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Index-based insurance is a generic term used to describe insurance policies with payoffs contingent on the value of some underlying index such as temperature, rainfall, or in the case of the present study, NDVI. Index insurance is generally targeted toward volumetric risk such as crop yields in agriculture, or electricity or natural gas demand in the energy sector.
Indeed, to be fair to the reader, the original intent of this research was to use the abundant data in the United States to investigate the efficiency of NDVI as an index for crop insurance in China, where data are limited and expensive. The reasoning was that if the general conditions for insurability held generally in the United States, they would likely hold true in China as well. Based on the results reported in this paper we were forced to rethink the strategy.
We selected this model after exploring both linear and log-linear models, since prior studies have suggested these to describe the relationship between NDVI and precipitation. However, these studies were describing relationships within a specific climate regime, and where grassland was the predominant ground cover. For the variety of locations we are assessing, the quadratic model presents a more comprehensive method of exploring the relationship between NDVI, cumulative precipitation, and growing degree-days. Initial regressions included mean temperature in addition to these variables, but mean temperature was not a significant variable in any of the locations, nor did it appear to contribute additional information relating to temperature, as this study is most interested in cases of extreme heat, best captured using the growing degree measure.
Although this yield regression may appear to suffer from endogeneity and multicollinearity, this would be true only if we found strong statistical relationships between precipitation and heat in the NDVI equation previously discussed. This was not the case. That we find no consistent relationship between heat and precipitation suggests that the yield regressions will be only minimally biased; but in a broader sense we cannot say that all regressions are free of bias or are efficient. However, our results are observational and not predictive, and with the intent of uncovering general properties we can tolerate bias and inefficiencies in some equations, so long as they do not hold in all equations.
Burn analysis is a common insurance term that simply means that frequencies of events are calculated directly from the historical record without reference to a parametric form of probability distribution.