Historic water prices over the last 50 years for water deliveries from the Central Valley Project are listed in the 2000 Irrigation Water Rates Manual available at the library of the Bureau of Reclamation in Sacramento. Finally, the acreage of each district is derived with the help of geographic information systems of the irrigation district boundaries. Researchers also obtained observations on more than 15,000 groundwater wells in the Central Valley. Groundwater is a virtually unregulated resource and in many areas it provides a substitute for surface water in the event of a shortage. The depth of groundwater varies significantly, both spatially and temporally, between years and between months within a year. Researchers calculated the average well depth in the month of March, the beginning of the growing season, for each of the years 1990 to 1998 and then averaged the depths over these years. The groundwater depth at each farm location is derived as a weighted average of all well locations, where the weight is the inverse of the distance of each well to the farm to the power of 2.14—the exponent that minimizes the sum of prediction errors from cross‐validation. In the cross‐validation step each well is excluded from the data at a time and the depth is calculated using all remaining wells. There are several soil databases of potential interest to this analysis. In order of increasing detail, they are the: National Soil Geographic Database that relies on the National Resource Inventory , State Soil Geographic Database and Soil Survey Geographic Database . While SURGO is the most detailed soil database designed to allow erosion management of individual plots,there is no uniform reporting requirement for the United States. Furthermore, the observations in the June Agricultural Survey include all farms in the vicinity of a longitude/latitude pair, and hence, choosing field characteristics of one individual plot appears inappropriate. Instead,bato bucket the study uses the more aggregated soil database STATSGO, which groups similar soils into polygons for the entire United States.

Average soil qualities are given for each polygon. Although this soil database gives a first approximation of the actual average soil qualities, there might be significant heterogeneity, which is addressed in the empirical section. Finally, farmland close to urban areas has an inflated value compared to farmland elsewhere because of the option value of the land for urban development . Plantinga et al. examine the effects of potential land development on farmland prices and find that a large share of farmland value, more than 80% in major metropolitan areas, is attributable to the option to develop the land for urban uses. This study therefore constructed a variable to approximate population pressure by summing the population in each of the 7049 Census Tracts from the 2000 Census divided by the inverted square of the distance of the tract to the farm. Table 3‐1 displays the data’s summary statistics. This section presents the estimates for the hedonic regression with farmland value per acre as the dependent variable. The results are listed in Table 3‐2. The table uses feasible generalized least squares weights that account for the spatial correlation of the error terms.10Researchers conducted three spatial tests to test whether spatial correlation is indeed a problem. One test is the Moran‐I statistic . However, since this test does not have a clear alternative hypothesis, researchers supplemented it with two Lagrange‐Multiplier tests involving an alternative of spatial dependence: the LM‐ERR test of Burridge and LM‐EL test of Anselin et al. .The normal test statistic for the Moran‐I is 16.8, and the Lagrangian multiplier test are χ 2 ‐distributed with test statistics of 299 and 289, respectively. Therefore, all tests indicate that spatial correlation is indeed present. Hence the standard ordinary least squares estimate underestimates the true variance‐covariance matrix—OLS assumes all errors to be independent, even though they are in fact correlated. This suggests that standard OLS estimates of standard errors for hedonic regression equations generally might be misleading if the error terms among observations in close proximity are correlated. In fact, it is not uncommon in hedonic studies for variables to be statistically significant, yet to switch signs between alternative formulations of the model. Table 3‐2 therefore uses feasible GLS to construct the most efficient estimator by premultiplying the data by .

In the second stage, researchers estimated the model and use White’s heteroscedasticity consistent estimator to account for the heteroscedasticity of the error terms . The estimates in Table 3‐2 are based on observations with a farmland value below $20,000 per acre and water prices below $20. Including higher value observations in the analysis increases the R‐square of the regression, but the variable with the greatest explanatory power becomes population density. At the same time, the confidence levels for soil quality and water availability are reduced. Farmland with values above $20,000 per acre is generally close to urban areas, and the value of this land reflects what is happening in the urban land market, and the value of the future potential to develop this land for urban use—not what is going on in the local agricultural economy. Including these observations creates large outliers and results in estimates that are mainly driven by these outliers.Second, the research team excluded irrigation districts with expensive water prices from the analysis to get a better estimate of the net value of water. Only the net value of water, the difference between gross value and delivery cost capitalizes into farmland values. As an example, if the gross discounted value of an acre‐foot of water were $1000 and the annual delivery cost $50, the net value of the water would be zero . The researchers therefore test the sensitivity of the results to variations in water price by excluding irrigation districts with high prices from the analysis to get a better estimate of the net value of water. The coefficients on the climatic variables appear reasonable. The result for degree‐days implies that the quadratic form peaks at 1630 degree‐days. This is consistent with the agronomic literature, which indicates degree‐day requirements of this order of magnitude for several important crops grown in the Central Valley.While the coefficients are borderline significant under the feasible GLS model, the p‐value on the hypothesis that the linear and squared term on degree‐days is jointly equal to zero is 0.008, and degree‐days as a group are hence highly significant. One potential problem in the estimation using both the linear and squared variable is the high degree of colinearity between the two variables,dutch bucket hydroponic which will reduce the significance level of each individual variable. The correlation coefficient between degree‐days and degree‐ days squared is 0.98.

Another problem is that the variation in climatic variables with the Central Valley, the main growing region, is limited. In a related paper that examines the effect of degree‐ days on farmland values in the Eastern United States, the degree‐days variables are comparable in size and highly significant. Because many tree crops need cool nights, increasing temperatures substantially above the required degree‐days to grow a crop can only be harmful. The sign of the regression coefficient on water availability in Table 3‐2 makes intuitive sense: rights to subsidized surface water are beneficial. However, water rights have a price, as well as a quantity dimension. As mentioned before, only the net value of water capitalizes into farmland values. Therefore, the study tested the sensitivity of its results to variations in water price by excluding irrigation districts with high prices from the analysis, to get a better estimate of the net value of water. Restricting the sample to observations that have water rights with water prices less than $30, $40, and $50, and using no price restriction at all decreases the value of an acre‐foot from $809 in Table 3‐2 to $625, $583, $524, and $395, respectively, as the hedonic regression only picks up the net benefit of the water right. The linearity of the coefficient on water rights is confirmed when dummies for different ranges of water rights are included.14 The sample includes districts with zero private or federal water rights. These are districts that depend primarily on groundwater and state water. Since state water is very expensive, it is excluded from the estimation.15 Finally, a greater depth to groundwater is harmful, as it would result in larger pumping costs, but the coefficient of this variable is not significant. Soil variables have intuitive signs as well, and four of the five soil variables are significant at the 5% level. Higher values of the variable K‐factor indicate increasing erodibility of the top soil. Similarly, a higher clay content is also less desirable, as is low permeability, which indicates a soil that does not hold water. Finally, population density has a big influence on land prices: this variable is highly significant and of a large magnitude compared to the sample mean. The potential to sell agricultural land for urban development is often the most profitable option for farmers. The research team conducted several sensitivity checks, which are listed in Appendix 1. The results on water availability are remarkably robust, while the results for the variable degree‐ days are more sensitive to the particular implementation. However, the latter might be explained by the limited climatic variation in this project’s sample study. The team conducted a similar analysis for the Eastern United States with much larger variation in climatic variables, and find results that are again very robust and similar to the ones presented above. The coefficients on the climatic variables can now be used to calculate the impact of climate change on farmland values in California.

The impact of climate change on farmland values can be derived by evaluating the hedonic function both at the current climate and at a new predicted climate.First, note that a decrease in availability of federal and surface water would have a large and significant impact on the value of farmland. The coefficient on water availability is between $400–$850 per AF, depending on the price a district pays for water.Because researchers modeled surface water availability as additively separable from other exogenous variables, the impact is easily derived as the product of the value per AF and the decrease in water availability.As mentioned before, recent hydrological studies for moderate‐temperate climates utilizing a smaller geographic scale discovered that despite the increase in annual precipitation, the runoff during the main growing season , might actually decrease as a seasonality effect dominates the annual effect.The decrease in runoff translates into decreasing surface water availability, where the magnitude depends on the seniority of water rights. More senior water rights holders always get served first and are hence less prone to a decrease in water availability. For the same reason, junior rights holders will face potentially large reductions in availability. Given that the estimated value for cheap water is $809 per AF, a modest reduction of just 0.5 AF per acre will lower the value of the affected farmland by approximately $400 per acre. In this study’s degree‐day model, changes in temperatures have nonlinear effects on the resulting number of degree‐days. In fact, the study’s approach is conservative in the sense that temperatures above the upper threshold b2 = 32°C are assumed to have no impact on plant growth and 35°C are the same. The approach therefore assumes the marginal effect of further temperature increases to be zero, while some agronomic studies argue it should be negative.Table 3‐3 lists the average area‐weighted impact of a change in climatic conditions for three uniform temperature increases.The research team used the coefficient estimates from Table 3‐2 that corrects for the spatial correlation of the error terms.For comparison, the area‐weighted value of all observations in this study’s sample is $4,265. On average, the value of farmland in California would decrease by $482 per acre, or around 11%, under the hottest 3°C increase scenario. However, the distribution of impacts is quite different, ranging from large damages to modest benefits. Existing areas with a very hot climate—especially farms in the Imperial Valley—would face much larger relative decreases in value, while farmland around the Delta with its natural cooling mechanism would benefit slightly from an increase in temperatures, and hence degree‐days. Given the linear structure of the hedonic equation, the aggregate impact is simply a linear combination of the regression coefficients, and hence is itself normally distributed.