Using insurance data to quantify the multidimensional impacts of warming temperatures on yield risk

COL data and the loss–cost ratio (LCR)

The COL data provide separate measures of yield and revenue losses below expected levels (paid indemnities). In addition, the COL data are disaggregated by type of cause, which is determined by a claims adjuster upon determination of payment; in total, we observe 44 reported causes. A particularly useful aspect of the COL data is that it distinguishes between moisture-related (e.g., drought and excess moisture) and purely temperature-related causes (e.g., heat stress) (Fig. 1). We merge the COL database with the Summary of Business (SOB) database56, a separate RMA database that contains county-level aggregate liabilities by crop. The merged data is then used to generate county-level aggregate and cause-specific variables equal to the ratio of losses to liabilities, or the LCR: ({rm{LCR}}_{it}=({sum }_{j}{rm{Losses}}_{it}^{j}){({rm{Liabilities}}_{it})}^{-1},) where ({rm{Losses}}_{it}^{j}) is the dollar value of realized indemnity payments in county i in year t due to cause j and Liabilitiesit is the maximum dollar value of indemnity payments in county i in year t. A key advantage of using the LCR variable instead of mean yields (as used in Schlenker and Roberts6, among others) is that it constitutes a measure of yield risk. While previous studies find that mean yields are predicted to decrease as a result of warming, these studies do not capture whether production will become more or less risky under warming. Indeed, the empirical finding on the negative impact of warming on mean yields in the literature does not necessitate that warming also increases downside yield risk around the new mean yields; these directional impacts need to be measured separately. Moreover, an appealing feature of the county-level LCR or crop insurance loss measures is that they capture downside risks of individual farms, whereas the county-level average yield data may not vary in response to idiosyncratic losses by farmers within a county. As a result, analyses that rely on yield data only will tend to underestimate the impact of warming on yield sensitivity. For a simulation-based demonstration of this, see Supplementary Discussion and Supplementary Table 6.

Fig. 1: Indemnity payment shares by cause of loss, 1989–2014.

Each portion of the pie chart represents the average share of indemnity payments in each crop due to a particular cause.

The county–year LCR data are matched to growing-season aggregates of precipitation and temperature exposure following the panel approach of Schlenker and Roberts6. Multivariate regression analysis is used to estimate the relationship between LCRs and weather covariates while controlling for county-level time-invariant confounders (county fixed effects), year fixed effects, and state-specific time trends. The LCRs, temperature, and precipitation vary substantially across both counties and years (Supplementary Fig. 1). Following previous studies, we focus on U.S. dryland counties, i.e., counties to the east of the 100th degree meridian. Some of these counties may rely partially on irrigation, but most corn grown in this region is rain-fed. Within this region, time-averaged LCRs demonstrate significant cross-sectional variation (Fig. 2).

Fig. 2: Spatial distribution of county-level aggregate loss–cost ratios (LCR), 1989–2014 averages (N = 30,261 for corn and N = 29,014 for soybeans).

The darker colors represent higher average LCRs.

We focus on five types of LCRs. The first type we consider is the total or aggregate LCR, which includes losses across all causes. The remaining four types are cause specific: heat, cold, drought, and excess moisture (The cold losses are the sum of cold wet weather, freeze, and frost losses). Drought exhibits the highest LCR of the four, is associated with approximately 50% of total losses, and is double the next largest cause (excess moisture), on average (Table 1). The average LCRs for heat and cold are similar in magnitude and roughly an order of magnitude lower than drought. It is important to recognize, however, that the determination of what causes a particular loss is based on the interpretations of adjusters and producers, which may not always align exactly with the true cause of losses. Nonetheless, the perceptions of adjusters and producers are just as important for understanding the ramifications of climate change, as they likely reflect how farmers adjust their behavior in response to warmer temperatures.

Table 1 Summary statistics for LCR, temperature, and precipitation variables, 1989–2014.

Annual variation between high temperatures and total LCRs at the aggregate level (across counties) exhibit positive correlation (Supplementary Fig. 2). Losses attributed to temperature extremes, excessive heat and cold, have varied over time but with opposite trends: heat losses are becoming more common while cold losses are becoming less so (Supplementary Fig. 3). Moisture-related losses, drought and excess moisture, appear to be more stable with no clear trends emerging over time (Supplementary Fig. 4). Degree days over 29 °C are positively correlated with the total, heat, and drought LCRs, which is consistent with high temperatures having both direct and indirect effects on yields (Table 1). Based on within-state variation, we also observe positive correlations between total, heat, and drought LCRs and degree days above 29 °C (Supplementary Fig. 5). Precipitation is less correlated with LCRs (Table 1) in total and for all causes except excess moisture; however, simple correlations likely understate the relationship given its nonlinear effect on yields.

Estimated weather impacts using multivariate regression

The multivariate regression model permits a broader understanding of the relationships between weather and losses. We first regress total LCRs at the county–year level against a piecewise linear function of temperature exposure and a quadratic function of cumulative precipitation. To control for unobserved sources of variation in the LCR, we included county fixed effects, year fixed effects, and state-specific time trends. County fixed effects control for unobserved factors, such as soil quality. The year fixed effects and state-specific trends control for time-varying unobserved factors, such as changes in the federal crop insurance program, as well as changes in behavior (e.g., enrollment, coverage level, contract choice). Goodness-of-fit and temperature cutoff results are reported in Supplementary Table 1. Further details on the regression model can be found in the “Methods” section.

The marginal effects of the weather variables exhibit highly nonlinear relationships between temperatures and precipitation with losses (the marginal effects of temperature and precipitation are reported in Fig. 3 and Supplementary Figs. 6 and 7). In the top row of Fig. 3, the slopes of the piecewise linear function correspond to the estimated temperature coefficients from Eq. (1). These graphs depict the impact of one additional day at each temperature on the overall LCR. For example, one additional day at 27 °C instead of a day below 10 °C within the fixed growing season reduces the LCR by a bit under 0.01 or one percentage point (or, put differently, by one cent per dollar of liability). Conversely, one additional day at 35 °C raises the LCR by just over 0.01. In corn, warmer temperatures begin to raise the LCR at about 30 °C and these effects intensify up to 40 °C. Similar estimated impacts are depicted for soybeans. We also note that the estimated temperature impacts are very similar to the estimated impacts in Schlenker and Roberts6: they find sharp decreases in yields beginning at 29 °C for corn and at 30 °C for soybeans. We also observe that additional exposure to so-called beneficial heat—temperatures below the first threshold—reduce the LCRs and at an increasing rate. Concerning precipitation, the estimated impacts reflect a concave relationship between crop yields and precipitation: at lower precipitation levels, additional rainfall reduces the LCR, but at higher levels of precipitation, it raises the LCR (Supplementary Fig. 7).

Fig. 3: Marginal effects of temperature on the heat and drought LCRs (N = 30,261 for corn and N = 29,014 for soybeans).

Dashed lines represent 95% confidence intervals and standard errors are clustered by year. For the drought LCRs and soybean heat LCR, the second cutoffs exceed 40 °C and the marginal effects in the last temperature intervals are too large to be reported.

The middle and lower panels of Fig. 3 highlight the role of temperature on heat and drought losses. In corn, warmer temperatures are associated with increased heat stress indemnities beginning at 30 °C, with the effects intensifying at 38 °C. Drought losses begin to increase significantly at 29 °C. In soybeans, heat and drought losses follow similar patterns, albeit at slightly higher thresholds: heat losses begin to increase at 33 °C and drought losses begin to increase at 30 °C. The estimated precipitation impacts follow different patterns (Supplementary Fig. 7). For both corn and soybeans, at lower levels of precipitation, additional rainfall reduces the losses associated with drought; however, at extreme levels those effects diminish to zero and even become positive in soybeans. Moreover, a 10% increase in precipitation from its mean reduces the drought LCR in both corn and soybeans by 0.008 and 0.012, respectively. Precipitation has no statistically significant effect on heat losses in soybeans or in corn.

In both crops, warmer growing seasons are associated with a reduction in both cold and excess moisture losses but these impacts are estimated with less precision (Supplementary Fig. 6). The reduction in cold losses is consistent with expectations, but the reduction in excess precipitation losses is less obvious and perhaps suggests an evaporative effect of warm temperatures. Indeed, if excessive rainfall is accompanied by high temperatures, this may reduce damages both by more quickly alleviating excess moisture conditions and by reducing the chances of damages arising from successive precipitation events in a short time span. The impacts of precipitation also generally conform with expectations with a 10% increase in precipitation from its mean increasing the excess moisture LCR in both corn and soybeans by about 0.008 and 0.006, respectively (Supplementary Fig. 7). Precipitation has no statistically significant effects on cold-related losses. The estimated impacts for soybeans largely demonstrate the same impacts as in corn.

Impact of uniform 1 °C warming on the overall LCR

Overall, the foregoing suggests that higher temperatures induce more heat and drought losses but reduce excess moisture- and cold-related losses. The net impacts of higher temperatures, however, cannot be easily ascertained, as contrasted with the impact of changes in precipitation, for example (reported in Supplementary Fig. 7). Therefore, we simulate a warming climate by increasing the daily minimum and maximum temperatures by 1 °C using the estimated coefficients from our five regression models (total LCR and the four cause-specific LCRs).

A uniform 1 °C warming for corn is associated with a wide range of heterogeneous impacts on the total LCR across counties ranging from −0.044 to 0.28 for corn and from −0.039 to 0.24 for soybeans (Fig. 4 and Supplementary Table 1). Generally, southern counties are adversely impacted by warmer temperatures, whereas northern counties are positively affected by warmer temperatures. For corn, the average impact across counties is 0.038 (p value = 0.023), which is approximately a 30% increase compared to the historical average of 0.12. Warming impacts on soybeans exhibit a similar pattern of results, although smaller in magnitude and statistically insignificant (an average increase of 0.011 with a p value of 0.23 compared to a historical average of 0.11).

Fig. 4: Spatial distribution of a 1 °C warming impact on the county-level average aggregate loss–cost ratio (LCR), 1989–2014 (N = 30,261 for corn and N = 29,014 for soybeans).

For the uniform 1 °C warming scenario, the predictions are based on the estimated coefficients of the total LCR model (assuming no precipitation changes). The darker colors represent greater impacts on the average LCRs.

Robustness of warming impacts

To assess the robustness of the results, we estimate the models and warming impacts with different specifications regarding quantifying temperature variables (Supplementary Table 2) and the LCR computed from different subsets of insurance products (Supplementary Table 3). The warming impacts remain robust across these two alternative models. We also consider additional control variables (Supplementary Table 4) such as variables that describe crop insurance participation patterns or additional weather variables (e.g., vapor pressure deficit) and test whether adding these variables improves out-of-sample predictions. The results suggest that these alternatives do not improve model performance, and we find that the results were robust to a range of other checks. Further details on the robustness of the results can be found in Supplementary Discussion.

Previous studies highlight the importance of considering adaptation in estimating warming impacts1,36. In our context, in addition to adaptation in crop production, the changes in insured liabilities as responses to changes in yield history and changes in the Federal Crop Insurance Program (FCIP) also need to be considered. Thus we conduct an additional set of robustness checks with respect to the consideration of potential adaptation using an approach suggested by Hsiang36. We compute warming impacts based on four alternative empirical models: a long-difference model, a cross-section model, and models with 5- and 10-year moving averages of the model variables (Supplementary Table 5). As noted in Hsiang36, estimated impacts based on approaches that exploit climatic variations over longer temporal frequencies implicitly allow for changes in beliefs or adaptation by individuals (in this case, farmers and the FCIP). Across all specifications, the impacts range from +17% (MA10) to +32% (BaseLine) for corn and from +11% (MA10) to +37% (LongDiff) for soybeans. We interpret this as strong evidence that, even with considering possible adaptations in crop production and insured liabilities, warmer temperatures tend to increase production risk and premium rates. See Supplementary Discussion for further details and discussion.

Cause-specific LCR warming impacts

The aggregate LCR increases associated with warming mask considerable differences among the individual causes. On a percent basis, losses associated with drought and heat are projected to increase by 92 and 105%, respectively, for corn and by 59 and 105%, respectively, for soybeans (p value < 0.01). Conversely, losses associated with excess moisture and cold are projected to decrease by 43 and 256%, respectively, for corn and by 59 and 234%, respectively, for soybeans (p value less than 0.05). However, in absolute terms the combined drought and heat increases are significantly larger than the combined excess moisture and cold decreases, thereby leading to a net increase in overall losses. As with the aggregate LCR, we find evidence of widespread spatial heterogeneity of the cause-specific losses associated with warming (Fig. 5).

Fig. 5: Spatial distribution of 1 °C warming impact on the county average cause-specific loss–cost ratio (LCR), 1989–2014 (N = 30,261 for corn and N = 29,014 for soybeans).

For the uniform 1 °C warming scenario, the predictions are based on the estimated coefficients of the four cause-specific LCR models (assuming no precipitation changes). The darker colors represent greater impacts on the average LCRs.

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