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Coping with Risk in Agriculture: Applied Decision Analysis, 3rd Edition

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Risk and uncertainty are inescapable factors in agriculture which require careful management. Farmers face production risks from the weather, crop and livestock performance, and pests and diseases, as well as institutional, personal and business risks. This revised third edition of the popular textbook includes updated chapters on theory and methods and contains a new chapter discussing the state-contingent approach to the analysis of production and the use of copulas to better model stochastic dependency. Aiming to introduce agricultural decision making, probability and risk preference, this book is an indispensable guide for students and researchers of agriculture and agribusiness management.

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14 Chapters

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1: Introduction to Risk in Agriculture



Introduction to Risk in


Examples of Risky Decisions in Agriculture, and their Implications

The development of agriculture in early times was partly a response to the riskiness of relying on hunting and gathering for food. Since then, farmers and others have tried to find ways to make farming itself less risky by achieving better control over the production processes. As in other areas of human concern, risk remains a seemingly inevitable feature of agriculture, as the examples below illustrate.

Example of institutional risk

A dairy farmer finds that the profitability of his herd is constrained by his milk quota. He now has the opportunity to buy additional quota, using a bank loan to finance the purchase. The farmer, however, has serious doubts about the profitability of this investment because he believes that milk quotas will be removed at some time in the future. Cancellation of quota would make the purchased quota valueless from that point in time. He also thinks it is likely that milk prices will drop significantly when the quotas go.


2: Decision Analysis: Outline and Basic Assumptions


Decision Analysis: Outline and Basic Assumptions


Basic Concepts

As explained in Chapter 1, decision analysis is the name given to the family of methods used to r­ ationalize and assist choice in an uncertain world. In this chapter we focus on the concepts and methods of decision analysis. Figure 2.1 provides an outline of the typical steps in decision analysis of a risky choice. These stages are discussed in turn below.

Establish the context

This first step is concerned with setting the scene and identifying the parameters within which risky choice is to be analysed. Particularly in a large organization, it may be important to take note of the level in the organizational structure at which the choice will be made. For example, different sorts of decisions may be made at different levels, perhaps with important strategic issues decided upon at board level, with key tactical decisions made by senior management and with a range of more routine choices made at the operational level. Identifying the level may lead to identifying the decision maker (DM) or makers – a critical need for proper conduct of the steps to follow. Similarly, it will be important to identify the stakeholders – those who will be affected by the outcomes of the decision. For a family farm, the principal stakeholders are farm family members who typically will be concerned with their standard of living and the continued survival of the family business.


3: Probabilities for Decision Analysis



Probabilities for Decision


Probabilities to Measure Beliefs

In the previous chapter we explained the components of a decision problem. One of the major components is the existence of uncertain events, also called states of nature, over which the DM has effectively no control. Probability distributions are usually used in decision analysis to specify those uncertainties.

The SEU model introduced in Chapter 2 implies the use of subjective probabilities to measure uncertainty. Because the notion of subjective probabilities may be unfamiliar to some readers, we first explain it. Then we provide some discussion of the thorny problem of bias in subjective assessments of probability, leading to a discussion of methods of eliciting and describing probability distributions. In the final section we explain Monte Carlo sampling from probability distributions, which is a frequently used method in decision analysis.

Different notions of probability

There are different ways of thinking about probability. Most people have been brought up in the frequentist school of thought. According to this view, a probability is defined as a relative frequency ratio based on a large number of cases – strictly, an infinite number. Thus, the probability of a flood in a particular area may be found from a sufficiently long historical trace of river heights. The data would be used to calculate the frequency of occurrence of a river height sufficient to overflow the banks.


4: More about Probabilities for Decision Analysis



More about Probabilities for Decision Analysis

Having introduced what might be called the basics of the principles and practice of using probability to measure beliefs for decision analysis, in this chapter we address some issues relating to the application of those principles, covering the derivation of probability distributions in situations where there are abundant, sparse or no data available for the task. We then introduce the Bayesian approach to updating prior probability judgements in light of new information. Finally, we address the thorny issue of how to account for situations where a number of uncertain quantities impinge on the outcomes of some risky choice and these quantities are correlated in some way.

The Relevance of Data in Probability Assessment

Making the best use of abundant data

Although we have argued in the previous chapter that all probabilities for decision analysis are necessarily subjective, for those occasions when there are abundant, reliable and relevant data that are pertinent to some uncertain quantity of interest, any sensible person will want to base probability judgements on such information. Probabilities in such cases may be viewed as ‘public’ because many people can be expected to share almost the same probabilities – at least once the information has been brought to their notice. Note, however, that everyone may not agree on the relevance of a given set of data. For example, farmers will often not share the confidence of a research agronomist that data from trials on the research station can be replicated on their own farms – scepticism that, unfortunately, is too often well founded.


5: Attitudes to Risky Consequences



Attitudes to Risky



In Chapter 2 we have shown how a simple risky decision problem, such as that faced by the dairy farmer thinking about insuring against foot-and-mouth disease (FMD), can be solved. The key step was to transform the risky consequences of an event fork into the DM’s certainty equivalents (CEs). However, the assessment of CEs can become very tedious if there are many such risky event forks. Moreover, the introspective capacity needed to decide on CEs rises with the number of branches emerging from the fork.

As explained in Chapter 2, the central notion in decision analysis is to break this assessment of consequences into separate assessments of beliefs about the uncertainty to be faced, and of relative preferences for consequences. In Chapters 3 and 4 we dealt with the former of these assessments. Now it is time to look in more detail at how preferences for consequences can be assessed and how those preferences can be encoded.

In Chapter 2 we laid the theoretical foundation for this chapter on utility theory via the presentation of the axioms of the subjective expected utility hypothesis. Readers might find it useful to review the


6: Integrating Beliefs and Preferences for Decision Analysis



Integrating Beliefs and

Preferences for Decision Analysis

Decision Trees Revisited

In Chapter 2 we introduced the notion of a decision tree to represent a risky decision. Recall that decision problems are shown with two different kinds of forks, one kind representing decisions and the other representing sources of uncertainty. We represented decision forks, where a choice must be made, by a small square at the node, and we represented event forks, the branches of which represent alternative events or states, by a small circle at the node. We showed how a decision tree can be resolved working from right to left, replacing event forks by their certainty equivalents (CEs) and selecting the optimal branch at each decision fork.

We now return to the simple example relating to insurance against losses from foot-and-mouth disease (FMD) to show how probabilities and utilities are integrated into the analysis. For convenience, the original decision tree developed in Chapter 2 (Fig. 2.2) is repeated here as Fig. 6.1. Note that the uncertainty about the future incidence of the disease is represented in the tree by the event fork with branches for ‘No outbreak’ and ‘Outbreak’. To measure the uncertainty here we need to ask the farmer for subjective probabilities for these two events. Suppose that, as explained in Chapter 3, the farmer assigns a probability of 0.94 to there being no outbreak and a complementary probability of 0.06 to an outbreak occurring. Similarly, the farmer is uncertain about what policy for control of the disease might be implemented if an outbreak occurs, as shown by the event forks further to the right in Fig. 6.1. Again, the farmer is able to assign some subjective values to these conditional probabilities of 0.5 and 0.5


7: Decision Analysis with Preferences Unknown



Decision Analysis with

Preferences Unknown

Efficiency Criteria

A difficulty often encountered in applying the SEU model lies in the elicitation of the DM’s utility function. The problem may be lack of access to the relevant person, inadequate introspective capacity on that person’s part, or the fact that more than one person may be involved. Similarly, in agriculture, it may be necessary to develop recommendations for a particular target group of farmers numbering perhaps some hundreds or even thousands. Efficiency criteria have been devised to allow some ranking of risky alternatives when the specific utility function (or functions) is not available.

Efficiency analysis depends on making some assumptions about preferences or, equivalently, about the nature of the utility function. Often bounds are placed on the level of risk aversion. Then, for all DMs to whom the assumptions apply, the various actions can be divided into an efficient set and an inefficient set. The inefficient set contains those actions that are dominated by (preferred less than) actions in the efficient set. The efficient set contains those actions that are not dominated. The optimal action for any individual will lie among the alternatives in the efficient set, provided that:


8: The State-contingent Approach to Decision Analysis


The State-contingent

Approach to Decision Analysis



Until relatively recently the analysis of production under uncertainty in agriculture had been d

­ ominated by the use of stochastic production functions and related methods. First proposed by Sandmo (1971) and refined by Just and Pope (1978) (JP), a stochastic production function can be specified to accommodate both increasing and decreasing output variance in inputs. The single-output JP production function has the general form:

y = g(x) + u = g(x) + h(x)0.5e (8.1)

where g(.) is the mean function (or deterministic component of production), h(.) is the variance function that captures the relationship between input use and output variation, and e is an index of exogenous production shocks with zero mean and variance sε2. This formulation allows inputs x to influence mean output E(y) and variance of output V(y) independently, since:

E(y) = g (x) and V(y) = h(x) sε2 (8.2)

Applying prices to inputs and outputs converts the above two functions into functions of expected net revenue and variance of net revenue, both in terms of input levels x. (For simplicity, we ignore the complication that uncertainty about output prices often also needs to be accommodated.) Then it is possible to find the level of inputs to maximize expected utility expressed via the approximate indirect utility function:


9: Risk and Mathematical Programming Models



Risk and Mathematical

Programming Models

A Brief Introduction to Mathematical Programming

Mathematical programming (MP) is the term used to describe a family of optimization methods that may be familiar to many readers. Therefore, only a brief introduction to these useful methods is provided here and readers needing to learn more by way of background are referred to one of the many introductory texts on the topic, such as Williams (2013).

Almost all optimization problems, including planning problems accounting for risk and uncertainty, can be expressed as the optimization of some objective function subject to a set of constraints. MP has been developed just for such problems. Unfortunately, however, many real-world planning problems are complex, especially when accounting for risk and uncertainty. The result is that, while most risk-planning problems can be formulated as MP models, at least conceptually, not all can be reliably solved using available algorithms. Sometimes it may not be possible to be sure that a generated solution is the true optimum. The models for some problems may grow so large that the computing task may be beyond the capacity of the computer or software being used.


10: Decision Analysis with Multiple Objectives



Decision Analysis with

Multiple Objectives

Introduction with Some Examples

In earlier chapters we have defined utility functions that indirectly embody an important trade-off:

­expected monetary return versus variance. Such a utility function represents a preference model for choice that captures the DM’s attitude to expected return and variance. Obtaining high returns and reducing exposure to variability are usually two conflicting objectives in decision making. We have shown in

Chapters 5 and 7 how to model the preference trade-off between these objectives. In many situations, however, the action chosen depends on how each possible choice meets several objectives, as the following examples show.

A dairy farmer has become concerned about some long-term negative impacts of the current system of milk production on the farm and is therefore considering changing this system. The current production system is a high-input/high-output system. Large amounts of resources are used per cow to produce a high milk yield. In the short term, this system gives the farmer a good income and a high status in the local community. However, because of its intensive nature, it may cause some environmental problems in the future, as well as some problems with cow health and welfare. In thinking about changing the production system, the dairy farmer might consider diverse possible objectives such as the following: (i) maximizing current farm income; (ii) maximizing farm income in the future; (iii) minimizing environmental damage; (iv) maximizing animal health and welfare;


11: Risky Decision Makingand Time



Risky Decision Making and Time

The Time Factor in Decision Analysis

In most of the earlier chapters, decision analysis has been set in the framework of a short time horizon.

In reality, however, farm and agribusiness managers make decisions about production, marketing and finance not just for the present but also for the longer run. For these long-term decisions, accounting for the factor ‘time’ is essential. Some ways of dealing with time in risky decision making are addressed in this chapter.

One important effect of accounting for time is that uncertainty generally increases the further into the future we look. Consequently, the need to account for risk is often greater in decision making for the long run. Unfortunately, accounting for time and for the greater uncertainty that is thereby entailed adds greatly to the complexity of analysis. As we shall explain, there are difficulties in extending the methods of decision analysis to long-run planning. Nevertheless, we believe that ways of considering such decisions that embody at least some key elements of the principles and methods outlined in earlier chapters are likely to lead to better decisions than those emerging from analyses that ignore risk or that seek to accommodate it only in some over-simplified way.


12: Strategies Decision Makers Can Use to Manage Risk


Strategies Decision Makers

Can Use to Manage Risk



We have emphasized that risk is everywhere and is substantially unavoidable. It follows that

­management of risk is not something different from management of other aspects of a farm, since every farm management decision has risk implications. There are, however, some types of farm management decisions that bear strongly on the riskiness of farming, and some of these are reviewed in this chapter. The treatment is general because, as we have shown, every decision should be considered in the context of the particular circumstances, notably the beliefs and preferences of the DM. Therefore, specific prescriptions about strategies to manage risk are seldom possible. Instead, we canvass some of the main areas where DMs can act to manage risk and indicate how choices in some of these areas might be analysed.

As outlined in Chapter 1, there are two reasons why risk in agriculture matters: risk aversion and downside risk. Moreover, we have argued that, at least in capitalist agriculture, the latter will often be at least as important as the former since extreme risk aversion by relatively wealthy DMs is irrational and unlikely to exist, at least for important risky choices. In the light of this view, it might seem natural to draw a distinction between management strategies that deal with risk aversion and management strategies that deal with downside risk. That, however, does not work well because effective strategies to manage downside risk will also have benefits in terms of increased utility for risk-averse DMs.


13: Risk Considerations in AgriculturalPolicy Making


Risk Considerations in

­Agricultural Policy Making



Our illustrations in earlier chapters demonstrate that the type and severity of risks confronting f­armers vary greatly with the farming system and with the climatic, policy and institutional setting. This is the case in both more developed countries (MDCs) and less developed countries (LDCs). Nevertheless, agricultural risks are prevalent throughout the world and, arguably, have increased over time, as is suggested by the food, fuel and finance crises that have beset the world since 2007. Moreover, climate change appears to be creating more risk for agriculture in many locations. These prevalent and prospective agricultural risks have naturally attracted the attention of many governments – groups of DMs who have so far received little focus in our discussion. In this chapter we address analysis of risk management from this rather different point of view.

In our treatment we deal first with government interventions that have risk implications. Governments should realize that they are an important source of risk, as explained in earlier chapters, in particular when interventions negatively affect the asset base of farms. Potentially successful interventions are not those that merely reduce variance or volatility, but those that increase risk efficiency and resilience (to shocks, such as occasions of severely reduced access to food in LDCs, or extreme weather conditions). In many cases, this means increasing the expected value rather than decreasing the variance. In regard to specific instruments whereby farmers can share risk with others, we argue below that only in the case of market failure is there any reason for government involvement. Market failure is most severe in the case of so-called ‘in-between risks’ or catastrophic risks. As explained later, in-between risks are risks that, by their nature, cannot be insured or hedged. Catastrophic risks are risks with low probabilities of occurrence but severe consequences. In this chapter we address issues in developing policies to manage these difficult risks as well as the management of some emerging risks, such as extreme weather, food-price spikes, food safety, epidemic pests and animal diseases, and environmental risks.


Appendix: Selected Software for Decision Analysis



Selected Software for

Decision Analysis

In developing the examples in this book, we made use of the following software:

@Risk and RiskOptimizer from Palisade Corporation. Available at:

(­ accessed 2 June 2014). data, later replaced with TreeAge Pro from TreeAge Software, Inc. Available at: http://www.treeage. com (accessed 2 June 2014).

GAMS from GAMS Development Corporation. Available at: (accessed

2 June 2014).

Logical Decisions from Logical Decisions. Available at: (accessed

2 June 2014).

Microsoft Excel, a component of Microsoft Office from Microsoft Corporation. Available at: http:// (accessed 2 June 2014).

ModelRisk from Vose Software. Available at: (accessed 2 June 2014).

Solver for Excel from FrontlineSolvers. Available at: (accessed 2 June 2014).

WhatsBest! from Lindo Systems Inc. Available at: (accessed 2 June 2014).



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