Pricing irrigation water in Pakistan: an evaluation of available options.
Sahibzada, Shamim A.
Irrigation water shortages have lately been a main area of concern
for policymakers and planners in Pakistan. Current literature on the
country's water resources predicts an alarming situation regarding
the availability of irrigation water in the future due to declining
water tables and serious financial, environmental, and social
constraints of developing big storage reservoirs. Since there is little
room to augment water supplies by building new dams, the existing
supply-driven surface irrigation system needs to be replaced by a
demand-based system with special focus on water use efficiency through
the introduction of an appropriate water pricing system. The present
study aims to evaluate several alternative water pricing systems in the
search for choosing one that will ensure efficient use of irrigation
water in Pakistan. A related objective is to test the extent of
sensitivity of the demand for irrigation water to a change in
alternative water prices. A major conclusion that emerges from this
research is that irrigation water shortages are the result of the
inflexibility of the present irrigation water supply system for
agricultural use and have little to do with the existing water pricing
practice in the country. Furthermore, the results of our water price
simulations exercise confirm the general perception that demand for
irrigation water is less sensitive to changes in alternative irrigation
water prices. Two findings from the pricing policy perspective are: (i)
irrigation water is not available in adequate quantity to farmers in the
nine sub-districts surveyed at almost all of the alternative prices in
Pakistan's irrigated agriculture sector since the predicted water
usage at all prices is greater than the actual usage for all districts;
and (ii) our empirical analysis indicates significant inefficiency of
resource allocation in respect of irrigation water as shown by its
positively large marginal value product to opportunity cost ratio.
1. INTRODUCTION
Agriculture is a major economic sector in Pakistan and 90 percent
of its output comes from irrigated farms. Water is a critical input for
agricultural productivity but its inadequate and untimely delivery
limits the farmers' use of other inputs, thus resulting in
considerably lower yields. Irrigation water shortages have lately been a
main area of concern for farmers, planners, and policy-makers in
Pakistan. Current literature on the country's water resources
predicts an alarming situation regarding the availability of irrigation
water in the future. Prospects for increasing water supplies are
considered dim since the development of water resources is approaching
its limits. Additional increases in water supply through the
construction of new storage reservoirs are also not possible due to
financial, environmental, and social constraints. This alarming
situation has generated a serious debate among experts as to how to cope
effectively with this potentially very serious scenario.
There is also a growing realisation on the part of the government,
as well as the donors, that past investment in irrigation has not paid
the expected returns mainly due to the sub-optimal and often wasteful
utilisation of existing irrigation facilities. Farmers are faced with
unreliable and inadequate water supply due to an inflexible and highly
inefficient irrigation water delivery system. Surface irrigation is a
public sector activity and is heavily subsidised since water rates are
abysmally low, thus putting an enormous fiscal drain on the national
exchequer. Budgetary constraints do not permit sufficient financial
outlays for proper maintenance of the irrigation system. Inadequate
attention given to the level and form of water charges, and to the need
for an appropriate mechanism for pricing irrigation water, has been a
critical policy lapse on the part of water sector planners in Pakistan.
Water pricing is an important way of improving water allocation and
encouraging users to conserve water resources. Critical issues related
to the operation and maintenance costs, the rate of return on
investment, and the provision of irrigation services on a sustained
basis are all directly and indirectly linked to water pricing policy.
A review of water pricing literature reveals that a variety of
methods for pricing water have been developed over time. These methods
differ in their implementation, the institutions they require, and the
information on which they are based [Tsur and Dinar (1997)]. A wide
range of literature addresses irrigation water management in general and
water pricing in particular [Rhodes and Sampath (1988); Cummings and
Nercissiantz (1992); Le Moigne, et al. (1992); Sampath (1992); Small and
Carruthers (1991); Shah (1993); Plasquellec, Burt, and Wolter (1994);
Tsur and Dinar (1995)]. Several studies [Rhodes and Sampath (1988);
Sampath (1992); and Dinar and Subramanian (1997)] focus on water pricing
methods practised in various countries. These methods include
volumetric, output, input, per unit area, tiered pricing, two-part
tariffs, betterment levy and water markets. The best water price is a
price that reflects opportunity costs or is marginal cost-based but it
is hard to implement. Two-part tariff pricing ensures cost recovery and
is a more realistic immediate objective from the point of view of
financial viability of water projects [Dinar and Subramanian (1997)].
Dinar and Subramanian (1997) while reviewing and comparing water
pricing experiences in 22 selected countries (Algeria, Australia,
Botswana, Brazil, Canada, France, India, Israel, Italy, Madagascar,
Namibia, New Zealand, Pakistan, Portugal, Spain, Sudan, Taiwan,
Tanzania, Tunisia, Uganda, United Kingdom, and the United States of
America) find variations in water pricing methods used by different
countries. The most common method used to charge for irrigation water is
reported to have been the average cost-based. Marginal costs are more
relevant but full marginal cost pricing has never been recommended
anywhere in the water sector since the situation of increasing average
cost frequently prevails in water development projects [Dinar and
Subramanian (1997)]. Use of two-part tariff system of water pricing,
even though a better option, is a rare phenomenon. Its different
versions are in operation in several countries. In Australia and Brazil,
a portion of capital costs is recovered from users [McGovern (1999);
Musgrave (1997) and Todt de Azevedo (1997)]. France is the only country
where water for irrigation is, generally sold on the binomial tariff basis [Dinar, Rosegrant, and Meinzen-Dick (1997)]. The binomial system
accounts for off-peak and on-peak costs. In the peak period, long-run
marginal capital costs plus marginal operating costs are recovered while
in the off-peak period only marginal operating costs are recovered.
The optimal volumetric pricing rule requires that the water price
be set equal to the marginal cost of water supply. Different
countries/regions use different versions of this method to charge for
water. Irrigation water charges consist of a volumetric water charge to
cover operation and maintenance costs, and a per hectare water charge to
recover the public investment in off-farm irrigation infrastructure
[Dinar and Subramanian (1997)]. California uses multi-rate volumetric
pricing for publically supplied water according to which prices range
between US$ 2 per acre foot to more than US$ 200 per acre foot [Tsur and
Dinar (1997)]. Following this method, water rates vary as the amount of
water consumed exceeds certain threshold values. In India, a volumetric
rate per estimated volume of water consumed is used in areas with pumped
irrigation and tubewells [Dinar and Subramanian (1997)]. These estimates
are based on crop water requirements. In the Jordan Valley, where most
of the agricultural activity is concentrated, water is provided through
pipes to more than three quarters of the irrigated land [Tsur and Dinar
(1997)]. Water authorities use volumetric pricing, but water is greatly
underpriced, and the price does little to induce efficient use of water
[Tsur and Dinar (1997)]. In Peru, the existing legislation defines two
classes of water tariffs, one for agricultural use and the other for
non-agricultural use. In general, tariffs do not reflect the true cost
of water. For agriculture, the volumetric water tariff includes three
components; (i) a "water users' association" component
intended to raise funds to finance operations and maintenance, the
conservation and improvement of common irrigation infrastructure, and
the administration budget; (ii) a water levy calculated as 10 percent of
the first component for financing agricultural development/special
irrigation projects; and (iii) an amortisation component to recover the
cost of public investments in irrigation storage infrastructure [Dinar
and Subramanian (1997)]. Chile and Mexico are the only two countries
that have developed water markets for selling and buying irrigation
water [Easter, Rosegrant, and Dinar (1998)].
In Pakistan, where agriculture uses 90 percent of irrigation water,
water rates charged to farmers have always been minimal. Because of the
nature of the irrigation system and because of the administrative
structure designed to supervise it, charges for irrigation water have
been made on an acreage--not a volume--basis [Lewis (1969); Chaudhry,
Majid, and Chaudhry (1993)]. These charges vary widely between crops.
This pattern of charges encourages wasteful use of the country's
most limited resources. The structure of water rates has long been
subject to criticism. It has been alleged that charges for irrigation
water discriminated between various crops in such a way as to distort
resource allocation. Moreover, it has generally been argued that water
was and is being provided by the public sector at appreciably less than
its marginal cost [Chaudhry, Majid, and Chaudhry (1993)]. Some awareness
of the different amount of water required by different crops has been
introduced by applying differential rates per acre, but these
differentials have not been fully compensated for the differences in
water use [Lewis (1969); Haufbauer and Akhtar (1970)]. Thus the
determination of an efficient pricing system for irrigation water has
become a serious issue especially in the backdrop of declining water
tables in the country.
The main objective of this paper is to evaluate several alternative
water pricing systems and choose one that will ensure efficient use of
irrigation water in Pakistan. A related objective is to test the extent
of sensitivity of the demand for irrigation water to a change in
alternative water prices. For this purpose, a single equation production
function (1)--Cobb-Douglas (CD)--will be specified and estimated first
and then the CD parameter estimates will be used to derive an input
demand function for irrigation water. The derived water demand function
will serve as a bridge between production function estimates and water
demand policy simulations in analysing alternative water pricing
systems.
The paper is organised in six sections. Section 1 is introductory
and gives an outline of the study. Section 2 discusses data, variables,
and the empirical model. The discussion of the empirical results is
reported in Section 3. Section 4 reports policy simulations. In Section
5, sensitivity analysis of the policy simulations has been carried out.
The last section, Section 6 summarises conclusions and policy
implications.
2. DATA, VARIABLES, AND EMPIRICAL MODEL
2.1. Data and Variables
The data used in this study are from a 1998 survey of 601 farmers
in Pakistan for the crop year 1997-98, conducted by the author for the
purpose of her doctoral research [Sahibzada (2002)]. A four-stage
sampling technique was used for the selection of a representative
sample. As a first step, three provinces--the North West Frontier
Province (NWFP), Punjab, and Sindh--were selected as major irrigation
water users. Balochistan was not included because it does not have a
noticeable share of irrigated agriculture vis-a-vis other provinces, at
the moment. At the second stage, tehsils (sub-districts) were selected
to represent average conditions in each province. The third stage
involved village selection, and the final stage represented the
selection of farmers. While the selection of provinces was self-evident,
the procedures adopted at the remaining three stages were as follows.
The survey was carried out in nine sub-districts selected from the four
regions, which were themselves selected on the basis of the
characteristic of growing a major crop. Lodhran (Punjab) for cotton;
Thatta (Sindh) for rice; Charsaddah (NWFP) for mixed crops and
Sugarcane; and Attock, Mianwali (Punjab) and Kulachi (NWFP) for
non-irrigated agriculture. Wheat, the staple food crop, was noticed to
be grown in almost all regions. The village selection was made using
concentric circles drawn on tehsil maps. To accomplish this task the
latest maps of the sampled sub-districts were collected from the office
of the Survey of Pakistan and the respective District Councils. The
selection of farmers constituted the last stage of sampling. The farmers
were randomly selected from three sub-districts of Punjab, two of Sindh,
and four of the NWFP. Thus the total sampled farmers in the selected 9
sub-districts aggregated to 601 respondents. A questionnaire was
formulated to obtain information on crop production and price, size of
farm, cropped area, irrigation water, labour, and use of tractor and
fertiliser. It is important to point out that water usage was measured
only as the number of irrigations in the crop year. The conventional
practice assumes an average of three acre inches of water per one
irrigation; more precise measurement is time-consuming and expensive,
and was not performed in this survey. Again, the estimate of irrigation
water used relied on the farmer's memory regarding water received
during the crop year. The data base from this survey appears to be
representative of the Indus Basin with respondents reporting production
of a number of irrigated crops including wheat, rice, maize, cotton,
sugarcane; tobacco, vegetables, and various fodder crops.
The analysis of this study relies on a single-equation production
function. The dependent variable is total aggregated output (Y) in
maunds (1 maund = 40 kgs), weighted by revenue shares. The surveyed
farmers have provided information on total production of each crop at
the individual farm level, and price per maund of each crop. An
established procedure (2) has been used to aggregate output. Data on
various inputs (irrigation, fertiliser man-days, tractor hours) have
been collected on a per acre basis, and cropped area at the farm level.
Data on fertiliser from the surveyed farmers were basically collected by
type (Urea, DAP, NP, NPK, etc.), in kilograms on per acre basis. These
were later converted into fertiliser nutrients in kilograms following
government's guidelines. (3) The fertiliser nutrients have been
derived mainly from urea, diammonium phosphate, calcium ammonium, etc.
Total fertiliser input (FERT) at the farm level has been obtained by
multiplying the per cropped acre fertiliser nutrient in kilograms with
total cropped area at the farm level. Data on labour have been collected
in man-days generally but also in working hours from several farmer
surveyed, by types of activities (Pre-sowing, Sowing, Hoeing,
Irrigation, Harvesting, and Threshing) on a per cropped acre basis. One
man-day is normally of eight hours. The data in working hours have been
converted into man-days by dividing the total by the number 8. Total
man-days input (MD) at the farm level has been obtained by multiplying
total man-days with total cropped area at the farm level. Data on
tractor hours have been collected on a per cropped acre basis. Total
tractor input (TH) in operational hours at the farm level has been
obtained by multiplying the per acre tractor input with total cropped
area at the farm level. Data on irrigation water (IRR) have been
collected from the surveyed farmers in number of irrigations per cropped
acre. One irrigation equals on average 3 acre inches of water. Total
irrigation input (IRR) in acre inches at the farm level has been
obtained by first multiplying the number of irrigations per acre with 3,
and then multiplying the data in inches with total cropped area at the
farm level. Data on total cropped area (TCA) have basically been
collected in acres at the farm level.
The dummy variables DFERT, DTRAC, and DIRRI, respectively for zero
observations (4) in respect of fertiliser, tractor, and irrigation, are
included in the model in order to correct for the presence of some zero
observations for these three inputs (see the discussion of the Battese
model later in Section 3.2). D1 to D7 are dummy variables for the seven
sub-districts which are included in the equation in order to capture
variations in soil quality and climatic conditions in different regions.
DMULTI is a multiple crop dummy showing the impact of crop
diversification, with DMULTI = 1 for farms growing more than one crop,
and = 0 for single-crop farms.
Descriptive statistics for all variables used in model estimation are given in Table 1.
2.2. Empirical Model
The most widely used forms of production functions in the analysis
of agriculture are the Cobb-Douglas (CD) and the Transcendental
(Translog). In our study, we initially used a Translog production
function, which is a flexible functional form and places no a priori restrictions on the production technology such as constant returns to
scale, homogeniety, separability, and constant elasticity of
substitution. This functional form is a second-order Taylor series
approximation, and thus requires a larger number of parameters to be
estimated. Consequently, multicollinearity is often a problem when
estimating the single-equation translog production function. The present
study was no exception. The results of the estimated translog model
showed some of the production elasticities to be negative, thus
resulting in several violations of regularity conditions. To avoid such
problems, the present study relied on the Cobb-Douglas functional form,
which is very popular in agricultural production studies because of its
parsimony in parameters, ease of interpretation, and computational simplicity. Several studies of Pakistan's agricultural sector have
used this form primarily because the resulting coefficients make it
possible to interpret the elasticities of production with respect to
inputs, and because the coefficients also indicate the relative
importance of each input with respect to output [Chaudhry and Kemal
(1974); Naqvi, et al. (1982, 1983, 1986); and Zuberi (1989)].
The Cobb-Douglas production function, which is considered here for
the estimation of input elasticities of the surveyed farmers, is defined
below for restricted (Model 1) and full (Model 2) data sets, the former
excluding and the latter including zero observations for fertiliser,
tractor hours, and irrigation water:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where
Ln = represents natural logarithm; [[beta].sub.k] (k = 1, 2, ....,
7), st (t -- 1, 2 ...., 7), and [gamma] are the unknown parameters to be
estimated, and [epsilon] is the usual random error term, which is
assumed to be normally distributed with zero mean and constant variance
N(0, [[sigma].sup.2]).
Y = represents total aggregated output (weighted by revenue shares)
at the farm level, divided by total man-days at the farm level;
FERT = total amount of fertiliser nutrients (in kilograms) used at
the farm level, divided by total man-days at the farm level;
MD = total amount of labour (in man-days) used at the farm level;
TH = total number of tractor hours used at the farm level, divided
by total man-days at the farm level;
IRR = total quantity of irrigation water (in inches) used at the
farm level, divided by total man-days at the farm level;
DFERT = dummy variable which has value of one if fertiliser usage
was positive, and zero for zero;
DTRAC = dummy variable which has value of one if tractor usage was
positive, and zero for zero;
DIRR = dummy variable which has value of one if irrigation usage
was positive, and zero for zero;
[D.sub.1] = district dummy variable which has value of 1 if
Mianwali sub-district, and 0 otherwise;
[D.sub.2] = district dummy variable which has value of 1 if Kulachi
sub-district, and 0 otherwise;
[D.sub.3] = district dummy variable which has value of 1 if Thatta
sub-district, and 0 otherwise;
[D.sub.4] = district dummy variable which has value of 1 if
Mirpurkhas subdistrict, and 0 otherwise;
[D.sub.5] = district dummy variable which has value of 1 if
Peshawar sub-district, and 0 otherwise;
[D.sub.6] = district dummy variable which has value of 1 if Lodhran
sub-district, and 0 otherwise;
[D.sub.7] = district dummy variable which has value of 1 if Attock
sub-district, and 0 otherwise;
DMULT = crop dummy variable which has value of 1 if more than 1
crop and 0 for only one crop.
It is a 4-input "per man-day model" (5) with its two
specifications (Models 1 and 2) and CRS-imposed. Model 1 is based on the
restricted data set in that zero observations for the three inputs,
fertiliser, tractor hours and irrigation water are excluded from model
estimation, while Model 2 uses the full data set.
Out of the original nine sub-districts, two, i.e., Charsadda and
Mardan, were used as the reference districts. Since the observations
from Mardan were very few (10 only), and the climatic conditions and
land quality of both the districts were almost the same, both were
merged and considered as the single reference district called March.
Since we also have reported zero values for irrigation water,
fertiliser, and tractor hours for some farms in the survey, in order to
correct for the presence of these zero observations, dummy variables for
zero observations in respect of the three inputs have been used in the
estimation of Model 2. This has been done following Battese, Malik, and
Gill (1996) and Battese (1997). The objective of using this approach is
to accommodate the users and non-users of these three inputs and still
obtain efficient and unbiased estimates using the full data set.
The Battese approach given in his 1996 and 1997 papers consists of
two proposed models which look different but in fact yield the same
results--a shift in the intercept for zero-valued observations. We have
adopted the approach used in the Battese, et al. (1996) in the current
study. Following the latter approach, a dummy variable (for instance
DIRR) is defined for each input, which has some zero observations in the
sample, as taking on a value of unity when the input has a positive
value, and a value of zero when the input has a zero value. The model is
then specified with two related terms--the dummy variable by itself and
a second term involving the dummy variable multiplied by the natural log
of the input; DIRR and DIRR In(IRR), for instance, where IRR is the
amount of irrigation water used. Thus we get two estimated coefficients
for each of the two terms when IRR is positive (i.e., get an intercept
shift and an estimated coefficient for In IRR) whereas both terms fall
out (i.e., have zero values) when IRR = 0. (6) Finally, since many of
the surveyed farmers grow more than one crop in a season, we have used a
dummy variable (DMULTI) for measuring the impact of multiple crops.
Since all parameters in the Cobb-Douglas function are elasticities
of production, the value of the marginal physical product (MPP) for a
specific input is given by:
[MPP.sub.k] = [delta][Y.sub.i]/[delta][X.sub.ki] = [b.sub.k]
([Y.sub.i/[X.sub.ki]) ... ... ... (3)
where
[Y.sub.i] represents the ith farmer's output, [X.sub.ki]
represents the level of inputs of the kth resource at the ith farm, and
[b.sub.k] is the regression coefficient of the kth input in a
Cobb-Douglas model. Following the customary practice, a point estimate
of marginal physical product (MPP) can be obtained by evaluating
Equation (13) at the mean value of each input. The marginal value
product (MVP) of each input at the farm level is then computed by
multiplying the MPP of each input at the farm level by the aggregate
output price. (7)
2.3. Input Demand Function for Irrigation Water and Policy
Simulations
As the main objective of the present study is to evaluate
alternative water pricing systems and to choose a price that ensures
efficient use of irrigation water, a detailed simulation exercise will
be carried out to find such a price. An efficient price will be one
which gives more efficient predicted water usage as compared to the
present actual water usage at the district level. Data on the present
actual water usage has been collected from the surveyed farmers and
aggregated at the sub-district level. For conducting the simulation
exercise, an input demand function for irrigation water, using the
Cobb-Douglas (CD) parameter estimates from Models 1 and 2, will be
derived and combined with various alternative prices for irrigation
water to predict water requirements at the district level.
The CD demand for irrigation water has been derived through
constrained cost minimisation, using a CD production function [Varian
(1992)]. In this problem, the choice variables are the inputs (the Xs)
while the input prices (the Ws) and output (Y) are parametric variables
which are assumed to be exogenous or given to the firm. The derived
irrigation water demand function is then used as a bridge between
production function estimation and water demand policy simulations in
analysing alternative water pricing systems. A detailed derivation of
the input demand function for irrigation water is given in the Technical
Appendix, but the basic equation for irrigation water demand is given as
follows.
[[??].sub.4] = [A.sub.0][Y.sup.[alpha]y][w.sup.[alpha]1.sub.1]
[w.sup.[alpha]2.sub.2][w.sup.[alpha]3.sub.3] / [w.sup.[alpha]4.sub.4]
... ... ... ... ... (5)
where,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[[??].sub.4] = Cost minimising demand for irrigation water;
Y = Aggregate farm output at the mean level;
[w.sub.1] = Price of fertiliser nutrient per kilogram;
[w.sub.2] = Price of labour per man-day of 8 hours;
[w.sub.3] = Price of tractor use per hour;
[w.sub.4] = Price of irrigation water per acre inch;
[b.sub.0] = Estimated coefficient of the constant;
[b.sub.1] = Estimated coefficient of fertiliser;
[b.sub.2] = Estimated coefficient of labour;
[b.sub.3] = Estimated coefficient of tractor; and
[b.sub.4] = Estimated coefficient of irrigation water.
2.4. Alternative Water Prices
The five water pricing systems which have been used in the basic
simulations exercise are MVP-based, Market-based, Average Cost-based,
short-run Marginal Cost-based, and long-run Marginal Cost-based. The
MVP-based price comes out from the analysis of the survey data. The
various cost-based prices have been derived in two ways. First,
secondary data on provincial expenditures on irrigation water supply
delivery have been used to calculate average variable and average
marginal cost per acre foot of water [Sahibzada (2002)]; Secondly,
estimates of long-run marginal costs, based on the review of feasibility
reports of small, medium, and large dams, and the expert opinion of
irrigation engineers have been used as an alternative price for
irrigation water in the simulation exercise [Sahibzada (2002)]. The
summarised discussion of alternative irrigation water prices used in the
basic simulations is presented in Table 2.
3. RESULTS AND ANALYSIS
Equations 1 (Model 1) and 2 (Model 2) have been estimated using the
computer software package EViews 3.1. Equation 1 is a 4-input "per
man-day" model in which both the LHS and the RHS variables have
been divided by man-days before taking their logs for model estimation,
and zero observations of the three inputs, fertiliser, tractor hours,
and fertiliser excluded. Thus, this model assumes constant returns to
scale. Since graphical analysis of the models' residuals and
White's test [White (1980)] have pointed towards the presence of
heteroskedasticity, which is a normal phenomenon in the analysis of
cross-sectional data, White's estimation procedure has been used to
correct for heteroskedasticity. The regression results of the two
specifications of this 4-input "totals" model are reported in
Table 3.
The regression results for the two specifications of the "per
man-day" model, with CRS-imposed, are discussed as follows. The
values of R-squared are 0.399 and 0.432 respectively for Models 1 and 2,
indicating that 40 to 43 percent of the variations in total aggregated
output per man-day is explained by the variables included in the models.
Most of the parameter estimates in Models 1 and 2 are statistically
significant at least at the 90 percent confidence level and most have
the expected signs. The sum of the parameter estimates of the four
traditional inputs (labour, fertiliser, water, and tractor) is equal to
unity in both the restricted as well as the full data sets, implying
that a one-percent increase in the four model inputs results in a
one-percent increase in aggregated output per man-day, since
constant-returns-to-scale has been imposed. The estimated coefficients
of irrigation (LIRR) are large and highly significant in both Models 1
and 2, i.e., 0.501 and 0.484, which means that a one-percent increase in
irrigation water input increases aggregate output per man-day by 0.5 and
0.48 percent respectively in the former and latter cases. The estimated
coefficient for fertiliser (LFERT) follows the irrigation coefficient in
size and significance. It is 0.308 in Model 1 and 0.265 in Model 2,
which says that a one-percent increase in fertiliser input increases
aggregate output per man-day by 0.31 percent and 0.26 percent
respectively in the former and latter cases, with both coefficients
again being highly significant. Labour (LMD) is third in line in the
input coefficient size, ranking with computed coefficient estimates of
0.172 and 0.134, implying that a one-percent increase in the labour
input will bring about 0.17 and 0.13 increase in aggregated output per
man-day respectively in Model 1 and Model 2, Tractor hours (LTH) have a
comparatively smaller estimated coefficients--0.117 and 0.019--in the
two specifications, and both are statistically insignificant.
Results regarding the district-specific dummy variables in the two
specifications show Thatta and Lodhran to be significantly less
productive and Peshawar to be more productive than the reference
districts of Mardan and Charsadda in both the restricted as well as the
full data sets. Kulachi and Mianwali are significantly less productive
than the reference districts, the former in Model 1, the latter in Model
2.
The multi-crop dummy variable coefficient is negative, significant
at 95 percent confidence level in the restricted data set and
significant at 99 percent confidence level in the full data. The
negative sign means that multiple crop farmers will have slightly less
aggregated output for given amounts of all four inputs as compared to
single crop farmers. This negative difference reflects the opportunity
cost of hedging against crop risk by planting multiple crops--the
related benefit is of course the reduced risk of monocrop failure
through a more diversified "crop portfolio".
Regression results of Model 2 include zero observations of
fertiliser, tractor, and irrigation. This requires that a procedure--the
Battese model--be used in order to combine both positive and zero input
observations in the model estimation. (8) Following Battese, et al.
(1996), dummy variables for zero observations of the three inputs are
defined to equal 1 for positive or non-zero observations, and equal to
zero for zero observations. Based on this definition, the signs of the
estimated coefficients for the three dummy variables (DFERT, DTRAC, and
DIRRI) are expected to be positive. The positive sign implies a positive
relationship between the intercept of the production function of the
users and the use of the inputs. When an input, for instance, irrigation
water is used, the intercept moves upwards, and vice versa. In Model 2,
it appears that the estimated coefficients for DFERT and DTRAC are
negative. The negative sign of the estimated coefficient in the case of
fertiliser may imply that owners of fertile land may not use fertiliser
because the use may result in lodging of the crops, since excessive use
of fertiliser damages the crops. Such cases are rare but can be found in
actual life. The negative sign of the estimated coefficient for DTRAC
seems simple to explain here. Since there are only 10 zero observations
out of 601 for tractor, variations in the dependent variable due to them
will be very negligible, even non-existent. Moreover, since the
estimated coefficients for both DFERT and DTRAC are not significantly
different from zero, the negativity problem in their context becomes
meaningless.
The coefficient estimate for DIRRI is positive and highly
significant. DIRRI's positive and significant estimated coefficient
means that the intercept of the production function for irrigated farms
is higher than that of the unirrigated farms, implying that there is a
positive relationship between the shift in the intercept and the use of
irrigation water. When a farmer uses irrigation, the intercept of his
production function moves upwards implying an increase in productivity;
when he stops using irrigation, the intercept moves downwards, causing a
decline in productivity.
Using the regression results of Models 1 and 2, the marginal
physical product (MPP) of irrigation water is calculated using Equation
3. Table 4 reports MPP and MVP of irrigation water. Marginal Value
Product (MVP) of irrigation water has been calculated by multiplying its
MPP with the aggregated output price. (9) The aggregated output price
has been calculated to be Rs 358.48 per maund (40 kgs) for the
restricted data set and Rs 350.59 per maund for the full data set. The
MPP of irrigation water varies between 49.69 kgs (1.242 maunds) per acre
inch for the restricted data set and 47.55 kgs (1.186 maunds) per acre
inch under the full data set. The MVP of irrigation water per acre inch
comes to Rs 445.23 and Rs 415.79, respectively, under restricted and
full data sets. These MVP estimates will be used as one of the several
alternative water prices in the simulation exercise. Table 4 also
reports the MVP to opportunity cost (OC) ratio, which is a measure of
use efficiency. Market price of irrigation water--Rs 200 per acre
inch--has been used as an approximation to the OC of irrigation water.
An MVP/OC ratio equal to one indicates efficient use of a resource and a
ratio greater/less than one indicates its under- and over-usage
respectively.
Since the calculation of input demand for irrigation water using CD
parameter estimates requires the use of input prices, and in our survey
no information on the prices of inputs was collected, hence average
prices charged for the services of these inputs have been used. These
average prices are quite consistent with those reported in Pakistan
(1998) which vary between Rs 100-150 per tractor ploughing (one
ploughing is completed in one tractor hour), Rs 202-210 per hour of
tubewell water (in one hour one acre inch of water is delivered), and Rs
70-80 per man-day of hired labour. The price of fertiliser per nutrient
kilogram is about Rs 15.00 [Pakistan (2001)]. Farm labour is in
man-days. One man-day is assumed to be eight hours of work and the mean
wage rate charged these days for agricultural labour is Rs 80.00 per
man-day [Pakistan (1998)]. This is a minimum norm although there is some
variation in the wage rate from place to place. The open market price
for one operational hour of tractor on average is Rs 120.00 [Pakistan
(1998)], even though variations do exist in the rates across
geographical divisions. As for irrigation water, it is not a common
practice to sell canal water, but its trading does take place in the
Punjab region of Pakistan. Tubewell water is frequently sold or
exchanged in Punjab since the market for tubewell water in Punjab is
more developed vis-a-vis other provinces. Variations in irrigation water
prices exist due to variations in soil, topography, season, the nature
of crops, the quality of water, and the availability of alternative
sources of water for irrigation. The price paid by farmers for tubewell
water in Punjab currently varies between Rs 100 and Rs 150 per hour, and
for canal water it varies between Rs 200 and Rs 250 per hour. In one
hour, about one acre inch of irrigation water is used by farmers. It is
generally believed that in the absence of formal water markets, Rs 200
per acre inch for canal water is a good approximation of the opportunity
cost of irrigation water.
4. POLICY SIMULATIONS
The derived demand function for irrigation water (Equation 4) has
been computed using coefficient estimates of Models 1 and 2 combined
with prices of the four inputs and aggregated output in order to
calculate the predicted water usage at the sub-district level. The
average prices for the three inputs--fertiliser, tractor hours, and
man-days--and aggregate output used in the CD production function
estimation have been discussed in Section 3.1. The summarised discussion
of alternative prices for irrigation water used in the basic simulations
is given in Table 2.
These simulations are called simulations at the base-line prices
and are reported in Table 6. These will be used as reference simulations
in the sensitivity analysis exercise.
Table 5 reports information on the various variables aggregated at
the district level for district level analysis. These variables include
the number of observations, farm output, the number of irrigations,
total cropped area (TCA), and total farm area (TFA), all aggregated at
the district level since simulations are carried out at the district
level. Aggregate output per irrigation (Output/Irri) and aggregate
irrigations per acre (Irrig/acre) are also included in Table 5.
For the computation of the predicted water usage at the
sub-district level, zero values for the dummy variables of other
districts are assumed, while that for the district for which water usage
is simulated is set equal to one. Other dummy variables, such as the
dummy variable for multiple crops (DMULTI) in Models 1 and 2, and dummy
variables for zero observations for fertiliser (DFERT), tractor hours
(DTRAC), and irrigation water (DIRRI) in Model 2 take on values equal to
the sub-district sample mean, i.e., averaged across all sample farms in
the sub-district.
Using the irrigation water demand function and the production
function coefficient estimates from Models 1 and 2, water usage in terms
of number of irrigations at the sub-district level is predicted. As
mentioned in an earlier section, the results of the base-line
simulations are reported in Table 6, which shows actual and predicted
water usage (in the number of irrigations) under alternative water
pricing systems at the sub-district level.
The first row in the table presents actual water usage in the
number of total irrigations aggregated at the sub-district level. Data
on actual water usage obtained from surveyed farmers were basically in
the number of irrigations per acre for individual farms. These have been
converted into total irrigations by multiplying by total cropped area at
the farm level for the estimation of several alternative regression
models. Figures in the parentheses in Table 6 are the number of
irrigations per acre which have been calculated by dividing the
aggregated irrigations at the sub-district level by the total cropped
area, also aggregated at the sub-district level (Table 5).
Looking at the base-line simulations in Table 6, two important
findings from the water pricing policy perspective are noted:
(i) Irrigation water is not available in adequate quantity to
farmers in almost all districts at all the alternative prices in
Pakistan's irrigated agriculture sector, as the predicted water
usage at all prices is greater than the actual usage for all districts.
The last column under Total in the same table shows this fact distinctly
since the total actual usage for all sub-districts is 60535 irrigations
as compared to the predicted usage of 86219 irrigations even at the
MVP-based price, which is the highest among the five alternate prices.
In percentage terms, total actual current water usage is 70-72 percent,
9 percent, 8 percent, 14 percent, and 47-49 percent of the predicted
water usage respectively at the MVP-based, AC-based, SRMC-based,
LRMC-based, and market-based prices. In other words, the inadequacy of
the current water usage can be seen from the fact that if irrigation
water is charged according to, say, the market-based price, even then
water requirements of the farmers in all subdistricts will be much more
than the current actual usage. This finding points towards the overall
general scarcity of irrigation water available to farmers.
(ii) Discussing the water requirements of the individual districts
and defining water use efficiency in terms of the highest agricultural
produce per unit of irrigation water, the table reports that Mirpur Khas stands out as the most efficient user of irrigation water, with 7.8
irrigations per acre and producing the maximum aggregated farm output;
its aggregate farm output per irrigation is the highest--18 maunds per
irrigation--followed only by Attock and Peshawar, with 16 and 11.5
maunds per irrigation (Table 5). At the same time, Mirpur Khas again is
the only district whose predicted water usage at the market-based price
for instance is 207 percent more than its current actual usage. In the
case of Attock, Kulachi, Lodhran, Mianwali, Peshawar and MarCh, this
percentage increase in the predicted water usage vis-a-vis the actual
usage is 78 percent for Attock, 118 percent for Kulachi, 31 percent for
Lodhran, 104 percent for Mianwali, 11 percent for Peshawar, and 64
percent for MarCh. Peshawar turns out to need much less water at the
market-based price specifically than the two districts (Attock and
Mirpur Khas) with which it competes on the basis of productivity per
irrigation. Its predicted water usage at this price registers an
increase of about 11 percent as compared to 78 percent for Attock and
207 percent for Mirpur Khas. The case of Thatta is unique. With low
productivity per irrigation (5 maund) and using the highest number of
irrigations (15) per acre, its predicted water usage at the market-based
price is the highest--236 percent more than its current usage. This
means that Thatta could be considered as a classic case of an
inefficient user of scarce water resource.
In the full data set, the nature of the change in predicted water
usage is the same for all eight districts but the magnitude of the
percentage change in the predicted water usage for two districts has
substantially increased. In the case of MarCh the percentage increases
from 64 percent to 265 percent, and for Kulachi it has increased from
118 percent to 517 percent. It may be mentioned here that almost all of
the zero observations for irrigations are found in Kulachi as it has
mainly rain-fed agriculture, and farmers in Kulachi get very little
irrigation water.
Tables 7 and 8 report the differences in the predicted water usage
from the base-line simulations reported in Table 6, both in absolute
terms and in percentage terms, as a result of a 10 percent increase and
a 10 percent decrease respectively in alternative water prices at the
sub-district level. Table 7 shows the outcome of an assumed 10 percent
increase in the alternative water prices on predicted water usage. A
look at the figures in the parentheses in both the restricted as well as
in the full data sets reveals that when water price is increased by 10
percent, the predicted water usage in all sub-districts decreases by
less than 10 percent, i.e., demand for water decreases by only 5
percent, which implies a price-inelastic demand for water usage. Table 8
presents the results of an assumed 10 percent decrease in alternative
prices on predicted water usage at the sub-district level. It shows
almost the same magnitude of price elasticity of demand in the
restricted data set, but in the full data set the degree of elasticity
is slightly more than that of the restricted set. In the case of 10
percent decrease in water prices, again the price elasticity of demand
for water is less than unity since the predicted water usage increases
by about 5 percent in Model 1 and 6 percent in Model 2 in response to a
10 percent decrease in alternative water prices.
5. SENSITIVITY ANALYSIS
Sensitivity analysis is a method of exploring the effects of using
alternative values of the estimated parameters of a model/project in
order to determine as to which parameters the project is most sensitive.
This is usually done by varying each parameter one at a time, keeping
the other parameters constant and calculating the consequent effect on
the baseline scenario. In the present study, two types of economic
analysis have been carried out. The first type is changing alternative
irrigation water prices by 10 percent upwards and downwards, holding
other variables constant, and the second type is changing alternative
parameter estimates, especially the input elasticity for irrigation
water, by 10 percent, keeping the baseline water prices constant. The
first type, which is called price policy simulations exercise, has
already been discussed as a part of the simulation exercise in Tables 7
and 8. The second type, called sensitivity analysis, is undertaken by
using a 10 percent increase/decrease in the elasticity for irrigation
water. Since CRS is imposed on both models, a 10 percent
increase/decrease in the input elasticity for irrigation water has been
accompanied with a simultaneous decrease/increase in the input
elasticities for fertiliser, tractor hour, and man-day, so that the
condition of the CRS remains imposed. The results of this exercise are
reported in Tables 9 and 10.
Tables 9 and 10 report differences in the predicted water usage
from the baseline simulations reported in Table 6, both in absolute
terms and in percentage terms, as a result of a 10 percent
increase/decrease in input elasticity for irrigation water, along with a
simultaneous 10 percent decrease/increase in input elasticities for
fertiliser, man-day, and tractor hour, using base-line water prices.
Table 9 presents changes in predicted water usage as a result of a 10
percent increase in the input elasticity for irrigation water and a
simultaneous 10 percent decrease in other input elasticities. Table 10
records the impact of a 10 percent decrease in the input elasticity for
irrigation water and a simultaneous 10 percent increase in input
elasticities for the other three inputs on predicted water usage.
A review of Table 9 highlights two points:
(i) A 10 percent increase in the water's estimated coefficient
along with a 10 percent decrease in the estimated coefficients of other
inputs shows a 17 percent and 13 percent increase in predicted water
usage, using two alternative prices--the MVP-based and the Market-based
respectively-wherein the change in the demand for water is more than the
change in the parameter estimates. Moreover, the impact of this change
in the estimated parameters has very little impact on predicted water
usage when the three cost-based (AC-based, SRMC-based, and LRMC-based)
base-line prices are used.
(ii) A 10 percent increase in the input elasticity for irrigation
water along with a simultaneous decrease in input elasticities for other
inputs brings two types of changes in the predicted water usage. First,
in the case of MVP-based and market-based prices, the relationship
between the change in the estimated parameters and the change in the
predicted water usage is positive, meaning that a 10 percent increase in
the estimated coefficient for irrigation water along with a 10 percent
decrease in the estimated coefficients for other inputs increases
predicted water usage by 17 percent using MVP-based prices, and by 13
percent using market-based prices. Secondly, the same 10 percent
increase in the water coefficient along with a 10 percent decrease in
other inputs' estimated coefficients decreases predicted water
usage when the three cost-based prices are used, though by a lesser
percentage (2 to 4 percent).
Table 10 reports the impact of a 10 percent decrease in the input
elasticity for irrigation water accompanied by a 10 percent increase in
input elasticities for fertiliser, man-day, and tractor hour. As would
be expected, the trend noticed in Table 9 is repeated in Table 10 but in
the opposite direction. Using the base-line MVP-based and market-based
prices, the predicted water usage decreases by more than 10 percent,
i.e., by 15 to 19 percent in the former and 13 to 15 percent in the
latter case respectively in the restricted and full data sets. The only
difference noticed in Table 10 is that changes in the predicted water
usage as a result of the change in the parameter estimates are in the
same direction at the four water prices (MVP-based, market-based,
AC-based, and LRMC-based), while in Table 9 this was not so. It means
that like the MVP-based and market-based price cases, a decrease in
predicted water usage is registered using the two cost-based prices in
response to a 10 percent decrease in the input elasticity for irrigation
water and a simultaneousl0 percent increase in input elasticities of
other inputs.
The analysis of the results of changes in various variables and
parameters reported in Tables 5 to 10 allows one to arrive at two
conclusions: (i) the demand for irrigation water is less sensitive to
changes in alternative irrigation prices at the district level in both
specifications of the 4-input "per man-day" model; and (ii) a
10 percent increase in the input elasticity for irrigation water along
with a simultaneous 10 percent decrease in the input elasticities for
fertiliser, man-day, and tractor hour increases water usage by 13 to 17
percent respectively at market-based and MVP-based prices in both data
sets. At the cost-based prices the change is in the opposite direction
and is less than 10 percent. A 10 percent decrease in the input
elasticity for irrigation water, along with a simultaneous 10 percent
increase in input elasticities for other three inputs, decreases
predicted water usage by 16 to 19 percent respectively at the market-
and MVP-based prices for the restricted data set, and by 13 and 15
percent for the full data set.
6. CONCLUSIONS AND POLICY IMPLICATIONS
Two major conclusions that emerge from this study may be summarised
as follow:
(1) Policy simulations results, presented in Tables 7 and 8, report
severe irrigation water shortages in all sample districts. At almost all
alternative prices, predicted water usage exceeds actual water usage in
all districts, which may mean that delivery systems do not deliver
enough water for the price to ration. Hence, at all prices of water used
in the simulations, the optimal amount of water is far more than is
delivered.
(2) The reported results also speak loudly about the price less
elastic of demand for irrigation water. A 10 percent increase/decrease
in all prices decreases/increases predicted water usage by less than 10
percent (5 percent only), which means that any increase in water price
will not reduce the demand for water.
The conclusions go against the general perception in Pakistan that
water is used inefficiently due to low water rates charged from farmers,
and that raising water rates would ensure water use efficiency. The
present analysis makes a strong case for increasing water supplies to
farmers.
Given the conclusions of the study, the policy-maker has two
options for increasing water supplies to farmers: (i) building new water
storage reservoirs, and (ii) improving the management of the water
delivery system. Siace additional increases in water supply through the
construction of new reservoirs are not possible (at least in the short
run) due to financial, environmental, social, and political constraints,
the most cost-effective and feasible solution appears to be the
improvement of the management of the water delivery system. Surface
water supply deliveries are very inefficient because of losses through
seepage and evaporation. Recent investigations have confirmed that water
losses in the tertiary water distribution system below the outlet are
very significant. While it may be difficult to avoid the losses in the
main canals, there is considerable scope for conserving the large losses
below the outlets [Sahibzada (2002)]. The on-going programme of Onfarm
Water Management, involving the improvement of the main watercourses and
their partial lining is a move in this direction. However, its
efficiency needs to be established especially since these improvements
are not extended to the farmers' distribution channels [Sahibzada
(2002)].
Irrigation water shortages are also the result of the inflexibility
of the irrigation water delivery system for agricultural use. Basically,
the irrigation system was designed a century ago--crop water
requirements were based on the then designed cropping intensity of 50-75
percent. This intensity has almost doubled over the years which requires
modernisation of the system to cope with the emerging scarcity problems.
As canals have not yet been remodelled, the existing capacity can not
provide adequate water to meet the current enhanced cropping intensity
requirements. Hence water availability is far below the needed level.
With regard to the price inelasticity of the demand for water,
existing irrigation water shortages are the root cause for that. If the
minimum crop water requirements are not adequately met, the demand for
water will not respond to a price change.
Two more findings are highlighted below.
(i) Subject to various limitations of data and modelling, our
empirical analysis indicates significant inefficiency of resource
allocation for irrigation water, as shown by its positively large MVP/OC
ratio (2.23 and 2.08) reported in Table 4, implying its under-usage.
This may also be the result of the scarcity of water supplies in
response to the crop water requirements of the farmers.
MVP of irrigation water seems to be considerably above its costs
(OC) under both specifications. In fact, irrigation water is not
entirely within the capacity of individual farmers to supply. For
example, the supply of irrigation water from tubewells is largely within
the capacity of farmers as individuals. Wells can not, however, provide
the required irrigation at economical costs in every part of the
country. For most areas, canals are the only effective means of
irrigation. It is possible, therefore, that the exploitation of
irrigation water has been held down by the lack of large-scale canal
irrigation facilities. Specifically, as mentioned earlier, the
inflexibility of the irrigation system may be a major reason for the
under-usage of irrigation water.
(ii) In terms of the water requirements of the individual districts
and defining water use efficiency in terms of the highest agricultural
produce per unit of irrigation water, Mirpur Khas stands out as the most
efficient user of irrigation water, with 7.8 irrigations per acre and
producing the maximum aggregated farm output--18 maunds per irrigation,
followed by Attock and Peshawar with 16 and 11.5 maunds respectively per
irrigation (Table 2).
The purpose of this study has been to evaluate various water
pricing systems and choose one for application that ensures water use
efficiency in the country. Contrary to what was assumed, the outcome of
the empirical analysis goes against the general perception that the
existing lower water rates lead to the inefficient use of irrigation
water. In view of the major conclusions of the study, the case for
introducing an appropriate water pricing system takes the second place
on the priority scale. Before any recommendation is made to charge
farmers a higher water price, it is essential that farmers are ensured
adequate and reliable water supplies at their farm gate.
Technical Appendix
IRRIGATION DEMAND FUNCTION
The input demand function for irrigation water is a function of
farm output and the four input prices (including irrigation water) under
cost minimisation. Assuming cost minimisation and using the first-order
conditions (FOC), the cost minimising demand for irrigation water is
derived as follows.
Our Objective Function
min C = [w.sub.1][X.sub.1] + [w.sub.2][X.sub.2] +
[w.sub.3][X.sub.3] + [w.sub.4][X.sub.4]
Subject to:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where,
[X.sub.1] = Fertiliser; [X.sub.2] = Labour; [X.sub.3] = Tractor;
and [X.sub.4] =Irrigation. wi are respective input prices. Dis are dummy
variables for zero observations for the three inputs (fertiliser,
tractor, and irrigation water): D1 = 1 when fertiliser use is positive,
D1 = 0 for zero fertiliser use; D2 =1 when tractor use is positive, D2 =
0 for zero tractor use; and D3 = 1 when irrigation use is positive, and
D3 = 0 for zero irrigation use. Ris and Cis are respectively regional
and multi-crop dummies, e represents exponent, bis, ris, pis, and mis
are parameters to be estimated. Cost minimisation problem for a firm can
be written as a constraint optimisation equation, as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [lambda] is the laGrangian multiplier. The first-order
conditions for cost minimisation are:
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Dividing Equations 1, 2, and 3 by Equation 4 and taking the second
term to the right-hand side of the equations, we get,
[w.sub.1] / [w.sub.4] = [b.sub.1] / [b.sub.4] x [X.sub.4] /
[X.sub.1]; [w.sub.2] / [w.sub.4] = [b.sub.2] / [b.sub.4] x [X.sub.4] /
[X.sub.2]; [w.sub.3] / [w.sub.4] = [b.sub.3] / [b.sub.4] x [X.sub.4] /
[X.sub.3]
After rearranging the terms,
(5) [X.sub.1] = [b.sub.1] / [b.sub.4] [w.sub.4] / [w.sub.1] x
[X.sub.4]
(6) [X.sub.2] = [b.sub.2] / [b.sub.4] [w.sub.4] / [w.sub.1] x
[X.sub.4]
(7) [x.sub.3] = [b.sub.3] / [b.sub.4] [w.sub.4] / [w.sub.3] x
[X.sub.4]
Substituting 5, 6, and 7 in production function,
(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
solving for [X.sub.4].
(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Equation 10 can be written as:
(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Equation 11 can be written as:
(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[[alpha].sub.y] = 1 / [SIGMA][b.sub.i]; [[alpha].sub.1] = [b.sub.1]
/ [SIGMA][b.sub.i]; [[alpha].sub.2] = [b.sub.2] / [SIGMA][b.sub.i];
[[alpha].sub.3] = [b.sub.3] / [SIGMA][b.sub.i]; [[alpha].sub.4] =
[b.sub.4] / [SIGMA][b.sub.i]
Y = aggregate farm output at the mean level;
[w.sub.1] = the price of fertiliser nutrient per kilogram;
[w.sub.2] = the price of labour per man-day of 8 hours;
[w.sub.3] = the price of tractor use per hour;
[w.sub.4] = the price of irrigation water per acre inch;
[b.sub.0] = estimated coefficient of the constant;
[b.sub.1] = estimated coefficient of fertiliser;
[b.sub.2] = estimated coefficient of labour;
[b.sub.3] = estimated coefficient of tractor;
[b.sub.4] = estimated coefficient of irrigation water; and
the power in the exponent can be written as:
([r.sub.1] / [SIGMA][b.sub.i]) [D.sub.1] ([r.sub.2] /
[SIGMA][b.sub.i]) [d.sub.2] ([r.sub.3] / [SIGMA][b.sub.i]) [D.sub.3] +
([P.sub.1] / [SIGMA][b.sub.i]) [R.sub.1] + ([P.sub.2] /
[SIGMA][b.sub.i]) [R.sub.2] + - - - + ([P.sub.7] / [SIGMA][b.sub.i])
[R.sub.7]
Author's Note: The paper draws on my PhD dissertation submitted to the State University of New York at Binghamton (USA), and a
great debt of gratitude is owed to my principal academic adviser,
Professor Thomas G. Cowing, for his advice and guidance throughout the
writing of my dissertation.
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(1) Single-equation approach has been criticised in the literature
on the ground that its use in estimating a production function results
in the simultaneity bias [Marschak and Andrews (1944); Walters (1963);
and Nerlove (1965)], but alternative methods of estimation have been
proposed by Zellner, Kmenta, and Dreze (1966) to avoid this bias
effectively in the estimation of the Cobb-Douglas production function.
(2) Aggregate Output per Unit of Land = Sum(wjQj)/Sum Aj for each
farm, where
Qj = output in maunds of cropj (one maund equals 40 kgs);
Pj = Price of cropj in Pak rupees per 40 kgs (Pak Rs 46 = US$1 in
1998);
wj = PjQj/[summation](PjQj) = weights based on revenue shares; and
Aj = Area under cultivation of cropj where the summation is across
crops grown for each farm.
(3) A Pocket Guide for Extension Workers (Islamabad: National
Fertiliser Development Centre, Planning and Development Division,
Government of Pakistan, 1997).
(4) The number of zero observations for the three inputs are:
Fertiliser (83); Irrigation Water (43); and Tractor Hours (10).
(5) Several alternative specifications of the 5-input model for
both CRS-imposed and CRS-not-imposed have been estimated. The estimated
elasticities of land (the fifth RHS variable) for all attempted
specifications have been negative and insignificant. The implied zero
elasticity of land conforms to recent empirical evidence [Ali and
Byerlee (2000) and Ahmad (2001)], which indicates strongly towards the
prevalence of a land degradation phenomenon in Pakistan. Given the
intractability of a zero input coefficient in the CD model, the land
input variable has been dropped from the production function for further
model estimation. After dropping the land from the production function,
a 4-input "totals" model with several specifications have been
estimated. Two best specifications ("per man-day" Models 1 and
2) have been selected for further analysis. The selection procedure is
based on both statistical testing and economic analysis [Sahibzada
(2002)].
(6) Since one uses natural logs to estimate the CD production
function, this requires that either In IRR is set equal to zero or IRR
is put equal to one (same thing) when DIRR is zero.
(7) Aggregate output price is calculated as follows:
(i) prices of various crops are weighted by revenue shares;
(ii) weighted crop prices are aggregated; and
(iii) aggregate output price at the mean level is used for
calculating MVP of the four inputs.
(8) Battese, Malik, and Gill (1996): discussion of the model is
given in Section 3.2.
(9) See footnote 7.
Shamim A. Sahibzada is Joint Director at the Pakistan Institute of
Development Economics, Islamabad.
Table 1
Descriptive Statistics for Variables Used in OLS Regression Analysis
Model 1 n=509)
Variable Mean S.Dev Mini. Maxi.
Y (Mds) 3.00 6.36 0.04 86.67
FERT (Kgs) 7.98 15.12 0.18 273.46
MD (Mdays) 318.38 556.4 3.25 6400
TH (Hrs) 0.25 0.21 0.01 2.08
IRR (Inches) 0.47 0.54 0.02 5.84
TCA (Acres) 13.85 22.86 0.50 300
DFERT -- -- -- --
DTRAC -- -- -- --
DIRRI -- -- -- --
D1(Mian) 0.12 0.33 0 1
D2 (Kola) 0.002 0.04 0 1
D3 (That) 0.21 0.41 0 1
D4 (Mirp) 0.11 0.31 0 1
DS (Pesh) 0.07 0.25 0 1
D6(Lodh) 0.25 0.44 0 1
D7 (Atto) 0.06 0.24 0 1
DMULTI 0.87 0.33 0 1
Model 2 (n=601)
Variable Mean S.Dev Mini. Maxi.
Y (Mds) 2.52 6.08 0.04 86.67
FERT (Kgs) 7.16 14.22 0.06 273.46
MD (Mdays) 309.09 528.81 1.94 6400
TH (Hrs) 0.26 0.22 0.01 2.08
IRR (Inches) 0.42 0.53 0.00 5.84
TCA (Acres) 15.05 23.59 0.5 300
DFERT 0.86 0.34 0 1
DTRAC 0.98 0.13 0 1
DIRRI 0.93 0.26 0 1
D1(Mian) 0.11 0.32 0 1
D2 (Kola) 0.13 0.33 0 1
D3 (That) 0.19 0.39 0 1
D4 (Mirp) 0.09 0.29 0 1
DS (Pesh) 0.06 0.24 0 1
D6(Lodh) 0.22 0.42 0 1
D7 (Atto) 0.05 0.22 0 1
DMULTI 0.82 0.38 0 1
Y = Total aggregated output (weighted by revenue shares) at the farm
level divided by total man-days at the farm level;
FERT = Total fertiliser nutrients (in kgs) at the farm level divided
by total man-days at the farm level;
MD = Total man-days at the farm level;
TH = Total Vactor hours at the farm level divided by total man-days
at the farm level;
IRR = Total irrigation (in acre inches) at the farm level divided by
total man-days at the farm level;
TCA = Total cropped area (acres) at the farm level;
DFERT = dummy variable for zero observations for fertiliser;
DTRAC = dummy variable for zero observations for tractor hours;
DIRRI = dummy variable for zero observations for irrigation water;
D1, ..., D7 dummy variables for seven sub-districts (Mianwali,
Kulachi, Thatta, Mirpurkhas, Peshawar, Lodhran and Attock
respectively); and
DMULTI = dummy variable for multiple crops.
Table 2
Assumed Irrigation Water Prices Used in Basic Simulations
(1) MVP-based The MVP-based price is the marginal value
product of irrigation water at the mean level
which has been calculated by multiplying the
marginal physical product of irrigation water
with aggregate output price. The MVP-based
prices will vary depending on whether we use
restricted or full version of Model 4. Using
Model 4.11, the MVP-based price comes to Rs
445.23 per acre inch while based on Model
4.22, it is Rs 415.79 per acre inch (Table
G.7).
(2) AC-based The AC-based price is the average variable
cost of water supply delivery and has been
calculated using O&M expenditures on the
irrigation system [reported in Sahibzada
(2002) Table 4.4 in Chapter Four]. This price
comes to Rs 7.8 per acre inch.
(3) SRMC- Price based on short-run marginal cost using
based-using prices net of inflation. GDP deflator
Deflated Prices [reported in Sahibzada (2002) Appendix to
Chapter Four] has been used to convert the
intermediate-run estimate of MC in current
prices into the same in real prices. This
estimate for our study has been calculated to
be Rs 5.7 per acre inch.
(4) LRMC- Price based on long-run marginal cost which
based-using is the intermediate-run MC plus 1 percent of
Deflated Prices construction costs on developing irrigation
water system in current prices comes to Rs
169 per irrigation [Sahibzada (2002) Chapter
Four]. This price has been converted into
real price through the use of GDP deflator,
resulting in Rs 17.8 per acre inch.
(5) Market Price It is the price farmers charge for selling
(informally) surplus irrigation water in
excess of their requirements to friends and
relatives. This informal market price is Rs
G00 per irrigation.
Source: Sahibzada (2002).
Table 3
Regression Results: Cobb-Douglas Production Function, Using OLS
Techniques
Model 1(n=509) Model 2 (n=601)
Est. Coeffs. t-value Est. Coeffs. t-value
Constant 1.259 4.06 (a) 0.706 1.33
LFERT 0.308 3.25 (a) 0.265 2.97 (a)
LMD 0.172 * 1.76 (c) 0.134 * 1.43
LTH 0.019 0.22 0.117 1.45
LIRR 0.501 4.81 (a) 0.484 4.96 (a)
DFERT -- -- -0.158 -0.33
DTRAC -- -- -0.131 -0.84
DIRRI -- -- 1.113 4.33 (a)
D1 (Mian) -0.321 1.84 (c) -0.408 -2.38 (a)
D2 (Kula) -1.696 -6.93 (a) -0.962 -1.89 (c)
D3 (That) -1.235 -6.59 (a) -1.296 -7.14 (a)
D4 (Mirp) 0.169 0.80 0.140 0.65
DS (Pesh) 0.728 3.72 (a) 0.727 3.84 (a)
D6 (Lodh) -1.64 -10.2 (a) -1.734 -11.3 (a)
D7 (Alto) 0.553 1.94 (c) 0.462 1.65 (c)
DMULTI -0.322 -2.05 (b) -0.347 -2.92 (a)
[R.sup.2] 0.399 -- 0.432 --
[R.sup.2]-adj 0.387 -- 0.418 --
(a) Significant at 1 percent confidence level.
(b) Significant at 5 percent confidence level.
(c) Significant at 10 percent confidence level.
* These results were computed from estimated results, and represent
the elasticity of output with respect to labour.
n = Number of observations.
Table 4
MPP, MVP, and MVP/OC Ratio of Irrigation Water
MPP (Per Acre
Inch) MVP (Pak Rs)
(Per Acre Inch) MVP/OC
Kgs (a) Mds (b) Mds (Pak Rs)
Model 1 (n=509) 49.69 1.242 445.23 (59.28) 2.23 (0.2964)
Mode12 (n=601) 47.45 1.186 415.79 (54.24) 2.08 (0.2713)
Figures in the parentheses indicate estimated standard errors for
the MVP and MVP/OC ratio of irrigation water.
(a) Kilograms.
(b) Mds = Maunds (One maund = 40 kilograms).
Table 5
Variables Aggregated at the District Level
Variable Atto Kula Lodh Mian Mirp
(A) Model 1
Obs. (a) 31 1 129 64 56
Agg. Farm Output (b) 8316 240 33642 29355 73570
Output/Irri 16.1 2.7 1.2 7.4 18
Agg. IRR (c) 517 90 26863 3938 4090
Irrig/Acre 3.4 3 7.2 5.7 7.8
TCA (d) 151 30 3757 686 524
TFA (e) 481 30 5847 1988 1354
TCA as a % of TFA 31.1 100 64.2 34.5 38.7
(B) Model 2
Obs. (a) 31 77 133 69 56
Agg. Farm Output (b) 8316 9530 34017 29792 73570
Output/Irri 16.1 8.7 1.2 7.4 18
Agg. IRR (c) 517 1091 27196 4003 4090
Irrig/Acre 3.4 0.6 7.1 5.6 7.8
TCA (d) 151 1920 3813 710 524
TFA (e) 481 5506 5952 2028 1354
TCA as a % of TFA 31.8 34.9 64.1 35 38.7
Variable Pesh That MarCh Total
(A) Model 1
Obs. (a) 35 109 84 509
Agg. Farm Output (b) 23382 91364 39446 299278
Output/Irri 11.5 5 8.4 4.9
Agg. IRR (c) 2026 18342 4669 60535
Irrig/Acre 7.7 15 11.3 8.6
TCA (d) 263 1222 413 7046
TFA (e) 558 3160 1076 14495
TCA as a % of TFA 47.1 38.7 38.4 48.6
(B) Model 2
Obs. (a) 36 113 86 601
Agg. Farm Output (b) 23442 92130 39994 310791
Output/Irri 11.5 4.9 8.5 4.9
Agg. IRR (c) 2030 18762 4718 62407
Irrig/Acre 7.7 15 11.3 6.9
TCA (d) 264 1243 417 9044
TFA (e) 559 3184 1086 20150
TCA as a % of TFA 47.2 39 38.4 44.9
(a) Number of observations at the district level;
(b) Farm output in maunds (1 maund = 40kgs), aggregated at the
district level;
(c) Irrigation water in number of irrigations aggregated at the
district level; one irrigation equals three acre inches of water;
and
(d, e) Total cropped area and size of the farm, both in acres, and
both aggregated at the district level.
Table 6
Predicted Water Usage (Number of Irrigations (a)) based on Alternative
Water Pricing Systems
Alternative Prices Atto Kula Lodh Mian Mirp
(A) Model 1(n = 509)
Current Actual Water 517 90 26863 3938 4090
Usage (b) (3.4) (3) (7.2) (5.7) (7.8)
MVP-based:
Rs 445.23 Per Acre Inch 616 132 23647 5404 8422
AC-based:
Rs 7.8 Per Acre Inch 4635 992 177934 40663 63374
SRMC-based:
Rs 5.7 Per Acre Inch 5420 1160 208081 47552 74112
LRMC-based:
Rs 17.8 Per Acre Inch 3071 657 117884 26940 41986
Market-based:
Rs 200 Per Ace Inch 616 196 35253 8056 12556
(B) Model 2 (n = 601)
Current Actual Water 517 1091 27196 4003 4090
Usage (3.4) (O.6) (7.1) (5.6) (7.8)
MVP-based:
Rs 415.79 Per Acre Inch 670 4616 26103 5877 8655
AC-based:
Rs 7.8 Per Acre Inch 5216 35916 203101 45726 67345
SRMC-based:
Rs 5.7 Per Acre Inch 6133 42225 238782 53759 79177
LRMC-based:
Rs 17.8 Per Acre Inch 3408 23463 132683 29872 43996
Market-based:
Rs 200 Per Acre Inch 976 6734 38080 8573 12627
Alternative Prices Pesh That MarCh Total
(A) Model 1(n = 509)
Current Actual Water 2026 18342 4669 60535
Usage (b) (7.7) (15.0) (8.6)
MVP-based:
Rs 445.23 Per Acre Inch 1506 41366 5126 86219
AC-based:
Rs 7.8 Per Acre Inch 11336 311266 38570 648770
SRMC-based:
Rs 5.7 Per Acre Inch 13257 364004 24105 758691
LRMC-based:
Rs 17.8 Per Acre Inch 7510 206218 25553 429819
Market-based:
Rs 200 Per Ace Inch 2246 61670 7642 128537
(B) Model 2 (n = 601)
Current Actual Water 2030 18762 4718 62407
Usage (7.7) (15.0) (11.3)
MVP-based:
Rs 415.79 Per Acre Inch 1489 27540 11797 86747
AC-based:
Rs 7.8 Per Acre Inch 11587 214283 91791 674965
SRMC-based:
Rs 5.7 Per Acre Inch 13623 251929 107918 793546
LRMC-based:
Rs 17.8 Per Acre Inch 7570 139988 59966 440946
Market-based:
Rs 200 Per Acre Inch 2172 40177 17210 126551
Note: Figures in parentheses are the number of Irrigations per.
acre at the district level.
(a) One irrigation equals three acre inches of water; and
(b) Number of irrigations at the district level based on survey data;
Table 7
Predicted Water Usage Assuming 10 Percent Increase in
Alternative Water Prices
Alternative Prices Atto Kula Lodh Mian Mirp
(A) Model 1 (n = 509)
Current Actual Water
Usage (b) 517 90 26863 3938 4090
MVP-based: 587 126 22547 5153 8031
Rs 489.8/ Acre Inch (-4.6) (-4.6) (-4.6) (-4.6) (-4.6)
AC-based: 4415 945 169471 38729 60360
Rs 8.6/ Acre Inch (-4.7) (-4.7) (-4.7) (-4.7) (-4.7)
SRMC-based: 5156 1103 197942 45236 70501
Rs 6.3/ Acre Inch (-4.9) (-4.9) (-4.9) (-4.9) (-4.9)
LRMC-based: 2927 626 112352 25675 40016
Rs 19.6/ Acre Inch (-4.7) (-4.7) (-4.7) (-4.7) (-4.7)
Market-based: 876 328 33616 7682 11973
Rs 220/ Acre Inch (-4.6) (-4.6) (-4.6) (-4.6) (-4.6)
(B) Model 2 (n = 601)
Current Actual Water 517 1091 27196 4003 4090
Usage (b)
MVP-based: 638 4394 24850 5594 8240
Rs 457.4/ Acre Inch (-4.8) (-4.8) (-4.8) (-4.8) (-4.8)
AC-based: 4960 34151 193122 43479 64036
Rs 8.6/ Acre Inch (-4.9) (-4.9) (-4.9) (-4.9) (-4.9)
SRMC-based: 5824 40100 226764 51053 75192
Rs 6.3/ Acre Inch (-5.0) (-5.0) (-5.0) (-5.0) (-5.0)
LRMC-based: 3242 22325 126249 28423 41862
Rs 19.6/Acre Inch (-4.8) (-4.8) (-4.8) (-4.8) (-4.8)
Market-based: 931 6411 36253 8162 12021
Rs 220/ Acre Inch (-4.8) (-4.8) (-4.8) (-4.8) (-4.8)
Alternative Prices Pesh That March Total
(A) Model 1 (n = 509)
Current Actual Water
Usage (b) 2026 18342 4669 60535
MVP-based: 1436 39443 4887 82210
Rs 489.8/ Acre Inch (-4.6) (-4.6) (-4.6) (-4.6)
AC-based: 10797 296464 36736 617917
Rs 8.6/ Acre Inch (-4.7) (-4.7) (-4.7) (-4.7)
SRMC-based: 12611 346271 42907 721727
Rs 6.3/ Acre Inch (-4.9) (-4.9) (-4.9) (-4.9)
LRMC-based: 7158 196540 24354 409646
Rs 19.6/ Acre Inch (-4.7) (-4.7) (-4.7) (-4.7)
Market-based: 2142 58806 7286 122568
Rs 220/ Acre Inch (-4.6) (-4.6) (-4.6) (-4.6)
(B) Model 2 (n = 601)
Current Actual Water 2030 18762 4718 62407
Usage (b)
MVP-based: 1418 26218 11231 82583
Rs 457.4/ Acre Inch (-4.8) (-4.8) (-4.8) (-4.8)
AC-based: 11018 203755 87284 641805
Rs 8.6/ Acre Inch (-4.9) (-4.9) (-4.9) (-4.9)
SRMC-based: 12937 23948 102488 753606
Rs 6.3/ Acre Inch (-5.0) (-5.0) (-5.0) (-5.0)
LRMC-based: 7203 133200 57060 419564
Rs 19.6/Acre Inch (-4.8) (-4.8) (-4.8) (-4.8)
Market-based: 2068 38249 16385 120480
Rs 220/ Acre Inch (-4.8) (-4.8) (-4.8) (-4.8)
Note: Figures in parentheses indicate percent change in the
predicted water usage as a result of 10 percent increase in
alternative water prices.
(a) One irrigation equals three acre inches of water.
(b) Number of irrigations at the district level based on
survey data.
Table 8
Predicted Water Usage Assuming 10 Percent Decrease in
Alternative Water Prices
Alternate Prices Atto Kula Lodh Mian Mirp
(A) Model 1 (n = 509)
Current Actual Water
Usage (b) 517 90 26863 3938 4090
MVP-based: 649 139 24923 5696 8877
Rs 400.7/ Acre Inch (5.4) (5.4) (5.4) (5.4) (5.4)
AC-based: 4885 1045 187539 42858 66795
Rs 7.02/ Acre Inch (5.4) (5.4) (5.4) (5.4) (5.4)
SRMC-based: 5730 1226 219957 50266 78341
Rs 5.1/ Acre Inch (5.7) (5.7) (5.7) (5.7) (5.7)
LRMC-based: 3237 693 124248 28394 44253
Rs 16.02/ Acre Inch (5.4) (5.4) (5.4) (5.4) (5.4)
Market-based: 968 207 37156 8491 13234
Rs 180/ Acre Inch (5.4) (5.4) (5.4) (5.4) (5.4)
(B) Model 2 (n = 601)
Current Actual Water
Usage (b) 517 1091 27196 4003 4090
MVP-based: 708 4874 27562 6205 9139
Rs 374.2/ Acre Inch (5.6) (5.6) (5.6) (5.6) (5.6)
AC-based: 5508 37922 214449 48280 71108
Rs 7.02 / Acre Inch (5.6) (5.6) (5.6) (5.6) (5.6)
SRMC-based: 6495 44720 252887 56934 83854
Rs 5.1/ Acre Inch (5.9) (5.9) (5.9) (5.9) (5.9)
LRMC-based: 3598 24774 140097 31541 46454
Rs 16.02 / Acre Inch (5.6) (5.6) (5.6) (5.6) (5.6)
Market-based: 1033 7110 40208 9052 13332
Rs 180/ Acre Inch (5.6) (5.6) (5.6) (5.6) (5.6)
Alternate Prices Pesh That March Total
(A) Model 1 (n = 509)
Current Actual Water
Usage (b) 2026 18342 4669 60535
MVP-based: 1588 43599 5402 9087
Rs 400.7/ Acre Inch (5.4) (5.4) (5.4) (5.4)
AC-based: 11948 328069 40652 683791
Rs 7.02/ Acre Inch (5.4) (5.4) (5.4) (5.4)
SRMC-based: 14013 384777 47679 801989
Rs 5.1/ Acre Inch (5.7) (5.7) (5.7) (5.7)
LRMC-based: 7916 217350 26932 453023
Rs 16.02/ Acre Inch (5.4) (5.4) (5.4) (5.4)
Market-based: 2367 64999 8054 135476
Rs 180/ Acre Inch (5.4) (5.4) (5.4) (5.4)
(B) Model 2 (n = 601)
Current Actual Water
Usage (b) 2030 18762 4718 62407
MVP-based: 1572 29080 12457 91597
Rs 374.2/ Acre Inch (5.6) (5.6) (5.6) (5.6)
AC-based: 12234 226255 96922 712678
Rs 7.02 / Acre Inch (5.6) (5.6) (5.6) (5.6)
SRMC-based: 14427 266810 114295 840422
Rs 5.1/ Acre Inch (5.9) (5.9) (5.9) (5.9)
LRMC-based: 7993 147810 63318 465585
Rs 16.02 / Acre Inch (5.6) (5.6) (5.6) (5.6)
Market-based: 2294 42422 18172 133623
Rs 180/ Acre Inch (5.6) (5.6) (5.6) (5.6)
Note: Figures in parentheses indicate percent change in the
predicted water usage as a result of a 10 percent decrease
in alternate water prices.
(a) One irrigation equals three acre inches of water.
(b) Number of irrigations at the district level based on
survey data.
Table 9
Predicted Water Usage Assuming 10 Percent Increase in the Elasticity
for IRR and 10 Percent Decrease in the Elasticities for FERT, MD,
and TH at the Base-line Alternative Water Prices
Alternative Prices Atto Kula Lodh Mian
(A) Model 1 (CRS-imposed)
Current Actual Water
Usage (b) 517 90 26863 3938
MVP-based: 722 154 27697 6330
Rs 445.23/Acre Inch (17.1) (17.1) (17.1) (17.1)
AC-based: 4453 953 170944 39065
Rs 7.8/Acre Inch (-3.9) (-3.9) (-3.9) (-3.9)
SRMC-based: 5128 1097 196858 44987
Rs 5.7/Acre Inch (-5.4) (-5.4) (-5.4) (-5.4)
LRMC-based: 3072 657 117925 26949
Rs 17.8/Acre Inch (0.0004) (0) (0.0004) (0.0004)
Market-based: 1034) 221 39704 9073
Rs 200/Acre Inch (12.6) (12.6) (12.6) (12.6)
(B) Model 2 (CRS-imposed)
Current Actual Water
Usage (b) 517 1091 27196 4003
MVP-based: 785 5408 30581 6885
Rs 415.79/Acre Inch (17.2) (17.2) (17.2) (17.2)
AC-based: 5090 35044 198172 44616
Rs 7.8/Acre Inch (-2.4) (-2.4) (-2.4) (-2.4)
SRMC-based: 5898 40610 229650 51703
Rs 5.7/Acre Inch (-3.8) (-3.8) (-3.8) (-3.8)
LRMC-based: 3454 23779 134471 30274
Rs 17.8/Acre Inch (1.3) (1.3) (1.3) (1.3)
Market-based: 1108 7628 43136 9712
Rs 200/Acre Inch (13.3) (13.3) (13.3) (13.3)
Alternative Prices Mirp Pesh That March
(A) Model 1 (CRS-imposed)
Current Actual Water
Usage (b) 4090 2026 18342 4979
MVP-based: 9865 1765 48451 6004
Rs 445.23/Acre Inch (17.1) (17.1) (17.1) (17.1)
AC-based: 60884 10891 299038 37054
Rs 7.8/Acre Inch (-3.9) (-3.9) (-3.9) (-3.9)
SRMC-based: 70114 12542 344370 42672
Rs 5.7/Acre Inch (-5.4) (-5.4) (-5.4) (-5.4)
LRMC-based: 42001 7513 206291 25562
Rs 17.8/Acre Inch (0.0004) (0.0004) (0.0004) (0.0004)
Market-based: 14141 2530 69455 8606
Rs 200/Acre Inch (12.6) (12.6) (12.6) (12.6)
(B) Model 2 (CRS-imposed)
Current Actual Water
Usage (b) 4090 2030 18762 4718
MVP-based: 10140 1745 32265 13821
Rs 415.79/Acre Inch (17.2) (17.2) (17.2) (17.2)
AC-based: 65711 11306 209083 89564
Rs 7.8/Acre Inch (-2.4) (-2.4) (-2.4) (-2.4)
SRMC-based: 76149 13102 242294 103790
Rs 5.7/Acre Inch (-3.8) (-3.8) (-3.8) (-3.8)
LRMC-based: 44589 7672 141875 60774
Rs 17.8/Acre Inch (1.3) (1.3) (1.3) (1.3)
Market-based: 14303 2461 45511 19495
Rs 200/Acre Inch (13.3) (13.3) (13.3) (13.3)
Alternative Prices Total
(A) Model 1 (CRS-imposed)
Current Actual Water
Usage (b) 60535
MVP-based: 100988
Rs 445.23/Acre Inch (17.1)
AC-based: 623282
Rs 7.8/Acre Inch (-3.9)
SRMC-based: 717768
Rs 5.7/Acre Inch (-5.4)
LRMC-based: 429970
Rs 17.8/Acre Inch (0.0004)
Market-based: 144764
Rs 200/Acre Inch (12.6)
(B) Model 2 (CRS-imposed)
Current Actual Water
Usage (b) 62407
MVP-based: 101630
Rs 415.79/Acre Inch (17.2)
AC-based: 658586
Rs 7.8/Acre Inch (-2.4)
SRMC-based: 763196
Rs 5.7/Acre Inch (-3.8)
LRMC-based: 446888
Rs 17.8/Acre Inch (1.3)
Market-based: 143354
Rs 200/Acre Inch (13.3)
Note: Figures in parentheses indicate percent change in predicted
water usage relative to the base-line case as a result of
a 10 percent increase in water elasticity along with a simultaneous
10 percent decrease in other inputs' elasticities.
(a) One irrigation equals three acre inches of water.
(b) Number of irrigations at the district level based on survey data.
Table 10
Predicted Water Usage Assuming 10 Percent Decrease in the Elasticity
for IRR and 10 Percent Increase in the Elasticities for FERT, MD, and
TH at the Base-line Alternative Water Prices
Alternative races Atto Kula Lodh Mian
(A) Model 1 (CRS-imposed)
Current Actual
Water Usage (b) 517 90 26863 3938
MVP-based:
Rs 445.23/Acre 497 106 19068 4358
Inch (-19.4) (-19.4) (-19.4) (-19.4)
AC-based: 4594 983 176350 40301
Rs 7.8 / Acre Inch (-0.01) (-0.01) (-2.6) (-0.01)
SRMC-based: 5459 1168 209554 47889
Rs 5.7 / Acre Inch (0.01) (0.01) (0.01) (0.01)
LRMC-based: 2918 624 112020 25600
Rs 17.8 / Acre Inch (-5.0) (-5.0) (-5.0 (-5.0)
Market-based: 771 165 29612 6767
Rs 200 / Acre Inch (-16) (-16.0 (-16.0) (-16.0)
(B) Model 2 (CRS-imposed)
Current Actual
Water Usage (b) 517 1091 27196 4003
MVP-based: 567 3905 22084 4972
Rs 415.79 / Acre (-15.4) (-15.4) (-15.4) (-15.4)
Inch
AC-based: 5257 36194 204676 46080
Rs 7.8 / Acre Inch (-0.01) (-0.01) (-0.01) (-0.01)
SRMC-based: 6266 43144 243978 54928
Rs 5.7 / Acre Inch (2.0) (2.0) (2.0) (2.0)
LRMC-based: 3312 22802 128945 29030
Rs 17.8 / Acre Inch (-2.8) (-2.8) (-2.8) (-2.8)
Market-based: 854 5883 33271 7490
Rs 200 / Acre Inch (-12.6) (-12.6) (-12.6) (-12.6)
Alternative races Mirp Pesh That March
(A) Model 1 (CRS-imposed)
Current Actual
Water Usage (b) 4090 2026 18342 4669
MVP-based:
Rs 445.23/Acre 6791 1215 33356 4133
Inch (-19.4) (-19.5) (-19.4) (-19.4)
AC-based: 62810 11235 308494 38226
Rs 7.8 / Acre Inch (-0.01) (-0.01) (-0.01) (-0.01)
SRMC-based: 74636 13351 366579 45424
Rs 5.7 / Acre Inch (0.01) (202.1) (0.01) (0.01)
LRMC-based: 39898 7137 195960 24282
Rs 17.8 / Acre Inch (-5.0) (-5.0) (-5.0) (-5.0)
Market-based: 10547 1886 51800 6419
Rs 200 / Acre Inch (-16.0 (-16.0) (-16.0) (-16.0)
(B) Model 2 (CRS-imposed)
Current Actual
Water Usage (b) 4090 2030 18762 4718
MVP-based: 7323 1260 23300 9981
Rs 415.79 / Acre (-15.4) (-15.4) (-15.4) (-15.4)
Inch
AC-based: 67868 11677 215945 92505
Rs 7.8 / Acre Inch (-0.01) (-0.01) (-0.01) (-0.01)
SRMC-based: 80900 13919 257411 110268
Rs 5.7 / Acre Inch (2.0) (2.0) (2.0) (2.0)
LRMC-based: 42756 7356 136045 58278
Rs 17.8 / Acre Inch (-2.8) (-2.8) (-2.8) (-2.8)
Market-based: 11032 1898 35103 15037
Rs 200 / Acre Inch (-12.6) (-12.6) (-12.6) (-12.6)
Alternative races Total
(A) Model 1 (CRS-imposed)
Current Actual
Water Usage (b) 60535
MVP-based:
Rs 445.23/Acre 69524
Inch (-19.4)
AC-based: 642993
Rs 7.8 / Acre Inch (-0.01)
SRMC-based: 764060
Rs 5.7 / Acre Inch
LRMC-based: 408439
Rs 17.8 / Acre Inch (-5.0)
Market-based: 107967
Rs 200 / Acre Inch (-16.0)
(B) Model 2 (CRS-imposed)
Current Actual
Water Usage (b) 62407
MVP-based: 73392
Rs 415.79 / Acre (-15.4)
Inch
AC-based: 680202
Rs 7.8 / Acre Inch (-0.01)
SRMC-based: 810814
Rs 5.7 / Acre Inch (2.0)
LRMC-based: 428524
Rs 17.8 / Acre Inch (-2.8)
Market-based: 110568
Rs 200 / Acre Inch (-12.6)
Note: Figures in parentheses indicate percent change in predicted
water usage relative to the base-line case as a result of
a 10 percent decrease in water elasticity along with a simultaneous
10 percent increase in other inputs' elasticities.
(a) One irrigation equals three acre inches of water.
(b) Number of irrigations at the district level based on survey data.
