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Do crop price expectations matter? An analysis of groundwater pumping decisions in Western Kansas
Agricultural Water Management 231 (2020) 106021
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Do crop price expectations matter? An analysis of groundwater pumping decisions in Western Kansas
T
Kunlapath Sukcharoen*, Bill Golden, Mallory Vestal, Bridget Guerrero West Texas A&M University, 2403 Russell Long Blvd., Canyon, 79015, United States
A R T I C LE I N FO
A B S T R A C T
Keywords: Agriculture Ogallala aquifer Price expectations Pumping decisions Irrigation Profit maximization
The Ogallala Aquifer is the main water resource for irrigated agricultural production in much of Western Kansas. It is hypothesized that as crop price expectations increase, producers will apply more water to increase yields in order to maximize profit. Using field-level panel data on groundwater pumped for irrigation in Western Kansas, this paper examines whether irrigated producers’ groundwater pumping decisions are consistent with the profit maximization framework by empirically testing if crop price expectations have a positive impact on the quantity of groundwater pumped. In general, the empirical results indicate that crop price expectations have no statistically significant impact on the quantity of groundwater pumped per acre. This suggests that groundwater pumping decisions are not consistent with the profit maximization framework and that irrigated producers consider groundwater as a fixed input possibly due to limited availability of groundwater in the area. Our econometric analysis also suggests that only a small portion of rainfall is effective.
1. Introduction Irrigated crop production in the High Plains region is highly dependent on groundwater pumped from the Ogallala Aquifer due to limited and variable rainfall. Agriculture is the major user of this limited resource, and simultaneously, is the main economic driver for the economy of Western Kansas, especially in the rural communities. Stakeholders, including local groundwater authorities, are continually considering ways to conserve resources for future generations, while keeping the regional economy viable. Intertemporal dynamic allocation models are often employed by economists to aid in the prediction of future groundwater use, crop acreage, and net farm income for policymakers (Terrell et al., 2002; Amosson et al., 2009; Golden and Johnson, 2013; Tewari et al., 2014). Economists generally assume that expected crop prices have a positive effect on the quantity of groundwater used to produce the commodity. However, anecdotal evidence suggests that irrigated producers consider groundwater a fixed production input and only vary this fixed input as rainfall varies. Because results of intertemporal dynamic allocation models are typically used as a basis to provide information for policymakers, there is a need to closely evaluate the relationship between expected crop prices and groundwater pumping in order to provide more accuracy in model results and provide better water use predictions.
⁎
The hypothesis that expected commodity prices have a positive effect on the per-acre quantity of groundwater used to produce the commodity is evaluated in this study. The overall objective of this study is to examine whether irrigated producers’ groundwater pumping decisions are consistent with the profit maximization framework by empirically testing if crop price expectations have a positive impact on the quantity of groundwater pumped. Specifically, statistical models are constructed to determine if and how expected crop prices affect the quantity of water applied to alfalfa, corn, grain sorghum, soybeans, and wheat, which are the major irrigated crops in Western Kansas. In addition, various proxies are used to evaluate crop price expectations, given that producers tend to have differing outlooks on prices. This paper is organized as follows. Section 2 describes the conceptual and empirical framework. Section 3 presents the data and preliminary analysis. Section 4 reports the empirical results. Lastly, Section 5 provides the conclusions drawn from the analysis. 2. Conceptual and empirical framework Economists generally assume that farmers’ irrigation decisions depend on not only crop choice, total number of irrigated acres, and cost of irrigation water, but also expected crop prices (Moore and Negri, 1992; Moore et al., 1994; Mullen et al., 2009; Adusumilli et al., 2011). This belief follows from the theory that rational crop producers will
Corresponding author. E-mail address: [email protected] (K. Sukcharoen).
https://doi.org/10.1016/j.agwat.2020.106021 Received 10 September 2019; Received in revised form 6 January 2020; Accepted 7 January 2020 0378-3774/ © 2020 Elsevier B.V. All rights reserved.
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wjt = X jt' β + θj + λt + εjt
maximize their expected profits associated with crop production. Specifically, based on a multi-crop production model developed by Moore et al. (1994), the goal of crop producers is to maximize their expected profit: m
Π(p, q, N , z ) =
⎛ ∑ πi (pi , q, ni; z ): w1, w 2, … , wm ⎜ ⎝ i=1 max
where Xjt is a vector of explanatory variables including normalized expected crop prices, the number of irrigated acres, and precipitation; β is a vector of parameters to be estimated; θj captures heterogeneity in field or farmer characteristics; λt captures the year fixed effects; and εjt is an idiosyncratic disturbance term. The fixed effects model does not allow us to examine the impact of field-specific variables – variables that are constant over time or across fields such as land quality characteristics. However, it is appropriate for our estimation objective of isolating the effects of expected crop prices. Identifying an appropriate proxy for expected crop price is a major challenge in a study of the relationship between farmers’ crop price expectations and groundwater pumping decisions. Different specifications have been used as proxies for expected crop prices in previous work regarding agricultural production decisions. For example, Houck and Gallagher (1976); Shumway and Chang (1980); Schoengold et al. (2006); Pfeiffer and Lin (2014), and Haile et al. (2017) use either an observed market price in the immediately preceding period or an average of past crop prices as a proxy for current crop price expectation. These price expectation specifications are based on an adaptive expectations model proposed by Nerlove (1958). Other studies, including Gardner (1976); McKenzie (2008); Pfeiffer and Lin (2014), and Haile et al. (2016) exploit the hypothesis that the price of a futures contract for next year’s crop is an unbiased predictor of the harvest-time crop price and use the harvest-time futures price as a proxy for farmers’ price expectations. Nevertheless, despite the vast literature on crop price expectations, there is not a universal agreement on the appropriate specification to use for empirical estimation of crop production decisions (Shideed and White, 1989; Nerlove and Bessler, 2001; Vitale et al., 2009). Within this study, various proxies for crop price expectations are employed to test whether crop price expectations have a positive effect on the quantity of groundwater pumped. In particular, following Nerlove’s (1958) adaptive expectations approach, we consider six alternative specifications of farmers’ crop price expectations. The first specification assumes that the expected crop price is an average of monthly crop prices in the preceding year. The second specification uses an average of monthly crop prices in the preceding three years as a proxy for crop price expectations. The third and fourth proxies for crop price expectations are a three-month average of previous-year pre and post-harvest prices, respectively. The fifth and sixth specifications use a three-year average of pre- and post-harvest prices, respectively, as a proxy for farmers’ crop price expectations.
m
∑ ni = N ⎞⎟ ⎠
i=1
(1)
where Π(⋅) is a multi-crop profit function; πi (⋅) is a profit function for crop i ; p = (p1 , p2 , …, pm ) ′ is a vector of expected crop prices for the m crops; q = (q1, q2 , …, qk ) ′ is a vector of variable input prices for the k inputs; ni is the number of irrigated acres planted to crop i ; N is the total number of irrigated acres; and z = (z1, z2, …, z h) ′ is a vector of h other exogenous variables including precipitation, land quality, and irrigation technology. To obtain an estimable groundwater extraction equation, this paper employs a normalized quadratic profit function suggested by Lau (1978) and Huffman (1988). Applying Hotelling’s lemma and the Envelope Theorem to the profit maximization problem in (1) yields the following estimable function for groundwater pumping decision for each crop i : k
m
wi (p, q, ni ; z ) = α i +
∑ γ ji pj j=1
α i , γ ji ,
ητi ,
+
h
∑ ητi qτ + νini + ∑ δsi z s τ=1
s=1
(2)
δsi
ν i , and are the parameters to be estimated. A crop where supply function for each crop i , yi (p, q, ni ; z ) or simply yi , can also be derived from the profit maximization problem in (1). As each profit function, πi (pi , q, ni ; z ) , is assumed to be convex in pi , each crop supply function is increasing in pi ; in other words, ∂yi / ∂pi > 0 (Moore and Negri, 1992). In addition, the concavity of the production function suggests that ∂yi / ∂wi > 0 . Using the implicit function theorem, this implies that: ∂wi >0 ∂pi
(3)
That is, as the expected crop prices, profit-maximizing producers will increase their groundwater use, as long as increased groundwater use increases crop yields and thereby profits. The objective of this paper is to examine whether producers’ irrigation decisions are consistent with the profit maximization framework by empirically testing whether crop price expectations have a positive effect on the quantity of groundwater used to produce the crop. To accomplish this, the quantity of groundwater pumped for each crop is assumed to be a function of normalized expected crop price, pi , and other explanatory variables. Let ni (pi ) denote the optimal number of irrigated acres planted to crop i and wi (pi ) denote the optimal per-acre quantity of groundwater pumped for crop i . The total quantity of groundwater pumped for crop i , qi (pi ) , can then be written as:
qi (pi ) = ni (pi )⋅wi (pi )
3. Data and preliminary analysis The data used in this study were from a 10-county region within Northwest Kansas Groundwater Management District 4 (GMD4) overlying the Ogallala Aquifer: Cheyenne, Decatur, Gove, Graham, Logan, Rawlins, Sheridan, Sherman, Thomas, and Wallace (Fig. 1). The 10 counties were selected mainly due to the availability of field-level groundwater use data. For this analysis, we constructed an unbalanced panel data set of annual data for over 2700 points of diversion (PDIV) within the district from 2001 to 20171 . We only consider the fields planted entirely to one crop. This is because data on how groundwater was allocated to specific crops when multiple crops were planted were not available. For each PDIV (typically a single water well), the data set contained annual groundwater pumped (acre-inches per acre), area irrigated (acres), crop planted, precipitation (inches), pumping cost (dollars per acre-inch), and expected crop prices2 .
(4)
Taking the derivative of Eq. (3) with respect to expected crop price gives:
∂qi ∂n ∂w = ⎜⎛ i ⎞⎟ ni + ⎛⎜ i ⎞⎟ wi p ∂ ∂pi i ⎠ ⎝ ∂pi ⎠ ⎝
(6)
(5)
where ∂wi/ ∂pi measures a direct effect on total groundwater pumped due to changes in per-acre groundwater application and ∂ni / ∂pi captures an indirect effect on total groundwater pumped due to changes in the number of irrigated acre. This study focuses on identifying ∂wi/ ∂pi (the direct effect of changes in expected crop price on groundwater use). This can be accomplished by estimating γii in Eq. (2). To identify producers’ year-to-year changes in per-acre quantity of groundwater pumped in response to yearly changes in expected crop prices, we estimate the following reduced form fixed-effects equation for each crop:
1 Note that while groundwater pumping data were available since the 1940s, natural gas industrial price data used for calculating pumping cost were only available beginning in January 2001. 2 Due to lack of location-specific input prices besides the pumping cost, other
2
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Fig. 1. Northwest Kansas Groundwater Management District No. 4. (Source: Kansas Department of Agriculture).
(USDA) Economic Research Service. For alfalfa, the price received was measured in dollars per ton. February, March, and April prices were used to compute the pre-harvest price, while May, June, and July prices were used to calculate the post-harvest price. For corn and soybeans, the price received was measured in dollars per bushel. For grain sorghum, the price received was measured in dollars per hundredweight. For these three crops (corn, soybeans, and grain sorghum), the preharvest price was calculated using June, July, and August prices, and the post-harvest price was computed using September, October, and November prices. For wheat, the price received was measured in dollars per bushel. March, April, and May prices were used to calculate the preharvest price, while June, July, and August prices were used to compute the post-harvest price. All price data used in the empirical analysis were normalized and the cost of pumping groundwater served as the numeraire. Descriptive statistics of per-acre groundwater pumped, area irrigated, precipitation, depth to water, and pumping cost for the study area are presented in Table 1. At each PDIV, the average annual quantities of groundwater pumped per acre for alfalfa, corn, grain sorghum, soybeans, and wheat were 12.69, 14.57, 9.06, 12.67, and 6.67 acre-inches, respectively. These average figures were calculated using only those fields that are planted entirely to one of the five crops. The quantity of per-acre groundwater pumped for alfalfa was found to be more volatile than for the other four crops. Depending on the crop choice, each water right owner irrigated an average of 69.09–112.75 acres. Each PDIV received an average of 10.38 in. of precipitation per year. Average depth to water is 102.13 feet, and average pumping cost is 99 cents per acre-inch. Descriptive statistics of six alternative proxies for farmers’ crop price expectations are reported in Table 2. With the exception of alfalfa, the three-year average of post-harvest prices (Proxy 6) gave the lowest mean non-normalized and normalized expected crop prices, while the three-month average of previous-year pre-harvest prices (Proxy 3) yielded the highest mean non-normalized and normalized expected crop prices. For the average expected alfalfa prices, the three-year
Data on annual groundwater pumped, area irrigated, and crops planted were obtained from the Water Information Management and Analysis System (WIMAS), which was created and is maintained by the Kansas Department of Agriculture, Division of Water Resources (KDADWR). Monthly precipitation data were retrieved from the PRISM Climate Group and spatially matched to each PDIV using the longitude and latitude of each PDIV. The total quantity of rainfall at each PDIV during October through December of the previous year and January through May of the current year was used to represent precipitation faced by a crop producer when he or she made a groundwater pumping decision. Following Rogers and Alam (2006), producers’ pumping cost per acre-inch of groundwater was computed as:
q = 0.00186⋅pg ⋅d
(7)
where 0.00186 is the quantity of natural gas (thousand cubic feet or Mcf) needed to pump one acre-inch of groundwater one foot, pg the natural gas price (dollars per Mcf), and d is depth to water (feet). Similar to Hendricks and Peterson (2012), pg was calculated as the average of the June and July natural gas industrial prices. Data for Kansas natural gas industrial price were obtained from the Energy Information Administration (EIA). County-level water depth data were retrieved from the Kansas Geological Survey’s Water Information Storage and Retrieval Database (WIZARD).3 Our analysis concentrated on the five most commonly irrigated crops in Northwest Kansas: alfalfa, corn, grain sorghum, soybeans, and wheat. Expected crop prices were constructed using Kansas monthly cash price data from 1997 to 2016. Data on price received for the five crops were taken from the United States Department of Agriculture
(footnote continued) input prices were highly correlated across observations and could not be included in the estimation. 3 County-level water depth data were used because field-level water depth data were only available for a small number of fields. 3
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month average of previous-year pre-harvest prices (Proxy 3) yielded the highest normalized expected alfalfa price. As expected, non-normalized expected crop prices are more volatile than normalized expected crop prices. Note that when the non-normalized expected crop price increases, the normalized expected crop price increases less in areas with a greater depth to water (due to the higher pumping cost). It is this source of variation in the normalized expected crop price that helps identify the impact of crop price expectations. The degree of dependence between the quantity of groundwater pumped and the six alternative proxies of farmers’ crop price expectations is reported in Table 3. This study considered three different measures of the degree of dependence: Pearson’s correlation coefficient, Spearman’s rho, and Kendall’s tau. The Pearson’s correlation coefficient (or simply the linear correlation coefficient) is a measure of the strength of the linear relationship between two variables of interest, whereas Spearman’s rho (i.e., Spearman’s rank correlation coefficient) and Kendall’s tau are measures of nonlinear association between two variables. For all crops, the degrees of linear and nonlinear dependence between the quantity of irrigation water pumped and the expected crop price were negative and statistically significant at the 1-percent level. The negative dependence coefficients indicated that both variables tend to move in the opposite direction. In other words, the quantity of groundwater pumped and crop price expectations were inversely related to each other. Nevertheless, the degrees of association were quite weak. For alfalfa and soybeans, regardless of the dependence measures considered, the strongest association was found when the three-year average of pre-harvest crop prices (Proxy 5) was used as a proxy for expected crop price. For corn and grain sorghum, the strongest linear correlation was also observed when the three-year average of pre-harvest crop prices (Proxy 5) was used as a proxy for expected corn and grain sorghum prices. However, when considering measures of nonlinear dependence, the degree of dependence was strongest for the case of corn when the three-month average of previous-year post-harvest prices (Proxy 4) was used as a proxy and for the case of grain sorghum when the average of monthly crop prices in the preceding year (Proxy 1) was used as a proxy. For wheat, the highest Pearson’s correlation coefficient and Spearman’s rho were found when the average of wheat prices in the preceding three years (Proxy) was used as a proxy. Kendall’s tau, on the other hand, suggested that the degree of association between the two variables was strongest when the expected wheat price was proxied by the average of monthly wheat prices in the preceding year (Proxy 1). Overall, the results from the correlation analysis indicated a weak negative relationship between crop price expectations and the quantity of groundwater applied per acre. These findings are consistent with Adusumilli et al. (2011) who found that expected crop price had a nonpositive impact on groundwater demand for the cases of grain sorghum, wheat, and cotton. These preliminary findings suggest that producers’ irrigation decisions may not be consistent with the profit maximization framework, which asserts that crop price expectations have a positive effect on the quantity of groundwater used to produce the crop.
Table 1 Groundwater pumped, area irrigated, precipitation, depth to water, and pumping cost for the study area. Variable
Mean
Std. Dev.
Annual groundwater pumped (acre-inches/acre) Alfalfa 12.69 7.64 Corn 14.57 5.81 Grain sorghum 9.06 5.67 Soybeans 12.67 5.21 Wheat 6.67 5.23 Area irrigated (acres) Alfalfa 69.09 49.35 Corn 112.75 56.12 Grain sorghum 82.00 58.01 Soybeans 102.68 42.03 Wheat 97.27 56.04 Precipitation (inches) 10.38 3.69 Depth to water (feet) 102.13 42.56 Pumping cost ($/acre-inch) 0.99 0.52
Minimum
Maximum
0 0 0.04 0 0
65.64 68.32 45.07 35.25 42.95
1 1 2 1 1 2.03 25 0.16
289 1545 650 525 414 23.39 202.67 3.16
Table 2 Alternative proxies for farmers’ crop price expectations. Variable
Non-normalized Prices
Normalized Prices
Mean
Std. Dev.
Mean
Std. Dev.
44.78 41.21 44.78 44.91 40.90 41.34
163.66 161.70 164.10 160.97 158.09 160.08
123.92 120.78 127.62 121.46 117.99 121.26
1.54 1.41 1.75 1.42 1.53 1.30
5.10 4.92 5.26 4.94 5.03 4.76
4.43 3.85 4.86 4.23 3.98 3.68
2.73 2.50 3.07 2.64 2.67 2.40
8.45 8.10 8.62 8.11 8.18 7.79
7.71 6.50 8.32 7.44 6.63 6.30
3.15 3.03 3.58 2.92 3.37 2.82
12.07 11.76 12.95 11.38 12.52 11.13
9.55 9.06 10.43 8.71 9.72 8.49
1.76 1.63 2.03 1.79 1.71 1.64
6.74 6.62 6.94 6.63 6.71 6.50
5.43 4.94 6.08 5.40 5.11 4.89
Expected alfalfa price Proxy 1 120.91 Proxy 2 118.75 Proxy 3 120.55 Proxy 4 119.12 Proxy 5 116.39 Proxy 6 117.24 Expected corn price Proxy 1 3.70 Proxy 2 3.60 Proxy 3 3.79 Proxy 4 3.59 Proxy 5 3.68 Proxy 6 3.49 Expected grain sorghum price Proxy 1 6.10 Proxy 2 5.92 Proxy 3 6.16 Proxy 4 5.88 Proxy 5 5.98 Proxy 6 5.71 Expected soybeans price Proxy 1 8.84 Proxy 2 8.59 Proxy 3 9.44 Proxy 4 8.43 Proxy 5 9.15 Proxy 6 8.16 Expected wheat price Proxy 1 4.97 Proxy 2 4.88 Proxy 3 5.02 Proxy 4 4.87 Proxy 5 4.92 Proxy 6 4.78
4. Empirical results
Notes: This study considers six alternative proxies for farmers’ crop price expectations: an average of monthly crop prices in the preceding year (Proxy 1), an average of monthly crop prices in the preceding three years (Proxy 2), a three-month average of previous-year pre-harvest prices (Proxy 3), a threemonth average of previous-year post-harvest prices (Proxy 4), a three-year average of pre-harvest prices (Proxy 5), and a three-year average of post-harvest prices (Proxy 6).
Parameter estimates from fixed effects regressions under various specifications of crop price expectations for alfalfa, corn, grain sorghum, soybeans, and wheat are reported in Tables 4–8, respectively. Note that the fixed effects regressions control for both field heterogeneity and time-fixed effects. For each respective crop, the results are quite consistent across the six alternative proxies for normalized expected crop prices. Depending on crop type and proxy employed, the fixed effects regression helps explain about 14.9–34.4 percent of the variation of quantity of groundwater pumped per acre. The estimation results for alfalfa are shown in Table 4. Regardless of the proxy employed, the coefficient on expected alfalfa price is negative
average of pre-harvest prices (Proxy 5) yielded the lowest non-normalized as well as normalized expected prices. On the other hand, the average of monthly crop prices in the preceding year (Proxy 1) gave the highest non-normalized expected alfalfa price, whereas the three4
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Table 3 Degree of dependence between the quantity of irrigation water applied and normalized expected crop price.
Alfalfa Pearson’s correlation Spearman’s rho Kendall’s tau Corn Pearson’s correlation Spearman’s rho Kendall’s tau Grain sorghum Pearson’s correlation Spearman’s rho Kendall’s tau Soybeans Pearson’s correlation Spearman’s rho Kendall’s tau Wheat Pearson’s correlation Spearman’s rho Kendall’s tau
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
−0.109** −0.164** −0.111**
−0.137** −0.168** −0.113**
−0.110** −0.164** −0.111**
−0.116** −0.167** −0.113**
−0.143** −0.177** −0.119**
−0.137** −0.171** −0.115**
−0.102** −0.176** −0.121**
−0.125** −0.174** −0.118**
−0.097** −0.170** −0.115**
−0.099** −0.182** −0.123**
−0.127** −0.173** −0.117**
−0.121** −0.175** −0.118**
−0.090** −0.175** −0.119**
−0.123** −0.172** −0.116**
−0.088** −0.163** −0.110**
−0.076** −0.170** −0.116**
−0.125** −0.169** −0.114**
−0.111** −0.169** −0.114**
−0.128** −0.189** −0.128**
−0.132** −0.183** −0.124**
−0.130** −0.175** −0.118**
−0.124** −0.192** −0.130**
−0.132** −0.183** −0.124**
−0.128** −0.181** −0.122**
−0.131** −0.198** −0.135**
−0.148** −0.199** −0.135**
−0.131** −0.191** −0.130**
−0.133** −0.196** −0.133**
−0.147** −0.193** −0.130**
−0.146** −0.195** −0.132**
Notes: ** denotes the rejection of the null hypothesis of no association at the 1 % significance level.
Table 5. The estimation results for corn do not give a clear answer concerning the role of expected corn price. We find no significant relationship between expected corn price and the quantity of irrigation water pumped when an average of monthly crop prices in the preceding year (Proxy 1), a three-month average of previous-year pre-harvest prices (Proxy 3), or a three-year average of post-harvest prices (Proxy 6) is used as a proxy for crop price expectations. When an average of crop prices in the preceding three years (Proxy 2) or a three-year average of pre-harvest prices (Proxy 5) is considered, the coefficient on expected corn price is negative and statistically significant at the 1 percent level, implying that corn producers respond to higher expected corn price by reducing the quantity of groundwater applied to corn acreage. However, for the case where a three-month average of previous-year preharvest prices (Proxy 3) is used as a proxy for expected crop price, we observe a significant positive relationship between expected corn price and the quantity of water pumped. Depending on the proxy selected, the fixed effects regression results suggest that expected prices of other crops significantly affect corn producers’ groundwater pumping decisions. Similar to the case of alfalfa, the precipitation variable is negative and statistically significant
but quite small and not statistically different from zero. This indicates that the expected alfalfa price has no statistically significant impact on the quantity of groundwater pumped per acre of alfalfa. The fixed effects regression results also indicate that there is no significant relationship between expected prices of the other four crops and alfalfa producers’ groundwater use decisions. As expected, the coefficients on precipitation are negative for all cases, ranging between -0.346 and -0.321. All of these coefficients are statistically significant at the 1 percent level. This implies that alfalfa producers reduce the quantity of groundwater pumped as rainfall increases. These findings also suggest that only a small portion of total rainfall is effective (i.e., can be used directly for crop production) as the magnitude of all rainfall coefficients is much smaller than one. In addition, we observe a significant inverse relationship between the number of irrigated acres and the quantity of groundwater pumped. This indicates that alfalfa producers with more irrigated acres use less water per acre than those with less irrigated acres. Specifically, we find that the quantity of groundwater pumped per acre is reduced by about 0.056-0.057 acre-inches as the number of irrigated acres increases by one acre. Estimates from the fixed effects regressions for corn are reported in Table 4 Fixed effects (FE) regression results for alfalfa.
Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
−0.003 (0.010) 1.476 (1.106) −0.448 (0.566) −0.211 (0.242) −0.234 (0.370) −0.346** (0.093) −0.056** (0.012) 0.164 1987
−0.009 (0.016) 1.287 (3.207) −0.852 (1.697) 0.193 (0.381) −0.160 (0.426) −0.321** (0.092) −0.057** (0.012) 0.164 1987
−0.008 (0.010) 0.228 (1.075) 0.065 (0.587) −0.071 (0.312) −0.083 (0.372) −0.343** (0.094) −0.056** (0.012) 0.164 1987
−0.003 (0.010) 0.789 (1.172) −0.243 (0.374) −0.036 (0.299) −0.260 (0.376) −0.325** (0.093) −0.056** (0.012) 0.163 1987
−0.004 (0.012) 1.095 (3.159) −0.798 (1.696) 0.035 (0.400) 0.074 (0.446) −0.322** (0.093) −0.057** (0.012) 0.163 1987
−0.013 (0.012) 0.924 (3.186) −0.809 (1.211) 0.497 (0.524) −0.343 (0.554) −0.334** (0.092) −0.057** (0.012) 0.165 1987
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects. 5
Agricultural Water Management 231 (2020) 106021
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Table 5 Fixed effects (FE) regression results for corn. Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
0.005 (0.003) 0.600 (0.315) −0.339** (0.149) 0.189** (0.067) −0.419** (0.084) −0.087** (0.021) −0.044** (0.006) 0.260 18,921
0.010** (0.004) −4.257** (0.854) 1.877** (0.419) 0.385** (0.102) −0.054 (0.112) −0.110** (0.021) −0.044** (0.006) 0.261 18,921
−0.005* (0.003) −0.522 (0.293) 0.217 (0.144) 0.319** (0.068) −0.301** (0.071) −0.098** (0.021) −0.044** (0.006) 0.260 18,921
0.006* (0.003) 1.201** (0.360) −0.635** (0.122) 0.127 (0.075) −0.385** (0.098) −0.099** (0.021) −0.044** (0.006) 0.261 18,921
0.009** (0.003) −3.891** (0.851) 1.879** (0.444) 0.335** (0.101) −0.186 (0.110) −0.099** (0.021) −0.044** (0.006) 0.261 18,921
0.011** (0.003) −1.465 (0.864) 0.365 (0.302) 0.254 (0.158) −0.025 (0.152) −0.102** (0.021) −0.044** (0.006) 0.260 18,921
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects.
additional acre of irrigated sorghum acreage results in a reduction in the per-acre quantity of groundwater pumped by approximately 0.0330.035 acre-inches. Estimates from the fixed effects regressions for soybeans are shown in Table 7. Regardless of the proxy used, the marginal effect of expected soybean price is not statistically significant. Depending on the proxy employed, expected prices of alfalfa and/or corn significantly affect soybeans producers’ groundwater pumping decisions. Similar to the case of grain sorghum, our estimation results suggest that there is no significant relationship between inches of precipitation and the quantity of irrigation applied per acre. As expected, the marginal effect of irrigated acres is negative and statistically significant. In particular, we find that the quantity of groundwater applied per acre is reduced by about 0.080-0.081 acre-inches as the number of irrigated acres planted to soybeans increases by one acre. The estimation results for wheat are reported in Table 8. Considering the role of expected wheat price, we find that the marginal effect of expected wheat price on the per-acre quantity of groundwater pumped is not statistically significant. These findings are consistent across the six proxies employed. We also find that for most cases there is no significant relationship between expected prices of the other four
at the 1 percent level. Specifically, the estimation results indicate that corn producers reduce the quantity of groundwater applied per acre by approximately 0.087 to 0.110 acre-inches for each additional inch of rainfall, confirming that only a small portion of rainfall is effective. We also find that the marginal effect of the number of irrigated acres is negative and statistically significant at the 1 percent level; each additional acre of irrigated land planted to corn results in a reduction in the quantity of groundwater extracted per acre by about 0.044 acre-inches. The estimation results for grain sorghum are presented in Table 6. Except when a three-year average of post-harvest prices (Proxy 6) is used as a proxy for expected crop prices, our results indicate that expected sorghum price does not significantly affect the quantity of groundwater pumped. When Proxy 6 is considered, we find a significant positive relationship between expected sorghum price and the quantity of irrigation water use. Similar to the case of alfalfa, there is no significant relationship between expected prices of the other four crops and sorghum producers’ irrigation decisions. Interestingly, the precipitation level does not significantly affect groundwater use decisions. Similar to the case of alfalfa and corn, the empirical results tells us that sorghum producers with more irrigated acres apply less groundwater per acre than those with less irrigated acres. Specifically, each Table 6 Fixed effects (FE) regression results for grain sorghum.
Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
−0.021 (0.022) −3.225 (2.437) 2.107 (1.202) 0.594 (0.537) −0.823 (0.733) −0.023 (0.158) −0.033** (0.011) 0.264 792
−0.030 (0.022) −6.980 (6.495) 4.469 (3.292) 0.699 (0.838) −0.774 (1.282) 0.001 (0.156) −0.034** (0.011) 0.263 792
−0.019 (0.027) −2.435 (1.733) 1.520 (0.847) 0.386 (0.484) −0.280 (0.457) −0.044 (0.162) −0.035** (0.012) 0.259 792
−0.005 (0.018) −0.173 (2.753) 0.350 (1.000) −0.197 (0.584) 0.151 (0.604) −0.024 (0.173) −0.034** (0.012) 0.256 792
−0.019 (0.016) −3.506 (5.859) 2.368 (3.155) 0.700 (0.944) −1.074 (1.274) 0.021 (0.161) −0.034** (0.011) 0.259 792
−0.016 (0.022) −11.202 (5.985) 4.426* (2.141) 1.630 (1.167) 0.462 (1.506) 0.008 (0.157) −0.034** (0.011) 0.265 792
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects. 6
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Table 7 Fixed effects (FE) regression results for soybeans. Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
−0.014 (0.008) 1.456 (1.055) −0.297 (0.499) −0.145 (0.264) −0.168 (0.236) 0.031 (0.099) −0.080** (0.017) 0.341 1849
−0.032** (0.012) 1.283 (3.013) −0.007 (1.560) 0.041 (0.327) −0.286 (0.292) 0.066 (0.101) −0.081** (0.017) 0.341 1849
−0.006 (0.008) 2.126* (0.841) −0.807 (0.427) −0.245 (0.245) −0.026 (0.197) 0.032 (0.099) −0.081** (0.017) 0.342 1849
−0.015 (0.009) −1.351 (1.232) 0.630 (0.405) 0.199 (0.298) 0.246 (0.276) 0.055 (0.100) −0.080** (0.017) 0.339 1849
−0.021* (0.008) 2.238 (2.883) −0.891 (1.521) 0.116 (0.334) −0.333 (0.273) 0.068 (0.101) −0.081** (0.017) 0.342 1849
−0.025* (0.011) −2.122 (3.471) 0.953 (1.270) 0.610 (0.549) −0.076 (0.485) 0.061 (0.102) −0.081** (0.017) 0.343 1849
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects.
for explaining groundwater extraction decisions and that we need to look for an alternative way to model groundwater use. In addition, we find that only a small portion of total rainfall can be used directly for crop production and considered effective. The estimation results show that, except for grain sorghum and soybeans, precipitation has a negative and statistically significant impact on the quantity of groundwater pumped per acre. This suggests that irrigated producers of alfalfa, corn, and wheat vary the quantity of groundwater pumped as rainfall varies. However, the magnitude of all rainfall coefficients is statistically different from - 1. Indeed, all precipitation coefficients are smaller than 0.35 acre-inches (in absolute value), implying that only a small portion of rainfall is effective for these producers. For grain sorghum and soybeans, we find no significant relationship between inches of precipitation and the quantity of groundwater pumped per acre. This implies that sorghum and soybeans producers are not sensitive to changes in the amount of rainfall.
crops and wheat producers’ irrigation decisions. Focusing on the role of precipitation, our empirical results indicate that an increase in precipitation leads to reduced groundwater extraction. Specifically, wheat producers reduce the quantity of irrigation water applied per acre by about 0.225 to 0.300 acre-inches for each additional inch of rainfall. Unlike the other four crops, wheat producers’ groundwater pumping decisions are not significantly affected by the number of irrigated acre planted to wheat. Overall, based on the marginal effect of expected price of own crop, we find that producers’ groundwater pumping decisions are not consistent with the profit maximization framework. In other words, the empirical results do not support the hypothesis that crop price expectations have a positive effect on the quantity of groundwater pumped per acre. In general, our results indicate that crop producers do not vary the quantity of groundwater applied per acre in response to higher expected own crop price. At first glance, this finding may seem counterintuitive. However, due to limited availability of groundwater in the area, it is possible that irrigated producers treat groundwater as a fixed input and do not react to a change in expected own crop price because they do not have capacity to pump more. These results suggest that the use of profit maximization framework may not be appropriate
5. Conclusions Using field-level panel data on groundwater pumped for irrigation in Northwest Kansas, this paper examines whether producers’ irrigation
Table 8 Fixed effects (FE) regression results for wheat. Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
0.011 (0.011) −0.990 (1.385) 0.216 (0.672) 0.090 (0.264) 0.132 (0.337) −0.253** (0.085) −0.017 (0.010) 0.149 1667
0.004 (0.016) −4.720 (3.513) 2.164 (1.694) 0.380 (0.426) 0.119 (0.480) −0.300** (0.083) −0.017 (0.010) 0.150 1667
0.005 (0.011) −1.764 (1.175) 0.752 (0.614) 0.213 (0.233) −0.046 (0.254) −0.264** (0.087) −0.017 (0.010) 0.149 1667
−0.008 (0.010) −2.603 (1.651) 0.585 (0.571) 0.621* (0.265) 0.467 (0.401) −0.225* (0.092) −0.018 (0.010) 0.153 1667
0.006 (0.011) −6.403* (3.117) 3.119 (1.598) 0.489 (0.434) −0.019 (0.469) −0.287** (0.081) −0.016 (0.010) 0.153 1667
0.006 (0.014) −3.825 (3.655) 1.105 (1.357) 0.369 (0.633) 0.758 (0.650) −0.294** (0.081) −0.017 (0.010) 0.151 1667
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects. 7
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Acknowledgements
decisions are consistent with the profit maximization framework by empirically testing whether crop price expectations have a positive impact on the quantity of groundwater pumped. To accomplish this, we assume that the quantity of groundwater pumped for a particular crop is a function of expected price of own crops, expected prices of other crops, precipitation, and the number of irrigated acres planted to that particular crop. All expected price data were normalized using the cost of pumping groundwater. The marginal effect of crop price expectations on groundwater pumping decisions is estimated using fixed effects methods. The fixed effects regressions control for both field- and timefixed effects. Except for the case of corn, the estimation results are generally robust across the six alternative proxies for producers’ crop price expectations considered. While the analysis focuses specifically on Western Kansas due to data availability, the results should be applicable to other regions overlying the Ogallala Aquifer. Based on the sign and the significance of the estimated marginal effects of crop price expectations on groundwater use, it can be concluded that producers’ groundwater extraction decisions are not consistent with the profit maximization framework. Overall, our empirical results indicate that crop price expectations have no statistically significant impact on the quantity of groundwater pumped per acre. These findings seem to suggest that irrigated producers consider groundwater as a fixed input and do not vary the per-acre quantity of groundwater use in response to a change in expected price of own crop. This is possibly because, given limited availability of groundwater in the area, producers do not have capacity to pump more water even if they would like to. This implies that the profit maximization framework may not be appropriate for modeling groundwater use. The implications of these findings could help improve the accuracy of the intertemporal dynamic allocation model – a commonly used tool for water policy design. Our estimation results also suggest that irrigated alfalfa, corn, and wheat producers in Northwest Kansas adjust the quantity of groundwater pumped in response to changes in precipitation. However, given the magnitude of the precipitation coefficients, producers can only use a small portion of rainfall directly for crop production. In other words, only a small portion of rainfall is effective. Irrigated sorghum and soybeans producers, on the other hand, do not vary the quantity of groundwater extracted in response to changes in the amount of rainfall. In the face of a declining water table in the Ogallala Aquifer, these findings suggest that a more effective rainfall management is needed in irrigated agriculture possibly through the use of soil moisture probes or the availability of better weather predictions. Several limitations of the analysis are noted. First, in order to focus on identifying the direct marginal effect of crop price expectations on the quantity of groundwater pumped, our econometric model assumes that groundwater applied per acre, for a given crop, is a function of expected crop prices relative to the cost of pumping, precipitation, and the number of irrigated acres. This simple model implicitly ignores the indirect marginal effect of price expectations on groundwater use through changes in land use. Second, due to data limitations, the model does not control for changes in farm programs, input prices, irrigation technology, and soil characteristics over the sample period. More robust results could be obtained by controlling for these variables. Third, while various proxies of price expectations are considered in the analysis, all proxies are constructed based on Nerlove’s (1958) adaptive price expectations approach, and the results may be sensitive to the specification of crop price expectations. Other price expectation models should be considered. Additional research questions include: Do the producers in northwest Kansas vary crop acreage in response to a change in expected crop price? If irrigated producers actually consider groundwater as a fixed input, how are profit maximization predictions impacted? How might spatial econometric techniques be used to improve the results? In addition, the actual irrigation efficiency and precipitation effectiveness remain to be quantified. These issues should be addressed in future research.
This research was supported in part by the Ogallala Aquifer Program, a consortium of the USDA Agricultural Research Service, Kansas State University, Texas A&M AgriLife Research, Texas A&M AgriLife Extension Service, Texas Tech University, and West Texas A&M University. A portion of funding for this research was provided by USDA to Project No. 2016-68007-25066, through the National Institute for Food and Agriculture’s Agriculture and Food Research Initiative, Water for Agriculture Challenge Area. Project website: ogallalawater. org. Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.agwat.2020.106021. References Adusumilli, N.C., Rister, M.E., Lacewell, R.D., 2011. Estimation of irrigation water demand: a case study for the Texas High Plains. In: Selected Paper Presented at the SAEA Annual Meeting, February 5-8. Corpus Christi, TX. Amosson, S., Almas, L., Golden, B., Guerrero, B., Johnson, J., Taylor, R., Wheeler-Cook, E., 2009. Economic Impacts of Selected Water Conservation Policies in the Ogallala Aquifer (No. 09–04). Arellano, M., 1987. Computing robust standard errors for within group estimators. Oxf. Bull. Econ. Stat. 49, 431–434. Gardner, B.L., 1976. Futures prices in supply analysis. Am. J. Agric. Econ. 58, 81–84. Golden, B., Johnson, J., 2013. Potential economic impacts of water-use changes in Southwest Kansas. J. Nat. Resour. Policy Res. 5, 129–145. Haile, M.G., Kalkuhl, M., Von Braun, J., 2016. Worldwide acreage and yield response to international price change and volatility: a dynamic panel data analysis for wheat, rice, corn, and soybeans. Am. J. Agric. Econ. 98, 172–190. Haile, M.G., Wossen, T., Tesfaye, K., von Braun, J., 2017. Impact of climate change, weather extremes, and price risk on global food supply. Econ. Disasters Clim. Change 1, 55–57. Hendricks, N.P., Peterson, J.M., 2012. Fixed effects estimation of the intensive and extensive margins of irrigation water demand. J. Agric. Res. Econ. 37, 1–19. Huffman, W.E., 1988. An econometric methodology for multiple-output agricultural technology. In: Capalbo, S.M., Antle, J.M. (Eds.), Agricultural Production: Measurement and Explanation. Resources for the Future, Washington, DC. Houck, J.P., Gallagher, P.W., 1976. The price responsiveness of U.S. corn yields. Am. J. Agric. Econ. 58, 731–734. Lau, L.J., 1978. Applications of profit functions. In: Fuss, M., McFadden, D. (Eds.), Production Economics. North Holland Publishing, Amsterdam. McKenzie, A.M., 2008. Pre-harvest price expectations for corn: the information content of USDA reports and new crop futures. Am. J. Agric. Econ. 90, 351–366. Moore, M.R., Gollehon, N.R., Carey, M.B., 1994. Multicrop production decisions in western irrigated agriculture: the role of water price. Am. J. Agric. Econ. 76, 859–874. Moore, M.R., Negri, D.H., 1992. A multicrop production model of irrigated agriculture, applied to water allocation policy of the Bureau of Reclamation. J. Agric. Res. Econ. 17, 29–43. Mullen, J., Yu, Y., Hoogenboom, G., 2009. Estimating the demand for irrigation water in humid climate: a case study from the southeastern United States. Agric. Water Manag. 96, 1421–1428. Nerlove, M., 1958. Adaptive expectations and Cobweb phenomena. Q. J. Econ. 72, 227–240. Nerlove, M., Bessler, D., 2001. Expectations, information and dynamics. In: Gardner, B.L., Rausser, G.C. (Eds.), Handbook of Agricultural Economics, pp. 155–206 Amsterdam, The Netherlands: North-Holland. Pfeiffer, L., Lin, C.-Y.C., 2014. The effects of energy prices on agricultural groundwater extraction from the High Plains Aquifer. Am. J. Agric. Econ. 96, 1349–1362. Rogers, D., Alam, M., 2006. Comparing Irrigation Energy Costs. Irrigation Management Series MF-2360. Kansas State University. Available online at. https://www. bookstore.ksre.ksu.edu/pubs/MF2360.pdf. Schoengold, K., Sunding, D.L., Moreno, G., 2006. Price elasticity reconsidered: panel estimation of an agricultural water demand function. Water Resour. Res. 42, W09411. Shideed, K.H., White, F., 1989. Alternative forms of price expectations in supply analysis for U.S. corn and soybean acreages. West. J. Agric. Econ. 14, 281–292. Shumway, C.R., Chang, A.A., 1980. Supply response of Texas field crops: an evaluation of the CET linear supply model. West. J. Agric. Econ. 5, 149–154. Terrell, B.L., Johnson, P.N., Segarra, E., 2002. Ogallala aquifer depletion: economic impact on the Texas high plains. Water Policy 4, 33–46. Tewari, R., Almas, L., Johnson, J., Golden, B., Amosson, S., Guerrero, B., 2014. Multi-year water allocation: an economic approach towards future planning and management of declining groundwater resources in the Texas Panhandle. Texas Water J. 5, 1–11. Vitale, J.D., Djourra, H., Sidib, A., 2009. Estimating the supply response of cotton and cereal crops in smallholder production systems: recent evidence from Mali. Agric. Econ. 40, 519–533.
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Do crop price expectations matter? An analysis of groundwater pumping decisions in Western Kansas
T
Kunlapath Sukcharoen*, Bill Golden, Mallory Vestal, Bridget Guerrero West Texas A&M University, 2403 Russell Long Blvd., Canyon, 79015, United States
A R T I C LE I N FO
A B S T R A C T
Keywords: Agriculture Ogallala aquifer Price expectations Pumping decisions Irrigation Profit maximization
The Ogallala Aquifer is the main water resource for irrigated agricultural production in much of Western Kansas. It is hypothesized that as crop price expectations increase, producers will apply more water to increase yields in order to maximize profit. Using field-level panel data on groundwater pumped for irrigation in Western Kansas, this paper examines whether irrigated producers’ groundwater pumping decisions are consistent with the profit maximization framework by empirically testing if crop price expectations have a positive impact on the quantity of groundwater pumped. In general, the empirical results indicate that crop price expectations have no statistically significant impact on the quantity of groundwater pumped per acre. This suggests that groundwater pumping decisions are not consistent with the profit maximization framework and that irrigated producers consider groundwater as a fixed input possibly due to limited availability of groundwater in the area. Our econometric analysis also suggests that only a small portion of rainfall is effective.
1. Introduction Irrigated crop production in the High Plains region is highly dependent on groundwater pumped from the Ogallala Aquifer due to limited and variable rainfall. Agriculture is the major user of this limited resource, and simultaneously, is the main economic driver for the economy of Western Kansas, especially in the rural communities. Stakeholders, including local groundwater authorities, are continually considering ways to conserve resources for future generations, while keeping the regional economy viable. Intertemporal dynamic allocation models are often employed by economists to aid in the prediction of future groundwater use, crop acreage, and net farm income for policymakers (Terrell et al., 2002; Amosson et al., 2009; Golden and Johnson, 2013; Tewari et al., 2014). Economists generally assume that expected crop prices have a positive effect on the quantity of groundwater used to produce the commodity. However, anecdotal evidence suggests that irrigated producers consider groundwater a fixed production input and only vary this fixed input as rainfall varies. Because results of intertemporal dynamic allocation models are typically used as a basis to provide information for policymakers, there is a need to closely evaluate the relationship between expected crop prices and groundwater pumping in order to provide more accuracy in model results and provide better water use predictions.
⁎
The hypothesis that expected commodity prices have a positive effect on the per-acre quantity of groundwater used to produce the commodity is evaluated in this study. The overall objective of this study is to examine whether irrigated producers’ groundwater pumping decisions are consistent with the profit maximization framework by empirically testing if crop price expectations have a positive impact on the quantity of groundwater pumped. Specifically, statistical models are constructed to determine if and how expected crop prices affect the quantity of water applied to alfalfa, corn, grain sorghum, soybeans, and wheat, which are the major irrigated crops in Western Kansas. In addition, various proxies are used to evaluate crop price expectations, given that producers tend to have differing outlooks on prices. This paper is organized as follows. Section 2 describes the conceptual and empirical framework. Section 3 presents the data and preliminary analysis. Section 4 reports the empirical results. Lastly, Section 5 provides the conclusions drawn from the analysis. 2. Conceptual and empirical framework Economists generally assume that farmers’ irrigation decisions depend on not only crop choice, total number of irrigated acres, and cost of irrigation water, but also expected crop prices (Moore and Negri, 1992; Moore et al., 1994; Mullen et al., 2009; Adusumilli et al., 2011). This belief follows from the theory that rational crop producers will
Corresponding author. E-mail address: [email protected] (K. Sukcharoen).
https://doi.org/10.1016/j.agwat.2020.106021 Received 10 September 2019; Received in revised form 6 January 2020; Accepted 7 January 2020 0378-3774/ © 2020 Elsevier B.V. All rights reserved.
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wjt = X jt' β + θj + λt + εjt
maximize their expected profits associated with crop production. Specifically, based on a multi-crop production model developed by Moore et al. (1994), the goal of crop producers is to maximize their expected profit: m
Π(p, q, N , z ) =
⎛ ∑ πi (pi , q, ni; z ): w1, w 2, … , wm ⎜ ⎝ i=1 max
where Xjt is a vector of explanatory variables including normalized expected crop prices, the number of irrigated acres, and precipitation; β is a vector of parameters to be estimated; θj captures heterogeneity in field or farmer characteristics; λt captures the year fixed effects; and εjt is an idiosyncratic disturbance term. The fixed effects model does not allow us to examine the impact of field-specific variables – variables that are constant over time or across fields such as land quality characteristics. However, it is appropriate for our estimation objective of isolating the effects of expected crop prices. Identifying an appropriate proxy for expected crop price is a major challenge in a study of the relationship between farmers’ crop price expectations and groundwater pumping decisions. Different specifications have been used as proxies for expected crop prices in previous work regarding agricultural production decisions. For example, Houck and Gallagher (1976); Shumway and Chang (1980); Schoengold et al. (2006); Pfeiffer and Lin (2014), and Haile et al. (2017) use either an observed market price in the immediately preceding period or an average of past crop prices as a proxy for current crop price expectation. These price expectation specifications are based on an adaptive expectations model proposed by Nerlove (1958). Other studies, including Gardner (1976); McKenzie (2008); Pfeiffer and Lin (2014), and Haile et al. (2016) exploit the hypothesis that the price of a futures contract for next year’s crop is an unbiased predictor of the harvest-time crop price and use the harvest-time futures price as a proxy for farmers’ price expectations. Nevertheless, despite the vast literature on crop price expectations, there is not a universal agreement on the appropriate specification to use for empirical estimation of crop production decisions (Shideed and White, 1989; Nerlove and Bessler, 2001; Vitale et al., 2009). Within this study, various proxies for crop price expectations are employed to test whether crop price expectations have a positive effect on the quantity of groundwater pumped. In particular, following Nerlove’s (1958) adaptive expectations approach, we consider six alternative specifications of farmers’ crop price expectations. The first specification assumes that the expected crop price is an average of monthly crop prices in the preceding year. The second specification uses an average of monthly crop prices in the preceding three years as a proxy for crop price expectations. The third and fourth proxies for crop price expectations are a three-month average of previous-year pre and post-harvest prices, respectively. The fifth and sixth specifications use a three-year average of pre- and post-harvest prices, respectively, as a proxy for farmers’ crop price expectations.
m
∑ ni = N ⎞⎟ ⎠
i=1
(1)
where Π(⋅) is a multi-crop profit function; πi (⋅) is a profit function for crop i ; p = (p1 , p2 , …, pm ) ′ is a vector of expected crop prices for the m crops; q = (q1, q2 , …, qk ) ′ is a vector of variable input prices for the k inputs; ni is the number of irrigated acres planted to crop i ; N is the total number of irrigated acres; and z = (z1, z2, …, z h) ′ is a vector of h other exogenous variables including precipitation, land quality, and irrigation technology. To obtain an estimable groundwater extraction equation, this paper employs a normalized quadratic profit function suggested by Lau (1978) and Huffman (1988). Applying Hotelling’s lemma and the Envelope Theorem to the profit maximization problem in (1) yields the following estimable function for groundwater pumping decision for each crop i : k
m
wi (p, q, ni ; z ) = α i +
∑ γ ji pj j=1
α i , γ ji ,
ητi ,
+
h
∑ ητi qτ + νini + ∑ δsi z s τ=1
s=1
(2)
δsi
ν i , and are the parameters to be estimated. A crop where supply function for each crop i , yi (p, q, ni ; z ) or simply yi , can also be derived from the profit maximization problem in (1). As each profit function, πi (pi , q, ni ; z ) , is assumed to be convex in pi , each crop supply function is increasing in pi ; in other words, ∂yi / ∂pi > 0 (Moore and Negri, 1992). In addition, the concavity of the production function suggests that ∂yi / ∂wi > 0 . Using the implicit function theorem, this implies that: ∂wi >0 ∂pi
(3)
That is, as the expected crop prices, profit-maximizing producers will increase their groundwater use, as long as increased groundwater use increases crop yields and thereby profits. The objective of this paper is to examine whether producers’ irrigation decisions are consistent with the profit maximization framework by empirically testing whether crop price expectations have a positive effect on the quantity of groundwater used to produce the crop. To accomplish this, the quantity of groundwater pumped for each crop is assumed to be a function of normalized expected crop price, pi , and other explanatory variables. Let ni (pi ) denote the optimal number of irrigated acres planted to crop i and wi (pi ) denote the optimal per-acre quantity of groundwater pumped for crop i . The total quantity of groundwater pumped for crop i , qi (pi ) , can then be written as:
qi (pi ) = ni (pi )⋅wi (pi )
3. Data and preliminary analysis The data used in this study were from a 10-county region within Northwest Kansas Groundwater Management District 4 (GMD4) overlying the Ogallala Aquifer: Cheyenne, Decatur, Gove, Graham, Logan, Rawlins, Sheridan, Sherman, Thomas, and Wallace (Fig. 1). The 10 counties were selected mainly due to the availability of field-level groundwater use data. For this analysis, we constructed an unbalanced panel data set of annual data for over 2700 points of diversion (PDIV) within the district from 2001 to 20171 . We only consider the fields planted entirely to one crop. This is because data on how groundwater was allocated to specific crops when multiple crops were planted were not available. For each PDIV (typically a single water well), the data set contained annual groundwater pumped (acre-inches per acre), area irrigated (acres), crop planted, precipitation (inches), pumping cost (dollars per acre-inch), and expected crop prices2 .
(4)
Taking the derivative of Eq. (3) with respect to expected crop price gives:
∂qi ∂n ∂w = ⎜⎛ i ⎞⎟ ni + ⎛⎜ i ⎞⎟ wi p ∂ ∂pi i ⎠ ⎝ ∂pi ⎠ ⎝
(6)
(5)
where ∂wi/ ∂pi measures a direct effect on total groundwater pumped due to changes in per-acre groundwater application and ∂ni / ∂pi captures an indirect effect on total groundwater pumped due to changes in the number of irrigated acre. This study focuses on identifying ∂wi/ ∂pi (the direct effect of changes in expected crop price on groundwater use). This can be accomplished by estimating γii in Eq. (2). To identify producers’ year-to-year changes in per-acre quantity of groundwater pumped in response to yearly changes in expected crop prices, we estimate the following reduced form fixed-effects equation for each crop:
1 Note that while groundwater pumping data were available since the 1940s, natural gas industrial price data used for calculating pumping cost were only available beginning in January 2001. 2 Due to lack of location-specific input prices besides the pumping cost, other
2
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Fig. 1. Northwest Kansas Groundwater Management District No. 4. (Source: Kansas Department of Agriculture).
(USDA) Economic Research Service. For alfalfa, the price received was measured in dollars per ton. February, March, and April prices were used to compute the pre-harvest price, while May, June, and July prices were used to calculate the post-harvest price. For corn and soybeans, the price received was measured in dollars per bushel. For grain sorghum, the price received was measured in dollars per hundredweight. For these three crops (corn, soybeans, and grain sorghum), the preharvest price was calculated using June, July, and August prices, and the post-harvest price was computed using September, October, and November prices. For wheat, the price received was measured in dollars per bushel. March, April, and May prices were used to calculate the preharvest price, while June, July, and August prices were used to compute the post-harvest price. All price data used in the empirical analysis were normalized and the cost of pumping groundwater served as the numeraire. Descriptive statistics of per-acre groundwater pumped, area irrigated, precipitation, depth to water, and pumping cost for the study area are presented in Table 1. At each PDIV, the average annual quantities of groundwater pumped per acre for alfalfa, corn, grain sorghum, soybeans, and wheat were 12.69, 14.57, 9.06, 12.67, and 6.67 acre-inches, respectively. These average figures were calculated using only those fields that are planted entirely to one of the five crops. The quantity of per-acre groundwater pumped for alfalfa was found to be more volatile than for the other four crops. Depending on the crop choice, each water right owner irrigated an average of 69.09–112.75 acres. Each PDIV received an average of 10.38 in. of precipitation per year. Average depth to water is 102.13 feet, and average pumping cost is 99 cents per acre-inch. Descriptive statistics of six alternative proxies for farmers’ crop price expectations are reported in Table 2. With the exception of alfalfa, the three-year average of post-harvest prices (Proxy 6) gave the lowest mean non-normalized and normalized expected crop prices, while the three-month average of previous-year pre-harvest prices (Proxy 3) yielded the highest mean non-normalized and normalized expected crop prices. For the average expected alfalfa prices, the three-year
Data on annual groundwater pumped, area irrigated, and crops planted were obtained from the Water Information Management and Analysis System (WIMAS), which was created and is maintained by the Kansas Department of Agriculture, Division of Water Resources (KDADWR). Monthly precipitation data were retrieved from the PRISM Climate Group and spatially matched to each PDIV using the longitude and latitude of each PDIV. The total quantity of rainfall at each PDIV during October through December of the previous year and January through May of the current year was used to represent precipitation faced by a crop producer when he or she made a groundwater pumping decision. Following Rogers and Alam (2006), producers’ pumping cost per acre-inch of groundwater was computed as:
q = 0.00186⋅pg ⋅d
(7)
where 0.00186 is the quantity of natural gas (thousand cubic feet or Mcf) needed to pump one acre-inch of groundwater one foot, pg the natural gas price (dollars per Mcf), and d is depth to water (feet). Similar to Hendricks and Peterson (2012), pg was calculated as the average of the June and July natural gas industrial prices. Data for Kansas natural gas industrial price were obtained from the Energy Information Administration (EIA). County-level water depth data were retrieved from the Kansas Geological Survey’s Water Information Storage and Retrieval Database (WIZARD).3 Our analysis concentrated on the five most commonly irrigated crops in Northwest Kansas: alfalfa, corn, grain sorghum, soybeans, and wheat. Expected crop prices were constructed using Kansas monthly cash price data from 1997 to 2016. Data on price received for the five crops were taken from the United States Department of Agriculture
(footnote continued) input prices were highly correlated across observations and could not be included in the estimation. 3 County-level water depth data were used because field-level water depth data were only available for a small number of fields. 3
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month average of previous-year pre-harvest prices (Proxy 3) yielded the highest normalized expected alfalfa price. As expected, non-normalized expected crop prices are more volatile than normalized expected crop prices. Note that when the non-normalized expected crop price increases, the normalized expected crop price increases less in areas with a greater depth to water (due to the higher pumping cost). It is this source of variation in the normalized expected crop price that helps identify the impact of crop price expectations. The degree of dependence between the quantity of groundwater pumped and the six alternative proxies of farmers’ crop price expectations is reported in Table 3. This study considered three different measures of the degree of dependence: Pearson’s correlation coefficient, Spearman’s rho, and Kendall’s tau. The Pearson’s correlation coefficient (or simply the linear correlation coefficient) is a measure of the strength of the linear relationship between two variables of interest, whereas Spearman’s rho (i.e., Spearman’s rank correlation coefficient) and Kendall’s tau are measures of nonlinear association between two variables. For all crops, the degrees of linear and nonlinear dependence between the quantity of irrigation water pumped and the expected crop price were negative and statistically significant at the 1-percent level. The negative dependence coefficients indicated that both variables tend to move in the opposite direction. In other words, the quantity of groundwater pumped and crop price expectations were inversely related to each other. Nevertheless, the degrees of association were quite weak. For alfalfa and soybeans, regardless of the dependence measures considered, the strongest association was found when the three-year average of pre-harvest crop prices (Proxy 5) was used as a proxy for expected crop price. For corn and grain sorghum, the strongest linear correlation was also observed when the three-year average of pre-harvest crop prices (Proxy 5) was used as a proxy for expected corn and grain sorghum prices. However, when considering measures of nonlinear dependence, the degree of dependence was strongest for the case of corn when the three-month average of previous-year post-harvest prices (Proxy 4) was used as a proxy and for the case of grain sorghum when the average of monthly crop prices in the preceding year (Proxy 1) was used as a proxy. For wheat, the highest Pearson’s correlation coefficient and Spearman’s rho were found when the average of wheat prices in the preceding three years (Proxy) was used as a proxy. Kendall’s tau, on the other hand, suggested that the degree of association between the two variables was strongest when the expected wheat price was proxied by the average of monthly wheat prices in the preceding year (Proxy 1). Overall, the results from the correlation analysis indicated a weak negative relationship between crop price expectations and the quantity of groundwater applied per acre. These findings are consistent with Adusumilli et al. (2011) who found that expected crop price had a nonpositive impact on groundwater demand for the cases of grain sorghum, wheat, and cotton. These preliminary findings suggest that producers’ irrigation decisions may not be consistent with the profit maximization framework, which asserts that crop price expectations have a positive effect on the quantity of groundwater used to produce the crop.
Table 1 Groundwater pumped, area irrigated, precipitation, depth to water, and pumping cost for the study area. Variable
Mean
Std. Dev.
Annual groundwater pumped (acre-inches/acre) Alfalfa 12.69 7.64 Corn 14.57 5.81 Grain sorghum 9.06 5.67 Soybeans 12.67 5.21 Wheat 6.67 5.23 Area irrigated (acres) Alfalfa 69.09 49.35 Corn 112.75 56.12 Grain sorghum 82.00 58.01 Soybeans 102.68 42.03 Wheat 97.27 56.04 Precipitation (inches) 10.38 3.69 Depth to water (feet) 102.13 42.56 Pumping cost ($/acre-inch) 0.99 0.52
Minimum
Maximum
0 0 0.04 0 0
65.64 68.32 45.07 35.25 42.95
1 1 2 1 1 2.03 25 0.16
289 1545 650 525 414 23.39 202.67 3.16
Table 2 Alternative proxies for farmers’ crop price expectations. Variable
Non-normalized Prices
Normalized Prices
Mean
Std. Dev.
Mean
Std. Dev.
44.78 41.21 44.78 44.91 40.90 41.34
163.66 161.70 164.10 160.97 158.09 160.08
123.92 120.78 127.62 121.46 117.99 121.26
1.54 1.41 1.75 1.42 1.53 1.30
5.10 4.92 5.26 4.94 5.03 4.76
4.43 3.85 4.86 4.23 3.98 3.68
2.73 2.50 3.07 2.64 2.67 2.40
8.45 8.10 8.62 8.11 8.18 7.79
7.71 6.50 8.32 7.44 6.63 6.30
3.15 3.03 3.58 2.92 3.37 2.82
12.07 11.76 12.95 11.38 12.52 11.13
9.55 9.06 10.43 8.71 9.72 8.49
1.76 1.63 2.03 1.79 1.71 1.64
6.74 6.62 6.94 6.63 6.71 6.50
5.43 4.94 6.08 5.40 5.11 4.89
Expected alfalfa price Proxy 1 120.91 Proxy 2 118.75 Proxy 3 120.55 Proxy 4 119.12 Proxy 5 116.39 Proxy 6 117.24 Expected corn price Proxy 1 3.70 Proxy 2 3.60 Proxy 3 3.79 Proxy 4 3.59 Proxy 5 3.68 Proxy 6 3.49 Expected grain sorghum price Proxy 1 6.10 Proxy 2 5.92 Proxy 3 6.16 Proxy 4 5.88 Proxy 5 5.98 Proxy 6 5.71 Expected soybeans price Proxy 1 8.84 Proxy 2 8.59 Proxy 3 9.44 Proxy 4 8.43 Proxy 5 9.15 Proxy 6 8.16 Expected wheat price Proxy 1 4.97 Proxy 2 4.88 Proxy 3 5.02 Proxy 4 4.87 Proxy 5 4.92 Proxy 6 4.78
4. Empirical results
Notes: This study considers six alternative proxies for farmers’ crop price expectations: an average of monthly crop prices in the preceding year (Proxy 1), an average of monthly crop prices in the preceding three years (Proxy 2), a three-month average of previous-year pre-harvest prices (Proxy 3), a threemonth average of previous-year post-harvest prices (Proxy 4), a three-year average of pre-harvest prices (Proxy 5), and a three-year average of post-harvest prices (Proxy 6).
Parameter estimates from fixed effects regressions under various specifications of crop price expectations for alfalfa, corn, grain sorghum, soybeans, and wheat are reported in Tables 4–8, respectively. Note that the fixed effects regressions control for both field heterogeneity and time-fixed effects. For each respective crop, the results are quite consistent across the six alternative proxies for normalized expected crop prices. Depending on crop type and proxy employed, the fixed effects regression helps explain about 14.9–34.4 percent of the variation of quantity of groundwater pumped per acre. The estimation results for alfalfa are shown in Table 4. Regardless of the proxy employed, the coefficient on expected alfalfa price is negative
average of pre-harvest prices (Proxy 5) yielded the lowest non-normalized as well as normalized expected prices. On the other hand, the average of monthly crop prices in the preceding year (Proxy 1) gave the highest non-normalized expected alfalfa price, whereas the three4
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Table 3 Degree of dependence between the quantity of irrigation water applied and normalized expected crop price.
Alfalfa Pearson’s correlation Spearman’s rho Kendall’s tau Corn Pearson’s correlation Spearman’s rho Kendall’s tau Grain sorghum Pearson’s correlation Spearman’s rho Kendall’s tau Soybeans Pearson’s correlation Spearman’s rho Kendall’s tau Wheat Pearson’s correlation Spearman’s rho Kendall’s tau
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
−0.109** −0.164** −0.111**
−0.137** −0.168** −0.113**
−0.110** −0.164** −0.111**
−0.116** −0.167** −0.113**
−0.143** −0.177** −0.119**
−0.137** −0.171** −0.115**
−0.102** −0.176** −0.121**
−0.125** −0.174** −0.118**
−0.097** −0.170** −0.115**
−0.099** −0.182** −0.123**
−0.127** −0.173** −0.117**
−0.121** −0.175** −0.118**
−0.090** −0.175** −0.119**
−0.123** −0.172** −0.116**
−0.088** −0.163** −0.110**
−0.076** −0.170** −0.116**
−0.125** −0.169** −0.114**
−0.111** −0.169** −0.114**
−0.128** −0.189** −0.128**
−0.132** −0.183** −0.124**
−0.130** −0.175** −0.118**
−0.124** −0.192** −0.130**
−0.132** −0.183** −0.124**
−0.128** −0.181** −0.122**
−0.131** −0.198** −0.135**
−0.148** −0.199** −0.135**
−0.131** −0.191** −0.130**
−0.133** −0.196** −0.133**
−0.147** −0.193** −0.130**
−0.146** −0.195** −0.132**
Notes: ** denotes the rejection of the null hypothesis of no association at the 1 % significance level.
Table 5. The estimation results for corn do not give a clear answer concerning the role of expected corn price. We find no significant relationship between expected corn price and the quantity of irrigation water pumped when an average of monthly crop prices in the preceding year (Proxy 1), a three-month average of previous-year pre-harvest prices (Proxy 3), or a three-year average of post-harvest prices (Proxy 6) is used as a proxy for crop price expectations. When an average of crop prices in the preceding three years (Proxy 2) or a three-year average of pre-harvest prices (Proxy 5) is considered, the coefficient on expected corn price is negative and statistically significant at the 1 percent level, implying that corn producers respond to higher expected corn price by reducing the quantity of groundwater applied to corn acreage. However, for the case where a three-month average of previous-year preharvest prices (Proxy 3) is used as a proxy for expected crop price, we observe a significant positive relationship between expected corn price and the quantity of water pumped. Depending on the proxy selected, the fixed effects regression results suggest that expected prices of other crops significantly affect corn producers’ groundwater pumping decisions. Similar to the case of alfalfa, the precipitation variable is negative and statistically significant
but quite small and not statistically different from zero. This indicates that the expected alfalfa price has no statistically significant impact on the quantity of groundwater pumped per acre of alfalfa. The fixed effects regression results also indicate that there is no significant relationship between expected prices of the other four crops and alfalfa producers’ groundwater use decisions. As expected, the coefficients on precipitation are negative for all cases, ranging between -0.346 and -0.321. All of these coefficients are statistically significant at the 1 percent level. This implies that alfalfa producers reduce the quantity of groundwater pumped as rainfall increases. These findings also suggest that only a small portion of total rainfall is effective (i.e., can be used directly for crop production) as the magnitude of all rainfall coefficients is much smaller than one. In addition, we observe a significant inverse relationship between the number of irrigated acres and the quantity of groundwater pumped. This indicates that alfalfa producers with more irrigated acres use less water per acre than those with less irrigated acres. Specifically, we find that the quantity of groundwater pumped per acre is reduced by about 0.056-0.057 acre-inches as the number of irrigated acres increases by one acre. Estimates from the fixed effects regressions for corn are reported in Table 4 Fixed effects (FE) regression results for alfalfa.
Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
−0.003 (0.010) 1.476 (1.106) −0.448 (0.566) −0.211 (0.242) −0.234 (0.370) −0.346** (0.093) −0.056** (0.012) 0.164 1987
−0.009 (0.016) 1.287 (3.207) −0.852 (1.697) 0.193 (0.381) −0.160 (0.426) −0.321** (0.092) −0.057** (0.012) 0.164 1987
−0.008 (0.010) 0.228 (1.075) 0.065 (0.587) −0.071 (0.312) −0.083 (0.372) −0.343** (0.094) −0.056** (0.012) 0.164 1987
−0.003 (0.010) 0.789 (1.172) −0.243 (0.374) −0.036 (0.299) −0.260 (0.376) −0.325** (0.093) −0.056** (0.012) 0.163 1987
−0.004 (0.012) 1.095 (3.159) −0.798 (1.696) 0.035 (0.400) 0.074 (0.446) −0.322** (0.093) −0.057** (0.012) 0.163 1987
−0.013 (0.012) 0.924 (3.186) −0.809 (1.211) 0.497 (0.524) −0.343 (0.554) −0.334** (0.092) −0.057** (0.012) 0.165 1987
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects. 5
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Table 5 Fixed effects (FE) regression results for corn. Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
0.005 (0.003) 0.600 (0.315) −0.339** (0.149) 0.189** (0.067) −0.419** (0.084) −0.087** (0.021) −0.044** (0.006) 0.260 18,921
0.010** (0.004) −4.257** (0.854) 1.877** (0.419) 0.385** (0.102) −0.054 (0.112) −0.110** (0.021) −0.044** (0.006) 0.261 18,921
−0.005* (0.003) −0.522 (0.293) 0.217 (0.144) 0.319** (0.068) −0.301** (0.071) −0.098** (0.021) −0.044** (0.006) 0.260 18,921
0.006* (0.003) 1.201** (0.360) −0.635** (0.122) 0.127 (0.075) −0.385** (0.098) −0.099** (0.021) −0.044** (0.006) 0.261 18,921
0.009** (0.003) −3.891** (0.851) 1.879** (0.444) 0.335** (0.101) −0.186 (0.110) −0.099** (0.021) −0.044** (0.006) 0.261 18,921
0.011** (0.003) −1.465 (0.864) 0.365 (0.302) 0.254 (0.158) −0.025 (0.152) −0.102** (0.021) −0.044** (0.006) 0.260 18,921
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects.
additional acre of irrigated sorghum acreage results in a reduction in the per-acre quantity of groundwater pumped by approximately 0.0330.035 acre-inches. Estimates from the fixed effects regressions for soybeans are shown in Table 7. Regardless of the proxy used, the marginal effect of expected soybean price is not statistically significant. Depending on the proxy employed, expected prices of alfalfa and/or corn significantly affect soybeans producers’ groundwater pumping decisions. Similar to the case of grain sorghum, our estimation results suggest that there is no significant relationship between inches of precipitation and the quantity of irrigation applied per acre. As expected, the marginal effect of irrigated acres is negative and statistically significant. In particular, we find that the quantity of groundwater applied per acre is reduced by about 0.080-0.081 acre-inches as the number of irrigated acres planted to soybeans increases by one acre. The estimation results for wheat are reported in Table 8. Considering the role of expected wheat price, we find that the marginal effect of expected wheat price on the per-acre quantity of groundwater pumped is not statistically significant. These findings are consistent across the six proxies employed. We also find that for most cases there is no significant relationship between expected prices of the other four
at the 1 percent level. Specifically, the estimation results indicate that corn producers reduce the quantity of groundwater applied per acre by approximately 0.087 to 0.110 acre-inches for each additional inch of rainfall, confirming that only a small portion of rainfall is effective. We also find that the marginal effect of the number of irrigated acres is negative and statistically significant at the 1 percent level; each additional acre of irrigated land planted to corn results in a reduction in the quantity of groundwater extracted per acre by about 0.044 acre-inches. The estimation results for grain sorghum are presented in Table 6. Except when a three-year average of post-harvest prices (Proxy 6) is used as a proxy for expected crop prices, our results indicate that expected sorghum price does not significantly affect the quantity of groundwater pumped. When Proxy 6 is considered, we find a significant positive relationship between expected sorghum price and the quantity of irrigation water use. Similar to the case of alfalfa, there is no significant relationship between expected prices of the other four crops and sorghum producers’ irrigation decisions. Interestingly, the precipitation level does not significantly affect groundwater use decisions. Similar to the case of alfalfa and corn, the empirical results tells us that sorghum producers with more irrigated acres apply less groundwater per acre than those with less irrigated acres. Specifically, each Table 6 Fixed effects (FE) regression results for grain sorghum.
Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
−0.021 (0.022) −3.225 (2.437) 2.107 (1.202) 0.594 (0.537) −0.823 (0.733) −0.023 (0.158) −0.033** (0.011) 0.264 792
−0.030 (0.022) −6.980 (6.495) 4.469 (3.292) 0.699 (0.838) −0.774 (1.282) 0.001 (0.156) −0.034** (0.011) 0.263 792
−0.019 (0.027) −2.435 (1.733) 1.520 (0.847) 0.386 (0.484) −0.280 (0.457) −0.044 (0.162) −0.035** (0.012) 0.259 792
−0.005 (0.018) −0.173 (2.753) 0.350 (1.000) −0.197 (0.584) 0.151 (0.604) −0.024 (0.173) −0.034** (0.012) 0.256 792
−0.019 (0.016) −3.506 (5.859) 2.368 (3.155) 0.700 (0.944) −1.074 (1.274) 0.021 (0.161) −0.034** (0.011) 0.259 792
−0.016 (0.022) −11.202 (5.985) 4.426* (2.141) 1.630 (1.167) 0.462 (1.506) 0.008 (0.157) −0.034** (0.011) 0.265 792
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects. 6
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Table 7 Fixed effects (FE) regression results for soybeans. Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
−0.014 (0.008) 1.456 (1.055) −0.297 (0.499) −0.145 (0.264) −0.168 (0.236) 0.031 (0.099) −0.080** (0.017) 0.341 1849
−0.032** (0.012) 1.283 (3.013) −0.007 (1.560) 0.041 (0.327) −0.286 (0.292) 0.066 (0.101) −0.081** (0.017) 0.341 1849
−0.006 (0.008) 2.126* (0.841) −0.807 (0.427) −0.245 (0.245) −0.026 (0.197) 0.032 (0.099) −0.081** (0.017) 0.342 1849
−0.015 (0.009) −1.351 (1.232) 0.630 (0.405) 0.199 (0.298) 0.246 (0.276) 0.055 (0.100) −0.080** (0.017) 0.339 1849
−0.021* (0.008) 2.238 (2.883) −0.891 (1.521) 0.116 (0.334) −0.333 (0.273) 0.068 (0.101) −0.081** (0.017) 0.342 1849
−0.025* (0.011) −2.122 (3.471) 0.953 (1.270) 0.610 (0.549) −0.076 (0.485) 0.061 (0.102) −0.081** (0.017) 0.343 1849
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects.
for explaining groundwater extraction decisions and that we need to look for an alternative way to model groundwater use. In addition, we find that only a small portion of total rainfall can be used directly for crop production and considered effective. The estimation results show that, except for grain sorghum and soybeans, precipitation has a negative and statistically significant impact on the quantity of groundwater pumped per acre. This suggests that irrigated producers of alfalfa, corn, and wheat vary the quantity of groundwater pumped as rainfall varies. However, the magnitude of all rainfall coefficients is statistically different from - 1. Indeed, all precipitation coefficients are smaller than 0.35 acre-inches (in absolute value), implying that only a small portion of rainfall is effective for these producers. For grain sorghum and soybeans, we find no significant relationship between inches of precipitation and the quantity of groundwater pumped per acre. This implies that sorghum and soybeans producers are not sensitive to changes in the amount of rainfall.
crops and wheat producers’ irrigation decisions. Focusing on the role of precipitation, our empirical results indicate that an increase in precipitation leads to reduced groundwater extraction. Specifically, wheat producers reduce the quantity of irrigation water applied per acre by about 0.225 to 0.300 acre-inches for each additional inch of rainfall. Unlike the other four crops, wheat producers’ groundwater pumping decisions are not significantly affected by the number of irrigated acre planted to wheat. Overall, based on the marginal effect of expected price of own crop, we find that producers’ groundwater pumping decisions are not consistent with the profit maximization framework. In other words, the empirical results do not support the hypothesis that crop price expectations have a positive effect on the quantity of groundwater pumped per acre. In general, our results indicate that crop producers do not vary the quantity of groundwater applied per acre in response to higher expected own crop price. At first glance, this finding may seem counterintuitive. However, due to limited availability of groundwater in the area, it is possible that irrigated producers treat groundwater as a fixed input and do not react to a change in expected own crop price because they do not have capacity to pump more. These results suggest that the use of profit maximization framework may not be appropriate
5. Conclusions Using field-level panel data on groundwater pumped for irrigation in Northwest Kansas, this paper examines whether producers’ irrigation
Table 8 Fixed effects (FE) regression results for wheat. Dependent Variable = Groundwater Pumped (Acre-Inches per Acre)
Expected alfalfa price Expected corn price Expected sorghum price Expected soybeans price Expected wheat price Precipitation Irrigated acres R-squared Number of observations
Proxy 1
Proxy 2
Proxy 3
Proxy 4
Proxy 5
Proxy 6
0.011 (0.011) −0.990 (1.385) 0.216 (0.672) 0.090 (0.264) 0.132 (0.337) −0.253** (0.085) −0.017 (0.010) 0.149 1667
0.004 (0.016) −4.720 (3.513) 2.164 (1.694) 0.380 (0.426) 0.119 (0.480) −0.300** (0.083) −0.017 (0.010) 0.150 1667
0.005 (0.011) −1.764 (1.175) 0.752 (0.614) 0.213 (0.233) −0.046 (0.254) −0.264** (0.087) −0.017 (0.010) 0.149 1667
−0.008 (0.010) −2.603 (1.651) 0.585 (0.571) 0.621* (0.265) 0.467 (0.401) −0.225* (0.092) −0.018 (0.010) 0.153 1667
0.006 (0.011) −6.403* (3.117) 3.119 (1.598) 0.489 (0.434) −0.019 (0.469) −0.287** (0.081) −0.016 (0.010) 0.153 1667
0.006 (0.014) −3.825 (3.655) 1.105 (1.357) 0.369 (0.633) 0.758 (0.650) −0.294** (0.081) −0.017 (0.010) 0.151 1667
Notes: Standard errors are in parentheses. The standard errors are heteroscedasticity and serial correlation consistent (Arellano, 1987). * and ** denote significance at the 5 % and 1 % levels. The fixed effects regressions control for both field heterogeneity and time-fixed effects. 7
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Acknowledgements
decisions are consistent with the profit maximization framework by empirically testing whether crop price expectations have a positive impact on the quantity of groundwater pumped. To accomplish this, we assume that the quantity of groundwater pumped for a particular crop is a function of expected price of own crops, expected prices of other crops, precipitation, and the number of irrigated acres planted to that particular crop. All expected price data were normalized using the cost of pumping groundwater. The marginal effect of crop price expectations on groundwater pumping decisions is estimated using fixed effects methods. The fixed effects regressions control for both field- and timefixed effects. Except for the case of corn, the estimation results are generally robust across the six alternative proxies for producers’ crop price expectations considered. While the analysis focuses specifically on Western Kansas due to data availability, the results should be applicable to other regions overlying the Ogallala Aquifer. Based on the sign and the significance of the estimated marginal effects of crop price expectations on groundwater use, it can be concluded that producers’ groundwater extraction decisions are not consistent with the profit maximization framework. Overall, our empirical results indicate that crop price expectations have no statistically significant impact on the quantity of groundwater pumped per acre. These findings seem to suggest that irrigated producers consider groundwater as a fixed input and do not vary the per-acre quantity of groundwater use in response to a change in expected price of own crop. This is possibly because, given limited availability of groundwater in the area, producers do not have capacity to pump more water even if they would like to. This implies that the profit maximization framework may not be appropriate for modeling groundwater use. The implications of these findings could help improve the accuracy of the intertemporal dynamic allocation model – a commonly used tool for water policy design. Our estimation results also suggest that irrigated alfalfa, corn, and wheat producers in Northwest Kansas adjust the quantity of groundwater pumped in response to changes in precipitation. However, given the magnitude of the precipitation coefficients, producers can only use a small portion of rainfall directly for crop production. In other words, only a small portion of rainfall is effective. Irrigated sorghum and soybeans producers, on the other hand, do not vary the quantity of groundwater extracted in response to changes in the amount of rainfall. In the face of a declining water table in the Ogallala Aquifer, these findings suggest that a more effective rainfall management is needed in irrigated agriculture possibly through the use of soil moisture probes or the availability of better weather predictions. Several limitations of the analysis are noted. First, in order to focus on identifying the direct marginal effect of crop price expectations on the quantity of groundwater pumped, our econometric model assumes that groundwater applied per acre, for a given crop, is a function of expected crop prices relative to the cost of pumping, precipitation, and the number of irrigated acres. This simple model implicitly ignores the indirect marginal effect of price expectations on groundwater use through changes in land use. Second, due to data limitations, the model does not control for changes in farm programs, input prices, irrigation technology, and soil characteristics over the sample period. More robust results could be obtained by controlling for these variables. Third, while various proxies of price expectations are considered in the analysis, all proxies are constructed based on Nerlove’s (1958) adaptive price expectations approach, and the results may be sensitive to the specification of crop price expectations. Other price expectation models should be considered. Additional research questions include: Do the producers in northwest Kansas vary crop acreage in response to a change in expected crop price? If irrigated producers actually consider groundwater as a fixed input, how are profit maximization predictions impacted? How might spatial econometric techniques be used to improve the results? In addition, the actual irrigation efficiency and precipitation effectiveness remain to be quantified. These issues should be addressed in future research.
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