On the Treatment of Heteroscedasticity in Area‐Yield/Group‐Risk  Crop Insurance

Furthermore, the differences in the estimated premium rates are large: at the 75% coverage level, the adjusted rate of 2.19% is 7.2 times larger than the unadjusted rate of 0.30%. [...] Empirical Treatment of Heteroscedasticity The treatment of possible heteroscedasticity in the crop insurance literature generally in- volves testing for homoscedasticity and if the yield data fails to reject they are assumed homoscedastic.3 Conversely, if the yield data rejects homoscedasticity the variance is gen- erally assumed to be proportional to the fitted values.4 Harri et al. [...] In the case of the pooled estimates, the mini- mum and maximum values become more economically reasonable than in the unconstrained procedure: for the pooled β̂ a minimum of -0.85 and maximum of 3.30 versus a minimum of -2.49 and maximum of 6.96 for the unconstrained county-level β̂. [...] The design of the simulation imitates the decision rules of the Standard Reinsurance Agreement. [...] To give an idea of the scope of rate differences, the two columns on the right hand side of Table 3 sum the dollar difference in premiums generated by different heteroscedasticity treatments.9 These calculations assume the private insurance company’s premium rates are correct such that if πp > πg the difference between the rates is the underpayment to the program and if πp < πg is the overcharge t.