UNIVERSITY OF MICHIGAN Poverty, Risk Aversion, and Inconsistent Choices Catalina Franco * This version: April 21, 2015 ABSTRACT We run a lab experiment in a large public university in Colombia to test whether poverty causes individuals to be more risk averse and to make inconsistent choices. Students at this institution come from different economics backgrounds but are at the same time homogenous in terms of characteristics such as cognitive ability and education level. We exploit the natural variation in economic backgrounds and the fact that tuition in this school is a good proxy of the income of the parents to identify the effect of giving a treatment that makes salient the relative economic well-being of subjects. We find that treated individuals make more inconsistent choices in risk lotteries regardless of their poverty condition. In addition, both, within- and between-subject evidence suggests that the poor become slightly risk averse when given the treatment. However, this effect is not statistically significant with the level of power in this sample. The poor and rich do not differ in terms of other parameters of prospect theory such as loss aversion or non-linear probability weighting. * I am grateful for invaluable guidance and support from Prof. Tanya Rosenblat and Prof. Raj Arunachalam. I would also like to thank Prof. Dean Yang, as well as the director and administrative assistant of the School of Economics at the National University of Colombia, and Leonardo Garzon and Andrea Sanchez for their compuatitonal and emotional support over the course of this project. 1
Transcript
UNIVERSITY OF MICHIGAN
Poverty, Risk Aversion, and Inconsistent Choices
Catalina Franco∗
This version: April 21, 2015
ABSTRACT
We run a lab experiment in a large public university in Colombia to test whether poverty
causes individuals to be more risk averse and to make inconsistent choices. Students
at this institution come from different economics backgrounds but are at the same time
homogenous in terms of characteristics such as cognitive ability and education level.
We exploit the natural variation in economic backgrounds and the fact that tuition in
this school is a good proxy of the income of the parents to identify the effect of giving a
treatment that makes salient the relative economic well-being of subjects. We find that
treated individuals make more inconsistent choices in risk lotteries regardless of their
poverty condition. In addition, both, within- and between-subject evidence suggests
that the poor become slightly risk averse when given the treatment. However, this effect
is not statistically significant with the level of power in this sample. The poor and rich
do not differ in terms of other parameters of prospect theory such as loss aversion or
non-linear probability weighting.
∗I am grateful for invaluable guidance and support from Prof. Tanya Rosenblat and Prof. Raj Arunachalam. Iwould also like to thank Prof. Dean Yang, as well as the director and administrative assistant of the Schoolof Economics at the National University of Colombia, and Leonardo Garzon and Andrea Sanchez for theircompuatitonal and emotional support over the course of this project.
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1 INTRODUCTION
Research focusing on the economic decisions of the poor suggests that the poor usually leavemoney on the table. For example, Banerjee and Duflo (2007) discuss how the poor tend tohave multiple occupations but do not specialize in any of them, possibly as a risk-spreadingstrategy. Furthermore, these authors document that the poor tend not to make investmentswith potentially high returns, and that the scale of their businesses is small, leading to un-realized economies of scale. Evidence along these lines is also provided by Duflo, Kremer,and Robinson (2011) in the setting of fertilizer use by farmers. Even though productivity canincrease up to 100% with the use of fertilizer and that it can be purchased at a relatively lowcost, farmers are unwilling to buy it. In addition to the lack of access to credit and insurancemarkets that the poor are likely to face, these behaviors might be at the core of explainingwhy it is difficult for some people to escape from poverty.
This paper explores how poverty may affect economic decision-making by studying howpeople’s choices vary when their relative economic position is made salient. In particular, westudy risk preferences as it has been argued that, if poor people are more risk averse, theirunwillingness to take risks would suggest a perpetuation of poverty.1 An impending prob-lem of any study attempting to analyze the causal relationship from poverty to risk aversionis that of reverse causality. Ideally, and and under the view that preferences can respond tothe environment2, we would randomly assign poverty conditions to test the hypothesis thatpovery causes risk aversion. Given the implausibiliy of conducting this exercise with real-lifestakes we propose a laboratory experiment.
Our experiment was conducted online with students from a large public university in Colom-bia. The main advantage of conducting the experiment in a country like Colombia is that asignificant portion of the population is classified as poor (headcount ratio of about 30% in2014), and inequality levels are also high (Gini coefficient of 0.54 in 2014). The combinationof a significant fraction of the population under the poverty line and high levels of inequalityprovides an ideal setting to observe a large variation in the economic status of the population.Furthermore, admission to this college is granted only through passing an admission examspecific to this institution. Given the prestige, admissions system, and size of this university,students in this college come from different economic backgrounds. In addition, the tuitionthat students pay is linked to the relative income and wealth of their parents, so students withmore economic needs pay a fraction of what wealthier students pay. In this sense, tuition isthe proxy for income that we will exploit in our analysis.
Our experiment is similar in spirit to that of Mani, Mullainathan, Shafir, and Zhao (2013) inwhich subjects were given either a high-stakes or low-stakes hypothetical financial scenariofor which they have to propose solutions after solving a cognitive task. The authors found
1The evidence on the correlation between risk preferences and income has been mixed (see the next section andthe discussion in Tanaka, Camerer, and Nguyen (2010)).
2See in particular, Malmendier and Nagel (2011), Nguyen (2011), and Beauchamp, Benjamin, Chabris, and Laib-son (2012).
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that the poor in the high-stakes scenario performed significantly worse in the cognitive testthan the poor in the low-stakes scenario and that the rich in both scenarios. In our experi-ment, the treatment consists of two parts: First, subjects are given a histogram of the tuitionpaid by participants in the experiment.3 Without telling them the values in each bin of thehistogram they are asked to select where they think they are in the distribution.4 Immediatelyafter this, they are told whether they were right or not and, if not, they are told where exactlythey are in the distribution. A similar procedure was followed for the control group with agraph about the number of students by subject area instead of the histogram. The idea ofshowing them their relative economic position is to trigger poverty (or non-poverty)-relatedthoughts. Second, following Mani et al. (2013), subjects in the treatment group are given afinancial scenario in which they have to explain how they would obtain the money to pay anextra fee of one million pesos (about US $400) to the university. Subjects in the control faceda scenario in which only 30,000 pesos (US$ 12) were needed.5.
Following the poverty priming, subjects solved three series of risk aversion lotteries and aRaven’s matrices task. The risk lotteries are based on Tanaka et al. (2010) which were devel-oped to capture the three prospect theory parameters: risk aversion, non-linear probabilityweighting, and loss aversion. We elicit risk preferences under prospect theory and not underthe expected utility framework as there is little evidence that individuals’ choices conformto expected utility theory (Rabin & Thaler, 2001, for example). While prospect theory alsohas disadvantages and the measuring instrument is not perfect, this setting allows us to, be-sides capturing the risk aversion coefficient, have a test of whether individuals in our samplechoose according to expected utility theory, and to find any systematic differences betweenloss aversion between the poor and the non-poor.
The main contribution of this paper is that it provides evidence for a causal effect of povertyon economic-decision making by using subjects who are homogeneous in various relevantcharacteristics, such as cognitive ability and education level, but who exhibit a natural varia-tion in their economic backgrounds that we can measure through the tuition they pay. Fur-thermore, we can conduct between-subject and within-subject analyses with the same indi-viduals.
The rest of this document is organized as follows. In section 2 we briefly discuss related lit-erature. Section 3 presents a detailed description of the experimental design and experimen-tal procedure. The data and discussion of results are presented in sections 4 and 5. Section 6concludes. The experimental instructions can be found in the appendix.
3The data of tuition for all students in the Bogota campus was requested to the university but it was not possibleto obtain it before running the experimental sessions.
4They receive an economic incentive in case their guess is correct so we expect that they reveal their true belief.5For reference, tuition of the subjects in this study ranged from 64,000 pesos to 2 million pesos.
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2 RELATED LITERATURE
As mentioned in the introduction, several studies have established an association betweenpoverty and counter-productive behavior. Since it is hard to find a causal relationship giventhe reverse causality issue, a series of recent studies attempt to find the causal relationshipof poverty on different outcomes such as cognitive ability and economic decision-makingthrough the use of lab and and lab-in-the field experiments. Spears (2011) assigns informalday laborers in India to rich and poor groups depending on the number of items each in-dividual is given as endowment. He finds that poor people who were randomly assigned tomake an economic choice performed worse in a cognitive task than people assigned to theno-choice treatment, that is, poor participants found decision making depleting. Mani et al.(2013) conduct a lab experiment in a mall in new Jersey. They find that poor participantsperform worse in a cognitive task when given a high-stakes hypothetical financial scenarioto think about while solving the cognitive test. The difference between the poor in the “hard”financial scenario and in the “easy” scenario is statistically significant, as it is when the com-parison is made between the poor in the hard scenario and the rich in any scenario. In thefield, Mani et al. (2013) exploit the variation in poverty given by the pre- and post-harvest sea-son. Before havest, when farmers are poor, they perform substantially worse in a cognitivetask than when they are rich, after the harvest.
In a similar vein, Carvalho, Meier, and Wang (2014) analyze cognitive function, inter-temporalpreferences, and risk and loss aversion in low-income households in the United States whowere assigned to perform these tasks before or after payday. These authors find evidencethat subjects were more present-biased before payday but they attribute this to external fac-tors such as liquidity constraints and not poverty per se. They do not find systematic differ-ences in cognitive tasks, risk aversion, and consistency of inter-temporal choices. Haushofer,Schunk, and Fehr (2013) study time preferences by experimentally assigning subjects to richor poor conditions after giving them a high or low endowment of points and letting themcomplete a real-effort task. Some participants in the “rich” group face a negative shock in thenumber of points they had accumulated that would leave them at the level of points of the“poor” . Similarly, some “poor” participants would receive a positive shock. The authors findthat experiencing a positive shock makes people more patient while experiencing the neg-ative shock makes them more present-biased. Further, persistently low or high incomes donot affect discounting. Then, what seems to matter is the shocks and not the income levels.
Regarding risk preferences, a few studies combine survey measures of household or indi-vidual characteristics with experimentally-elicited risk aversion. The pioneer study of Binswanger(1980) finds no relationship between wealth and risk attitudes as well as the study of Mosleyand Verschoor (2005). Dohmen et al. (2011), Nielsen (2001) and Yesuf and Bluffstone (2009)document a positive correlation between income and risk aversion. To cover all possibilities,Wik et al. (2004) report a negative relationship between wealth and risk aversion.
Given the difficulty of establishing a causal relationship between income and risk prefer-ences with observational data, two studies have used an instrumental variable approach to
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attack the reverse causality problem. Guiso and Paiella (2008) use data form the Bank of ItalySurvey of Household Income and Wealth to analyze the answers to a hypothetical questionabout the willingness to take risk. Instrumenting wealth with widfall gains or level of edu-cation of the household head’s father shows that higher levels of wealth predict lower riskaversion. Tanaka et al. (2010) combine household surveys with experimental measures intwo villages in Vietnam. They use rainfall as an instrument for the mean level of income ofthe village as well as household individual income. Although they find no effect for individualincome, they find that individuals living in wealthier villages are less loss averse and less riskaverse (at the 10% level).
Haushofer and Fehr (2014) provide a survey of recent advances in the causal effect of povertyon risk preferences and time dicounting. They emphasize the channels through which povertymay be affecting individuals’ risk and time references. They argue that poverty causes nega-tive affect and stress, and that these two, in turn, cause higher risk aversion and impatience.
Finally, a study that is related to ours in terms of the experimental design is Campos-Vazquez and Cuilty (2014). With college students in Mexico, the authors administer a framingthat is intended to bring up different types of emotions such as sadness and anger. Followingthis, they elicit risk preferences using the lotteries proposed in Tanaka et al. (2010). They findthat risk and loss aversion react differently depending on the type of emotions that subjectsexperience.
3 EXPERIMENTAL DESIGN
3.1 ELICITATION OF RISK PREFERENCES
A variety of methods to elicit risk preferences can be found in the literature. Following ex-pected utility theory (EUT), standard measures to elicit risk preferences are multiple pricelists as in Holt and Laury (2002), and selection of the preferred gamble to play as in Eckeland Grossman (2008).6 An alternative approach is given by prospect theory (PT). As opposedto EUT, PT proposes a “value function” in which the argument is the payoff of the gamble,xi , instead of W + xi as in EUT. Second, the value function captures “loss aversion”, that is,the idea that people are more sensitive to losses than to gains even if the two have the samemagnitude. Third, the value function is concave in the gains domain but convex in the lossdomain, capturing the fact that people are observed to be risk averse over gains (prefer a sureoutcome instead of a 50% probability gamble with the same expected payoff) but risk lovingover losses (prefer a gamble with 50% chance of losing x and 50% of losing zero than los-ing x/2 for sure). Fourth, PT acknowledges the fact that people do not weight outcomes bytheir objective probabilities but by transformed probabilities or decision weights, which arecomputed using a probability weighting function w(p). The weighting function proposed byTversky and Kahneman (1992) overweights low probabilities and underweights high proba-
6In a survey paper about risk preferences elicitiation methods, Charness, Gneezy, and Imas (2013) provide anextensive list of these two methods and other incentivized and non-incentivized methods.
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bilities. A detailed review of PT after 30 years of its inception is given in Barberis (2013).
Given the experimental support of the main features of PT, this paper uses a method toelicit the three PT parameters (risk aversion, loss aversion, and non-linear probability weight-ing). In the context of developing countries, Tanaka et al. (2010) propose a series of lotteriesfrom which these parameters can be inferred. One of the advantages of this method is that itprovides a way to test whether EUT holds by conducting a statistical test of the values of theparameteres against their prediction under EUT (in particular, if α, the probability weightingparameter is equal to 1, EUT cannot be rejected).
The utility function for outcomes x and y ocurring with probabilities p and q , respectively,is the following:
U (x, p; y, q) ={
v(y)+w(p)(v(x)− v(y) for x > y > 0 or x < y < 0
w(p)v(x)+w(q)v(q) for x < 0 < y
Where the value function is defined as7:
v(x) ={
x1−σ for x > 0
−λ(−x)1−σ, for x < 0
And, following (Prelec, 1998), the weighting probability function is w(p) = e[−(−lnp)α].
The parameters of interest are σ, the curvature of the value function, λ, the curvature ofthe value function of negative relative to positive prospects, and α, the parameter in the non-linear weighting probability function. Usually,σ > 0 means risk aversion,σ = 0, risk neutrality,and σ < 0, risk loving. Here we adopt the ranges defined by Holt and Laury (2002) (see foot-note 16). A higher level of λ is associated with more loss averse individuals, and α < 1 meansthat individuals overweight low probabilities and underweight high probabilities.
The lotteries used in the second survey of this experiment are shown in Table 1. The pay-offs correspond to the original presented in (Tanaka et al., 2010) multiplied by 100 to convertthem to meaningful values in Colombian currency. Two versions of these lotteries were pre-sented to the subjects. In the baseline survey, they were shown only the first two series withslightly modified payoffs (multiplied by 80 instead of by 100). Section 3.4 explains the rea-soning for this design choice. In the second survey they were asked all three series. Eachseries was shown in different screens. Participants were instructed to select their preferredchoice between A and B in each row. In the second survey, they were also asked at whichrow they would like to switch from column A to column B if they were to choose a singleswitching point. This differs from Tanaka et al. (2010) and other studies using the same elic-itation mechanism. Given the possibility of inconsistencies in individuals’ choices, mono-tonic switching is enforced in those studies which amounts to assuming hat individuals are
7As mentioned in Liu (2013) and Liu and Huang (2013), the value function in this case is modified with respect to
the one proposed in Tanaka et al. (2010) for ease of comparison with the convential EU CRRA form: u(x) = x1−σ1−σ
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rational. We asked both, the choices in each row and the switching point, to have a measureof comparison between choices under both circumstances.
Table 1: Three series of lotteries based on Tanaka, Camerer, and Nguyen (2010)Series 1
Column A Column B Expected payoff difference (A - B)Row no. If 1 to 3 comes out If 4 to 10 comes out If 1 comes out If 2 to 10 comes out
Row no. If 1 to 5 comes out If 6 to 10 comes out If 1 to 5 comes out If 6 to 10 comes out1 2,500 pesos -400 pesos 3,000 pesos -2,100 pesos 600 pesos2 400 pesos -400 pesos 3,000 pesos -2,100 pesos -450 pesos3 100 pesos -400 pesos 3,000 pesos -2,100 pesos -600 pesos4 100 pesos -400 pesos 3,000 pesos -1,600 pesos -850 pesos5 100 pesos -800 pesos 3,000 pesos -1,600 pesos -1,050 pesos6 100 pesos -800 pesos 3,000 pesos -1,400 pesos -1,150 pesos7 100 pesos -800 pesos 3,000 pesos -1,100 pesos -1,300 pesos
The first two lotteries allow to obtain values for σ and α. This is done by setting up a sys-tem of inequalities depending on the choices made by the individuals. For example, if theindividual changes from column A to column B in row 5 in series 1, and row 7 in series two,the following set of four inequalities hold:
From the values in Table 1, the first two inequalities capture that, in series 1, column Awas preferred to B in row 4 and column B was preferred to column A in row 5. The sameholds for the last two inequalities in rows 6 and 7 of series 2. Solving these four inequalitiesyields a range of values for σ and α. A similar strategy is followed obtain a range for λ giventhe approximate value of σ obtained from the previous step. For example, if subjects changefrom column A to B in row 4 in series 3, the following two inequalities must hold:
−λ ·4001−σ+1001−σ >−λ ·2,1001−σ+3,0001−σ (5)
−λ ·4001−σ+1001−σ <−λ ·1,6001−σ+3,0001−σ (6)
In general, since our payoffs are just a scaled version of the original in (Tanaka et al., 2010),we use the values they report in the appendix for each combination of switching points.8
3.2 TASKS AND INCENTIVES
This experiment uses two types of tasks: cognitive and risk preferences. Following Mani etal. (2013), the cognitive task is a set of increasingly more difficult questions from the Raven’smatrices test. Subjects are instructed that they need to solve as many questions as possible(out of 10) in a two-minute interval. If this task is chosen for payment, they receive 1,000 pe-sos for each correct answer.
The elicitation of risk preferences task follows Tanaka et al. (2010). As explained in the pre-vious section, the three series of lotteries are designed to measure the parameters of prospecttheory: curvature of the value function (σ), and loss aversion (λ), as well as the parameter of(Prelec, 1998)’s probability weighting function (α). If any of the series from this task is chosenfor payment, subjects receive the value in pesos in the column of their choice (A or B) in therow selected for payment (see Table 1). If the loss lottery is chosen for payment and the valuein the row selected for payment is negative, the amount is deducted from the participationfee of 2,000 pesos.
3.3 TREATMENT
The main goal of this paper is to establish whether there is a causal relationship from povertyto risk aversion and cognitive ability. Since testing of the latter is basically replicating Mani
8We checked that we were able to obtain the values they report in the tables.
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et al. (2013) we follow a similar strategy to theirs. The main difference is that in our study,instead of simply presenting subjects with an easy and difficult financial scenario, we givethem information about their relative position among all the participants in the experimentalong with the financial scenario.
Since we know the information regarding their major and tuition paid from a survey wherewe collected demographics, we make two types of graphs that are shown to the treatment andcontrol groups. Subjects in the treatment group initially see a histogram of tuition paid byparticipants in the experiment. This graph contains 10 unlabeled ranges of tuition, and sub-jects are asked to guess in which range they think the value of the tuition they pay lies. Thisguess is incentivized, i.e., they receive 1,000 pesos if their answer is correct. Following this,they are shown the same graph but now with labels. They see a message on the screen tellingthem where they thought they were and where they really are in the graph. Finally, in thenext screen they are shown the financial scenario which, in the case of the treatment group,requires them to think about a hypothetical increase in the value of the current semester’stuition of one million pesos. 9 The graph is intended to show them their relative economicwell-being as measured by the tuition amount they pay among all participants in the experi-ment.
In the control group, participants see a bar graph containing the number of undergraduatestudents by subject areas (e.g. engineering, health sciences, economic sciences, etc.). Similarto the treatment group, subjects were asked to guess in which bar they thought the numberof students in their department would be. They see in the following screen the labeled graphalong with a message telling them if their guess was correct or not. This is also incentivizedwith 1,000 pesos. The financial scenario that follows is about paying an amount of around30,000 pesos besides what they already pay for tuition in the current semester.10 In addition,the choices of the control group in the graphs shown to the treatment group were also ob-tained after both groups had finished all the tasks.
3.4 EXPERIMENTAL PROCEDURE
The experiment was conducted online with students from the National University of Colom-bia, Bogota campus. The subjects were recruited in December, 2014 when a pilot of a similarexperiment took place in the computer lab of the Economic Sciences department. An an-nouncement containing the information of this experiment was sent in March, 2015 to thestudents who had signed up for the pilot. The students who were interested in participatingfilled out a form reporting their demographic information as well as the amount of tuitionthey paid this semester. In total, 106 students signed up.
9The 75th percentile of the tuition distribution is close to one million pesos so, for about 75% of the sample, theincrease proposed in this hypothetical situation is of more than 100% of what they actually pay per semester.For reference, the monthly minimum wage is near 650,000 pesos.
10While 30,000 pesos can be as high as almost half of the tuition the poorest students pay, it is not a difficultamount to obtain even for the poorest families.
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After signing up, the subjects filled out two online surveys with a space of one week be-tween each. In the first survey subjects completed the first two series in Tanaka et al. (2010)with the lottery payoffs multiplied by a factor of 0.8 (see Table 1). The purpose of elicitingrisk preferences in the first survey was to have a baseline measure of risk aversion for allparticipants, as well as to familiarize them with the task they would solve after receiving thetreatment in survey 2. Before proceding with the task, they were shown an example of howthe payments from the lotteries were calculated, and were required to select the paymentthey would receive under a specific outcome in the example. Also, participants answeredquestions about past negative economic shocks in their households, financial literacy, levelof education of their parents, expected salary in their first job after graduation, among otherrelated questions. Of the 106 students who signed up, 98 completed the first survey11.
Having collected a baseline measure of risk preferences in survey 1, we were able to charac-terize individuals according to their level of risk aversion. Subjects who answered the baselinerisk lotteries in a coherent way were divided into two groups according to their risk aversionparameter σ. Following the categorical description of risk types in Holt and Laury (2002),subjects with σ lower than 0.15 were classified as risk neutral or loving whereas subjects withσ greater or equal to 0.15 were classified as risk averse. Since we did not enforce monotonicswitching as Tanaka et al. (2010) and others using this method have done, a fraction of thesubjects (46%) were inconsistent in their lottery choices.12
The reason to ask their choice in every row instead of asking for a switching point is that,since the series of lotteries they would face in survey 2 were almost the same, we did not wantthem to remember the row in which they would switch. If subjects realize that the lotterieswere practically the same and they recall the row in which they switched, they may simplyanswer what they recall and not what they prefer at the moment of solving the task after ex-periencing the treatment. This may potentially confound the treatment effect inducing a biastoward less risk aversion if in fact the treatment makes people choose less risky options or theopposite. Further, another reason to not enforce monotonic switching is to address the factthat some subjects simply do not put effort to solve the tasks so the treatment effect mightbe affected by subjects choosing at random. Therefore, knowing who is inconsistent allowsto estimate the treatment effect for those who are inconsistent and those who are not, andcompare the two estimates.
With the distiction between risk types and inconsistent choices in mind, we block random-ized treatment assignment in the three blocks: risk-averse subjects, risk-neutral or risk-loving
11Given that this experiment was conducted online there might be concerns about who decides to participate.However, since we recruited from the pool of students who initially showed interest to participate in the in-person sessions, we do not think we will get any biases different from the ones arising in the lab context.
12By inconsistent we mean that they were switching back and forth from columns A and B or that they startedchoosing column B and then switched to column A. As seen in Table 1, the difference in expected payoffs be-tween column A and B is positive up to row 7 and then becomes negative. It is not unusual to see inconsistentchoices in elicitation of risk preferences using lotteries, see for example Holt and Laury (2002).
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subjects, and inconsistent subjects. This is done with the aim of reducing the variability com-pared to when randomization is done for the whole sample, as well as to increase the powerby having equal numbers of treated and control subject in each block.
After subjects were randomized within their corresponding block, they responded survey2. From the 98 subjects who responded survey 1, 96 also responded survey 2. The procedureof survey 2 was similar to that of survey 1; that is, they read the instructions and then chosewhat payment they would receive if the row shown in the example was chosen for payment.Following this, subjects received the treatment. Then, they solved the two tasks and they werereminded of the hypothetical scenario in between the two tasks.13 In this case, for the risk lot-teries we asked both, the choice in every row, as well as the switching point. At the end of thesurvey, one of the tasks, including those in survey 1, was chosen at random for payment. Theparticipation fee was 2,000 pesos (about US$0.8) and they could receive up to 170,000 pesos(about US$68). On average, subjects received 7,000 pesos (5,600 pesos if we exclude one per-son who earned 138,000 pesos) which were paid in cash one week after completing survey 2.
3.5 HYPOTHESES
The design of this study allows to make between- and within-subject risk-preference andinconsistency comparisons. In the between-subject part, we can compare subjects who re-ceived the control treatment with those who received the relative expectations shock in theireconomic position. Under the within-subject approach, we can compare individuals in ei-ther treatment against their baseline rate of inconsistency or measure of risk.
While in the control group we do not expect to trigger any thoughts related to economicwell-being by giving subjects a graph unrealted to financial concerns and an “easy” financialscenario, different reactions can arise in the treatment group. If their guess about their rela-tive position in the histogram is to the right of the truth, knowing their real relative positionwould make individuals feel poorer that they thought they were. If their guess is to the left,they would feel realtively richer than they thought they were. Presumably, the intensity of thisrelative expectations shock would depend on how far the guess and the truth are.
Another possible case is that subjects guessed correctly their position in the histogram. Acorrect guess may suggest that they are more aware of the relative well-being but we cannotdiscard that it was a matter of luck. In this case, there is no clear implication on how the treat-ment might work.
If the treatment is effective, and if, as suggested by the literature, poor individuals are morerisk averse, the hypothesis that can be derived from this description is that individuals whoexperience a negative shock in their expections (are poorer than they thought) would make
13Due to restrictions in the design of the online surveys, it was not possible to randomize the order in which theactivities were solved so everybody did the risk lotteries first, and the cognitive task second.
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less risky choices after the treatment compared to subjects in the control group and to them-selves in survey 1. Those who get the positive shock (are richer than they thought) may be-have in the opposite way. Moreover, the farther away they are from the truth, the larger weexpect the treatment effect to be. However, given the small number of observations we wouldbe unable to measure the intensity of the treatment.
In the case of the control group we do not expect to see any systematic difference betweenrich and poor individuals’s responses in the first and second survey to the risk aversion task.
4 DATA
From the 96 subjects who participated in the experiment, 56 were assigned to the treatmentgroup and 40 to the control group14. We analyzed about 25 covariates at the baseline to checkthat the treatment was indeed randomly assigned. Table 2 shows the treatment and controlgroups means for a selected group of characteristics. We find that even with the imbalancein the sample sizes, all characteristics except one, are balanced in the overall sample. Theunbalanced characteristic is the residential strata, which is an index between 1 and 6 that isused to determine the utilities bills for households (households in strata 1 pay the lowest billsand, in strata 6, the highest). The variable poor, which is defined as the median split of thetuition values in the sample (591,000 pesos) is around 50% in both groups by construction.
If we analyze balance within the randomization blocks, we find that other characteristicsare not balanced as a result of the difference between the original treatment assignment andthe one that ocurred de facto.15
Table 2 also shows the mean level of the risk aversion coefficient obtained for individu-als who made consistent choices in the lotteries in survey 1. According to the classificationproposed by Holt and Laury (2002)16, individuals in the treatment and control groups in thissample (in randomization blocks 1 and 2) are slightly risk averse. The statistical equality ofrisk aversion also holds when comparing poor vs. non-poor within treatment and controlgroups.
A clarification is need to be made at this point. As described previously, the self-reportedswicthing point in the lotteries was not elicited in the baseline survey to avoid subjects re-porting the number that they remembered instead of their true preferences at the moment ofanswering survey 2. Therefore, in survey 2 we have two measures of the switching point forconistent individuals: one obtained from the row-by-row choices, and the other from the re-
14An unanticipated turn of events generated this imbalance in the sample sizes of the two groups. Despite thereduction in power that this may generate, we are still able to find some results.
15In particular in the block that randomized treatment among risk-neutral or risk-loving individuals, 3 of the 25covariates show statistical differences.
16A summary of the 9 ranges classifying relative risk aversion based on a CRRA utility function proporsed by Holtand Laury (2002) is the following: If σ < -0.15, risk loving, if -0.15 < σ < 0.15, risk neutral, if 0.15 < σ < 0.41,slightly risk averse, if 0.41 < σ < 0.68, risk averse, if σ > 0.68, very risk averse.
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Table 2: Balance of characteristics
Control Treatment
Age 21.75 22.16
Gender 0.45 0.43
Strata 3.00 2.66**
School type: 1=private, 0=public 0.60 0.52
No. of past negative economic events 1.53 1.29
Financial literacy (avg. of 5 questions) 0.80 0.82
GPA 3.82 3.78
Semester 6.68 7.39
Tuition (pesos) 661,154 498,299
Admission score 678.80 672.66
SISBEN 0.98 1.02
Mother’s level of education 2.58 3.02
Father’s level of education 2.85 2.75
Currently works 0.43 0.50
Expected wage after graduation 1,732,500 1,795,536
Poor (median split of tuition) 0.48 0.52
No. of inconsistent choices 0.70 0.66
Sigma (risk aversion coefficient) 0.26 0.23
*** p<0.01, ** p<0.05, * p<0.1
ported switching point. We find that a large number of those who were consistent row-by-rowdo not report the same switching point as can be implied from their choices. In fact, somesubjects report values that are quite far from what is implied by their row-by-row choices.Since the mean switching point reported by consistent individuals who reported the sameswitching point as their row-by-row choices is statistically equal and very close in value tothe switching point reported by inconsistent individuals, from now on we use measures ofthe PT parameters that are derived from the implied switching point in the case of consistentindividuals, and the reported switching point in the case of inconsistent individuals.
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In terms of inconsistencies in lottery choices, the rate of inconsistencies is around 0.7which means that, out of the two lotteries that subjects solved at the baseline, treated andcontrol individuals made inconsistent choices in almost 1 of them. Moreover, the differencesbetween poor and rich within the treatment and control groups are not statistically signifi-cant. The poor in the treatment seem to be slightly more inconsistent with a p-value of thedifference between poor and non-poor of 0.106.
Figure 1 shows the histogram that was shown to participants in the treatment group (withnumbers from 1 to 10 instead of the tuition ranges) as well as the histogram that can be con-structed from the beliefs about the relative position that both, treated and control, reported.Since there is a high peak in the proportion of students paying less than 217,000 pesos, thefirst bar in the histogram was split in two, so the amplitude of the first two ranges was modi-fied accordingly. Past the first two bars, the distribution seems to get close to a gaussian dis-tribution. A χ2 test of equality of reported beliefs between the treatment and control groupdoes not reject the null that their choices were the same.
Figure 1: Histogram constructed from actual tuition values and reported beliefs
Regarding the reported beliefs of participants, more people thought they were in the mid-portion of the distribution (ranges 4 and 5) and at the top of the distribution than what issuggested by the actual tuition values. In constrast, fewer subjects thought they were in thefirst 3 bins of the histogram, especially bin 3, which is the bin right below the bin where themedian is. A cumulative distribution plot of the same data (not shown) suggests that the em-pirical CDF of the reported beliefs first-order stocastically dominates the empirical CDF of
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the actual values. Moreover, even if the percentage of subjects by bin matches the actual dis-tribution (as in bin 6), it does not mean that those students guessed correctly their relativeposition.
Since we are unable to randomly assign a poverty condition to individuals, we take ad-vantage of the natural variation in socioeconomic conditions to assess the effect of differenttypes of relative expectations shocks regarding poverty. Depending on where subjects thinkthey are in the histogram of tuition, they may experience a negative shock (they are in factpoorer that they thought), no shock (they accurately guess their relative position in the distri-bution), or a positive shock (they are richer than they thought). The proportion of individualsin each type of relative poverty expectations shock is summarized in Table 3. For both treatedand control individuals we report the shock they received in guessing their position in thehistogram of tuition. For the control group their relative position choices were elicited afterthey had solved all the tasks so there is no effect of this on their performance on the Raven’stest or risk lotteries choices.17
Table 3: Proportion of individuals by type of shock
Negative shock No shock Positive shock
All C 41.0% 30.8% 28.2%
T 33.9% 42.9% 23.2%
Poor C 52.6% 31.6% 15.8%
T 27.6% 58.6% 13.8%
Non-poor C 30.0% 30.0% 40.0%
T 40.7% 25.9% 33.3%
In general, a large fraction of individuals do not guess their position in the tuition distri-bution correctly with the exception of the poor in the treatment group in which close to 60%received no shock. The proportions of individuals in each type of shock is high enough sothat, in most cases, it is possible to perform the statistical analyses presented in the next sec-tion. A statistical test of whether the differences across treatment and control by type of shocknever rejects the null at the 5% level. Only for the poor experiencing a negative shock or noshock, the differences between the proportions in the treatment and control groups are sta-tistically important at the 10% level.
17Of the 40 subjects in the control group, 39 responded this question.
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5 RESULTS
5.1 RAVEN’S MATRICES COGNITIVE TEST
As explained in section 3, the treatment in this experiment consisted in giving individuals ashock of relative expectations. That is, we elicited where they thought they were in the dis-tribution of tuition which, at this college, is a proxy for income, and then we gave them ahypothetical financial scenario. After they selected the bin of the histogram in which theythought the value of the tuition they pay was, we told them if they guessed correctly, or theexact point where their tuition was in the histogram if they guessed incorrectly. This mech-anism leads to three types of shocks: a negative shock if they selected a point to the right ofwhere they really are, no shock if they guessed correctly, and a positive shock if they selecteda point to the left of where they really are. We would like to interpret the negative shock asproducing the feeling of being poorer than they thought they were and viceversa for the pos-itive shock.
We examine the different types of shocks in Table 4. We compare poor individuals inthe treatment group with individuals in three comparison groups: other poor in the treat-ment (those who did not experience a negative shock), non-poor individuals in the treat-ment group, and individuals in the control group. The first two panels of the table show,for each comparison group, the mean of the poor in the treatment who received a negativeshock (left-hand side of the table), as well as the means of individuals in each comparisongroup who received different types of shocks. For example, in the first panel, the poor whoexperienced a negative shock had, on average, 2.57 correct answers in the Raven’s test. Theright-hand side of the table shows the means of other poor subjects in the treatment who ex-perienced no shock or a positive shock. The means of those two groups are 4.24 and 4 correctanswers, respectively, and the difference between each of these groups and the group on theleft is statistically significant at the 5% level as shown by the p-values in parenthesis belowthe mean values. The sample size for each comparison is reported below the p-values.
The second panel of Table 4 compares the poor in the treatment group who received a neg-ative shock with non-poor in the treatment group who received each of the three shocks. Inthis case, relative to the non-poor with a negative shock or no shock, the poor with a negativeshock correctly responded fewer Raven’s matrices questions, and these differences are statis-tically significant at the 5% level. Relative to the non-poor who experienced a positive shock,the poor receiving a negative shock did no perform worse in a statistical sense although themean values differ by more than one correct question.
Finally, the last panel of Table 4 compares the mean of correct answers between the poorin the treatment group who received a negative shock and the control group. On average, in-dividuals in the control group solved 3.56 questions of the Raven’s test correctly. Even thoughthe difference relative to the poor with a negative shock is of one question, the comparison isnot statistically significant. Relative to the poor in the control group, who solved 3.79 ques-tions correctly on average, the poor in the treament receiving a negative shock performed
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Table 4: Mean of correct answers in Raven’s test by type of shock received
Comparison group: Poor in treatment group
Negative shock No shock Positive shock
Mean 2.57 vs. 4.24 4.00P-value of difference (0.036) (0.036)Sample size 24 11
Comparison group: Non-poor in treatment group
Negative shock Negative shock No shock Positive shock
Mean 2.57 vs. 4.09 4.14 3.88P-value of difference (0.032) (0.044) (0.147)Sample size 18 14 15
Comparison group: Control group
Negative shock Control - all Control - poor Control - non-poor
Mean 2.57 vs. 3.56 3.79 3.35P-value of difference (0.175) (0.102) (0.326)Sample size 46 26 27
worse by solving 1.22 fewer questions correctly. This difference is close to be significant atthe 10% level. The comparison with the non-poor in the control group is not statistically sig-nificant.
From Table 4 it can be inferred that poor individuals who experienced a negative shockperformed significantly worse in the cognitive test than individuals who received the sameor different type of shock in the treatment group. No other pairwise comparisons (with thecontrol group) yield statistically significant differences. However, these comparisons do notrepresent the causal effect of the treatment. The causal effect in our setting is characterizedby the following expression:
Where Yi (0) and Yi (1) are the potential outcomes, i.e, the outcome that would be realizedby individual i by not receiving, and receiving the treatment, respectively. Di is the assigne-ment to treatment variable, Pi is the poverty status (poor or non-poor), and Si is the type ofshock that the individual received (negative, positive, or no shock). As mentioned before, to
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obtain the last variable, we collected the responses from the control group to the histogramshown in the treatment.
We first analyze the causal effect of the treatment regardless of what type of shock individ-uals receive. In the case of the cognitive test, this exercise amounts to replicating Mani et al.(2013). The results from the replication are reported in Table 5. According to the findings ofthese authors, poor individuals receiving the “hard” financial scenario perform significantlyworse in the Raven’s test while no difference is observed for the non-poor. As shown in thefirst column of Table 5, we do not find any significant difference between the poor in thetreatment group in our sample. There is also no difference between the non-poor in the treat-ment and control groups despite the fact that this difference is close to 0.7 more questionsanswered correctly by the non-poor in the treatment group. If we compare the performanceof the poor vs. the non-poor within treatment and control, we also do not see any statisticaldifference.
Table 5: Effects of treatment on cognitive test and inconsistent choices in risk lotteries
One advantage of our analysis is that our sample is homogenous in terms of cognitive abil-ity as is implied by the fact that students at this university must pass a very demanding ad-missions exam. In this sense, any concerns about heterogeneity in cognitive ability or levelof education is taken care of with this sample. The downside of this is that students at thiscollege might not be representative of the typical poor and that is why we do not replicateMani et al. (2013). To see if there is any difference betweeen the poor depending on the typeof shock they receive we estimate the treatment effect conditioning on this variable in Table 6.
Table 6 shows, for each type of shock, the mean of the control group in the first column,and the difference between the treatment and control means in columns 2 and 3. Column 2shows the comparison without including any controls while column 3 includes the controls
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Table 6: Causal effect of different types of shocks on correct answers to cognitive test
Dependent variable: Number of correct Raven’s test questions
Difference (T - C)Mean control group No controls Controls
which were found to be unbalanced in each row of the table.18 Similar to the correlationson Table 4, Table 6 shows that there does not seem to be a statistically significant negativetreatment effect for poor individuals under any type of shock. It is noticeable, however, thatthe magnitude of the coefficient for the treated poor under the negative shock is important.Compared to the poor control group individuals who would have received a negative shock,the poor in the treatment answer correctly about one fewer question. As implied by the largestandard errors in all these regressions, we lack power to find this effect to be significant.This is due to the fact that we only had 96 subjects to begin with, the imbalance in the defactotreatment assignment, and that stratifying the sample further reduces the number of obser-
18Randomization was successful for overall treatment and control groups but there is no reason why balancewould hold when stratifying the sample by type of shock. In general, not many covariates were unbalancedwhen stratifying the sample. We include the appropriate covariates as controls in column 3.
19
vations with which each regression is estimated. We argue, however, that the magnitude ofthe coefficient for poor individuals facing a negative shock is economically significant andsupports the results in Mani et al. (2013).
5.2 RISK PREFERENCES AND CHOICE INCONSISTENCIES
In this section we analyze the choices made by subjects in the risk lotteries. In contrast withother studies using the same elicitation instrument that we use, we can investigate choiceinconsistencies because we elicited both, row-by-row choices as well as the switching point.We can also study inconsistent choices because, given the high level of education in our sam-ple, we do not observe inconsistencies to be the norm as it may be true in populations withvery low levels of education. Further, an important reason to study choice inconsistenciesis that it provides an answer to the more general question of the causal effect of poverty oneconomic decision-making.
Table 5 above shows the causal effect of the treatment on inconsistent choices in any of thethree lotteries in survey 2. As seen in column 3, the poor in the control group have a very lowlevel of inconsistencies which is not statistically different from zero.19 In contrast, the poor inthe treatment group make 31% more inconsistent choices and this is statistically significantat the 5% level. For the non-poor, the inconsistency level is close to a third in the controlgroup, and is not statistically different from that of the treatment group. Hence, being ex-posed to the treatment causes poor individuals to make more inconsistent choices than theirpeers in the control group.
To further decompose the finding that the poor under the treatment make more inconsis-tent choices, we explore the causal effects of different types of shocks in Table 7. The poorreceiving a negative shock or no shock make systematically more inconsitent choices thanpoor individuals who would have experienced the same type of shock in the control group.This effect is not present for non-poor individuals in any of the three types of shocks nor forpoor individuals experiencing a positive shock. In sum, receiving information that they arepoorer that they thought or simply that they are in the low part of the distribution affects thechoices that poor indviduals make in the risk aversion lotteries. Since inconsistent choicesare characterized by switching back and forth from column A to B in the risk lotteries, it is un-clear if they decide to do this in order to diversify risks. If this was the case, it would suggestthat the risk aversion of the poor in the treatment group would be higher than in the controlgroup. However, as we will explain, this is not the case.
Given that we collected information about risk preferences in the baseline survey, we cancompare how inconsistent choices and the risk aversion coefficient change from survey 1 tosurvey 2. Table 8 shows the results for the inconsistency outcome defined as having incon-sistencies in any of the first two lotteries in survey 2 minus having inconsistencies in any of
19For reference, if out of the three lotteries, individuals in the control group would have made inconsistentchoices in one of them on average, the mean of this variable would be 0.33.
20
Table 7: Causal effect of different types of shocks on inconsistent choices
Dependent variable: Any inconsistent choice in three risk lotteries
Difference (T - C)Mean control group No controls Controls
the two lotteries of survey 1, that is, we first difference the dummy variable measuring anyinconsistency. Since we are clustering the standard errors at the individual level to accountfor the within-subject correlation, we do not report results for the different types of shocks.
The table shows that the rich in the control group substantially reduced the proportion ofinconsistencies by almost 29%. Similarly, the poor in the control group reduced even furtherthe proportion of inconsistencies by 8 more percentage points but this difference is not sta-tistically different from zero. Comparing the non-poor in the treatment with the non-poor inthe control leads to a finding similar to what we described previously: the treatement causesindividuals to make more inconsistent choices. In the case of the first-differences regression,this means that compared to the non-poor in the control group whose rate of inconsistencieswas reduced by 29% in survey 2, the non-poor in the treatment group actually had an increase
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in the rate of inconsistency. The interaction between poverty status and the treatment indi-cates that the poor in the treatment group had an inconsistency rate that is not statisticallydifferent from the non-poor in the same group. Then, poor and non-poor individuals in thetreatment do not show reductions in the inconsistency rates between survey 1 and survey 2as is observed for subjects in the control group.
Table 8: First differences regression of outcomes in survey 1 and survey 2
Change in choiceinconsistency
Change in sigma
Poor -0.083 -0.260*(0.166) (0.137)
Treatment 0.323** -0.305**(0.138) (0.136)
Poor*treatment -0.092 0.414**(0.197) (0.198)
Constant -0.286** 0.280***(0.122) (0.100)
Observations 96 52R-squared 0.104 0.096
Standard errors clustered at the individual level
*** p<0.01, ** p<0.05, * p<0.1
Regarding the parameters of prospect theory that can be obtained from the elicitation lot-teries, Table 9 shows the causal effect of the relative poverty expectations shock on risk aver-sion, non-linear probabilities weighting parameter, and loss aversion. As a reminder, thevariables that we use for this part are a combination of the switching point observed fromthe row-to-row choices for consistent individuals and the self-reported switching point forinconsistent individuals. While the sign for risk and loss aversion in the case of the pooris positive, these differences relative to the control group are not statistically different fromzero. Although not significant, these coefficients suggest that poor individuals in the treat-ment group become more risk averse and more loss averse than individuals in the controlgroup. Specifically, the average risk aversion parameter in the control group (0.316) wouldclassify poor individuals in this group as slightly risk averse. A risk aversion coefficient thatis higher by 0.164 in the case of the treated poor would classify them as risk averse instead ofslightly risk averse according to the ranges proposed by Holt and Laury (2002).
We find a significant difference (at the 10% level) in the risk aversion coefficient betweenthe treated and control non-poor (see column 2 of Table 9). The risk aversion coefficient
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for the non-poor in the control group is high (0.524), so a difference of -0.203 for the treatednon-poor would leave them at the level of slight risk aversion. This result suggest that becom-ing aware that they are on the top of the distribution induces them to make less risk aversechoices.
Table 9: Effect of treatment on prospect theory parameters
To further investigate the effect of the different types of relative poverty expectations shocks,Table 10 shows the mean of the risk aversion coefficient by type of shock. In general, themean for the non-poor in the control group is higher that the mean of the poor across allshock types, that is, non-poor subjects tend to be more risk averse than poor subjects in thecontrol group regardless of the type of shock. There is no clear pattern of how the poor reactto the treatment by type of shock. For example, the difference between poor in the treatmentand poor in the control with a negative shock is zero, it is positive in the no shock case, andalmost zero in the positive shock case. In none of these cases the differences are statisticallysignificant.
The result that the non-poor are less risk averse under the treatment is completely ex-plained by a large negative difference between the treated and control non-poor facing a pos-itive shock. The differences between the non-poor in the treated and control groups are notstatistically different in the other two types of shocks (although the sign in the negative shockgoes in the same direction as that in the positive shock). To summarize the findings, the non-poor are less risk averse when their relative position in the distribution is made salient andthis happens when they become aware that they are richer than they thought.
These two results may suggest one possible reason why it is often thought that the poor aremore risk averse. It might be that the poor are not more risk averse, as our results suggest, butthat rich people who are fully aware of their relative well-being are willing to take more risksthan when they are not aware of this. The risk preferences of the poor, on the other hand,
23
are unresponsive to knowing their relative position in the distribution. Even if they receive apositive shock and feel richer, they are still at the bottom of the distribution so making morerisky choices might result in important losses that they cannot afford.
Table 10: Causal effect of different types of shocks on risk aversion
Dependent variable: Risk aversion coefficient
Difference (T - C)Mean control group No controls Controls
Furthermore, based on the lottery choices reported in survey 1 we can analyze how therisk aversion coefficient changed between survey 1 and survey 2 for the 52 individuals whomade consistent choices in survey 1. The results are shown in Table 8 above. We find thatthe non-poor in the control group became more risk averse relative to survey 1. The poor inthe control did no experience a substantial change with respect to their baseline risk aver-sion (although the difference relative to the non-poor is significant at the 10% level). Thenon-poor in the treatment did not experience a large change in their risk aversion (around-0.025), while the poor became more risk-averse (increase in σ of about 0.13). Even thoughthis increase is relatively large it is found not to be significant in results not shown.
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The results (not shown) for the non-linear probability weighting function parameter andloss aversion do not show important differences between treated and control in any of theshock types. In general, the parameter of the probability weighting function is statisticallydifferent from 1, suggesting that EUT is not the right framework to describe the data in thissample.
6 CONCLUSIONS
This paper exploited the natural variation in economic backgrounds of students at a largepublic university in Colombia to provide evidence on the causal effect of poverty on risk aver-sion and inconsistent choices in an experimental setting. Relative to other papers with sim-ilar research designs, our sample consists of individuals that are homogeneous in importantways, mainly in terms of their cognitive ability and education level, but come from differenteconomic backgrounds. Furthermore, the college collects tuition depending on the level ofincome of the parents, so we have an objective measure of relative economic well-being. Weclassify as poor as those who are below the median tuition in our sample.
We adopted a prospect theory approach to measure risk preferences as prospect theory hasbeen found to be more in line with the choices made by people than expected utility theory.The instrument we used are a series of lotteries designed by Tanaka et al. (2010) to capturethe three parameters of prospect theory: risk aversion, non-linear weighting probability pa-rameter, and loss aversion. In addition, to see whether the main result in Mani et al. (2013)replicated in our sample, subjects responded a short version of the Raven’s test with a timelimit of two minutes.
The treatment that we administered consisted in asking subjects to guess where the valueof the tuition they pay was in a histogram of the tuition paid by participants in the experi-ment. Subjects were told whether they guessed correctly (in which case they earned money)or, if not, they were told exactly where their tuition was in the distribution. Participants re-ceived a negative shock (were shown to be poorer than they though they were), no shock (ifthey guessed correctly), or a positive shock (were shown to be richer than they thought). Fol-lowing this, another treatment along the lines of Mani et al. (2013) was given.
We found that, in the case of the Raven’s cognitive test, poor individuals in the treatmentgroup who receive a negative shock (are poorer than they thought) obtain about 1 fewer ques-tion correct compared to individuals in the control group who would have received a negativeshock had they been administered the treatment. Even though this difference is not statisti-cally significant, it might be relevant in real-life stakes. Poor individuals who face a situationin which their poverty is made salient may exhibit lower cognitive performance.
Contrary to what other studies implementing the risk lotteries designed by Tanaka et al.(2010) have done, we elicited individuals’ choices in every row of the lotteries as well as
25
the monotonic switching point. This allows us to measure inconsistencies in choices, e.g.whether they switch back and forth from column A to column B in the lotteries. This type ofbehavior can have economic consequences, at least in terms of the final payment they receivein the experiment, as some choices have higher expected payoffs than others so choosing atrandom may imply a lower potential final payment. We find very strong evidence that beingin the treatment group increases the probability of making inconsistent choices in any givenlottery. This is true for all individuals regardless of their poverty condition. If we discriminateby the type of shock that subjects receive as a result of the treatment, it becomes evident thatthis effect is led by the poor experiencing a negative or no shock.
Furthermore, since we collected baseline information about lottery choices, we can com-pare the change in inconsistencies in a within-subject regression. We find that subjects inthe control group reduced their rate of inconsistencies in survey 2 by around 30 percentagepoints while those in the treatment did not reduce it or even increased it sligthly. Therefore,the treatment not only causes individuals to be more inconsistent in the cross-section butalso compared to their baseline rate of inconsistencies. We interpret this as evidence thatpeople may make choices that are not optimal in an economic sense whenever their relativeeconomic situation is made salient.
Finally, we analyzed the parameters of prospect theory. We did not find significant differ-ences between the treated and the control (or the poor and non-poor) in terms of the non-linear probability weighting parameter nor loss aversion. The estimated value of the proba-bility weighting parameter is close to 0.75, which implies that expected utility theory (whichassumes α = 1) can be rejected. The loss aversion parameter is between 3.1 and 3.5, which issimilar to what other studies have found (see Liu (2013) and Tanaka et al. (2010)).
Regarding risk aversion, we find that the non-poor in the treatment group exhibit lowerrisk aversion than the non-poor in the control group but this could be because the level ofrisk aversion in the control group is very high compared to the whole sample. Analyzingthe different types of shocks suggests that the significant reduction is coming from the non-poor in the treatment group who experience a positive shock. The poor, on the other hand,become more risk averse but power is not enough to make this difference statistically signif-icant. Nevertheless, the change suggests that relative to the poor in the control who can beclassified as slightly risk averse, the poor in the treatment become risk averse according tothe classification in Holt and Laury (2002). From the analysis of the change in sigma betweensurvey 1 and survey 2, we conclude that the poor become more risk averse as a result of thetreatment but the change is also not statistically significant.
Overall, we find suggestive evidence that when their economic condition is made salient,the poor might be leaving money on the table by making choices that are inconsistent. Inaddition, the poor become slightly more risk averse as a result of the treatment but it is un-clear if the lack of statistical significance is due to low power or to the fact that the increaseis really not large. Further research is needed to see whether inconsistencies in the lotterychoices presented in this experiment extrapolate to real-world decision-making. If they do
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extrapolate, the main finding of this paper could lead to policy formulations such as havingcounseling offices so that the poor can obtain help in terms of analyzing the possible out-comes of any financial decisions they want to make.
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Appendix: Experimental Instructions (survey 2)Thank you for taking part in this study! We would like to know your decision making pro-
cess in completing the activities below. There are not right or wrong answers. You are onlyrequired to select the options that best reflect your preferences. At the end of the session yourtotal payment will be determined. After the information is recorded in the system we will in-form you via email when and how we will distribute the payment.
This activitiy shoudl be completed in ONE SESSION. Saving your answers to continue ata later time is not allowed. If you cannot complete thissurvey in one session you will not beallowed to take part in the study any more. The estimated time to complete this survey is15 minutes, but you may take as long as you need as long as do not close the session. Somequestions will have a time limit.
INSTRUCTIONS (for risk aversion lotteries)
For each row please indicate whether you prefer option A or B. At the end of the survey thetask used in determining your payment will be chosen. If this task is selected, one of the rowswill be chosen randomly. Every row is equally likely to be selected, so you should carefullyselect your preferences. If a negative value is showed, it means you may lose a portion of yourearnings. The following is an example of how activities will be displayed.
[EXAMPLE]
Your gains will depend upon your choices and luck. For example, in row number 5, let usassume that you chose column B. In that case you may win 6,500 pesos or 500 pesos. Theamount you will receive will depend upon the random number, between 1 and 10, that willbe selected at the end of the survey 2. If the number selected is 1 you will receive 6,500 pesosin addition to the 2,000 amount you will receive for taking part in the survey.
Example: Let us assume that the row selected for payment is 6. If in that row you chosecolumn A and the randomly selected number is 3. What would be your earnings?A. 4,000 pesos B. 3,000 pesos C. 6,800 pesos D. 500 pesos
INSTRUCTIONS (for Raven’s test)
In this task you will chose the option that will be a better match for the missing figure ineach image group, as shown in the following example:
[EXAMPLE]
In this case, the correct option is option 3. You will have 2 minutes to complete this task.You should answer correctly the higher number of questions to increase your earnings. If thisactivity is chosen randomly at the end of the survey you will receive 1,000 pesos for everyquestion answered correctly.
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INSTRUCTIONS (for treatment)
The following graph depicts the participants in this survey according to tuition ranges. Barheights represent the percentage of participants in each range and the width represents theamplitude of the range. Students with more economic needs will be located towards the leftof the distribution while wealthier students will be towards the right of the distribution.
You must select the bin which you believe corresponds to the tuition amount you pay. Ifyou chose correctly you will receive 1,000 pesos.
The option you selected in the previous page is correct. THE RANGE IN WHICH YOURTUITION PAYMENT LIES IS ___ORThe option you selected in the previous page is incorrect. THE RANGE IN WHICH YOUR TU-ITION PAYMENT LIES IS ___
Below is a hypotetical situation to which you must provide potential solutions AT THE ENDof this session, after completing all of the tasks. You have 30 seconds to read and understandthe situation before start completing the tasks.
Consider that this semester the University has determined to charge students with a one-time payment to rebuild deteriorated infrastructure, regardless of whether you use such in-frastructure. The one-time payment is in the amount of one million pesos and the paymentmust be completed by the end of the current semester. This means that the tuition amountwill be increased by one million pesos. How would you collect the money required to paysuch amount?
After completing all of the tasks you must provide at least three (3) different ways in whichyou would collect the money, you will have 2 minutes to complete your answers. Your pay-ment for taking part in this survey will depend upon the quality of your answers.
