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

Scheierling, Susanne M.

Young, Robert A.

English

Research Papers in Economics

Measuring Foregone Direct Benefits of Irrigation Water Transfers: The Effect of Model Specification
Susanne M. Scheierling, Water Anchor, The World Bank, 
and Robert A. Young, Department of Agricultural and Resource Economics, Colorado State University
Introduction
In the arid parts of western North America irrigated 
agriculture continues to be by far the largest and often 
the lowest-valued water use. Growing urban water 
demands and a rise in the values placed on environment 
and instream flows have intensified the competition for 
limited water supplies. Market transfers of irrigation 
water to higher valued uses can be expected to play an 
increasingly important role for meeting these changing 
demands and improving the economic efficiency of 
water resource allocation. 
Economic evaluation of proposed water rights transfers 
involves estimating if the direct economic benefits (DB) 
and secondary economic benefits (SB) in the receiving 
(purchasing) sector, net of physical transport and 
transactions costs are greater than the foregone direct 
economic benefits (FDB) and foregone secondary 
benefits (FSB) in the sector where the water is presently 
used. 
An important but still controversial question of policy 
significance is conceptualizing and measuring the 
magnitude of FDB resulting from water rights transfers 
from irrigated agriculture. In addition to its role in 
studying water allocation policy, this information may 
be significant for assuring adequate compensation for 
sellers of water rights. Information on FDB is typically 
lacking because prices in properly functioning water 
markets, which in principle would adequately reflect the 
underlying foregone direct benefits, are often not 
observed and need to be estimated via modeling 
procedures. 
Research Approach
The theoretical basis for determining by how much producers would be worse 
off from a reduction in water supply is the neoclassical theory of production 
and the theory of the firm (Young 2005). 
The basic measure for the value of an un-priced limited input such as water is 
the residual economic rent attributable to that input. The general conceptual 
framework assumes: If the physical production function and the optimal 
quantities of all the other inputs are known and input and product prices 
reflect competitive market conditions, then these inputs’ distributive shares 
can be deducted from the total value of product and the remaining economic 
rent can be imputed to the unpriced input (the residual claimant).
In the agricultural sector the so-called residual imputation method via 
enterprise budgeting has been the most frequently used approach to 
approximating the residual rent, especially in ex ante contexts. More advanced 
versions of the calculations can be performed by mathematical programming 
or even computable general equilibrium.
Although conceptually straightforward, in practice several problematic issues 
arise which so far have not been much examined in the literature. Even 
accurately specifying the physical production function, specifying 
technologies, and assigning correct prices for outputs and, in particular, non-
water owned inputs are challenging. If, for example, in a long-run context of 
analyzing FDB owned inputs are neglected in calculating the residual 
claimant for water, then the value assigned to water is erroneously large 
because it includes returns not just to water, but to the ignored owned inputs. 
Results from such analyses would yield exaggerated estimates of FDB from 
decreased water supplies.
Previous Research
Early approaches to estimating FDB (e.g. Wollman, 1963; Hartman and 
Seastone 1970) relied on value-added measures (payments to primary 
resources) from regional Leontief input-output-type models. These were 
criticized (e.g. by Young, 2005) as overstatements of FDB for assuming zero 
opportunity costs for non-water value added elements. Representative residual 
or linear programming-based farm-model estimates include Hamilton, 
Whittlesey and Halverson (1989), Chang and Griffin (1992) and Taylor and 
Young (1995). 
Some of the estimates in the literature have only inadequately accounted for 
non-water owned inputs. And, to our knowledge, none of the FDB estimates 
has so far been specified in terms of consumptive use as the measure of water 
input.  In part, this is because consumptive use is, in practice, difficult to 
observe and some modeling approach is necessary.
Method of Study
Employing a linear-programming-based agronomic/economic model of crop 
production for a northern Colorado irrigation district (for details, see 
Scheierling, Young and Cardon 2006), we develop measures of foregone 
direct benefits (FDB) under four model specifications:
• FDB is shown first with a specification that calculates residual rents as 
returns to owned inputs (revenues minus contractual costs). These results are 
compared with what we regard to be a more theoretically correct specification 
that also deducts estimated opportunity costs of non-water owned inputs (here 
measured by values of non-irrigated land and a charge for management).
• We then calculate each of these estimates on a per-unit water basis: FDB 
per unit water delivered, and FDB per unit water consumed.
Table 1 presents a sample unit budget that illustrates how our analysis is built up for a 
representative crop (corn silage in this example). Data refer to 1993. The columns 
show the calculations for net returns for both specifications regarding owned inputs: 
where their opportunity costs are ignored, and where estimated charges for owned 
inputs are deducted. The charge for management is assumed to be 5% of total 
revenues. For the opportunity cost of land, we use an estimate of the net returns to 
non-irrigated winter wheat on similar soils. Water delivered, using flexible pipe 
technology and four irrigation events, is estimated to be 2.5 acre feet per acre, while 
water consumed is estimated to be about 1.51 acre feet per acre. 
The bottom of Table 1 shows estimated FDB in net income per acre foot of water 
delivered and water consumed for each owned-input specification:
• FDB estimates per unit delivered are considerably (about 40%) larger where 
owned input charges are assumed to be zero. 
• For each owned input price specification, the FDB estimate is significantly (about 
65%) higher for the consumptive use specification than for the delivery version. 
Model Results for the Irrigation District
Table 2 gives our results from the model, which represents cropping patterns with the 
five main crops (alfalfa hay, corn grain, corn silage, edible dry beans, and sugar 
beets) in the irrigation district. These crops are assumed to be irrigated according to 
the distribution of existing practices, allowing us to specify delivery and consumption 
per acre for each crop. 
For the irrigation district as a whole, when owned inputs are neglected, FDB 
estimates per unit delivered are 46% higher than when they are included.  And, of 
course, FDB for the consumptive use specification are larger than that for delivery—
in inverse proportion to their estimated quantity per acre.
Conclusions
It is seen that a wide range of FDB estimates per acre foot is derived depending on 
the chosen model specification. As indicated above, for the input costs specifications, 
we prefer the specification in which an estimated opportunity cost is charged for 
owned inputs: management and non-irrigated lands.  
For the water quantity measures, the consumptive use measure indicates that the 
“high” prices observed on Colorado water markets may in part reflect actual FDB in 
consumptive use terms as much as reflecting the conventional assumption of 
unearned rents from strong urban and environmental demands.
Literature Cited
Chang, C., and R.C. Griffin. 1992. “Water Marketing as a Reallocative Institution in 
Texas.” Water Resources Research 28(3):879-90.
Hamilton,J.R., N.K. Whittlesey, and P. Halverson. 1989. “Interruptible Water 
Markets in the Pacific Northwest.” American Journal of Agricultural 
Economics 71(1):63-75.
Hartman, L.M., and D. Seastone. 1970. Water Transfers: Economic Efficiency and 
Alternative Institutions. Resources for the Future.  Baltimore: John Hopkins 
Press.
Scheierling, S.M., R.A. Young, and G.E. Cardon. 2006. “Determining the Price-
Responsiveness of Demands for Irrigation Water Deliveries versus 
Consumptive Use.” Journal of Agricultural and Resource Economics 29(2): 
328-45.
Taylor, R.G., and R.A. Young. 1995. “Rural-to-Urban Water Transfers: Measuring 
Direct Foregone Benefits of Irrigation Water under Uncertain Water 
Supplies.” Journal of Agricultural and Resource Economics 20(2):247-62.
Wollman, N. 1963. The Value of Water in Alternative Uses. Albuquerque: 
University of New Mexico Press.
Young, R.A. 2005. Determining the Economic Value of Water. Concepts and 
Methods. Washington, DC: Resources for the Future.
For Further Information
Susanne M. Scheierling: sscheierling@worldbank.org
Robert A. Young: ryoung@lamar.colostate.edu
Table 2: Estimates of Net Income for Irrigation District (40,000 Acres)
Without Owned Inputs With Owned Inputs
Value/Cost Value/Cost
Description for District for District
Net Return 8,367,467                       6,373,573                    
Annual Cost of Water Supply 2,067,067                       2,067,067                    
Net Income 6,300,400                       4,306,506                    
Water Delivery 120,324 acre feet 120,324 acre feet
Net Income per Acre Foot of Water Delivery 52.36                             35.79                          
Consumptive Use 63,504 acre feet 63,504 acre feet
Net Income per Acre Foot of Consumptive Use 99.21 67.81
Table 1: Estimates of Net Income for Corn Silage (1 Acre)
Four irrigations (each with a net infiltration of 3 inches) with flexible pipe
Without Owned Inputs With Owned Inputs
Value/Cost Value/Cost
Description per Acre per Acre
A.  Total Revenue 530.67 530.67
B. Variable Costs
a. Seed      36.00 36.00
b. Fertilizer
 1. Anhydrous Nitrogen 9.12 9.12
 2. 10-34-0 w/zn 7.50 7.50
c. Chemicals
 1. Lasso II 15 G (Herbicide) 5.45 5.45
 2. Banvel (Herbicide) 4.66 4.66
 3. Counter (Insecticide) 15.75 15.75
d. Irrigation Operation & Maintenance 14.25 14.25
e. Machinery/Equipment (Custom)
 1. Disc 6.00 6.00
 2. Plow 15.00 15.00
 3. Apply Anhydrous Nitrogen 6.00 6.00
 4. Apply Herbicide 4.00 4.00
 5. Plant 10.00 10.00
 6. Row Crop Cult 6.00 6.00
 7. Row Crop Cult 6.00 6.00
 8. Ditch 8.00 8.00
 9. Combine 98.00 98.00
10. Truck 12.25 12.25
f. Management (5% of total revenue) 0.00 26.53
g. Interest on Variable Costs (9% for 4 months) 7.92 8.72
Total  Variable Costs 271.89 299.22
C. Annual Overhead and Annualized Capital Costs
a. Real Estate Taxes 10.00 10.00
b. Irrigation Equipment 11.99 11.99
c. Land Charge (Non-Irr. Winter Wheat) 0.00 22.79
d. Overhead Costs (5% of total variable costs) 13.59 14.96
Total Overhead and Capital Costs 35.58 59.74
D. Net Return 223.20 171.71
E. Annual Cost of Water Supply
a. Variable Cost of Water Supply 20.18 20.18
b. Fixed Cost of Water Supply 31.5 31.5
Total Cost of Water Supply 51.68 51.68
F.  Net Income 171.52 120.03
Water Delivery 2.50 acre feet 2.50 acre feet
Net Income per Acre Foot of Water Delivery 68.61 48.01
Consumptive Use 1.51 acre feet 1.51 acre feet
Net Income per Acre Foot of Consumptive Use 113.59 79.49
Objective of Study
Our purpose is to show how different model 
specifications lead to different measures of FDB and 
perhaps to differing policy conclusions. (We ignore the 
separate but important question of FSB.)  Two aspects 
of this task are of interest here:
• How to properly identify and price non-
contractual inputs (those assumed to be owned by the 
firm), such as (a) management and entrepreneurial 
skills, and (b) land and other (non-water) natural 
resources. 
• How to specify the measure of water input. The 
most often-used measure is (a) delivery (defined as the 
difference between water withdrawn and the amount of 
water lost in transit from the point of withdrawal to the 
point of delivery). (b) But consumptive use (or net 
water depletion, defined as delivery minus return
flows—the amount of water returned via surface 
runoff and/or deep percolation) is perhaps of more 
significance. It is the water that is evaporated, 
transpired, incorporated into plant products, or 
otherwise removed from the immediate water 
environment. Some western States require that water 
rights transfers be limited to the estimated 
consumptive use, so the downstream uses dependent 
on return flows are not damaged. 

Measuring Foregone Direct Benefits of Irrigation Water Transfers: The Effect of Model Specification

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics