04/11/2012
A Supply-Response Model Under Invariant Risk Preferences

A Supply-Response Model Under Invariant Risk Preferences

In this article we first develop a theoretically consistent supply-response model for producers with invariant preferences facing price risk, and then we empirically apply the model for a group of Cretan olive-oil producers. For doing so, we estimate a Generalized Leontief cost function and we use the price distribution historically faced by individual farmers to induce three different representations of price risk corresponding to the second, third and fourth lp norms. These risk measures are combined with the estimated cost-structure to provide three separate representations of the efficient frontier for the representative producer.

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The earliest studies of producer response to price risk incorporated measures of the mean and the variance of price into otherwise standard empirical supply-response relationships (Behrman, 1968). It was left to Sandmo (1971) to provide a sound theoretical model of producer response to price risk in an expected-utility setting. He showed that risk-averse producers facing price risk would produce less than risk-neutral producers facing the same mean price.

A long line of empirical and theoretical contributions (Batra and Ullah, 1974; Lin, Dean, and Moore, 1974; Just, 1974; Dillon and Scandizzo, 1978; Pope, 1980; Appelbaum and Katz, 1986; Chavas and Holt, 1990, 1996; Coyle, 1992) have followed from these early roots. Perhaps not surprisingly, much of the specific focus was on the effect of price risk on agricultural-supply response. Although specific modelling choices vary, two broad classes of models emerged: models in the Markowitz (1952) and Tobin (1958) tradition that characterize risky decision making in terms of trade offs between risk (as measured by variance) and return (as measured by the mean); and models hewing more closely to the expected-utility theory.

Few, if any, economic models have had the empirical impact of the Markowitz-Tobin model. For example, even the most naive modern-day stock pickers are familiar with such concepts as a stock’s beta that are firmly rooted in the Markowitz-Tobin model. But criticisms of the Markowitz-Tobin framework are also familiar. For many, perhaps the most telling is that Markowitz-Tobin is consistent with the expected-utility framework only under restrictive (and unattractive) assumptions on either the ex post utility function or on the distribution of returns.

This concern, however, is considerably mitigated by two considerations. Epstein (1986), by adapting Machina’s (1982) local-utility function approach, showed that all preference structures satisfying a seemingly innocuous assumption on systematic changes in risk aversion can be characterized by a local mean-variance preference functional. The second arises from the apparent empirical weaknesses in the expected-utility framework captured by the accumulation (and empir- ical verification of) a variety of behavioral and empirical paradoxes associated with its predictions.

Its strained relationship with the expected-utility framework is only one of the criticisms leveled at the Markowitz-Tobin framework. Another arises from concerns about the appropriateness of the variance (standard deviation) as a measure of risk. Despite its intuitive appeal, the variance is best suited to returns distribution that are normal. The presence of (or distinct preferences over) either skewness or kurtosis in the distribution of returns, however, undermines the suitability of the variance as a measure of risk. Responding to just such concerns, Quiggin and Chambers (2004) introduced the invariant preference class. That class generalizes the mean-variance class by allowing for more general risk measures than the variance while preserving its intuitive and analytic tractability by continuing to represent choice in terms of a trade off between risk and return.

This paper has two goals. First, develop a theoretically consistent, yet empirically tractable, supply-response model for producers with invariant preferences facing price risk. Second, empirically implement that supply-response model for a group of Cretan olive-oil producers. To achieve the second goal, we estimate the cost function for a representative olive-oil producer and a time- series representation of the empirical olive-oil price distribution historically faced by producers. From the latter, we induce a representation of its mean and three separate measures of price risk that correspond, respectively, to the second, third, and fourth lp norms. These measures of risk and return are then used along with the estimated cost structure to induce three separate repre- sentations of the efficient frontier for the representative olive-oil producer. 

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