Measuring Tail Risk in the Farmer Price Index Difference using POT-EVT - Silvina Rosita Yulianti; Muhammad Bayu Nirwana; Khrisna Putri Maharani; Ahmad Zaakiy Hidayat; Andreas Ronny Wijaya (ZERO: Jurnal Sains, Matematika dan Terapan, 2026)
Farmer welfare suffers when the Farmer Price Received Index does not keep up with the Farmer Price Paid Index, and common ratio-based measures such as the Farmers' Exchange Rate do not capture sharp drops well. This study measures the extreme downside risk of the Index Difference (ID), the difference between the two indices. Because agricultural price data are heavy-tailed and not normally distributed, a Peaks-over-Threshold (POT) model based on the Generalized Pareto Distribution is fitted to the loss variable Loss = -ID, using monthly Indonesian data from January 2006 to December 2023 (216 observations). Risk is measured by Value at Risk (VaR) and Expected Shortfall (ES). At the 95th-percentile threshold, 11 exceedances give a slightly negative, near-zero shape parameter, and the 99% VaR and ES for ID are about -6.44 and -6.81. Applying POT-EVT to a farmer welfare indicator is a new contribution, and the estimates are exploratory, intended to illustrate the potential of ID-based early warning and insurance-trigger design rather than to support immediate application. With only 11 exceedances, however, these uses remain suggested rather than demonstrated, and the tail estimates should be read with caution.