There are three further issues about equation that bear noting. First, it is likely that the error terms are correlated among nearby geographical areas. For example, unobserved soil productivity is likely to be spatially correlated. In this case, the standard OLS formulas for inference are incorrect since the error variance is not spherical. In absence of knowledge on the sources and the extent of residual spatial dependence in land value data, we adjust the standard errors for spatial dependence of an unknown form following the approach of Conley . The basic idea is that the spatial dependence between two observations will decline as the distance between the two observations increases.Throughout the paper, we present standard errors calculated with the Eicker-White formula that allows for heteroskedasticity of an unspecified nature, in addition to those calculated with the Conley formula. Second, it may be appropriate to weight equation . Since the dependent variable is county level farmland values per acre, we think there are two complementary reasons to weight by the square root of acres of farmland. First,growing raspberries in pots the estimates of the value of farmland from counties with large agricultural operations will be more precise than the estimates from counties with small operations and the weighting corrects for the heteroskedasticity associated with the differences in precision. Second, the weighted mean of the dependent variable is equal to the national value of farmland normalized by total acres devoted to agriculture in the country.
MNS estimate models that use the square roots of the percent of the county in cropland and total revenue from crop sales as weights, respectively. We also present results based on these approaches, although the motivation for these weighting schemes is less transparent. For example, they both correct for particular forms of heteroskedasticity but it is difficult to justify the assumptions about the variance covariance matrix that would motivate these weights. Further, although these weights emphasize the counties that are most important to total agricultural production, they do so in an unconventional manner. Consequently, the weighted means of the dependent variable with these weights have a non-standard interpretation. Third to probe the robustness of the hedonic approach, we estimate it with data from each of the Census years. If this model is specified correctly, the estimates will be unaffected by the year in which the model is estimated. If the estimates differ across years, this may be interpreted as evidence that the hedonic model is misspecified. As the previous section highlighted, the hedonic approach relies on the assumption that the climate variables are orthogonal to unobserved determinants of land values. We begin by examining whether these variables are orthogonal to observable predictors of farm values. While this is not a formal test of the identifying assumption, there are at least two reasons that it may seem reasonable to presume that this approach will produce valid estimates of the effects of climate when the observables are balanced. First, consistent inference will not depend on functional form assumptions on the relations between the observable confounders and farm values. Second, the unobservables may be more likely to be balanced . Table 3A shows the association of the temperature variables with farm values and likely determinants of farm values and 3B does the same for the precipitation variables.
To understand the structure of the tables, consider the upper-left corner of Table 3A. The entries in the first four columns are the means of farmland values, soil characteristics, and socioeconomic and locational characteristics by quartile of the January temperature normal, where normal refers to the long run county average temperature. The means are calculated with data from the five Censuses but are adjusted for year effects. Throughout Tables 3A and 3B, quartile 1 refers to counties with a climate normal in the lowest quartile, so, for example, quartile 1 counties for January temperature are the coldest. The fifth column reports the F-statistic from a test that the means are equal across the quartiles. Since there are five observations per county, the test statistics allows for county-specific random effects. A value of 2.37 indicates that the null hypothesis can be rejected at the 5% level. If climate were randomly assigned across counties, there would be very few significant differences. It is immediately evident that the observable determinants of farmland values are not balanced across the quartiles of weather normals. In 120 of the 120 cases, the null hypothesis of equality of the sample means of the explanatory variables across quartiles can be rejected at the 5% level. In many cases the differences in the means are large, implying that rejection of the null is not simply due to the sample size. For example, the fraction of the land that is irrigated and the population density in the county are known to be important determinants of the agricultural land values and their means vary dramatically across quartiles of the climate variables. Overall, the entries suggest that the conventional cross-sectional hedonic approach may be biased due to incorrect specification of the functional form of observed variables and omitted variables. With these results in mind, Table 4 implements the hedonic approach. The entries are the predicted change in land values from the benchmark increases of 5 degrees in temperatures and 8% in precipitation from 72 different specifications.
Every specification allows for a quadratic in each of the 8 climate variables. Each county’s predicted change is calculated as the sum of the partial derivatives of farm values with respect to the relevant climate variable at the county’s value of the climate variable multiplied by the predicted change in climate . These county-specific predicted changes are then summed across the 2,860 counties in the sample and reported in billions of 1997 dollars. For the year-specific estimates, the heteroskedastic-consistent and spatial standard errors associated with each estimate are reported in parentheses. For the pooled estimates, the standard errors reported in parentheses allow for clustering at the county level. The 72 sets of entries are the result of 6 different data samples, 4 specifications,plant pot with drainage and 3 assumptions about the correct weights. The data samples are denoted in the row headings. There is a separate sample for each of the Census years and the sixth is the result of pooling data from the five Censuses. Each of the four sets of columns corresponds to a different specification.The second specification follows the previous literature and adjusts for the soil characteristics in Table 2, as well as per capita income and population density and its square. MNS suggest that latitude, longitude, and elevation may be important determinants of land values, so the third specification adds these variables to the regression equation.The fourth specification adds state fixed effects. The exact controls are noted in the rows at the bottom of the table. Within each set of columns, the column “[1]” entries are the result of weighting by the square root of farmland. Recall, this seems like the most sensible assumption about the weights. In the “[2]” and “[3]” columns, the weights are the square root of the percentage of each county in cropland and aggregate value of crop revenue in each county. We initially focus on the first five rows, where the samples are independent. The most striking feature of the entries is the tremendous variation in the estimated impact of climate change on agricultural land values. For example, the estimates range between positive $265 billion and minus $422 billion, which are 19% and -30% of the total value of land and structures in this period. An especially unsettling feature of these results is that even when the specification and weighting assumption are held constant, the estimated impact can vary greatly depending on the sample.
For example, the estimated impact is roughly $200 billion in 1978 but essentially $0 in 1997, with specification #2 and the square root of the acres of farmland as the weight. This finding is troubling because there is no ex-ante reason to believe that the estimate from an individual year is more reliable than those from other years.23 Finally, it is noteworthy that the standard errors are largest when the square root of the crop revenues is the weight, suggesting that this approach fits the data least well. Figure 1 graphically summarizes these 60 estimates of the effect of climate change. This figure plots each of the point estimates, along with their +/- 1 standard error range. The wide variability of the estimates is evident visually and underscores the sensitivity of this approach to alternative assumptions and data sources. An eyeball averaging technique suggests that together they indicate a modestly negative effect. Returning to Table 4, the last row reports the pooled results, which provide a more systematic method to summarize the estimates from each of the 12 combinations of specifications and weighting procedures.The estimated change in property values from the benchmark global warming scenario ranges from -$248 billion to $50 billion . The weighted average of the 12 estimates is -$35 billion, when the weights are the inverse of the standard errors of the estimates. This subsection has produced two important findings. First, the observable determinants of land prices are poorly balanced across quartiles of the climate normals. Second, the hedonic approach produces estimates of the effect of climate change that are sensitive to specification, weighting procedure, and sample and generally are statistically insignificant. Overall, the most plausible conclusions are that either the effect is zero or this method is unable to produce a credible estimate. In light of the importance of the question, it is worthwhile to consider alternative methods to value the economic impact of climate change. The remainder of the paper describes the results from our alternative approach. We now turn to our preferred approach that relies on annual fluctuations in weather about the monthly county normals of temperature and precipitation to estimate the impact of climate change on agricultural profits. Table 5 presents the results from the estimation of four versions of equation , where the dependent variable is county-level agriculture profits and the weather measures are the variables of interest. The weather variables are all modeled with a quadratic. The data for these and the subsequent tables are from the 1987, 1992, and 1997 Censuses, since the profit variable is not available earlier in earlier Censuses. The specification details are noted at the bottom of the table. Each specification includes a full set of county fixed effects as controls. In columns and , the specification includes unrestricted year effects and these are replaced with state by year effects in columns and .Additionally, the columns and specifications adjust for the full set of soil variables listed in Table 1, while the columns and estimating equations do not include these variables. The first panel of the table reports the marginal effects and the heteroskedastic-consistent standard errors of each of the weather measures. The marginal effects measure the effect of a 1-degree change in mean monthly temperatures at the climate means on total agricultural profits, holding constant the other weather variables. The second panel reports p-values from separate F-tests that the temperature variables, precipitation variables, soil variables, and county fixed effects are jointly equal to zero. The third panel of the table reports the estimated change in profits associated with the benchmark doubling of greenhouse gases and the Eicker-White and Conley standard errors of this estimate. Just as in the hedonic approach, we assume a uniform 5 degree Fahrenheit and 8% precipitation increases. This panel also reports the separate impacts of the changes in temperature and precipitation. When the point estimates are taken literally, it is apparent that the impact of a uniform increase in temperature and precipitation will have differential effects throughout the year. Consider the marginal effects from the column specification, which includes the richest set of controls. For example, a 5- degree increase in April temperatures is predicted to decrease mean county-level agricultural profits by $1.35 million, compared to annual mean county profits of approximately $12.1 million. The increase in January temperature would reduce agricultural profits by roughly $0.70 million, while together the increases in July and October temperature would increase mean profits by $1.45 million. The increase in precipitation in January and July is predicted to increase profits, while the October and April increase would decrease profits.