Decision Aiding
An MCDM analysis of agricultural risk aversion

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Abstract

In modelling farm systems it is widely accepted that risk plays a central role. Furthermore, farmers’ risk aversion determines their decisions in both the short and the long run. This paper presents a methodology based on multiple criteria mathematical programming to obtain relative and absolute risk aversion coefficients. We rely on multiattribute utility theory to elicit a separable additive multiattribute utility function and estimate the risk aversion coefficients, and apply this methodology to an irrigated area of Northern Spain. The results show a wide variety of attitudes to risk among farmers, who usually exhibit decreasing absolute risk aversion and constant relative risk aversion.

Introduction

Risk is present in all agricultural management decisions, as a result of price, yield and resource uncertainty. If farmers were risk-neutral, it would be irrelevant to consider risk in their decision-making process, since their responses could be represented by the maximization of expected profit. However, farmers’ generalized risk aversion results in production decisions that conflict with those that would be regarded as optimal from a social point of view. This fact has caused agricultural economists to pay a great deal of attention to the stabilization features of agricultural policies aimed at reducing farming risk.

The degree of attention being paid to the behaviour of agricultural producers operating under conditions of risk has recently been increased by the progressive liberalization of world agricultural markets (Hope and Lingard, 1992; Berg, 1997; Oglethorpe, 1997), and the ever-increasing importance of environmental considerations (Lambert, 1990; Babcock, 1992; Parks, 1995; Babcock and Hennessy, 1996; Bontems and Thomas, 2000).

Expected utility theory (EUT) was forgotten until Von Neuman and Morgesten (1944) defined the axioms of cardinal utility theory, explaining the reasons behind individual choices involving risk. EUT has been the basis for much of the decision-making theory, and assumes that:

  • The decision-maker’s preferences comply with the axioms of ordering, continuity and independence. These axioms have been the subject of severe criticism in many applied studies (a review can be found in Starmer, 2000). However, EUT has the support of most agricultural economists (Schoemaker, 1982; Robison and Hanson, 1997).

  • There is a utility function U that assigns a numerical value to each alternative. As most economic decisions are expressed in monetary terms, the utility function may have wealth as argument (U(W)), measuring the satisfaction obtained from a given amount of money. However, the satisfaction from either a gain or a loss (U(X)) may also be used (Hardaker et al., 1997, p. 94–95). In doing so, EUT allows the ranking of alternatives within the context of risk.


The seminal works of Pratt (1964) and Arrow (1965) paid attention to one of the key elements of decision theory, i.e., the measure of risk aversion of the economic agents. These authors proposed two indicators that overcame the limitations in the use of a cardinal utility function in order to compare differences in risk attitudes. The first is the absolute risk aversion coefficient (ra). Mathematically, this coefficient is calculated as follows:1ra(W)=−U(W)U(W)andra(W)=ra(X)=−U(X)U(X)This coefficient can be interpreted as the percentage change in marginal utility caused by each monetary unit of gain or loss (Raskin and Cochran, 1986). Thus, the coefficient ra takes either positive or negative values for risk-loving or risk-averse economic agents respectively.

When the coefficient decreases as monetary value increases we have decreasing absolute risk aversion (DARA). Alternatively, if the coefficient increases under the same set of circumstances we have increasing absolute risk aversion (IARA). Finally, if the coefficient does not change across the monetary level, the decision-maker exhibits constant absolute risk aversion (CARA), which implies that the level of the argument of the utility function does not affect his or her decisions under uncertainty.

Since ra is not a non-dimensional measure of risk aversion, its value is dependent on the currency in which the monetary units are expressed. To overcome the impossibility of comparing risk aversion among different economic agents Pratt (1964) and Arrow (1965) devised a non-dimensional measure; the relative risk aversion coefficient (rr):2rr(W)=−WU(W)U(W)=Wra(W)=Wra(X)This second coefficient measures the percentage change in marginal utility in terms of the percentage change in the monetary variable; hence, rr represent the elasticity of the marginal utility function, which ranges from 0.5 (slightly risk-averse) to 4 (extremely risk-averse).3 As with the absolute risk aversion coefficient, we can find decreasing, constant or increasing relative risk-aversion behaviour (DRRA, CRRA and IRRA, respectively).

All theoretical aspects of EUT related to agricultural economics have been discussed in classic works such as those of Dillon (1971), Anderson et al. (1977), Barry (1984), Robison and Barry (1987) and Hardaker et al. (1997).

According to Young (1979), Lins et al. (1981) and Robison et al. (1984) there are three basic methods of measuring the attitudes to risk of agricultural producers:

  • Direct estimation of the utility function: This method involves direct interaction with the decision-maker, who expresses his or her preferences among various alternatives. Regression techniques then enable us to obtain their utility function. Examples can be found in Officer and Halter (1968), Francisco and Anderson (1972), Lin et al. (1974), Dillon and Scandizzo (1978), Halter and Mason (1978), Bond and Wonder (1980), Hamal and Anderson (1982), Sri-Ramaratmam et al. (1987) and Feinerman and Finkelshtain (1996).

  • Experimental methods: This can be regarded as a variant of the previous method, in which real bets are used instead of hypothetical gains and losses. See for example Binswanger, 1980, Binswanger, 1981 and Binswanger and Sillers (1983).

  • Observed economic behaviour: This method was developed in order to represent risk behaviour, tuning the models to fit actual data by adjusting the risk aversion coefficients, usually along with other coefficients. Furthermore, these models rely on either production theory under uncertainty (econometric models) or cropping pattern selection (mathematical programming). Wolgin (1975), Moscardi and Janvry (1977), Antle, 1987, Antle, 1989, Myers (1989), Chavas and Holt, 1990, Chavas and Holt, 1996, Pope and Just (1991), Saha et al. (1994), Saha (1997) and Bar-Shira et al. (1997) present good examples of the first category, while for the latter we have Wiens (1976) and Brink and McCarl (1978).


All the above approaches have their drawbacks (see Young, 1979; Binswanger, 1980 and Lins et al., 1981), which are most important in the direct estimation method due to interviewer bias, the selection of probabilities,4 reluctance to play lottery games, lack of reality in the scenarios in place and/or insufficient experience on the part of the decision-maker in the evaluation of hypothetical situations.

Even though these limitations can be reduced, to a certain extent, by adopting the experimental method, this has often proved difficult to implement in practice, since the financial cost involved in a real situation with many producers is too high.

With respect to observed economic behaviour there are also some difficulties, such as the influence of other non-monetary objectives in the decision-making process (e.g. leisure, management complexity, etc.) and constraints (financial limitations, lack of technical information, etc.) that ‘contaminate’ attitudes to risk. If this method is adopted, therefore, it would not be suitable for explaining any behaviour that differs from profit maximization purely in terms of risk aversion.

In considering the econometric approach, the need for long time series and/or cross-sectional data on input use, production level and other relevant economic variables limits this alternative to specific groups of farmers for whom first-class data are available, which is a rather uncommon situation in agriculture.

In this paper we present a methodology based on mathematical programming that enables us to discriminate between the effect of the risk attitude of the producer on his or her decision-making and other criteria. This methodology, which resorts to the multiple criteria paradigm to estimate risk aversion coefficients, requires a minimum amount of data, making this a pragmatic approach to any real agricultural system in spite of the limited availability of data.

The paper is organized as follows: Section 2 explains the methodology used to calculate farmers’ risk aversion coefficients. Section 3 presents the area of study in which the methodology was employed, while the results are summarized in Section 4. We conclude the paper by drawing some important conclusions about the pragmatic advantages of this approach.

Section snippets

Decision theory and the analysis of risk attitudes

One of the basic principles of classical economic theory is that entrepreneurs behave as profit maximizers. Following this principle, the decision-making of agricultural producers could be adequately modelled by the maximization of single-objective models. Real-life observations refute this simplification.

Expected utility theory was a first step in the direction of broadening the profit maximizer assumption and including higher moments of the expected profit. However, EUT has been criticised

Case study

The case study is a community of irrigators located in Northern Spain, Los Canales del Bajo Carrión, in the county of Palencia. This community has 6554 irrigated hectares and 889 farmers. It has a typical continental climate, 780 m above sea level, with long, cold winters and hot, dry summers. Rain falls mostly in spring and autumn. During winter the main crops are wheat and barley, in the summer mainly maize, sugar beet and sunflower. During the summer it is necessary to irrigate to bring the

Estimation of the multiattribute utility functions

Utilising the methodology explained in Section 2, we were able to obtain the weighting (wi) that each farmer attached to the optimization of each objective.

The results show that the maximization of total gross margin is the most important objective with an average weighted importance of 56.4%, followed by the minimization of risk with an average weighting of 31.8%. The objectives of the maximization of leisure time and the minimization of working capital, with relative weights of 9.2% and 2.5%,

Conclusions

The principal conclusions to be drawn from this study can be summarized as follows.

Regarding the methodology:

  • Since farmers’ decision-making processes simultaneously involve several different objectives, it has been shown that the reduction of the problem to a utility function with a sole monetary attribute does not fully explain his/her behaviour. Our approach includes non-monetary objectives in a multicriteria decision-making technique in order to overcome this limitation.

  • The methodology

Acknowledgements

Thanks are due to Prof. Carlos Romero for his comments on an earlier draft of this paper. The authors are also particularly in debt to reviewer #2, whose pedagogical comments about the possible drawbacks of the methodology led to improvements in the paper. The research was co-financed by the European Union (research project WADI, EVK1-CT-200-0057), the Spanish Comisión Interministerial de Ciencia y Tecnologı́a (research project LEYA, REN2000-1079-C02-02) and the Regional Government of Castilla

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