Crop Production/Industries, Resource /Energy Economics and Policy,

Banerjee, Swagata (Ban)

Martin, Steven W.

English

Research Papers in Economics

Econometric versus Engineering Prediction of Water Demand  
and Value for Irrigation 
 
Swagata “Ban” Banerjee 
PO Box 197, Delta Research and Extension Center, Mississippi State University,  
Stoneville, MS 38776 
Telephone: (662) 686-7390 
Fax: (662) 686-7336 
E-mail: g_horse2000@yahoo.com, banerjee@drec.msstate.edu
(Corresponding Author) 
 
and 
 
Steven W. Martin  
PO Box 197, Delta Research and Extension Center, Mississippi State University,  
Stoneville, MS 38776 
Telephone: (662) 686-3234 
Fax: (662) 686-7334 
E-mail: smartin@ext.msstate.edu
 
 
 
 
 
Selected Poster prepared for presentation at the American Agricultural Economics  
Association Annual Meeting, Orlando, FL, July 27-29, 2008. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Copyright © 2008 by Swagata “Ban” Banerjee and Steven W. Martin. All rights reserved. 
Readers may make verbatim copies of this document for non-commercial purposes by any 
means, provided that this copyright notice appears on all such copies.   
Introduction 
 
  Agriculture in many parts of the United States, including the Mid-south in general and 
Mississippi in particular, has been plagued with the nagging problem of limited water supply in 
recent years (USGS, 2007). For example, the aquifer level under the alluvial soil to the 
immediate east of the Mississippi River (Mississippi River Alluvial Aquifer) has been declining 
(YMD, 2008; Figures 1, 2, and 3). A declining water supply has possibly been made worse due 
to the droughts of 2006 and 2007. Additionally, policies in the future may further restrict usage 
of water for irrigating crops. Last but not least, the recent interest in alternative fuels may create 
different crop mixes in the Delta region creating different water demands on the alluvial aquifer. 
Therefore, a method of evaluating the water needs of different crops and the value of water to 
each crop similar to Banerjee et al. (2007) would provide agricultural producers with valuable 
information.  
  Policymakers also need better tools to devise programs and policies to deal with such 
water shortages. A model that combines a land allocation model with the crop- and region-
specific water use coefficients (proxy for net irrigation water requirements by crop) is proposed 
to estimate irrigation water demand and hence estimate water value through crop acreage. This 
land allocation model is based on a portfolio type analysis that not only incorporates measures of 
risks and returns, but also allows for agronomic and other influences. 
 
Objectives 
  The overall objective of this study was to develop a method of precisely predicting 
agricultural water demand for irrigating corn and cotton in Mississippi. In particular, the 
following steps let us fulfill the basic objective of developing such a method of prediction:  
   1. Develop an econometric model of crop irrigated acreage allocation based on expected 
  1 
prices, expected yields, expected crop returns, variances and covariances of crop returns, 
and total irrigated acres by crop. 
   2. Employ the acreage forecasts from the estimated econometric model to the relevant actual 
water use data in Mississippi to estimate water demand by crop, and compare and contrast the 
predicted results from this econometric approach against those from the traditional engineering 
approach that uses the initial crop distribution to predict water demand.  
     Steps 1 and 2 allowed a precise estimation of crop irrigated acreage a year in advance, 
thus enabling us to calculate the value of water saved in terms of irrigated acreage.   
   3. From the above water demand estimates for the econometric and engineering approaches, 
use simulated prediction scenarios to determine responsiveness of the econometric approach vis-
à-vis the engineering approach to certain economic and institutional variables, and calculate 
“slippage” – a measure to distinguish between the two approaches. The value of water saved by 
differing the crop mix allows the calculation of the value per acre-inch of water on a crop-by-
crop basis. Calculation of “slippage” (one minus the ratio of the econometric change to the 
physical change in total water demand) enables us to visualize this difference as in related 
literature (Tareen, 2001; Banerjee, 2007).  
 
Data and Research Methods/Procedures 
  Data for this study was primarily obtained from U. S. Department of Agriculture – 
National Agricultural Statistics Service (USDA-NASS) (2007) (data on state planted and 
irrigated acres by crop, and yields by crop), Commodity Research Bureau (data on futures prices 
by crop), U. S. Department of Agriculture – Economic Research Service (USDA-ERS) (2007) 
(data on variable costs by crop), and Yazoo Mississippi Delta (YMD) Joint Water Management 
  2 
District (2008) (data on water use by crop). A time series for Mississippi starting in 1984 and 
ending in 2003 was chosen for the sample. Years 2004 and 2005 were chosen for out-of-sample 
forecasts as the latest irrigated acreage data available for all crops for comparison were until 
2005.  
 
Theoretical Modeling 
•  The representative firm maximizes expected utility (EU) from total profits under 
competition. 
•  Stochastic prices and yields make profits of a farming enterprise uncertain. 
•  Given this uncertainty, acreage allocation is modeled using the EU hypothesis where 
farmers are assumed to be risk-averse. 
•  Water demand is a derived demand, derived from the optimal choice of irrigated acreage 
allocation. 
•  The appropriate acreage response modeling strategy is to examine the changes in the 
cropping mix patterns committed to irrigation when the economic and institutional 
parameters of the problem, such as profitability of different crops and availability of total 
irrigated acreage, change. 
•  Farmers apply water on a per-acre basis and water application is a function of the crop 
planted to those acres. This makes these models theoretically consistent with the risk-
averse farmer’s decision-making framework. 
•  Therefore, the representative farmer is assumed to maximize his/her utility of profits (Πi) 
and come up with an optimal choice of irrigated acreage (Ai) for each crop: 
 A
*
i = Ai(Πj , σjj, σjk, A, T ¯   , G ¯   ),      ∀  i,  j, k  = 1, . . . , n,       j > k, 
  3 
 where    Πj is     u         the expected profit accruing from the j
th crop,  
              σjj denotes the variance in profit for the j
th crop,  
              σjk the covariance of profit between the j
th and k
th crops,   
              A is total irrigated acres,  
              T   ¯        is technology, and  
              G   ¯      governmental programs. 
      The vector of covariances accounts for the mechanism of risk spreading by    
      farmers via the portfolio effect. Technology and government programs were considered  
      fixed in estimating the model.   
 
Empirical Modeling 
  Step 1: Expected profits and the variances and covariances of expected profits were 
calculated using futures prices, past yields (Holt, 1999) and covariances between those prices 
and yields (Bohrnstedt and Goldberger, 1969). The irrigated acres of each of the four crops 
(corn, cotton, rice, and soybeans) were then linearly regressed on expected profits, variances and 
covariances of profits from all four crops, and total irrigated acres (Figure 4). This yielded a set 
of crop acreage predictions (Banerjee et al., 2007).  
 Step  2: Irrigated acreage forecasts obtained from the acreage allocation equations were 
employed to the actual water use data (Figure 5) available from YMD (2008) for obtaining the 
current and future water demand estimates. Specifically, predicted acreage times the relevant 
water use coefficient (2002-2007 annual average water used by each crop) equaled the average 
annual water demand in acre-inches for each crop.  
  Step 3: By varying some of the economic and institutional parameters, the responsiveness 
  4 
of irrigated acres was determined. Specifically, once the base simulation was created at the end-
point within the sample, 2003, several types of simulations were conducted out of the sample to 
determine how our model compared with the physical model. This was done by altering prices, 
yields, costs, and total irrigated acres to reflect out-of-sample data for two consecutive years 
(2004 and 2005). One such simulation assumed an institutionally forced reduction of total 
available irrigated acreage by 50,000 acres. The resulting water demand estimates obtained by 
our econometric approach were compared and contrasted with the conventional alternative, 
physical/engineering, approach through the calculation of “slippage.” This provided insights into 
the appropriate model for forecasting crop acreage, and hence for forecasting agricultural water 
demand (Table 1).  
  In addition, as an out-of-sample forecast, prices projected by Food and Agricultural 
Policy Research Institute (FAPRI) (2008) for 2016 were used to forecast water demand through 
irrigated acreage predictions. Based on this simulation, the conventional engineering approach 
was compared with the econometric approach proposed.  
 
Results and Discussion 
 Respective R
2 values for the corn, cotton, rice, and soybean equations are 0.92, 0.95, 
0.96, and 0.91. About 50% of the variables are significant with their expected signs, and about 
80% of the significant variables have their expected signs. Perhaps the most interesting result 
emerging from the irrigated acreage model is the expected profit of cotton in its own equation is 
negative and significant, indicating that cotton producers tend to shift cotton acres out of 
irrigation and into dry land, reducing the percentage of irrigated cotton, when expected profit 
from cotton production goes up and vice versa.  
  5 
Reduction-in-Irrigation-Capacity Scenario 
  Assuming there was a 50,000 acres policy-induced decrease in irrigation in 2006 over 
2005, the differences between the physical and econometric models would result in an increase 
of water savings of around 25%, as measured by “slippage,” by shifting water out of irrigation 
from rice and soybeans into corn and cotton (Table 1). [The same for a policy-induced 33,000-
acre reduction (FRDPA, 2001) in a study on the Flint River Basin in Georgia was between 19% 
and 24%, depending on if acres were reduced simultaneously with prices or sequentially, like in 
the current study (Banerjee et al., 2007).]  
  Using 2016 FAPRI price projections ($2.99/bushel for corn, $0.60/lb for cotton, 
$8.87/cwt for rice, and $6.37/bushel for soybeans), the slippage is also approximately 25%, with 
all the directional impacts (shifts in water demand) of relevant crops as shown in Table 1, and 
hence not reported. The FAPRI projections use ending stock prices, and the projections for all 
the crops under study are not different enough to illustrate a greater change in the difference 
between the two approaches than already illustrated using 2006 prices. However, with higher 
prices resulting in a major shift in acres from cotton and other crops to corn in 2007 and 2008, 
this percentage savings of water is presumed to be more pronounced for a study using current 
commodity prices.    
 
Conclusions 
  Dependable and predictable water supply is vitally important for agricultural producers 
and hence for the general well-being and economic development of a state/region. A 
physical/engineering model would not consider any changes in economic or institutional 
conditions. Hence it would not account for changes in crop mix over time due to economic or 
  6 
institutional changes. Our model takes into account such changes and reallocates irrigated acres 
in the new economic or institutional regime by accounting for substitution and expansion effects.    
The proposed method is based on water requirements of individual crops, thus capturing the 
intrinsic value of each crop relative to its water-requiring potential. Thus, with the successful 
introduction and implementation of the proposed model, farmers will have a better and more 
scientific method of anticipating water demand and value for their crops not only in the wake of 
a short supply due to natural causes, but also due to government policy that restricts water use. 
Policymakers will have a more precise method to calibrate acreage reduction programs to meet 
targeted levels for reductions in agricultural water use. Future research could focus on a county-
level study with otherwise similar irrigation data.  
 
References 
Banerjee, S.B., I.Y. Tareen, L.F. Gunter, J. Bramblett, and M.E. Wetzstein. “Forecasting 
  Irrigation Water Demand: A Case Study on the Flint River Basin in Georgia.” Journal of 
  Agricultural and Applied Economics 39,3(December 2007):641-655. 
Bohrnstedt, G.W., and A.S. Goldberger “On the Exact Covariance of Products of Random    
 Variables.”  Journal of the American Statistical Association 64,328(December 
 1969):1439-42. 
Commodity Research Bureau (CRB), CRB InfoTech CD – Futures, 2007.  
Flint River Drought Protection Act (FRDPA). House Resolution 17, Georgia General Assembly,    
 2001. 
Food and Agricultural Policy Research Institute (FAPRI). “Commodity Price Projections.” 
  Center for Agricultural and Rural Development (CARD), Iowa State University. Website: 
  7 
  http://www.fapri.org/Outlook2001/Tables/CPrices.xls (accessed April 29, 2008). 
Tareen, I.Y. “Forecasting Irrigation Water Demand: An Application to the Flint River Basin.” 
  Unpublished Ph.D. Dissertation, Department of Agricultural and Applied Economics, 
  The University of Georgia, Athens, 2001.  
United States Department of Agriculture – Economic Research Service (USDA-ERS). “Briefing 
  Room Farm Income and Costs: Commodity Costs and Returns.” Website: 
  http://www.ers.usda.gov/briefing/farmincome/costsandreturns.htm (accessed July 17, 
 2007). 
United States Department of Agriculture – National Agricultural Statistics Service (USDA-
 NASS).  Website:  http://www.usda.gov/nass/ (accessed April 29, 2008). 
United States Geological Survey (USGS). Website: 
  http://ms.water.usgs.gov/ms_proj/eric/delta/index.html (accessed April 29, 2008). 
Yazoo Mississippi Delta (YMD) Joint Water Management District. Website: 
  http://www.ymd.org/ (accessed May 20, 2008). 
  8 
 
 
 
Figure 1. Schematic of an Aquifer 
  9 
 
 
Source: Yazoo Mississippi Delta Joint Water Management District’s Water Use and Aquifer 
Trends in the Mississippi Delta 2006 Report 
 
Figure 2. Water Level Change, 2005-2006 
  10 
 
 
Source: Yazoo Mississippi Delta Joint Water Management District’s Water Use and Aquifer 
Trends in the Mississippi Delta 2007 Report 
 
Figure 3. Water Level Change, 1997-2007 
  11 
430,901
630,901
830,901
1,030,901
1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002
Year
A
c
r
e
s
 
Source: http://www.nass.usda.gov/Statistics_by_State/Mississippi/Search/index.asp
Figure 4. Total Irrigated Acres, Census Years, MS, 1982-2002 
  12 
 
Source: http://www.ymd.org/pdfs/wateruse/Water%20Use%20Report%202007.pdf
Figure 5. Water Use, Acre-Inches, MS Delta, 2002-2007 Annual Average 
 
0.00
10.00
20.00
30.00
40.00
Water Use 
2002 2003 2004 2005 2006 2007
Year 
 
Corn
Cotton
Rice
Soybean
  13 
Table 1.  Slippage in Measuring Change in Water Demand,
a Mississippi, 2005 - 2006 
                                                                                                                  
          
Crop Water  Use
b       Change in Water Demand
c 
                                                  Physical        Econometric             
 _______________________________________________________                                                                     
 
Corn    9.70     -33,012         118,116
d  
 
Cotton   6.40   -112,188 -27,104   
 
Rice 35.34   -289,225 -485,154       
 
Soybeans 8.18  -170,825  -361,668
_______________________________________________________ 
                                                                                                               
Total     -605,250  -755,810   
 
Slippage
e     -0.2488
f  
_______________________________________________________                                                                       
a Change in water demand is measured in acre-inches (1 acre-inch = 27,150 gallons). 
b Measured in acre-inches per acre, based on 2002-2007 annual average (YMD, 2008).  
c Change in physical (econometric) water demand = physical (econometric) crop  
distribution times the change in crop irrigated acreage times the relevant water use  
  14 
coefficient. Crop distribution assumes no other major users of water. The only other  
major water user in the state is catfish, but it has not used groundwater every year  
in the period 2002-2007 (YMD, 2008).   
d A positive (negative) change indicates an increase (decrease) in water demand. 
 e Slippage = 1 – (econometric change in water demand / 
physical change in water demand).  
f Slippage using FAPRI 2016 price projections ($2.99/bushel for corn, $0.60/lb for cotton, $8.87/cwt for rice, and 
$6.37/bushel for soybeans) turned out be a very close 0.2483. 
 
 
  15

Econometric versus Engineering Prediction of Water Demand and Value for Irrigation

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