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Article Excerpt
1. Introduction
In the expected utility (EU) model, the utility function u(x) describes the risk attitude of decision makers (Keeney and Raiffa 1976). The curvature of the utility function u(x) reflects whether decision makers are risk averse (a concave utility function) or risk seeking (a convex utility function). Local measures of the utility function curvature, such as the well-known Pratt-Arrow coefficient of risk aversion, indicate how strongly decision makers exhibit their risk attitude. A lot of research in decision making under risk has focused on relating local measures of risk aversion to choice behavior. Pennings and Smidts (2000), for example, found that the degree of risk aversion is important in explaining owner-managers' trading behavior (i.e., the choice of relatively safe fixed-price contracts versus risky spot market transactions). In this paper, however, we are interested in the global shape of the utility function u(x) and how that global shape relates to choice behavior. Global shape is defined here as the general shape of the utility function over the entire outcome domain: fully concave, fully convex, or S-shaped (convex/concave).
An S-shaped utility function has been proposed in prospect theory (Kahneman and Tversky 1979). In prospect theory, the shape of a decision maker's utility function is assumed to differ between the domain of gains and the domain of losses. The proposed convex/concave utility function predicts risk-seeking behavior in the domain of losses and risk-averse behavior in the domain of gains. Evidence for convex/concave utility functions across the total outcome domain has been found by Fishburn and Kochenberger (1979), Hershey and Schoemaker (1980), Budescu and Weiss (1987), and Kuhberger et al. (1999), among others.
In this paper, we conjecture that structural decision behavior is more strongly linked to the global shape of u(x) than to local measures of risk aversion. In particular, the occurrence of an S-shaped utility function may imply fundamentally different behavior because decision makers will code outcomes into gains and losses, as compared to decision makers with fully concave of fully convex utility functions, who do not appear to think in terms of gains and losses.
Our objective is twofold. First, we analyze the extent of heterogeneity in the global shape of the utility function of real-business decision makers. Second, we test whether the shape of the utility function is linked to differences in organizational behavior. Organizational behavior is operationalized here as the owner-manager's design of the production process. We will show that the global shape of the utility function is related to organizational behavior, whereas the local measure is not.
First, we empirically demonstrate the relationship between the global shape of the utility function and organizational behavior. Next, we discuss the causal direction of this relationship: Is organizational behavior driving the shape of the utility function or is it the other way around?
2. Decision Context
To test the relationship between the shape of the utility function and organizational behavior, a decision context is required that is not masked by situational variables and where the decision maker has a prominent influence on the organizational form of the firm. The decision context of Dutch hog farmers meets these requirements. Dutch hog farmers are owner-managers who determine how they organize their firm and who are all exposed to the same economic environment (i.e., the volatile cash market of slaughter hogs). In hog farming, two production sys tems are distinguished: the "open production system" (OPS) and the "closed production system" (CPS). In the OPS, both piglets and feeds ate bought; piglets ate raised to be slaughter hogs in three to four months (during that period the hogs ate fattened until their slaughter weight is about 90 kilograms) and sold in the cash market or through forward contracts. The CPS is similar to the OPS, except that the owner-manager breeds piglets instead of buying them.
A consequence of the chosen production system is that owner-managers who choose the OPS are more often and more explicitly confronted with input costs than are managers who choose the CPS. In particular, the expense of buying piglets (the costliest input in the production process) may make the input costs more salient to the OPS managers, and thus may affect their decision making and risk preferences. It may induce them to think more often or more easily in terms of gains and losses, with the costs of production as a reference point. We therefore may expect that OPS managers will be more inclined to think in terms of gains and losses, and thus will more often exhibit an S-shaped utility function. CPS managers, on the other hand, ate not naturally provided with a reference point and are thus less stimulated to think in gains and losses terms. We therefore may expect that CPS managers will more often exhibit a fully concave of fully convex utility function describing their risk preferences.
3. Method
3.1. Assessing the Utility Function
We assessed the utility function of 332 hog farmers by means of computer-guided interviews. The utility function was measured using the certainty equivalence method (Keeney and Raiffa 1976, Smidts 1997). The certainty equivalents were obtained through choice-based matching (Keeney and Raiffa 1976, Fischer et al. 1999). In designing the lottery task for the hog farmers, we took into account the research findings on the sources of bias in assessment procedures for utility functions (Hershey et al. 1982, Hershey and Schoemaker 1985, Tversky et al. 1988). The main sources of bias arise when the assessment does not match the subjects' real decision situation. An important decision for hog farmers to make on a regular basis concerns the selling strategy of their slaughter hogs. They can choose a fixed-price forward contract or sell the hogs in the (risky) spot market. The lottery task fits this decision context, and the price per kilogram live hog weight is the main attribute. Another important research design issue involves the dimensions of the lottery; that is, the probability and outcome levels to be used in eliciting risk preferences. The outcome levels range from 2.34 to 4.29 Dutch guilder (1.06 Euro to 1.95 Euro) per kilogram live weight, representing all price levels of slaughter hogs that have occurred in the last five years. We chose a probability of 0.5 in the lotteries, expressing this stochastic nature of commodity prices (prices can rise or fall with equal probability), because various researchers have shown the stochastic behavior of commodity prices (Schwartz 1997, Hilliard and Reis 1999).
The measurement procedure was computerized and took about 20 minutes. The respondents were given a choice between three alternatives: Alternative A was a 50/50 chance of receiving a relatively high price or a relatively low price; Alternative B was a fixed price; and Alternative C indicated indifference. The assessment of the certainty equivalent was an iterative process. If the respondent chose Alternative A (the 50/50 high/low price), the computer would generate a higher fixed price (Alternative B) than the previous one, thus making Alternative B more attractive. If the respondent chose the fixed price (Alternative B), the computer would generate a lower fixed price the next time, thus making Alternative A (the 50/50 high/low price) more attractive. The choice between A and B was repeated until the respondent chose C (indicating indifference), after which a new lottery would start.
Nine points were assessed, corresponding to utilities of 0.125, 0.250, 0.375, 0.500, 0.625, 0.750, and 0.875 (plus two consistency measurements on utilities 0.500 and 0.625). For details on a similar elicitation procedure, see Pennings and Smidts (2000). Furthermore, accounting data was available from the firms involved, including information about their production systems (OPS versus CPS).
3.2. Assessing the Shape of the Utility Function To assess the shape of the utility function we apply two different methodologies. This allows us to test the robustness of our empirical results. If there is truly a relationship between the shape of the utility function and the production system employed, both methods should yield the same result, ensuring that our results are method invariant. In particular, we show that the relationship between the shape of the utility function and the choice of the production system does not depend on the particular choice of the...
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