Farmers' Subjective Probabilities in Northern Thailand: Reply

The comment by Knight, Johnson, and Finley (KJF) raises some important issues regarding the methods used in eliciting and evaluating probability assessments and the effects of these methods on the reliability of our findings. To summarize, KJF's comments concern the scoring rule used in elicitation, determination of the range of the variables examined, the evaluation method, and the assumption that farmers' utility functions for reward payoffs were linear. This reply addresses these concerns to determine their effect on the reliability of our findings and provide insights for further research in this important area. In some aspects, the difference between what KJF recommend and what we applied was a matter of practicality. Strictly applying theoretically correct concepts with farmers who speak a different language and live in another culture is difficult. The method used to elicit subjective probability distributions followed the "visual counter" technique as described by Anderson, Dillon, and Hardaker. To induce farmers to take the elicitation process seriously, a monetary reward of a meaningful magnitude was offered for correctly predicting actual occurrences. KJF's first comment indicates that "rational" assessors, to maximize their expected score and payment, would have assigned one of the five intervals with a probability of one, leaving the other intervals with an assignment of zero probability. That is, KJF believe because of expected utility maximization, that all or most of the farmers would make a categorical statement by allocating all of the coins to a single interval using our methodology. In addition, KJF question the assumption of linear utility functions and the use of significant payments for results. Two factors are most important in eliciting true beliefs from individuals using probability assessment methods-getting individuals to take the process seriously and using scoring rules that will provide incentive to reveal true expectations. Taking the process seriously is the first-order factor of importance in probability assessment, as first recognized by Gauss as early as 1821 (Hampton, Moore, and Thomas). A reward for being correct helps individuals to be honest in revealing what they believe would happen. The factor of second-order importance is a proper scoring rule which encourages an assessor to give statements that accurately reflect his beliefs. In regard to whether proper scoring rules are preferable to other rules because they encourage the assessor to reflect on his true beliefs, Bessler recently wrote, "This point must, it seems, be taken on faith since I know of no study, psychological or otherwise, which empirically tests the validity of the proper rule" (p. 18). KJF correctly note that a linear scoring rule was used in our study. This was done for several reasons. First, it could be easily communicated to small semicommercial farmers and they could understand it easily to state judgments on the outcome of an uncertain event. Farmers could visibly examine the range and intervals and easily grasp how they would be scored. Using more complex, theoretic lly better rules which make explicit reference to logarithms or squares may not be practical when working with untrained subjects, or even most ornary people as suggested by Savage (1971). Second, risk-averse persons will not, in general, make categorical statements if they are to be rewarded based on actual outcomes. Therefore, the reward payoff was intentionally set sufficiently large to allow farmers to exhibit risk-averse behavior in making judgments and discourage them from making a categorical statement. Under risk aversion, maximization of expected utility is not equivalent to maximization of the expected score. In a part of the original study not reported in Grisley and Kellogg, the same farmers' preferences to risk taking were elicited using a gambling approach similar to that of Binswanger. All the farmers exhibited risk-averse behavior (Grisley). Winkler and Murphy (1970) have shown that a riskaverse assessor would "hedge away from a categorical forecast (i.e., toward a forecast in which all the probabilities are equal" (p. 148). A risk taker would hedge toward a categorical forecast. In our study, no categorical statements were made as KJF indicated rational assessors would have done, because coins were allocated to all five intervals by almost all farmers. This result provides further evidence of risk-averse behavior. However, risk aversion by itself is not sufficient to show that the linear scoring rule is proper. The linear scoring rule has been shown to be proper by Raiffa and Winkler (1969) in The authors are, respectively, an assistant professor of agricultural economics, Pennsylvania State University, and a professor of agricultural economics, University of Illinois. The authors express their appreciation to Spiro E. Stefanou and Kalyan Chatterjee for their helpful comments. Review was coordinated by Richard E. Just, editor.