The 2.5 mile x 2.5 mile climate polygons are intersected with the agricultural area to derive the agricultural area in each polygon. The climatic variables in a county are simply the area-weighted average of the variables for each climate grid. In this analysis we use the monthly average temperature and precipitation for the 30 years preceding each census year.The existing literature has generally represented the effect of climate on agriculture by using the monthly averages for January, April, July and October.However, from an agronomic perspective, this approach is less than optimal. First, except for winter wheat, most field crops are not in the ground in January; most are planted in April or May and harvested in September or October . Second, plant growth depends on exposure to moisture and heat throughout the growing season, albeit in different ways at different periods in the plant’s life cycle; therefore, including weather variables for April and July, but not May, June, August or September, can produce a distorted representation of how crops respond to ambient weather conditions. The agronomic literature typically represents the effects of temperature on plant growth in terms of cumulative exposure to heat, while recognizing that plant growth is partly nonlinear in temperature. Agronomists postulate that plant growth is linear in temperature only within a certain range, between specific lower and upper thresholds; there is a plateau at the upper threshold beyond which higher temperatures become harmful. This agronomic relationship is captured through the concept of degree days, defined as the sum of degrees above a lower baseline and below an upper threshold during the growing season. Here we follow the formulation of Ritchie and NeSmith and set the lower threshold equal to 8◦C and the upper threshold to 32◦C. In other words, a day with a temperature below 8◦C results inzero degree days; a day with a temperature between 8◦C and 32◦C contributes the number of degrees above 8◦C; and a day with a temperature above 32◦C degrees contributes 24 degree days. Degree days are then summed over the growing period, represented here by the months from April through September.Following Ritchie and NeSmith , the level beyond which temperature increases become harmful is set at 34◦C.

A complication with degree days is that the concept is based on daily temperature while our climate records consist of monthly temperature averages. Thom develops the necessary relationship between daily and monthly temperature variables under the assumption of normality. This relationship is used to infer the standard deviation of daily temperature variables from monthly records. Degree days are then derived using the inverse Mills ratio to account for the truncation of the temperature variable.Before we present our regression results we first examine whether the spatial correlation of the error terms as described in the previous section is indeed present. We conduct three tests of spatial correlation for all counties east of the 100th meridian using the same set of exogenous variables as in the estimation of the hedonic equation in Table 3 below, including state fixed effects. One test is the Moran-I statistic . However, since this does not have a clear alternative hypothesis, we supplement it with two Lagrange-Multiplier tests involving an alternative of spatial dependence, the LM-ERR test and LM-EL test. The results are shown in the first three rows of Table 2. Note that they are rather insensitive to the chosen weighting matrix.The spatial correlation of the error terms is quite large and omitting it will seriously overstate the true t-values. For example, the t-values using standard OLS that does not correct for the spatial correlation or the heteroscedasticity of the error terms are up to nine times as large, with an average value of 2.2 for the model presented in the first column of Table 3. In the following we use a two stage procedure. In the first stage we estimate the parameter of spatial correlation and premultiply the data by . In the second stage we estimate the model and use White’s heteroscedasticity consistent estimator to account for the heteroscedasticity of the error terms. In previous climate assessments, it has been customary to estimate a linear regression model. Since farmland values have to remain non-negative, and given the highly skewed distribution of farmland values in Table 1 a semi-log model appears preferable. To determine which model better fits the data, we conduct a PE-test . We use 10,000 bootstrap simulations to get a better approximation of the finite sample distribution of the estimate. The t-value for rejecting the linear model in favor of the semilog model is 873, while the t-value of rejecting the semi-log model in favor of the linear model is 0.01.

We therefore focus the remainder of our analysis on the semi-log model.Results of the log-linear hedonic regression under the Queen standardized weighting matrix are displayed in the first two columns of Table 3. We present results with and without state fixed effects. The reason for including fixed effects is that this can control for the possibility that there are unobserved characteristics common to all farms within a state,40 litre plant pots such as state-specific taxes and uneven incidence of crop subsidies due to differences in cropping patterns across states. The concern is that the identification of the climate coefficients in the hedonic model might otherwise come primarily from variation in government programs that target specific crops. However, it should be noted that since we rely on a nonlinear functional form, the estimation procedure still uses variation between states in the identification of the coefficients. We find that inclusion of fixed effects does not reduce the significance level of the climatic variables. At the same time, the parameter of spatial correlation is virtually unchanged when we include fixed effects, suggesting that there are indeed spill-over effects that are based on spatial proximity rather than an administrative assignment to a particular state. The estimated coefficients on the climatic variables are consistent with the agronomic literature. The optimal number of growing degree days in the 8◦C − 32◦C range peaks at 2400 degree days for the pooled model in column 1 of Table 3. This is close to the optimal growing condition for many agricultural commodities when one adjusts for the length of the growing season . Degree days above 34◦C are always harmful.13 Precipitation peaks at 79 cm or approximately 31 inches, which also is close to the water requirements of many crops, when adjusted for the length of the growing season. Other variables have intuitive signs as well. Income per capita and population density are important and highly significant determinants of farmland value: higher population pressure translates into higher farmland values, albeit at a decreasing rate. Similarly, higher incomes drive up the price of farmland. Two soil variables are significant at the 5% level in the pooled model: better soils, as measured by a soil quality index, result in higher farmland values; and a lower minimum permeability, which indicates drainage problems, reduces farmland value. The effect of the former is quite large: farmland with 100% of soils in the best soil class categories are 35% more valuable compared to farmland with 0% in the top soil classes. The variable K-factor is significant at the 10% level in three out of the five regressions using state fixed effects. It indicates higher erodibility of the fertile top soil, which is harmful. Percent clay frequently switches sign and is not significant in most models; neither is the average water capacity of the soil. We have suggested that degree days and precipitation over the growing season better represent the effect of climate on agriculture than the alternative specification of monthly averages of untransformed temperature and precipitation.

To assess this claim, we conduct an encompassing test to determine which model is better at predicting the effects of climate change. In order to do so, we split the sample into two subsets: the northern-most 85% of the counties in our sample are used to estimate the parameters of both models in order to derive the prediction error for the southern-most 15%, i.e., we see which model calibrated on moderate temperatures is better at predicting the values for warmer temperatures. The results offer clear confirmation of the superiority of the degree days model. Even though this model has less than one third the number of climate variables included in the alternative, we can reject the null hypothesis of equal forecasting accuracy in favor of the degree days model with a t-statistic of 2.94 .14 Kaufmann emphasizes that the parameter estimates in the model using undemeaned climate variables often vary between models. This is not surprising in light of the strong multi-colinearity between the climate variables that leads to frequent switching of the parameter estimates, sometimes with large marginal effects. This can be seen in our data as well, as shown in an appendix available from the authors on request. Summarizing briefly, when the monthly climatic variables for January, April, July and October are included, the only variables which are significant in the pooled model between all census years are July temperature and April and October precipitation ; none of the other 10 monthly climate variables in the pooled model is significant even at the 10% level. Further, the coefficients on July temperature imply that farmland value peaks at an average temperature of 22◦C ≈ 72◦F, which seems rather low given agronomic research showing that plant growth is linear in temperature up to about 32◦C. There are other anomalous results, but as the coefficients are not significant, we do not discuss them further here. The results of the degree days model are very reasonable in the light of the agronomic literature. But how robust are they across plausible alternative specifications of variables and data? Here we briefly describe several sensitivity tests. A more complete discussion is given in the appendix available on request. We test the stability of the five climatic coefficients across the several census years in our pooled model. During this period there were some significant changes in farmland values east of the 100th meridian; the overall farmland value in this region declined by 32% between 1982 and 1987 in real terms, and increased by 13% between 1987 and 1992, and 14% between 1992 and 1997.