Correlated yield-price scenarios under the M-13 framework • FCIP Calibrated and Synthetic Data Catalogue

Introduction

Comparing insurance alternatives requires evaluating each under identical states of nature; otherwise differences in simulated luck are confounded with differences in contract value. This article documents the third stage of the FCIP data system: the generation, for every calibrated transaction, of 500 joint yield–price realizations under the stochastic framework RMA itself uses to rate revenue coverage (the M-13 simulation methodology). Two design choices matter economically. First, adopting the agency’s own distributional assumptions means that any wedge between simulated and actuarially implied outcomes reflects the data, not a competing model. Second, the use of common random numbers across contract alternatives is the simulation analogue of a within-subject experimental design: it removes between-alternative sampling variation from counterfactual contrasts, a standard variance-reduction technique in stochastic simulation.

Notation

Let i index producer-level contracts (aggregated transactions carried forward from the calibration stage), j(i) their insurance pools, and d = 1, \dots, 500 the scenario index. Denote by y^{a}_{i} the approved yield; by p^{h}_{jt} the harvest-price discovery value and \nu_{jt} the price volatility factor established for the pool; and by (m_{j}, s_{j}) the mean and standard deviation parameters of the pool’s standardized yield distribution recorded in the actuarial data. The actuarial records also supply, for each pool, a pair of 500-element standardized draw vectors \{z^{(d)}_{j}\} (yield) and \{u^{(d)}_{j}\} (price) whose joint ordering encodes RMA’s assumed yield–price dependence, indexed by the pool’s beta-distribution identifier.

The scenario system

Location and scale. Yield draws are anchored to the contract by scaling the pool’s standardized distribution to the approved yield:

\mu_{i} = \frac{y^{a}_{i}\, m_{j}}{100}, \qquad \sigma_{i} = \frac{y^{a}_{i}\, s_{j}}{100}.

Yield realizations. Scenario d yields are the location–scale transform of the standardized draws, censored at zero:

y^{(d)}_{i} = \max\!\left(0,\; z^{(d)}_{j}\, \sigma_{i} + \mu_{i}\right).

Price realizations. Prices are lognormal around the harvest-price discovery value with a mean-preserving drift correction, capped at twice that value as in the rating pipeline:

p^{(d)}_{j} = \min\!\left(2\, p^{h}_{jt},\; \exp\!\left(u^{(d)}_{j}\, \nu_{jt} + \lambda_{jt}\right)\right), \qquad \lambda_{jt} = \ln p^{h}_{jt} - \frac{\nu_{jt}^{2}}{2},

where the drift term \lambda_{jt} ensures E\!\left[\exp\!\left(u\,\nu + \lambda\right)\right] = p^{h}_{jt} under standard-normal u; i.e., simulated prices are unbiased for the discovery price before censoring.

Rate anchoring. Each contract also carries a lookup rate: the revenue rating rate obtained by evaluating the premium calculator at a rate yield set to the mean of the contract’s recovered rate yield and its calibrated yield. This anchors the scenario system to the same rating surface used in the choice-set stage.

Common anchors for correlation. To preserve cross-alternative and cross-scale dependence, each scenario carries two aggregate paths alongside the contract-level draws: the pool-average yield path \bar{y}^{(d)}_{j} = \frac{1}{n_j}\sum_{i \in j} y^{(d)}_{i} (with n_j the number of contracts in pool j), which drives area-plan triggers, and the state–commodity–type–practice average price path, which anchors group price movements. Because individual, area, and no-insurance alternatives are all evaluated on the same indexed draws, the within-scenario correlation between a farm’s outcome and its area index, the determinant of basis risk in area products (Miranda, 1991), is preserved by construction.

The combined collection

A companion collection joins the calibrated yields with their scenario sets into a single analysis file, renaming the observed contract elections with a revealed_ prefix so that the producer’s actual choice is never conflated with the counterfactual alternatives evaluated on the same draws, a safeguard for revealed-preference work.

What the scenarios measure

The scenario system is the measurement engine behind the program’s risk-reduction evidence. Evaluating observed FCIP policies on these draws, Tsiboe et al. (2025) estimate that a one percent increase in mean revenue induced by crop insurance is associated with a 2.25 percent reduction in inter-crop-year revenue variability, with the effect concentrated in the individual revenue and yield protection plans that dominate participation: plans that generally raise mean revenue and reduce its variability simultaneously. The same machinery supports prospective analysis: because proposed instruments can be priced and simulated on identical draws, Tsiboe and Turner (2025) evaluate a buy-up Price Loss Coverage option before enactment, finding that pairing it with existing farm-based insurance reduces revenue variability by 23 percent relative to no risk management, at higher expected government cost per unit of variability removed.

Limitations

The scenarios are unconditional draws for the study year under RMA’s distributional assumptions: beta-family yields, lognormal prices, and the agency’s assumed dependence structure. They embed no weather realization, no spatial correlation beyond the pool anchors, and no model risk adjustment; conclusions that are sensitive to tail behavior should be stress-tested against the 500-draw sampling error, which is nontrivial for extreme quantiles. The censoring of prices at twice the discovery value, inherited from the rating pipeline, truncates the upper price tail in high-volatility years.

Data availability

Two collections, one file per crop year: the scenario sets (revenue_draw_<year>.rds, publicly hosted) and the combined calibrated-revenue files (calibrated_revenue_<year>.rds, hosted on a private repository; an access token is available on request from the author, ftsiboe@hotmail.com):

# Public collection
piggyback::pb_download(
  file = "revenue_draw_2022.rds", dest = tempdir(),
  repo = "ftsiboe/USFarmSafetyNetLab", tag = "revenue_draw")

# Private collection: first store the token provided on request
Sys.setenv(GITHUB_PAT = "<token provided on request>")
piggyback::pb_download(
  file = "calibrated_revenue_2022.rds", dest = tempdir(),
  repo = "ftsiboe/rfcipCalibrate", tag = "calibrated_revenue")

Recommended citation

Tsiboe, F. (2026). Correlated yield–price scenarios under the M-13 framework. In FCIP calibrated and synthetic data catalogue. https://ftsiboe.github.io/rfcipCalibrate/articles/revenue-draws.html

Data users should additionally cite Tsiboe, Turner, and Yu (2025).

Disclaimer

This product uses data provided by USDA/RMA but is neither endorsed by nor affiliated with USDA or the U.S. Government.

References

Miranda, M. J. (1991). Area-yield crop insurance reconsidered. American Journal of Agricultural Economics, 73(2), 233–242. https://doi.org/10.2307/1242708

Tsiboe, F., & Turner, D. (2025). Incorporating buy-up price loss coverage into the United States farm safety net. Applied Economic Perspectives and Policy, 47. https://doi.org/10.1002/aepp.13536

Tsiboe, F., Turner, D., & Yu, J. (2025). Utilizing large-scale insurance data sets to calibrate sub-county level crop yields. Journal of Risk and Insurance, 92(1), 139–165. https://doi.org/10.1111/jori.12494

Tsiboe, F., Turner, D., Williams, B., Miller, M., Baldwin, K., & Dohlman, E. (2025). Risk reduction impacts of crop insurance in the United States. Applied Economic Perspectives and Policy, 47(5), 1832–1847. https://doi.org/10.1002/aepp.13513

U.S. Department of Agriculture, Risk Management Agency (USDA-RMA). (n.d.). M-13 handbook and rating methodology. https://www.rma.usda.gov