Demand for Irrigation Water for Pistachio Production from
Depleting Groundwater Resources in Rafsanjan County
Prepared for
Oral presentation in Conference on Iran's Economy, 2010
October 15-17, 2010 at the University of Chicago (USA)
Organised by
University of Chicago and University of Illinois at Urbana-Champaign
Tinoush Jamali Jaghdani∗
Bernhard Brümmer†
September 30, 2010
Abstract
Depletion of groundwater resources is an international problem, and groundwater is probably the
world's most extracted raw material. The agriculture sector is one of the biggest users of groundwater
resources for irrigation activities and plays an important role in the depletion of these resources. Up
to now the main focus of the economic studies on groundwater resources has been quantity based management between two regimes: optimal control and competitive pumping. As a result, the estimation
of demand function for groundwater resources is the rst step to do any policy recommendation in this
eld of research. However, only scarce attention has been given to empirical studies of the demand structure of groundwater resources by the help of econometrics and considering the quality of the resources
and the spatial eect of groundwater users on each other in a context of a single aquifer. Therefore,
an empirical estimation of the demand function for individual users and considering water quality and
spatial eects of the individual users enhances further economic analysis and results in better policy
recommendations. In this study, we have focused on the economic aspects, groundwater quality and the
spatial eect of groundwater users for a derived demand function for irrigation water in pistachio production of the Rafsanjan aquifer in the south eastern part of Iran. The eld study has been conducted
during November 2008- February 2009. Spatial econometrics has been applied for the estimation of the
derived demand function for groundwater in pistachio production. Results show that spatial correlation
signicantly aects the estimated demand function, as well as water pumping prices and quality.
Key words: Groundwater resources, derived demand function, pistachio, Rafsanjan, spatial eects
PhD student in Dept of Agricultural Economics and Rural Development, member of Center for Statistics (ZfS),
Georg-August-Universität Göttingen, Germany. email: [email protected]
†
Professor and head of Agricultural Market Analysis in Dept. of Agricultural Economics and Rural Development,
Georg-August-Universität Göttingen, Germany. email: [email protected]
∗
1
1
Introduction
During the second half of the 20th century, groundwater withdrawals have increased, up to the point
that they now supply half of the world's population (UNICEF, 1998). It is said that groundwater is
the world's most extracted raw material (IHP_UNESCO, 2007). This extra use has caused water
1
table draw downs and depletion of groundwater resources (aquifer ) in many parts of the world which
highlights the importance of groundwater management. Intensive use of groundwater leads to a wide
array of social, economic and environmental consequences such as land subsidence, increases in the
vulnerability of agriculture and other uses to climate change, increases in pumping costs, etc. (Burke,
2003, p.70). Combining this fact with the resource's acute scarcity in many parts of the world, makes
the development of rules for allocating the resource eciently among competing uses over time and
space necessary (Xepapadeas and Koundouri, 2004, p.1). An economist thinks of groundwater as
something that can be treated as a potentially valuable resource like many others such as gold or
silver (Shaw, 2005, p.202). The main focus of the economic studies on groundwater resources have
been quantity based management between two regimes: optimal control and competitive pumping.
In order to do such a comparison, variables aecting the groundwater use must be dened. As a
result, the study of groundwater demand or willingness to pay (WTP) for groundwater is part of
a strategy for the management of this resource, in the sense that it provides information about
the eects of control variables on groundwater use (Koundouri, 2004a, p.716).
The availability
of the groundwater data with acceptable quality is a major problem in the groundwater studies.
The specic pattern of groundwater abstraction for irrigation has not been mapped consistently at
any national, regional or global scale. The same is true of hydrological mapping and groundwater
occurrences (Burke, 2003, p.68). The diculty of obtaining appropriate hydrologic and economic
data is one of the main barriers for the development of the models (Koundouri, 2004b, p.716) as
aquifers are wide and pumps are dispersed over a large area. Estimation of demand for groundwater
resources is the core of the following paper.
Irrigated agriculture is principle user of the major
sedimentary aquifers of the Middle East, North Africa, North America and Asian alluvial plains of
the Punjab and Terai (Björklund et al., 2009, p.132). As agriculture is the biggest groundwater user
in many parts of the world, factors eecting agricultural demand for water is of high interest.
Base on FAO database (AQUASTAT), Iran is the fth country in the list of the top 20 countries
of using groundwater for irrigation (Shah et al., 2007, p.400). Groundwater resources provide more
than 60 percent of irrigation water in Iran (Jamab, 2004, p.4).
This accounts for more than 50
km3 of water (Assadollahi, 2009). There are 629 aquifers which are recognized throughout Iran;
however 35.2
km3 from the total extraction (68 percent) comes from 176 aquifers which have negative
balances. From this group, 88 aquifers are already in the red zone (Jamab, 2004, p.4). There are
dierences among the speculations and the estimations on the total water use and the share of the
groundwater use in Iran. Figure 1 shows groundwater and surface water withdrawal for irrigation
1
In hydrology, rock layer that contains water and releases it in appreciable amounts. The rock contains water-lled
pore spaces, and, when the spaces are connected, the water is able to ow through the matrix of the rock. An aquifer
may also be called a water-bearing stratum, lens, or zone (Britannica On-line Encyclopedia)
2
Figure 1: Share of groundwater from total irrigation water and all water uses
from the whole water withdrawal. Figure 1 has been made by the help of three dierent data sources.
Base on Assadollahi (2009), irrigation water accounts for 90% of groundwater withdrawal in Iran.
This shows the importance of the groundwater resources and the necessity of economic instruments
for resource management especially in agricultural sector.
This study has tried to recognize factors eecting groundwater resource demand in pistachio
production of the Rafsanjan aquifer in the southeastern part of Iran. In order to do a better empirical
estimation for any further policy recommendations, groundwater quality and spatial correlation of
irrigation water demand are also considered as inuencing factors a long as the water quantity, input
prices, output level and pistachio garden structure. A eld study has been done during November
2008 - February 2009.
2
Literature Review
2.1 Water demand estimation in industry and agriculture
In crop production and agricultural activities especially in arid and semi arid areas, water is an
important input which usually can't be received through market activities. Therefore it is categorized
as a non-market good and its value has to be estimated through direct and indirect non-market
valuation methods. Econometric models are one of the main tools for estimation demand of water
3
when farm-level microeconomic data in agriculture or the same data for industrial enterprises are
available.
The reduced form approach, derive demand function from cost function (Shephard's
lemma) or prot maximizing input demand function (Hotelling's lemma) are three main methods
for estimating the demand function for water.
The main problem with such researches is the no
availability of farm level data most of the time.
As a consequence, aggregated regional or district level data have been used for demand estimation. It could be said that Nieswiadomy (1985) and Nieswiadomy (1988) were one of the rst
attempts for irrigation water demand estimation. His latter study shows that output constant water
demand elasticity is only -0,25. He uses panel data from the period of 1970-1980 for the high plains
of Texas in cotton and grain sorghum production.
Ogg and Gollehan (1989) apply the reduced
form approach to estimate the water demand elasticity for eld crops with the help of county level
data.
The results show that irrigation water is highly inelastic.
Renzetti (1992) has done one of
the comprehensive studies on industrial water demand in Canadian manufactures with the help of
Shephard's lemma.
The results show inelastic demand (-0,38).
One of the prominent irrigation
water demands studies has been done by Moore et al. (1994) in the central plains of the United
States. They check three dierent models of short-run input use. These models are the allocatable
xed input model, variable input model and satiscing model. Prot maximization, and as a result
Hotteling's lemma, is considered for direct estimation of irrigation water demand. They conclude
that the xed allocatable input model explains multi crop water use better.
econometric studies on water demand is Schoengold et al.
by a linear function.
(2006).
One of the recent
They estimate water demand
Water consumption is regressed on water price, wage, farm characters and
fuel price without any discussion on underlying cost or prot functions. Water price is signicant
with a negative sign. They conclude that better management alone can result in signicant water
conservation.
2.2 Groundwater resources demand and inuential factors
Few studies have focused on groundwater demand by considering aquifer specic characters. Kanazawa
(1992) is one of the rst studies which looks at economic and hydrogeologic factors which aect the
marginal pumping cost. As pumping and extraction data were not available, regional-district aggregated data are used. He concludes that single-equation analysis are inappropriate when marginal
pumping costs are endogenous to the amount of pumping. Koundouri and Xepapadeas (2004) check
the shadow price of groundwater in crop irrigation by considering Shephard's lemma and the distance
function approach. They consider water level as an explanatory variable in the demand function.
They use panel data of agricultural productions over 3 periods on Cyprus Island. They conclude
that non-internalized costs of currently observed myopic groundwater are signicant. Thus, benets
from optimally managing these resources could be substantial. As Koundouri and Xepapadeas (2004)
stated, it can be recognized that analyzing groundwater demand systems with a focus on aquifer
structure and economic aspects has not been given high attention. But slowly its importance and
usages is attracting the attention of economics and water resource management.
4
It must be added that not only considering quantity aspects of aquifers in the empirical estimation
of demand function has not developed but the quality aspects have also been neglected. Considering
quality change as an economic aspect with external eects plays a big role in decision making and
optimal management of the resource (Koundouri, 2004a, p.11)
Actually, economic aspects of water quality in irrigation systems is a relatively young eld in
economic research. Kan et al. (2002) analyze the microeconomics of irrigation water with saline water. They develop a production function by considering electric conductivity (EC) as an inuencing
factor. Simulation is used to check the saline water eect on cotton and tomato production by the
help of data from experimental elds. While the results suggest increases in salinity decrease prots
regardless of crop type, there is ambiguity surrounding the relationship between changes in salinity
and the optimal applied water usage. Regarding the conditions, water use could be increasing or
decreasing. Roseta-Palma (2002) develops a theoretical framework for an optimal control model by
considering quality as an inuential factor as quantity. She concludes that intervention may lower
quantity while improving quality or vice versa. Therefore, the economic benet of control may not
be signicant. Knapp et al. (2006) apply simulation for the Roseta-Palma (2002) theoretical model.
They conclude that in a long run scenario, 500-1500 years, the benets of control could be high but a
small share belongs to quality control. Brozovic et al. (2006) present a theoretical framework for optimal management of groundwater by considering spatial aspects pf water pumping. They conclude
that spatial factors may cause improvements in the benets from optimal control of groundwater
resources.
2.3 Groundwater demand estimation in Iran
Abdolahi-Ezzatabadi and Soltani (1996) estimate the dierent functions in order to forecast the
external cost of water pumping and over drafting of the Rafsanjan aquifer. Results show that in
the future, external costs will cover more than 70 percent of pumping costs.
Mirzai-khalilabadi
and Chizari (2004) estimate the optimal level of water use with the cost minimization assumption.
Sabuhi, Soltani and Zibai (2007) estimate an optimal control model for the Narimani aquifer in the
Khorasan province. Results of the demand function show that a tax policy is the best instrument
for sustainable use of the groundwater resource. Abdolahi-Ezzatabadi (2008) simulates the eect of
policies on the welfare level and water resources. The results of the simulation show that instruments
such as a tax will be successful under low discount rates and economic stability.
When discount
rates are high, regulatory instruments are ecient. Shajari et al. (2009) estimate the price elasticity
for irrigation water of date production in Jahrom. Results show that the water price is highly elastic.
As mentioned above, in this study, the quality of irrigation water and the spatial eect of water
users are considered as probable factors which may play an important role in the size of economic
demand for the irrigation water which has to be provided from groundwater. The idea of this study
is to see the possible eect of market factors, water quality and quantity factors and the spatial
factor on the demand for groundwater resources with the help of an econometric model. It will also
5
be possible to see the size of these eects for further policy decisions.
3
The model
The main model follows Nieswiadomy (1988) and Koundouri and Xepapadeas (2004) which is based
on the shephard's lemma. Their approach has been considered for the establishment of the empirical
model. Regarding the Shephard's lemma, factor demand could be estimated by deriving the cost
function on the factor price. The additional factors in the rst step are water salinity and acidity. In
general, the structural cost function literature treats product quality as exogenous and unobserved
in the analysis because it is unobservable in most cases. Quality is usually assumed to be unrelated
to the other endogenous variables in the analysis. This is often done because of the diculties in
collecting data on product quality, which can be quite laborious and cost-inhibiting. In many analysis, however, the assumption of exogenous, unobservable quality is incorrect because the products
are dierentiated on some quality attribute. This creates biases in the parameter estimates, which
can lead to inaccurate inferences (Boland and Marsh, 2006). Therefore salinity (EC) and acidity
(PH) are considered as 2 indices for water quality which aects the overall approach towards using
other inputs and the level of output. Therefore the main short run variable cost is considered as
follows:
Ci = C(ri , rwi , ECi , P Hi , Yi , ni ; xi )
where
rw
inputs;
Y
is water price (here variable costs of water pumping);
is level of crop production;
n
is land allocated to crop;
r
is the vector of prices of other
x
is a vector of factors which are
taken as given in the short run (in this case, aquifer characters and garden structure);
run restricted cost function of crop and
i
C
is the short
is the index for water user.
∂Ci (ri , rwi , ECi , P Hi , Yi , ni ; xi )
= wi (ri , rwi , ECi , P Hi , Yi , ni ; xi )
∂rwi
In this case, the factor price is the water pumping cost.
The above mentioned model is acceptable if each observation is considered as the independent
unit with independent decisions on production and cost. But if there would be any possibility that
input use or production level is inuenced by spill over eects or any geographical factor regarding
neighborhood and the distance from them, the above mentioned model for cost or derived demand
has to be reconsidered by taking into account this extra factor (Cohen and Paul, 2003). The water use
of each farmer per hectare can not be considered as a totally independent factor from the neighboring
farms which are using the same pump under the same property right conditions. On the other hand
the structures of gardens and the decision of water use per hectare for the pumps near each other
could be similar.
This is the motivation for studying the derived demand function for irrigation
water per hectare with the strong assumption of spatial correlation on water consumption among
neighboring farms. Spatial linkage can be made with the help of spatial autoregressive (SAR) error
or spatial lag (Anselin, 1999). Therefore if a translog function is considered for the cost function,
6
Figure 2: The map of study area
the derived demand function with spatial lag can be written as follows for water use per hectare:
if
and
W
X
is a vector of the dependent variable which is a natural logarithm of water use per hectare
is the matrix of independent variables which is a natural logarithm of input prices and other
explanatory variables in the above model and
β
as the estimated coecient, the following spatial
lag model can be estimated as the derived demand function:
W = λM W + Xβ + where M is a spatial weight matrix. It must be added that such estimation is possible if we assume
constant returns to scale.
4
Field study and data
4.1 Study area
Field work has been conducted for almost 3.5 months during November- February 2008-2009 in
the Rafsanjan county in the south eastern part of Iran (gure 2 ). The main reason for selecting
Rafsanjan was its unique agricultural production pattern and its size. Table 1 shows some general
characters of the Rafsanjan aquifer. This aquifer is divided into 3 parts which are connected from
the bottom but each part has a bit of a dierent storativity coecient. In addition, there is an under
7
Table 1: General information about the Rafsanjan aquifer
County's total area
12000
Population
km2
290000
Crop production
Only Pistachio
Estimated planting area
Estimated 80000-100000 ha
Area of aquifer
km2
3
million m
3
million m
4108
Annual extraction
680
Share of agriculture
660
Storativity coecient
5%
Annual drop of water level
72 cm
Aquifer condition
Red Zone
m
m
source of data: The Oce of Basic Water Resources Studies
last access 28.09.2010, http://217.66.216.141/tolidat/ab-zirzamini.asp
Average height from sea level
1609
Average depth of water table
55
ground water ow from south to north.
Back to the last hydro-geological report (Kawab, 2002),
3
there is 136 million m inow and 31 million
m3
outow from the aquifer. The general hydrograph
of Rafsanjan shows an annual drop of 72 cm on average. (Figure 3 )
There are more than 1300 deep active wells in the Rafsanjan plain and most of them are providing
irrigation water for pistachio gardens and very few are used for other usages. It is almost impossible
to add new wells to the system and the aquifer has almost been shared by the same operators
during last 20 years.
There is no permanent river in the area and irrigation depends solely on
groundwater. This area is borders the desert and has a very arid climate. According to the Iran
Meteorological Organization, annual precipitation in Rafsanjan is almost 90 mm. Combining waterlevel data with satellite radar observations provides evidences for annual 50 cm of land subsidence
and land deformation in Rafsanjan aquifer as a result of intensive groundwater use (Motagh et al.,
2008).
4.2 Pistachio production
Pistachio (Scientic name: Pistacia vera L) is a small tree and its nut is the main non oil agricultural
export from Iran.
At the moment, Iran and the USA are the biggest pistachio producers and
exporters in the world. Good quality pistachio is a very special nut and needs very hot summers and
very cold winters which is the case in Rafsanjan. Rafsanjan is almost the biggest pistachio producing
area in Iran and as it is mentioned the whole area is specialized in pistachio production during the
recent years and there is almost no other agricultural production in the area.
Dierent types of
pistachio can be found in the area which need dierent treatment and have dierent quality and
prices in the market. It can be said that after saron, pistachio is the most expensive agricultural
crop in Iran.
8
Figure 3: Rafsanjan Hydrograph (1984-2009)
4.3 Field work
According to the high price of pistachio and the unique pattern of water use in Rafsanjan, this area
has been selected for the eld study. Two stage random sampling has been followed for the data
gathering.
Regarding dierent water quality that can be found in the study area, and the high
cost of water quality studies, the already available random sample of 60 wells which are seasonally
controlled for water quality has been considered as the rst stage sample selection. The Rafsanjan
Water Authority (RWA) has selected 60 agricultural wells randomly around the aquifer and checks
the chemical and quality factors such as, EC, PH, SAR, etc.
seasonally.
So the quality change
factors of the aquifer can be observed. I could acquire this data for a period of 4 years.
The survey has been done by 2 dierent types of questionnaires. The questionnaire concerning
wells has been designed and checked with irrigators, pumpers and well representants. This questionnaire contains information covering the well ownership, technical aspects, historical trends, well
management, labor force, energy consumption, maintenance, water cahrge and property value. The
household questionnaire contains questions about garden management, garden structure, the harvest value of crops, household socioeconomic structure, inputs, garden operational costs, processing
costs, water provision costs and water trade. I could cover the cost items for a one year period of
agricultural production and 2 years of crop yield levels and selling prices. The goal was to design a
production - cost questionnaire which could cover both big and small farmers.
This area has very heterogeneous farm and well ownership. The ownership pattern can be divided
9
Figure 4: Geographical position of wells and farms
into 2 periods: before and after the revolution (1979). Most of the wells set up before the revolution
are owned by large producers or a mix of large owners and smallholders. But all of the revolutionary
wells are characterized by smallholder ownership. As the sample of wells was random, both groups
were included in the sample.
In order to carry out the survey, I have contacted the wells' representants rst and interviewed
them with the questionnaire concerning wells. I then contacted the farmers. Interviews with large
landlords were conducted with their representants in the oce or in the eld most of the time. It
was sometime the case that interviews were as long as one day as items had to be checked in the
books. On side of the smallholders, I have randomly interviewed some of the farmers which were
using the same well based on the size of the farms. As is mentioned, the ownership pattern is very
diverse. There are cases where 2-3 wells belonged to one landlord or where one well is owned by 200
people. Finally 57 wells' representants have been interviewed with more than 157 farmers which are
dispersed around the aquifer. It must be added that in Iran due to the Law of Fair Distribution
of Water (1983), people receive the legal permission to use groundwater and it is a public good.
However this permission is a form of property ownership and has a very high value according to
water charge levels of wells and water quality.
Figure 4 shows the position of target wells in the
study area.
10
4.4 Description of data
The detailed cost data from the pumps' side and farms' side are extracted from questionnaires and
entered into the database (MSACCESS 2003).
Queries have been used for aggregation.
Pumps
and farms are dealt with separately. In the following paragraphs, some of the data structure and
variables which are used in the model for estimation are described .
Table shows a summary of
Table 2: Descriptive Summary of the variables
Variables
Mean
sd
Min
Max
Water use per ha (Cubic meter)
8875
4198.40
2261
23730
Pistachio Product per ha (2007)-kg
1589.0
952.85
1.0
5134.3
Fertilizer Manure index price (Rial / day)
677.0
974.75
118.1
6848.4
Labour price (Rial / day)
83797
17949.00
42305
133653
Size of the farm (ha)
9.6215
25.23
0.1125
224.9325
PH
7.566
0.38
6.700
8.600
EC
6453
3885.00
1314
21000
No of tree per ha
1234.7
899.89
354.4
4940.6
Average age of farm trees
25.66
8.96
5.00
65.00
Mashin index price (Rial/hour )
40746
19756.14
7500
157930
No of pieces
3.503
2.59
1.000
15.000
Water pumping cost (Rial / cubic meter)
383.78
394.98
56.24
1567.86
Water level (meter)
62.95
30.70
14.83
138.02
variables used in the establishment of the model.
Irrigation water and pumping costs
Through variable costs of wells, the variable cost of
pumping is calculated. As the pumps do not have water contour, the ow rate of the pumps is asked
(Lit/S ) and checked. Later on by considering the number of o days , the total size of pumped
water is calculated as follows for one year:
W aterF low ∗ W orkingDay ∗ 24Hours ∗ 3600Second
By considering the farmer share from the well, the annual share of each farmer from the above
pumped water is calculated and considered as water input level of the farm (or farm water quota).
The dependent variable of water use per hectare is calculated by dividing the whole water quota on
the size of the farm.
Production Level
There are dierent brands of pistachios available in the study area and many
farmers process, dry and separate good and bad quality pistachios.
Some farmers do only the
processing and drying but not the separation and some large farmers sell the whole crop fresh without
doing any processing. Many farmers produce dierent brands at the same time. As separation of
the cost spent for each brand was almost impossible, the aggregate level of pistachio production is
11
considered as the production level of each farm.
The target area met unexpected coldness during the spring of 2008. In spite of all costs which
farms have paid for operations during the 2007-2008 agricultural year, the crop production of summer
2008 reduced dramatically. Therefore, 2007 high yield production has been used with expenditures
during 2007-2008 for establishing the cost function and as a result, the factor demand function. It
must be added that there where some young gardens in the sample which show no crop production.
Manure and fertilizer costs and prices
Farmers use many dierent brands of chemical fertilizer
(phosphate, nitrate, sulphate, etc.), dierent types of manure (cow, sheep, chicken or sh) or natural
fertilizers (agribiosol, agrihum, etc.). There are farmers using all of the above mentioned elements
and there are farmers using only some.
In order to have a price index representing manure and
fertilizer prices in a cost function without having any zeros on the right side of the equation, an
aggregate price index has been establish for manure-fertilizer by considering quantitative weight.
The following aggregation formula has been used to establish the price index for manure, chemical
fertilizers and natural fertilizers for each farmer:
n
P
P riceIndex =
P iX i
i=1
n
P
(1)
Xi
i=1
where
Xi
is quantities and
Pi
is the price of that quantity (fertilizer or manure in this case) paid by
the farmer.
Pesticide price
Farmers use dierent pesticides in the garden such as amitraz, endosulfan and
herbicides at dierent volumes. Therefore a single aggregate price index has been established for
pesticides and herbicides together. The same aggregate arithmetic weighted index has been used by
the help of equation 1.
Machinery cost and price
There are dierent types of machinery used in the pistachio gardens
which can be categorized as pesticide distribution, hole digging, soil ploughing, soil rotating, etc.
Dierent machine operations have dierent prices. Therefore an aggregated price index has been
established for Machinery by the help of equation 1.
Labour cost and lab our price
There are also dierent types of prices for labour and their
dierent activities (such as pruning, manure or fertilizer distribution, harvest, processing, irrigation,
etc.) which are paid by farmers. Large farms employ annual labour with specic insurance regarding
the Iran Labour Law. The aggregate price index is established for labour force as a daily price. The
annual labour cost has been changed to a daily labour cost. Extra costs for daily or annual labour
such as food are also considered.
12
Garden structure
Age and number of trees per hectare are 2 indices which have been considered
as factors representing garden structure in the derived demand function.
As there were dierent
trees with dierent ages in each garden, an aggregated age index is also developed for each garden.
5
Results
All of the analysis has been done with the R and spdep package. Table 2 shows the simple OLS
Table 3: OLS Estimation of log-linear function
(Intercept)
Estimate
Std. Error
t value
Pr(>|t|)
13.7657
2.4104
5.71
0.0000
lgPRODUCTHA
0.0448
0.0353
1.27
0.2057
lgwaterprice86
-0.2724
0.0427
-6.38
0.0000
lgmashin
0.0977
0.0772
1.27
0.2075
lgFertManPrice
-0.0296
0.0426
-0.69
0.4892
lglaborp
0.0963
0.1611
0.60
0.5510
lgHA
-0.0845
0.0271
-3.12
0.0022
PH
-0.3388
0.1132
-2.99
0.0033
lgEC
-0.1839
0.0771
-2.39
0.0183
lgTREEHA
-0.1954
0.0671
-2.91
0.0041
lgsand
-0.0108
0.0293
-0.37
0.7120
lgNoOfPieces
-0.0411
0.0520
-0.79
0.4300
lglevel1
-0.0010
0.0012
-0.81
0.4188
lgAgeIndexG
0.0558
0.0988
0.57
0.5727
Residual standard error:
.
0.414
.
143 degrees of freedom
.
.
Multiple R-squared:
.
0.3521
.
Adjusted R-squared:
.
0.2932
.
5.979
.
F Statistics: .
.
.
.
.
estimation of the water demand from pumps. Log-linear function is considered for the estimation
of elasticities.
As it was mentioned, the dependent variable (lgWATERHA) is the average water
use per hectare on each farm.
We can see that production per hectare (logPRODUCTIONHA )
has positive eect on water demand but was not signicant.
The water table (loglevel) is not a
signicant factor which is a signal that connecting economic and hydrogeological factors may need
more attention. The two water quality factors are also signicant. The signs are also as expected but
it seems that the demand towards PH is much more elastic than EC. The price indices of other inputs
are not signicant. One of the interesting results was the eect of the number of trees per hectare
(logTREEHA) and the size of the farm (logHA) which aects the demand elasticity negatively. Age
of the trees is not signicant (logAgeIndex ).
In order to check the spatial relation, spatial neighborhood has been established and, the Moran
test has been applied to determine the spatial correlation of logarithm of applied water per hectare.
13
Table 4: Spatial Lag Regression
Coecients:(asymptoticstandarderrors)
Estimate Std. Error Zvalue
(Intercept)
68.957
24.136
28.569
lgPRODUCTHA
0.057
0.0251
22.777
lgwatepumpingcost
-0.201
0.0402
-50.106
lgmashin
0.064
0.0678
0.9383
lgFertManPrice
-0.04054
0.0372
-10.912
lglaborp
0.0915
0.1405
0.6508
lgHA
-0.0635
0.0239
-26.486
PH
-0.1364
0.103
-13.297
lgEC
-0.093
0.068
-13.703
lgTREEHA
-0.110
0.0602
-18.275
lgsand
-0.011
0.026
-0.4507
lgNoOfPieces
-0.0388
0.045
-0.8489
lglevel1
-0.001
0.001
-0.9407
Rho: 0.45934, LR test value:19.019, p-value:1.2943e-05
Pr(>|z|)
0.004278
0.022743
0.000000
0.348069
0.275194
0.515145
0.008083
0.183632
0.170595
0.067631
0.652219
0.395922
0.346848
Asymptotic standard error: 0.092303
z-value: 4.9765, p-value: 6.4752e-07
Wald statistic: 24.765, p-value: 6.4752e-07
Log likelihood: -67.24174 for lag model
Moran's I test under normality
data: log of Water per hactare
Moran I statistic
standard deviate = 8.9125,
p-value < 2.2e-16
alternative hypothesis: two.sided
sample estimates:
Moran I statistic
0.398534391
Expectation
-0.006410256
Variance
0.002064380
. Figure 5 shows the spatial neighborhood which was established by considering neighbors in the
distance of 18,5 km. This value has been found in order to keep the separation of the rst and second
region as there is a mountain between the two and not having any island in the weight matrix. The
weight matrix has been established by considering inverse distances. These results are the motivation
to do spatial econometrics (gure 6 ). Dierent spatial models have actually been checked for the
demand function. But for easier interpretation, the spatial lag has been presented and used (table 4
). The rho variable is highly signicant. Nevertheless, it seems that the water quality variable and
this spatial matrix are multicollinear. The quality factor has lost its signicance. Therefore it is not
easy to eliminate them. But it is clear that these two factors are also spatially correlated.
14
15
Figure 5: Spatial neighborhood
Figure 6: Spatial Correlation
6
Conclusion
In this paper factors aecting the demand function for irrigation water from depleting groundwater
resources has been analyzed. Not only economic factors but also hydrogeological and water quality
factors are considered in this study. The results show that spatial aspects of water use and water
quality are important. The results also show that any change in behavior and water consumption of
any neighbor has a positive eect on the other neighbors in the area. Thus it must be pointed out
that any decision or action made concerning water use in an area must be collective by covering all
users on the area.
Number of trees per hectare and the size of the farm, show two other important aspects of
any decision. Tree reduction and land unication can be another way for saving water. It seems
that high EC negatively aects the demand but not too much and high PH is a danger for the
production system.
The results of this model can be used for any optimal control analysis and
policy recommendation by considering the quality, quantity and spatial eects of pumps.
As this ongoing study is not over yet, the eciency of the estimates could be improved by doing
simultaneous system estimation of the cost function and derived demand functions with specically
dened constraints for the model. That is the next step of this ongoing research.
Acknowledgments. We thank Iran Water Resources Management Company (IWRMC) for pro-
viding piezometric data. T. J J. gratefully acknowledges the guidance and help of Mr. A. N.
Esfandiari and A. G Alizadeh during the eld research. Thanks also go to Rafsanjan Irrigation
Water Authority for their cooperation and all local people for their patience and cooperation
16
during eld surveys.
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