Fixed Effects Infatuation

The fashionable thing to do in applied econometrics, going on 15 years or so, is to find a gigantic panel data set, come up with a cute question about whether some variable x causes another variable y, and test this hypothesis by running a regression of y on x plus a huge number of fixed effects to control for "unobserved heterogeneity" or deal with "omitted variable bias."  I've done a fair amount of work like this myself. The standard model is:

y_i,t = x_i,t + a_i + b_t + u_i,t

where a_i are fixed effects that span the cross section, b_t are fixed effects that span the time series, and u_i,t is the model error, which we hope is not associated with the causal variable x_i,t  conditional on a_i and b_t.

If you're really clever, you can find geographic or other kinds of groupings of individuals, like counties, and include group-by-year fixed effects:

y_i,t = x_i,t + a_i + b_g,t + u_i,t

The generalizable point of my lengthy post the other day on storage and agricultural impacts of climate change, was that this approach, while useful in some contexts, can have some big drawbacks. Increasingly, I fear applied econometricians misuse it.  They found their hammer and now everything is a nail.

What's wrong with fixed effects? 

A practical problem with fixed effects gone wild is that they generally purge the data set of most variation.  This may be useful if you hope to isolate some interesting localized variation that you can argue is exogenous.  But if the most interesting variation derives from a broader phenomenon, then there may be too little variation left over to identify an interesting effect.

A corollary to this point is that fixed effects tend to exaggerate attenuation bias of measurement errors since they will comprise a much larger share of the overall variation in x after fixed effects have been removed.

But there is a more fundamental problem.  To see this, take a step back and think generically about economics.  In economics, almost everything affects everything else, via prices and other kinds of costs and benefits.  Micro incentives affect choices, and those choices add up to affect prices, cost and benefits more broadly, and thus help to organize the ordinary business of life.  That's the essence of Adam's Smith's "invisible hand," supply and demand, and equilibrium theory, etc.  That insight, a unifying theoretical theme if there is one in economics, implies a fundamental connectedness of human activities over time and space.   It's not just that there are unobserved correlated factors; everything literally affects everything else.  On some level it's what connects us to ecologists, although some ecologists may be loath to admit an affinity with economics.

In contrast to the nature of economics, regression with fixed effects is a tool designed for experiments with repeated measures.  Heterogeneous observational units get different treatments, and they might be mutually affected by some outside factor, but the observational units don't affect each other.  They are, by assumption, siloed, at least with respect to consequences of the treatment (whatever your x is).  This design doesn't seem well suited to many kinds of observational data.

I'll put it another way.  Suppose your (hopefully) exogenous variable of choice is x, and x causes z, and then both x and z affect y.  Further, suppose the effects of x on z spill outside of the confines of your fixed-effects units.  Even if fixed effects don't purge all the variation in x, they may purge much of the path going from x to z and z to y, thereby biasing the reduced form link between x and y. In other words, fixed effects are endogenous.

None of this is to say that fixed effects, with careful account of correlated unobserved factors, can be very useful in many settings.  But the inferences we draw may be very limited.  And without care, we may draw conclusions that are very misleading. 

Can crop rotations cure dead zones?

It is now fairly well documented that much of the water quality problems leading to the infamous "dead zone" in the Gulf of Mexico (pictured above) come from fertilizer applications on corn. Fertilizer on corn is probably a big part of similar challenges in the Chesapeake Bay and Great Lakes.

This is a tough problem.  The Pigouvian solution---taxing fertilizer runoff, or possibly just fertilizer---would help.  But we can't forget that fertilizer is the main source of large crop productivity gains over the last 75 years, gains that have fed the world.  It's hard to see how even a large fertilizer tax would much reduce fertilizer applications on any given acre of corn.

However, one way to boost crop yields and reduce fertilizer applications is to rotate crops. Corn-soybean rotations are most ubiquitous, as soybean fixes nitrogen in the soil which reduces need for applications on subsequent corn plantings.  Rotation also reduces pest problems.  The yield boost on both crops is remarkable.  More rotation would means less corn, and less fertilizer applied to remaining corn, at least in comparison to planting corn after corn, which still happens a fair amount.

I've got a new paper (actually, an old but newly revised), coauthored with Mike Livingston of USDA and Yue Zhang, a graduate student at NCSU, that might provide a useful take on this issue.  This paper has taken forever.  We've solved a fairly complex stochastic dynamic model that takes the variability of prices, yields and agronomic benefits of rotation into account. It's calibrated using the autoregressive properties of past prices and experimental plot data.  All of these stochastic/dynamics can matter for rotations. John Rust once told me that Bellman always thought crop rotations would be a great application for his recursive method of solving dynamic problems.

Here's the jist of what we found:

Always rotating, regardless of prices, is close to optimal, even though economically optimal planting may rotate much less frequently.  One implication is that reduced corn monoculture and fertilizer application rates might be implemented with modest incentive payments of $4 per acre or less, and quite possibly less than $1 per acre.

In the past I've been skeptical that even a high fertilizer tax could have much influence on fertilizer use. But given low-cost substitutes like rotation, perhaps it wouldn't cost as much as some think to make substantial improvements in water quality.

Nathan Hendricks and coauthors have a somewhat different approach on the same issue (also see this paper).  It's hard to compare our models, but I gather they are saying roughly similar things.

More fun with MARS

(But not as much fun as watching Stanford dominate Oregon last night).

In a recent post I discussed the potential of multivariate adaptive regression splines (MARS) for crop analysis, particularly because they offer a simple way of dealing with asymmetric and nonlinear relationships. Here I continue from where I left off, so see previous post first if you haven’t already.

Using the APSIM simulations (for a single site) to train MARS resulted in the selection of four variables. One of them was related to radiation which we don’t have good data on, so here I will just take three of them, which were related to: July Tmax, May-August Tmax, and May-August Precipitation. Now, the key point is we are not using those variables as the predictors themselves, but instead using hinge functions based on them. The below figure shows specifically what thresholds I am using (based on the MARS results from previous post) to define the basis hinge functions.  

I then compute these predictor values for each county-year observation in a panel dataset of US corn yields, then subtract county means from all variables (equivalent to introducing county fixed effects), and fit three different regression models:

Model 1: Just quadratic year trends (log(Yield) ~ year + year^2). This serves as a reference “no-weather” model.

Model 2: log(Yield) ~  year + year^2 + GDD  + EDD + prec + prec^2. This model adds the predictors we normally use based on Wolfram and Mike’s 2009 paper, with GDD and EDD meaning growing degree days between 8 and 29 °C and extreme degree days (above 29 °C). Note these measures rely on daily Tmin and Tmax data to compute the degree days.

Model 3: log(Yield) ~  year + year^2 + the three predictors shown in the figure above. Note these are based only on monthly average Tmax or total precipitation.

The table below shows the calibration error as well as the mean out-of-sample error for each model. What’s interesting here is that the model with the three hinge functions performs just as well as (actually even a little better than) the one based on degree day calculations. This is particularly surprising since the hinge functions (1) use only monthly data and (2) were derived from simulations at a single site in Iowa. Apparently they are representative enough to result in a pretty good model for the entire rainfed Corn Belt.

Model	Calibration R2	Average root mean square error for calibration	Average root mean square error for out-of-sample data  (for 500 runs)	% reduction in out-of-sample error
1	0.59	0.270	.285	--
2	0.66	0.241	.259	8.9
3*	0.68	0.235	.254	10.7

*For those interested, the coefficients on the three hinge terms are -.074, -.0052, and -.061 respectively

The take home here for me is that even a few predictors based on monthly data can tell you a lot about crop yields, BUT it’s important to account for asymmetries. Hinge functions let you do that, and process-based crop models can help identify the right hinge functions (although there are probably other ways to do that too).

So I think this is overall a promising approach – one could use selected crop model simulations from around the world, such as those out of agmip, to identify hinge functions for different cropping systems, and then use these to build robust and simple empirical models for actual yields. Alas I probably won’t have time to develop it much in the foreseeable future, but hopefully this post will inspire something.

Weather, storage and an old climate impact debate.

This somewhat technical post is a belated followup to a comment I wrote with Tony Fisher, Michael Hanemann and Wolfram Schlenker, which was finally published last year in the American Economic Review.  I probably should have done this a long time ago, but I needed to do a little programming.  And I've basically been slammed nonstop.

First the back story:  The comment re-examines a paper by Deschanes and Greenstone (DG) that supposedly estimates a lower bound on the effects of climate change by relating county-level farm profits to weather.  They argue that year-to-year variation in weather is random---a fair proposition---and control for unobserved differences across counties using fixed effects.  This is all pretty standard technique.

The overarching argument was that with climate change, farmers could adapt (adjust their farming practices) in ways they cannot with weather, so the climate effect on farm profits would be more favorable than their estimated weather effect.

Now, bad physical outcomes in agriculture can actually be good for farmers' profits, since demand for most agricultural commodities is pretty steep: prices go up as quantities go down.  So, to control for the price effects they include year fixed effects.  And since farmers grow different crops in different parts of the country and there can be local price anomalies, they go further and use state-by-year fixed effects so as to squarely focus on quantity effects in all locations.

Our comment pointed out a few problems:  (1) there were some data errors like missing temperature data apparently coded with zeros and much of the Midwest and most of Iowa dropped from the sample without explanation; (2) in making climate predictions they applied state-level estimates to county-level baseline coefficients, in effect making climate predictions that regress to the state mean (e.g., Death Valley and Mt. Witney have different baselines but the same future); (3) all those fixed effects wash out over 99 percent of weather variation, leaving only data errors for estimation; (4) the standard errors didn't appropriately account for the panel nature of the spatially correlated errors.

These data and econometric issues got the most attention.  Correct these things and the results change a lot.  See the comment for details.

But, to our minds, there is a deeper problem with the whole approach.  Their measure of profits was really no such thing, at least not in an economic sense: it was reported sales minus a crude estimate of current expenditures.  The critical thing here is that farmers often do not sell what they produce.  About half the country's grain inventories are held on farm.  Farms also hold inventory in the form of capital and livestock, which can be held, divested or slaughtered.  Thus, effects of weather in one year may not show up in profits measured in that year.  And since inventories tend to be accumulated in plentiful times and divested in bad times, these inventory adjustments are going to be correlated with the weather and cause bias.

Although DG did not consider this point originally, they admitted it was a good one, but argued they had a simple solution: just include the lags of weather in the regression. When they attempted this, they found lagged weather was not significant, and thus that this issue was unimportant.  This argument is presented in their reply to our comment.

We were skeptical about their proposed solution to the storage issue.  And so, one day long ago, I proposed to Michael Greenstone, that we test his proposed solution. We could solve a competitive storage model, assume farmers store as a competitive market would, and then simulate prices and quantities that vary randomly with the weather.  Then we could regress sales (consumption X price) against our constructed weather and lags of weather plus price controls. If the lags worked in this instance, where we knew the underlying physical structure, then it might work in reality.

Greenstone didn't like this idea, and we had limited space in the comment, so the storage stuff took a minimalist back seat. Hence this belated post.

So I recently coded a toy storage model in R, which is nice because anyone can download and run this thing  (R is free).  Also, this was part of a problem set I gave to my PhD students, so I had to do it anyway.

Here's the basic set up:

y    is production which varies randomly (like the weather).
q    is consumption, or what's clearly sold in a year.
p    is the market price, which varies inversely with q (the demand curve)
z    is the amount of the commodity on hand (y plus carryover from last year).

The point of the model is to figure out how much production to put in or take out of storage.  This requires numerical analysis (thus, the R code).  Dynamic equilibrium occurs when there is no arbitrage: where it's impossible to make money by storing more or storing less.

Once we've solved the model, which basically gives q, p as a function of z, we can simulate y with random draws and develop a path of q and p.  I chose a demand curve, interest rate and storage cost that can give rise to a fair amount of price variability and autocorrelation, which happens to fit the facts.  The code is here.

Now, given our simulated y, q and p, we might estimate:

(1)   q_t = a + b0  y_t + b1 y_{t-1} + b2 y_{t-2} + b3 y_{t-3} +  ... + error

(the ... means additional lags, as many as you like.  I use five.)

This expression makes sense to me, and might have been what DG had in mind: quantity in any one year is a function of this year's weather and a reasonable number past years, all of which affect today's output via storage.  For the regression to fully capture the true effect of weather, the sum of b# coefficients should be one.

Alternatively we might estimate:

(2)   p_t q_t = a + b0  y_t + b1 y_{t-1} + b2 y_{t-2} + b3 y_{t-3} +  ... + error

This is almost like DG's profit regression, as costs of production in this toy model are zero, so "profit" is just total sales.   But DG wanted to control for price effects in order to account for the pure weather effect on quantity, since the above relationship, the sum of the b# coefficients is likely negative.  So, to do something akin to DG within the context of this toy model we need to control for price.  This might be something like:

(3)  p_t q_t = a + b0  y_t + b1 y_{t-1} + b2 y_{t-2} + b3 y_{t-3} +  ... + c p_t + error

Or, if you want to be a little more careful, recognizing there is a nonlinear relationship, we might have a more flexible control for p_t, and use a polynomial. Note that we cannot used fixed effects like DG because this isn't a panel.  I'll come back to this later.  In any case, with better controls we get:
 
(4)   p_t q_t = a + b0  y_t + b1 y_{t-1} + b2 y_{t-2} + b3 y_{t-3} +  ... + c1 p_t  + c2 p_t^2 + c3 p_t^3 +  error

At this point you should be worrying about having p_t on both the right and left side.  More on this in a moment.  First, let's take a look at the results:

Equation 1:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)     1.68       1.32    1.28     0.20
y               0.39       0.03   15.62     0.00
l.y             0.23       0.03    9.17     0.00
l2.y            0.10       0.03    3.83     0.00
l3.y            0.07       0.03    2.66     0.01
l4.y            0.07       0.03    2.69     0.01
l5.y            0.06       0.03    2.34     0.02

The sum of the y coefficients is 0.86.  I'm sure if you put in enough lags they would sum to 1. You shouldn't take the Std. Error or t-stats seriously for this or any of the other regressions, but that doesn't really matter for the points I want to make. Also, if you run the code, the exact results will differ because it will take a different random draw of y's, but the flavor will be the same.

Equation 2:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  4985.23     166.91   29.87        0
y             -72.15       3.19  -22.63        0
l.y           -43.67       3.20  -13.64        0
l2.y          -22.52       3.21   -7.03        0
l3.y          -15.61       3.21   -4.87        0
l4.y          -13.58       3.19   -4.26        0
l5.y          -12.26       3.19   -3.85        0

All the coefficients are negative.  As we expected, good physical outcomes for y mean bad news for profits, since prices fall through the floor.  If you know a little about the history of agriculture, this seems about right.  So, let's "control" for price.

Equation 3:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  2373.15     167.51   14.17        0
y             -28.12       2.91   -9.66        0
l.y           -17.72       2.10   -8.43        0
l2.y          -11.67       1.63   -7.17        0
l3.y           -8.07       1.57   -5.16        0
l4.y           -5.99       1.56   -3.84        0
l5.y           -5.68       1.54   -3.68        0
p               7.84       0.44   17.65        0

Oh, good, the coefficients are less negative.  But we still seem to have a problem.  So, let's improve our control for price by making it a 3rd order polynomial:

Equation 4:
            Estimate Std. Error       t value Pr(>|t|)
(Intercept)  1405.32          0  1.204123e+15     0.00
y               0.00          0  2.000000e-02     0.98
l.y             0.00          0  3.000000e-02     0.98
l2.y            0.00          0  6.200000e-01     0.53
l3.y            0.00          0 -3.200000e-01     0.75
l4.y            0.00          0 -9.500000e-01     0.34
l5.y            0.00          0 -2.410000e+00     0.02
poly(p, 3)1  2914.65          0  3.588634e+15     0.00
poly(p, 3)2  -716.53          0 -1.795882e+15     0.00
poly(p, 3)3     0.00          0  1.640000e+00     0.10

The y coefficients are now almost precisely zero. 

By DG's interpretation, we say that weather has no effect on profit outcomes and thus climate change is likely to have little influence on US agriculture.  Except in this simulation we know that in the underlying physical reality is that one unit of y ultimately has a one unit effect on the output.  DG's interpretation is clearly wrong.

What's going on here? 

The problem comes from an attempt to "control" for price.  Price, after all, is a key (the key?) consequence of the weather. Because storage theory predicts that prices incorporate all past production shocks, whether they are caused by weather or something else, in controlling for price, we remove all weather effects on quantities.  So, DG are ultimately mixing up cause and effect, in their case by using a zillion fixed effects. One should take care in adding "controls" that might actually be an effect, especially when you supposedly have a random source of variation.  David Freedman, the late statistician who famously critiqued regression analysis in the social sciences and provided inspiration to the modern empirical revolution in economics, often emphasized this point.

Now, some might argue that the above analysis is just a single crop, that it doesn't apply to DG's panel data. I'd argue that if you can't make it work in a simpler case, it's unlikely to work in a case that's more complicated.  More pointedly, this angle poses a catch 22 for the identification strategy: If  inclusion of state-by-year fixed effects does not absorb all historic weather shocks, then it implies that the weather shocks must have been crop- or substate-specific, in which case there is bias due to endogenous price movements even after the inclusion of these fixed effects. On the other hand, if enough fixed effects are included to account for all endogenous price movements, then lagged weather by definition does not add any additional information and should not be significant in the regression.  Prices are a sufficient statistic for all past and current shocks.

All of this is to show that the whole DG approach has problems.  However, I think the idea of using lagged weather is a good one if combined with a somewhat different approach.  We might, for example, relate all manner of endogenous outcomes (prices, quantities, and whatever else) to current and past weather. This is the correct  "reduced form."  From these relationships, combined with some minimalist economic structure, we might learn all kinds of interesting and useful things, and not just about climate change.   This observation, in my view, is the over-arching contribution of my new article with Wolfram Schlenker in the AER

I think there is a deeper lesson in this whole episode that gets at a broader conversation in the discipline about data-driven applied microeconomics over the last 20 years.  Following Angrist, Ashenfelter, Card and Krueger, among others, everyone's doing experiments and natural experiments.  A lot of this stuff has led to some interesting and useful discoveries.  And it's helped to weed out some applied econometric silliness.

Unfortunately, somewhere along the way, some folks lost sight of basic theory.   In many contexts we do need to attach our reduced forms to some theoretical structure in order to interpret them.  For example, bad weather causing profits to go up in agriculture actually makes sense, and indicates something bad for consumers and for society as a whole.

And in some contexts a little theory might help us remember what is and isn't exogenous.

Taking crop analysis to MARS

I couldn’t bear to watch the clock wind down on October without a single post this month on G-FEED. So here goes a shot at the buzzer…

A question I get asked or emailed fairly often by students is whether they should use a linear or quadratic model when relating crop yields to monthly or growing season average temperatures. This question comes from all around the world so I guess it’s a good topic for a post, especially since I rarely get the time to email them back quickly.  If you are mainly interested in posts about broad issues and not technical nerdy topics, you can stop reading now.

The short answer is you can get by with a linear model if you are looking over a small range of temperatures, such as year to year swings at one location. But if you are looking across a bigger range, such as across multiple places, you should almost surely use something that allows for nonlinearity (e.g., an optimum temperature somewhere in the middle of the data).

There are issues that arise if using a quadratic model that includes fixed effects for location, a topic which Wolfram wrote about years ago with Craig McIntosh. Essentially this re-introduces the site mean into the estimation of model coefficients, which creates problem of interpretation related to a standard panel model with fixed effects.

A bigger issue that this question points to, though, is the assumption by many that the choice is simply between linear and quadratic. Both are useful simple approaches to use, especially if data is scarce. But most datasets we work with these days allow much more flexibility in functional form. One clear direction that people have gone is to go to sub-monthly or even sub-daily measures and use flexible spline or degree day models to compute aggregate measures of temperature exposure throughout the season, then use those predictors in the regression.  I won’t say much about that here, except that it makes a good deal of sense and people who like those approaches should really blog more often.

Another approach, though, is to use more flexible functions with the monthly or seasonal data itself. This can be useful in cases where we have lots of monthly data, but not much daily data, or where we simply want something that is faster and easier than using daily data. One of my favorite methods of all time are multivariate adaptive regression splines, also called MARS. This was developed by Jerome Friedman at Stanford about 20 years ago (and I took a class from him about 10 years ago). This approach is like a three-for-one, in that it allows for nonlinearities, can capture asymmetries, and is a fairly good approach to variable selection. The latter is helpful in cases where you have more months than you think are really important for crop yields.

The basic building block of MARS is the hinge function, which is essentially a piecewise linear function that is zero on one side of the hinge, and linearly increasing on the other side. Two examples are shown below, taken from the wikipedia entry on MARS.

MARS works by repeatedly trying different hinge functions, and adds whichever one gives the maximum reduction in the sum of squared errors. As it adds hinge functions, you can have it added by itself or have it multiply an existing hinge in the model, which allows for interactions (I guess that makes it a four-for-one method). Despite searching all possible hinge functions (which covers all variables and hinges at all observed values of each variable), it is a fairly fast algorithm. And like most data mining techniques, there is some back-pruning at the end so it isn’t too prone to overfitting.

For a long time I liked MARS but couldn’t figure out how to apply it to data where you want to include spatial fixed effects to account for omitted variables. Unlike models with pre-determined predictors, such as monthly average temperature or squared temperature, MARS has to search for the right predictors. And before you know what the predictors are, you can’t substract out the site-level means as you would in a fixed-effect model. So you can’t know what the predictors are until you search, but you can’t search if you can’t compute the error of the model correctly (because you haven’t included fixed-effects.)

One semi-obvious solution would be to just ignore fixed-effects, find the hinge-function predictors, and then rerun the model with the selected predictors but including fixed effects. That seems ok but all the problems of omitted variables would still be affecting the selection process.

Recently, I settled on a different idea – first use a crop simulation model to develop a pseudo-dataset for a given crop/region, then run MARS on this simulated data (where omitted variables aren’t an issue) to find the predictors, and then use those predictors on an actual dataset, but including fixed effects to account for potential omitted variables.

I haven’t had much time to explore this, but here’s an initial attempt. First, I used some APSIM simulations for a site in Iowa that we ran for a recent paper on U.S. maize. Running MARS on this, allowing either monthly or seasonal average variables to enter the model, results in just four variables that are able to explain nearly 90% of the yield variation across years. Notice the response functions (below) show the steepest sensitivity for July Tmax, which makes sense. Also, rainfall is important but only up to about 450mm over the May-August period. In both cases, you can see how the results are definitely not linear and not symmetric. And it is a little surprising that only four variables can capture so much of the simulated variation, especially since they all contain no information at the sub-monthly time scale.

Of course this approach relies on assuming the crop model is a reasonable representation of reality. But recall we aren’t using the crop model to actually define the coefficients, just to define the predictors we will use. The next step is to then compute these predictors for actual data across the region, and see how well it works at predicting crop yields. I actually did that a few months ago but can’t find the results right now, and am heading off to teach. I’ll save that for a post in the near future (i.e. before 2015).

Climate Change and Resource Rents

With the next IPCC report coming out, there's been more reporting on climate change issues.  Brad Plumer over a Wonkblog has nice summary that helps to illustrate how much climate change is already "baked in" so to speak.

I'd like to comment one point.  Brad writes "Humans can only burn about one-sixth of their fossil fuel reserves if they want to keep global warming below 2ºC."

I'd guess some might quibble with the measurement a bit, since viable reserves depends on price and technology, plus many unknowns about much fossil fuel there really is down there.  But this is probably in the ballpark, and possibly conservative.

Now imagine you own a lot of oil, coal and/or natural gas, you're reading Brad Plumber, and wondering what might happen to climate policy in the coming years.  Maybe not next year or even in the next five or ten years, but you might expect that eventually governments will start doing a lot more to curb fossil fuel use.  You might then want to sell your fossil fuels now or very soon, while you can.   If many resource owners feel this way, fossil fuel prices could fall and CO2 emissions would increase.  

This observation amounts to the so-called "green paradox."  Related arguments suggest that taxing carbon may have little influence on use, and subsidizing renewable fuels and alternative technologies, without taxing or otherwise limiting carbon-based fuels, might make global warming worse, since it could push emissions toward the present.

Research on these ideas, mostly theoretical, is pretty hot in environmental economics right now.  It seems like half the submissions I manage at JEEM touch on the green paradox in one way or another.  

All of it has me thinking about a point my advisor Peter Berck often made when I was in grad school. At the time, we were puzzling over different reasons why prices for non-renewable resources--mostly metals and fossil fuels--were not trending up like Hotelling's rule says they should.  Peter suggested that we may never use the resources up, because if we did, we'd choke on all the pollution.  Resource use would effectively be banned before it could be used. If resource owners recognized this, they'd have no incentive to hold or store natural resources and the resource rent (basically the intrinsic value based on its finite supply) would be zero, which could help explain non-increasing resource prices.

For all practical purposes, Peter understood the green paradox some 15-20 years ago.  Now the literature is finally playing catch up.  

David is a confirmed genius

The MacArthur Foundation just confirmed what we've known all long: that G-FEED's very own David Lobell is a genius.  Hopefully the $625k that MacArthur is forking over will free up David to do some additional blogging on his preferred choice of tennis racquet.

Big congrats to David!!

The noise lovers

I try not to use this blog much for rants, but it’s an easy way to post more frequently. So… we’ve been getting some feedback on our recent paper on drought stress in U.S. maize, some of it positive, some not. One thing that comes up, as with a lot of prior work, is doubts about how important temperature is. Agronomists often talk about how important the timing of rainfall is. And about how heat doesn’t hurt nearly as much if soils are very moist. To me this is another way of saying (1) other factors matter too and (2) there are interactions between temperature and other factors. The answer to both of these is “Of course!”

I am struck by the similarity of these discussions to those that Marshall posted about the empirical work on conflict. They go something like this:

Person A: “We’ve looked at the data and see a clear response that people tend to wake up when you turn the lights on”
Person B: “But people also wake up because they went to bed early last night and aren’t tired any more.”
A: “Yeah, ok”
B: “And the lights probably won’t wake them up if they are passed out drunk.”
A: “Ok, great point”
B: “I’ve woken up thousands of times in my 30-year career, and rarely did I get woken because someone turned the light on”
A: “ok”
B: “So then how can you possibly claim that turning on lights causes people to wake up”
A: “What? Are you serious? Did you even read the paper?”
B: “I don’t need to, I am an expert on waking up.”

And so on. I sometimes don’t know whether people seriously don’t understand the difference between explaining some vs. all of the variance, or if they just look for any opportunity to plug their own area of expertise. When we claim to see a clear signal in the data, it is not a claim that there is no noise around that signal. And some of the noise might include interactions with other variables. In fact, if there wasn’t any noise then the signal would have been known long ago.

The other day I was thinking of replacing my old tennis racquet, so I went to Google and typed in “prince thunder” (the name of my current racquet).  Turns out the top results were about a song that the artist Prince wrote called Thunder. Does that mean that Google is entirely useless? No, it means there is some error if you try to predict what someone wants based only on a couple of words they type. But with their enormous datasets, they are pretty good at picking up signals and getting the answer right more often than not. For most people typing those words, they were probably looking for the song.

Back to the crop example. Of course, heat will matter less or more depending on the situation. And of course getting rainfall right before key stages is more important than getting it after. These are both reasons for the scatter in any plot of heat (or any other variable) against yields. But neither of those refutes the fact that higher temperatures tend to result in more water stress, and lower yields. Or in Sol and Marshall’s case, that higher temperatures tend to increase the risk of conflict.

I sometimes think if one of us were to discover some magic combination of predictors that explained 95% of the variance in some outcome, there would be a chorus of people saying “you left out my favorite 5%!” Don’t get me wrong, there are lots of legitimate questions about cause and effect, stationarity, etc. that are worth looking into. But how much time should we really spend having the same old conversation about the difference between a signal and noise? 

Yet more cleverness: getting ambient temperature data from cellphones

Following up on an earlier post about some smarty-pantses that figured out how to use cell phone towers to extract estimates of local rainfall, many of these same smarty-pantses have now figured out how to use those same cell phones to provide information on local temperatures.  Here's the new paper, just out in Geophysical Research Letters [HT: Noah Diffenbaugh]:

Crowdsourcing urban air temperatures from smartphone battery temperatures
A. Overeem, J. C. R. Robinson, H. Leijnse, G. J. Steeneveld, B. K. P. Horn, and R. Uijlenhoet

Accurate air temperature observations in urban areas are important for meteorology and energy demand planning. They are indispensable to study the urban heat island effect and the adverse effects of high temperatures on human health. However, the availability of temperature observations in cities is often limited. Here we show that relatively accurate air temperature information for the urban canopy layer can be obtained from an alternative, nowadays omnipresent source: smartphones. In this study, battery temperatures were collected by an Android application for smartphones. A straightforward heat transfer model is employed to estimate daily mean air temperatures from smartphone battery temperatures for eight major cities around the world. The results demonstrate the enormous potential of this crowdsourcing application for real-time temperature monitoring in densely populated areas.

They validate their technique in a few big cities around the world, and it looks pretty neat.  As shown in their Fig 2, which shows temperatures for London over a 4-month period and is reproduced below, raw changes in battery temperature are highly correlated with variation in ambient temperature (compare the orange line and black line, reported correlation r=0.82), and their heat transfer model is able to get the levels close to right (compare the blue dots with the black line).

What we really want to know, of course, is whether this can also work in places where the weather-observing infrastructure is currently really poor (e.g. most of Africa), and thus were techniques like this could be extra useful.  It seems like there are a couple hurdles.  First, you need a lot of people with smartphones.  According to this article, smartphone penetration in Africa is currently around 20%, but Samsung (who might know) puts it at less than 10%.  Nevertheless, smartphone adoption appears to be growing rapidly (you can find them in just about any tiny rural market in western Kenya, for instance), and so this might not be such a limitation in a few years.  And something the authors worry about in colder and richer climes -- that their battery temperature readings are biased because people are in heated or air-conditioned buildings a lot -- is much less of a worry in places where people are outside more and don't keep their houses at a perfect 70F.

Second, to get temperature levels right, it appears that the authors have to calibrate battery temperatures in a given area to data on observed temperatures in that area -- which is obviously not helpful if you don't have observed data to start with.  But if all you care about is temperature deviations -- e.g. if you're running a panel model that is linear in average temperature -- then it seems like the raw battery temperature data give you this pretty well (see figure).  Then if you really need levels -- say you want to estimate how a crop responds to temperatures above a given threshold -- you could do something like David did in his 2011 paper on African maize and add these deviations back to somebody else's estimate of the climatology (David used WorldClim).

Given this, the authors' optimism on future applications seems fitting:


"In the end, such a smartphone application could substantially increase the number of air temperature observations worldwide. This could become beneficial for precision agriculture, e.g., for optimization of irrigation and food production, for human health (urban heat island), and for energy demand planning."

But hopefully the expansion of this technique into rural areas won't have to wait for observed data with which to calibrate their heat transfer model.  If that London plot above is representative, it seems like just getting the raw battery data could be really helpful.

The future of crop demand

It is common to hear statements about needing to increase food production by 70%, or even to double it, by 2050. In the past I’ve tried to avoid such statements, mainly because I hadn’t really dug into the sources behind them. But as part of prepping for a new class I’m teaching in the fall, I decided to take a closer look. And what I found, maybe not surprisingly, is a lot of confusion.

For starters, the baselines are often different, with some using 2000, some 2005-07, and some 2010. More importantly, the definition of “food” can be quite different, with some referring to cereal production, some to all calorie production, and some simply to the total value of agricultural output. And the studies use different assumptions about drivers of demand, like incomes or biofuel policies, so it’s often not clear how much differences are driven by assumptions in the models themselves vs. the inputs into the models.

Here’s a quick rundown of the common citations. First and foremost is the FAO, which produced the commonly cited 70% number. Last year they actually revised this down to 60% in their new projections, but not because the projected demand changed very much, but because they up-revised their estimate of actual output in 2006. The baseline for the FAO number is still 2006, so the 60% refers to an increase over a 44-year period. And the 60% refers to price-weighted aggregate of output, so that part of the 60% is simply a shift toward producing higher value stuff. Total cereal production only rises 46%, from roughly 2 to 3 billion tons per year. About two-thirds of that increase occurs by 2030. In terms of calorie consumption, global per capita consumption rises by 11%, and total calorie consumption rises by 54%.

The “doubling” statement, as far as I can tell, comes mainly from a 2011 paper by David Tilman and colleagues that said calorie demand would double between 2010 and 2050, and protein demand would rise by 110%. That was mainly based on extrapolating historical patterns of cereal and protein demand as a function of income, combined with projections of income growth. Coincidentally, doubling of production is also what we found in the baseline simulations we did for a climate adaptation analysis published earlier this year in ERL, and discussed in a prior post.

I won’t take time here to bore you with details of the methods in FAO vs. Tilman vs. others. But it seems a lot of the disparity is not so much the methods as the input assumptions. For example, FAO has world GDP per capita growing at an average rate of 1.4%, which they acknowledge as conservative. In contrast, Tilman has a global per capita GDP growth rate of 2.5% per year. Over a 40-year period, that translates to an increase of about 75% for FAO but 170% for Tilman! In our paper, we had a rate in between of 2% per year based on USDA projections. The reason we still get a doubling with lower income growth than Tilman is probably because we had a larger biofuel demand. (Note that my coauthors Uris Baldos and Tom Hertel have since switched to using income projections from a French group, which - maybe not surprisingly - are a little more pessimistic than the American ones.)  Now, global per capita growth rates only tell us so much, because what mainly matters for demand is how incomes grow at lower and middle income levels where people most rapidly increase consumption with higher income. Unfortunately, studies don’t usually report for the same sets of countries, and I’m too lazy to try to recompute. But the global numbers suggest pretty important differences at all income levels.

To me, it’s always useful to compare these projections to historical growth rates. Below I plot global cereal production from FAO since 1961. A couple of things are clear. First, production was about 150% higher in 2010 than 50 years earlier. Second, the growth rate appears pretty linear at a clip of roughly 28 million tons per year. A naive extrapolation gives an increase of 1.1 billion tons over a 40 year period from 2010 to 2050. For reference, I show what a 50% and 100% increase from 2010 trend levels would be. Obviously the 50% number (or the FAO’s 46%) are closer to this naive extrapolation than a doubling. 

This isn’t to say that the doubling number is definitely wrong, but just that it would mean a significant acceleration of cereal demand, and/or a significant shift of calorie consumption away from cereal-based products. It would be really nice if someone could systematically explore the sources of uncertainty, but my guess for now is that income growth is a big part of it. Unfortunately, this means our hope for narrowing uncertainty is largely in the hands of economists, and we know how good they or anyone else are at predicting GDP growth . But for those who work mainly on supply side questions, it’s mostly good enough just to know that demand for crop production will rise by 50% or more, because even 50% is a pretty big challenge.

(Note: for anyone interested in a summary of an unrelated recent paper on extreme heat, see here. And for an exchange we had about adaptation in the US see here. Wolfram told me a blog about the latter is coming, but as I told him, so is Christmas.)