Dr. Matthieu Stigler (ETH Zurich) “With big data come big problems: pitfalls in measuring basis risk for crop index insurance.”

Abstract

New satellite sensors will soon make it possible to estimate field-level crop yields, showing a great potential for agricultural index insurance. This paper identifies an important threat to better insurance from these new technologies: data with many fields and few years can yield downward biased estimates of systemic risk, a fundamental metric in index insurance. To demonstrate this bias, we use state-of-the-art satellite-based data on agricultural yields in the US and in Kenya to estimate and simulate basis risk. We find a substantive downward bias leading to a systematic overestimation of insurance quality. In this paper, we argue that big data in agriculture can lead to a new situation where the number of variables N largely exceeds the number of observations T. In such a situation where T << N, conventional asymptotics break, as evidenced by the large bias we find in simulations. We show how the high-dimension, low-sample-size (HDLSS) asymptotics, together with the spiked covariance model, provide a more relevant framework for the T<< N case encountered in index insurance. More precisely, we derive the asymptotic distribution of the relative share of the first eigenvalue of the covariance matrix, a measure of systemic risk in index insurance. Our formula accurately approximates the empirical bias simulated from the satellite data, and provides a useful tool for practitioners to quantify bias in insurance quality.