Nonlinear Temperature Effects Indicate Severe Damages to U.S. Crop Yields Under Climate Change

It's been a long haul, but my coauthor Wolfram Schlenker and I have finally published our article with the title of this blog post in the Proceedings of the National Academy of Sciences. We've been told that it would show up on the early-edition website this week. It hasn't shown up there yet so I guess it will come out tomorrow [Friday 8/28], probably late afternoon EST.

UPDATE: You can find the article here.

We set out to develop a better statistical model linking weather and U.S. crop yields for corn, soybeans and cotton, the largest three crops in the U.S. in production value. Our major new finding is that (by far) the best predictor of yield is a measure of extreme heat: how much temperatures exceed about 29C (84F) during the growing season. The threshold varies somewhat by crop--29C is the threshold for corn. Below this threshold, warmer temperatures are more beneficial for yields, but the damaging effects of temperatures much above 29C are staggeringly large.

A good measure extreme heat is degree days above 29C. This is calculated as (Degrees Above 29C x Days) summed up for all time (including fractions of days) at each temperature above 29C. The more degree days above 29C, the lower are corn yields. Historically, average degree days above 29C during the growing season were about 57. Under the slow warming scenario (we cut emissions to 50 percent of 1991 levels by 2050) this number is projected to rise to 194 by 2070-2099 and corn yields are estimated to decline by 46 percent. Under the fast-warming (business as usual) scenario, degree days above 29C are projected to increase to about 413, and estimated corn yields decline 82 percent.

To measure degree days precisely we had to carefully account for variation in temperatures over time and space. This contrasts with earlier studies that compare yields to average weather outcomes. The problem with averages is that they dilute nonlinearities--effects of the extremes--which are clearly important for crop growth and yield. So, our study begins by accounting for entire temperature distribution between each day's minimum and maximum and across all days in the growing season. We also develop fine scale estimates over space and consider only areas devoted to agricultural production.

We're going to make this weather data set (it's huge--some 300G unzipped and reshaped) publicly available for all to use very soon. Look for a link on my website or Wolfram's in a day or two.

These technical data issues are important because maximum temperatures often exceed 29C during the day, while the daily average hardly ever does. As a result, previous studies tend to make extreme heat appear less important than it is in reality.

Of course things vary a lot by location. The above numbers are area-weighted averages. For some visual perspective, see this earlier post where I show a plot for Indiana.

When we look at potential implications for climate change, two things are troubling: First, as described above, the amount temperatures are expected to exceed 29C is predicted to increase rapidly. Second, somewhat surprisingly, we find no evidence that farmers in the warmer south have been successful in adapting to the higher frequency of temperatures above 29C. This is troublesome as we hoped to learn from warmer regions how farmers might adapt to more frequent temperature extremes. But we can't find any evidence that farmers in the south are any better at dealing with extreme temperatures than farmers in the north, even though they experience the extremes more often. This is not to say farmers or seed companies won't discover new varieties or techniques to deal with extreme heat later this century, but it casts some doubt that such change can be easilyachieved.

These big estimated impacts are important because the U.S. is by far the largest producer and exporter of agricultural commodities. This is especially true for corn and soybeans, which are two out of the world's four most important staples (the other two are wheat and rice). If U.S. yields go down a lot, it drives up prices of staple food commodities all around the world. Almost surely the poor in other parts of the world, particularly developing countries that import food, would suffer far more than the U.S. would.

There are three major caveats: (1) CO2 fertilization may offset some of these negative effects--something still under significant debate; (2) Seed companies (Monsanto) might develop more heat tolerant crops in the future (but we find little evidence of adaptation in the past); and (3) Farmers will be able to offset some of the losses by shifting where they grow different kinds of crops.

To my mind, what this study makes very clear is that the worldwide face of agriculture is going to change dramatically. Even in the best-case scenario, in which losses in areas like the U.S. are made up with gains elsewhere, we will see different crops cultivated all around the world.

But with projected damages this large for the world's biggest bread basket, no clear evidence of adaptation to warmer temperatures in the historical data, and with projections already rather dismal for much of tropics and subtropics, at present I don't know why we should be particularly optimistic.

Below is the abstract and summary of major results.


The United States produces 41% of the world's corn and 38% of the world's soybeans. These crops comprise two of the four largest sources of caloric energy produced and are thus critical for world food supply. We pair a panel of county-level yields for these two crops plus cotton (a warmer-weather crop) with a new fine-scale weather data set that incorporates the whole distribution of temperatures within each day and across all days in the growing season. We find yields increase with temperature until about 29±C for corn, 30±C for soybeans, and 32±C for cotton, but temperatures above these thresholds are very harmful. The slope of the decline above the optimum is significantly steeper than the incline below it. The same nonlinear and asymmetric relationship is found when we isolate either time-series or cross-sectional variations in temperatures and yields. This suggests limited historical adaptation of seed varieties or management practices to warmer temperatures because the cross-section includes farmers' adaptations to warmer climates and the time-series does not. Holding current growing regions fixed, area-weighted average yields are predicted to decrease by 30-46% before the end of the century under the slowest (B1) warming scenario and decrease by 63-82% under the most rapid warming scenario (A1FI) under the Hadley III model.

A summary of most of the major results:

1) Yield growth increases gradually with temperature up to 29-32 degrees Celsius, depending on the crop, and then decrease sharply for all three crops. We're simultaneously controlling for precipitation, soils, and many other factors. Here's the key figure showing the relationship together with the current temperature distributions for these crops (click for higher resolution):

2) Holding current growing regions fixed, area-weighted average yields are predicted to decrease by 30-46% before the end of the century (2070-2099) under the slowest Hadley III warming scenario B1 ( a slow-warming scenario that supposes we cut back sharply on CO2 emissions in the near future), and decline by 63-82% under the most rapid warming scenario A1FI (a business-as-usual scenario wherein CO2 emissions continue to grow as currently projected). Note that the Hadley III model does predict sharp increases in extremely warm temperatures. Losses could be different for other climate change models. Hadley III is the climate model used by the IPCC in their most recent report. Short run impacts (2020-2049) are pretty big too. The figures below summarize impacts across statistical models and climate change scenarios (click for larger image).

3) Our statistical model predicts out-of-sample actual yields much better than previous statistical models, about 40% better for cotton and over 300% better for corn and soybeans.

4) The same distinctive nonlinear relationship between yields and temperature is observed in both the pure cross-section of counties (average yield in comparison to average temperature distribution) and the aggregate year-to-year time series. We find this result particularly remarkable since underlying comparisons ("sources of identification" in econometric jargon) are so different and the time-series serves as one of most viable natural experiments available to economists. Since the cross-sectional comparisons account for farmers' adaptive responses to differing climates and the times series does not, this finding strongly suggests farmers in warmer southern climates haven't been able to adjust their management practices to offset the damaging effects of extreme heat.

5) The nonlinear relationship between yield and temperature observed in cooler northern states is similar to the one observed in warmer southern states.

6) The nonlinear relationship between yield and temperature observed between 1950 and 1977 was the same as the one observed between 1978 and 2005. This result suggests that these crops have not become more heat tolerant over time. Despite this, we acknowledge that seed companies may breed or engineer more heat tolerant plants in the future.

Note that we have done some more recent research (not yet published--see the link to the Indiana graph above) that does show some more interesting variation in heat tolerance over time. The likely reason this does not show up in our PNAS study is that the Indiana study looks much further back in time. Since heat tolerance appears to have first increased and then decreased over a relatively short span of time, average heat tolerance in the first half of our PNAS sample is actually quite similar to the latter half. Such are the annoyances of publication lag...

Monsanto claims to have developed more heat tolerant corn, but we have not seen to data to verify this claim. To us right now (yes, this is speculative and not in the paper), it looks like there is a tradeoff between heat tolerance and yield potential. That is, more heat tolerant corn could have lower yields in both very hot and more temperate years.

7) Greater precipitation partially mitigates damages from extremely high temperatures. This suggests areas with access to plenty of inexpensive irrigation water should be able to cope with extreme temperatures better than areas without irrigation. How much irrigation water will be available is less clear and surely depends on location--this is not something we investigated.

Please see the paper and the (long) supplement for more details. Sorry, we didn't feel like paying the extra $1000 to make the article freely available (ungated) immediately. It's now available to academics and should be freely available to everyone else soon enough (6 months, I think). You can also find a lot of detail in our NBER working paper. Email me if you want a copy the paper and supplement and I'll send you one within a day or two.


  1. Yes, at least for now it looks like GMO-ing is a zero-sum game trading off yields for other resilient proteins structures. Hopefully will be more powerful later this century.

    I'm coming to the realizing cheap electricity can be a surrogate in the future if rainfall or aquifers aren't optimal for irrigation. Powering directly the creation of clean water and powering controlled environment harvests, potentially growing grains like hotohuse tomatoes. Very speculative.

  2. Great research - love your approach and the conclusions are frightening (but better that we know, and have our eyes wide open).

    One other mitigating factor I can imagine is longer growing seasons - any idea how much this could counterbalance the fall in yields? (probably not much, just curious)

  3. R,

    Thanks for your comment and good questions.

    We did investigate adjusting growing seasons by moving everything back one month (see the supplement). This does offset damages a little (I recall about about 10 percentage points in the long-run worst-case scenario, but see the supplement for a precise number). We were wary about moving things much earlier since the sunlight and sun orientation would shift so much and the the model implicitly holds these fixed.

  4. Thanks Michael, the extensive explanations are very clear. I have attributed improved robustness of crop yields to rainfall and soil quality variation to seed improvements over time, and figured the same was true for temperature variations as well - clearly (now) not! Have you done any work that would net out adaptation actions - allowing the growing regions to shift - and predicting the total impact on crop production? -- jeff hopkins

  5. Hey Jeff,

    Thanks for your note. We haven't tried to predict changing cropping areas because to do that we think it's critical to model prices. Which means modeling supply and demand for the whole world. And also means evaluating climate change impacts for the whole world.

    Yeah, it's an iddie bit ambitious.

    But we are actually moving in that direction. Slowly but surely...

  6. Interesting glance on the subject, I wasn`t aware of so much problems considering this.


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