income. The game tree for the indemnity insurance treatment is presented in Figure 4. Figure 4: Indemnity insurance offer to farmer j The index insurance treatment In the index insurance treatment, before the realization of the first-stage shock, farmer j receives a private offer to take up actuarially fair index insurance at t = 0. The insurance can be characterized as: m Ix = 1/4 P Ix (2) where m Ix is the insurance premium which is set at 18 ETB and P Ix is the pay out when A = 1 and is set at 72 ETB. The expected outcomes, µ Ix, is 70 ETB and the expected 12

13 variance of outcomes, (σ 2 ) Ix, is 1584 ETB. As such the index insurance experiment has the same expected outcome as the other two experiments but increases the variance relative to the benchmark experiment where farmer j has no option to take insurance. The imperfect correlation of the index with actual losses implies that where there is no first-stage shock but farmer j has paid the insurance premium (-18 ETB) and experiences a loss to income (28 ETB) she is worse off (10 ETB) than she would have been if she would have not purchased the insurance (28 ETB). This state is the downside basis risk state and occurs with a probability of three-twelfth. There is, however, also a probability that there is a first-stage shock and farmer j has paid the insurance premium (-18ETB) and experiences no loss to income (100 ETB) but still receives the claim payment. In that case she is better off than she would have been if she had not purchased the insurance (154 ETB). This state is called upside basis risk and occurs with a probability of 1/12. The game tree for the index insurance treatment is presented in Figure 5. Figure 5: Index insurance offer to farmer j 13

14 2.1.4 The within-subject treatment In the within-subject treatment, and again before the realization of the first-stage shock, farmer j received a private lottery which randomly assigned them to receive either no insurance offer (benchmark treatment), an indemnity insurance offer, or an index insurance offer. If farmer j received an insurance offer she decided in private, at t = 0, if she wanted to accept or reject the offer. When asked to make the conditional strategic transfer decision, farmer i was asked to make transfers decisions conditional on j experiencing losses under five conditions: 1. j was not offered insurance; 2. j accepted the indemnity insurance offer; 3. j rejected the indemnity insurance offer; 4. j accepted the index insurance offer; 5. j rejected the index insurance offer. The payoffs are determined based on j s actual draw and decision, the realization of the shock and the relevant conditional strategic transfer decision by i. 2.2 Risk preference elicitation Risk preferences were elicited to understand to what extent the attitudes towards risk of individuals effect their evaluation of their peers ex-ante decisions to increase or decrease risk, and consequently their redistribution decisions. Risk preferences were elicited by means of different multiple price lists (MPL) and a Binswanger ordered lottery selection (OLS-BW). In the OLS-BW respondents made one decision between six prospects that differed in terms of the average and variance of the pay out (Binswanger, 1980). In all lotteries, the respondent had the chance of winning with a fixed probability of 50%. The first lottery did not involve any risk while risk increased over the remaining lotteries. The respondent s choice directly determined her level of risk aversion. In the MPL experiment respondents repeatedly made choices between a safe amount and a lottery within six price 14

15 lists which represented different risk environments (e.g. Bruhin et al. 2010, Callen et al. 2014). The lotteries differed between price lists in terms of winning and losing, and in terms of the chances to win or to lose (25%, 50%, and 75%). Within the 17 decision rows of a price list, the prospect stays the same, while the safe amount is increasing, starting with the lowest amount of the lottery up to the highest. With increasingly safe amounts, based on their attitudes to risk respondents will change their decision at some point in the price list and prefer the safe amount over the prospect. An individual s switching point is used to calculate the certain equivalent (CE) as a measure of the respondents risk preferences. In total, our participants were required to answer 102 binary questions within the six price lists. For the risk preference elicitation farmers were informed that they would receive a base-payment of 50 ETB irrespective of the outcomes of the experiment. They were also informed that they would be able to win an additional 0 to 160 ETB depending on the decisions in the experiment. If a choice with the possibility of losing 160 ETB was drawn, the respondent was given en endowment of 160 ETB before making decisions within this price list. Losses were then decimated from the respondents endowment. The final pay out for the redistribution and risk elicitation experiments was determined through a random lottery after all experiments were played, to avoid wealth or portfolio effects. First, there was a random draw to determine if the risk preference experiment or the redistribution experiment was paid. In case the risk preference experiment was drawn, another draw determined if the pay out was based on one of the six MPLs or the OLS-BW. In case the MPL was selected, an additional two draws determined which of the 17 rows of which price list was paid. Finally, if the participant had chosen the lottery over the safe amount the outcome of the lottery was drawn. The payment was done privately. The payment process was demonstrated to the respondents before the experiments started. 3 Effects of treatments on transfers Figure 6 shows the average levels of transfers i makes to j when j receives an insurance offer as compared to the benchmark no insurance offer treatment for the within-subject 15

16 comparison conducted in treatment 4. The within-subject treatment allows us to control for individual heterogeneity in transfer behavior. Average transfers when no insurance offer is made to j and j experiences a loss are 15 ETB out of the 100 ETB endowment i receives. When j is offered indemnity insurance i transfers less on average (5 ETB). When j takes up index insurance i does not transfer less on average (14 ETB) as compared to the situation where j receives no insurance offer. Figure 7 presents average transfers separated by the state of the first-stage shock {A j = 0, 1}. Average transfers are lower with and without the first-stage shock when j decides to take indemnity insurance (payoff j=70 ETB). Even though there was no difference in the aggregate between average transfers when j was not offered insurance as compared to when j took index insurance in Figure 6, transfers when j takes index insurance are lower in case of a first-stage shock (j receives claim payment, payoff j=82 ETB) and slightly higher (2.17 ETB) in case of no first-stage shock (basis risk, j receives no claim payment, payoff j=10 ETB). The blue bars in Figure 8 present the same transfer data as those presented in Figure 7. The maroon bars present the payoff to j before transfers. On average, transfers seem to decrease when the payoff to j increases. One exception is the case of the index insurance treatment when there is no first-stage shock, which is the case of basis risk. In this state j paid a premium, experienced losses but did not receive an index insurance claim payment. Despite the lower pay-off to j in comparison to the No insurance treatment, transfers by i, on average, do hardly increase. This suggests that i s do not compensate j s more when they experience basis risk. Figure 9 presents a within-subject comparison of the level of transfers when j decides not to take up insurance. In all cases the gross payoff to j before transfers is the same (28 ETB). Despite this, i significantly reduces transfers when j decides not to take indemnity insurance and in the case when j decides not to take index insurance. 16

17 Figure 6: Comparison of average transfers per treatment if j takes insurance Transfers i to j (j insured) within subject comparison Transfers (ETB) No insurance Index insurance Indemnity insurance Confidence:.99, **.95, *.90 Figure 7: Average transfers if j takes insurance by first-stage shock Transfers i to j (j insured) within subject comparison Transfers (ETB) ** first stage shock No insurance Index no first stage shock Indemnity Confidence:.99, **.95, *.90 17

18 Figure 8: Gross payoffs and transfers when j takes insurance Transfers i to j (j insured) within subject comparison first stage shock no first stage shock Transfers (ETB) No insurance Indemnity Index No insurance Indemnity Index Blue bars: transfers from i to j; Maroon bars: payoff j before i makes transfers Figure 9: Mean transfers if j takes no insurance, by first-stage shock Tranfers i to j (j NOT insured) within subject comparison Transfers (ETB) first stage shock No insurance Index no first stage shock Indemnity Confidence:.99, **.95, *.90 18

19 Figure 18 in Appendix C presents a balance test based on OLS regressions of relevant household and farm characteristics to check if the randomization process has led to any unbalance of observables between the different treatment arms. Figure 18 shows that there are no significant differences between the treatments. Appendix E presents the histograms and kernel densities of the transfers for the different treatments. The normal Gaussian distribution is not an attractive assumption for the distributions underlying transfers. By design transfers are constrained to lie in an interval between zero and 100 ETB. Looking at the raw data shows a spike at zero, indicating that some individuals gravitate to a contribution level of zero. The statistical analysis I conduct therefore considers the data-generating process by which respondents decide to contribute zero or a positive amount as a separate process from the data-generating process where respondents decide on the amount they transfer (Mullahy, 1986; Cameron and Trivedi, 1998; Botelho et al., 2009). Appendix F presents tables for the transfer data when binned at intervals of 5 and 10. From these tables it appears that a truncated-at-zero beta interval regression is appropriate for the estimation of the positives. The likelihood function for the overall hurdle model is constructed as the product of two likelihoods. The first component is the likelihood that the subject contributed zero or a positive amount and uses a probit specification. The second component is the likelihood that the subject contributed a positive amount, conditional on them making a positive contribution. Let Φ 1 (α 1 x) represent the probability that the contribution is positive, and let f 2 (x, α 2, β) = {Γ(α 2 + β)/[γ(α 2 )Γ(β)]}x α2 1 (1 x) β 1 be the conditional distribution of the positive contribution, following Ferrari and Cribari-Neto (2004), where α 2 > 0 and 0 x 1. Let Φ 2 (x, α 2, β) denote the cumulative beta distribution. This re-parametrization of the beta distribution implies parameters µ and ϕ where µ = α 2 /(α 2 +β) and ϕ = α 2 +β, so that α 2 = µϕ and β = (1 µ)ϕ. The advantage of this re-parametrization is that we can directly specify the mean and variance of the dependent variable x as E(x) = µ and V ar(x) = µ(1 µ)/(1 + ϕ). The general form of the hurdle model likelihood function is 19

20 then L = {1 Φ 1 (α 1 + βx)} {Φ 1 (α 1 + βx)} i Ω 0 i Ω 1 {f 2 {Γ(α 2 + β)/[γ(α 2 )Γ(β)]}x α2 1 (1 x) β 1 } i Ω 1 (3) where Ω 0 = {i y i = 0} denotes the zero contributions and Ω 1 = {i y i 0} denotes the positive contribution, and Ω 0 Ω 1 = {1, 2,..., N}. Taking the natural logarithm of both sides and rearranging terms, we see that the log likelihood can be written as ln(l) = ln{1 Φ 1 (α 1 + βx)} + ln{φ 1 (α 1 + βx)} i Ω 0 i Ω 1 + lnf 2 {Γ(α 2 + β)/[γ(α 2 )Γ(β)]}x α2 1 (1 x) β 1 } i Ω 1 (4) Since the likelihood function is separable with respect to the parameter vectors β 1 and β 2, the log likelihood function can always be written as the sum of the log likelihoods from two separate models: a binomial probability model and a beta interval regression. Table 1 presents the parameter estimates from the maximum likelihood estimation of the Hurdle model. 1 When comparing transfers in the situations where j s have decided to reduce their risk (Indem) to the transfers in the benchmark no insurance treatment, the negative signs and significance levels of α 1 show that i s are significantly less likely to transfer to j s who decide to reduce their risk. The µ and ϕ parameters show that, conditional on making transfers, they also transfer significantly less. The fact that there are no differences in this general picture when comparing column (1a), (1b) and (1c) shows that these results are independent of the prevalence of the first-stage shock. When comparing the estimated parameters for the transfers in the situation where j s have decided to increase their risk (Index) to the transfers in the benchmark no insurance treatment, the parameters in the columns (1a), (1b), and (1c) do not show 1 Table 8, 9, and 10 in Appendix A present OLS regressions of transfers, Probit regressions of the probability of transferring (which is similar to the α 1 parameter in the Hurdle model) and OLS regressions conditional on making transfers respectively (which is comparable to the conditional beta interval regression, assuming a beta distribution.) 20

21 the same picture. When j s have decided to increase their risk the negative sign of the α 1 s shows that i s are significantly less likely to make transfers in all states but that the decrease in likelihood is especially high in the situation where there is no downside basis risk. Conditional on making transfers the negative signs of the µ and ϕ in column (1b) show that i s transfer significantly less to j s in the case of a first-stage shock. However, the positive and significant sign of µ and the positive sign of ϕ show that in the cases of downside basis risk transfers are significantly higher. When comparing transfers in the situations where j s have decided to not reduce their risk (Indem) after an ex-ante opportunity to do so to transfers in the benchmark no insurance treatment, the negative signs of α 1 show that i s are significantly less likely to transfer to j s who decide to not reduce their risk. This effect is only significant and substantial in the cases where there is no first-stage shock. The non-significance of the µ and ϕ in both column (2a) and (2b) shows that there are no significant differences in the level of transfers. When comparing the estimated parameters for the transfers in the situation where j s have decided to not increase their risk (Index) to the transfers in the benchmark no insurance treatment the picture is slightly different. The substantially negative and significant signs for α 1 in column (2a) and (2b) show that i s are significantly less likely to transfer to j s. Conditional on making transfers, the negative and significant µ also shows that i s transfer significantly less. 4 Conceptual framework Lisa: Assumptions: 1. Empathetic preferences 2. No redistribution when there are no losses Check paper: neither selfish nor exploited Cox: Extension of revealed altruism: First-mover chooses a stochastic set (in stead of feasible set) In the baseline the first mover can make a change in the endowed set that the dictator gets: - Maximum feasible payoff is the baseline - Maximum feasible payoff in the indemnity case 21

22 Table 1: Maximum likelihood estimates of the Hurdle model for transfers Transfer (j insured) Transfer (j NOT insured) (1a) (1b) (1c) (2a) (2b) Shock No shock Shock No Shock Indem vs. no ins α (.14) (.06) (.18) (.21) (.19) µ (.06) (.10) (.08) (.10) (.07) ϕ ** (.15) (.24) (.19) (.22) (.17) joint p no Index vs. no ins α * (.14) (.22) (.19) (.22) (.18) µ * -.17** (.06) (.12) (.07) (.11) (.07) ϕ (.26) (.16) joint p ** Index vs. indem α (.10) (.16) (.12) (.17) (.12) µ ** -.27 (.06) (.11) (.07) (.10) (.07) ϕ.49.46* ** (.13) (.24) (.16) (.22) (.15) joint p * N Note: Hurdle; α 1 estimate of odds-ratio for probit; µ and ϕ estimates for beta interval regression; Confidence:.99, **.95, *.90; Robust standard errors with clustering at respondent level reported in parentheses; (1a): Full sample; (1b): Sample first-stage shock; (1c): Sample no first-stage shock; (2a): Sample first-stage shock; (2b) Sample no first-stage shock 22

23 I investigate transfer motives based on a simple conceptual model of social preferences in two-person games based on Charness and Rabin (2002) s social preferences model. Let i, j denote two individuals in a two-person group and x = (x i, x j ) denote an allocation of wealth out of some set X of feasible allocations. X i is the monetary payoff of person i. The self-interest hypothesis states that the utility of individual i only depends on x i : u(x i ) = x i (5) Individual i has social preferences if for any given x i person i s utility is affected by variations of x j, where i j. Let s assume i s preferences are given by: U i (x j, x i ) = x j (ρ r + σ s + θ q) x i (1 ρ r σ s θ q) (6) where r = 1 if x i > x j, and r = 0 otherwise; s = 1 if x i < x j, and s = 0 otherwise; q = 1 if, in i s perception, j has misbehaved, and q = 0 otherwise. The parameters ρ, σ and θ reflect different social preferences. In this model I assume that the marginal rate of substitution between i s and j s outcomes, x j and x i, is not constant (as opposed to Charness and Rabin, 2002) but instead is characterized by the convex indifference curves of Cobb-Douglas preferences. The negative substitution effect between own and others income is especially relevant in the context of this study where participants are poor farmers and we can assume that there is an income effect affecting their decision to trade-off own and others income. Equation (6) states that i s utility is a product of her own material payoff and j s material payoff, where the weight i places on j s payoff is a result of i s distributional preferences and i s perception of the intention of j s behavior. The parameters ρ and σ capture a range of distributional preferences that depend on ex post outcomes. Social welfare preferences state that 1 ρ σ > 0 (Andreoni and Miller, 2002; Yaari and Bar Hillel, 1984). Competitive preferences state that σ ρ 0. Inequality aversion states that σ < 0 < ρ < 1 (Loewenstein et al., 1989; 23

24 Bolton and Ockenfels, 2000; Fehr and Schmidt, 1999). The parameter θ models implicit punishment, which assumes people are motivated to treat those who are behaving fair better than those who are not (Rabin, 1993; Segal and Sobel, 2004; Dufwenberg and Kirchsteiger, 2004; Falk and Fischbacher, 2006). These models assume that i s values for the extent to which they weigh j s welfare vary with i s perception of player j s intentions. Charness and Rabin (2002) model implicit punishment by assuming that θ > 0 if, in i s perception, j has engaged in unfair behavior. This essentially assumes that i lowers ρ by amount θ. It is important to emphasize that it is not the expectation of future material benefits that drives this form of reciprocity. Implicit punishment as defined above differs fundamentally from behavior in repeated interactions that is motivated by future material benefits. Therefore, implicit punishment in one-shot interactions is often called strong reciprocity in contrast to weak reciprocity that is motivated by long-term self-interest in repeated interactions Fehr and Schmidt (2006:662). 4.1 Transfers based on social preferences Farmer i s and j s net payoff in the experiments after transfers from i to j, τ, is given by x i and x j respectively. Gross payoffs before transfers are given by p i and p j respectively. Equation (6) can the be rewritten into: U i (x j, x i ) = (p j + τ) (ρ r + σ s + θ q) (p i τ) (1 ρ r σ s θ q) (7) It follows from equation (7) that log U i = (ρ r + σ s + θ q) log(p j +τ)+(1 ρ r σ s θ q) log(p i τ) (8) U i τ = (ρ r + σ s + θ q) p j + τ (1 ρ r σ s θ q) p i τ (9) τ = (ρ r + σ s + θ q)p i (1 ρ r σ s θ q)p j (10) 24

25 where r = 1 if x i > x j, and r = 0 otherwise; s = 1 if x i < x j, and s = 0 otherwise; q = 1 if, in i s perception, j has misbehaved, and q = 0 otherwise. If x i > x j, p i = 100, and 10 p j 82 in the states where i can transfer and we assume pure distributional preferences τ ρ = p i + p j and τ p j = ρ 1. This implies that transfers are strictly linearly increasing in ρ and strictly linearly decreasing in p j for all distributional preferences 2. If we assume that i has distributional preferences and in i s perception j has misbehaved, τ p j are strictly decreasing in p j and in θ. = ρ θ 1 and τ θ = p i p j, implying that transfers If x i < x j, p i = 100, and 10 p j 82 and we assume pure distributional preferences, τ σ = p i + p j and τ p j = σ. This implies that transfers are strictly linearly increasing in σ 3 for all distributional preferences and transfers are strictly increasing in p j for social welfare preferences and strictly decreasing in p j for competitive and inequality averse preferences. If we assume that i has distributional preferences and in i s perception j has misbehaved, τ p j = σ θ and τ θ = p i p j. In the experiments p i > p j so transfers are always increasing in θ while transfers will be always decreasing in p j for competitive and inequality averse preferences but can be either increasing or decreasing, depending on the values of σ and θ, for social welfare preferences 4 Cox and Sadiraj s (2005) model for distributional preferences result in the same predictions for τ p j. 2 For pure distributional preferences and p j = 10; τ[0, 45] this means that for 0.09 ρ 0.5 U i = 0 τ is the global maximum for 0 < τ < 45. For ρ < 0.09 it is τ = 0; for p j = 28; τ[0, 36], this means that for 0.22 ρ 0.5 U i = 0 is the global maximum for 0 < τ < 36. For ρ < 0.22 it is τ = 0 ; for pj = 70, this τ means that for 0.41 ρ 0.5 U i = 0 is the global maximum for 0 < τ < 15. For ρ < 0.41 it is τ = 0; for τ p j = 82, this means that for 0.45 ρ 0.5 U i = 0 is the global maximum for 0 < τ < 15. For ρ < 0.45 τ it is τ = 0. 3 Intuition: For (p j + τ) σ (p i τ) σ ) an increase in σ always makes the left factor increase more than the right factor decreases so an increase in σ always leads to an increase in τ 4 In the data there are no individuals which transfer such that x i < x j in all two (TNoIns,TGEN); three (TGEN, TCY, TCN; or TGEN, TRY, TRN); or six (TNoIns, TGEN, TCY, TCN, TRY, TRN) treatment variations. In TNoIns (0), TGEN (2), TCN (1), TCY (28), TRN (2), TRY (52, 21 2). Will attribute these to error, especially because difference in TCY is 30 ETB and TRY is 18 ETB. Three ways to deal with this are: 1. Let the tremble, Luce or Fechner errors soak these up; 2. Truncate the transfers such that x i = x j; 3. Delete these respondents from the estimation. 25

26 4.2 Predictions about implicit punishment When individuals make decisions about redistributing income to others they do not necessarily apply distributional preferences uniformly. Rather in their choices to apply distributional preferences they may incorporate others intentions, actions or perceptions thereof (Rabin, 1993; Fehr and Gaechter, 2000; Dufwenberg and Kirchsteiger, 2004; Cappelen et al., 2007; Cox, Friedman and Gjerstad, 2007; Cox, Friedman and Sadiraj, 2008; Cox and Sadiraj, 2010). In these How are intentions, actions or perceptions evaluated? Based on norms? Look at the revealed altruims paper Cox: Extension of revealed altruism: First-mover chooses a stochastic set (in stead of feasible set) In the baseline the first mover can make a change in the endowed set that the dictator gets: - Maximum feasible payoff is the baseline - Maximum feasible payoff in the indemnity case One potential explanation for i to implicitly punish j is that i has social preferences and i beliefs that j knows that i has social preferences and i has beliefs about j s risk preferences from which i may infer if j, by purchasing insurance, is taking a kind or unkind action (Rabin, 1993) Cox et al., 2007; 2008). If i beliefs j is risk averse and j purchases actuarially fair indemnity insurance i will be neutral about her effect on player j and will transfer based on pure distributional preferences. However, if i believes that player j is risk averse but player j does not take actuarially fair indemnity insurance then i believes that j is taking an action to reduce her own utility in order to hurt i. Farmer i may then perceive j s action as unkind, leading to a relatively lower transfer to j when j experiences a loss. In the same way, if player i believes j is risk averse i may reciprocate j by reducing transfers if j takes index insurance and experiences losses. Based on i s belief about j s risk preferences i may also be able to infer to what extent j is being kind or unkind. If j is perceived by i as being highly risk averse j s decision to not take indemnity insurance may be perceived by i as more unkind than when i perceives j to be moderately risk averse. An action which is perceived by i as relatively less kind may also be reciprocated by a relatively less kind action translated into a higher θ and hence a relatively lower transfer from i to j. Another potential explanation for i to apply reciprocal-fairness motives when making 26

27 transfer decisions is that within the informal risk-sharing arrangements that i and j are a part of there is a norm about responsibility for risk-taking which is known by both i and j. If j assumes that i has social preferences and j makes a decision which deviates from this norm i perceives j s behavior as unfair and punishes j by reducing transfers. For example, if there is a shared norm between i and j that individuals should choose strategies which reduce risk and j takes index insurance i may interpret j s behavior as a deviation from their shared norm and may punish j by reducing transfers. 5 Behaviour consistent with social preferences As set out in the conceptual framework several latent decision-making processes may explain i s observed choices in the experiments: self-interested preferences, pure distributional preferences and distributional preferences with implicit punishment. The latter of these preferences can only explain i s behavior in the indemnity and index insurance treatments because these are preceded by a decision of j to either increase or decrease her risk exposure. To this action i may respond by implicit punishment. I will use a finite mixture model to estimate the parameters of each decision process while simultaneously estimating the probability that each process applies to the sample, overall, and in each treatment variation (Harrison and Rutström, 2008; Bruhin, Fehr-Dudda and Epper, 2010; Conte, Hey and Moffatt, 2011). To do so I estimate a grand likelihood function that allows each theory to co-exist and have different weights. Harrison and Rustrom, 2008: Mixture models have a long pedigree in statistics, stretching back to Pearson (1894). Modern surveys of the development of mixture models are provided by Titterington et al. (1985), Everitt (1996) and McLachlan and Peel (2000). Mixture models are also virtually identical to latent class models used in many areas of statistics, marketing and econometrics, even though the applications often make them seem quite different (e.g., Goodman 1974a, 1974b; Vermunt and Magidson 2003). In experimental economics, El-Gamal and Grether (1995) estimate a finite mixture model of Bayesian updating behavior, and contrast it to a related approach in which individual subject behavior is classified completely as one type of the other. Stahl and Wilson (1995) 27

28 develop a finite mixture model to explain behavior in a normal form game, differentiating between five types of boundedly rational players.7 actual behavior of may explain transfers in all treatments while pure distributional preferences In this section I use the predictions based on the social preferences model developed in Section 3 to explain differences in transfers between the treatments. First I consider how many observations in the game are consistent with predictions for different social preference models. Table 2 shows the explanatory power of various models, under the appropriate restrictions for the ρ and θ parameter. Individuals are categorized as behaving according to self-interested preferences if they transfer 0 ETB in the conditional strategic transfer decisions. Individuals are categorized as behaving according to distributional preferences when their transfers are strictly decreasing in the the payoff of j, p j. Individuals are categorized as behaving according to reciprocal-fairness preferences if they respond to j s insurance decision by reducing transfers relatively to what they would have transferred otherwise. This is observable for the transfer decisions conditional on j not taking insurance as compared to the benchmark treatment (τ Im j i < τ Ino j i and τ Ix j i < τ Ino j i ) and in the cases where i s make transfers which are lower than the benchmark treatment, despite j s being worse-off in terms of gross payoffs (τ p j=10 i < τ p j=28 i ). Table 2 shows that between 4-25% of behavior can be explained by self-interested preferences where individuals transfer 0. Between 56-90% by a model of distributional preferences in which transfers are strictly increasing in p j. A minimum of 25% of individuals s behavior is consistent with a model of distributional preferences where individuals punish j by reducing the weighting of the ρ parameter by θ and thereby reducing transfers. Overall, individuals act more self-interested when peers are protected by indemnity insurance or when peers have taken on additional risk but receive a claim payment. They act less self-interested and more based on distributional preferences when peers have taken risk but experience losses which are not protected. However, even though they are transferring based on distributional preferences, the level of transfers to peers is significantly lower than their ρ (as retrieved from the benchmark No insurance experiment) predicts which indicates that they behave according to reciprocal-fairness preferences by reducing ρ by an amount θ. 28

29 Table 2: Consistency of behavior with social preference models Self- Pure Implicit interest distributional punishment A=1 A=0 A=1 A=0 A=1 A=0 No insurance 11 (15%) 10 (9%) 62 (85%) 106 (91%) Indemnity 18 (25%) 26 (22%) 43 (60%) 65 (56%) 30 (41%) 54 (47%) Index 15 (21%) 5 (4%) 24 (33%) 81 (70%) 55 (75%) 82 (71%) Total # observations A=1: first-stage shock; A=0: no first-stage shock Figure 10: Behaviour consistent with self-interested preferences Behaviour consistent with self interested preferences within subject comparison Frequency first stage shock No insurance Index no first stage shock Indemnity 29

30 Figure 11: Behaviour consistent with distributional preferences Frequency Behaviour consistent with pure distributional preferences within subject comparison first stage shock no first stage shock * No insurance Index Indemnity Table 3: LPM regressions within-subject analysis social preference models Self- Distributional Implicit interest Preferences punishment A=1 A=0 A=1 A=0 A=1 A=0 (1a) (1b) (2a) (2b) (3a) (3c) Indem vs. no ins (.12) (.05) (.05) (.05) Index vs. no ins (.10) (.02)* (.06) (.06) Index vs. indem (.05) (.04) (.07) (.08)* (.07) (.05) N SE Session v v v v v v FE Session Note: LPM: P r[τ = Model T r] = α + β 1 I S ; Confidence:.99, **.95, *.90; Robust standard errors with clustering at Session level reported in parentheses; A=1: first-stage shock; A=0: no first-stage shock 30

31 5.1 Explaining implicit punishment In Section 3.3 two mechanisms were presented which may explain i s reciprocal-fairness behavior: 1. i s beliefs about j s risk preferences; 2. Shared norms, held by both i and j about risk-taking where it is hypothesized that i s will punish j s when j s take on additional risk. If there would be a shared norm between i and j it was hypothesized that punishment would be more likely between i s and j s from the same informal risk-sharing group. Table 4 shows that there are no significant differences between punishment when j is a member of i s own Iddir or when j is a member of another Iddir. Table 4: Punish risk-taking comparing j from own or different iddir No Indem Index Likelihood Level Likelihood Level (1a) (2a) (3a) (4a) j own iddir (vs. j different iddir) N Se Session v v v v FE Session Note: (1a; 2a) LPM: P r[θ i = 1] = α + β 1 Iddir i,s ; (1b; 2b) OLS: θ i = α + β 1 Iddir i,s ; θ[0, 1]; Confidence:.99, **.95, *.90; Robust standard errors with clustering at Session level reported in parentheses; j own iddir is 1; j different iddir=0 The latter result, however, does not exclude the explanation of the existence of a societal norm which dictates risk-taking behavior which is shared by members of a society at a larger scale than that of the informal risk-sharing arrangement. The explanation of a shared norm is supported by fact that on average there is punishment when j s take on additional risk (don t take indemnity insurance or take index insurance). However, it is not supported by the fact that there is also punishment when j s don t take on risk (don t take index insurance). The second explanation for punishment based on i s beliefs about j s risk preferences does support these findings. Punishment of not taking index insurance can be explained by i s believing that peers are risk-loving and therefore, as rational actors, should take up index-insurance and, when they don t, interpreting this as an action which intends to harm i. 40% of i s in the sample belief that their peers are more than 60% likely to take 31

32 up index insurance which I use as a proxy for i s beliefs about j s risk preferences (more likely to take up index insurance is more risk-loving). 42% of the sample can be classified as risk-loving, based on the MPL. i s beliefs about j s risk preferences are thus measured directly and indirectly. Directly by asking i about their expectations about j s insurance decisions (likely to take indemnity insurance: risk averse; likely to take index insurance: risk-loving) and indirectly by assuming that i projects own risk preferences onto j. Table 5: Punish risk-taking (no indemnity) based on i s beliefs and risk preferences Likelihood Level (1a) (1b) (1c) (1d) (1e) (2a) (2b) (2c) (2d) (2e) i s belief **.006**.006** about j s risk (.01) (02) (.02) (.002) (.003) (.003) preferences Binswanger.27**.26**.05**.05** (.11) (.11) (.03) (.02) MPL, p=1/ (.10) (.12) (.02) (.02) N Se Session v v v v v v v v v v FE Session Note: (1a) LPM: P r[θi Im=0 = 1] = α+β 1 E(R j ) i,s ; (1b) LPM: P r[θi Im=0 = 1] = α+β 1 BW i,s ; (1c) LPM: P r[θi Im=0 = 1] = α + β 1 MP L i,s ; (1d) LPM: P r[θi Im=0 = 1] = α + β 1 E(R j ) i,s + β 2 BW i,s ; (1e) LPM: P r[θi Im=0 = 1] = α + β 1 E(R j ) i,s + β 2 MP L i,s ; (2a) OLS: θi,s Im=0 = α + β 1 E(R j ) i,s + ɛ i,s ; (2b) OLS: θi,s Im=0 = α + β 1 BW i,s + ɛ i,s ; (2c) OLS: θi,s Im=0 = α + β 1 MP L i,s + ɛ i,s ; (2d) OLS: θi,s Im=0 = α + β 1 E(R j ) i,s + β 2 BW i,s + ɛ i,s ; (2e) OLS: θi,s Ix=1 = α + β 1 E(R j ) i,s + β 2 MP L i,s + ɛ i,s ; Confidence:.99, **.95, *.90; Robust standard errors with clustering at Session level reported in parentheses; i s belief about j s risk preferences ranges from 0-10 where 10 is most risk averse. Binswanger has been rescaled from 0 to 2 with 2 being most risk averse; MPL ranges from -1 to 1 with 1 being most risk averse. Table 5 shows that if i beliefs that j is more risk averse i is more likely to punish j and punishes j more for not protecting herself by taking indemnity insurance (not significant). i is also more likely to punish j and punish j more for not taking indemnity insurance when i is more risk averse 5. Table 6 shows that if i beliefs that j is more risk averse i is significantly more likely to punish j for taking additional risk by taking up index insurance and the level of punishment is also significantly higher if j is believed to be more risk averse. i is also more likely to punish j and punish j more for taking 5 Here I assume that i s risk preferences serve as a proxy for i s beliefs about j s risk preferences 32

33 Table 6: Punish risk-taking (index) based on i s beliefs and risk preferences Likelihood Level (1a) (1b) (1c) (1d) (1e) (2a) (2b) (2c) (2d) (2e) i s beliefs.03*.04**.04*.004* about j s risk (.02) (.02) (.02) (.002) (.004).004 preferences Binswanger.26**.19**.03*.02 (.12) (.11) (.02) (.02) MPL, p=1/2.19* (.19)**.04*.04 (.11) (.11) (.02) (.03) N Se Session v v v v v v v v v v FE Session Note: (1a) LPM: P r[θi Ix=1 = 1] = α + β 1 E(R j ) i,s ; (1b) LPM: P r[θi Ix=1 = 1] = α + β 1 BW i,s ; (1c) LPM: P r[θi Ix=1 = 1] = α + β 1 MP L i,s ; (1d) LPM: P r[θi Ix=1 = 1] = α + β 1 E(R j ) i,s + β 2 BW i,s ; (1e) LPM: P r[θi Ix=1 = 1] = α + β 1 E(R j ) i,s + β 2 MP L i,s ; (2a) OLS: θi,s Ix=1 = α + β 1 E(R j ) i,s + ɛ i,s ; (2b) OLS: θi,s Ix=1 = α + β 1 BW i,s + ɛ i,s ; (2c) OLS: θi,s Ix=1 = α + β 1 MP L i,s + ɛ i,s ; (2d) OLS: θi,s Ix=1 = α + β 1 E(R j ) i,s + β 2 BW i,s + ɛ i,s ; (2e) OLS: θi,s Ix=1 = α + β 1 E(R j ) i,s + β 2 MP L i,s + ɛ i,s ; Confidence:.99, **.95, *.90; Robust standard errors with clustering at Session level reported in parentheses; i s belief about j s risk preferences ranges from 0-10 where 10 is most risk averse. Binswanger has been rescaled from 0 to 2 with 2 being most risk averse; MPL ranges from -1 to 1 with 1 being most risk averse. index insurance when i is more risk averse. Table 7 shows that if i beliefs that j is more risk averse i is significantly less likely to punish j and punish j less for not taking additional risk by taking up index insurance. i is also less likely to punish j and punish j less for not taking index insurance when i is more risk averse. One might belief that risk preferences proxy for other factors that could explain punishment such as wealth or education levels. When the following observables are added to the regressions in Table 4, 5 and 6 the parameter estimates for i s beliefs about j s risk preferences, Binswanger and MPL remain unchanged: tropical livestock units (TLU), land size, size of irrigated land, contributions to Iddir; number of shocks experienced by farmer; number of times farmer has received contributions from other Iddir members. The results in this section suggest i s punishment is most likely explained by i s beliefs about j s risk preferences from which i infers kind or unkind behavior. 33

34 Table 7: Punish not taking risk (no index) based on i s beliefs and risk preferences Likelihood Level (1a) (1b) (1c) (2a) (2b) (2c) I s belief -.02** -.04** ** about j s risk (.01) (.01) (.002) (.002) preferences MPL, p=1/ (.09) (.10) (.01) (.02) N Se Session v v v v v v FE Session Note: (1a) LPM: P r[θi Ix=0 = 1] = α+β 1 E(R j ) i,s ; (1b) LPM: P r[θi Ix=0 = 1] = α+β 1 MP L i,s ; (1c) LPM: P r[θi Ix=0 = 1] = α+β 1 E(R j ) i +β 2 MP L i,s ;(2a) OLS: θi,s Ix=0 = α+β 1 E(R j ) i,s +ɛ i,s ; (2b) OLS: θi,s Ix=0 = α+β 1 MP L i,s +ɛ i,s ; (2c) OLS: θi,s Ix=0 = α+β 1 E(R j ) i,s +β 2 MP L i,s +ɛ i,s ; Confidence:.99, **.95, *.90; Robust standard errors with clustering at Session level reported in parentheses; i s belief about j s risk preferences ranges from 0-10 where 10 is most risk averse; MPL ranges from -1 to 1 with 1 being most risk averse. 6 Conclusion In this paper I show that individuals willingness to redistribute income to peers with losses is influenced by their peers decisions to protect themselves or take-on additional risk before losses occur. If peers protect themselves through indemnity insurance, which reduces the variance of outcomes, individuals are more likely to behave self-interested and average transfers are significantly reduced, suggesting crowding-out of redistribution. However, if peers take on additional risk and experience losses individuals do redistribute some of their own income according to distributional preferences but significantly less than the transfers they make when peers losses are purely caused my misfortune. This significant reduction in transfers after peers risk-taking can be explained by reciprocalfairness preferences where individuals punish peers for behavior which they perceive as unfair. This perception of unfair behavior is not explained by the existence of norms about risk-taking behavior which dictates that people should not take risk but rather by individuals inferring kind or unkind behavior from their peers actions based on the beliefs they have about the others risk preferences. If peers are believed to be risk averse than risk-taking is punished, if peers are believed to be risk loving than actions which reduce risk are punished. 34

35 A Effects of treatment on transfers Figure 12: Mean transfers if j takes insurance Transfers i to j (j insured) within subject comparison Transfers (ETB) No insurance Indemnity Index Transfers (ETB) No insurance Index insurance Indemnity insurance (a) mean beta-interval reg transfers > 0 Confidence:.99, **.95, *.90 (b) mean OLS, within-subject comparison Tr4 Figure 13: Mean transfers if j takes insurance by first-stage shock Transfers i to j (j insured) within subject comparison Transfers (ETB) ** No insurance Indemnity Index No insurance Indemnity Index first stage shock no first stage shock Transfers (ETB) ** first stage shock No insurance Index no first stage shock Indemnity (a) mean beta-interval reg tranfers> 0 Confidence:.99, **.95, *.90 (b) mean OLS, within-subject comparison Tr4 35

36 Figure 14: Mean transfers if j takes no insurance, by first-stage shock * ** Tranfers i to j (j NOT insured) within subject comparison Transfers (ETB) ** No insurance Indemnity Index No insurance Indemnity Index first stage shock no first stage shock Transfers (ETB) first stage shock No insurance Index no first stage shock Indemnity (a) mean beta-interval reg transfers > 0 Confidence:.99, **.95, *.90 (b) mean OLS, within-subject comparison Tr4 Figure 15: Probability of transfers {0, 1} Observations No insurance Indemnity Index No insurance Indemnity Index first stage shock no first stage shock Observations No insurance Indemnity Index No insurance Indemnity Index first stage shock no first stage shock Transfer=0 Total nr. of transfer decisions Transfer>0 Transfer=0 Total nr. of transfer decisions Transfer>0 (a) transfers {0, 1} if j takes NO insurance (b) transfers {0, 1} if j takes insurance B Models distributional preferences B.1 Fehr and Schmidt s distributional preferences The Fehr-Schmidt model (1999), like the Charness and Rabin (2002) model has linear indifference curves for distributional preferences. The utility function is: U i (x j, x i ) = x i α max{x j x i, 0} β max{x i x j, 0} (11) 36

37 Table 8: OLS regressions transfers Transfer i to j (j insured) Transfer i to j (j NOT insured) (1a) (1c) (1b) (2a) (2b) Shock No shock Shock No Shock Indem vs. no ins (.82) (1.91) (.97) (1.24) (.99)* Index vs. no ins (.82) (2.53)** (.91) (1.23) (.90) Index vs. indem (.64) (1.00)** (.76) (.99) (.72) N Note: OLS: τ = α + β 1 T r S + ɛ; Confidence:.99, **.95, *.90; Robust standard errors with clustering at respondent level reported in parentheses; A=1: first-stage shock; A=0: no firststage shock (1a): Average transfers full sample; (1b): Average transfers in case j experienced first-stage shock; (1c): j no first-stage shock; (2a): j first-stage shock; j no first-stage shock Table 9: Probit regressions probability of transferring Transfer i to j (j insured) Transfer i to j (j NOT insured) (1a) (1c) (1b) (2a) (2b) Shock No shock Shock No Shock Indem vs. no ins (.04) (.06) (.04) (.04) (.04) Index vs. no ins (.03) (.06) (.03)* (.05) (.04) Index vs. indem (.03) (.05)* (.04) (.04) (.03)* N Note: Probit: τ = Φ(α + β 1 T r S + ɛ); Confidence:.99, **.95, *.90; Robust standard errors with clustering at respondent level reported in parentheses;a=1: first-stage shock; A=0: no first-stage shock (1a): Average transfers full sample; (1b): Average transfers in case j experienced first-stage shock; (1c): j no first-stage shock; (2a): j first-stage shock; j no first-stage shock 37

38 Table 10: OLS conditional on making transfers Transfer i to j (j insured) Transfer i to j (j NOT insured) (1a) (1c) (1b) (2a) (2b) Shock No shock Shock No Shock Indem vs. no ins (.81) (1.54) (.92) (.92)* Index vs. no ins (.78)* (1.61) (.87) (1.12)** (.87)** Index vs. indem (.69) (1.28) (.80) (1.05) (.76) N Note: Conditional OLS: τ τ > 0 = α + β 1 T r S + ɛ; Confidence:.99, **.95, *.90; Robust standard errors with clustering at respondent level reported in parentheses; A=1: first-stage shock; A=0: no first-stage shock (1a): Average transfers full sample; (1b): Average transfers in case j experienced first-stage shock; (1c): j no first-stage shock; (2a): j first-stage shock; j no first-stage shock In this equation α represents disutility to i from having a lower payoff than j and β represents the disutility to i from having a higher payoff than the other player. Generally it is assumed that α β; player i has a higher disutility from disadvantageous inequality than from advantageous inequality. For the decision-making problem posed to i s in the dictator games in this study disadvantageous inequality is irrelevant. Equation (24) can thus be reduced to: U i (x j, x i ) = x i β(x i x j ) (12) If utility is assumed to be linear in i s and j s payoff than transfers will be: x i x j 2 if β >.5 τ = 0 if β.5 (13) To get predictions of continuous transfers we can assume Cobb-Douglas preferences. The difference between x i and x j can then be expressed as 1 x i x j difference. We then get: which is increasing in the 1 U i (x j, x i ) = x iα ( ) ( 1 α) (14) x i + x j 38

39 1 log U i [(p j + τ)(p i τ)] = α log (p i τ) + (1 α) log 1 (1 α) log( (p i τ) (p j + τ) ) (15) 1 log U i [(p j + τ)(p i τ)] = α log (p i τ) (1 α) log ( p i p j 2τ ) (16) δu i δτ = α p i τ (p i p j 2τ) (2 2α) (p i p j 2τ) 2 (17) δu i δτ = α p i τ (2 2α) (p i p j 2τ) α p i τ = (2 2α) (p i p j 2τ) (18) (19) αp i + αp j + 2ατ = 2p i 2αp i 2τ + 2ατ (20) αp i + αp j 2p i + 2αp i = 2τ (21) τ = α 2 p i α 2 p j + p i αp i (22) τ = (1 α 2 )p i α 2 p j (23) δτ δp j = α 2 (24) This implies transfers are strictly decreasing in p j. B.2 Bolton and Ockenfels distributional preferences with relative income The Bolton-Ockenfels model of distributional preferences assumes that i likes own income and dislikes income inequality, but the utility function takes the non-linear form where the second argument represents relative income: U i (x j, x i ) = v(x i, x i (x i + x j ) ) (25) They assume that the function v is globally non-decreasing and concave in the first argument and strictly concave in the second argument, and satisfies v 2 (m, 1/2) = 0 for all m. 39

40 Therefore equation (26) can be rewritten into: log U i (x j, x i ) = log x i + log ( ) (26) x i + x j p i τ log U i [(p j + τ)(p i τ)] = log (p i τ) + log ( (p i τ) + (p j + τ) ) (27) log U i [(p j + τ)(p i τ)] = log (p i τ) + log ( p i τ p i + p j ) (28) x i δu i δτ = 1 p i τ + p i + p j p i τ 1 p i + p j (29) This means δu i δτ δu i δτ = 2 p i τ = 0 (30) is a constant and i maximizes utility by transferring 0. If we now assume Cobb-Douglas preferences over the arguments defining v we get: x i U i (x j, x i ) = x iα ( ) β (31) x i + x j p i τ log U i [(p j + τ)(p i τ)] = α log (p i τ) + β log ( (p i τ) + (p j + τ) ) (32) log U i [(p j + τ)(p i τ)] = α log (p i τ) + β log ( p i τ p i + p j ) (33) δu i δτ = α p i τ + p i + p j p i τ β p i + p j (34) δu i δτ = α β p i τ = 0 (35) This means δu i δτ modify v into: is a constant and i maximizes utility by transferring 0. If we slightly U i (x j, x i ) = v(x i, x i x j ) (36) where i evaluates own income relative to j s income and we take Cobb-Douglas prefrences we get: U i (x j, x i ) = x iα ( x i x j ) β (37) log U i [(p j + τ)(p i τ)] = α log (p i τ) + β log (p i τ) β log (p j + τ) (38) 40

41 δu i δτ = α p i τ β p i τ β p j + τ (39) This implies transfers are strictly decreasing in p j. δu i δτ = β(p i τ) = ( α β)(p j + τ) (40) τ = β α p i (1 + β α )p j (41) δτ δp j = (1 + β α ) (42) B.3 Cox and Sadiraj (2005) The Cox and Sadiraj (2005) model represents other-regarding preferences with a modified CES utility function of an agent s own and the other agents monetary payoff, weighted by the altruism parameter θ 0: 1 α U i (x j, x i ) = (xα i + θxα j ) if α (, 1) \ 0 x i x θ j if α = 0 (43) This utility function is assumed to be monotonically increasing in x i and x j and to have indifference curves that are negatively-sloped and convex to the origin except for the boundary value of θ = 0, in which case the model is equivalent to the model of selfregarding preferences. (45) gives: 1 α U i (x j, x i ) = [(p i τ) α + θ(p j + τ) α ] if α (, 1) \ 0 (p i τ)(p j + τ) θ if α = 0 (44) δu i (x j, x i ) δτ = 1 p i τ + θ p j + τ (45) τ = which implies τ is decreasing in p j. θ 1 + θ p i θ p j (46) 41

42 C Balance and consistency Figure 7 provides a balance test based on OLS regressions of relevant household and farm characteristics, comparing different treatments. The balance test shows that the treatments are balanced. A test of the consistency of transfer decisions across similar treatments was conducted comparing treatment T1 and T4.1; T2 and T4.2 and T3 and T4.3. If the application of social preferences to transfer decisions is consistent within the population, there should be no significant differences between T1 and T4.1; T2 and T4.2 and T3 and T4.3 despite the fact that these are conducted with a difference sample. The tests conducted are the probabilities of farmers transferring exactly τ i = x i x j 2. The tests are presented in Figure 8. There are no significant differences except for the comparison in the second column where farmers in T4.2 are significantly less likely to transfer the exact difference than farmers in T2. Figure 16: Balance test Note: Balance test: OLS regressions. Dependent variables in columns. Confidence:.99, **.95, *.90. Robust standard errors with clustering at session level reported in parentheses. TLU=Tropical Livestock Units. 42