Empirical Estimation of Cropland Decisions

ONLINE RESOURCE 2

Empirical Estimation of Cropland Decisions

This online resource provides detailed information on our econometric estimation of cropland equations that explain allocation of land across crops with a range of economic and climate variables based on historical data, with emphasis on the role of climate change. These estimation models account statistically for changes in cropland using explanatory variables such as market prices, wateravailability, and climate conditions, which are described in detail below. We first present the summary statistics of the data used in the econometric estimation and the specifications including details about the explanatory variables for each cropland equation.

1. Data Summary Statistics

Table 1 presents the summary statistics of the data used in the estimations. The data period spans from the early 1950s to 2008. The starting year of cropland data varies slightly by crop. While cropland data for most crops start from 1952, wheat and pasture start from 1949. All data end in 2008. Price data are at the state level and obtained from sources of the U.S. Department of Agriculture (USDA), mostly from National Agricultural Statistics Service (NASS) and Economic Research Service (ERS). California state level prices reflect the smallest geographic unit for which consistent price data are available and markets are spatially integrated statewide. All prices are converted into real prices using the gross domestic product deflator (Bureau of Economic Analysis).

Table 1 Summary statistics of variables used in the estimation of cropland equations

Note: for prices we use the local standard units which vary by crop from bushels, pounds and 2000 pound tons. For some crops (such as irrigated pasture) the local unit is acres.

2. Model Specification

We specify 13 cropland equations, each associated with an individual crop that currently hassignificant land area in Yolo County. Each equation includes cropland of a specific crop as thedependent variable and a set of climate variables, prices, and other factors as independent (orexplanatory) variables. Below, cropland is expressed as a function of these independent variables.Our guiding principle, in specifying each equation, is that cropland depends on marketconditions, water availability, climate considerations, and other agronomic factors such as croprotations which may be specific to the crop in question. (Estimating full models of supply response is beyond the scope of the current study.)

For the estimation models used for each product, the following conventions in denotingvariables are used: cropland and prices (real price deflated by a gross domestic product deflator)variables begin with capital letters, A for the area measure of cropland and P for the price. This capital letter isfollowed by the commodity name in lower case. We denote precipitation as Prcp. The subscriptat the end of the variable denotes the year for which the data are used. So, for example, thesubscript, t‐i, indicates that the variable is lagged by i periods. More definitions follow thepresentation of these 13 cropland equations that describe historical changes in cropland are asfollows:

Aricet = f (Pricet‐1, Pcornt‐1, Dind, Prcpt‐1, Prcpt‐2, GDDsummer)

Acornt = f (Pcornt‐1, Pbarleyt‐1, Palfalfat‐1, Dind, Prcpt‐1, Prcpt‐2, GDDsummer)

Awheatt = f (Pwheat t‐1, Atomato t‐1, Dind, Prcp, Prcp t‐1, Prcp t‐2, GDDwinter)

Aalfalfat = f (Palfalfat‐2, Dind, Prcp t‐1, Prcp t‐2, Prcp t‐3, GDDwinter)

Asafflowert = f (Psafflower t‐1, Pcorn t‐1, Dind, Prcp t‐1, Prcp t‐2, GDDsummer)

Apasturet = f (Ppasture t‐1, Pbarley t‐1, Pwheat t‐1, Dind, Prcp t‐1, Prcp t‐2, GDDsummer)

Atomatot = f (Ptomato t‐1, Arice t‐1, Psafflower t‐1, Dind, Prcp t‐1, Prcp t‐2, GDDwinter)

Aothervegt = f (Atomato t‐1, Pcorn t‐1, Pwheat t‐1, Dind, Prcp t‐1, Prcp t‐2, GDDsummer)

Aprunet = f(Pprunet‐5,6,7, Pgrape t‐6, Dind, Prcp t‐1, Prcp t‐2, Chill)

Agrapest = f(Pgrapet‐1,2,3, Aprune t‐2, Dind, Prcp t‐3, Prcp t‐4, Chill)

Amfruitt = f(Pmfruitt‐1,2,3, Palmond t‐5, Dind, Prcp t‐3, Prcp t‐4, GDDsummer, Chill)

Aalmondt = f(Palmondt‐5,6,7, Pwalnut t‐3, Pprune t‐3, Dind, Prcp t‐1, Prcp t‐2, Chill)

Awalnutt = f(Pwalnutt‐5, Palmond t‐3, Pprune t‐3, Dind, Prcp t‐4, Prcp t‐5, Chill)

Further variable definitions are as follows:

A commodityjt = acres of commodityjat period t, where j = rice, corn, wheat, alfalfa, safflower,pasture, tomato, other vegetables (denoted as otherveg), prune, grape, other miscellaneousfruit (denoted as mfruit), almond, and walnut.

P commodityjt‐i =real (deflated) price of commodityj, at period t‐i (lagged by i periods)

Dind = binary variable that separates the period between before and after Indian Valleyreservoir, if year<1975, Dind = 1, otherwise Dind = 0.

GDDsummer = ten year moving average of growing degree days for spring and summermonths, beginning on April 1 and ending on August 31

GDDwinter = ten year moving average of annual growing degree days for winter and springmonths, beginning on November 1 and ending May 31

Chill = ten year moving average of annual winter chill hours

Prcpt‐i = total precipitation at period t‐i

Pprunet‐5,6,7 = three year moving average of lagged prices, Pprunet‐5, Pprunet‐6, Pprunet‐7,

Pgrapet‐1,2,3 = three year moving average of lagged prices, Pgrapet‐1, Pgrapet‐2, Pgrapet‐3,

Pmfruitt‐1,2,3 = three year moving average of lagged prices of miscellaneous fruits, Pmfruitt‐1,Pmfruitt‐2, Pmfruitt‐3,

Palmondt‐5,6,7 = three year moving average of lagged prices, Palmondt‐5, Palmondt‐6, Palmondt‐7

In each equation, product market conditions are represented by own product price andprices of substitute crops. Price data used in our analysis are obtained from the U.S. Departmentof Agriculture (USDA) sources (USDA/National Agricultural Statistics Service [NASS]). TheUSDA publishes prices of major agricultural commodities, and the state level is the smallestgeographic unit for which consistent price data are available. Statewide, markets are spatiallyintegrated and price is highly correlated within relatively large regions allowing us to useCalifornia prices for Yolo County. All prices are converted into real prices using the grossdomestic product deflator. Note that in many annual cropequations we used prices that were lagged one period because cropland decisions are usuallymade based on the information available prior to the crop year, with an exception of alfalfa,which usually is grown for multiple years once the field is developed. For perennial crops, weused prices of much more distant lags, since many orchard crops take three to seven years fromthe time of planting until commercial harvest. Nevertheless, the specific lag may differ for eachorchard crop and is not known with certainty. Multiple lags form a moving average of ownprices. The concept is that the perennial cropland harvested in year t is based largely onplanting decisions made several years in the past.

The climate variables used are annual growing degree days and winter chill hours, mostly withthe former for annual crops and the latter for perennial crops. Note that climate variables hereare intended to represent the general trend of climate rather than year‐to‐year short‐termchanges in weather. Thus, to smooth out short‐term fluctuations and identify a long‐term trend,we use a ten‐year moving average of each climate variable. The effects of irrigation watersupply are captured by two lagged precipitation variables and a variable for the effect of wateravailability from a nearby reservoir (Dind). Most California crops are irrigated, andprecipitation here is used as a proxy representing irrigation water availability. In California, oneimportant supplier of irrigation water is reservoirs, and previous years’ rainfall is important forreplenishing water supply in reservoirs. We had to use a proxy for the reservoir storage level because a time series for reservoir storage that was long enough to match with our production data was not available. The dummy variable, Dind, captures the effect of theIndian Valley reservoir, which began operating in 1976 and increased flexibility in supplyingwater in Yolo County farmland. The reference period for this binary variable isthe period of post‐Indian Valley reservoir.

The GDDwinter variable reflects the winter growing season. Most wheat produced in YoloCounty is spring wheat that is planted in winter. The Sacramento Valley produces a large share of California’s fall‐sown hard red wheat, along with fall sown hard white wheat, barley, oats, and triticale. Most wheat cultivars have a late fall‐sown and spring grown habit and are day‐length insensitive. In Sacramento Valley, wheat is planted in November and harvested in June (University of California Cooperative Extension 2009). The GDDwinter is also used for tomatoes andalfalfa, even though these crops are mainly summer‐harvested crops. In Yolo County, tomatoesintended for early harvest are planted as early as February. Alfalfa is a perennial crop and thefirst harvest occurs in April in California (planted in October) (University of CaliforniaCooperative Extension 2003). The GDD during the winter season is particularly relevant tothese crops because they usually have sufficient growing degree days during the summer inCalifornia.

We also include variables representing prices of substitute or rotation crops where these arerelevant. In Sacramento Valley, irrigated small grains are grown in rotation with alfalfa, cotton,corn, rice, safflower, and a wide range of vegetable crops. The choice of rotation crops alsodepends on the specific site and the economic prospects for the rotation crops (March andJackson 2008; University of California, Division of Agriculture and Natural Resources 2006). Foreach equation, we report the models that include variables which had significant effects andexplained more of the variation in cropland.

Finally, a just few comments on technical issues related to econometric methods are needed. Forthe regression techniques to generate unbiased parameter estimates, the data must betransformed to meet certain statistical properties. Of particular relevance here, explanatoryvariables used in the model are transformed to have constant mean and variance over time. Weconducted specification tests which evaluate statistical properties of all the time series (Enders 2004, Engle and Granger 1987). In order to satisfy the needed conditions,we used each variable in a first difference form. For example, the dependent variable in eachmodel is the year‐to‐year change incropland, and the explanatory variables are also representedas year‐to‐year changes. That is, in the estimated models, we regress the first difference incropland on the first differences of explanatory variables.

3. Estimation Results

Among the field and vegetable crops, own prices are found to be important for rice and wheatland decisions (P≤0.01). For these crops, the favorable own price contributes to theexpansion of cropland, and likewise, the unfavorable own price has a negative effect on cropland (Table 2 below).

Own price of tomatoes is found statistically significant at P≤0.1. Irrigation water availability alsoaffects cropland decisions. Our regressions use previous years’ precipitation as a proxy forirrigation water availability; the effects are positive for alfalfa and corn, and negative for wheatand safflower (P≤0.06). Among the field crops considered here, the most water‐intensive crops(per acre basis) are rice and alfalfa. For rice, own price is significant butprecipitation variables are not, indicating the relative importance of economic variables overwater availability for rice land. This conjecture is supported by crop values per hectare of land, which,averaged over the last ten years, (1999–2008) were $1,823 for alfalfa and $2,517 for rice. Theresults on wheat and safflower are also consistent with their low dependence on irrigation andlow per‐hectare value. Thus, abundant water supply would induce farmers to shift away fromthese crops and the opposite would occur with constrained water supply. Note that the wheatequation includes current period precipitation, as well as two previous years’ precipitation,because the current year’s precipitation season ends in April which is many months before thewheat planting time in November.

Summer temperatures (as represented by the GDDsummer variable) did not directly affect theallocation of cropland among crops in Yolo County.9 The minor changes in temperature duringthe months of April, May, June, July, and August for the past 100 years apparently have hadlittle effect on the planting pattern. Winter temperatures (as represented by the GDD wintervariable) had significant effects on cropland equations for both alfalfa and wheat (P≤0.01 and0.02, respectively).Warmer winter growing seasons (November 1 through May 31) have had anegative effect on wheat land, but a positive effect on alfalfa land. In many winter wheatgrowing regions in the United States, winter kill caused by a harsh winter is a major risk(Wiersma 2006), but this is not a problem in California. In California, spring wheat varieties donot require a period of cool growing conditions (vernalization) to trigger reproductive growth(Chouard 1960).

Negative effects of GDDwinter on wheat land are difficult to explainphysiologically. Wheat is successfully adapted to conditions in the southern Central Valleywhere it is generally warmer in the winter than it is in Yolo County. For alfalfa production, awarmer winter is expected to provide favorable conditions, particularly since alfalfa varietiescommonly planted in northern California are either semi‐dormant or non‐dormant (Putnam etal. 2007). In the Sacramento Valley, alfalfa is harvested six to seven times a year, with its firstharvest beginning in April, thus warmer conditions in the spring would increase productionand income.

For orchard crops, the prune and grape land equations have significant own price effects (P0.05). For grapes, this may be due to increased wine consumption and demand in the United States. Precipitation variables show some differences between annual and orchard crops. Orchard crops may be more resilient to water availability since they tend to use drip irrigation, and use a smaller share in total costs for irrigation than annual crops (University of California Cooperative Extension). Finally, no one plants orchards without already securing access to water and this is a very long term consideration, not dependant on short run fluctuations.

The data also indicate that winter chill hours have statistically significant relationships with acres of prunes and miscellaneous fruits ( P0.05), and for walnuts (P0.08). These effects indicate that an increase in winter temperatures is associated with a decrease in cropland for these crops. Walnuts and prunes are among the fruits which require significant numbers of chill hours (Table 1 in the text). Further calculation indicates that 1% change in chill hours induces also about 1% change in cropland for prunes and walnuts, but about 1.7% change for miscellaneous other fruits.

Table 2 Estimation results of cropland regression for rice, wheat, safflower, alfalfa, corn, irrigated pasture, tomatoes, other vegetables, grapes, prunes, almonds, walnuts, and miscellaneous fruit (variable definitions are provided in the previous model specification subsection).

The number of asterisks indicates different levels of significance: *** for 1% level of significance, ** for 5% of significance, and * for 10% level of significance.

4. Additional Discussion ofEconometric Model Specifications

4.1 Selection of explanatory variables

In on-line resource 2 section 2 “Model Specification”, we provided the cropland allocation equations and a discussion of how we selected the variables. This sub-section provides more detailed discussion of model specification, focusing on selection ofexplanatory variables.

Model selection is guided by economic principles reflecting farmer incentives, previous cropland allocation literature, data availability, and information criteria that minimize the loss of information. While economic principles help us with the general selection of concepts to represent, the specificchoice of candidate variables is dictated by data availability. Data for candidate variables must have been available at the county level annually for a long time period. Once the candidate variables are selected, we check the possibility of correlations among the variables (to avoid severe multicollinearity) and we apply the statistical information criteria to evaluate the models among the competing specifications. While we outline below the exact steps involved in variable selection, we do not provide the full detailed test results because the entire procedure involves many test results. The steps used in variable selection are:

1. The basic rationale behind choosing each economic category of variable or concept is presented in the main text. These categories are: own price of the crop, prices of substitute crops, climate variables, water availability, and agronomic constraints.