Risk Preferences and Development Revisited
A Risk-Income Paradox∗
Ferdinand M. Vieider†
Peter Martinsson§
Nghi Truong‡
Pham Khanh Nam¶
April 28, 2014
Abstract
We obtain rich measures of the risk preferences of farmers in Vietnam. We put
the findings in perspective by comparing the risk preferences of the farmers to risk
preferences obtained in 30 different countries using the same experimental tasks.
Far from being particularly risk averse, our farmers are on average risk neutral and
thus more risk tolerant than Western subject populations, but less risk tolerant than
subjects in the poorest developing countries. This provides strong direct evidence of
a risk-income paradox, since risk tolerance increases with income for our farmers (in
accordance with most previous findings in the literature). These results obtain under
a variety of modeling approaches and with nonparametric data. At the same time,
preferences estimated in a structural model with an explicit stochastic structure
perform well at predicting behavior, from the purchase of lottery tickets to risk
management on the farm, thus validating our measures.
Keywords: risk preferences; development; external validity;
JEL-classification: C93; D03; D80; O12
∗
This study was financed by EEPSEA. We are grateful to Jack Knetsch and Peter P. Wakker for
helpfull comments. All errors remain ours.
†
Corresponding author: WZB Berlin Social Science Center, Reichpietschufer 50, 10785 Berlin, Germany. Email: ferdinand.vieider@wzb.eu; Tel: +49-30-25491426
‡
WZB Berlin, Germany
§
University of Gothenburg, Sweden
¶
University of Economics Ho-Chi-Minh-City, Vietnam
1
1
Introduction
People in developing countries have often been assumed to be very risk averse, with
such risk aversion potentially resulting in sub-optimal behavior. We experimentally
measure the risk preferences of poor Vietnamese farmers. The richness and quality of
the data collected is unprecedented in a development context, and allows us to revisit
the received wisdom through the estimation of structural models, backed up by nonparametric data. We show that—far from conforming to the stereotype of extreme risk
aversion—Vietnamese farmers are on average risk neutral. Comparing their risk preferences to data obtained with other subject populations using the same experimental
procedures, we conclude that Vietnamese farmers are significantly less risk averse than
American students (or for that matter, general Western population samples), while being more risk averse than Vietnamese students (or other developing country samples).
In addition, we find a strong negative correlation between risk aversion and income
amongst farmers. This indicates a risk-income paradox, whereby risk aversion decreases
with income within countries, but increases with national income between countries. Our
measures are further validated by their good correlations with real world behavior.
We need to ask ourselves why such high risk tolerance has not been detected before. Most papers experimentally measuring risk preferences in developing countries
have concluded that participants are very risk averse (Akay, Martinsson, Medhin and
Trautmann, 2012; Binswanger, 1980; Yesuf and Bluffstone, 2009).1 Most of these studies
used a task introduced in a pioneering paper by Binswanger (1980), which continues to
be extremely popular in development economics (e.g., Attanasio, Barr, Cardenas, Genicot and Meghir, 2012; Bauer, Chytilová and Morduch, 2012; Cole, Giné and Tobacman,
2012; Yesuf and Bluffstone, 2009). The Binswanger task has the distinctive feature of
capping risk preferences at risk neutrality, so that it cannot detect risk seeking behavior.
Comparison is made difficult by the fact that the same task has rarely been used in Western countries. It has the further disadvantage of not allowing for the detection of noise or
rationality violations, which may further compound the over-estimation of risk aversion
in asymmetric choice lists (Andersson, Tyran, Wengström and Holm, 2013). A modified
1
There are some exceptions to this rule. Henrich and McElreath (2002) found risk seeking in certainty
equivalents obtained with hypothetical 50-50 prospects with a Tanzanian tribe, but attributed this to
the characteristics of the tribe, lacking a comparison sample. Doerr, Toman and Schmidt (2011) found
risk seeking with Ethiopian farmers using a choice list à la Holt and Laury (2002).
2
Binswanger task developed by Eckel and Grossman (2008) has indeed been shown to
over-estimate risk aversion relative to other tasks (Reynaud and Couture, 2012). While
there is considerable evidence that farmers employ risk averse strategies in their real
decisions (Jayachandran, 2006; Rosenzweig and Binswanger, 1993), this type of evidence
does not lend itself to comparison with Western populations, which generally have much
lower risk exposure. Indeed, many elements other than the small stake risk preferences
measured in experiments may play into such decisions—we will return to this point in
the discussion.
Our data also hold an interest outside of the development context. There has recently
been an increased move towards the collection of data with non-student population
samples. Donkers, Melenberg and Van Soest (2001) analyzed risk attitudes of a large
sample of the Dutch population with a hypothetical lottery question. Dohmen, Falk,
Huffman, Sunde, Schupp and Wagner (2011) and Dohmen, Falk, Huffman and Sunde
(2012) analyzed risk attitudes of German general population samples using qualitative
survey questions. Booij, Praag and Kuilen (2010) obtained hypothetical measurements
allowing for the estimation of structural models, and von Gaudecker, van Soest and
Wengström (2011) used several incentivized measures with a large sample of the Dutch
population. Most recently, Barseghyan, Molinari, O’Donoghue and Teitelbaum (2013)
estimated a model of risk taking based on choices of deductible plans in home and auto
insurance. Choi, Kariv, Müller and Silverman (2013) studied budget allocations of a
Dutch general population sample and investigated their conformity to basic rationality
principles. And Sutter, Kocher, Glätzle-Rützler and Trautmann (2013) examined the
predictive power of experimentally elicited risk preferences for behavior of adolescents.
We add to these studies in several ways. Other than Donkers et al. (2001) or Dohmen
et al. (2011), we obtain a very rich set of measurements that are fully incentivized
conducting a controlled experiment. Other than Sutter et al. (2013), who use a simple
certainty equivalent over 50-50 gains, we estimate structural models incorporating an
explicit stochastic structure. This aspect is similar to von Gaudecker et al. (2011), to
which we add by estimating likelihood-sensitivity for both gains and losses. We do,
however, have a subject pool that is representative only of the local village population,
and not of the country at large.
This paper proceeds as follows. Section 2 describes our subject pool, the measurement tasks, and the general setup of the experiment. Section 3 introduces the theoretical
3
setup and discusses the econometric specifications used. Section 4 presents the aggregate
results and puts them into perspective by comparing them to the risk attitudes of students across 30 countries. Section 5 examines the predictive power of our risk preference
measures. Section 6 discusses the results and concludes the paper.
2
Experimental setup
We recruited 207 farmers in the Vietnamese villages Phu Hiep, Phu Loi and Phu Quoi
in An Giang province, close to the border with Cambodia alongside the Tien river. The
villages were chosen since we could obtain the backing of the local party authorities.
No systematic selection effects are likely to be caused by this—we will discuss this point
more at length below. The households were randomly chosen from a complete population
list of the three villages. There was a 100% participation rate of our target population.
This means that our sample is representative of the village reality of Southern Vietnam,
although we cannot claim representativeness outside of this specific subject pool. No
party official was present at any time during the experiment or questionnaire tasks,
and subjects were reassured that their data would be treated anonymously and seen by
nobody but the researchers.
The median household in our sample has an income of 9.9m Dong per capita per
year. This corresponds to $1.32 per capita per day for the median households in current exchange rates at the time of the experiment, and to $2.89 in purchasing power
parity (PPP ; calculated using World Bank data for 2011). The corresponding means
are $2.26 (sd: 3.38) and $4.95 (sd: 7.39) respectively. About 24% of our subjects fall
below the official poverty line of the Vietnamese government.2 Income was measured by
asking farmers about different categories of income and then aggregating across those
categories (see supplementary materials for questionnaire). Since most farmers in the
region produce for the market, and since we ran our experiments not too long after
the main harvest season, the information was relatively recent and hence easy to remember. Given the importance of income for our study, we also compare our sample
to the corresponding figures for comparable population groups, as obtained from the
2
The poverty line applied here is based on “Decision of the Prime Minister 9/2011/QD-TTG: Promulgating standards of poor households, poor households to apply for stage from 2011 to 2015”, in which
the poverty line for rural areas is 400,000 Dong per capita per month and for urban areas it is 500,000
Dong per capita per month.
4
Vietnamese statistical office (www.gso.gov.vn). The income per capita of our farmers
is indeed not significantly different from the one of the rural population in Vietnam at
large (t(198) = −1.01, p = 0.312, two-sided t-test).
We also have significant variation in terms of age with a mean of 49.9 years and a
standard deviation of 13.5 (range: 23-87), and education, recorded in 9 categories, with
a mean of 2.2 and a standard deviation of 0.92. All subjects were literate. All but 6
household heads were male.
Table 1: decision tasks, amounts in 1000s of Dong
gains
losses
mixed
(1/2: 40; 0)
(1/2: 80; 0)
(1/2: 160; 0)
(1/2: 240; 0)
(1/2: 240; 80)
(1/2: 240; 160)
(1/8: 160; 0)
(1/8: 160; 40)
(2/8: 160; 0)
(3/8: 160; 0)
(5/8: 160; 0)
(6/8: 160; 0)
(7/8: 160; 0)
(7/8: 160; 40)
(1/2: -40; 0)
(1/2: -80; 0)
(1/2: -160; 0)
(1/2: -160; -40)
(1/2: -160; -80)
0∼(1/2: 160; z*)
(1/8: -160; 0)
1/8: -160; -40)
(2/8: 160; 0
(3/8: -160; 0)
(5/8: -160; 0)
(6/8: -160; 0)
(7/8: -160; 0)
(7/8: -160; -40)
We elicit certainty equivalents (CEs) to measure risk preferences. CEs provide a rich
amount of information, are easy to explain to subjects, and the sure amounts of money
to be used in the elicitation are naturally limited between the lower and upper amount
of the prospect. They are also flexible enough to allow for the detection of risk-seeking
as well as risk neutral and risk averse behavior. This makes them well-suited to estimate
structural models of decision making (Abdellaoui, Baillon, Placido and Wakker, 2011;
Bruhin, Fehr-Duda and Epper, 2010). Overall, we elicited 44 CEs per subject. The
tasks used for the elicitation procedure where chosen so as to allow for the estimation of
multi-parameter models, and were tested in extensive pilots with students before being
deployed in the field. Table 1 provides an overview of the decision tasks, and figure 1
shows an example of a choice list. Prospects are described in the format (p : x; y), where
p is the probability of obtaining x, and y obtains with a complementary probability 1−p,
|x| > |y|. Outcomes are shown in thousands of Dongs. The highest loss is smaller than
the largest gain. This was necessary to limit financial exposure, since all subjects who
were randomly selected to play the loss part would be given an endowment equal to the
5
highest loss possible. In addition to the prospects over gains and losses, we used one
mixed prospect, which is necessary to obtain a measure of loss aversion. In this case, we
obtained the value z* which satisfies the indifference 0 ∼ (1/2 : 160; −z), where z varied
in a choice list from 160 to 16.3
Figure 1: Example of choice list to elicit a CE
Gains were administered before losses, which took part from an endowment (see
Etchart-Vincent and L’Haridon, 2011, for evidence that it does not matter whether
losses take place from an endowment or are real). We also had prospects with unknown
or vague probabilities that will not be analyzed here, and which were always presented
in block after the risky prospects. The prospects were presented to subjects in a fixed
order, whereby first 50-50 prospects were presented in order of ascending expected value,
and then the remaining prospects were presented in order of increasing probability. The
fixed order was kept so as to make the task less cognitively demanding for subjects,
since in the fixed ordering only one element would change from one decision task to the
next, which could be easily pointed out by the enumerator. To test whether such a fixed
ordering of tasks might influence decisions, we ran a large-scale pilot at Ho-Chi-MinhCity University involving 330 subjects. The pilot revealed no differences between the
fixed ordering used here and a random ordering (results available upon request).
CEs were elicited in individual interviews by a team of 18 enumerators. The enumerators were extensively trained before going to the field, and had acquired experience by
3
The choice tasks (though not the instructions, this experiment being run in individual interviews)
and payoffs were the same as the ones used by L’Haridon, Martinsson and Vieider, 2013 in experiments
with students across 30 countries. For an overview of the tasks, see the instructions available for
download at www.ferdinandvieider.com/instructions.html.
6
running the same experiment with students. They were furthermore supervised in the
field by one of the authors. The actual experiment was preceded by a careful explanation
of the decision tasks involved. The subjects were told that they would face choices between amounts of money that could be obtained for sure and risky allocations, in which
different amounts would obtain with some probabilities indicated next to them. They
then learned that the interview would consist in a number of such tasks that would differ
in the amounts they offered as well as the likelihood with which these amounts obtained.
At the end, one of the tasks would be extracted at random, and one of the lines in which
they had indicated a choice between a sure amount and the prospect would be played
for real money (the standard procedure in this sort of task: Abdellaoui et al., 2011;
Baltussen, Post, van den Assem and Wakker, 2010; Bruhin et al., 2010; Choi, Fisman,
Gale and Kariv, 2007). Losses were only introduced once all the gain prospects had been
played. Small breaks were taken between the different parts of the elicitation procedure.
Once a subject had understood the general structure, he was presented an example
of a decision task for risky gains. The enumerator then explained why for a safe amount
equal to the lower amount in the prospect, he would likely prefer to take the prospect.
Equivalently, once the sure amount reached the highest amount to be won in the prospect,
the subject would be explained that he would most likely prefer the sure amount. This
would lead naturally to a point at which a subject should switch from the prospect
to the sure amount. At which amount this would happen would be purely up to the
farmer’s preference. Most farmers understood this very quickly. If farmers wanted to
switch multiple times, enumerators were instructed to simply record such choices. This,
however, never happened. This is likely due to the detailed explanations, to the nature
of the certainty equivalent task in which only the sure amount changes from choice to
choice and which is thus straightforward to understand.
Since all farmers were literate, they were shown the lottery depiction and the amounts
involved on the interview sheet. Every time a major change occurred in the decision tasks
(e.g. from risk to ambiguity or from gains to losses), the enumerator pointed out the
change and gave additional explanations of what this would involve. In the course of
the explanation, farmers were also shown bags containing numbered ping pong balls
that would be used for the random extraction, and were encouraged to examine their
contents. This served to make the decision problems more tangible and concrete.
The prospects concerned payoffs between 0 and 320,000 Dong, which were added
7
to a fixed participation payment of 8,000 Dong. These are substantial sums, with the
expected payoff from participation corresponding to about 6 days’ per capita income of
the median household, and the highest prize to over 10 days. This indicates a general
tendency by which PPP conversions used for developing countries underestimate the
amounts used if one were to employ income instead of prices as a gauge. Notice how,
given the well-established finding of risk aversion increasing in stakes (Binswanger, 1980;
Fehr-Duda, Bruhin, Epper and Schubert, 2010; Holt and Laury, 2002; Kachelmeier and
Shehata, 1992; Santos-Pinto, Astebro and Mata, 2009), this tends to bias our findings
against risk tolerance. Notice also that the payoffs we offer are at least as high as most
of the payoffs offered in similar studies in developing countries (for instance, Attanasio
et al., 2012, have average payoffs of about $2, corresponding to about 1 day’s pay; Yesuf
and Bluffstone, 2009 have an average payoff of about 3 days of pay).
The overall quality of our data is good, which likely reflects the careful procedures
followed in explaining the tasks. About 25% of our subjects violated first order stochastic
dominance at least once for gains, and about 31% for losses. This is in line with violations obtained with student samples from the West. Abdellaoui, Bleichrodt, L’Haridon
and Van Dolder (2013) found about 20% of subjects to violate stochastic dominance
in a laboratory experiment with students using individual interviews. L’Haridon et al.
(2013) observe violation rates between 17% and 37% with Western student subjects in
experimental sessions using the same tasks. Overall violations relative to total number
of CEs in our farmer data amount to only about 3.0% for gains, and to 4.3% for losses.
3
3.1
Theory and Econometrics
Theoretical setup
The results presented in this paper are stable to using most major theories, including
expected utility theory (EUT ) and prospect theory (PT ). The main modeling approach
in the paper is motivated by obtaining the highest possible descriptive accuracy, conditional on keeping the analysis tractable from an empirical point of view. We will adopt
a reference-dependent modeling approach throughout. Such an approach is an integral
part of prospect theory (Kahneman and Tversky, 1979). It was first proposed for expected utility by Markowitz (1952), in an attempt to accommodate the observation of
lottery and insurance purchase by the same person, and has by now been widely adopted
8
into EUT in both theory and empirical analysis (Diecidue and van de Ven, 2008; Kőszegi
and Rabin, 2007; Sugden, 2003; von Gaudecker et al., 2011). We will adopt the reference
point to be zero throughout—a standard assumption in this type of literature.
We will start by representing our preferences through a PT model.
Reference-
dependent expected utility as well as its dual theory (Yaari, 1987) are special cases
of this model, so that it will later be easy to restrict the parameters in convenient ways
for the empirical analysis. We describe decisions for binary prospects. For outcomes that
fall purely into one domain, i.e. x > y ≥ 0 or 0 ≥ y > x, we can represent the utility of
a prospect ξ, U (ξ), as follows:
U (ξi ) = wj (pi )v(xi ) + [1 − wj (pi )]v(yi )
(1)
whereby the probability weighting function w(p) is a strictly increasing function that
maps probabilities into decision weights, and which satisfies w(0) = 0 and w(1) = 1; the
superscript j indicates the decision domain and can take the values + for gains and −
for losses; and v(.) represents a utility or value function which indicates preferences over
outcomes, with a fixed point such that v(0) = 0, and v(x) = −v(−x) if x < 0. Contrary
to EUT, utility curvature in the full PT model cannot be automatically equated with
risk preferences, since the latter are determined jointly by the utility and the weighting
function (Schmidt and Zank, 2008). For mixed prospects, where x > 0 > y, the utility
of the prospect can be represented as:
U (ξi ) = w+ (pi )v(xi ) + w− (1 − pi )v(yi )
(2)
In our experimental tasks, we elicit certainty equivalents, such that by definition ce ∼
(x, p; y), where ∼ indicates indifference. We can represent the certainty equivalents
estimated according to the model just presented as follows:
ce
ˆ i = v −1 wj (pi )v(xi ) + (1 − wj (pi ))v(yi )
(3)
In order to specify the model set out above, we need to determine the functional forms
9
to be used. For utility we use a power function. This is the most popular function in the
empirical literature and it has some desirable theoretical qualities (Wakker, 2008). Our
conclusions do not change qualitatively if we use an exponential value function instead.
We thus adopt the following functional form:
v(x) =




xµ
if x > 0
(4)


 −λ(−x)ν
if x ≤ 0
where the parameter λ indicates loss aversion, generally represented as a kink in the
utility function at the origin (Abdellaoui, Bleichrodt and Paraschiv, 2007; Köbberling
and Wakker, 2005).
For probability weighting, we adopt the 2-parameter weighting function proposed
by Prelec (1998) (Other functional forms from the two-parameter family deliver similar
results. One-parameter forms are, on the other hand, not well suited to describe our
data, for reasons that will become apparent below):
j
w(p) = exp(−β j (−ln(p))α )
(5)
For β = 1, this function conveniently simplifies to the 1-parameter function proposed
by Prelec, which has a fixed point at 1/e ' 0.368, and which has been developed to fit
typical aggregate data from the West. In its complete specification, β is a parameter
that governs mostly the elevation of the weighting function, with higher values indicating
a lower function. Since this indicates the weight assigned to the best outcome for gains,
and the weight assigned to the worst outcome for losses, a higher value of β indicates
increased probabilistic pessimism for gains, and increased probabilistic optimism for
losses. The parameter α governs the slope of the probability weighting function, with α =
1 indicating linearity of the weighting function (the EUT case), and α < 1 representing
the typical case of probabilistic insentivity.
The latter is best characterized in terms of upper or lower subadditivity (Tversky and
Wakker, 1995), whereby the same difference in terms of probabilities results in a smaller
difference in probability weights away from the endpoints of p = 0 and p = 1 than close to
them. This results in the characteristic inverse S-shaped weighting function (Abdellaoui,
10
2000; Bleichrodt and Pinto, 2000; Kilka and Weber, 2001; Wu and Gonzalez, 1996).
Lower subadditivity is often referred to as the possibility effect and can be formalized
for a constant ≥ 0 as w(q) − w(0) ≥ w(q + p) − w(p) whenever q + p ≤ 1 − . Upper
subadditivity is commonly known as the certainty effect, and can be formalized for a
constant 0 ≥ 0 as w(1) − w(1 − q) ≥ w(p + q) − w(p) whenever p ≥ 0 .
3.2
Stochastic modeling and econometric specification
The model considered so far is fully deterministic, assuming that subjects know their
preferences perfectly well and execute them without making mistakes. Even more importantly, it assumes that we can capture such preferences perfectly in our model. We now
abandon this restrictive assumption and introduce an explicit stochastic structure. We
start by rewriting the utility of a prospect as U (ξ) = V (ξ) + ξ , where V (ξ) represents
utility as we observe and model it, whereas ξ is an error term that picks up everything
that is not captured in modeled utility, be it errors in utility calculation, unobservable
characteristics of the decision maker, or noise deriving from the mis-specification of our
model relative to the true underlying decision process generating the data (Train, 2009).
Given this setup, the certainty equivalent we observe will thus be equal to the certainty equivalent calculated from our model plus some error term, or cei = ce
ˆ i + i . We
assume this error to be normally distributed, i ∼ (0, σi2 ), meaning that we are estimating a Probit model (see again Train, 2009). We can now express the probability density
function ψ(.) for a given subject n and prospect i as follows
ψ(θn , σnij , ξi ) =
1
σnij
φ
ce
ˆ niθ − ceni
σnij
(6)
where φ is the standard normal density function, and θ = {µ, ν, λ, αj , β j , } indicates
the vector of parameters to be estimated.4 The subscript n to the parameter vector θ
indicates that we will let the parameters depend linearly on the observable characteristics
of decision makers, such that θ̂ = θ̂k + βX, where θ̂k is a vector of constants and
X represents a matrix of observable characteristics of the decision maker. Finally, σ
indicates a so-called Fechner error (Hey and Orme, 1994). The subscripts emphasize
that we are allowing for three different types of heteroscedasticity following Bruhin, Fehr4
Modeling choices in terms of descrete choice econometrics instead does not qualitatively change our
conclusions—see stability analysis in the supplementary materials.
11
Duda and Epper (2010), whereby n indicates as usual the observable characteristics of
the decision maker (solving the issue indicated by Andersson et al., 2013), j indicates
the decision domain (gains vs. losses vs. mixed domain), and i indicates that we allow
the error term to depend on the specific prospect, or rather, on the difference between
the high and low outcome in the prospect, such that σi = σ|xi − yi |.
These parameters can now be estimated by maximum likelihood procedures (see
Myung, 2003, for a short and intuitive introduction to the concept of maximum likelihood). To obtain the overall likelihood function, we now need to take the product of the
density functions above across prospects and decision makers:
L(θ) =
N Y
Y
ψ(θn , σnij , ξi )
(7)
n=1 i
where θ is the vector of parameters to be estimated such as to maximize the likelihood
function. Taking logs, we obtain the following log-likelihood function:
LL(θ) =
N X
X
n=1
ln [ψ(θn , σni , ξi )]
(8)
i
We estimate this log-likelihood function in Stata using the Broyden-Fletcher-GoldfarbShanno optimization algorithm. Errors are always clustered at the subject level.
4
4.1
The risk-income paradox
Modeling choice and data fit
We start by describing risk preferences in the aggregate and by showing the risk-income
paradox. To do this, we first simplify the model described above. In prospect theory, the
utility and probability weighting parameters are generally collinear to some extent (Zeisberger, Vrecko and Langer, 2012). Given that risk preferences are expressed in utility
and weighting functions jointly, the full model is not well-suited for comparing groups in
terms of risk preferences. It is also cumbersome for regression analysis, since regressors
may influence utility curvature and probability weighting in opposite directions, making
the effect in terms of risk preferences harder to appreciate. We thus simplify the model
presented above by assuming utility to be linear, so that u(x) = x, thus modeling risk
preferences entirely through subjective probability transformations.
12
This dual EU function was first proposed by Preston and Baratta (1948) and was
later axiomatized for rank-dependent utility by Yaari (1987). Figure 2 shows the fit of
this function to the non-parametric data points for gains (the figure for losses is shown
in the supplementary materials). The function can be seen to trace the data closely
across the probability space. The dimension that is not well represented by the function
is, somewhat unsurprisingly, the one deliberately inserted to separate utility curvature
from probability weighting at p = 0.5. The flip-side of this is that the function is more
tractable and has a more immediate interpretation in terms of risk preferences. Indeed,
the parameter β can now be interpreted as a risk aversion parameter, while α still
indicates probabilistic sensitivity. To emphasize this new interpretation, we will refer to
this function as the risk-preference function.
Figure 2: Fit of risk preference function to non-parametric data
We will adopt this function throughout the paper. We consider the neglect of the
utility dimension a price worth paying for the increased empirical tractability, since most
interesting action for moderate stakes is reckoned to take place along the probabilistic
dimension (Fehr-Duda and Epper, 2012). All the results reported hereafter remain stable
if we use the full PT model instead; the main results are also stable to using a oneparameter EUT specification (although we lose some interesting dynamics registered in
the sensitivity parameter). Estimations of an EUT formulation are shown in appendix A,
and for the full PT model in appendix B. The supplementary materials also show decision
parameters estimated at the individual level and a description of their distribution.
13
Finally, we also adopt a simplified version of loss aversion. According to the model
presented above, the loss aversion parameter will always be influenced by probability
weighting and/or utility curvature (Schmidt and Zank, 2005). This seems undesirable,
since effects on e.g. probability weighting for gains and for losses will have effects on
estimated loss aversion even when behavior for mixed prospects does not change. We
will thus adopt a ‘behavioral’ definition of loss aversion, according to which λ = x/−y.
The parameter will thus be purely recovered from the mixed prospect, and will not be
influenced by what happens in the pure gain and pure loss domains.
4.2
Risk preference comparison
Table 2 shows a regression comparing the parameter estimates for farmers to those of
American and Vietnamese students (the corresponding estimations for EUT are shown
in appendix A). The student data were obtained using the same experimental tasks as
the one used with the farmers and stakes are the same in terms of PPP.5 The regression
controls for the sex of the respondent to address concerns that differences may be driven
by gender effects that are often found for risk (Croson and Gneezy, 2009). Indeed, we
find that women are less sensitive to probabilistic change for both gains and losses, as
well as less risk tolerant for losses.
Table 2: Comparison between farmers and Vietnamese and US students
N=424, LL=-33,294
students US
students Vietnam
female
constant
α+
β+
α−
β−
λ
σ
0.309***
(0.053)
0.236***
(0.053)
-0.140***
(0.048)
0.492***
(0.031)
0.220***
(0.053)
-0.036
(0.054)
0.049
(0.044)
0.821***
(0.042)
0.353***
(0.060)
0.221***
(0.056)
-0.105**
(0.052)
0.535***
(0.032)
-0.144**
(0.060)
-0.026
(0.065)
-0.114**
(0.055)
1.069***
(0.047)
0.099
(0.144)
-0.128
(0.093)
0.131
(0.101)
1.664***
(0.068)
-0.141***
(0.021)
-0.088***
(0.020)
0.027
(0.022)
0.300***
(0.011)
We find both student groups to be significantly more sensitive to probabilistic change
than farmers. This holds for both gains and losses, and is consistent with the interpretation of the sensitivity parameter as a proxy for rationality or numeracy (Tversky and
Wakker, 1995; Wakker, 2010). Students also show less noise in their decisions compared
5
The data for American students were obained using sessions instead of individual interviews. For
Vietnamese students, we obtained the data partially in interviews using identical procedures as for
farmers, partially in sessions. We pool the data since we did not find any differences between the
two methods (except for loss aversion)—see supplementary materials for the regression and additional
discussions.
14
to the farmers, which is consistent with comparisons of students and general population
groups in the West (Choi et al., 2013; Huck and Müller, 2012). The farmers are slightly
(but not significantly) less risk tolerant than Vietnamese students for gains, as indicated
by the negative coefficient for the β + parameter. The farmers are, however, significantly
more risk tolerant than the American students for both gains and losses. Indeed, American students exhibit decision patterns as they have typically been estimated in the West,
with a β + parameter significantly larger than one.6 For loss aversion we find again that
our farmers are intermediate between the two student populations, although none of the
differences are significant. Estimations using EUT show the same ordering of preferences,
and are shown in the appendix.
Figure 3: Risk-preference functions for gains, farmeres versus students
Figure 3 shows the three risk preference functions for gains together with the nonparametric data points (for losses see supplementary materials). The risk-preference
function for farmers is more elevated than the one of the American students up to and
including p = 5/8, and becomes very similar and somewhat lower for the two highest
probability levels respectively. Compared to Vietnamese students, the risk preference
functions are very similar up to at least p = 3/8, after which the two functions start to
diverge, as reflected in the farmers’ lower probabilistic sensitivity.
The comparison results may appear surprising, given a large number of studies show6
For the prospect theory formulation shown in the appendix, β + = 1 cannot be rejected, so that the
function reduces to its one-parameter formulation. This estimate is thus at the lower end of the range
of estimates obtained in Western countries—see Booij et al. (2010).
15
ing risk aversion as the prevalent pattern in decisions under risk—virtually all of which
were conducted in Western, industrialized, countries. To investigate the stability of these
findings—and to be able to discuss average risk preferences over all choices with one simple measure—we now take the risk premium, given by EV − CE, averaged over all gain
prospects (in PPP Euros; PPP US Dollars obtain by multiplication with 1.2). We here
concentrate on gains—an equivalent analysis for losses is shown in appendix C. Farmers
have a significantly lower risk premium than American students (z = −2.07, p = 0.039,
two-sided Mann Whitney test), and a (non-significantly) larger risk premium than Vietnamese students (z = 1.54, p = 0.123). While American students are significantly risk
averse (z=4.67, p<0.001; two-sided Wilcoxon signed-rank test), the farmers are on average risk neutral (z=0.23, p=0.815), and Vietnamese students are on average risk seeking
(z = −2.38, p = 0.017).
Figure 4: Risk preferences in relation to GDP per capita, farmers and students
Nor are these two comparison groups of American and Vietnamese students exceptional. To illustrate this point, we use the data from experiments with students in 30
countries described by Vieider, Lefebvre, Bouchouicha, Chmura, Hakimov, Krawczyk
and Martinsson (2014b). They were obtained using the exact same prospects and payoffs (in terms of PPP) as used with our farmers. Figure 4 plots the country average
of the mean risk premium from the student experiments against the (log of) GDP per
capita, thus putting the results into perspective. There is a strong positive correlation
between the log of GDP per capita and the risk premium (ρ = 0.56, p = 0.001, N = 31;
16
Spearman correlation). These results are also consistent with recent evidence from a
survey eliciting the hypothetical willingness to pay of economics students for various
lotteries in a large sample of countries (Rieger, Wang and Hens, 2014).
Seen in this context, we can revisit the issue of potential selection effects. Since our
villages were selected in a procedure that may be considered as good as random, and
since we used random selection within the villages, we mentioned above that selection
effects appear unlikely. The comparison of income in our sample with the one of the
Vietnamese rural population at large also showed no differences in this important dimension. The evidence just presented seems to reinforce that impression, as the data
point for Vietnamese farmers falls exactly were we would expect it to fall based on the
relation with GDP (assuming that farmers are more risk averse because of their lower income, and/or more advanced age, and/or lower education—see below). And once again,
this appears not to be an isolated case. Using a similar experiment to elicit risk preferences with a representative sample of the rural population in the Ethiopian heartland,
Vieider, Beyene, Bluffstone, Dissanayake, Gebreegziabher, Martinsson and Mekonnen
(2014a) found risk seeking to be the prevalent aggregate pattern. Converting the outcomes to the same measures used here, the average risk premium of that population was
found to be −0.451. Notice that in figure 4 this data point would show up relative to
the Ethiopian students in a roughly equal position to the one for Vietnamese farmers
relative to Vietnamese students. This evidence is also consistent with risk seeking of
Ethiopian farmers found by Doerr et al. (2011) and the results from Tanzania reported
by Henrich and McElreath (2002).
4.3
Risk preferences and income
So far we have only considered aggregate preferences. The next step will be to look into
individual characteristics and their correlation with risk preferences. In particular, in
this section we are interested in income, as well as some other general demographics,
to show the complete risk income paradox (correlations with behavior will be examined
in the next section). Table 3 shows the results of a regression of risk preferences on
income per person, education, age and sex of the respondent (z-values are used for age,
education, and income). Our subject pool is reduced to 197 subjects, since for the
remaining subjects one of the four observable characteristics is not reported.
17
Table 3: Effects of income on risk preferences
N=197, LL = −16, 382
income
education
age
female
constant
α+
β+
α−
β−
λ
σ
-0.007
(0.036)
0.053
(0.037)
-0.075**
(0.032)
0.141
(0.169)
0.489***
(0.032)
-0.074**
(0.030)
0.030
(0.040)
0.025
(0.051)
0.223
(0.364)
0.820***
(0.043)
-0.007
(0.031)
0.060
(0.043)
-0.062**
(0.031)
0.120
(0.101)
0.529***
(0.031)
0.078*
(0.046)
0.028
(0.129)
-0.027
(0.053)
-0.385***
(0.104)
1.095***
(0.049)
-0.065**
(0.028)
0.174**
(0.088)
0.094
(0.089)
0.832
(0.663)
1.676***
(0.073)
-0.009
(0.006)
-0.016**
(0.007)
0.017
(0.011)
-0.078***
(0.026)
0.312***
(0.012)
Standard errors in parentheses, * p<0.10, ** p<0.05, *** p<0.01
We start by looking at the elevation of the risk preference function. For both gains
and losses, we find risk tolerance to increase in income, as indicated by the negative
coefficient for β + and the positive coefficient for β − . Loss aversion is also found to
decrease in income. These effects are stable if we use an expected utility model instead
(see appendix A), and hold also if we run a simple OLS with the mean risk premium used
for the international comparison above (see supplementary materials). Together with the
comparison data discussed above, this provides strong evidence of a risk-income paradox,
whereby risk tolerance increases in income within countries, but decreases in income per
capita between countries. The same relationship of risk tolerance with income has also
been found in Ethiopia by Vieider et al. (2014a), using land owned and altitude as proxies
for income. A positive relation between risk tolerance and income has furthermore
frequently been reported in Western population samples (e.g., Dohmen et al., 2011;
Donkers et al., 2001; Hopland, Matsen and Strøm, 2013; von Gaudecker et al., 2011).
This brings us to the other demographic variables. Probabilistic sensitivity for both
gains and losses decreases with age. Given how sensitivity is taken to be an indicator of
rationality, this corresponds well to what we would expect. Also, the result corresponds
closely to the results of L’Haridon et al. (2013), who find sensitivity to decrease in age
and increase in grade point average. It is also in general agreement with findings by
Choi et al. (2013), who found violations of rationality principles to increase with age
and decrease with education and income (the latter effect is not significant in our data).
Loss aversion is also found to increase in education. This is contrary to the findings
of Gächter, Johnson and Herrmann (2010), but in agreement with the findings by von
Gaudecker et al. (2011).
An important issue is whether our findings are indeed driven by income, and not by
18
wealth. Wealth has sometimes been used as a proxy for risk preferences in the development economics literature, with larger farmers assumed to be less risk averse (Feder,
Just and Zilberman, 1985). To capture wealth levels we use the first two components
from a principal component analysis into which all variables capturing wealth in our data
set are entered (Filmer and Pritchett, 2001). Table 4 reproduces the results from table
3 controlling for these wealth indicators.7 The wealth controls do not show any significant effects. This goes against the traditional assumption of risk tolerance increasing in
wealth, a point to which we will return in the discussion.
Table 4: Income regression with wealth controls
N=185, LL = −15383
income
education
age
female
pc1
pc2
constant
α+
β+
α−
β−
λ
σ
-0.002
(0.052)
0.074
(0.045)
-0.055
(0.036)
0.126
(0.196)
-0.003
(0.027)
-0.004
(0.042)
0.486***
(0.033)
-0.079**
(0.034)
0.022
(0.041)
0.025
(0.057)
0.174
(0.360)
0.025
(0.035)
0.033
(0.050)
0.818***
(0.044)
0.008
(0.042)
0.092**
(0.036)
-0.053
(0.036)
0.135
(0.100)
-0.009
(0.024)
0.036
(0.037)
0.528***
(0.032)
0.116**
(0.054)
0.092
(0.101)
-0.005
(0.061)
-0.322***
(0.119)
-0.051
(0.042)
0.012
(0.046)
1.101***
(0.051)
-0.065**
(0.028)
0.174**
(0.088)
0.065
(0.083)
0.562
(0.570)
-0.017
(0.042)
0.068
(0.060)
1.694***
(0.076)
-0.000
(0.009)
-0.014**
(0.006)
0.016
(0.010)
-0.069**
(0.027)
-0.015***
(0.005)
-0.005
(0.008)
0.314***
(0.012)
Standard errors in parentheses, * p<0.10, ** p<0.05, *** p<0.01
More importantly for the purpose of this section, the effect of income only results
reinforced from the introduction of wealth controls. Given the large effect of income and
the absence of wealth effects on risk preferences, this raises the question of the origin of
the relationship between the two. We cannot directly address issues of causality in our
data set. Nevertheless, we will return to this issue in the discussion.
5
Preferences and behavior
In this section, we address the question whether risk preferences as we measured them can
‘predict’ real world behavior, i.e. whether they correlate with activities we would expect
them to correlate with. Previous evidence is mixed on this point, but predominantly
concludes that this kind of preference measurements perform badly at predicting real
7
Wealth is positively correlated with income, as one might expect. However, the correlations of our
income measure with the first principal component is relatively modest at r=0.31.
19
world behavior (see Liu, 2012, and Liu and Huang, 2013, for recent exceptions). For
instance, Sutter et al. (2013) recently found in a large-scale study that risk preferences
had almost no predictive value for adolescents’ behavior. Giné, Townsend and Vickery
(2008) and Cole, Giné and Tobacman (2012) measured risk preferences in randomized
controlled trials to study the uptake of rainfall insurance in India, and even found risk
aversion to be negatively correlated with insurance purchase decisions. We hypothesize
that part of this low predictive power of experimentally measured risk preferences may
be due to the restrictiveness of the measures obtained on the one hand, and to the
deterministic nature of the data on the other.8 For instance, all three studies mentioned
obtained measures for 50-50 prospects over gains.9 The risks involved in decisions such as
smoking or insurance purchase, however, may be better characterized as low probability
losses.
To explore whether our data perform better at predicting behavior, we start by
correlating our structural estimates with a number of general types of behavior that one
may expect to be influenced by risk preferences, such as saving, buying lottery tickets,
and smoking. Here as well as below, we only use variables for which we had a clear ex
ante hypothesis on the expected direction of the effects. We also control for the same
population characteristics as above. There is one more methodological caveat to be
mentioned. In order to be able to estimate a structural model with several parameters,
we maintain the econometric structure set forth above. Conceptually, however, it must
be clear that the behavioral variables in the regression ought now to be seen as dependent
variables, with the risk preferences taking the place of the explanatory variables. The
alternative would be to estimate the parameters at the individual level and to then enter
them into a regression as independent variables. This has, however, the disadvantage
that only point estimates of the parameters are used, and that they are all treated as
independent entries. This is avoided in a structural estimation, which we thus consider
to be methodologically sounder.
The regression is reported in table 5. We start by looking at lottery buying behav8
Several other explanations for a negative relation between risk aversion and insurance purchase are
possible. Clarke (2011) derives a EUT-based model in which insurance purchase is hump-shaped in risk
aversion in the presence of basis risk. Liquidity constraints of the poorest farmers, who are also likely
to be the most risk averse, is another potential explanation. And to the extent that the Binswanger
task used in these studies may measure mainly loss aversion, even in the absence of basis risk such loss
aversion may play against purchasing insurance if monetary outlays are modeled as losses.
9
If following Sutter et al. (2013) we use CEs over 50-50 prospects instead of our structural model,
we indeed fail to spot the correlations obtained with our structural model.
20
Table 5: predicting risk behavior
N=197, LL = −16, 289
lottery
savings
smoker
education
age
income
female
constant
α+
β+
α−
β−
λ
σ
0.035
(0.064)
-0.000
(0.047)
0.038
(0.080)
0.050
(0.036)
-0.077**
(0.034)
-0.018
(0.048)
0.099
(0.139)
0.444***
(0.075)
-0.193**
(0.090)
-0.084**
(0.034)
0.016
(0.073)
0.037
(0.040)
0.002
(0.044)
-0.059**
(0.026)
0.190
(0.311)
0.954***
(0.094)
-0.060
(0.068)
-0.036
(0.043)
0.063
(0.070)
0.065*
(0.038)
-0.075**
(0.035)
-0.000
(0.033)
0.116
(0.080)
0.540***
(0.076)
0.061
(0.097)
-0.142***
(0.053)
-0.067
(0.067)
0.057
(0.111)
-0.015
(0.049)
0.148*
(0.086)
-0.408***
(0.083)
1.138***
(0.102)
-0.326**
(0.142)
-0.076
(0.079)
0.182
(0.122)
0.215**
(0.091)
0.068
(0.074)
-0.044*
(0.026)
0.736
(0.509)
1.799***
(0.165)
-0.030
(0.022)
-0.045***
(0.008)
-0.004
(0.024)
-0.011*
(0.006)
0.011
(0.012)
-0.003
(0.010)
-0.082***
(0.021)
0.335***
(0.029)
Standard errors in parentheses, * p<0.10, ** p<0.05, *** p<0.01
ior, encoded as a dummy variable indicating whether farmers buy (1) or do not buy
(0) lottery tickets. This is often indicated as a classical case where objectively given
probabilities describe the outcome generating process well (especially the type of lottery
tickets typically bought by farmers have a given probability of winning, unlike state
lotteries where the prize will in part depend on the number of tickets with the winning
combination of numbers). We find two significant effects: the likelihood of buying lottery
tickets decreases in loss aversion, and it increases in risk seeking for gains. Given that
buying a lottery means incurring a certain loss to obtain a risky gain, this exactly fits a
model of lottery buying behavior.10
We also find some interesting effects for saving behavior, entered as z-scores of total
liquid savings. Arguably, saving may be determined by many factors, amongst which
time preferences, on which we have no data. Nevertheless, risk aversion may play a
role in determining so-called precautionary saving.11 We find savings to increase in risk
tolerance for gains and to decrease in risk tolerance for losses. Risk aversion for losses
resulting in larger amounts of saving exactly indicates a pattern of precautionary saving
as hypothesized above. The pattern for gains is harder to interpret. The most likely
explanation is that farmers with higher income save more, as well as being more risk
10
This conclusion assumes that monetary outlays to obtain a good are perceived as losses. Such an
interpretation is not uncontroversial. For a summary of the dispute, and an adversarial collaboration
finding that oulays are indeed perceived as losses, see Bateman, Kahneman, Munro, Starmer and Sugden
(2005)
11
Savings amounts are quite small, so that this variable cannot be though of as capturing wealth,
which we have seen above to have no effect on risk preferences.
21
Table 6: predicting risk behavior on the farm
α+
β+
α−
β−
λ
σ
-0.243
(0.208)
-0.071
(0.206)
-0.064
(0.089)
0.061
(0.037)
-0.073**
(0.033)
-0.024
(0.038)
0.549***
(0.080)
0.705**
(0.288)
-0.230*
(0.124)
0.137
(0.084)
0.008
(0.039)
0.019
(0.047)
-0.064***
(0.022)
0.744***
(0.067)
-0.444***
(0.124)
-0.103
(0.136)
0.020
(0.073)
0.062*
(0.033)
-0.076**
(0.033)
0.001
(0.030)
0.535***
(0.058)
-0.666**
(0.323)
0.538***
(0.196)
-0.051
(0.113)
0.080
(0.095)
-0.017
(0.054)
0.070
(0.048)
1.103***
(0.099)
0.419
(0.570)
-0.318**
(0.129)
0.059
(0.125)
0.152*
(0.083)
0.082
(0.091)
-0.054**
(0.021)
1.671***
(0.114)
-0.069*
(0.038)
0.041
(0.051)
-0.024
(0.022)
-0.009
(0.006)
0.023**
(0.010)
-0.013**
(0.006)
0.317***
(0.019)
N=197, LL = −16, 309
rent out land
migration to city
borrowed money
education
age
income
constant
Standard errors in parentheses, * p<0.10, ** p<0.05, *** p<0.01; controls are z-scores
tolerant. This explanation is made plausible by the fact that savings are significantly
correlated with income (r=0.41, p<0.001), and that the coefficient of income drops once
we insert savings. Notice, however, how this cannot explain the findings for losses.
Indeed, income remains a strong predictor of risk preferences for losses even when savings
are inserted into the regression, and it is actually the more risk averse farmers who save
more. We do not find significant predictive power of our preference measures for smoking.
We next look at some types of behavior that relate more closely to risk management
practices on the farm. These are, in particular, whether a farmer rents out his land
to cope with the risk of flooding (the largest environmental risk to our farmers living
alongside the Mekong). This is an unequivocally risk averse strategy (Jayachandran,
2006). We also include a dummy indicating whether the household head migrates to the
city in order to work there for part of the year, and a dummy indicating whether he has
borrowed significant sums of money over the last five years, both of which may be seen
as risk accepting strategies.12
Table 6 shows the regression results. Leasing out one’s land instead of cultivating it
oneself is found to correlate with all parameters but sensitivity for gains and loss aversion:
a farmer is more likely to rent out his land the more insensitive he is to probabilities of
12
A variable of much interest in the literature is technology adoption, often under the form of willingness to switch to new crops. We did capture such behavior in our data. It turns out, however, that
the switching behavior is very much influenced by command and control policies of the party. From
interviews we thus gathered that some farmers had switched to new rice varieties proposed by the government, while others had switched back after observing poor performace of the newly adopted varieties.
In sum, it is unclear whether switching crop indicates a risk seeking or risk averse strategy in our sample,
or part of both, so that the variable is not well suited for this analysis.
22
losses, and the more risk averse he is, with the latter of these effects holding for both
gains and losses. Leasing out one’s land is indeed a very risk averse strategy. From a few
interviews conducted subsequently with farmers who leased out their land, it appears that
the risk premium paid is around 50% on average, i.e. the rental fee obtained is 50% lower
than the average income from cultivating the land. In terms of risk tolerant strategies,
we find no effect for the indicator whether the household has borrowed money over the
last five years. This may be because, contrary to our initial hypothesis, this variable
may capture not only money borrowed for investment purposes, but also borrowing for
emergencies or consumption smoothing. The likelihood of migration to work in the city,
on the other hand, is decreasing in loss aversion (suggesting a status quo effect, see
Kahneman, Knetsch and Thaler, 1991) and in risk aversion for gains, and is increasing
in risk tolerance for losses, thus being significantly correlated with risk seeking in our
experiment as expected. Overall our risk preference measures thus perform quite well in
terms of correlations with behavior.
6
Discussion
The results presented in this paper break radically with some assumptions on risk preferences of rural populations in developing countries. Far from finding high levels of risk
aversion amongst poor farmers, we find farmers in Vietnam to be quite risk tolerant in
comparison to typical Western populations. On the other hand, the finding is in line
with results on students in developing countries, and with some more recent evidence
on farmers in Ethiopia. In this larger context, selection effects appear unlikely to play a
role for our data. At the same time, our measures appear to be validated by their good
predictive performance. We have furthermore shown a clear increase in risk tolerance
with income within the farmer sample itself. This is the first paper to show such a
clear relationship between risk tolerance and income in the developing world. Together,
the within-country and between-country relationships with income in opposite directions
sum up to a risk-income paradox. Possible explanations for this paradox are discussed
by Vieider, Chmura and Martinsson (2012).
Given how strong the relationship with income is, it seems unlikely that other factors
would constitute a better explanation for these aggregate risk preferences. In particular,
we do not think that our data can be explained in any way by noise or systematic error.
23
While answering randomly on our choice lists would produce risk neutrality on average,
the choice patterns we find are clearly not random. Indeed, the number of violations of
first order stochastic dominance of our farmers are comparable to violation rates observed
in the West with students. In terms of our own data, overall violation rates are indeed
slightly lower for farmers than for Vietnamese students. Letting the error term depend
on observable characteristics of subjects further helps to avoid that spurious effects are
picked up in the comparisons or regression analysis (Andersson et al., 2013).
For the development literature, the high level of risk tolerance we find in the aggregate
poses the issue of what may hold back technology adoption on the farm. To the extent
that preferences cannot be blamed for this, we may look at other factors that hinder
adoption. Indeed, Feder (1980) remarks how “risk and risk-aversion have been used to
explain differences in input use and the relative rate of adoption of modern technologies
by farmers of different sizes. But different patterns of behavior are observed in different
regions, and thus the impact of risk and risk-aversion needs to be examined in relation
to other factors and constraints [...]” (p. 263). Several indications in this direction are
also provided in the recent literature. Karlan, Osei, Osei-Akoto and Udry (2012) present
results suggesting that it is the sheer amount of risk exposure that makes investments
unprofitable in some cases. Mobarak and Rosenzweig (2012) present evidence that risk
taking in production goes up once farmers are sheltered from the worst risks through
insurance. This suggests that risk averse coping behavior may be driven by external
constraints, rather than or in addition to individual preferences (Feder et al., 1985).
Indeed, Dercon and Christiaensen (2011) recently showed willingness to take risks
in production to be directly linked to the severity of the welfare consequences resulting
from adverse shocks. Maccini and Yang (2009) showed that rainfall during the first
year after birth significantly affects the lifetime outcomes of girls, with bad rainfall
during that year resulting in smaller body size, less education, and reduced lifetime
income. Avoiding risks may indeed be the optimal action in the face of such extreme
risk exposure (notice also the stark contrast with the tendency of over-insuring even
modest risk in Western countries—see Sydnor, 2010).13 The absence of borrowing and
credit facilities furthermore makes it nigh-impossible to smooth income or consumption
without recurring to risk avoiding strategies (Morduch, 1994; 1995). While some informal
13
This is also consistent with theories that model the poor to be risk averse until a subsistance income
is achieved, and much more risk tolerant thereafter—see e.g. Moscardi and Janvry (1977); Lopes and
Oden (1999); Young (1979)
24
risk sharing mechanisms may exist, the latter are usually imperfect. There is increasing
evidence that farmers switch to higher-payoff crops if they can cover themselves at least
partially against their high levels of risk exposure (Cole, Giné and Vickery, 2013; Karlan
et al., 2012; Kurosaki and Fafchamps, 2002; Mobarak and Rosenzweig, 2012).
Nevertheless, we also find evidence that individual preferences do play a role in production decisions. This contributes to the debate on the extent to which measurements
of preferences can be used to predict real world behavior (Samuelson, 2005). The external validity of risk preference measures is controversial. Investigating how risk and time
preferences relate to real world behavior in a large sample of adolescents, Sutter et al.
(2013) recently concluded that experimentally measured risk preferences had almost no
predictive value for real world behavior (although time preference measures performed
better). Dimmock, Kouwenberg and Wakker (2012) found only weak predictive power of
experimentally measured ambiguity preferences on stock market participation. Giné et
al. (2008) and Cole, Giné and Tobacman (2012) even found risk aversion to bear a negative relation to insurance purchase decisions. Contrary to the findings in these papers,
our measures of risk preferences perform rather well at predicting behavior.
We attribute this increased external validity mostly to the richness of our measures,
which can capture within-subject variability in preferences across different probability
levels and decision domains (gains versus losses). Such elements have proved helpful
in explaining many different types of real world behavior (see Barberis, 2013, for an
extensive review). Barseghyan et al. (2013) showed that allowing for non-linear transformations of probabilities adds significant explanatory power in the modeling of insurance
deductible choices. The overwhelming majority of preference studies in development
obtained only one single estimate per subject. This may have limited the predictive
power of such measures, since typical measurement over 50-50 gains are likely to provide a poor approximation for behavior involving, e.g., small probability losses, such as
insurance decisions. They also do not allow for the estimation of stochastic models of
choice, and may thus be contaminated by noise. An example of the latter case may be
Tanaka, Camerer and Nguyen (2010), who measured risk preferences using three choice
lists, and solved a parallel equation system to estimate the parameters of a prospect
theory model. The authors also make simplifying assumptions which we deem quite
restrictive. In particular, their functional assumptions limit the extent to which a probability weighting function—and hence risk preferences more in general—can differ from
25
the typical aggregate functions found in the West. Our results strongly suggest that
both flexible functional forms and an explicit stochastic structure are necessary to fit the
data well and improve predictive power.
26
A
The risk-income paradox under EUT
The estimations in this appendix are based on the model presented in the main text,
by assuming the weighting function to be the identity function, i.e. w(p) = p. We thus
obtain the dual of the function used in the main text and model preferences through
the subjective transformation of outcomes. A one-parameter power function is used
throughout.
Table 7 shows the comparison between Vietnamese farmers, Vietnamese students,
and American students. The famers can be seen from the constant to have a somewhat
convex utility function for gains (though not significantly so). Vietnamese students have
a slightly more convex function, while American students have a significantly lower utility
parameter (and thus a more concave function). For losses, both student populations
have a more concave utility function than farmers (see supplementary materials for more
evidence on losses).
Table 7: Subject pool comparison, EUT
N=424, LL = −33, 728
students US
students Vietnam
female
constant
µ
ν
λ
σ
-0.209**
(0.083)
0.110
(0.093)
-0.076*
(0.044)
1.110***
(0.075)
0.247***
(0.061)
0.124**
(0.063)
0.087
(0.065)
0.813***
(0.048)
-1.037**
(0.514)
0.569
(0.656)
-0.167
(0.198)
2.312***
(0.493)
-0.154***
(0.018)
-0.097***
(0.020)
0.034
(0.021)
0.316***
(0.012)
Table 8 shows the effect of income per capita on utility curvature. For gains, we
find risk aversion as incorporated in the µ parameter to significantly decrease in income.
While we find a similar effect for losses, it fails to reach significance.
Table 8: Effects of income on risk preferences, EUT
N=197, LL = −16, 689
income
education
age
constant
µ
ν
λ
σ
0.072**
(0.030)
-0.068**
(0.032)
-0.077
(0.061)
1.125***
(0.077)
-0.054
(0.042)
0.017
(0.050)
0.000
(0.050)
0.805***
(0.048)
0.627
(0.458)
-0.288**
(0.139)
-0.382
(0.400)
2.551***
(0.564)
-0.002
(0.005)
-0.021***
(0.007)
0.020*
(0.011)
0.325***
(0.012)
27
B
Subject pool comparison under PT
Table 9 shows the subject pool comparison using the full PT model. Utility for gains
can be seen to be slightly convex for our farmers, an effect that is marginally significant
(χ2 (1) = 3.63, p = 0.057). Utility is more convex for Vietnamese students and linear for
American students, although neither of the two differences is statistically significant. To
examine the results in terms of risk preferences, however, we must consider them jointly
with the results on probability weighting. Both student populations are significantly
more probabilistically sensitive than the farmers. American students are also marginally
significantly more pessimistic than the farmers, as indicated by the higher value of β + .
However, the difference between farmers and American students on utility curvature and
the elevation of the probability weighting function jointly is highly significant (χ2 (1) =
15.59, p < 0.001). While Vietnamese farmers show significant probabilistic optimism
(χ2 (1) = 4.13, p = 0.042, rejecting β + = 1), for American students we cannot reject the
hypothesis that β + = 1 (χ2 (1) = 0.27, p = 0.605), which corresponds to typical findings
from the West. The results for losses are similar and will not be discussed further.
Table 9: Subject pool comparison, PT
µ
ν
λ
α+
β+
α−
β−
σ
students US
-0.072
(0.093)
-0.073
(0.098)
-0.449
(0.348)
0.317***
(0.050)
0.157*
(0.092)
0.348***
(0.058)
-0.195*
(0.116)
-0.140***
(0.018)
students Vietnam
0.072
(0.096)
0.247*
(0.132)
-0.577*
(0.335)
0.227***
(0.052)
0.017
(0.093)
0.212***
(0.055)
0.153
(0.158)
-0.089***
(0.020)
female
-0.153
(0.098)
0.050
(0.127)
-0.451
(0.293)
-0.129***
(0.047)
-0.074
(0.091)
-0.103**
(0.051)
-0.085
(0.127)
0.029
(0.021)
1.093***
(0.049)
1.228***
(0.061)
1.687***
(0.249)
0.490***
(0.031)
0.884***
(0.057)
0.532***
(0.031)
1.266***
(0.083)
0.301***
(0.011)
N=425, LL = −33, 261
constant
28
C
Non-parametric analysis for losses
We here show the non-parametric between country analysis for losses. Figure 5 shows
the same relationship between the aggregate risk premium of the country and GDP per
capita as in the text, but for losses instead of gains. Once again, there is a strong positive
correlation between the (log of) GDP per capita and the risk premium (ρ = 0.699, p <
0.001, N = 31, Spearman correlation). The Vietnamese farmers can now be seen to be
significantly more risk seeking than the Vietnamese students (z = 3.01, p = 0.003, MannWhitney test). Overall, the paradox is reproduced: risk tolerance decrease in GDP per
capita between countries, but increases in income within our sample (see main text for
structural model; see supplementary materials for non-parametric regressions).
Figure 5: Risk preferences in relation to GDP per capita for losses, farmers and students
29
References
Abdellaoui, Mohammed (2000) ‘Parameter-free elicitation of utility and probability
weighting functions.’ Management Science 46(11), 1497–1512
Abdellaoui, Mohammed, Aurélien Baillon, Lætitia Placido, and Peter P. Wakker (2011)
‘The rich domain of uncertainty : Source functions and their experimental implementation.’ American Economic Review 101, 695–723
Abdellaoui, Mohammed, Han Bleichrodt, and Corina Paraschiv (2007) ‘Loss aversion under prospect theory: A parameter-free measurement.’ Management Science
53(10), 1659–1674
Abdellaoui, Mohammed, Han Bleichrodt, Olivier L’Haridon, and Dennie Van Dolder
(2013) ‘Source-dependence of utility and loss aversion: A critical test of ambiguity
models.’ University of Rennes 1 working paper
Akay, Alpaslan, Peter Martinsson, Haileselassie Medhin, and Stefan Trautmann (2012)
‘Attitudes toward uncertainty among the poor: an experiment in rural ethiopia.’ Theory and Decision 73(3), 453–464
Andersson, Ola, Jean-Robert Tyran, Erik Wengström, and Håkan J. Holm (2013) ‘Risk
aversion relates to cognitive ability: Fact or fiction?’ IFN Working Paper No. 964
Attanasio, Orazio, Abigail Barr, Juan Camilo Cardenas, Garance Genicot, and Costas
Meghir (2012) ‘Risk pooling , risk preferences , and social networ.’ American Economic
Journal: Applied Economics 4(2), 134–167
Baltussen, Guido, Thierry Post, Martijn J. van den Assem, and Peter P. Wakker (2010)
‘Random incentive systems in a dynamic choice experiment.’ working paper
Barberis, Nicholas C. (2013) ‘Thirty years of prospect theory in economics: A review
and assessment.’ Journal of Economic Perspectives 27(1), 173–96
Barseghyan, Levon, Francesca Molinari, Ted O’Donoghue, and Joshua Teitelbaum (2013)
‘The nature of risk preferences: Evidence from insurance choices.’ American Economic
Review 103(6), 2499–2529(31)
Bateman, Ian, Daniel Kahneman, Alistair Munro, Chris Starmer, and Robert Sugden
(2005) ‘Testing competing models of loss aversion: an adversarial collaboration.’ Journal of Public Economics 89(8), 1561–1580
Bauer, Michal, Julie Chytilová, and Jonathan Morduch (2012) ‘Behavioral foundations
of microcredit: Experimental and survey evidence from rural india.’ The American
30
Economic Review 102(2), 1118–1139
Binswanger, Hans P. (1980) ‘Attitudes toward risk: Experimental measurement in rural
india.’ American Journal of Agricultural Economics 62(3), 395–407
Bleichrodt, Han, and Jose Luis Pinto (2000) ‘A parameter-free elicitation of the probability weighting function in medical decision analysis.’ Management Science 46(11), 1485–
1496
Booij, Adam S., Bernard M. S. van Praag, and Gijs van de Kuilen (2010) ‘A parametric analysis of prospect theory’s functionals for the general population.’ Theory and
Decision 68(1-2), 115–148
Bruhin, Adrian, Helga Fehr-Duda, and Thomas Epper (2010) ‘Risk and rationality:
Uncovering heterogeneity in probability distortion.’ Econometrica 78(4), 1375–1412
Choi, Syngjoo, Raymond Fisman, Douglas Gale, and Shachar Kariv (2007) ‘Consistency
and heterogeneity of individual behavior under uncertainty.’ The American Economic
Review 97(5), 1921–1938
Choi, Syngjoo, Shachar Kariv, Wieland Müller, and Dan Silverman (2013) ‘Who is
(more) rational?’ American Economic Review, forthcoming
Clarke, Daniel J. (2011) ‘A theory of rational demand for index insurance.’ working paper
Cole, Shawn, Xavier Giné, and James Vickery (2013) ‘How does risk management influence production decisions? evidence from a field experiment.’ working paper
Cole, Shawn, Xavier Giné, and Jeremy Tobacman (2012) ‘Barriers to household risk
management: Evidence from india.’ American Economic Journal: Applied Economics
Croson, Rachel, and Uri Gneezy (2009) ‘Gender differences in preferences.’ Journal of
Economic Literature 47(2), 1–27
Dercon, Stefan, and Luc Christiaensen (2011) ‘Consumption risk, technology adoption and poverty traps: Evidence from ethiopia.’ Journal of Development Economics
96(2), 159–173
Diecidue, Enrico, and Jeroen van de Ven (2008) ‘Aspiration level, probability of success
and failure, and expected utility.’ International Economic Review 49(2), 683–700
Dimmock, Stephen G., Roy Kouwenberg, and Peter P. Wakker (2012) ‘Ambiguity attitudes and portfolio choice: Evidence from a large representative survey.’ working
paper
Doerr, Ulrike, Omar Mahmud Toman, and Ulrich Schmidt (2011) ‘Overconfidence and
31
risk management of ethiopian farmers.’ Working paper, University of Kiel
Dohmen, Thomas, Armin Falk, David Huffman, and Uwe Sunde (2012) ‘The intergenerational transmission of risk and trust attitudes.’ Review of Economic Studies
70(2), 645–677
Dohmen, Thomas, Armin Falk, David Huffman, Uwe Sunde, Jürgen Schupp, and Gert G.
Wagner (2011) ‘Individual risk attitudes: Measurement, determinants, and behavioral
consequences.’ Journal of the European Economic Association 9(3), 522–550
Donkers, Bas, Bertrand Melenberg, and Arthur Van Soest (2001) ‘Estimating risk attitudes using lotteries: A large sample approach.’ Journal of Risk and Uncertainty
22(2), 165 – 95
Eckel, Catherine C., and Philip J. Grossman (2008) ‘Men, women, and risk aversion:
Experimental evidence.’ In ‘Handbook of Experimental Economics Results Vol. 1’
pp. 1061–1073
Etchart-Vincent, Nathalie, and Olivier L’Haridon (2011) ‘Monetary incentives in the
loss domain and behavior toward risk: An experimental comparison of three reward
schemes inclusing real losses.’ Journal of Risk and Uncertainty 42, 61–83
Feder, Gershon (1980) ‘Farm size, risk aversion, and the adoption of new technology
under uncertainty.’ Oxford Economic Papers 32(2), 263–282
Feder, Gershon, Richard E. Just, and David Zilberman (1985) ‘Adoption of agricultural
innovations in developing countries: A survey.’ Economic Development and Cultural
Change 33(2), 255–298
Fehr-Duda, Helga, Adrian Bruhin, Thomas F. Epper, and Renate Schubert (2010) ‘Rationality on the rise: Why relative risk aversion increases with stake size.’ Journal of
Risk and Uncertainty 40(2), 147–180
Fehr-Duda, Helga, and Thomas Epper (2012) ‘Probability and risk: Foundations and
economic implications of probability-dependent risk preferences.’ Annual Review of
Economics 4(1), 567–593
Filmer, Deon, and Lant H. Pritchett (2001) ‘Estimating wealth effects without expenditure Data—Or tears: An application to educational enrollments in states of india*.’
Demography 38(1), 115–132
Gächter, Simon, Eric J. Johnson, and Andreas Herrmann (2010) ‘Individual-level loss
aversion in riskless and risky choices.’ Technical Report 2010-20, CeDEx discussion
32
paper series
Giné, Xavier, Robert Townsend, and James Vickery (2008) ‘Patterns of rainfall insurance
participation in rural india.’ World Bank Economic Review 22, 539–566
Henrich, Joseph, and Richard McElreath (2002) ‘Are peasants risk averse decision makers?’ Current Anthropology 43(1), 172–181
Hey, John D., and Chris Orme (1994) ‘Investigating generalizations of expected utility
theory using experimental data.’ Econometrica 62(6), 1291–1326
Holt, Charles A., and Susan K. Laury (2002) ‘Risk aversion and incentive effects.’ American Economic Review pp. 1644–1655
Hopland, Arnt O., Egil Matsen, and Bjarne Strøm (2013) ‘Income and choice under
risk.’ Working Paper Series 14313, Department of Economics, Norwegian University
of Science and Technology
Huck, Steffen, and Wieland Müller (2012) ‘Allais for all: Revisiting the paradox in a
large representative sample.’ Journal of Risk and Uncertainty 44(3), 261–293
Jayachandran, Seema (2006) ‘Selling labor low: Wage responses to productivity shocks
in developing countries.’ Journal of Political Economy 114(3), 538–575
Kachelmeier, Steven J., and Mohamed Shehata (1992) ‘Examining risk preferences under
high monetary incentives: Experimental evidence from the people’s republic of china.’
American Economic Review 82(5), 1120–1141
Kahneman, Daniel, and Amos Tversky (1979) ‘Prospect theory: An analysis of decision
under risk.’ Econometrica 47(2), 263 – 91
Kahneman, Daniel, Jack L. Knetsch, and Richard H. Thaler (1991) ‘Anomalies: The
endowment effect, loss aversion, and status quo bias.’ Journal of Economic Perspectives
5(1), 193–206
Karlan, Dean, Robert Darko Osei, Isaac Osei-Akoto, and Christopher Udry (2012) ‘Agricultural decisions after relaxing credit and risk constraints.’ Working Paper 18463,
National Bureau of Economic Research, October
Kilka, Michael, and Martin Weber (2001) ‘What determines the shape of the probability
weighting function under uncertainty?’ Management Science 47(12), 1712–1726
Köbberling, Veronika, and Peter P. Wakker (2005) ‘An index of loss aversion.’ Journal
of Economic Theory 122(1), 119 – 131
Kőszegi, Botond, and Matthew Rabin (2007) ‘Reference-dependent risk attitudes.’ The
33
American Economic Review 97(4), 1047–1073
Kurosaki, Takashi, and Marcel Fafchamps (2002) ‘Insurance market efficiency and crop
choices in pakistan.’ Journal of Development Economics 67(2), 419–453
L’Haridon, Olivier, Peter Martinsson, and Ferdinand M. Vieider (2013) ‘All over the
map: Heterogeneity of risk preferences across individuals, contexts, and countries.’
working paper
Liu, Elaine M. (2012) ‘Time to change what to sow: Risk preferences and technology
adoption decisions of cotton farmers in china.’ Review of Economics and Statistics
95(4), 1386–1403
Liu, Elaine M., and JiKun Huang (2013) ‘Risk preferences and pesticide use by cotton
farmers in china.’ Journal of Development Economics 103, 202–215
Lopes, Lola L, and Gregg C Oden (1999) ‘The role of aspiration level in risky choice: A
comparison of cumulative prospect theory and SPÂA theory.’ Journal of Mathematical
Psychology 313, 286–313
Maccini, Sharon, and Dean Yang (2009) ‘Under the weather: Health, schooling, and
economic consequences of early-life rainfall.’ American Economic Review 99(3), 1006–
1026
Markowitz, Harry (1952) ‘The utility of wealth.’ Journal of Political Economy 60(2), 151–
158
Mobarak, A. Mushfiq, and Mark R. Rosenzweig (2012) ‘Selling formal insurance to the
informally insured.’ Yale Economics Department Working Paper No. 97
Morduch, Jonathan (1994) ‘Poverty & vulnerability.’ American Economic Review, Papers
and Proceedings 84(2), 221–225
(1995) ‘Income smoothing and consumption smoothing.’ Journal of Economic Perspectives 9(3), 103–114
Moscardi, Edgardo, and Alain de Janvry (1977) ‘Attitudes toward risk among peasants:
An econometric approach.’ American Journal of Agricultural Economics 59(4), 710–
716
Myung, In Jae (2003) ‘Tutorial on maximum likelihood estimation.’ Journal of Mathematical Psychology 47(1), 90–100
Prelec, Drazen (1998) ‘The probability weighting function.’ Econometrica 66, 497–527
Preston, Malcolm G., and Philip Baratta (1948) ‘An experimental study of the auction-
34
value of an uncertain outcome.’ The American Journal of Psychology 61, 183–193
Reynaud, Arnaud, and Stéphane Couture (2012) ‘Stability of risk preference measures:
results from a field experiment on french farmers.’ Theory and Decision 73(2), 203–221
Rieger, Marc Oliver, Mei Wang, and Thorsten Hens (2014) ‘Risk preferences around the
world.’ Management Science
Rosenzweig, Mark R., and Hans P. Binswanger (1993) ‘Wealth, weather risk, and the
composition and profitability of agricultural investments.’ Economic Journal 103(January), 56–78
Samuelson, Larry (2005) ‘Economic theory and experimental economics.’ Journal of Economic Literature 43(1), 65–107
Santos-Pinto, Luís, Thomas Astebro, and José Mata (2009) ‘Preference for skew in lotteries: Evidence from the laboratory.’ MPRA Paper
Schmidt, Ulrich, and Horst Zank (2005) ‘What is loss aversion?’ Journal of Risk and
Uncertainty 30(2), 157–167
(2008) ‘Risk aversion in cumulative prospect theory.’ Management Science 54(1), 208–
216
Sugden, Robert (2003) ‘Reference-dependent subjective expected utility.’ Journal of Economic Theory 111(2), 172–191
Sutter, Matthias, Martin G Kocher, Daniela Glätzle-Rützler, and Stefan T Trautmann
(2013) ‘Impatience and uncertainty: Experimental decisions predict adolescents’ field
behavior.’ American Economic Review 103(1), 510–531
Sydnor, Justin (2010) ‘(over)insuring modest risks.’ American Economic Journal: Applied Economics 2(4), 177–199
Tanaka, Tomomi, Colin F. Camerer, and Quang Nguyen (2010) ‘Risk and time preferences: Linking experimental and household survey data from vietnam.’ American
Economic Review 100(1), 557–571
Train, Kenneth (2009) Discrete choice methods with simulation (Cambridge; New York:
Cambridge University Press)
Tversky, Amos, and Peter P. Wakker (1995) ‘Risk attitudes and decision weights.’ Econometrica 63(6), 1255–1280
Vieider, Ferdinand M., Abebe Beyene, Randall A. Bluffstone, Sahan Dissanayake, Zenebe
Gebreegziabher, Peter Martinsson, and Alemu Mekonnen (2014a) ‘Measuring risk pref-
35
erences in ethiopia: Further evidence on a risk-income paradox, and on risk and religion.’ WZB Working Paper
Vieider, Ferdinand M., Mathieu Lefebvre, Ranoua Bouchouicha, Thorsten Chmura, Rustamdjan Hakimov, Michal Krawczyk, and Peter Martinsson (2014b) ‘Common components of risk and uncertainty attitudes across contexts and domains: Evidence from
30 countries.’ Journal of the European Economic Association, forthcoming
Vieider, Ferdinand M., Thorsten Chmura, and Peter Martinsson (2012) ‘Risk attitudes,
development, and growth. macroeconomic evidence from experiments in 30 countries.’
WZB Working paper
von Gaudecker, Hans-Martin, Arthur van Soest, and Erik Wengström (2011) ‘Heterogeneity in risky choice behaviour in a broad population.’ American Economic Review
101(2), 664–694
Wakker, Peter P. (2008) ‘Explaining the characteristics of the power (CRRA) utility
family.’ Health Economics 17(12), 1329–1344
(2010) Prospect Theory for Risk and Ambiguity (Cambridge: Cambridge University
Press)
Wu, George, and Richard Gonzalez (1996) ‘Curvature of the probability weighting function.’ Management Science 42(12), 1676–1690
Yaari, Menahem E. (1987) ‘The dual theory of choice under risk.’ Econometrica 55(1), 95–
115
Yesuf, Mahmud, and Randall A. Bluffstone (2009) ‘Poverty, risk aversion, and path
dependence in low-income countries: Experimental evidence from ethiopia.’ American
Journal of Agricultural Economics 91(4), 1022–1037
Young, Douglas L. (1979) ‘Risk preferences of agricultural producers: Their use in extension and research.’ American Journal of Agricultural Economics 61(5), 1063
Zeisberger, Stefan, Dennis Vrecko, and Thomas Langer (2012) ‘Measuring the time stability of prospect theory preferences.’ Theory and Decision 72(3), 359–386
36