Climate change to increase crop failure in U.S.

The literature has documented that climate change is likely to reduce crop yields of harvested acres in the United States. This study uses panel data methods to document that climate change could also reduce harvested area. We find that ‘crop failures’ are sensitive to spring and fall temperature conditions. Using perturbations of temperature and precipitation conditions, we show that a uniform 1 ∘C increase in temperature across the U.S. with no adaptation is expected to cause about 3.2 million additional failed acres in the United States, which is equal to a 0.9% decline in acreage. These harmful impacts are predicted to be stronger in the southern than northern United States. For illustrative purposes, we also examine a uniform 3 ∘C warming scenario with no adaptation, and project that damage increases to 11 million lost acres, about a 3% decrease in crop acreage. Projected increases in local precipitation have little effect. The effect of crop failure must be added to previously measured reductions in crop yields from harvested acres, implying climate change is likely to be more harmful to American crop production than previously thought.


Introduction
There have now been many empirical studies of the effect of weather on crop yields, both in the United States [1][2][3] and around the world [4][5][6][7]. These empirical studies measure crop yields as crop output per harvested hectare (e.g. bushels of corn/hectare of harvested cropland) using panel methods. Such studies have consistently found that warmer temperatures from climate change are likely to reduce the yield per hectare, especially in temperate and tropical regions [1,5].
We add to this literature by analyzing another consequence of weather and climate change: not only does weather affect the yield per harvested hectare, but weather also causes crop failures that prevent planted hectares from ever being harvested. Recent studies using crop growth models have shown that climate change is expected to increase crop failure rates [8][9][10][11]. That is, on top of reducing yield of harvested hectares, climate change could also reduce the number of hectares harvested. Empirical studies applying panel data methods to harvest ratios (the ratio of harvested acreage to planted acreage) [12][13][14] have also measured a link between weather and acreage loss. Finally, studies in yield variability [15][16][17] have also shown that the impact of weather and climate change are not limited to average yield. Previous yield studies, which take yield on harvested acreage as its dependent variable, do not account for this acreage effect.
To this end, we analyze the relationship between crop failure and weather using a well-known panel fixed effects model [18][19][20]. Data from U.S. Census of Agriculture (henceforth 'Census') are used to identify year-to-year shifts in crop failure. Our outcome variable of interest is 'crop failure rate,' defined as the ratio of acreage with complete loss of output to the entire planted acreage. An increase in crop failure rate is thus equivalent to a decrease in harvested acreage. This data is joined with a weather and climate dataset carefully collected to reflect the distribution of cropland across the U.S. We aim to explore whether the crop failure rate is sensitive to weather each year, and to project the impact of climate change on crop failure. Figure 1 presents the distribution of this crop failure rate across the United States. The figure clearly demonstrates that this crop failure rate is related with climate. While 2.5% of planted acreage experience crop failure in U.S., this crop failure rate differs a great deal across the country. Counties in the Corn Belt, the Mississippi River basin, and the Pacific Northwest experience low crop failure rates, while counties west of the 100th meridian with dry climate have high average failure rates ( figure 1(a)). Crop failure rates also show significant variation from one year to another, with years such as 2002 and 2012 showing high levels of crop failure ( figure 1(b)). In this study, we use this year-to-year variation in crop failure rate, in conjunction with variations in weather, to identify the relationship between climate and crop failure rates. We also use findings from this analysis to project future changes in crop failure rates under different climate change scenarios.
The rest of the paper is structured as follows. In section 2 we present our data and the empirical strategy that we use to identify the crop failureweather relationship and to project future crop failure changes. The results of this analysis are presented in section 3. Section 4 discusses the implications of this study's findings and concludes.

Crop failure rate in U.S
Data for the outcome variable is obtained from the U.S. Census of Agriculture, which flags cropland as 'failed' when it has been neither pastured nor harvested. Note that this is a county average for the entire year, so we do not know the precise date of the crop failure. All harvested croplands are excluded from 'failed cropland,' even when the yield is anomalously low. Cropland is defined as the summation of harvested cropland, failed cropland, fallowed cropland, and idled cropland. Crop failure rates are calculated by dividing the failed acreage by total cropland acreage for that given year [21].
Three points are worth mentioning with regards to the outcome data. First, the definition of crop failure in this study is considerably stronger than those of previous crop growth model studies (e.g. [11]). These previous studies defined failures as incidents of low yield, with the threshold being decided by the historical yield records in each county. These studies are hence measuring 'yield failure,' and the results of these studies overlap with the yield-weather studies in the empirical literature. The crop failure definition used in this study, on the contrary, requires the harvested yield to be zero.
Second, we note that a recent study [14] has studied a phenomenon similar to crop failure. The study relied on corn and soybean 'harvest ratios,' defined as the ratio of harvested acreage to planted acreage. Harvest ratios, unfortunately, capture two phenomena: crop failure rates and planted acreage used for hay and silage [22,23]. The Census' definition of crop failure, on the contrary, just measures crop failure rates.
Third, while the definition of 'crop failure rate' places the entire cropland acreage at the denominator, it is useful to think of an alternative definition with planted acreage as the denominator. Planted acreage is defined as the summation of harvested and failed acreage. If the ratio of failed acreage to planted acreage decreases by 1% due to climate change, this impact should be added to previous estimates of climate change impact on harvested yield. We thus discuss the share of failed acreage in planted acreage in section 4.

Weather and climate data
Weather data are obtained from a daily 4 kmresolution dataset covering the entire U.S. [24]. Daily mean temperature and precipitation data are collected, and are aggregated to the seasonal level. Climate data, which are used for the projection of climate change impact, are obtained from the PRISM Long Term Average for years 1991-2020 [25], which provide 800 m-resolution data on present-day climate.
Importantly, all weather and climate variables are weighted by a 'cropland layer,' which specifies the placement of croplands within a given county. We construct this layer from a series of 30 m-resolution National Land Cover Database (NLCD) assessments [26], which has shown an accuracy of over 90% in distinguishing croplands. We use the latest version of NLCD assessment available, NLCD 2019. We define a NLCD pixel to be 'cropland' if it has been designated as 'cultivated crops' for at least six times out of its eight assessment series (2001,2004,2006,2008,2011,2013,2016,2019). Each weather and climate grid is weighted by the number of cropland pixels included. This ensures that the data that we are using accurately reflects the weather and climate experienced by farms. The cropland layer we used for the analysis is presented in supplementary figure 1.

Empirical strategy 2.2.1. Crop failure-weather relationship
We construct a panel fixed effects model that relates the yearly crop failure rate to seasonal weather conditions. We use seasonal average temperature and precipitation as the independent variable, with a quadratic specification: where y it is the crop failure rate of county i in year t, α i is the county-fixed effect term of county i, T ist and p ist the average daily temperature and monthly precipitation of county i in season s, year t. Similar model specifications have been widely used in the empirical literature, especially for purposes of projecting gross domestic product trends under climate change [18,20]. The α i term is a key component of this model, as it controls for county-fixed time invariant characteristics (e.g. soil characteristics). The model thus uses random variations in year-to-year weather to analyze the relationship between weather and crop failure rates [27].
Assuming that the long-term response of crop failures would be comparable to the short-term response, we can estimate the impact of a 1 • C increase in seasonal average temperature. For a county whose average temperature for season s is τ , the marginal effect of temperature on the crop failure rate is (see supplementary information for derivation): where y and T s refers to the average crop failure rate and average temperature, and theβ 1s andβ 2s are the estimates of the coefficients obtained from the fixed effects regression (equation (1)). The E(·) is the expectation operator. In section 3, we use estimates of this 'marginal effect' to characterize the crop failure-weather relationship. The standard error of these marginal effects are obtained by running 1000 bootstraps with repeated sampling. Note that because we do not have precise dates when each crop failed, we cannot do an event study that ties each failure to the weather of the immediate days before the failure occurred.
The marginal effects across the sample between crop failure rates and temperature and precipitation show how weather affects current crop failure rates. For example, if the marginal effects are an increasing function of temperature, then there is a convex relationship between the temperature and crop failure (U-shaped curve). If the marginal effects are more or less constant over different temperature levels, the underlying relationship is linear.
For sensitivity analysis, we construct six alternative models, combining different datasets and regression methods. We check if the results are robust to removal of data-missing counties, changes in data collection method (use of county centroids instead of cropland layer weights), and use of acreage as regression weights (supplementary table 1 and supplementary figures 2-9).

Crop failure rate under climate change
We use estimates of the fixed effect model to project how crop failure rates will evolve under a changing climate. We use the fitted model from equation (1) and calculate the difference in average failure rate. As this projection exercise is intended to be merely illustrative, we do not rely on specific climate model projections. We instead project the impact of uniform increases in temperature by 1 • C, 2 • C, and 3 • C. This study just examines weather changes and therefore does not account for adaptation.
For example, we take the following procedure for projecting crop failure rate under 3 • C warming. For a county with an average seasonal temperature and average monthly precipitation of τ 1 , τ 2 , τ 3 , τ 4 , ρ 1 , ρ 2 , ρ 3 , ρ 4 for the four seasons, we augment this by 3 • C and calculate the difference inȳ estimates. This would be equivalent to calculating the following: where thef(·) are the fitted model from equation (1) consisting of β and γ estimates. The future crop failure rate is calculated by adding this differential to the county's average crop failure rate. Of course, climate change also affects precipitation patterns across the U.S. To assess the role of precipitation across different change scenarios, we run a series of different simulations to assess the role of this heterogeneity. We start with a temperature increase projection with no changes in precipitation. We then run two projections with uniform increase in precipitation by 5% and 7% across all U.S. We then run a projection based on [28], with heterogeneous precipitation increase over different regions and temperature increases: 5.67%, 2.64%, and 7.79% increase in precipitation for western, central, and eastern U.S. for 3 • C warming, 2.91%, 0.61%, 3.03% and 2.73%, 2.07%, and 5.22% increase for all 1 • C and 2 • C warming scenarios.
Lastly, for the 3 • C warming scenario, we also refer to [29] to project region-and-season-specific precipitation changes (supplementary table 2). In this scenario, the United States is divided into seven climate zones following [30], and different increases in precipitation are assigned to each zone. We compare projection results from these models to understand the role of precipitation faced with a warming climate. Note that the projection results presented here are meant to be illustrative, and do not include the detailed projections from general circulation models. Note also that these projections also do not account for any adaptations that farmers may make to future climate scenarios.

Crop failure and seasonal weather
From the regression analysis of crop failure rates on weather, one can analyze the relationship between seasonal temperature and crop failure rates. The results reveal very different effects across seasons. Winter and summer temperatures have hill-shaped effects on crop failures with maximum rates at 8 • C and 39 • C, respectively. In contrast, spring and especially autumn temperatures have U-shaped effects on crop failure rates, with minimums at 13 • C and 7 • C, respectively. Cold temperatures are harmful, but hot temperatures are especially destructive. The harmful effects from warmer temperatures are consistent with yield study results [1], but the hill-shaped relationships in the winters and summers are not.
We can also interpret the estimates in figure 2 as a measure of the effect of a marginal increase in seasonal average temperature. Using this framework, we see that a 1 • C warming would be beneficial (decreasing crop failure, negative marginal effect) for regions with a warm winter, cold spring and cold  autumn temperatures, but harmful for regions with cold winter, warm spring, cold summer, and warm autumn.
Crop failure rates are sensitive to precipitation as well, as shown in figure 3. Fall precipitation has a small harmful impact on crop failures. With the remaining seasons, crop failures are a U-shaped function of precipitation. Low levels of precipitation can cause failures especially in the spring. But more crop failures appear to be associated with high levels of precipitation, especially in spring. Figure 3 measures the marginal effect of precipitation increase at different mean levels of precipitation. The figure shows that dry (wet) regions would benefit (lose) from marginal increases in winter, summer, and especially spring precipitation. Changes in autumn precipitation will have a minimal impact on crop failure.
These temperature and precipitation marginal effects are robust to using acreage in a weighted regression, alternative interpolations of weather, and removal of outliers (supplementary table 1, supplementary figures 2-9). Using the estimated temperature coefficients, we find that a marginal 1 • C warming increases mean crop failure rates by 1.1% (from 2.5% to 3.6%). Using the precipitation coefficients, a uniform 1 cm month −1 increase in precipitation will decrease the crop failure rate by 0.2% (from 2.5% to 2.3%).

Climate change impact on crop failure
Using the above model, we project the additional increases in failed acreage that would occur given a few climate change scenarios assuming no adaptations. We present here the results of a uniform 3 • C warming, accompanied with region-and-season specific precipitation changes. For comparison purposes, we project the change under different temperature increase scenarios (supplementary figures [10][11][12][13][14][15][16].  cropland. Failed acreage is thus expected to more than double from the current level (9 million acres). Southernmost counties, which tend to be warmer, see the largest increase in crop failure, while cooler northern counties see the smallest change. The average increase in crop failure rates is 4.96% in the southern counties (additional loss of 6.3 million acres) and 2.1% in the northern counties (additional loss of 4.4 million acres).
The predicted outcomes under 3 • C warming do not vary substantially with alternative precipitation scenarios (supplementary figures 14-16, supplementary table 3). With no change in precipitation, the crop failure rate increase is 3.54%. The change in precipitation only leads to a 0.05% decrease in crop failure rate. For region-specific precipitation increase of 5.67%, 2.64%, and 7.79% increase for western, central, and eastern U.S., the crop failure rate increase is 3.51%. Assuming uniform increases of 5% and 7% precipitation, the crop failure rate increase is 3.50%. The spatial distributions of predicted crop failure increase also are very similar. Figures 4(a) and (b) show that with the exception of a few counties in the Great Plains, the shift from universal precipitation increase to region-and-season specific precipitation increase has little effect on the crop failure rate increase. Precipitation changes are also insignificant for less intense warming scenarios (1.05% versus 1.01% for 1 • C warming, and 2.23% versus 2.19% for 2 • C warming, supplementary figures 10-13, supplementary table 3). Figure 5 compares 3 • C projection results with those from less severe warming scenarios, all scenarios using regional precipitation increases. We find that the failed acreage rapidly rises as climate change strengthens. With no adaptation, the loss in acreage is 3.19 million, 6.85 million, and 10.98 million acres for 1 • C, 2 • C, and 3 • C temperature rise, respectively. This corresponds to 0.85%, 1.83%, and 2.94% of the entire acreage. The standard deviation of crop failure rate also increases from 3.37% (1 • C warming) to 3.53% (2 • C warming), and 3.79% (3 • C warming) for the three scenarios.

Discussion and conclusion
The purpose of this study is to explore the effect of climate change on crop failure rates. The empirical literature has largely focused on the effect of climate change on yields of harvested acres. The literature has consequently overlooked how climate change may increase failure rates which affect the number of harvested acres observed. The study gathers data collected by farm on crop failures that lead to county failure rates. This panel data set of crop failure rates is then regressed on weather using county fixed effects to control for county level variables. We adopt the standard quadratic model of weather used in the panel literature of crop yields and economic growth.
We find that crop failure rates are indeed sensitive to both temperature and precipitation. The effect is convex (U-shaped) as one might expect from the yield literature. Both cold and hot temperatures can be harmful, and both drought and flooding can be as well. The temperature effects differ by season and are especially large in autumn. The smaller precipitation effects are especially large in the spring. Crop failure rates are currently 2.5% in the United States. Our model predicts that, even with concomitant precipitation increases, crop failure rates would increase by 1.1% • C −1 increase in temperature without adaptation. By itself, a 1 • C warming is predicted to increase crop failure rates by 1.5% in the South (1.9 million acres) but only 0.6% in the North (1.3 million acres). More extensive warming increases the damage. With no adaptation, a uniform 3 • C warming with no adaptation is predicted to increase crop failure rates by 4.9% in the South but only by 2.2% in the North. Precipitation increases just slightly reduce these effects. A 3 • C temperature rise leads to a disproportionately larger damage compared to a 1 • C warming. The increases in failed acreage from 1 • C warming with concomitant precipitation increases (3.2 million acres total, with 1.3 million acres in the North and 1.9 million acres in the South) amount to 1.1% of planted acreage.
This study follows the panel weather literature and looks at deviations of seasonal temperature over time. But it is important to note that some of the results are consistent with the hypothesis that extreme temperatures cause crop failure. Both spring and autumn temperatures have a U-shaped effect on crop failure. The marginal effect of warming on crop failures in the South is higher than in the North. Warmer summer temperatures are harmful. These are outcomes one would expect if extreme temperatures caused crop failure. The one result that is not consistent with the extreme temperature hypothesis is that summer temperatures have a hill-shaped effect rather than a U-shaped effect on crop failure.
Combining the results in the literature concerning climate impacts on yields per harvested acres and the results in this paper on crop failure rates (reduced harvested acres) suggest larger damages from warming than previously predicted. The yield studies found that a 1 • C increase in temperature would cause a 5%-7% drop in harvested yield per hectare of major crops in the United States [7]. Adding the expected crop failure rates from the results of this study, 3.2 million lost acres, would mean that the true effect of 1 • C warming would be a 6%-8% aggregate loss, with no adaptation. The effects in the North are slightly smaller with a 5.6%-6.6% loss, and the effects in South would be larger, with 7%-9% loss.
Future research could explore more temporally precise crop failure rates to discern exactly when crop failures occur and what weather preceded these events. This would help understand the precise effect of frosts, extreme hot days, and multiple consecutive hot days (heat waves).
Our study approached the issue of crop failures from a definition different from previous crop growth model studies; we analyzed failure to harvest, rather than a conspicuous drop in yield. While previous panel model studies on acreage reduction have been focused on an indirect measure of crop failure (harvest ratio), this study is the first to apply the framework to a direct measure of the event, as captured in the Census of Agriculture. The results of this study corroborate the findings from previous agronomic studies, and show that climate change will lead to more frequent crop failures.
This study assumes uniform changes in climate in order to illustrate the magnitude of future outcomes. Given that climate models predict different climate changes across the country and across seasons, the projections presented here are merely illustrative. Future research is needed to combine the response functions found in this paper with realistic climate projections from different General Circulation Models using different emission scenarios.
For some purposes such as crop insurance, it may be helpful to calculate failure rates by specific crops, as some crops may be more sensitive than others. Cropspecific failure modeling would also inform crop specific insurance premiums by county.
The analysis followed the panel weather literature and adopted a quadratic model of weather. Future research could explore more flexible functional forms such as fractional response models [31]. The model presented here simply measures the shortrun effect of weather on failure rates. In the long run as climate changes, farmers may be able to adapt to these risks and reduce these predicted failure rate. Of course, these adaptation might have other effects as well such as raising cost or lowering expected yield. These adaptations are not accounted for in this analysis. Recent advances disentangling long-run climate change effects from short-run effects could help address this shortcoming [32,33].

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.