Resumo

Crop yield insurance is one of the main risk management tools in the Brazilian agribusiness. The total premium collected by insurers surpassed BRL2 bi in 2018. The usual model of crop insurance consists in reimburse the producer in crop shortfall years, covering the difference between the harvested financial amount and the coverage purchased. To calculate the premiums, a regression model is estimated for the historical yields and from its residual values, the likely claims are calculated. Thus, methodological treatments to residuals are fundamental aspect to the pricing process.

Two primaries heteroskedasticity assumptions have been maintained in the area-yield insurance literature: (i) that residuals are homoskedastic, and (ii) that the changes in the yield standard deviation are proportional to the changes in the yield, keeping the coefficient of variation constant (proportional heteroskedasticity). Our main objective is to estimate the residuals behavior in function of the yields. This approach is different from the literature once it does not suppose any previous variance structure. To evaluate the robustness, we evaluate premiums from different methodologies.

We present a broad overview evolution of the crop insurance pricing methods. Initially, an outlook of the Brazilian crop insurance market and how the government agricultural risk management programs (PSR, Proagro) work. Following, how the literature treats the crop yield insurance contracts and particularly claims, from seminal Halcrow (1949) work to more recent approach for actuarial structures for pricing crop yield insurance. Finally, we present the main methodological aspects on the time series treatment, including residuals’ heteroskedasticity, probability distribution.

We used data from the IBGE’s SIDRA and also PAM data, which is yearly updated and discloses information about planted area and produced amount of temporary and permanent crops. To model the yield time series, planted area, and produced amount, we gathered data for three crops in municipal aggregation level: soybeans, rice and wheat. These crops figure between the seven biggest crops in PSR. We used non-parametric trend models, choosing the ideal smoothing parameter value, tested different heteroskedasticity assumptions. Finally, we calculated insurance rates by the Loss-Cost method.

Based on the results, we could verify the assumptions adoption over residuals volatility for crop yield time series influence crop yield insurance premiums calculated through the loss-cost method. In general, one can stand that adopting one of the two discussed assumption tends to, in average, increase the empirical crop insurance rate. Yet, a case-to-case verification is recommended, once Parana, the biggest market in PSR, regarding the soybean crop presented empirical rates higher than proportional ones.

Results bring a Brazilian rural insurance market outlook, that regardless its expansion, always had small area penetration in country-level. One of the main reasons is the appraisal that insurance premiums charged by insurers are not compatible to farmers risk, generating the anti-selection spiral. In our paper, 80% of the evaluated counties presented lower premium rates for the empirical estimation against proportional estimation, suggesting the residuals analysis could reduce charged rates, making the product more accessible to farmers, broadening its coverages.

Halcrow, H. G. (1949) Actuarial Structures for Crop Insurance. Journal of Farm Economics, 31(3), 418. Harri, A., Coble, K. H., Ker, A. P., & Goodwin, B. J. (2011) Relaxing heteroskedasticity assumptions in area-yield crop insurance rating. American Journal of Agricultural Economics, 93(3), 703–713. Ker, A. P., & Tolhurst, T. N. (2019) On the Treatment of Heteroskedasticity in Crop Yield Data. American Journal of Agricultural Economics, 101(4), 1247–1261. Xiao, Y., Wang, K., & Porth, L. (2017) A bootstrap approach for pricing crop yield insurance. China Agricultural Economic Review, 9(2), 225–2