All farms within a county that is considered irrigated are pooled in the regression equation. The problem with this approach is that water rights can vary considerably on a sub-county level. More fundamentally, in irrigated areas the water input comes from groundwater or from precipitation falling elsewhere, and local precipitation is not a valid measure of water supply. In such cases a better measure is access to irrigation water, on an irrigation district level, as employed in an application to California by Schlenker et al. . The main weather variables used by DG are growing degree days, growing-degree-days squared, precipitation, and precipitation squared. All models include soil controls, county fixed effects and year fixed effects, and the regressions are area-weighted.To avoid confounding our comparison with changes in specification, we use the same variables and the same weighting, as well as the same observations.Columns and of Table 1 replicate results in Table 8 of DG using their original data set, for corn and soybeans, respectively. Our replication of DG differs slightly from DG’s original due to a coding error in DG that we corrected . Columns and replicate DG’s regression model using our reconstruction of the weather data using their specification. Columns and include one additional variable, the square root of degree days above 34◦C,plastic planters bulk to account for extreme temperatures. DG include such a variable to measure the potentially harmful effect of extreme heat on profits in Table 6 of their paper, but not in their yield regression.
Columns and also use a slightly different calculation for degree days that accounts for within-day temperature variation.For each model, the table reports the variance explained by the weather variables, model comparison statistics, and predicted climate-change impacts under Hadley II and Hadley III scenarios.Our recalculated weather data differ from DG in several ways and we highlight only a few here. The greatest differences likely stem from culling of missing values and relying on weather stations with relatively complete temperature and precipitation records. In DG and in columns and , degree days are calculated using the daily average of the minimum and maximum. That is, all time within each day is treated as if it were fixed at the average. In degree-day calculations for columns and , we account for variation between the minimum and maximum in each day, which matters given the nonlinear relationship between temperature and degree days and the important influence of extremely warm temperatures on impacts. For both corn yields and soybean yields , the fit improves markedly going from to while predicted losses under climate change simultaneously become more severe. Specifically, columns and show that DG’s degree days and precipitation variables explain 12.6% and 15.3% of the yield variance not explained by fixed effects. Our replication using corrected data but the same specification explains about twice the variance, a strong indication of data errors in DG. Predicted losses for corn under climate change also increase from a statistically insignificant 1 percent to a strongly significant 11.5 percent under the Hadley II scenario used by DG. We report both the standard error following DG’s regression as well as a standard error that adjusts for the spatial correlation of the error terms while accounting for the panel structure following Conley .
Predicted losses become more extreme under the Hadley III scenario. Under Hadley III losses increase to 44.5 percent . While a discussion of the validity or the accuracy of either model is beyond the scope of this paper, it should be noted that earlier research against which DG compare their results relied on the Hadley III model, and we believe an appropriate comparison should leave the climate forecasts unchanged.9 Similar but somewhat more adverse predictions are reported for soybeans. In columns and , we add extremely warm temperatures and account for within-day temperature variation. Here the fit increases for both crops by about 25 percent relative to the columns and predicted damages increase by nearly 50 percent. Using the column model and Hadley III climate change scenarios predicted losses are 65.6 percent for corn and 75.7 percent for soybeans. The second and third rows of the table present pair-wise non-nested J-tests to compare the different models. DG’s model with their data is rejected when compared against either of our replications with new data, with t-statistics in excess of 15. In columns of Table 2 we present the same set of comparisons for the profit regressions. A similar pattern emerges, with both the fit improving and projected damages generally increasing as we change the weather data, account for extreme temperatures, account for within-day temperature variations, and move from Hadley II to Hadley III climate projections. The overall explanatory power of weather for profits is poor, however. DG’s weather data and model explain just 0.5 percent of the residual variance after removing fixed effects. Our new data nearly triples that performance to 1.4 percent, and it increases slightly to 1.5 percent with an accounting for extreme temperatures and within-day temperature variations.
Projected damages range from -6 percent using DG’s data under the Hadley II climate change scenario to -53 percent using the same model, our replicated data, and the Hadley III scenario. While these estimates are statistically significant, the standard errors are economically large, equal to over 20 percent for the Hadley III predictions when our new data are used and we account for spatial correlation. In columns of Table 2 we present the same set of results in columns with one critical difference: we use state-by-year fixed effects in place of state fixed effects. While DG find insignificant impacts in their original paper using both year fixed effects and state by-year fixed effects, the two diverge in our replication. We find significant damages in the former and insignificant impacts under the latter under all weather data sets and climate change scenarios, although the confidence intervals of the latter are very wide. As explained in footnotes 4 and 5 of DG, state-by-year fixed effects have the advantage of capturing regional price effects, which is especially useful if production of certain crops is concentrated geographically. For example, California produces 85 percent of the lettuce grown in the U.S. A country-wide yearly fixed effect would not capture the fact that crops specific to California might face unique price shocks. However,collection pot any crop-specific price response works as natural “insurance” for farmers that grow the crop. Prices move in the opposite direction from production shocks: If yields decline, prices increase, and vice versa.10 Accounting for region-specific price responses should therefore make predicted impacts more negative as it cancels out the counterbalancing price response. It is counter-intuitive that predicted changes in profits are negative and significant in a regression using year fixed effects, yet turn insignificant when one includes state-by-year fixed effects to capture region-specific price responses. What other effects apart from regional price effects might explain why the results become less damaging and insignificant with the use of state-by-year fixed effects? A concern with the use of state-by-year fixed effects is that they absorb a significant amount of weather variance. After removing county and state-by-year fixed effects, remaining weather variance pertains only to yearly within-state deviations from county means, as for example the amount by which northern Iowa is warmer than normal in a given year compared to how much southern Iowa is warmer than normal in the same year. Generally, whenever northern Iowa is warmer than normal, so is southern Iowa, because temperatures vary smoothly in space. DG report a significant amount of within-state weather variation in their Table 2. But it turns out this variation is largely an artifact of errors in their weather data, which exhibit large discontinuous shifts across neighboring counties as discussed above. Statistics that summarize weather variation in DG’s data set and our own are reported in Table 3. The table summarizes regressions of degree days against different sets of fixed effects: an intercept; county fixed effects; county plus year fixed effects; and county plus state-by-year fixed effects. For each data set and set of fixed effects the table reports the R-square, the standard deviation of the residual weather variation not absorbed by the fixed effects ,11 and the fraction of residuals with an absolute value greater than 1 degree Fahrenheit. While the overall standard deviations of temperatures are relatively similar in DG’s measure and our replication , the two diverge drastically once we include fixed effects.
The residual standard deviation of DG’s temperature measure is 2.69F with county fixed effects and 2.38F with county plus state by-year fixed effects. Our measure, on the other hand, has a residual standard deviation of 1.49F with county fixed effects and just 0.35F with county plus state-by-year fixed effects. These differences suggest a noise to signal ratio of DG’s weather of about 7 to 1 in their preferred fixed-effects model.12The preceding section shows that predicted yield impacts from climate change are negative and significant if improved weather data, a measure of extreme temperatures, and more recent climate change predictions are used in the estimation. The results from the profit regressions are mixed but weigh on the negative side, and have larger standard errors that include both sizable damages or sizable benefits. In this section we consider potential problems arising from the use of current profits to measure long-run economic impacts from weather. Our premise is that this measure omits storage and perhaps other financial or technological mechanisms that likely smooth this measure of short-run profits in the presence of weather-induced fluctuations and lead the short-run impact of weather on profit to understate the long-run impact of a permanent shift in climate. DG construct their estimate of profit by subtracting annual production expense from annual farm revenues. While production expense is essentially the cost associated with the crops grown in that year, the farm revenue is not necessarily the revenue from crops grown in that year – it is revenue from crops sold in that year. In high-yielding years farmers accumulate stocks for the major field crops in the U.S. ; in low-yielding years they deplete stocks accumulated in earlier years. Storage is thus one way for farmers to smooth weather-related shocks over time. It also creates a substantial disconnect between the weather-related shock and DG’s metric for the impact of that shock, sales minus reported costs.Other factors besides storage could cause the short-run response to weather to understate the long-run response to climate. For example, if the short-run response to a sudden increase in temperature is to pump more groundwater, this strategy may be less sustainable and/or more costly over the long-run permanent increase in temperature as compared to the short run transitory increase, due to depletion of the groundwater resource. Another reason could be that after a bad yield shock, a livestock producer expects higher future feed prices, and therefore chooses to slaughter breeding stock in anticipation of higher future costs. Such a reduction in cattle inventories could temporarily increase sales in a way that would not be feasible in the long run . The important point is that, for many reasons, sales-minus costs do not, in general, reflect the full economic impact of the current weather shock. Or, put another way, there may be technologies like storage, irrigation, and liquidation of capital or inventories that act to smooth profits in the face of transitory shocks. Since climate change would be permanent,such short-term smoothing technologies would not be available. DG’s claim that the short run response to weather overestimates what would be the long-run response to climate change cannot therefore be generally correct. The most plausible argument against these dynamic considerations of storage, irrigation, and livestock inventory adjustments is DG’s use of year or state-by-year fixed effects to control for prices.In the competitive storage model , for example, the motive to accumulate or deplete inventories comes entirely from speculation about prices. In bad-weather years prices increase, giving farmers an incentive to deplete inventories and in good-weather years prices fall, giving farmers an incentive to replenish their inventories. The essential question is whether year or state-by year fixed effects can suitably control for these dynamic considerations, all of which would tend to bias DG’s profit regression toward zero weather effects.