Matthieu Stigler, Apratim Dey, Andrew Hobbs, David Lobell
arXiv 29 Sep 2022 · Econometrics
arXiv:2209.14611 · PDF · DOI · OpenAlex · Extracted main text
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 basis 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 crop insurance can lead to a new situation where the number of variables $N$ largely exceeds the number of observations $T$. In such a situation where $T\ll N$, 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 $T\ll N$ 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 systematic 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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Stigler, M. and D. Lobell (2021) Optimal index insurance and basis risk decomposition: an application to Kenya, Tech self | 0.811 | 4 | 2 | 100% |
| 2 | Ahn, J., J. S. Marron, K. M. Muller, and Y.-Y. Chi (2007) The High-Dimension, Low-Sample-Size Geometric Representation Holds under Mild Conditions | 0.737 | 5 | 2 | 60% |
| 3 | Conradt, S., R. Finger, and R. Bokusheva (2015) Tailored to the extremes: Quantile regression for index-based insurance contract design | 0.644 | 2 | 2 | 100% |
| 4 | Hall, P., J. S. Marron, and A. Neeman (2005) Geometric Representation of High Dimension, Low Sample Size Data | 0.644 | 2 | 2 | 100% |
| 5 | Johnstone, I. M (2001) On the Distribution of the Largest Eigenvalue in Principal Components Analysis | 0.644 | 2 | 2 | 100% |
| 6 | Deines, J. M., R. Patel, S.-Z. Liang, W. Dado, and D. B. Lobell (2021) A million kernels of truth: Insights into scalable satellite maize yield mapping and yield gap analysis from an extensive ground… | 0.511 | 2 | 1 | 100% |
| 7 | Jin, Z., G. Azzari, C. You, S. Di Tommaso, S. Aston, M. Burke, and D… (2019) Smallholder maize area and yield mapping at national scales with Google Earth Engine self | 0.511 | 2 | 1 | 100% |
| 8 | Koenker, R. and J. A. F. Machado (1999) Goodness of Fit and Related Inference Processes for Quantile Regression | 0.511 | 2 | 1 | 100% |
| 9 | Carter, M., A. de Janvry, E. Sadoulet, and A. Sarris (2017) Index insurance for developing country agriculture: a reassessment | 0.511 | 2 | 1 | 100% |
| 10 | Aoshima, M., D. Shen, H. Shen, K. Yata, Y.-H. Zhou, and J. S. Marron (2018) A survey of high dimension low sample size asymptotics | 0.405 | 1 | 1 | 100% |
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