14 Chapters

## 3: Probabilities for Decision Analysis

J.B. Hardaker; R.B.M Huirne; J.R. Anderson CAB International PDF

3

Probabilities for Decision

Analysis

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.

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## 8: The State-contingent Approach to Decision Analysis

J.B. Hardaker; R.B.M Huirne; J.R. Anderson CAB International PDF

The State-contingent

Approach to Decision Analysis

8

Introduction

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:

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## 12: Strategies Decision Makers Can Use to Manage Risk

J.B. Hardaker; R.B.M Huirne; J.R. Anderson CAB International PDF

Strategies Decision Makers

Can Use to Manage Risk

12

Introduction

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.

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## 6: Integrating Beliefs and Preferences for Decision Analysis

J.B. Hardaker; R.B.M Huirne; J.R. Anderson CAB International PDF

6

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

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## 13: Risk Considerations in AgriculturalPolicy Making

J.B. Hardaker; R.B.M Huirne; J.R. Anderson CAB International PDF

Risk Considerations in

­Agricultural Policy Making

13

Introduction

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.

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