European Review of Agricultural Economics Advance Access published May 8, 2013
European Review of Agricultural Economics pp. 1–38
doi:10.1093/erae/jbt006
Expected utility or prospect theory
maximisers? Assessing farmers’ risk
behaviour from field-experiment data
Géraldine Bocquého†,††, *, Florence Jacquet‡
and Arnaud Reynaud§
†
Received November 2011; final version accepted February 2013
Abstract
We elicit the risk preferences of a sample of French farmers in a field-experiment
setting, considering both expected utility and cumulative prospect theory. Under the
EU framework, our results show that farmers are characterised by a concave utility
function for gain outcomes implying risk aversion. The CPT framework confirms
this result, but also suggests that farmers are twice as sensitive to losses as to gains
and tend to pay undue attention to unlikely extreme outcomes. Accounting for loss
aversion and probability weighting can make a difference in the design of effective
and efficient policies, contracts or insurance schemes.
Keywords: risk preferences, experimental economics, loss aversion, probability
weighting, France
JEL classification: C93, D81, Q12
1. Introduction
For decades, risk has been a central feature of studies in the field of agricultural economics because it is intrinsic to agricultural production, and it
plays a key role in the decisions farmers make every day. For instance, risk
has been shown to be a crucial element in understanding crop diversification
(Serra et al., 2009), contract choice (Zheng, Vukina and Shin, 2008; Dubois
and Vukina, 2009), insurance take-up (Mahul, 2003; Coble, 2004) or innovation adoption (Abadi Ghadim, Pannell and Burton, 2005; Kallas, Serra and
Gil, 2010). Behaviour under risk typically results from the interplay of
the risk level faced by decision-makers and their own sensitivity to risk,
*Corresponding author: INRA, UMR 210 Economie Publique (INRA-AgroParisTech), avenue Lucien
Brétignières, 78850 Thiverval-Grignon. France. E-mail: [email protected]
# Oxford University Press and Foundation for the European Review of Agricultural Economics 2013;
all rights reserved. For permissions, please email [email protected]
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INRA, UMR 210 Economie Publique, France; ‡INRA, UMR 1110
MOISA, France; §Toulouse School of Economics-INRA, UMR 1081
LERNA, France; ††Present address: IIASA, Ecosystems Services and
Management Program, Austria
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G. Bocquého et al.
1 It is fair to say that in earlier tests no theory was identified as a clear-cut winner, and that data
used to support one theory or the other depend on the problem considered and the individual
characteristics included in the model (Harless, 1992; Starmer, 1992; Hey and Orme, 1994). The
stochastic specification of the choice model has also important consequences on the fit between
the decision theory tested and the data (Loomes and Sugden, 1998).
2 Following Harrison and Rutström (2008: 69), in this paper, a structural model refers to a global
model of decision where the ‘core’ preference parameters are to be estimated. This denomination is used in contrast with the more common approach of estimating (linear) reduced-form
equations for each parameter of interest. However, in this paper, the term ‘structural’ does not
give any information about the way error terms are specified.
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i.e. their risk preferences. The latter being key factors in explaining variability
in behaviour between decision-makers, a lot of effort has been devoted to
measure farmers’ risk preferences with reliable direct methods. In experimental methods, they are elicited from real choices between lotteries (see
the seminal papers by Binswanger (1980) or Binswanger (1981)). In revealed
preference methods, they are imputed from the divergence between observed
farmers’ decisions (input use, output choice) and expected decisions in the
absence of risk (see, for instance, Antle, 1987, 1989 or Chavas and Holt
1996). Although the two methods differ greatly in terms of underlying
assumptions, they do have in common the fact that farmers are usually
assumed to be expected utility (EU) maximisers, in accordance with the
theory initially developed by von Neumann and Morgenstern (1947).
One advantage of EU theory is the explicit distinction it makes between risk
exposure and risk preferences, through using probabilities and a utility function (Chavas, Chambers and Pope, 2010). Furthermore, it can be applied very
easily, while appealing alternative theories are lacking (Just and Peterson,
2010). However, its long-term dominance in agricultural economics is questionable for several reasons. First, since the work of Allais (1953), psychologists and economists have provided substantial evidence that individuals do
not necessarily behave according to the key assumptions underlying EU
theory. Their behaviour seems indeed to deviate from EU in predictable and
systematic ways. For instance, observed levels of risk aversion for small
stakes are inconsistent with those observed for high stakes under EU theory
(Rabin, 2000). Second, over the last few years, empirical testing of EU
against alternative theories for decision-making under risk has provided evidence in favour of the latter (e.g. Loomes, Moffatt and Sugden, 2002;
Mason et al., 2005; Tanaka, Camerer and Nguyen, 2010).1
In this paper, we seek to elicit farmers’ risk preferences under EU theory
and the competing prospect theory (PT). We use Tanaka, Camerer and
Nguyen’s (2010) experimental design on a sample of French farmers.
However, we estimate structural models of preferences instead of calculating
preference parameters analytically.2 This approach is more accurate for multiparameter models such as PT models because all parameters are jointly estimated. In addition, we investigate how parameters correlate with several
farmer and farm characteristics.
Among the available non-EU theories, PT (Kahneman and Tversky, 1979;
Tversky and Kahneman, 1992) is now viewed as the most convincing
Expected utility or prospect theory maximisers
Page 3 of 38
3 Pennings and Smidts (2003) investigated reference dependence on a sample of Dutch hog farmers but using non-parametrical methods. Reynaud and Couture (2012), Herberich and List (2012),
Menapace, Colson and Raffaelli (2012) and Hellerstein, Higgins and Horowitz (2013) elicited risk
preferences from farmers from France, Illinois, Italy and the US Corn Belt, respectively, but only
under EU theory.
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one (Camerer, 1998; Starmer, 2000). Indeed, PT features two key factors in
explaining EU anomalies, namely reference dependence and probability
weighting. Whereas EU theory does not distinguish between gains and
losses, in PT outcomes are classified as either gains or losses with respect
to a reference point, and people are allowed to behave differently in each of
the two outcome domains. Probability weighting refers to people’s tendency
to distort objective probabilities, which is accounted for in PT through a nonlinear valuation of outcomes with respect to objective probabilities. Assuming
PT instead of EU potentially leads to a very different understanding of
farmers’ decisions (e.g. Tuthill and Frechette, 2004; Mattos, Garcia and
Pennings, 2008).
In addition, PT fits the agricultural context particularly well. On the one
hand, it is likely that farmers do have reference points for outcome valuation,
such as target prices on the futures markets (based on production costs) (Kim,
Brorsen and Anderson, 2010), subsistence incomes and solvency thresholds in
the context of production choices (e.g. Mahul, 2000), and pollution thresholds
(Qiu, Prato and McCamley, 2001). Collins, Musser and Mason (1991) investigated the relationship between preference reversals and changes in income
with data from grass seed growers. The results show that, after a loss of
income, farmers change their behaviour from risk aversion to risk seeking.
On the other hand, there is a growing body of empirical evidence that
farmers rely on subjective probabilities rather than objective probabilities
(e.g. Eales et al., 1990; Hardaker and Gudbrand, 2010). At the same time,
extreme events, in the sense that they are rather unlikely but entail dramatic
consequences, are more and more common. Climate models indeed forecast
higher growing-season temperatures with greater damage to agricultural production and larger impacts on farm income (Battisti and Naylor, 2009), while
price volatility on commodity markets tends to increase. It is most probable
that farmers behave towards such extreme events in a specific way. In this
context, the weighting of probabilities depending on the likelihood of
events and the outcomes at stake may be more and more relevant to modelling
farmers’ decision-making process.
Our results contribute to a better characterisation of farmers’ decisionmaking under risk in two ways. First, rather than relying on results from
laboratory experiments with student samples, we provide experimental field
evidence that PT preferences may better describe farmers’ behaviour than
EU preferences. Second, we provide agricultural economists with measures
of farmers’ preferences, in relation to farmer and farm characteristics. Specifically, we are not aware of any earlier attempt to elicit PT preferences in the
context of a developed country.3 Evidence in favour of non-EU preferences is
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G. Bocquého et al.
expected to help understand farmers’ decision-making and to design adequate
policy instruments.
In Section 2, we describe the most popular alternatives to EU theory and
review the few studies that elicited farmers’ risk preferences under non-EU
theories and with experimental methods. In Section 3, we review some of
the research fields in agricultural economics where PT preferences were
shown to or are likely to matter. In Section 4, we describe our experimental
protocol, while the estimation procedure for the EU and CPT risk preferences
are laid out in Section 5. Results are presented in Section 6, and Section 7
concludes.
2.1. Non-EU theories of decision-making under risk
Numerous theories have been proposed as alternatives to EU (for a complete
review, see Starmer, 2000). In this section, we present the decision-weighting
theories, which proved to be the most convincing. They all accommodate
probability weighting, and some of them reference dependence as well. We
focus on the way decision-weighting theories relate to each other, both historically and technically.
The study of decision-making under risk has been dominated by EU theory
since the work of von Neumann and Morgenstern (1947). Although empirical
data quickly demonstrated the existence of systematic violations (see Allais,
1953, paradox for instance), the rigorous axiomatic basis, simplicity of use
and normative appeal led researchers to prefer EU to alternative theories for
decades. Originally defined for risk situations where the space of possible
events and the corresponding probabilities were objectively known by the
decision-maker, it was extended by Savage (1954) to subjective probabilities.
However, subjective EU has been criticised for its lack of generality (see
Ellsberg’s, 1961, paradox).
Decision-weighting theories emerged at the beginning of the 1980s, notably
thanks to insights from the psychological experimental research. Today, they
constitute the main alternative to EU. They hold in common preferences over
prospects that are non-linear in probabilities. Before any decision is made, objective probabilities are converted into subjective probabilities, or decision
weights. Among the class of decision-weighting theories, two well-known
sub-classes are of particular interest: sign-dependent theories (e.g. Kahneman
and Tversky’s, 1979, PT) and rank-dependent theories (e.g. Quiggin’s, 1982,
rank-dependent EU theory).
Kahneman and Tversky’s (1979) separable PT4 features a probability
weighting function which directly converts probabilities into decision
weights, low probabilities being overweighted and high probabilities
4 Separable prospect theory is sometimes referred to as original PT, in contrast to the more recent
cumulative version by Tversky and Kahneman (1992).
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2. Relevant literature
Expected utility or prospect theory maximisers
Page 5 of 38
2.2. Experimental elicitation of farmers’ risk preferences under
non-EU theories
As highlighted in Section 1, investigations about farmers’ risk preferences
based on non-EU theories are scarce. Here, we review the few recent exceptions, including those focusing on rural people in general.
Tanaka, Camerer and Nguyen (2010), Liu (2013) and Nguyen and Leung
(2009) are the closest to our own study because they use a similar experimental design to elicit CPT preferences. The method was originally developed
5 Safety-first and focus-loss constrained models are earlier and popular attempts to emphasise the
role of crisis situations (hunger, bankruptcy) in farmers’ decision-making (Roy, 1952; Kataoka,
1963; Boussard and Petit, 1967; Boussard, 1969; Moscardi and de Janvry, 1977).
6 Yaari’s (1987) dual theory incorporates the same type of rank-dependent decision weights but
assumes risk neutrality. Its pedagogical virtues lie in its intermediary position between expected
value models and rank-dependent EU models.
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underweighted. However, this specification has the drawback of violating
first-order stochastic dominance. In fact, the main contribution of separable
PT to the understanding of decision-making lies in its framing of outcomes
relative to a labile reference point, upper values representing gains and
lower values losses. A two-part utility function captures the difference in
behaviour in the two outcome domains. On the one hand, the curvature in
the gain domain is reflected in the loss domain, meaning that concavity
for gains implies convexity for losses (reflection effect and ‘S-shape’ utility
function). On the other hand, the slope varies between the two outcome
domains. It is usually steeper for losses than for gains, meaning that the disutility of a loss is stronger than the utility of a similar gain (loss aversion
concept). The reflection effect and the slope difference also apply to the probability weighting function, which increases the contrast between gain and loss
behaviour.
Some years later, to satisfy stochastic dominance, Quiggin (1982) developed
in the rank-dependent EU theory the idea of decision weights involving cumulative probabilities instead of single probabilities. Cumulative probabilities are
first transformed through the probability weighting function and then combined
into decision weights. Finally, the decision weight attached to a given outcome
depends on its likelihood (as in separable PT), and on its ranking relative to
the other outcomes of the prospect with respect to the amount at stake. Thus,
rank-dependent preferences are not separable in outcomes. The consequence
for decision-making is that extreme outcomes (because of extreme stakes or
very low probabilities) are particularly affected by decision weights. The
usual empirical finding is the overweighting of high- and low-ranked outcomes,
and the underweighting of middle-ranked outcomes.5 This behaviour pattern is
represented by an ‘inverse S-shape’ probability weighting function.6
Finally, Tversky and Kahneman (1992) combined in cumulative PT (CPT)
the most remarkable features of separable PT and rank-dependent EU theory,
namely gain-loss framing and cumulative decision weights.
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G. Bocquého et al.
3. Why PT matters in agricultural economics
Within the PT framework, utility curvature, loss aversion and probability
weighting all affect the way individuals evaluate risky outcomes, which in
turn modifies their behaviour. Thus, evaluating farmers’ risk preferences assuming PT rather than EU may help better explain farmers’ decision-making.
Several studies provide arguments for why it may matter if we are to deliver
more accurate modelling and predictions. In this section, we provide a review
of these arguments in the context of developed countries, focusing first on
the phenomena linked to reference dependence, namely the reflected utility
curvature and loss aversion, and then on probability weighting.
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by Tanaka, Camerer and Nguyen (2010) who applied it to a sample of rural
Vietnamese households. The authors pointed out that CPT describes their
data better than EU (with a reflected utility function at zero), with evidence
in favour of utility concavity in the gain domain, loss aversion and an
‘inverse S-shape’ probability weighting function. Liu (2013) obtained
similar results for Chinese cotton farmers. Nguyen and Leung (2009) used
the same sample as Tanaka, Camerer and Nguyen (2010) but focused on behaviour in relation to occupation. Farmers, who represented 46 per cent of
their sample, were found to be significantly less loss-averse than non-farmers.
Harrison, Humphrey and Verschoor (2010) tested separable PT and EU
theory, but in the gain domain only. They used a large sample of people from
rural Ethiopia, India and Uganda. They reported a significant underweighting
of probabilities over a wide range of probabilities, giving the function either
an S or a convex shape. However, when they allowed separable PT and EU
to explain the data at the same time, they found significant mixing proportions
close to 0.5, meaning that each model fits one half of the data better.
Similarly, Galarza (2009) focused on EU and CPT in the gain domain only.
The author analysed the responses of small-scale cotton producers from Peru.
Like Harrison, Humphrey and Verschoor (2010), Galarza showed that,
overall, subjects distort probabilities, but that mixing proportions for EU
and CPT are significant. About 30 per cent of the cotton producers exhibit
EU while 70 per cent behave according to CPT.
In the context of developed countries, we are not aware of any attempt to
estimate experimentally the parameters of some non-EU model from
farmers’ choices. However, Pennings and Smidts (2003) investigated nonparametrically sign-dependency behaviour on Dutch hog farmers. After measuring each respondent’s utility, they found evidence for mixed preferences, in
relation to farmers’ strategy and organisation. Farmers who buy piglets exhibit
mostly an ‘S-shape’ utility function (55 per cent) (i.e. concave for gains and
convex for losses), whereas farmers who breed their own piglets mostly
exhibit a fully concave or convex utility function (89 per cent).
Expected utility or prospect theory maximisers
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3.1. Reference dependence
As mentioned earlier, reference dependence means that subjects care about
changes in wealth, i.e. deviations from the reference point, rather than in
the absolute initial or final wealth level as in von Neumann and Morgenstern’s
(1947) EU theory. It implies a different behaviour depending on the sign of the
wealth deviation, either positive or negative. It was shown empirically that
this difference in behaviour proceeds from two phenomena: behaviour
towards gains is reflected in the loss domain and losses loom larger than gains.
3.1.1. Reflection effect
3.1.2. Loss aversion
If farmers behave according to PT, they are more sensitive to losses than to
equivalent gains. In a recent study, Liu and Huang (2013) highlighted the significant role of loss aversion in explaining pesticide use by Chinese cotton
farmers by combining experimental measures with survey results. The
authors suggested that more loss-averse farmers spray smaller amounts of
pesticide than less loss-averse farmers because they are more sensitive to
health deterioration.
Even if such a direct relationship cannot be tested in all cases, the agricultural literature provides several examples of deviations from a typical EU
7 To ensure participation in the insurance scheme, the insurance premium should equal (or be
lower than) the decision-maker’s risk premium, which depends on the decision-maker’s degree
of risk aversion. Otherwise, the decision maker is expected to refuse insurance.
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If farmers are PT maximisers, they are expected to be mostly risk averse in the
gain domain, but mostly risk seeking in the loss domain. Insurance demand is
one prominent example where this type of reflected behaviour can explain
deviations from what EU theory predicts. If individuals are risk-averse whatever the outcome domain as postulated by EU theory, it is in their best interest
to purchase insurance because they are willing to pay a small guaranteed
amount, the insurance premium, to avoid a potential but much larger loss.7
However, voluntary insurance is not always observed in the field, including
in the agricultural sector. Farmers’ participation in multiperil crop insurance
has historically been low in a number of countries, until substantial
premium subsidies or compulsory measures were implemented by public authorities, notably in the USA (Glauber, 2004; Enjolras and Sentis, 2011).
Several explanations for this striking phenomenon were provided. One is
that insurers face asymmetries of information (adverse selection and moral
hazard problems) and high administrative costs, which implies high insurance
premiums compared with farmers’ risk premiums. Another possible explanation is that insurance schemes compete at the farm level with other
risk-hedging strategies. A last explanation involves the reflection effect: if
farmers are risk-seeking for losses, it is rational for them to not insure and
bear the risk of a potential high loss, rather than pay an insurance premium
which is viewed as a small but certain loss.
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G. Bocquého et al.
8 The endowment effect is a specific form of the status quo bias (Samuelson and Zeckhauser,
1988).
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behaviour which may be explained by loss aversion. We distinguish between
two empirical manifestations of loss aversion, the gain-loss framing effect and
the endowment effect.
The gain–loss framing effect is the most obvious empirical observation revealing loss aversion: loss-averse individuals are not equally sensitive to a
good, service or monetary unit if it is perceived as a gain or a loss. For instance, in crop production contracts, the base price can be considered as a reference point, and performance incentives like quality rewards as deviations
from this point. Two frames are possible in such contracts: a high base
price, along with penalties for poor performance, or a relatively low base
price combined with rewards for good performance (Just and Wu, 2005).
Loss aversion implies that penalties and rewards are not perfect substitutes
as is the case in EU, penalties looming larger than rewards. Thus, to keep
farmers’ participation rate unchanged, a contract involving penalties should
provide farmers with a higher base price than a contract involving commensurate rewards. Hence, loss aversion has implications on the optimal contract
design: reward systems are to be preferred over penalty systems because they
minimise the contractor’s costs.
Gain –loss disparity also influences the efficiency of public incentives, depending on whether they are designed as penalties or bonuses. Unlike the contract setting, a general recommendation is to prefer a penalty system to induce
desired behaviour. For instance, Huijps et al. (2010) provided empirical evidence that dairy farmers are more sensitive to penalties than to bonuses
when urged to adopt new milking practices to improve cattle health.
The endowment effect is another empirical manifestation of loss aversion.8
It refers to the fact that people demand more to give up an object, good or
service (willingness-to-accept) than they are willing to pay to acquire it
(willingness-to-pay) (Thaler, 1980; Kahneman, Knetsch and Thaler, 1991).
In other words, the disutility of giving up an object is greater than the
utility of acquiring it. The endowment effect has potentially important implications on farmers’ willingness to comply with agri-environmental schemes.
Such schemes grant farmers for reducing pesticide use (Christensen et al.,
2011), growing nitrogen fixing crops (Espinosa-Goded, Barreiro-Hurlé and
Ruto, 2010) or providing ecosystem services (Wossink and Swinton, 2007),
for instance.
Furthermore, the dynamics of innovation adoption and abandonment is an
other important research field where the endowment effect may play a significant role. Huijps et al. (2010) provided empirical evidence in the case of
milking practices aimed at improving cattle health. Farmers who had
already implemented a given practice were asked if they would abandon
this practice in response to different levels of decrease in costs and efficiency.
The farmers who had not were asked if they would implement the practice in
response to cost and efficiency increases of the same magnitude. The authors
Expected utility or prospect theory maximisers
Page 9 of 38
found that, when faced with symmetric stimuli, farmers who have already
adopted an innovation are less willing to change their behaviour than nonadopters, and that transaction costs are not high enough to explain such a
reluctance to change.
3.2. Probability weighting
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Farmers who are PT maximisers distort objective probabilities into decision
weights. Extreme-ranked and unlikely outcomes are overweighted compared
with middle-ranked and likely outcomes. The success of single-peril insurance
such as hail insurance can partly be explained by probability weighting. Contrary to multiperil schemes, single-peril schemes have usually been successfully managed by the private sector (Glauber, 2004; Enjolras and Sentis,
2011). Even if single perils have potentially dramatic consequences on
farmers’ income, they are rare and moral hazard behaviour is limited due to
their uncontrollability. Thus, insurers have been able to offer low insurance
premiums relative to farmers’ risk premiums, which is sufficient under EU
to explain participation in the scheme. Nevertheless, probability weighting
may be another explanation. Single perils like hail are typically high-impact
low-probability losses for which farmers may be extremely sensitive. Thus,
because of the overweighting of these perils, farmers may purchase insurance
in greater numbers than predicted by EU.
In addition, probability weighting provides further insights with respect to
probabilistic insurance. It is an insurance scheme where there is a small probability that the insured is not compensated for damage, in exchange for a reduction in the insurance premium. As outlined by Kahneman and Tversky
(1979) and later by Wakker, Thaler and Tversky (1997), the overweighting
of extreme outcomes has in this case a negative effect on the demand for probabilistic insurance. Wakker, Thaler and Tversky (1997: 7) showed indeed that
people ‘dislike probabilistic insurance and demand more than a 20 per cent
reduction in the premium to compensate for a 1 per cent default risk’. In
other words, people attach great importance to eliminating the smallest
chance of failure. In fact, all insurances are probabilistic, including crop insurances. Most often, insurance contracts specify explicitly some cases in which
the claim is not to be paid, and other risks on the insurer’s side such as insolvency or fraud always implicitly exist (Wakker, Thaler and Tversky, 1997).
Thus, not accounting for farmers’ probability weighting is likely to mask
the high cost of adding exclusion situations in insurance contracts or of abrading, even slightly, farmers’ confidence in the insurance system.
A second research area in which probability weighting has important implications is the design of contracts. Similarly to insurance policies, any real contract setting includes some low-probability explicit and implicit default risks
leading to losses for the contractee. In the case of crop production contracts, a
failure from the contractor has potentially dramatic consequences on farmers’
income, especially if the crop is new because the relevant market may be
still developing and alternative selling opportunities scarce (see for instance
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G. Bocquého et al.
4. Experimental protocol
4.1. Experimental design and procedure
Our experimental design is adapted from Tanaka, Camerer and Nguyen’s
(2010) risk task.9 It consists of three series of choices, which are variants of
Holt and Laury’s (2002) multiple price lists. In practical terms, subjects are
presented with a succession of pairs of binary lotteries, each pair being composed of a safe lottery (option A) and a risky lottery (option B). They are asked
to pick one lottery in each row. In the first row, the expected value of lottery A
is higher than the expected value of lottery B. As one proceeds down the rows,
the expected value of lottery B increases more quickly than the expected value
of lottery A, and in the last row the expected value of lottery B is higher than
the expected value of lottery A. In the first two series, payoffs are all positive,
whereas in the third and last series, lotteries mix positive and negative payoffs.
To enforce monotonicity, subjects are asked to pick the row in which they
9 Tanaka, Camerer and Nguyen’s (2010) experiment is made up of a risk task aiming at measuring
CPT parameters and a time task aiming at measuring time preference parameters. However, the
two tasks are unrelated and can be implemented independently.
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Alexander et al. (2012) in the context of perennial bioenergy crops). Thus, to
ensure the participation of farmers who may distort probabilities, contractors
should compensate for or minimise the counterparty risk, even if it may seem
insignificant at first sight. The simplest incentive is to substantially increase
the base price. However, a more cost-effective option would be to reduce
the likelihood of the counterparty risk as perceived by farmers, or diminish
its potential consequences. In the first case, contractors could provide more
information about their commercial strategy and partners in order to
increase farmers’ trust. In the second case, they could sign up to a partnership
with other crop traders or processors, each partner committing to buy each
other’s feedstock in the event of one partner’s failure.
Price hedging is a third example where probability weighting may be
helpful in explaining farmers’ behaviour. In developed countries, the
gradual elimination of public price regulation and market protection
systems have contributed to increasing the price volatility of agricultural commodities. However, it was reported that few farmers resort to derivatives
markets to hedge price risk (less than 10 per cent according to Garcia and
Leuthold, 2004). Mattos, Garcia and Pennings (2008) investigated this
paradox by analysing the impact of cumulative probability weighting on
soya bean producers’ optimal position on the futures market. They found
that probability weighting affects producers’ position more than changes in
utility curvature and loss aversion. More importantly, they showed that
when probability weighting increases towards the overweighting of extreme
events, the utility of resorting to futures decreases quickly. Hence, probability
weighting is one possible explanation for farmers exhibiting little interest in
financial instruments to hedge against price risk.
Expected utility or prospect theory maximisers
Page 11 of 38
10 The difference in expected payoff between lotteries is not shown to respondents. The effect of
providing expected value information is not well documented (Harrison and Rutström, 2008).
11 For instance, the net margin of a traditional rape/wheat/barley rotation is around 430 euros/ha/
year in a French cereal-growing region (Bocquého and Jacquet, 2010).
12 Real money incentives are recommended to ensure respondents’ commitment to the experiment and avoid hypothetical bias (Harrison and Rutström 2008: 123).
13 The use of different currency units for lottery payoffs and for real payments is a procedure that
has been followed by other experimentalists dealing with large payoffs, either in the laboratory
(e.g. Abdellaoui, Bleichrodt and L’Haridon, 2008) or in the field (e.g. Galarza, 2009). As highlighted by an anonymous referee, it may add ambiguity to the task at hand. It may also introduce
a complex set of heterogeneous behaviour if some farmers understood the exchange rate to be 2
per cent while others did not. In Section 6.3.1, we thus test for the sensitivity of our results to the
exchange rate.
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prefer lottery B to lottery A. Subjects who are very risk-averse may never
switch – and always choose lottery A – and subjects who are very riskseeking may choose the risky lottery in the first row – and always choose
lottery B. Risk neutral subjects would switch when lottery B overtakes
lottery A in terms of expected value.
The 33 lottery choices submitted to each subject are displayed in Table 1.10
We used substantial amounts of money from 10 to 6,000 euros in absolute
value, the mean expected payoff being about 205 euros. This high payoff
range has two advantages. On the one hand, farmers are presented with
money values that they are used to handling in their production choices.11
On the other hand, because individuals exhibit a quasi-linear utility at low
stakes (Rabin, 2000; Holt and Laury, 2002), we increase the chance of detecting utility curvature.
The experiment was carried out from February to June 2010 as part of a larger
survey. It took place after a 2-hour face-to-face interview aimed at collecting,
inter alia, farmer and farm characteristics and understanding the drivers for the
adoption of agricultural innovations. The experiment lasted around half an hour
and was divided into three different tasks: a risk task, an ambiguity task and a
time task. In this paper, we analyse only the results from the risk task. A comprehensive introduction of methods and goals, as well as examples, was given to
respondents prior to the experiment to ensure a good comprehension of the task
at hand. Subjects were provided with an initial endowment of 15 euros for their
participation. After the subject had completed all three series, one row was randomly selected and the lottery initially chosen played for real money.12
As we were not able to pay the full payoffs (ranging from 2600 to 6,000
euros in the risk task), at the beginning of the experiment respondents were
advised that they would receive only a percentage of the payoffs. However,
the exact amount was not announced. The predetermined percentage of 2
per cent was noted on a sheet of paper and enclosed in an opaque envelope
prior to visiting respondents. The envelope was laid on the table in front of
each respondent at the beginning of the experiment.13 If selected, loss lotteries
were played for real just like gain lotteries, but the initial endowment ensured
that final earnings were not negative. The average earning from the three tasks
was 19 euros. All instructions given to respondents are provided in Appendix
Page 12 of 38
G. Bocquého et al.
Table 1. Experimental design
Expected payoff
difference (A –B)
Option A
Option B
Series 1
1
2
3
4
5
6
7
8
9
10
11
12
Prob 30%
400
400
400
400
400
400
400
400
400
400
400
400
Prob 70%
100
100
100
100
100
100
100
100
100
100
100
100
Prob 10%
680
750
830
930
1060
1250
1500
1850
2200
3000
4000
6000
Prob 90%
50
77
50
70
50
60
50
52
50
39
50
20
50
25
50
240
50
275
50
2155
50
2255
50
2455
Series 2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Prob 90%
400
400
400
400
400
400
400
400
400
400
400
400
400
400
Prob 10%
300
300
300
300
300
300
300
300
300
300
300
300
300
300
Prob 70%
540
560
580
600
620
650
680
720
770
830
900
1000
1100
1300
Prob 30%
50
50
50
50
50
50
50
50
50
50
50
50
50
50
Series 3
1
2
3
4
5
6
7
Prob 50%
250
40
10
10
10
10
10
Prob 50%
240
240
240
240
280
280
280
Prob 50%
300
300
300
300
300
300
300
Prob 50%
2210
60
2210
245
2210
260
2160
285
2160
2105
2140
2115
2110
2130
Design adapted from Tanaka et al. (2010). Lottery payoffs are in euros.
23
217
231
245
259
280
2101
2129
2164
2206
2255
2325
2395
2535
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Row
Expected utility or prospect theory maximisers
Page 13 of 38
A in supplementary data at ERAE online, and record sheets are in Appendix B
in supplementary data at ERAE online.
4.2. Sample
14 According to Harrison and List’s (2004) terminology, our experiment belongs to the class of
artefactual field experiments (non-standard population, but abstract framing).
15 More precisely, the sample is a stratified random sample. In the following analysis, statistical
weights are used in order to make the final sample representative of the initial pool of farmers.
16 The response rate is much higher than in other field experiments. For instance, Galarza (2009)
reported a response rate of 54 per cent in his risk experiment with Peruvian farmers, and
Harrison (2007) a rate of 40 per cent in his risk experiment about the Danish population.
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We elicited preferences from a population of farmers,14 whereas most experimental studies rely on a laboratory setting which involves a university student
population. This last practice can be criticised for at least three reasons. First,
there are no grounds for systematically generalising all the results drawn from
student responses to other people. Second, in the overwhelming majority of
cases, there is no rational sampling, and thus the students who participate in
the experiment are not representative of an economically significant population. Third, students are more homogeneous than the broader population
with respect to important socio-demographic characteristics like age and education. Thus, drawing preferences from a student sample may fail to reveal all
diversity in behaviour. As stressed by Harrison and List (2004), field
approaches are indeed complementary to laboratory approaches to give
sharper and more relevant inferences about real behaviour.
We constructed our sample of farmers from 64 rural towns in Bourgogne, in
the east of France. The region of Bourgogne has a diverse agricultural production, including cereal crops, livestock, market vegetables and wine. This diversity increases the possibility of detecting heterogeneity in individual
behaviour. We randomly selected 232 subjects from the pool of farmers
living in the chosen towns,15 first contacted them by post, and followed up
a few days later with a phone call to make an appointment. Among them,
85 subjects were excluded because of wrong profession or contact information. In the end, 111 farmers were surveyed and 107 participated in the experiment, corresponding to a response rate of 73 per cent (excluding farmers who
refused to participate, lacked time or did not show up).16 We believe that the
induced selection bias is not critical. Indeed, when they were contacted,
farmers were informed about a 2.5-hour survey but they were informed
neither about the experiment nor the real payment mechanism. In addition,
we measured key variables expected to modify risk preferences such as
wealth (FarmSize variable), trust (Trust) and background risk (WheatRisk).
As a result, there is little chance that a farmer’s decision to participate, i.e. the
probability of being included in the sample, was influenced by his or her own
risk preferences or some unmeasured variable affecting risk preferences.
Table 2 gives some descriptive statistics of farmer and farm characteristics
thought to influence risk preferences. On average, the farmers were about 48
Page 14 of 38
G. Bocquého et al.
Table 2. Descriptive statistics
Description
Age
NbChildren
EducSup
Trust
FarmSize
LandOwned
DeffPayment
Livestock
IdleLand
IndivOwner
NoSuccessor
North
WheatRisk
Number of
observations
Std.
Dev.
47.68
1.11
0.32
8.85
1.15
0.47
0.21
1.69
0.32
0.41
0.96
0.21
0.26
0.25
0.23
0.24
0.03
0.42
0.43
0.03
0.59
0.49
0.26
0.44
0.24
0.43
3.29
0.55
102
Variable WheatRisk is the mean of several Likert-type items measuring farmers’ perception of their exposure to
several types of risk with respect to wheat production (1 ¼ not important at all, 5 ¼ very important): climatic
risk, management risk, location risk, price risk, cost risk. Variable Trust is a dummy corresponding to farmers’
answer to the following question: ‘Generally speaking, would you say that most people can be trusted or that you
can’t be too careful in dealing with people?’
years old (Age) and had one child living in the household (NbChildren). One
third had at least a secondary-school education level (EducSup). The mean
farm size was 169 ha (FarmSize), with one-third of the land being owned
by the farmer (Landowned). The mean extra-agricultural part of the households’ income was 26 per cent (ExtraInc). Breeding farms (Livestock) represented 24 per cent of the sample. As mentioned earlier, other variables that
may modify individual risk preferences are whether farmers trusted other
people (Trust) and the background risk they faced (WheatRisk).
Unobserved location variables such as soil and climate can jointly affect
risk preferences. We control for such location-specific characteristics with
regional fixed effects, and thus focus on intra-regional variations of risk preferences. With the North dummy variable, we distinguish between the southern part of the sampling area which corresponds to the fertile plain of the
Saône river and the northern part which corresponds to the limestone
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ExtraInc
Age of the subject (years)
Number of children in the household
Dummy if education level beyond secondary
school
Dummy if self-reported as trusting other people
Total arable area (100 ha)
Proportion of land out of the arable area which
is owned
Proportion of the household income coming
from another profession than farming
Dummy if uses deferred payments
Dummy if has livestock
Proportion of idle land out of the arable area
in 2009
Dummy if the farm is a sole proprietorship or
a society with only one associate
Dummy if has no successor despite looking
for one
Dummy if farm located in the northern part
of the study area
Importance of risk faced on soft wheat
(1– 5 score)
Mean
value
Expected utility or prospect theory maximisers
Page 15 of 38
plateau of Bourgogne. On the plateau, soils are relatively poor and the climate
is semi-continental, with long and harsh winters. Using North–South rather
than town fixed effects minimises the risk of imprecise estimates and large
standard errors inherent to fixed-effect models: the within-group variation
of risk preferences is maximum (a lot of farmers in each region) while the
loss of degrees of freedom is minimum (only two regions). Furthermore, in
our sample, all farmers have land in several towns, including in several of
the 64 selected towns. As a result, the town information is not relevant to
capture location-specific soil and climate factors.
5. Estimation methods
5.1. EU (with a reflected utility function at zero)
Let us first assume that the utility of income follows a two-piece power specification (Tversky and Kahneman, 1992; Wakker, 2008):
yr
if y ≥ 0
u(y) =
,
(1)
−(−y)r if y , 0
where y is the lottery payoff and r is an anti-index of risk aversion for gains
(r . 0). Indeed, in the gain domain (y ≥ 0), this utility specification implies
risk seeking (utility convexity) for r . 1, risk neutrality (linearity) for r ¼ 1
and risk aversion (concavity) for r , 1. Because u(.) is symmetrical with
respect to 0, the interpretation of r for gains is reflected for losses, i.e. r . 1
stands for risk aversion (utility concavity).17
17 Strictly speaking, utility functions complying with von Neumann and Morgenstern’s (1947) EU
theory are defined only over positive amounts that correspond to absolute wealth levels: they
are either fully concave (for a risk averse behaviour) or fully convex (for a risk seeking behaviour).
However, in the recent experimental literature, EU can have a broader meaning and involve
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A flexible way of eliciting preference parameters from experimental data is
the estimation of structural models, as initially proposed by Harless and
Camerer (1994). In particular, this approach is suitable for specifications
that involve several preference parameters like CPT. In this paper, we
present the different EU and CPT structural models that will be estimated
in Section 6. Although not based on any theory, it is widely assumed that
under PT one’s reference point corresponds to the status quo, or, equivalently,
one’s current assets (Kahneman and Tversky, 1979). In our experiment,
because the initial endowment is given before farmers make any choice, it
is supposed to be integrated into current assets. Thus, all farmers care about
the difference between final assets and current assets (including the initial endowment), i.e. the lottery payoffs. For the sake of simplicity, we ignore
current assets in the estimation procedure: the reference point is zero and
final assets are the lottery payoffs.
Page 16 of 38
G. Bocquého et al.
In the experiment, subjects are asked to choose between lottery A (yA,1, pA;
yA,2) and lottery B (yB,1, pB; yB,2) over a series of j questions. At each question,
the EU of subject i for each lottery (A or B) is written as follows:
ri
ri
EUA
i (y) = pA × yA,1 + (1 − pA ) × yA,2 ,
(2a)
i
i
+ (1 − pB ) × yrB,2
,
EUBi (y) = pB × yrB,1
(2b)
B
DEU
= EUA
i − EUi .
i
(3)
We then build upon Manski and Lerman’s (1977) random utility model to
develop an empirical model of choice. Utility is broken down into a deterministic
part (Equation (3)) which contains the preference parameter(s) to be estimated
(ri), plus a random part capturing unobserved heterogeneity (1i). Preference parameters are supposed to depend on observable individual characteristics (vector
Xi) through a linear relationship which is constant over subjects:
ri = u0 + uXi
∀i,
(4)
where u0 and vector u are coefficients to be estimated. The binary choice between
lottery A or B can thus be described by the following latent regression model:
A if d∗i . 0
EU
,
(5)
d∗i = Di (Xi ) + 1i , and di =
B otherwise
where 1 is a normally distributed error term with mean zero and known variance
v. We can derive from the above equation the probability that subject i will choose
lottery A:
Pr(choose lottery A|Xi ) = Pr(DEU
i + 1i . 0|Xi )
= 1 − Pr(1i ≤ −DEU
i |Xi )
= 1 − F(−DEU
i (Xi ))
(6)
= F(DEU
i (Xi )),
utility functions that are defined over positive and negative lottery payoffs, and are domainspecific (e.g. Harrison and Rutström, 2008; Tanaka, Camerer and Nguyen, 2010; Nguyen, 2011).
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where yA,1, yA,2 and yB,1, yB,2 are the payoffs of each lottery A or B, respectively; and pA and pB are the probabilities associated with the left payoffs of
each lottery A or B. Assuming that subjects follow a utility-maximising behaviour, observed choices are driven by a latent choice index D which is
the difference between the utilities for lotteries A and B (Harrison and Rutström, 2008), that is under EU:
Expected utility or prospect theory maximisers
Page 17 of 38
where F(.) denotes the standard normal distribution function. The right-hand
side thus lies in the interval [0;1] for any value of DEU
i . We estimate the risk
preference parameters ri with maximum likelihood methods. The likelihood
of the observed choices, conditional on the EU and power utility specifications
being true, is as follows:
EU
ln LEU (d, X; r) =
)
×
I(
d
=
A)
+
ln[1
−
F(D
)]
×
I(
d
=
B)
,
ln F(DEU
k
k
k
k
k
(7)
r̂ = arg max ln LEU (d, X; r).
(8)
Since the power specification might appear very restrictive, one may consider
other functional forms for utility, for instance to allow for varying degrees
of relative risk aversion. Here, we consider a variant of Saha’s (1993) expopower (EP) specification (Holt and Laury, 2002; Abdellaoui, Barrios and
Wakker, 2007):
[1 − exp(−bya )]/b if y ≥ 0
u(y) =
,
(9)
[1 − exp(b(−y)a )]/b if y , 0
where a and b are indexes of risk aversion for gains (a . b .0). The EP specification accommodates the usual empirical finding of a decreasing absolute risk
aversion and an increasing relative risk aversion. When a ¼ 1, absolute
risk aversion is constant, and when b tends to 0, relative risk aversion is
constant as in the power specification. Replacing the power utility by an EP
utility in Equations (2a) and (2b) leads to a new likelihood function L EP. The
maximum-likelihood joint estimation for risk parameters a and b is therefore:
(â , b̂ ) = arg max ln LEP (d, X; a, b).
(10)
5.2. Cumulative PT
An alternative paradigm for subjects’ behaviour could be CPT, with a power
utility function exhibiting a different slope in the gain and the loss domain
(Tversky and Kahneman, 1992):
⎧
⎨
ys
0
u(y) =
⎩
−l(−y)s
if y . 0
if y = 0 .
if y , 0
(11)
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where k indexes the different lottery choices pooled over subjects (k¼(i, j)), I is
the indicator function; and dk ¼ A[B] denotes the choice of lottery A[B]. The
maximum-likelihood estimation for the risk parameter is therefore:
Page 18 of 38
G. Bocquého et al.
where v(.) is a probability weighting function which is is strictly increasing
from the unit interval into itself, and satisfies v(0) ¼ 0 and v(1) ¼ 1. The
form of the weighting function has widely been discussed. Following
Tanaka, Camerer and Nguyen (2010), we prefer Prelec’s (1998) specification:
v( p) = exp[−(− ln p)g ],
(13)
where g is the parameter controlling the curvature of the probability weighting
function (g . 0).20 This parameter can be interpreted as an index of likelihood
sensitivity, with g ¼ 1 reflecting the absence of probability distortion (v(p) ¼
p).21 In other words, as g decreases (g , 1), the distinction between different
levels of probability gets more and more blurred, and probabilities tend to be
perceived as all being equal. This is the normal assumption, backed by a substantial amount of empirical evidence, and giving to the weighting function
18 In PT, risk behaviour depends on other factors besides utility, namely loss aversion and probability weighting. Thus, s is no longer an index of risk behaviour but just a measure of utility
curvature.
19 In the original specification of CPT by Tversky and Kahneman (1992), two distinct parameters
control utility curvature, one for the gain domain and one for the loss domain. However, in
most empirical applications they are merged (see Wakker (2010: 267 –271) for an explanation
of the analytical reasons justifying such a simplification).
20 CPT can also accommodate different curvatures for the probability weighting function depending on the outcome domain. However, in most empirical applications, it is assumed that a single
parameter operates in both domains, like for the utility function.
21 Originally, Prelec (1998) proposed a two-parameter function, one parameter standing for likelihood sensitivity, and one parameter for pessimism. Indeed, the prevailing empirical finding is
that deviation from linear probability weighting results from a combination of both phenomena.
Whereas likelihood sensitivity is viewed as a consequence of cognitive limitations in the perception of objective probabilities, pessimism is considered as a motivational distortion of probabilities which depends on outcome ranks. If the decision-maker is pessimistic, bad outcomes are
overweighted while good outcomes are underweighted. Optimism is defined by the opposite
behaviour. Likelihood sensitivity affects the curvature of the probability weighting function,
while pessimism affects its elevation. However, the effect of pessimism on probability weighting
was found to be low compared with likelihood sensitivity, and, as such, is often ignored in empirical applications (see Wakker, 2010, for more details).
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In this specification, s is an anti-index of utility concavity for gains (s . 0)18,19
and l is the decision-maker’s coefficient of loss aversion (l . 0). The decisionmaker is more (resp. less) sensitive to losses than to gains when l . 1 (resp.
l , 1). The usual empirical finding is l . 1, along with s , 1 (concave
utility in the gain domain).
Following Tversky and Kahneman (1992), decision weights defined over
cumulative probabilities are introduced. The value of any binary lottery (y1,
p; y2) is as follows:
⎧
⎪
⎨ v( p) · u(y1 ) + [1 − v( p)] · u(y2 ) if y1 ≥ y2 ≥ 0 or
,
y1 ≤ y2 ≤ 0
PU(y1 , p; y2 ) =
⎪
⎩
v( p) · u(y1 ) + v(1 − p) · u(y2 )
if y1 , 0 , y2
(12)
Expected utility or prospect theory maximisers
Page 19 of 38
k
+ ln[1 −
F(DCPT
k )]
(14)
× I(dk = B) .
The maximum-likelihood estimation for (s, l, g) is then:
(ŝ , l̂ , ĝ ) = arg max ln LCPT (d, X; s, l, g).
(15)
It should be mentioned that the original experiment by Tanaka, Camerer
and Nguyen (2010) is such that any combination of choices in the three
series determines a particular interval for the CPT parameter values. As a
result, an identification of parameters through maximum likelihood is possible
in theory. The implementation was done in STATA following the procedure
for survey data (svy: prefix). In particular, the standard errors are clustered
to correct for the possibility that responses from the same subject are correlated. The STATA program uses maximum likelihood routines for structural
choice models adapted from Harrison and Rutström (2008).
6. Results
6.1. Raw results
The distribution of switching points from the 107 farmers is shown in Table 3.
For each subject, we also calculate the corresponding CPT parameters using
the analytical ‘midpoint technique’.22 Then, we derive estimates of mean
values and corresponding standard errors for the underlying population. We
22 Thanks to Tanaka, Camerer and Nguyen’s (2010) specific design, bounds for l and g can be jointly inferred by crossing responses to Series 1 and Series 2, each series providing several possible
combinations of intervals for s and g. Then, depending on the s value previously elicited, conditional bounds for l can be inferred from Series 3. Parameter values are approximated by taking
the midpoint of intervals. When there is no switch, the values at the boundary are used.
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an ‘inverse S-shape’. In the case of a binary prospect such as a lottery, it
characterises an overweighting of the low-probability outcome and an underweighting of the high-probability outcome. If g . 1, the function takes the
less conventional ‘S-shape’. At the extreme, if g is very high, probabilities
tend to be perceived as either 0 or 1. In CPT, risk behaviour results from
the interplay of utility curvature, loss aversion and probability weighting.
Note that the CPT model reduces to the EU-power model (Equation (1)) if
l ¼ 1 and g ¼ 1.
The derivation of the likelihood function for CPT follows the same steps
than for EU. By denoting DCPT the difference in prospect utilities, the likelihood of the observed choices, conditional on our CPT specification being true,
is written as follows:
ln LCPT (d, X; s, l, g) =
ln F(DCPT
k ) × I(dk = A)
Page 20 of 38
G. Bocquého et al.
Table 3. Distribution of switching points
Proportion of respondents
Switching point
Series 2
Series 3
15.0
2.8
0.9
26.2
1.9
0.9
2.8
7.5
14.0
1.9
4.7
8.4
1.9
1.9
2.8
1.9
2.8
8.4
4.7
3.7
2.8
6.5
10.3
7.5
14.0
13.1
24.3
4.7
3.7
38.3
100.0
107
4.7
32.7
100.0
107
22.4
100.0
107
find that, on average, the parameter s controlling utility curvature is 0.51 (with
a 95 per cent confidence interval of [0.41,0.62]) and the loss aversion parameter l is 3.76 (with a 95 per cent confidence interval of [2.93,4.58]). Regarding
the likelihood sensitivity parameter, we find that the mean value of g is 0.65
with a 95 per cent confidence interval of [0.56,0.73]). These estimates are in
line with those calculated with similar methods by Tanaka, Camerer and
Nguyen (2010) and Liu (2013) for rural people from developing countries.23
6.2. Estimation of structural models of risk preferences
In this section, we estimate various decision models, namely the two EU
models and the CPT model defined in Section 5. For each model, we consider
(i) uniform risk preferences among farmers (model 1), (ii) varying preferences
driven by farmer characteristics (model 2), (iii) varying preferences driven by
farm characteristics (model 3) and (iv) varying preferences driven jointly by
farmer and farm characteristics (model 4).24
23 Tanaka, Camerer and Nguyen (2010) and Liu (2013) reported mean values of about 0.60 (between
0.59 and 0.63) and 0.52, respectively, for utility convexity (s in this paper) and of about 2.63 and
3.47 for loss aversion (l). They found values of 0.74 and 0.69 for likelihood sensitivity (g).
24 We intended to detect potential multicollinearity between farmer and farm characteristics by
computing the variance inflation factor for each variable. All coefficients were found to be
lower than 2, meaning that there is no major multicollinearity problem (the threshold is around
10).
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1
2
3
4
5
6
7
8
9
10
11
12
13
14
Never
Total
Number of observations
Series 1
Expected utility or prospect theory maximisers
Page 21 of 38
6.2.1. EU (with a reflected utility function at zero)
6.2.2. Cumulative PT
Table 6 gives the parameter estimates for the more elaborate CPT specification. The three risk parameters s, l and g estimated with model 1 are all significantly different from 1 at the 1 per cent level, implying a non-linear utility
function, loss aversion and probability weighting. The estimated mean value
for s is 0.28 (with a 95 per cent confidence interval of [0.25,0.31]), consistent
25 One exception is Harrison (2007) who reported that there was no evidence to reject constant relative risk aversion for the Danish population. In addition, (Harrison and Rutström 2008: 77) outlined that increasing relative risk aversion might be an artifact of the specification used to
account for errors in subjects’ choices.
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Table 4 reports the EU estimates, assuming a power specification for utility. In
model 1, the parameter r controlling utility curvature is estimated to be 0.21,
with a 95 per cent confidence interval between 0.17 and 0.25. Figure 1 displays the distribution of the r values predicted by model 4. It indicates that
farmers exhibit a quite uniform behaviour towards the high payoffs considered
in the experiment. The risk aversion index 1 2 r is predicted to be over 0.5 for
the whole sample, meaning that farmers are very risk-averse in the gain
domain and very risk-seeking in the loss domain. It contrasts with the moderate values obtained with other experimental data from developed countries.
However, as shown in Table 4, we could not find any significant effect of individual characteristics on the r parameter.
Table 5 gives the risk parameter estimates for the flexible EP utility form.
With model 1, â is 0.29 and b̂ is 0.12, the 95 per cent confidence intervals
being [0.25, 0.33] and [0.08, 0.16], respectively. Since â is significantly
less than 1 and b̂ is significantly more than 0, risk preferences appear to be
characterised by a decreasing absolute risk aversion and an increasing relative
risk aversion (in the gain domain). These results are in line with those usually
obtained in laboratory settings with student populations (e.g. Holt and Laury,
2002).25 In contrast with the power specification, we observe from model 4
that many farmer and farm characteristics have a significant influence on
the EP risk parameters. Usually, each characteristic affects only one of the
two a and b parameters. Variables NbChildren, EducSup, FarmSize, ExtraInc, Livestock and IdleLand are significant determinants of a but not of b,
whereas Trust, LandOwned, IndivOwner and North are significant determinants of b only. This result supports the use of the EU–EP specification to
better describe farmers’ risk behaviour. As expected, the more educated and
trusting the farmers, the larger the farm (a proxy for wealth) and the higher
the proportion of extra-agricultural income (a proxy for income stability),
the lower the risk aversion (for gains). On the contrary, livestock breeders,
farmers with more idle land, individual owners and farmers facing poorer
growing conditions tend to be more risk averse than the others (in the gain
domain). The global effect of Age on risk aversion is unclear as it affects a
and b in opposite directions.
Model 1
Model 2
Model 3
Coef.
Std. err.
Coef.
Std. err.
r Constant
Age
NbChildren
EducSup
Trust
FarmSize
LandOwned
ExtraInc
DeffPayment
Livestock
IdleLand
IndivOwner
NoSuccessor
North
WheatRisk
0.212***
(0.020)
0.097
0.002
0.012
0.088
20.071
20.001
20.113
0.017
0.022
(0.106)
(0.002)
(0.015)
(0.062)
(0.137)
(0.018)
(0.109)
(0.121)
(0.048)
Model p-value
Number of observations/clusters
3,531/107
Specific tests on estimated coefficients (p-values)
r: Constant ¼ 1
0.000
0.118
3,399/103
Coef.
Std. err.
Coef.
Std. err.
0.029
(0.111)
0.018
20.820
0.070
0.029
20.059
0.046*
(0.034)
(0.571)
(0.043)
(0.045)
(0.050)
(0.027)
20.206
0.004
0.003
0.060
0.007
0.024
20.119
0.021
20.020
0.032
20.514
0.101
0.059
20.088
0.034
(0.310)
(0.003)
(0.019)
(0.053)
(0.093)
(0.043)
(0.145)
(0.089)
(0.042)
(0.064)
(0.751)
(0.144)
(0.057)
(0.082)
(0.031)
0.099
3,498/106
Standard errors allow for our survey data design, including clustering effects.
*p , 0.1, **p , 0.05, ***p , 0.01.
0.346
3,366/102
G. Bocquého et al.
Covariate
Model 4
Page 22 of 38
Table 4. Maximum likelihood estimates of preferences using the EU–power model
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Expected utility or prospect theory maximisers
Page 23 of 38
with a concave utility in the gain domain and a convex utility in the loss
domain. However, it is slightly higher than when estimated with the
EU-power model, meaning that some of the utility curvature is captured by
loss aversion or probability weighting. Indeed, the loss aversion parameter
l is estimated to be significantly different from 1 and equal to 2.28 on
average, with a 95 per cent confidence interval between 1.80 and 2.75. It
means that farmers are about twice as sensitive to losses as to equivalent
gains. Similarly, the likelihood sensitivity parameter g is estimated to be significantly different from 1. Its mean value is 0.66, with a 95 per cent confidence interval between 0.50 and 0.81. This provides some evidence of
probability distortion in the expected direction: the weighting function is
‘inverse S-shaped’ and low-probability extreme events are overweighted.
Our estimates of the loss aversion and likelihood sensitivity parameters are
very similar to the values reported by Tversky and Kahneman (1992) for a
student sample (2.25 for loss aversion, 0.61 for likelihood sensitivity in the
gain domain and 0.69 for likelihood sensitivity in the loss domain).
Figure 2 represents the distributions of ŝ , l̂ and ĝ as predicted by model
4. The distribution of ŝ is similar to that obtained with the EU–power specification, that is to say homogeneity over farmers and a mean value denoting a
strongly concave utility function in the gain domain (ŝ , 0.5). However, the
distribution is shifted towards the right, showing once again that some of the
utility curvature has been transferred to the other risk parameters l and g. The
predicted l and g vary much more than the predicted s. Indeed, a sizeable proportion of farmers is expected to be extremely loss-averse (l̂ . 5) or, on the
contrary, loss-seeking (l̂ , 1). Also, many farmers tend to be extremely sensitive to low-probability extreme events (ĝ close to 0), while a few farmers
tend to underweight them (ĝ . 1).26
26 In Figure 2, the distribution of ĝ is represented on the interval [25,5]. Thus, the 25 farmers for
whom the predicted likelihood sensitivity was greater than 10 were excluded from the graphic.
These farmers perceive probabilities as being either 0 or 1.
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Fig. 1. Distribution of the r values predicted by the EU–power model under heterogeneous
preferences (model 4).
Model 1
Model 2
Model 3
Coef.
Std. err.
Coef.
Std. err.
a Constant
Age
NbChildren
EducSup
Trust
FarmSize
LandOwned
ExtraInc
DeffPayment
Livestock
IdleLand
IndivOwner
NoSuccessor
North
WheatRisk
0.288***
(0.018)
0.388
20.000
0.007
20.003
20.106
20.010
20.097
20.102
0.045
(0.268)
(0.004)
(0.024)
(0.082)
(0.072)
(0.035)
(0.101)
(0.095)
(0.097)
b Constant
Age
NbChildren
EducSup
Trust
FarmSize
LandOwned
ExtraInc
0.119***
(0.022)
0.250*
20.003
20.004
20.123*
0.093
0.008
0.138
20.028
(0.132)
(0.002)
(0.012)
(0.068)
(0.184)
(0.029)
(0.168)
(0.173)
Coef.
Std. err.
Coef.
Std. err.
0.158
(0.111)
0.010
20.267
0.053
0.072
0.026
0.024
(0.044)
(0.527)
(0.052)
(0.046)
(0.034)
(0.026)
0.078
0.005**
0.058**
20.222***
20.078
20.143***
20.031
20.280***
0.036
0.215***
2.663**
0.034
20.055
20.115
0.030
(0.245)
(0.003)
(0.023)
(0.058)
(0.063)
(0.033)
(0.132)
(0.084)
(0.041)
(0.053)
(1.205)
(0.062)
(0.039)
(0.104)
(0.022)
0.551***
20.010**
20.027
20.246
20.144**
20.000
0.208**
0.269
(0.203)
(0.004)
(0.018)
(0.155)
(0.057)
(0.059)
(0.084)
(0.167)
0.311***
(0.112)
G. Bocquého et al.
Covariate
Model 4
Page 24 of 38
Table 5. Maximum likelihood estimates of preferences using the EU–EP model
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20.041
(0.044)
20.015
1.131*
20.085
20.031
0.056*
20.047*
Model p-value
Nb. of obs. /clusters
3,531/107
Specific tests on estimated coefficients (p-values)
a: Constant ¼ 1
b: Constant ¼ 0
0.000
0.000
0.763
3,399/103
0.160
3,498/106
Standard errors allow for our survey data design, including clustering effects.
*p , 0.1, **p , 0.05, ***p , 0.01.
(0.042)
(0.594)
(0.090)
(0.041)
(0.033)
(0.025)
20.007
20.005
20.904
0.088***
0.047
0.171***
20.033
0.000
3,366/102
(0.016)
(0.033)
(0.876)
(0.033)
(0.042)
(0.064)
(0.026)
Expected utility or prospect theory maximisers
DeffPayment
Livestock
IdleLand
IndivOwner
NoSuccessor
North
WheatRisk
Page 25 of 38
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Model 1
Model 2
Model 3
Coef.
Std. Err.
Coef.
Std. Err.
s Constant
Age
NbChildren
EducSup
Trust
FarmSize
LandOwned
ExtraInc
DeffPayment
Livestock
IdleLand
IndivOwner
NoSuccessor
North
WheatRisk
0.280***
(0.013)
0.232**
0.001
20.000
0.041
20.116***
0.006
20.019
0.058
0.015
(0.097)
(0.002)
(0.012)
(0.043)
(0.042)
(0.013)
(0.085)
(0.072)
(0.034)
l Constant
Age
NbChildren
EducSup
Trust
FarmSize
LandOwned
ExtraInc
DeffPayment
Livestock
2.275***
(0.241)
6.620***
20.061*
20.060
22.073***
0.211
20.017
0.179
22.199*
0.641
(1.918)
(0.033)
(0.196)
(0.544)
(0.473)
(0.209)
(1.099)
(1.121)
(0.487)
Coef.
Std. Err.
0.133
(0.169)
0.002
20.382
0.012
0.039
20.022
0.043
(0.059)
(1.992)
(0.043)
(0.034)
(0.029)
(0.033)
3.956***
(1.494)
0.210
(0.796)
Coef.
Std. Err.
0.014
0.003
20.008
0.056
20.085**
0.002
20.044
0.069
20.003
0.021
0.103
0.033
0.024
20.051
0.026
(0.211)
(0.003)
(0.031)
(0.062)
(0.042)
(0.021)
(0.111)
(0.084)
(0.026)
(0.044)
(0.452)
(0.041)
(0.063)
(0.037)
(0.039)
10.708***
20.085**
0.385
22.719**
20.131
0.116
1.131
23.112***
0.707
21.003
(3.728)
(0.041)
(0.334)
(1.268)
(0.721)
(0.419)
(1.479)
(1.117)
(0.732)
(0.645)
G. Bocquého et al.
Covariate
Model 4
Page 26 of 38
Table 6. Maximum likelihood estimates of preferences using the CPT model
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IdleLand
IndivOwner
NoSuccessor
North
WheatRisk
0.655***
3,531/107
Specific tests on estimated coefficients (p-values)
s: Constant ¼ 1
l: Constant ¼ 1
g: Constant ¼ 1
0.000
0.000
0.000
0.286
0.010
0.013
0.262
22.202***
20.003
20.516
20.356
20.068
0.002
3,399/103
(0.564)
(0.012)
(0.059)
(0.186)
(5.237)
(0.052)
(0.390)
(0.321)
(0.152)
0.399
(0.846)
0.169
21.871
0.277*
0.039
20.173
0.029
(0.232)
(7.776)
(0.154)
(0.216)
(0.198)
(0.200)
0.507
3,498/106
Standard errors allow for our survey data design, including clustering effects.
*p , 0.1, **p , 0.05, ***p , 0.01.
21.116*
20.664
21.168
1.062
20.937
20.329
0.028
20.036
0.372
29.153***
20.060
20.868
20.284
20.136
0.297
22.924
20.044
0.161
20.259
20.009
0.000
3,366/102
(12.692)
(0.607)
(1.332)
(0.869)
(0.653)
(1.897)
(0.027)
(0.062)
(0.336)
(6.638)
(0.121)
(0.810)
(0.223)
(0.149)
(0.267)
(4.745)
(0.434)
(0.207)
(0.525)
(0.185)
Page 27 of 38
Model p-value
Nb. of obs. /clusters
(0.077)
(24.960)
(0.543)
(0.701)
(0.610)
(0.384)
Expected utility or prospect theory maximisers
g Constant
Age
NbChildren
EducSup
Trust
FarmSize
LandOwned
ExtraInc
DeffPayment
Livestock
IdleLand
IndivOwner
NoSuccessor
North
WheatRisk
21.662
20.544
0.006
1.183*
20.618
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Page 28 of 38
G. Bocquého et al.
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The last two columns of Table 6 give additional information on the relationship between risk behaviour under CPT and individual characteristics. First,
we observe that trusting farmers exhibit a utility function which is significantly more concave (in the gain domain) than that of non-trusting farmers,
meaning that trust tends to increase risk aversion (in the gain domain). At
first sight, this seems to contradict previous results under the EU–EP specification. However, at the same time, Trust strongly shifts the g parameter
towards 1: trusting farmers are more able to discriminate between probabilities, and thus are less prone to probability distortion, than non-trusting
farmers. One explanation may be that trusting farmers rely more on the objective information they are given. This link may result in a negative relationship
between farmers’ overall risk aversion (for gains) and trust. As regards loss
aversion, low values are explained by the effect of Age, EducSup and ExtraInc
while high values are explained by the effect of IdleLand. As expected, the
older and the more educated the farmer, and the more stable the household
income, the lower the loss aversion. Nguyen and Leung (2009) reported a
similar effect of education on loss aversion in a Vietnamese context.
There do not appear to be major differences in risk behaviour in relation to
liquidity constraints, which are represented by farmers’ use of deferred payments (DeffPayment). This result holds whatever the decision model. It conflicts with some empirical and theoretical studies that demonstrate the positive
impact of liquidity constraints on risk aversion due to a shortening of decisionmakers’ time horizon and a reduction of their ability to smooth consumption
over time (Gollier, 2001; Guiso and Paiella, 2008).
Moreover, we cannot find any significant effect of farm risk on risk preferences, background risk being proxied by the risk farmers face on wheat production (Wheat Risk). This result contrasts with the theoretical predictions of
Gollier and Pratt (1996) and Quiggin (2003) about the influence of background risk on decision-making. However, even when inducing an explicit
background risk in a laboratory setting, Lusk and Coble (2008) found that
the effect of background risk on risk preferences was not particularly large.
The authors presented three possible explanations: the existence of some uncontrolled background risk, the prevalence of non-EU behaviour among subjects and the tendency to assess independent risks in isolation rather than
jointly. These three explanations may apply in our case. First, uncontrolled
background risk can arise from other farm activities than wheat production,
or even extra-agricultural activities. In addition, although we were cautious
about accounting for wheat risks that were unlikely to be covered in the
short term, some of them may still be lower in reality due to uncontrolled
coverage mechanisms. In other words, farmers may have considered residual
wheat risks instead of full wheat risks when making the lottery choices.
Second, as shown by Quiggin (2003), independent risks are complementary
under rank-dependent preferences, that is, aversion to foreground risk is
reduced by the presence of an independent background risk. Gollier and
Pratt (1996) proved the opposite for EU preferences. Thus, if preference functionals are actually mixed among subjects and situations (Harrison and
Expected utility or prospect theory maximisers
Page 29 of 38
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Fig. 2. Distribution of the risk parameter values predicted by the CPT model under heterogeneous preferences (model 4).
Page 30 of 38
G. Bocquého et al.
Rutström, 2009), our analysis based on single preference models does not
allow the two opposing phenomena to be disentangled. Third, it seems reasonable to think that farmers easily disregard farm risk when assessing the risk on
abstract lotteries. Further research could assess to what extent framing affects
the effect of background risk on preferences.
6.3. Robustness checks
6.3.1. Exchange rates
6.3.2. Estimation strategy
One underlying assumption of the maximum likelihood estimation is the independence of observations. This assumption may not hold in our experiment
since the choices made by a single farmer in each of the three series are not independent of one another. A within-subject clustering would not fully correct
for it because each series is an ordered list. We thus adopt another strategy
which consists in restricting the observed responses in each ordered list to the
preferred lottery and the lottery being immediately dominated. For instance,
if a subject switches at line 6 in task 1, then we simply keep the two observations
indicating that in line 5 lottery A is preferred to lottery B, and in line 6 lottery B
is preferred to lottery A. As a result, the maximum number of observations per
individual is restricted to 6 (two observations per series).
In Table 8, Column 2, we report the CPT parameters estimated by
maximum likelihood on this restricted set of observations. It can be seen
27 In our experiment the maximal loss is 800 euros, in the ambiguity task not presented in this
paper. Since the initial endowment is 15 euros, the upper bound of the exchange rate is around
2 per cent (15/800 ¼ 1.9 per cent).
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To estimate the preference parameters, we have assumed that each farmer had
assessed the lotteries with respect to the payoffs presented in the game.
However, farmers were only paid a fraction of the lottery gains, based on
an exchange rate (2 per cent) which was disclosed at the end of the experiment. Since farmers were told that their initial endowment (15 euros)
ensured positive final earnings, they may have inferred that the upper bound
of the exchange rate was around 2 per cent.27 To check whether our assumption was problematic, we have re-estimated model 1 for the three decision
frameworks, assuming that farmers were using a 1 and a 2 per cent exchange
rate.
The estimates for the risk parameters are found to be very similar to those
obtained with the original lottery payoffs (Table 7). This is not surprising
since multiplying all outcomes by the same positive constant does not
modify the distribution of the latent index Di = UiA − UiB because the three
specifications rely on a power (or EP) form (Wakker, 2008). As an additional
robustness check, we have also re-estimated the models when the initial endowment is integrated into the utility function. Estimates of r, a, b, s, l
and g are not significantly affected.
Expected utility or prospect theory maximisers
Page 31 of 38
Table 7. Maximum likelihood estimates of preferences assuming different exchange rates
Exchange rate
1%
2%
0.212***
0.212***
0.212***
0.288***
0.119***
0.289***
0.119***
0.289***
0.119***
0.280***
2.275***
0.655***
3,531/107
0.281***
2.275***
0.655***
3,531/107
0.281***
2.275***
0.655***
3,531/107
Standard errors allow for our survey data design, including clustering effects.
*p , 0.1, **p , 0.05, ***p , 0.01.
Table 8. Estimates of CPT preferences using different estimation strategies
Structural models
Full set of
observations
s
0.280*** (0.013)
l
2.275*** (0.241)
g
0.655*** (0.077)
Nb. of obs./clusters 3,531/107
Restricted set
of observations
Midpoint
technique
0.325*** (0.018)
2.110*** (0.191)
0.679*** (0.006)
3,531/107
0.512*** (0.053)
3.756*** (0.415)
0.647*** (0.042)
3,531/107
Standard errors are in parentheses. They allow for our survey data design, including clustering effects in the case of
structural models.
*p , 0.1, **p , 0.05, ***p , 0.01.
that the parameters estimated on the full set of observations (Column 1) are in
fact quite similar. It indicates that the dependence of observations from a
given subject is not likely to be problematic in our case. As a last check,
we also report in Table 8, Column 3, the parameter values obtained with
the midpoint technique used by Tanaka, Camerer and Nguyen (2010).
These values were already presented in Section 6.1. Once again, estimated
values are similar except for loss aversion which appears to be greater with
the midpoint technique.
6.3.3. Reference point
An implicit assumption of the two-piece utility specification in the CPT model
(and in the EU model with reflected utility) is that a farmers’ reference point is
unique and equals zero. However, it was shown that reference points might be
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EU– power
r
EU– EP
a
b
CPT
s
l
g
Number of observations/clusters
None
Page 32 of 38
G. Bocquého et al.
strictly positive or negative, especially when they depend upon individual
expectations (Kó´szegi and Rabin, 2006). In our experiment, as mentioned
earlier, the initial endowment is probably the farmers’ reference point as it
corresponds to a status quo situation. As a robustness check, we have estimated several CPT models with a reference point varying from 2150 to
100 euros with 10-euro increments.
We report the sensitivity of the log-pseudolikelihood and the three risk
parameters to the reference point in Figure 3. The log-pseudolikelihood
reaches a maximum (27027.34) for a reference point of 260 euros, but the
curve is very flat around this point. In fact, the log-pseudolikelihood curve
exhibits a plateau for reference points ranging from 280 to 10 euros, thus including zero. In addition, over this range, parameter values are quite similar,
except for l values which increase quickly as soon as the reference point is
250 euros or less. As a consequence, our estimations are robust to errors in
the assumed reference point.
7. Conclusion
Alternatives to EU theory such as PT have the potential to give new insights
into farmers’ behaviour in a risky environment. We first review some empirical evidence and implications of farmers being PT maximisers in different
fields such as crop insurance, contract design, market finance and innovation
adoption. We then estimate structural preference models in the EU and CPT
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Fig. 3. Sensitivity of the log-pseudolikelihood and CPT preferences to the assumed reference point.
Expected utility or prospect theory maximisers
Page 33 of 38
Supplementary data
Supplementary data are available at ERAE online.
Acknowledgements
The authors thank Stéphanie Mulet-Marquis, Stéfanie Nave and Flora Pennec for having conducted most of the field survey and experiment. For helpful comments and suggestions, the
authors are grateful to Olivier L’Haridon as well as the conference participants at WBEE, Florence, AFSEE, Schoelcher and EAAE, Zurich. We are grateful to Dr Suzette Tanis-Plant for fruitful discussions in English. We would also like to thank three anonymous referees for their
insightful comments. This work has been completed within the Futurol research and development project. Some financial support was provided by the French state innovation agency
OSEO and the ADEPRINA association.
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