Tuesday, March 10, 2015

Buying Conservation--For the Right Price

Erica Goode has an inspiring article about the benefits of conservation tillage, which has been gaining favor among farmers.  No-till farming can improve yields, lower costs, and improve the environment.  Just the kind of thing we all want to hear--everybody wins!

One important thing Goode doesn't mention: USDA has been subsidizing conservation tillage, and these subsidies have probably played an important role in spreading adoption.

Subsidizing conservation practices like no-till can be a little tricky.  After all, while this kind of thing has positive externalities, farmers presumably reap rewards too.  There are costs involved with undertaking something new. But once the practice is adopted and proven, there would seem to be little need for further subsidies.  The problem is that it can be difficult to take subsidies away once they've been established.

In practice, the costs and benefits of no till and other conservation practices vary.  Some of this has to do with the type of land.  No-till can be excellent for land in the Midwest with thick topsoil.  In the South, where topsoil is thin, maybe no so much.  So, for some farmers conservation practices are worthwhile; for others, the hassle may not be worth the illusive future benefits.  Ideally, policy would provide subsidies to the later, not the former.  But how do policy makers differentiate?  In practice, they don't; everybody gets the subsidies.

Can we do better? Together with some old colleagues at USDA, I've been thinking about this question for a long time, and we recently released a report (PDF) summarizing some of the most essential ideas (here's the Amber Waves short take).

In short, yes, we can do better.  The basic idea involves a form of price discrimination, implemented using augmented signup rules.  Sign ups for conservation programs operate like an auction: farmers submit offers for enrollment, offers are ranked nationally, and the best offers are selected.  The problem is that, when farmers compete on a national scale, farmers happy to do no-till conservation without any subsidies at all are pitted against farmers for whom the private benefits conservation tillage are dubious.  A lot of the subsides probably end up going to farmers who would do it anyway.

Alternatively, signups could impose a degree of local competition, such that the worst offers for any set of observable characteristics--say farms in a crop district with land of similar quality--would be rejected regardless of their national-level standing.  This kind of local competition would garner more competitive offers from no-till farmers who would use the practice even without subsidies.

It's difficult to tell how much more conservation we buy for the tax payer buck using these techniques.  We can't really know without testing the mechanisms on real signups. This is where real policy experiments could have a lot of added value.  Will USDA give it a try? Only time will tell...

Friday, February 20, 2015

For your weekend viewing pleasure

In case you somehow happened to miss yesterday's "Hadoop World Conference" in San Jose, we bring you the following video of GFEED's own Sol Hsiang -- who despite looking very sharp in his suit + earpiece/headset thingy, conspicuously fails to use the word "hadoop", and conspicuously fails to get introduced by Obama, as the speaker before him did.

Since Sol no longer posts, hopefully this video will at least partially sate loyal GFEED readers' desire for Hsiang-related blog activity.  Have a good weekend!

Monday, February 16, 2015

Siestas and climate change

Lately I’ve been thinking about siestas. And not just because of the extremely warm summer – I mean February – we are having in California. Taking an afternoon break is probably one of the oldest and most widespread adaptations humans have in the face of hot weather. Better to work hard in the morning and late afternoon when the heat is not too bad, and take a break when you would otherwise be unproductive. For example, I was never so willing to wake up at 4am as when I was doing field work in Sonora, Mexico in July – it meant I could get most of the day’s work done by lunch and not face the afternoon sun and heat. I can only guess that a similar strategy explains Max’s daily naps in his office, though Berkeley isn’t typically all that hot.

Although humans have widely adopted this practice, we don’t typically think of it as a strategy for how we grow crops. But various studies seem to suggest that the best way to adapt to extreme heat may be to have crops take a break. This can be done on two different time scales. In a day, we can select for crops that slow down growth during hours that are the hottest, and have the highest vapor pressure deficits. This avoids using water at the times when the efficiency of using water would be lowest. A nice recent review by Vincent Vadez and colleagues discusses some of the ways crop scientists are selecting for this trait. As I’ve mentioned in past posts, it’s a strategy we are trying to evaluate as a possible adaptation to climate change. It probably helps a little, but it’s not clear how much.

At longer time scales, it’s possible to just scrap the idea of growing a crop during the peak of the summer, and instead try to fit in two crops that straddle this period. This is the idea behind a recent paper we have led by my student, Chris Seifert, on double cropping trends and potentials in the US. Part of the challenge of double cropping is that it pushes the late summer crop (typically soybean) into greater risks of frost damage at the end of the season. But with warming temperatures, crops develop more quickly and the frost dates recede. This idea has been around for a while, but the idea of the paper was to simulate how much more viable the practice is actually becoming and will continue to become. 

The basic approach was to develop a realistic model of phenology for a wheat-soy double crop, and see how often the two crops can be squeezed in between the last frost of spring and the first frost of fall. Below is a summary of the projected suitability (% years of survival) for current and future conditions under two emission scenarios (top is low emissions, RCP4.5, and bottom is high emission, RCP8.5). The current simulated limits match pretty well where existence of double cropping extends in reality (roughly to the south of Illinois). But by mid-century the area suitable has shifted at least a full state northward, and by 2100 is roughly double or triple the current suitable area depending on emission. It’s also slightly interesting that really warm scenarios actually make this particular system less suitable in the South, because wheat can’t vernalize properly.

The other thing the paper looks at is whether warming has already encouraged a spread of double cropping. The data to look at double-cropping are pretty coarse in spatial resolution and short in time, but the trends do seem consistent with the simulated increase in suitability. For example, the figure below shows the fraction of reported double-cropping (red line) in states that historically have had frost limitations vs. the simulated suitability in those states for three different thresholds of survival (survival = soy maturing before first frost).

Just to be clear, this isn’t a definite gain relative to sticking with a single summer crop of corn or soybean. That would depend on prices and yields, both of which will also depend on what climate is doing. And even if it’s a gain, it could well still be worse than what could be achieved in the current climate with a single crop (for reasons we get into in the paper). Just like taking a siesta may make you more productive than if you didn’t, but not more productive than you’d be without the hot weather. But if nothing else it is an intriguing option that could make sense in a lot more places than it used to. And for many places it falls in the category of things that wouldn’t make much sense without climate change, because of the frost constraint, which I think is a key criterion for a truly effective adaptation.

Overall, maybe the lesson here is the corollary of what Marshall blogged about a few months ago. If we are learning that people’s response to heat is empirically not that different from crops, maybe it follows that strategies people have adopted to deal with heat can give us an idea of what might work well with crops. And maybe with all the heat lately – at least in the Western U.S. – people should start taking more siestas too. Max must just be testing out his adaptation strategy.

Wednesday, February 11, 2015

Measuring yields from space

[This post is co-written with Florence Kondylis at the World Bank, and a similar version was also posted over at the World Bank's Development Impact blog.]

One morning last August a number of economists, engineers, Silicon Valley players, donors, and policymakers met on the UC-Berkeley campus to discuss frontier topics in measuring development outcomes. The idea behind the event was not that economists could ask experts to create measurement tools they need, but instead that measurement scientists could tell economists about what was going on at the frontier of measuring development-related outcomes.  One topic that generated a lot of excitement -- likely due to David Lobell's charm at the podium -- was the potential for a new crop of satellites to remote-sense (i.e. measure) important development outcomes.

Why satellite-based remote sensing?
The potential ability to use satellites to measure common development outcomes of interest excites researchers and practitioners for a number of reasons, chief among them the amount of time and money we typically have to spend to measure these outcomes the “traditional” way (e.g. conducting surveys of households or firms).  Instead of writing large grants, spending days traveling to remote field sites, hiring and training enumerators, and dealing with inevitable survey hiccups, what if instead you could sit at home in your pajamas and, with a few clicks of a mouse, download the data you needed to study the impacts of a particular program or intervention?

The vision of this “remote-sensing” based approach to research is clearly intoxicating, and is being bolstered by the vast amount of high-resolution satellite imagery that is now being acquired and made available.  The recent rise of “nano-“ or “micro”-satellite technology – basically, fleets of cheap, small satellites that image the earth in high temporal and spatial resolution, such as those being deployed by our partner Skybox – could hold particular promise for measuring the types of outcomes that development folks often care about.  This is perhaps most obviously true in agriculture, where unlike in the manufacturing sector, most production takes place outside.

How does it work?
For most agricultural crops – particularly the staple crops grown by African smallholders, such as maize – pretty much anyone can look at a field and see the basic difference between a healthy highly productive crop and low-yielding crop that is nutrient or moisture stressed.  One main clue is color: healthy vegetation reflects and absorbs different wavelengths of light than less-healthy vegetation, which is why leaves on healthy maize plants look deep green and leaves on stressed or dead plants look brown.  Sensors on satellites can also discern these differences in the visual wavelengths, but they also measure differences at other wavelengths, and this turns out to be particularly useful for agriculture.  Healthy vegetation, in turns out, absorbs light in the visible spectrum and reflects strongly in the near infrared (which the human eye can’t see), and simple ratios of reflectance at these two wavelengths form the basis of most satellite-based measures of vegetative vigor – e.g. the familiar Normalized Difference Vegetation Index, or NDVI.   High ratios basically tell you that you’re looking at plants with a lot of big, healthy leaves.

The trick is then to be able to map these satellite-derived vegetation indices into measures of crop yields.  There are two basic approaches (see David's nice review article for more detail).  The first combines satellite vegetation indicies with on-farm yield observations as collected from the typical household or agricultural surveys.  By regressing the “true” survey-based yield measure on the satellite-based vegetation index, you get an estimated relationship between the two that can then be applied to other agricultural plots that you observe in the satellite data but did not survey on the ground.  The second approach combines the satellite data with pre-existing estimates of the relationship between final yield and vegetative vigor under various growing conditions (often as derived from a crop simulation model, which you can think of as an agronomist’s version of a structural model). Applying satellite reflectance measures to these relationships can then be used to estimate yield on a given plot.  A nice feature of this second approach is that it is often straightforward to account for the role of other time-varying factors (e.g. weather) that also affect the relationship between vegetation and final yield.

How well does it work?
These approaches have mainly been applied to larger farm plots in the developed and developing world, at least in part because until very recently the available satellite imagery was generally too coarse to resolve the very small plot sizes (e.g. less than half an acre) common in much of Africa.  For instance, the resolution of the MODIS sensor is 250m x 250m, meaning one pixel would cover more than 15 one-acre plots. Nevertheless, these approaches have been shown to work surprisingly well on these larger fields.  Below are two plots, both again from David and co-author's work, showing the relationship between predicted and observed yields for wheat in Northern Mexico, and maize (aka “corn”, for Americans) in the US Great Plains.   Average plot sizes in both cases are > 20 hectares, equivalent to at least 50 one-acre plots.

Top plot:  wheat yields in northern Mexico, from Lobell et al 2005.  Bottom plot:  corn yields in the US Great Plains, from Sibley et al 2014

Although success is somewhat in the eyes of the beholder here, the fit between observed and satellite-predicted yields is pretty good in both of these cases, with overall R2s of 0.63 in the US case and 0.78 in the Mexico case.  And, at least in both of these cases, the “ground truth” yield data was not actually used to construct the yield prediction – i.e. they are using the second approach described above.  This was possible in this setting because these were crops and growing conditions for which scientists have a good mechanistic understanding of how final yield relates to vegetative vigor.

From rich to poor, big to small
Applying these approaches much of the developing world (e.g. smallholder plots in Africa) has been harder.  This is not only because of the much smaller plot sizes, and thus the difficulty (impossibility, often) of resolving them in existing satellite imagery, but also because of a lack of either (i) ground truth data to develop the satellite-based predictions, and/or (ii) a satisfactory mechanistic understanding in these environments of how to map yields to reflectance measures.

New data sources from both the ground and sky are starting to make this possible.  Sensors on the new micro-satellites mentioned above often have sub-meter resolutions, meaning smallholder plots are now visible from space (a half-acre plot would be covered by over 2000 pixels).  Furthermore, this imagery is being acquired often enough to ensure at least a few cloud-free images during the growing season -- not a small problem in the rainy tropics.

Working with David and some collaborators in Kenya, Uganda, and Rwanda, we are linking this new imagery with ground-based yield data we are collecting to understand whether the satellite data can capably predict yields on heterogeneous smallholder plots.  Below is a map of some of the smallholder maize fields we have mapped and are tracking in Western Kenya, as part of an ongoing experiment with smallholder farmers in the region.

Locations of some plots we are tracking in Western Kenya

Some of the long run goals of this work are to (i) allow researchers who have already have information on plot boundaries and crop choice to use satellite images to estimate yields, and (ii) to allow researchers who do not have plot boundaries but who are interested in broader-scale agricultural performance (eg. at the village or district level) a way to track yields at that scale. This work is ongoing, but given the experience in developed countries, we are hopeful.

Some challenges.
Nevertheless, there are clear challenges to making this approach work at scale, and clear limitations (at least in the near term) to what this technology can provide.   Here are a few of the main challenges:

  1. Which boundaries and which crops. To measure outcomes at the level of the individual farm plot, satellite-based measures will be most easily employable if the researcher already knows the plot boundaries and knows what crop is being grown.   As satellite imagery improves and as computer vision algorithms are developed to remotely identify plot boundaries, both of these constraints will likely be relaxed, but the researcher will still need some ground information on which plots belong to whom. 
  2. Measurement error. Even with plot boundaries in hand, the fact that satellite imagery will not be able to perfectly predict yields means that using satellite-predicted yields as an outcome will likely reduce statistical power (although it’s not immediately clear how much noisier satellite estimates will be, given that survey based measures of these outcomes – e.g. from farmer self reports – are likely also measured with error.)  This almost certainly means that this technology will not be equipped to discern small effects in the smaller-sized ag RCTs that often get run.
  3. Moving beyond yield.  Finally, even with plot boundaries in hand and well-powered study, satellites are going to have a hard time measuring many of the other outcomes we care about – things like profits or consumption expenditure.  Satellites might in the near term be able to get at related outcomes such as assets (something we’re also working on), but it’s clearly going to be hard to observe most household expenditures directly. 

Putting these difficulties together, should we just abandon this whole satellite thing?  We think not, for two reasons.  The first reason is that as we (hopefully) improve our ability to accurately measure smallholder yields from space, this ability would provide a clear compliment to existing surveys.  For instance, if yields are a primary outcome, imagine just being able to do a baseline survey (where field boundaries are mapped) and then measure your outcome at follow-up from the sky.  This will make an entire study both faster and cheaper, which should allow for larger sample sizes, which will in turn help deal with the measurement error issue above.

Second, we still have a surprisingly poor understanding of why some farms, and some farmers, appear to be so much more productive than others.  Is it the case that relatively time-invariant factors like soil type and farmer ability explain most of the observed variation, or are time-varying factors like weather more important?  Satellite data might be particularly useful for this question (David's review paper, and his earlier G-FEED post, gives some really nice examples), because you can assemble huge samples of farm plots that can then be easily followed over time.  Satellite data in this setting therefore might afford more power, and you can do it all in your pajamas.

Tuesday, February 10, 2015

Crop Insurance and the Disincentive to Adapt to Extreme Heat

Francis Annan and I have a new paper that looks at US crop insurance and whether it gives farmers a disincentive to adapt to extreme heat.  The increased frequency of extreme heat under climate change is predicted to lower corn and soybean yields going forward.  Reducing the sensitivity to extreme heat would go a long way in avoiding some of the predicted damages, but there has been no observable progress in relative heat sensitivity over the last six decades. One possible explanation is that government policies bail out farmers and give them a disincentive to adapt.

The United States Federal Crop Insurance Program (FCIP) has gained tremendous momentum in recent decades and has become one of the major agricultural support program in the United States. Created in the 1930s, the crop insurance programs have undergone many developments through the revisions in various federal farm bills, acts, and assistance programs. The 1994 "Crop Insurance Reform Act" had the goal to eliminate annual disaster programs. It made participation in the insurance program mandatory to be eligible for disaster payments. This act implemented catastrophic (CAT) coverage to protect producers against major losses at no cost to producers. In recent years, legislative mandates have further increased the premium subsidy, in addition to the introduction of new insurance products. As a result the program has experienced tremendous growth in participation, especially following the 1994 act (Annan, Tack, Harri and Coble).

The fraction of total crop insurance premiums that is subsidized by the government greatly increased between 1981-2013, especially following the 1994 Crop Insurance Reform Act as shown in the following graph. Subsidy ratios increased from 20% in the early 1980s to 60% in recent years for both corn and soybeans.

The following figures show total planted area for corn and soybeans as solid lines, which has remained rather constant between 1981-2013.  The dashed line shows the planted area that is insured under the federal crop insurance program.  There is a large increase over time and by now almost all planted area is insured.

Did the increase in insured area increase the sensitivity to extreme heat?  We run a regression where we link log yields in a county on four weather variables: moderate heat, extreme heat and a quadratic in season-total precipitation (April-September). We also include county fixed effect, year fixed effects to pick up shifts in overall price levels or regulatory changes and county-specific quadratic time trends as there have been different warming trends across the US (Burke and Emerick). Finally, we interact the weather measures with the fraction of the area that is insured.  The results are given in the following table.

Columns (a) replicate the standard weather-yield relationship. We find that extreme heat has a harmful effect that is an order of magnitude larger than the beneficial effect of moderate heat.  The results also indicate am inverted-U-shape for precipitation that is comparable to previous results and implies an optimal amount for precipitation that is comparable to agronomic estimates. Columns (1b) and (2b) interact the weather-sensitivity of yields with the fraction of the area planted that is insured. The weather-sensitivity of an uninsured field is the coefficients on the weather variable, while the sensitivity of an insured field is the sum of the coefficient on the weather variable and the interaction term. We find that for both corn and soybeans, insured areas exhibit the same sensitivity to beneficial moderate heat, but are more sensitive to fluctuations in extreme heat.  The sensitivity to extreme heat is 67% larger for insured corn than for uninsured corn and 43% larger for insured soybeans than uninsured soybeans.

We conduct various sensitivity checks: The results are comparable whether we use a common quadratic time trend for all counties, a state-specific quadratic time trend, or the county-specific quadratic time trends.  Most importantly, the results are consistent whether we estimate them for the years 1981-2013, 1981-1996, or 1997-2013. Average subsidy rates in the first half are 27% but increase to 55% in the second half as the insured planted area increase from roughly one-fourth to three-fourth while the total planted area remains constant.  While insurance coverage is endogenous, our coefficients of interest interact it with exogenous weather variation. The interacted coefficients correctly identify the sensitivity of the insured field, however, it could be because insured fields are different (e.g., marginal land that is ensured has higher sensitivities), or because crop insurance gives a disincentive to reduce the damaging effects. We believe it is the latter: the heterogeneity story seems unlikely given that we account for county fixed effects, year fixed effects as well as county-specific time trends during a time period when insurance coverage greatly increases. The marginal decision on which areas to insure hence greatly changes over our study period.

Wednesday, January 28, 2015

Food Waste Delusions

A couple months ago the New York Times convened a conference "Food for Tomorrow: Farm Better. Eat Better. Feed the World."  Keynotes predictably included Mark Bittman and Michael Pollan.  It featured many food movement activists, famous chefs, and a whole lot of journalists. Folks talked about how we need to farm more sustainably, waste less food, eat more healthfully and get policies in place that stop subsidizing unhealthy food and instead subsidize healthy food like broccoli.

Sounds good, yes? If you're reading this, I gather you're familiar with the usual refrain of the food movement.  They rail against GMOs, large farms, processed foods, horrid conditions in confined livestock operations, and so on.  They rally in favor of small local farms who grow food organically, free-range antibiotic free livestock, diversified farms, etc.  These are yuppies who, like me, like to shop at Whole Foods and frequent farmers' markets.  

This has been a remarkably successful movement.  I love how easy it has become to find healthy good eats, bread with whole grains and less sugar, and the incredible variety and quality of fresh herbs, fruits, vegetables and meat.  Whole Paycheck Foods Market has proliferated and profited wildly.  Even Walmart is getting into the organic business, putting some competitive pressure on Whole Foods. (Shhhh! --organic isn't necessarily what people might think it is.)

This is all great stuff for rich people like us. And, of course, profits.  It's good for Bittman's and Pollan's book sales and speaking engagements.  But is any of this really helping to change the way food is produced and consumed by the world's 99%?  Is it making the world greener or more sustainable?  Will any of it help to feed the world in the face of climate change?

Um, no.  

Sadly, there were few experts in attendance that could shed scientific or pragmatic light on the issues.  And not a single economist or true policy wonk in sight. Come on guys, couldn't you have at least invited Ezra Klein or Brad Plummer?  These foodie journalists at least have some sense of incentives and policy. Better, of course, would be to have some real agricultural economists who actually know something about large-scale food production and policies around the world. Yeah, I know: BORING!

About agricultural polices: there are a lot of really bad ones, and replacing them with good policies might help.  But a lot less than you might think from listening to foodies.  And, um, we do subsidize broccoli and other vegetables, fruits, and nuts.  Just look at the water projects in the West. 

Let me briefly take on one issue du jour: food waste.  We throw away a heck of a lot of food in this country, even more than in other developed countries.  Why?  I'd argue that it's because food is incredibly cheap in this country relative to our incomes.  We are the world's bread basket.  No place can match California productivity in fruit, vegetables and nuts.  And no place can match the Midwest's productivity in grains and legumes.  All of this comes from remarkable coincidence of climate, geography and soils, combined with sophisticated technology and gigantic (subsidized) canal and irrigation systems in the West.  

Oh, we're fairly rich too.  

Put these two things together and, despite our waste, we consume more while spending less on food than any other country.  Isn't that a good thing?  Europeans presumably waste (a little) less because food is more scarce there, so people are more careful and less picky about what they eat. Maybe it isn't a coincidence that they're skinnier, too.

What to do? 

First, it's important to realize that there are benefits to food waste.  It basically means we get to eat very high quality food and can almost always find what we want where and when we want it.  That quality and convenience comes at a cost of waste.  That's what people are willing to pay for.  

If anything, the foodism probably accentuates preference for high quality, which in turn probably increases waste.  The food I see Mark Bittman prepare is absolutely lovely, and that's what I want.  Don't you?

Second, let's suppose we implemented a policy that would somehow eliminate a large portion of the waste.  What would happen?  Well, this would increase the supply of food even more.  And sinse we have so much already, and demand for food is very inelastic, prices would fall even lower than they are already.  And the temptation to substitute toward higher quality--and thus waste more food--would be greater still.  

Could the right policies help?  Well, maybe.  A little. The important thing here is to have a goal besides simply eliminating waste.  Waste itself isn't problem. It's not an externality like pollution.  That goal might be providing food for homeless or low income families.  Modest incentive payments plus tax breaks might entice more restaurants, grocery stores and others to give food that might be thrown out to people would benefit from it.  This kind of thing happens already and it probably could be done on a larger scale. Even so, we're still going to have a lot of waste, and that's not all bad. 

What about correcting the bad policies already in place?  Well, water projects in the West are mainly sunk costs.  That happened a long time ago, and water rights, as twisted as they may be, are more or less cemented in the complex legal history.   Today, traditional commodity program support mostly takes the form of subsidized crop insurance, which is likely causing some problems.  The biggest distortions could likely be corrected with simple, thoughtful policy tweaks, like charging higher insurance premiums to farmers who plant corn after corn instead of corn after soybeans.  But mostly it just hands cash (unjustly, perhaps) to farmers and landowners.  The odds that politicians will stop handing cash to farmers is about as likely as Senator James Inhofe embracing a huge carbon tax.  Not gonna happen.

But don't worry too much.  If food really does get scarce and prices spike, waste will diminish, because poorer hungry people will be less picky about what they eat.

Sorry for being so hard on the foodies.  While hearts and forks are in the right places, obviously I think most everything they say and write is naive.  Still, I think the movement might actually do some good.  I like to see people interested in food and paying more attention to agriculture.  Of course I like all the good eats.  And I think there are some almost reasonable things being said about what's healthy and not (sugar and too much red meat are bad), even if what's healthy has little to do with any coherent strategy for improving environmental quality or feeding the world.  

But perhaps the way to change things is to first get everyones' attention, and I think foodies are doing that better than I ever could.

Saturday, January 17, 2015

The Hottest Year Ever Recorded, But Not in the Corn Belt

Here's Justin Gillis in his usual fine reporting of climate issues, and the map below from NOAA, via the New York Times.

Note the "warming hole" over the Eastern U.S., especially the upper Midwest, the all important corn belt region.  We had a bumper crop this year, and that's because while most of the world was remarkably warm, the corn belt was remarkably cool, especially in summer.

Should we expect the good fortune to continue?  I honestly don't know...

Monday, January 12, 2015

Growth Effects, Climate Policy, and the Social Cost of Carbon (Guest post by Fran Moore)

Thanks to my thesis advisor (David) for this opportunity to write a guest post about a paper published today in Nature Climate Change by myself and my colleague at Stanford, Delavane Diaz. G-FEED readers might be familiar with a number of new empirical studies suggesting that climate change might affect not just economic output in a particular year, but the ability of the economy to grow. Two studies (here and here) find connections between higher temperatures and slower economic growth in poorer countries and Sol has a recent paper showing big effects of tropical cyclones on growth rates. Delavane and I simply take one of these empirical estimates and incorporate it into Nordhaus’ well-known DICE integrated assessment model (IAM) to see how optimal climate policy changes if growth-rates are affected by climate change.

The figure below shows why these growth effects are likely to be critical for climate policy. If a temperature shock (left) affects output, then there is a negative effect that year, but the economy rebounds the following year to produce no long-term effect. If growth rates are affected though, there is no rebound after the temperature shock and the economy is permanently smaller than it would otherwise be. So if temperature permanently increases (right), impacts to the growth rate accumulate over time to give very large impacts.

No IAMs so far have incorporated climate change impacts to economic growth. Of the three models used by the EPA to determine the social cost of carbon, two (PAGE and FUND) have completely exogenous growth rates. DICE is slightly more complicated because capital stocks are determined endogenously by the savings rate in the model. But any climate impacts on growth rates are very very small and indirect, so DICE growth rates are effectively exogenous.

We take the 2012 estimate by Dell, Jones and Olken (DJO) as our starting point and modify DICE in order to try and accurately incorporate their findings. We needed to make three major changes: firstly we split the global DICE model into two regions to represent developed and developing regions because DJO find big growth effects in poor countries but only modest effects in rich; secondly, we allowed temperature to directly affect growth rates by affecting either the growth in total factor productivity or the depreciation of capital, calibrating the model to DJO; and finally, since DJO estimates are the short-run impact of weather fluctuations, we explicitly allow for adaptation in order to get the response to long-term climate change (making some fairly optimistic assumptions about how quick and effective adaptation will be).

The headline result is given in the graph below that shows the welfare-maximizing emissions trajectory for our growth-effects model (blue) and for our two-region version of the standard DICE model (red). DICE-2R shows the classic “climate policy ramp” where mitigation is increased only very gradually, allowing emissions to peak around 2050 and warming of over 3°C by 2100. But our growth-effects model gives an optimal mitigation pathway that eliminates emissions in the very near future in order to stabilize global temperatures well below 2°C.

I think its worth just pointing out how difficult it is to get a model based on DICE to give a result like this. The “climate policy ramp” feature of DICE output is remarkably stable – lots of researchers have poked and prodded the various components of DICE without much result. Until now, the most widely discussed ways of getting DICE to recommend such rapid mitigation was either using a very low discount rate (a la Stern) or hypothetical, catastrophic damages at high temperatures (a la Weitzman). One of the main reasons I think our result is interesting is that it shows the climate policy ramp finding breaks down in the face of damages calibrated to empirical results at moderate temperatures, even including optimistic adaptation assumptions and standard discounting.

There are a bunch more analyses and some big caveats in the paper, but I won’t go into most of them here in the interests of space. One very important asterisk though is that the reason why poor countries are more sensitive to warming than rich countries has a critical impact on mitigation policy. If poorer countries are more vulnerable because they are poor (rather than because they are hot), then delaying mitigation to allow them time to develop could be better than rapid mitigation today. We show this question to be a big source of uncertainty and I think it’s an area where some empirical work to disentangle the effect of temperature and wealth in determining vulnerability could be pretty valuable.

I’ll just conclude with some quick thoughts that writing this paper has prompted about the connection between IAMs and the policy process. It does seem very surprising to me that these IAMs have been around for about 20 years and only now is the assumption of exogenous economic growth being questioned. Anyone with just a bit of intuition about how these models work would guess that growth-rate impacts would be hugely important (for instance, one of our reviewers called the results of this paper ‘obvious’), yet as far as I can tell the first paper to point out this sensitivity was just published in 2014 by Moyer et al.. This is not just an academic question because these models are used directly to inform the US government’s estimate of the social cost of carbon (SCC) and therefore to evaluate all kinds of climate and energy regulations. The EPA tried to capture possible uncertainties in its SCC report but didn’t include impacts to economic growth and so comes up with a distribution over the SCC that has to be too narrow: our estimate of the SCC in 2015 of $220 per ton CO2 is not only 6 times larger than the EPA’s preferred estimate of $37, but is almost twice the “worst case” estimate of $116 (based on the 95th percentile of the distribution). So clearly an important uncertainty has been missing, which seems a disservice both to climate impact science and to the policy process it seeks to inform. Hopefully that is starting to change.

So that’s the paper. Thanks again to the G-FEEDers for this opportunity and I’m happy to answer any questions in the comments or over email.
-Fran (fcmoore@stanford.edu)

Saturday, January 10, 2015

Searching for critical thresholds in temperature effects: some R code

If google scholar is any guide, my 2009 paper with Wolfram Schlenker on the nonlinear effects of temperature on crop outcomes has had more impact than anything else I've been involved with.

A funny thing about that paper: Many reference it, and often claim that they are using techniques that follow that paper.  But in the end, as far as I can tell, very few seem to actually have read through the finer details of that paper or try to implement the techniques in other settings.  Granted, people have done similar things that seem inspired by that paper, but not quite the same.  Either our explication was too ambiguous or people don't have the patience to fully carry out the technique, so they take shortcuts.  Here I'm going to try to make it easier for folks to do the real thing.

So, how does one go about estimating the relationship plotted in the graph above?

Here's the essential idea:  averaging temperatures over time or space can dilute or obscure the effect of extremes.  Still, we need to aggregate, because outcomes are not measured continuously over time and space.  In agriculture, we have annual yields at the county or larger geographic level.  So, there are two essential pieces: (1) estimating the full distribution of temperatures of exposure (crops, people, or whatever) and (2) fitting a curve through the whole distribution.

The first step involves constructing the distribution of weather. This was most of the hard work in that paper, but it has since become easier, in part because finely gridded daily weather is available (see PRISM) and in part because Wolfram has made some STATA code available.  Here I'm going to supplement Wolfram's code with a little bit of R code.  Maybe the other G-FEEDers can chime in and explain how to do this stuff more easily.

First step:  find some daily, gridded weather data.  The finer scale the better.  But keep in mind that data errors can cause serious attenuation bias.  For the lower 48 since 1981, the PRISM data above is very good.  Otherwise, you might have to do your own interpolation between weather stations.  If you do this, you'll want to take some care in dealing with moving weather stations, elevation and microclimatic variations.  Even better, cross-validate interpolation techniques by leaving one weather station out at a time and seeing how well the method works. Knowing the size of the measurement error can also help correcting bias.  Almost no one does this, probably because it's very time consuming... Again, be careful, as measurement error in weather data creates very serious problems (see here and here).

Second step:  estimate the distribution of temperatures over time and space from the gridded daily weather.  There are a few ways of doing this.  We've typically fit a sine curve between the minimum and maximum temperatures to approximate the time at each degree in each day in each grid, and then aggregate over grids in a county and over all days in the growing season.  Here are a couple R functions to help you do this:

# This function estimates time (in days) when temperature is
# between t0 and t1 using sine curve interpolation.  tMin and
# tMax are vectors of day minimum and maximum temperatures over
# range of interest.  The sum of time in the interval is returned.
# noGrids is number of grids in area aggregated, each of which 
# should have exactly the same number of days in tMin and tMax
days.in.range <- function( t0, t1 , tMin, tMax, noGrids )  {
  n <-  length(tMin)
  t0 <-  rep(t0, n)
  t1 <-  rep(t1, n)
  t0[t0 < tMin] <-  tMin[t0 < tMin]
  t1[t1 > tMax] <-  tMax[t1 > tMax]
  u <- function(z, ind) (z[ind] - tMin[ind])/(tMax[ind] - tMin[ind])  
  outside <-  t0 > tMax | t1 < tMin
  inside <-  !outside
  time.at.range <- ( 2/pi )*( asin(u(t1,inside)) - asin(u(t0,inside)) ) 
  return( sum(time.at.range)/noGrids ) 

# This function calculates all 1-degree temperature intervals for 
# a given row (fips-year combination).  Note that nested objects
# must be defined in the outer environment.
aFipsYear <- function(z){
  afips    = Trows$fips[z]
  ayear    = Trows$year[z]
  tempDat  = w[ w$fips == afips & w$year==ayear, ]
  Tvect = c()
  for ( k in 1:nT ) Tvect[k] = days.in.range(
              t0   = T[k]-0.5, 
              t1   = T[k]+0.5, 
              tMin = tempDat$tMin, 
              tMax = tempDat$tMax,
              noGrids = length( unique(tempDat$gridNumber) )

The first function estimates time in a temperature interval using the sine curve method.  The second function calls the first function, looping through a bunch of 1-degree temperature intervals, defined outside the function.  A nice thing about R is that you can be sloppy and write functions like this that use objects defined outside of the environment. A nice thing about writing the function this way is that it's amenable to easy parallel processing (look up 'foreach' and 'doParallel' packages).

Here are the objects defined outside the second function:

w       # weather data that includes a "fips" county ID, "gridNumber", "tMin" and "tMax".
        #   rows of w span all days, fips, years and grids being aggregated
tempDat #  pulls the particular fips/year of w being aggregated.
Trows   # = expand.grid( fips.index, year.index ), rows span the aggregated data set
T       # a vector of integer temperatures.  I'm approximating the distribution with 
        #   the time in each degree in the index T

To build a dataset call the second function above for each fips-year in Trows and rbind the results.

Third step:  To estimate a smooth function through the whole distribution of temperatures, you simply need to choose your functional form, linearize it, and then cross-multiply the design matrix with the temperature distribution.  For example, suppose you want to fit a cubic polynomial and your temperature bins that run from from 0 to 45 C.  The design matrix would be:

D = [    0          0          0   
            1          1           1
            2          4           8
           45     2025    91125]

These days, you might want to do something fancier than a basic polynomial, say a spline. It's up to you.  I really like restricted cubic splines, although they can over smooth around sharp kinks, which we may have in this case. We have found piecewise linear works best for predicting out of sample (hence all of our references to degree days).  If you want something really flexible, just make D and identity matrix, which effectively becomes a dummy variable for each temperature bin (the step function in the figure).  Whatever you choose, you will have a (T x K) design matrix, with K being the number of parameters in your functional form and T=46 (in this case) temperature bins. 

To get your covariates for your regression, simply cross multiply D by your frequency distribution.  Here's a simple example with restricted cubic splines:

DMat <- rcspline.eval(0:45)
XMat <- as.matrix(TemperatureData[,3:48])%*%DMat
fit <- lm(yield~XMat, data=regData)

Note that regData has the crop outcomes.  Also note that we generally include other covariates, like total precipitation during the season,  county fixed effects, time trends, etc.  All of that is pretty standard.  I'm leaving that out to focus on the nonlinear temperature bit. 

Anyway, I think this is a cool and fairly simple technique, even if some of the data management can be cumbersome.  I hope more people use it instead of just fitting to shares of days with each maximum or mean temperature, which is what most people following our work tend to do.  

In the end, all of this detail probably doesn't make a huge difference for predictions.  But it can make estimates more precise, and confidence intervals stronger.  And I think that precision also helps in pinning down mechanisms.  For example, I think this precision helped us to figure out that VPD and associated drought was a key factor underlying observed effects of extreme heat.

Monday, December 22, 2014

Prettiest pictures of 2014

The next person that says big data, puts a fiver in the "most overused terms in meetings in the year 2014" jar. I am excited about the opportunities of ever larger micro datasets, but even more thrilled by how much thought is going into the visualization of these datasets. One of my favorite macho nerd blogs Gizmodo just put up a number of the 2014 best data visualizations. If you also think that these are of so purdy, come take Sol's class at GSPP where he will teach you how to make graphs worthy of this brave new word.

Source: Gizmodo.