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.

ABSTRACT

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.

Leakage from Carbon Offsets

As I've described in some of my earlier posts [1, 2, 3], there is a big problem with CO2 cap-and-trade policy that counts carbon from fossil fuels but does not count carbon from forestry and agriculture. The problem is fossil fuels will be replaced by other energy sources, like biofuels, that can affect the carbon balance in powerful and sometimes indirect ways. For example, biofuel consumption will be derived from land. This ultimately puts pressure on prices of agricultural commodities. Higher commodity prices leads to more crop production and higher crop production ultimately comes from deforestation.

It's hard to tell how large this problem may be. But the fact that 20 percent of carbon emissions come from deforestation suggests it could matter a lot.

Right now alternative sources of carbon sequestrations and emissions are being targeted by carbon offsets. If you feel guilty about burning fossil fuels you can go to places like TerraPass.com or www.Carbonfund.org to buy offsets for your emissions. Carbon offsets are also playing a big role in the Waxan-Markey bill. But leakage, the problem I described yesterday that did not make it into an otherwise wonderful NY Times article, makes these offsets smaller than you probably think.

So how much do offsets actually influence the carbon balance?

Here's a rough calculation based on some of my current research with Wolfram Schlenker. (This is a bit wonkish.)

Our research finds that worldwide demand for the world's four most important crops, wheat, rice, corn and soybeans, is highly inelastic. Our estimated demand elasticity is -0.05. This means prices need to double to get the world to reduce consumption by 5 percent. Our estimated supply elasticity is about 0.1. This means the farmers of the world will produce about 10 percent more if prices double. We find that basically all the supply response comes from expansion of crop area as opposed to greater production per acre.

A big assumption I'm going to make is that cropland expansion ultimately comes from deforestation. It may be that some new cropland comes from range or pasture and then the lost pastureland and rangeland is replace by deforestation. There's nothing about our study that makes these particular links explicit, but at present I don't believe it's far from the truth. I'm making lots of other small implicit assumptions but it's too much to get into in a blog post.

The figure below shows how to connect demand and supply to the amount of "leakage" in carbon offset policies. Leakage increases as the size of the supply elasticity increases relative to the size of the demand elasticity. With a supply elasticity about twice as large as demand, the amount of leakage is about two-thirds. That is, for every 3 acres of forestland preserved (prevented from switching to crops), 2 acres are deforested somewhere else. That's about what's drawn in the figure (but in reality both curves are steeper and the price increase is much greater).
So you need to buy about three times as much offsets as you think you do to be truly carbon neutral.

Yes, I'm making tons of assumptions and extrapolating big time. But based on what I know now I think this estimate is a reasonable one.

The carbon offset organizations say they account for leakage. I'm more than a little skeptical. The problem is the that leakage can occur on the other side of the planet from where the offsets happen. And if one carbon offset company doesn't account for leakage (a very hard thing to do) then its carbon offsets will be cheaper, which kind of mucks up incentives for the other companies to account for leakage.

Update: Here is a link to a rough draft of our research that estimates the elasticities. The paper does not look at leakage but I think the next draft will. I rounded the numbers a bit for simplicity.

Note also that there are some kinds of carbon offsets that probably wouldn't have much of a leakage problem. Like paying farmers to control methane emissions from livestock (yeah, it's what you think it is). But I think offset potential for everything besides [preventing] deforestation is small potatoes.

On the front lines of carbon offsets

A really nice article in the New York Times about paying Brazilian farmers to not clear forests and plant soybeans.

QUERENCIA, Brazil — José Marcolini, a farmer here, has a permit from the Brazilian government to raze 12,500 acres of rain forest this year to create highly profitable new soy fields....

Mr. Marcolini says he cares about the environment. But he also has a family to feed, and he is dubious that the group’s initial offer in the negotiation — $12 per acre, per year — is enough for him to accept.

“For me to resist the pressure, surrounded by soybeans, I’ll have to be paid — a lot,” said Mr. Marcolini, 53, noting that cleared farmland here in the state of Mato Grosso sells for up to $1,300 an acre.

....Deforestation, a critical contributor to climate change, effectively accounts for 20 percent of the world’s carbon dioxide emissions and 70 percent of the emissions in Brazil. Halting new deforestation, experts say, is as powerful a way to combat warming as closing the world’s coal plants.

But until now, there has been no financial reward for keeping forest standing. Which is why a growing number of scientists, politicians and environmentalists argue that cash payments — like that offered to Mr. Marcolini — are the only way to end tropical forest destruction and provide a game-changing strategy in efforts to limit global warming...

Both the most recent draft of the agreement and the climate bill passed by the House in late June in the United States include plans for rich countries and companies to pay the poor to preserve their forests.

The payment strategies may include direct payments to landowners to keep forests standing, as well as indirect subsidies, like higher prices for beef and soy that are produced without resorting to clear-cutting.

...But getting the cash incentives right is a complex and uncharted business.

...Brazil and Indonesia lead the world in the extent of their rain forests lost each year. The forests are felled to help feed the world’s growing population and meet its growing appetite for meat. Much of Brazil’s soy is bought by American-based companies like Cargill or Archer Daniels Midland and used to feed cows as far away as Europe and China. In Indonesia, rain forests are felled to plant palms for the palm oil, which is a component of biofuels.

...Last year, with a grant from Norway that could bring the country $1 billion, it created an Amazon Fund to help communities maintain their forest. National laws stipulate that 80 percent of every tract in the upper Amazon — and 50 percent in more developed regions — must remain forested, but it is a vast territory with little law enforcement. Soy exporters officially have a moratorium on using product from newly deforested land.

I have a hard time seeing how U.S. farmers can do much carbon offsetting. But it's a different story for places like Brazil and Indonesia.

But carbon offsets like this raise lots of difficult (and interesting) economic questions. Even if Mr. Marcolini takes $12/acre to preserve his forest, and preservation is somehow perfectly enforced, what's to prevent him or someone else from plowing down a forest of the same size somewhere else? Restricting deforestation on the fringe just pushes commodity prices higher and encourages more deforestation. This problem, called "leakage" or "slippage" in policy and academic circles, is the key issue not raised by the NY Times article.

I cannot envision how to prevent leakage of offsets without taking a more comprehensive approach. For this kind of thing to work we need to count, and put a price on, ALL the carbon.

Cash for Clunkers: A good natural experiment for measuring effects of air pollution?

Okay, I know everyone, including me, has complained about C4C not providing all that much in terms of CO2 abatement. But there must be a fair amount of other pollution benefits, like reductions in NOx, SOx, and CO, all of which have reasonably well-measured negative externalities, like infant mortality and asthma.

Another benefit could be for researchers. This seems like a decent natural experiment for looking at effects of air pollution. In at least in some parts of the country this must have reduced air pollution by a measurable amount. It helps that the program was implemented so quickly and during the more-polluted summer months. It looks like all $3 billion (or more) will be spent by Monday. There have been a few air pollution natural experiments in recent years but there must be room for another.

Alternatively, it shouldn't be too hard to calculate air pollution differences based on what we know about the cars clunked and bought under the program. Couple that and/or measured differences with earlier studies on the effects of air pollution on mortality, asthma, and other ailments, and we'd have the makings of a nice benefit analysis. Sans stimulus, of course (GM says they are ramping up production).

Aside: how does one do welfare analysis of stimulus effects anyway? This may be a stupid question, partly a product of my not being a macroeconomist. If anyone who reads this knows where I should look I'd be interested in learning about it.

More on Cash for Clunkers

Max Auffhammer writes to keep me current on Cash for Clunkers. (Thanks Max!)

Mathew Kahn does his own back-of-the envelope calculation.

And Christopher Knittel does more than a back-of-the-envelope calculation.

I think my calculations, though stated a little different, are very much in a ballpark of what these guys found. That's kind of cool because I threw those numbers together pretty quickly. Given that, I think I'll gloat a little: I beat these guys by a week!

Camp Resources (aka: boot camp for budding environmental economists"

I'm in beautiful Asheville, NC listening and watching to a bunch of interesting papers, mostly given by graduate students. Here's the program.

When located in places like Asheville I wish they could figure out a way to do these things outside.

It was tough getting in to the boot camp this year: only 20% of proposed papers were accepted.

Hopefully I'll write a little more about what I've learned a little later.

Don't count out ethanol yet

Mark Thoma points us to a nice article concisely summarizing how "reality pricked ethanol's bubble."

I'm not a big fan of ethanol policy. But don't count out ethanol when oil is trading at $75 and corn and natural gas (which is key for fertilizer prices) remain cheap. If world demand recovers as markets are now speculating, we'll be seeing more ethanol, even without additional government mandates.

Carbon from clunkers: A back of the envelope calculation

According to preliminary data from the Cash for Clunkers program, the average car clunked had MPG of 15.8 and these were replaced with cars with 25.4 MPG. Let's say a typical driver drives 15,000 miles/year. That amounts to nominal savings of 15000/15.8 - 15000/25.4 = 358.8 gals./year.

According to the EPA, each gallon of gas burned creates 19.4 pounds of CO2. So the nominal annual savings in carbon emissions is about 3.5 tons of CO2.

Approximating actual carbon savings is a lot more difficult. Among other things, we need to consider (a) how long the clunked car would have remained on the road were it not clunked; (b) the car the buyer would have bought had he/she not been enticed with subsidies into buying a higher-mileage vehicle; (c) when he/she would have bought that other car; (d) whether buying a new higher-MPG car causes the buyer to drive more.

These are difficult issues and I don't have hard data to answer them. So it goes--this is a back-of-the-envelope calculation.

The assumptions:

First I'm going to assume that the total fleet size does not change. Each car clunked is going to be replaced by a new car that can easily be produced using the excess car manufacturing capacity currently available.

Second, I'm going to assume that people are not generally going to drive more as a result of the Cash for Clunkers program. While I do expect the newly purchased vehicles will be driven more than the cars clunked, the difference will be made up by fewer miles driven on other less-used cars. I'm going to assume that these fewer miles will be evenly distributed across other cars in the fleet. Furthermore, I'm going to assume that other cars in the fleet have average 20 MPG, which lies about halfway between the clunkers and the new cars replacing the clunkers.

Third, I'm going to assume each car clunked would have remained in use for another five years. I don't have a good justification for this number. It just seems about right to me.

Fourth, I'm going to assume (b) and (c) are a wash. That is, I'm going to assume that the $3500-$4500 incentive to buy a higher mileage vehicle just offsets the general increase in MPG that occurs over time as CAFE standards rise and technology improves. So I'm assuming each car purchased under the Cash-for-Clunkers program has the same mileage as the car that would have bought at some future point in time.

Fifth, I'm going to assume that of the 15000 miles that is about the typical distance driven in a new car, about 10000 miles come from the car clunked and 5000 miles come from another 20 MPG cars that the buyer may have access to.

I think these assumptions imply that each car clunked saves about

5 x 19.4 x (5000/20 - 5000/25.4 + 10000/15.8 - 10000/25.4) = 28,359 lbs of carbon

So, each car clunked saves about 14 tons of CO2.

What's a ton of carbon worth? That's another hard question. The current offset price, which is probably a lot less than the social value, is in the ballpark of $4/ton. High-end estimates of the value appear to be around $100/ton, which would put the social value at about $1400 per car.

Of course, there are other kinds of pollution savings besides CO2 and I'm not counting those. The social vlaue could be larger.

And this is a rough calculation. Please write a comment about any assumptions or calculations that may be way off the mark.

But right now it looks to me like Cash for Clunkers wouldn't be an especially good deal in normal-economy times. But the stimulus effects of the program might easily tilt the balance in current lousy-economy times. It sure beats digging holes and filling them up.

Update: Cash for Clunkers is over now. But these calculations, similar calculations by others, and arguments made by Brad Delong, Jim Hamilton, and others, have convinced me C4C was far less than ideal. The biggest benefit was the stimulus and that seemed to work reasonably well. To some extent, the verdict on stimulus is still out: it will be interesting to see if car sales are sustained now that the program is over. But I don't see how destroying the clunkers could have been socially beneficial.

News isn't information. It's about inciting conflict.

Funny and sad post from Paul Krugman today:

Long ago I said that if liberals said the Earth was round, while conservatives said it was flat, the news headlines would read “Shape of the planet: both sides have a point.” But I encountered a new wrinkle today.

I was tentatively scheduled to be on a broadcast dealing with — well, I won’t embarrass them. But first they had to find someone to take the opposite view. And it turned out that they couldn’t — which led to canceling the whole segment.

In a way this goes beyond my original point, which was the unwillingness of the news media to referee a controversy by actually reporting the facts. Now it seems that a fact isn’t worth reporting unless someone is prepared to deny it.

Okay, everyone likes to complain about the media and all of its biases. Journalists I know in DC take offense at this line of attack, and rightly so, because most journalists don't let personal agendas into their reporting.

Unless it sells.

And that's the point. Journalists are selling a product. Like all salesmen, they adjust their pitch to whatever sells best. If they don't adjust they'll lose their job.

What sells best, unfortunately, is inciting conflict. The beauty is that they can do this and appear objective using the standard he-said/she-said approach. If the facts come down squarely on one side, reporting it that way is less interesting and makes reporters vulnerable to claims of bias.

Another unfortunate fact is that genuine ambiguity is uncomfortable for most audiences. Most prefer salacious conspiracy theories and political horse races over underlying intellectual challenges. While some can present information about difficult tradeoffs in a captivating way, it's a hard thing to do.

The end result of all this is that we have media (most of it anyway) reporting on political conflict and popularity contests but precious little about the underlying issues. Key facts are often never presented and the analysis, well, usually there isn't any.

Who's to blame? We the people get the news we deserve. If you don't like it (or even if you do but know it's wrong and socially destructive) then don't watch it or read it.

Is cash for clunkers like paying farmers to plow up perfectly good crops?

Jim Hamilton over at econbrowser doesn't like cash for clunkers. He compares the policy to the Agricultural Adjustment Act of 1933, which paid farmers to slaughter livestock and plow up perfectly good crops.

It does seems strange to destroy perfectly useful capital. But destroying old and polluting capital (clunkers) can be a bit different than destroying nondurable goods like crops. It's different because old cars pollute more than new cars and because this is an unusual time when a lot of excess car production capacity sits idle. If destroying a few clunkers causes idle factories and labor to be put to good use producing new less-polluting cars, then there could be a genuine social benefit. Indeed, it would seem that, as a first approximation, each clunker clunked would be replaced by a new car produced using resources that would otherwise be sitting idle. Since each new car created clearly embodies more social value than each car destroyed, it doesn't seem such a bad deal. And I'm not even counting multiplier effects.

But I do concur with Professor Hamilton's assessment of the Agricultural Adjustment Act of 1933. Destroying crops and livestock didn't stimulate new demand or otherwise put people back to work. It just raised prices by shifting supply inward, which made matters worse.

A key difference is that the short-run supply curve for agricultural goods is almost vertical due to scarcity of viable cropland while the supply curve for cars is flat, especially when there is a lot of excess capacity.

Update:From bloomberg:

Vehicles to be scrapped under the cash for clunkers, aimed at boosting U.S. new car sales, averaged 15.8 miles per gallon, compared with 25.4 miles per gallon for the new vehicles purchased, according to Transportation Department data.

...As of today, the Transportation Department had received about 157,000 dealer applications for funds totaling $664 million, as the agency works through a backlog that reached hundreds of thousands of online submissions, LaHood told reporters today.

So about 73% are going for the $4500 credit for a 10 MPG increase over the $3500 for a 4 MPG increase. Most people seem to be trading their SUVs for fuel-efficient sedans.

Why would Libertarians attack Michael Pollan?

There are things I like and things I don't like about Michael Pollan's influential books. On balance, I think there is more to like about them than not. But I certainly don't see Michael Pollan as anti-Libertarian. In fact, I find his writing sympathetic toward Libertarian views. He advocates individuals to make better food choices. And he sees government regulation as a key problem with our food system, not a solution.

Anyway, it just surprised me to see the title "Libertarians Attack Michael Pollan." After reading the article, which is good, I wondered if its title may be a little misleading. It's not so hard to see why a hyperbolic farmer might be a little unhappy with Pollan's writings. While I'm no Libertarian, I also kind of wonder whether most would identify with today's American Enterprise Institute.