Massetti et al. - Part 1 of 3: Convergence in the Effect of Warming on US Agriuclture

Emanuele Massetti has posted a new paper (joined with Robert Mendelsohn and Shun Chonabayashi) that takes another look at the best climate predictor of farmland prices in the United States.  He'll present it at the ASSA meetings in Philadelphia - I have seen him present the paper at the 2013 NBER spring EEE meeting and at the 2013 AERE conference, and wanted to provide a few discussion points for people interested in the material.

A short background: several articles of contributors to the g-feed blog have found that temperature extremes are crucial at predicting agricultural output. To name a few: Maximilian Auffhammer and coauthors have shown that rice have opposite sensitivities to minimum and maximum temperature, and this relationship can differ over the growing season (paper). David Lobell and coauthors found that there is a highly nonlinear relationship between corn yields and temperature using data from field trials in Africa (paper), which is comparable to what Michael Roberts and I have found in the United States (paper).  The same relationship was observed by Marshal Burke and Kyle Emerick when looking at yield trends and climate trends over the last three decades (paper).

Massetti et al. argue that average temperature are a better predictor of farmland values than nonlinear transformations like degree days.  They exclusively rely on cross-sectional regressions (in contrast to the aforementioned panel regressions), re-examining earlier work Michael Hanemann, Tony Fisher and I have done where we found that degree days are better and more robust predictors of farmland values than average temperature (paper).

Before looking into the differences between the studies, it might be worthwhile to emphasize an important convergence in the sign and magnitude of predicted effect of a rise in temperature on US agriculture.  There has been an active debate whether a warmer climate would be beneficial or detrimental. My coauthors and I have usually been on the more pessimistic side, i.e., arguing that warming would be harmful. For example, a +2C and +4C increase, respectively, predicted a 10.5% and 31.6 percent decrease in farmland values in the cross-section of farmland values (short-term B1 and long-term B2 scenarios in Table 5)  and a 14.9 and 35.3 percent decrease in corn yields in the panel regression (Appendix Table A5).

Robert Mendelsohn and various coauthors have consistently found the opposite, and the effects have gotten progressively more positive over time.  For example, their initial innovative AER paper that pioneered the cross-sectional approach in 1994 argued that "[...] our projections suggest that global warming may be slightly beneficial to American agriculture." Their 1999 book added climate variation as an additional control and argued that "Including climate variation suggests that small amount of warming are beneficial," even in the cropland model.  A follow-up paper in 2003 further controls for irrigation and finds that "The beneficial effect of warmer temperatures increases slightly when water availability is included in the model."

There latest paper finds results that are consistent with our earlier findings, i.e., a +2C warming predicts decreases in farmland values of 20-27 percent (bottom of Table 1), while a +4C warming decreases farmland values by 39-49 percent. These numbers are even more negative than our earlier findings and rather unaffected whether average temperatures or degree days are used in the model.  While the authors go on to argue that average temperatures are better than degree days (more on this in future posts), it does change the predicted negative effect of warming: it is harmful.

Yet another way of estimating the damaging effects of extreme heat on yields

Following up on Max's post on the damaging effects of extreme heat, here is yet another way of looking at it.  So far, my coauthor Michael Roberts and I have estimated three models that links yields to temperature:

1. An eighth-order polynomial in temperature
2. A step function (dummy intervals for temperature ranges)
3. A piecewise linear function of temperature

Another semi-parametric way to estimate this to derive splines in temperature.  Specifically, I used the daily minimum and maximum temperature data we have on a 2.5x2.5mile grid, fit a sinusoidal curve between the minimum and maximum temperature, and then estimated the temperature at each 0.5hour interval.  The spline is evaluated for each temperature reading and summed over all 0.5hour intervals and days of the growing season (March-August).

So what is it good for? Well, it's smoother than the dummy intervals (which by definition assume constant marginal impact within each interval), yet more flexible than the 8th-order polynomial, and doesn't require different bounds for different crops like the piecewise linear function.

Here's the result for corn (the 8 spline knots are shown as red dashed lines), normalized relative to a temperature of 0 degree Celsius.

The regression have the same specification as our previous paper, i.e., the regress log yields on the flexible temperature measure, a quadratic in season-total precipitation, state-specific quadratic time trends as well as county fixed effects for 1950-2011.  

Here's the graph for soybeans:

A few noteworthy results: The slope of the decline is similar to what we found before:  A linear approximation seems appropriate (restricted cubic splines are forced to be linear above the highest knot, but not below). In principle, yields of any type of crop could be regressed on these splines.