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The value of information under ambiguity: a theoretical and experimental study on pest management in agriculture

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Abstract

This article addresses the value of information that affects the ambiguity faced by a decision maker. Our analysis is applied to the case of a farmer whose production can be damaged by a pest attack with unknown probability, this damage being reduced if the farmer decides to use a pesticide. Early warning systems have precisely been implemented in many countries to help farmers avoid inappropriate decisions in terms of pesticide use. We investigate, both theoretically and experimentally, how farmers value these systems. We propose a two-state self-insurance model in which an \(\alpha\)-MaxMin Expected Utility farmer may use pesticides that reduce the loss in the accident state while incurring a cost in both states. Her decision to self-insure or not depends on risk and ambiguity attitudes. We compile and compare the value of two types of information leading to a reduction of ambiguity and analyze their properties with respect to ambiguity attitude. Both types of information are valued positively if the farmer is ambiguity averse. We conduct a framed field experiment in which farmers and agricultural students have to decide whether or not to apply pesticides depending on risk, ambiguity and the associated monetary gains resulting from pesticide cost. The experimental findings support the theory. The average value of information among all participants is between €0.9/ha and €3.3/ha depending on the information gain.

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Notes

  1. All following theoretical results obtained with this framework do not depend on the application context and are generic in nature.

  2. See Ghirardato et al. (2004) and Peter Klibanoff and Stanca (2021) for an axiomatic foundation. Since we consider a binary state space, criterion (1) is a also a special case of Choquet Expected Utility and biseparable preference.

  3. Notice that in a two-state setup, any set of priors is trivially centrally symmetric.

  4. Stated otherwise, \({{\bar{c}}}\) is the buying price of the random variable that pays I in the accident state and 0 in the non-accident state.

  5. Roberts et al. (2009) consider a framework with risk so that the information leads to an update of the probability of attack.

  6. See also Peysakhovich and Karmarkar (2016).

  7. Indeed, the average probability is \({{\bar{p}}}-a_1/4\) if the farmer receives information L, \({{\bar{p}}}\) if she receives no information, and \({{\bar{p}}}+a_1/4\) if she receives information H. Proposition  2 then implies \({{\bar{c}}}_L< {{\bar{c}}}_1< {{\bar{c}}}_H\).

  8. As recalled in the introduction this result is also obtained by Carpentier (1996) in a framework with risk-averse farmer and no ambiguity.

  9. More precisely, v and r increase with c if and only if the farmer has aversion both to ambiguity and risk (\(\alpha >1/2\) and \(U''<0\)) or if the farmer loves both ambiguity and risk (\(\alpha <1/2\) and \(U''>0\)).

  10. Students were in a training for a Brevet de Technicien Superieur (BTS) which corresponds to an undergraduate-level degree.

  11. Some values of pesticide costs are extreme compared to real values, but this range of amounts allows us to observe for which pesticide costs participants modify their behavior. A sufficiently large range is needed to observe such changes.

  12. Among farmers, females are younger than males whereas there are no difference in age between males and females among students.

  13. More precisely, we randomly drew one situation and one level of pesticide cost and considered the decision taken by the farmer for this case. A blind draw of one ball in the urn was to simulate the random draw of the pest attack. In the situation with ambiguity, the white balls contain either a blue or a red paper and this ball was opened if it was drawn. The random draw of a pest attack depends on the situation that is drawn because this situation defines the probability of the pest attack. The random draw of decision number in the selected situation is done at the end of the experiment by a participant drawing without seeing a decision number.

  14. For instance, for a participant who chooses three times to use pesticide, we approximate her maximum pesticide cost as equal to 40 Euros. Excluding these observations does not change the results.

  15. Many different levels of ambiguity preference parameters exist that depend on the value of the participant’s risk preference parameter. For simplicity, we report ambiguity preference parameters for the specific risk preference parameter \(\beta =0.9994\) that is close to risk neutrality, i.e., \(\beta =1\). The method is identical for other levels of risk preference parameters.

  16. In Appendix  C.1, we report the values when we exclude inconsistent decisions. The results are similar.

  17. We do not exclude inconsistent participants, as the results are qualitatively the same.

  18. We do not use the maximum pesticide cost in \(A_4\) for comparisons among ambiguity-averse and ambiguity-loving participants because decisions in \(A_4\) serve to define the participants’ ambiguity preferences.

  19. Because they do not include risk and ambiguity preferences as explaining variables, we ran models (1) and (2) including all situations, and the coefficients are qualitatively similar.

  20. Appendix C.3 details the p-values of the Wilcoxon signed-rank tests comparing the value of information for the different types of ambiguity reduction.

  21. We run the regressions for all other thresholds of pesticide costs between 50 and 120 and find qualitatively same results. The regressions are available upon request.

  22. More precisely, the variation in \({{\bar{c}}}\) from \(A_4\) to \(A_2\) or \(PA-A_2\) is lower for farmers, in absolute terms.

  23. Based on the theoretical model we can compile that if \(\Delta x \ne 0\), then \(\frac{\partial v}{\partial (\Delta x) c} = \frac{\partial r}{\partial (\Delta x) c}\) is close to -1. The estimation in Table  8 is \(-7.5/10=-0.75\). This lower slope can be explained by the fact that the actual decision of the farmers in the experiment may be different from the theoretical prediction. In addition, the compilation of the slope for a variation in cost of €10 is lower compared to the slope for a very small variation.

  24. See Böcker and Finger (2016) and Lee et al. (2019) for recent reviews of policy instruments for reducing pesticide use.

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Acknowledgements

We would like to thank Edwige Charbonnier for her assistance in the preparation and organization of the experiments that are reported in this article.

Funding

This work received financial support from the Ecophyto—PSPE2 program, France within the VESPA project. Partial financial support has also been given by the National agency for research in agricultural, food and environment (INRAE) and the Grenoble Applied Economics Laboratory (GAEL).

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Authors and Affiliations

  1. University of Toulouse, INRAE, UR 875 Applied Mathematics and Computer Science laboratory, 31326, Castanet Tolosan, France

    Stéphane Couture

  2. Univ. Grenoble Alpes, INRAE, CNRS, Grenoble INP, GAEL, 38000, Grenoble, France

    Stéphane Lemarié & Sabrina Teyssier

  3. Univ. Grenoble Alpes, CNRS, INRAE, Grenoble INP, GAEL, 38000, Grenoble, France

    Pascal Toquebeuf

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  1. Stéphane Couture
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Correspondence to Stéphane Couture.

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Couture, S., Lemarié, S., Teyssier, S. et al. The value of information under ambiguity: a theoretical and experimental study on pest management in agriculture. Theory Decis 96, 19–47 (2024). https://doi.org/10.1007/s11238-023-09942-y

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