Water and Fertilizer Efficiency in Rice Production

Case Study: Krishna River Basin, India

A Thesis

Submitted By

Yaning (Jennifer) Shen

In partial fulfillment of the requirements For the degree of

Master of science

In

Economics

Tufts University, Graduate School of Arts and Sciences

May, 2012

Advisor: Dr. Jeffrey Zabel

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Abstract: Rice production in India is facing potential shortages in the future, and this may be due to various factors

including water and labor shortages, growing populations, and a slowing rate of technical progress.

Although rice is a water-intensive crop, water productivity in rice production is especially low. Stresses

on water supply, including the potential impact of climate change, suggest a growing need for economic

policies that enable increases in water efficiency levels in rice production. Fertilizers are used as a

temporary solution in India to maintain increasing rates of production levels. The primary goals of this

paper are twofold: first, to assess the current level of water and fertilizer inefficiency using a stochastic

production frontier model for the study region in the Krishna River Basin of India; and second, to analyze

and discuss the potential increase in water efficiency as a result of volumetric water pricing schemes.

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Acknowledgments

First and foremost, I would like to thank my advisor, Dr. Jeffrey Zabel, for his guidance and support

throughout the completion of my thesis; and my thesis committee members, Dr. David Dapice and Dr.

Richard Vogel. I am very grateful to the Tufts Institute of the Environment and the Water: Systems,

Science, and Society (WSSS) Program at Tufts for granting me research fellowships and providing

continuous research guidance and connections to the leaders of the field of water, agriculture, and

economics. I would like to thank Dr. Annette Huber-Lee for her guidance in the planning process of my

research, and for connecting me with various international research institutes to acquire my agricultural

data. I would also like to thank Dr. Palanisami and Dr. Krishna Reddy of the International Water

Management Institute in Hyderabad for welcoming me to their institute, and kindly sharing data and

results with me to further my own research; and N.S. Praveen Kumar for collecting the data, and allowing

me access to his data on rice production and results. I would like to thank Dr. Somanathan for kindly

sharing his data, Stata files, and results, helping me reach conclusions on the price elasticity of irrigation

water. Finally, thank you to my family and friends for your constant love and support.

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Introduction

Rice, a major staple in most Asian countries, is facing potential shortages in the future

due to growing populations and a slowing rate of technical progress. As an extremely water

intensive crop, sustained growth in production has become increasingly difficult as new

irrigation opportunities diminish. One reason for this phenomenon may be low water

productivity due to its over-use in production, since the marginal cost of water is often close to

zero. For nations like India and China, a temporary solution to the water productivity issue is to

subsidize fertilizer, increasing rice yield per unit of water utilized. Fertilizer usage also faces

problems of inefficiency, however, due to a lack of understanding on required amounts and

methods of efficient application. There are also known negative externalities associated with the

application of fertilizers, including the release of chemicals to the soil, reductions in soil quality,

and detrimental impacts to drinking water quality. These and other complex externalities

surrounding rice production, paired with the growing influence of population growth and climate

change on water supply, suggest a growing need for new economic policies that enable increases

in current rice production efficiency levels, improve existing water allocation schemes, and

provide higher funding in research and development of new agricultural technologies and seed

varieties.

Inefficiencies in water and fertilizer application have large implications for the amount of

rice produced given extremely limited resources. If strides can be made towards the increased

efficiency of crop input usage, sustainable food production problems in the future may be

mitigated. Future trends in demand for rice in India are still unclear, however. High population

growth rates may increase total demand for rice in the future. The counterforce to this trend is

the possibility that rice consumption per capita decreases when a country’s GDP per capita

increases, i.e. rice may be a Giffen good. The current public consensus is that regardless of the

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trend in demand for rice, overall water stress in India will increase in the future due to population

growth, increased consumption of fruits and vegetables, and the impending threat of climate

change.

To increase the efficiency of agricultural inputs in rice production, some have proposed

improved pricing schemes for water (Veettil et al. 2011). Pricing water per unit volume, also

called volumetric pricing, may help decrease overutilization, thus allowing for an improved

allocation mechanism of a scarce resource. Water pricing has many policy complications,

however, including the daunting task of implementation, the necessity for water users

associations (WUAs), and the problem of farmer compliance. When considering the issue of

farmer compliance, a pressing issue is that irrigation involves a great deal of fixed costs, and any

rise in the variable cost of irrigation water prices may potentially hurt farm incomes and

employment. If fixed costs are greater than variable costs, a scenario that often occurs with

regards to irrigation water, prices charged at the marginal cost level may drive farmers out of

business (Dinar and Mody, 2004). The increased burden of volumetric pricing may be incredibly

unpopular among farmers, as a result. Although the problem of farmer compliance is a

legitimate concern, another paper on rice farmers in the Krishna River Basin in India shows that

above a threshold water price, farmers actually prefer volumetric water pricing, because they

wish to only pay for water utilized (Veettil et al., 2011).

Overall, there remains an urgent need to increase agricultural production rates to keep up

with the pace of population growth, despite complex policy implications. The two general steps

toward higher levels of production are to either introduce new technologies in the field, or to

increase efficiency levels. This paper will explore the latter, measuring the potential for

achieving higher levels of input efficiency, and proposing potential policy solutions. Previous

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studies on irrigation water pricing in India discuss the advantages of alternate pricing schemes

and measure water pricing elasticity, but do not propose potential prices and corresponding water

savings as a result of volumetric water pricing. Veettil et al. (2011) discuss the efficiency

increases of volumetric pricing and explore the price elasticities of choosing different

hypothetical water pricing scenarios. Somanathan and Ravindranath (2006) conduct a pilot

study in a similar watershed in Andhra Pradesh and Karnataka to measure marginal values of

water and price elasticity of irrigation. While this study will utilize irrigation water elasticity

estimates and methodologies of previous studies to calculate technical efficiency and input

efficiency levels, this research will present preliminary prices and corresponding water savings

(from incremental increases in price per meters cubed of water utilized). The primary goals of

this paper are twofold: first, to assess the current level of water and fertilizer inefficiency using a

stochastic production frontier model for the study region in the Krishna River Basin of India; and

second, to analyze and discuss the potential increase in water efficiency as a result of alternative

water pricing schemes. Given the increasing threats of climate change on reservoir levels, the

efficient use of water will become increasingly important. Based on projected future water

supply, the alternative water pricing schemes suggested in this paper may lead to more efficient

water allocation. Although the overall feasibility, and detailed cost-benefit comparisons of

alternative water pricing schemes or other agricultural policies are beyond the scope of this

paper, this study will qualitatively discuss potential implementation requirements, caveats and

policy complications.

Study Area and Data Description

The general study area chosen for this paper is the Krishna River Basin, which covers

three large states in India: Karnataka, Maharashtra, and Andhra Pradesh, totaling approximately

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258,000 km2. Given current demand, there is a shortage of water supply in the basin, leading to

a critical need to solve water allocation conflicts (Yee et al., 2009). Rice production in the

Krishna basin is exclusively based on canal irrigation, involving a network of canals that carry

water from large reservoirs to the region’s rice fields. Increased demand for water in the region

has led to many instances of basin closure, as well as stream flow depletion. N.S. Praveen

Kumar of the International Water Management Institute (IWMI) in Hyderabad collected data on

rice production inputs and costs in collaboration with Dr. K. Palanisami and Dr. K. Krishna

Reddy. A total of 240 farmers were randomly surveyed, from six randomly selected villages, of

three randomly selected mandals (of 39 total mandals in the region). A mandal, or tehsil, is an

administrative division in India that consists of a city or town, and possibly additional towns and

villages. The data collection period was between 2009 and 2010.

The primary data collected includes general farm-level characteristics, irrigation levels,

crop calendar, production costs for each stage of the rice cultivation process (nursery, planting to

flowering stage, flowering to harvest, harvesting cost, harvesting/threshing, and total water use),

qualitative data on farmers willingness to adapt to climate change, farm household expenditure,

farm adaptation actions, and farmers’ observations on changes in weather/climate in the past five

years. Prices and quantity of fertilizer and pesticides used throughout the process of rice

cultivation are included. The data also includes a questionnaire on whether or not farmers used

weather-based crop insurance. This data will be used to measure current levels of input

inefficiency within rice production in the Krishna River basin. Table 1 shows summary statistics

of variables utilized in this study from IWMI.

The data on water prices, marginal value and elasticity of irrigation water demand are

from Somanathan and Ravindranath (2006). Their elasticity of water demand and marginal

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values were calculated based on results from a survey conducted in the Upper Papagni watershed

in Karnataka and Andhra Pradesh that included questions on the selling price, profits of pump

owners and farmers, and price differentials between irrigated and unirrigated land. More details

on how Somanathan and Ravindranath obtained elasticity estimates of irrigation water demand

are explained in more detail in Part II of this study. The authors conducted the survey in six

mandals in the basin, and randomly chose five hamlets from each mandal. Afterwards, the

authors surveyed all suppliers and recipients of water. Since water quantity estimates were based

on a survey and thus may be inaccurate, the authors used seller’s water use during the growing

season of the buyer as an instrument for water prices. Their elasticity of demand estimates, and

their results on the marginal value of water using land price differentials will be utilized in this

study to analyze the potential effects of pricing. The values used from Somanathan and

Ravindranath’s paper are described in Part II of this study.

Part I: Technical and Input Efficiency

Literature Review

Given population growth rates, a major policy concern in the developing world is future

food availability. Sustainable development requires consistent increases in production volume

for all agricultural goods, and this depends heavily on the capacity of farms in developing

nations and their production efficiency. Recent studies have explored the topic of production

efficiency within the agricultural sector, assessing trends in total factor productivity (TFP) as

well as input efficiency levels. A commonly cited paper is Battese and Coelli (1995) on

technical inefficiency effects in the stochastic frontier production function. Using ten years of

data on paddy farms from an Indian village, the authors extend the previously existing research

on stochastic production frontier models by introducing a production frontier for panel data.

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They conclude that the error terms derived from the stochastic frontier production function can

be used to calculate overall technical efficiency levels, and their model specification allows for

the estimation of technical change as well as time-varying inefficiencies.

Battese and Coelli’s production frontier framework influenced many studies related to

input efficiency, and has been extended for studies on agriculture in developing nations. Huang

et al. (2010) used a production frontier framework to estimate production functions for rice,

wheat, and cotton in China. Their study focused specifically on the issue of labor productivity as

a result of China’s labor policies. Farms in China may over-utilize labor, because China’s

commune system is designed to restrict rural laborers to farming. This may cause a relatively

low marginal product of labor across all farms in rural China. Increased fertilizer use in

agriculture has been a source of concern as well; by 1996, the average use of chemical fertilizer

reached 251 kilograms per hectare. Using farmer survey data, the authors model a translog

stochastic production frontier function to approximate the coefficients for three groups of inputs:

labor, fertilizer, and other inputs. Empirical results show a positive relationship between average

farm size and technical efficiency, and a low marginal productivity of labor. Overall, these

results suggest that increasing labor and fertilizer usage may be ineffective for increasing yields

in the future.

Another study based on agriculture in China that uses Battese and Coelli’s framework is a

paper by Jin et al. (2010), which assesses productivity trends in China’s agricultural sector

between 1990 and 2004. Their results showed an approximate 1.8% gain in TFP during the

1980s and early 1990s, and this increase is mostly attributed to positive technological change. A

more pressing issue is the TFP growth trend of crops after 1995, due to increasing concerns

about the sustainability of China’s agricultural sector. While the target rate for a healthy

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agricultural sector is approximately 2% per year, the growth rates for many crops remained

below the target rate between 1995 and 2004. One positive sign is that the rate of growth of

outputs actually outpaced the growth of inputs within the grain economy. Indeed, other

commodities besides maize, capsicum, and dairies had an annual growth rate in excess of the 2%

target rate. Although the authors conclude that changes in technology caused China’s healthy

agriculture growth rate, there have been declines in efficiency levels among some farms. The

authors do not identify the key cause of the efficiency decline; instead, they conclude that

China’s TFP growth would have been considerably higher if production efficiency had not

decreased.

The previous studies mentioned have focused on overall technical efficiency levels of

associated with farming practices, without any measures on the efficiency levels of specific farm

inputs. Karagiannis et al. (2003) introduced an input-specific measure of technical efficiency for

vegetable cultivation in Greece. The focus of their paper was to derive measures that can target

the efficiency levels of water, specifically, within Greek agriculture. Input-specific technical

efficiency levels can be compared across different management techniques, allowing

policymakers to adopt best practices based on water efficiency. Their measurement approach is

especially useful for comparisons across different technological innovations developed during

the past few years, including cultivation practices that involve new types of mechanical

equipment, irrigation techniques, and high-yield seed varieties. Their findings from the Greek

agricultural economy show that on average, irrigation water efficiency is much lower than

overall technical efficiency, with a mean of 47.20% compared to a mean of 70.17%. Farmers

may be able to achieve considerable water savings if irrigation systems are improved. Factors

that negatively affect water efficiency include chemical use and farming intensity, whereas

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education and greenhouse technologies are positively associated with water efficiency.

Karaggianis et al. (2003) found a shadow price of irrigation water of 18.9 Drs per m3, a price that

is much higher than the market price in Crete, which ranges from 11 to 15 Drs per m3. Since the

shadow price is calculated through the maximum price a farmer is willing to pay for increasing

the water supply constraint by one unit, it could be considered as the upper bound price of water,

not including nonuse values (Tsur, 2005). Overall, Karagiannis et al.’s paper contributed to the

agricultural efficiency literature by establishing a concrete metric for measuring input efficiency

levels.

This paper will utilize their input efficiency metric to measure the water and fertilizer

input efficiency levels of farmers in the Krishna basin.

Methodology

The production frontier associated with the technology of rice farms is modeled using a

stochastic frontier production function based on the following model introduced by Aigner et al.

(1977) and Meeusen and Van den Broek (1977), and later extended by Battese and Coelli (1995):

𝑦! = 𝑓 𝑥!;  𝛽 exp 𝜀! (1)

𝑦! = exp  (𝑥!𝛽 + 𝑣! − 𝑢!) (2)

where 𝑖 represents each individual farm, 𝑥 is a vector of farm inputs, 𝛽 is a vector of parameters,

and 𝜀! is the error term. Aigner et al. (1977) introduced an error term comprised of two

components, one normally distributed and the other from a one-sided distribution:

𝜀! = 𝑣! − 𝑢! (3)

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with 𝑣!, the symmetric disturbance, assumed to be an i.i.d.    𝑁 0,𝜎!! random error independently

distributed of 𝑢!1; and 𝑢! is assumed to be a non-negative stochastic random variable that

represents the technical inefficiency of production. Aigner et al. introduced an error term

composed of two parts in order to address previous problems with production function

estimation. Production functions before were either too sensitive to the existence of outliers, or

were probabilistic functions that allowed observations to lie beyond the frontier. The 𝑢!’s

specify stochastic, one-sided disturbances below the theoretical production frontier. This

eliminates observations that could potentially lie beyond the production frontier.

The 𝑢!’s are obtained by truncating a normal distribution at zero, resulting in a mean of

𝑧!𝛿 and a variance 𝜎!!. The 𝑧! term represents a vector of explanatory variables associated with

the technical inefficiency of production for each farm. The 𝛿 represents a vector of coefficients.

The 𝑢!’s and 𝑣!’s are independently distributed for all 𝑖 = 1,2,… ,𝑁. Equation 4 shows how the

inefficiency effects, 𝑢!, could be specified further.

𝑢! = 𝑧!𝛿 + 𝑝!                 (4)    

The 𝑝!’s are defined by truncation of the normal distribution with zero mean and variance, 𝜎!!,

such that the point of truncation is −𝑧!𝛿, i.e. 𝑝! ≥ −𝑧!𝛿.

Empirically, I will estimate the translog stochastic production frontier to determine the

technical efficiency of rice production in the Krishna Basin. The model includes various inputs

such as labor, fertilizer, pesticides, water, and other inputs (costs of seeds, machinery, and

overhead). The measured results from the translog stochastic production frontier will help

determine input efficiency and overall technical efficiency of production for each farm. Results

from determining the current levels of input efficiencies for each farmer will shed light on the

                                                                                                               1  Battese  and  Coelli  state  that  the  assumption  at  the  𝑢!′𝑠  and  the    𝑣!′𝑠  are  independently  distributed  for  all  i=1,2,…,N  is  a  simplifying  and  restrictive  condition.  

  13  

approximate level of efficiency that rice farms in the region are operating under. Let the rice

production frontier be approximated by the following translog function:

ln𝑦! = 𝛼! + 𝛼!𝑙𝑛𝑥!"!!!! + 𝛼!"𝑙𝑛𝑥!"𝑙𝑛𝑥!"

!!!!

!!!! +  𝑣! − 𝑢! (5)

where 𝑥 represents the quantity of each input, and 𝑗 ∈ 𝐽 is the number of all inputs: labor 𝑙,

fertilizer 𝑓, pesticides 𝑝, water 𝑤, and other inputs 𝑜. The one-sided error term 𝑢! is Aigner et

al.’s (1977) inefficiency effect term defined earlier in Equation 3.

To measure the output-oriented technical efficiency, we use the following equation

derived from Battese and Coelli’s framework in their 1995 paper:

𝑇𝐸! = exp −𝑢! = exp −𝑧!  𝛿 − 𝑤! = 𝑦! {𝑓 𝑥! ,𝑤!;𝛽 exp 𝑣! } (6)

The output-oriented technical efficiency sheds light on the maximum potential efficiency gains,

or output increases, given the current level of input use (Palanisami et al., 2010). The problem

with this metric is that it does not highlight the efficiency levels of specific inputs. It is possible

that the water efficiency levels for each farmer are actually very low, but other inputs such as

fertilizer and labor replace the loss in efficiency due to irrigation water. This study therefore

uses the input-oriented metric of efficiency proposed by Karagiannis et al. (2003). This metric is

measured after empirically estimating the translog production function, and calculating the

elasticity of supply for each input in question. Assuming that the log of rice yield follows a

translog production function (Equation 5), taking the partial derivative of the log of yield with

respect to the log of water leads to the elasticity of supply of water, shown in Equation 7.

Equation 8 utilizes Karagiannis et al.’s (2003) derivation to specify the input efficiency (IE) of

water.

𝜁!" =!"!!"!

∗ !!!!= !"#!!

!"#!!= 𝛽! + 𝛽!"𝑙𝑛𝑥!"

!!!!!! + 2𝛽!!𝑙𝑛𝑤!  ;    𝑤 = 𝑤𝑎𝑡𝑒𝑟 (7)

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𝐼𝐸!! = exp!!!"± !!"

! !!!!!!!

!!!!   ; 𝑖 = 1,… , 𝐼  𝑓𝑎𝑟𝑚𝑒𝑟2 (8)

We can similarly derive the input efficiency levels of other inputs using Karagiannis et al.

(2003), such as fertilizer and labor. (See equations 13 and 14 in the Appendix for derivation of

fertilizer input efficiency) The authors’ framework allows for a metric of comparison across

farmers with regards to their relative efficiency levels in each input. The empirical results for the

rice farmers in the Krishna Basin are presented in the next section.

Empirical Results

The 𝑓𝑟𝑜𝑛𝑡𝑖𝑒𝑟 command in Stata uses maximum likelihood estimation and the Newton-

Raphson method to calculate coefficients and error terms of stochastic production frontiers. I

use Stata and potential translog production models (Equation 5 shows a general form of the

translog), to construct four potential stochastic production frontier models, presented in Table 2.

Standard errors of each coefficient estimate are included in parentheses. Model 1 is the simplest

stochastic production frontier, comprising the logs of each input: labor, fertilizer, pesticide,

water, and other. The input other includes cost of seeds, transportation, and machine usage. To

test the goodness-of-fit, one test statistic to calculate is the prediction R-squared, which is 0.3029

for Model 1.

The prediction R-squared for Model 1 is not very high, suggesting that the model may not

sufficiently fit the data. Goodness-of-fit statistics may not be considerably important parameters

to derive in the context of a stochastic production frontier model, however. The purpose of

production frontier models is to calculate the efficient level of production for each farmer, and to

                                                                                                               2  See  Karagiannis  et  al.  (2003)  for  the  derivation  of  the  input  efficiency  formula.  

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assess tradeoffs between inputs of production. Stochastic production frontier models do not

predict actual yields; models utilized for the purpose of yield prediction may warrant heavier

emphasis on goodness-of-fit. The high p-values for lfert and lwater therefore do not suggest that

these two inputs should be excluded from the model. I use the Wald test of joint significance to

identify whether or not the inputs used in the model are significant as a group. This resulted in a

Wald statistic of 37.03, which is significant at a one-percent significance level. We thus have

statistically significant evidence to reject the null hypothesis that none of the inputs included in

the model have predictive power.

Models 2 and 3 are intermediate stochastic production frontier models. Model 2 includes

the log of each input and their squared terms, while Model 3 includes the log of each input and

the set of potential interaction terms. Both test whether or not the included group of nonlinear

terms is jointly statistically significant. The resulting Wald statistic for the hypothesis that all

coefficients of Model 2 are zero is 49.62, which is statistically significant at a one-percent

significance level. We can thus reject the null hypothesis that the coefficients of all the inputs

and their squared terms are equivalent to zero. I use the likelihood ratio test to compare Model 1

and Model 2. The resulting chi-statistic from the likelihood ratio test is 9.237, with a p-value of

.009869, which is statistically significant at a 1% level. The likelihood ratio test thus presents

statistically significant evidence that Model 2 is an improvement in model fit (UCLA, 2012).

For Model 3, the resulting Wald statistic is 88.74, which is also statistically significant at

a one-percent significance level. We can thus reject the null hypothesis that the coefficients of

all included independent variables in Model 3 are equal to zero. The likelihood ratio test

compares Model 3 to Model 2 in terms of goodness-of-fit, resulting in a chi-statistic of 12.16 and

  16  

a p-value of 0.002292. There is statistically significant evidence at a 1% significance level that

Model 3 is an improvement in model fit.

After finding joint significance for both the squared terms of the inputs, and the set of

potential interaction terms, I tested the joint-significance of the full translog production frontier

model, presented as Model 4 in Table 2. The Wald statistic for the hypothesis that all the

coefficients are zero is 152.83, which is statistically significant at a one-percent significance

level. We can thus reject the null hypothesis that the inputs, their squared terms, and their

interaction terms have coefficients equal to zero. Model 4, the full translog production frontier

model, thus passes the Wald test of joint significance. The likelihood ratio test comparing Model

4 to Model 3 results in a chi-statistic of 8.279 and a p-value of 0.01593, which is statistically

significant at a 5% level. This final likelihood ratio test comparing Model 4 and Model 3 shows

that there is statistically significant evidence that Model 4 is an improvement in fit.

This analysis proceeds with the results from Model 4, the full translog production frontier

model, because the model also incorporates potential tradeoffs between inputs utilized in rice

production. Analyses in the literature that utilize a stochastic production frontier typically do not

give much attention to functional form, because the frontier is used as a tool for comparing

current levels of production to the theoretical ideal. Comprehensive diagnostic checking is thus

not necessary for the purposes of this analysis. The inclusion of interaction and squared terms

within the stochastic frontier production function also leads to more accurate estimates of

technical and input-specific efficiency levels. To estimate technical efficiency levels of each

farmer in the basin, the first step is to calculate each farmer’s inefficiency estimate, 𝑢!3, using the

estimation results from Model 4. Each farmer’s technical efficiency level, in percentage terms,

is calculated by plugging these inefficiency estimates into Equation 6.                                                                                                                3  The  specification  of  the  inefficiency  estimate,  𝑢! ,  is  shown  in  Equation  4.    

  17  

Table 3 presents the distribution of output-oriented efficiency levels for rice farmers in

the Krishna basin. The measurement of technical efficiencies for each farmer portrays the

relationship between observed production and an ideal level of production. The technical

efficiencies for farmers are high, at an average technical efficiency level of 91.0%. Most farmers

in the river basin are thus achieving close to their maximum potential level of output as

determined by the production frontier, given the quantity of inputs utilized. Graph 1 shows the

distribution of TE levels across the 240 farmers. The graph shows that in general, farmer TE

levels range between 86% and 99%; the largest deviations from this general range include TE

levels that only dip down to 77%. Overall, the technical efficiency of these farmers is high, and

the variation in efficiency levels across the sample is low. High technical efficiency levels do

not necessarily mean that the farmers are overall very efficient producers – the high percentages

instead show that farmers sampled in the Krishna River Basin achieve similar levels of overall

production. The similarity among producers in their production levels may be due to various

factors including farm size, weather conditions, and local governmental regulations. Since the

technical efficiency estimate only measures overall production efficiency, the TE estimates may

not be presenting a holistic picture of rice farming in the Krishna basin, especially with respect to

water and fertilizer-specific efficiency levels. The next step is thus to use Karagiannis et al.’s

(2003) input efficiency estimation procedure to compare farmer TE levels with their respective

water and fertilizer efficiency levels.

Using equations 7 and 8 from the Methodology section, I derive input-efficiencies (IE)

for water and fertilizer for each farmer in the sample. Table 4 presents the summary statistics and

distribution of irrigation water input efficiencies across the sampled farmers. We can see that the

distribution of input efficiencies of water for farmers is very different from the overall technical

  18  

efficiencies. Farmers achieve a very low level of water input efficiency, at an average of 16.9%.

These results are striking, because the low average water efficiency suggests that the relatively

high technical efficiency levels may potentially be driven by other inputs, such as fertilizer.

Graph 2 presents the spread of irrigation water input efficiency levels across farmers. As shown,

the variation in water IE levels are much wider than the variation in TE levels; the IE estimates

are generally on the low-end, ranging from 0 to 20%, but reaches as high as 60%. The wide

variation in input efficiency levels indicates that some farmers are more effective at water

application than others, or less prone to overutilization.

An interesting extension to the water efficiency results is to analyze the relationship

between farmer location in the catchment area (head, middle, tail) and their water efficiency

levels. Since farmers receive irrigation water at regular intervals, based on release schedules of

the canal, there may be differences in water extracting behavior between farmers located closer

to the water source in comparison to those located further away. Table 8 shows a simple

regression of water input efficiency levels on the dummy variables of being located at the head

of the canal (head), and at the end of the canal (end). This regression shows that there is some

evidence of water input efficiency levels being higher for farmers at the end of the canal. This

may be due to a variety of factors, including the major possibility that farmers located at the end

of the canal do not have as much irrigation water to extract as those located near the source.

Further studies of the relationship between water efficiency levels and characteristics of farms

and farmers may be a valuable study for policymaking in the future. The results from this

current study can only cite correlation because there is no sufficient instrumental variable to

isolate the impact of geographic location on water efficiency.

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High technical efficiency and low water efficiency levels leads to the possibility that

efficiency levels of other inputs may be driving the high overall production efficiency levels.

The literature states that fertilizer application has been a major contributor to higher yields in

developing nations. Using the same equations derived by Karaggianis et al. (2003), I derived

input-efficiency estimates of fertilizer for each farmer in the basin. Table 4 presents the summary

statistics and distribution of input-oriented efficiency levels of fertilizer. The average fertilizer

efficiency level is extremely high at an average of 99%, nearly the maximum level. Graph 3

displays the small variation in fertilizer efficiency levels across farmers, reaching a low end of

98.8%. The remarkable contrast between water and fertilizer efficiency levels suggests that high

output-oriented technical efficiency levels for the rice farmers in the Krishna basin are currently

being driven by fertilizer use. From the best of my knowledge, no previous studies compared

water efficiency to fertilizer efficiency levels.

These empirical results on efficiency levels support the hypothesis that farmers in the

Krishna basin are using an excess amount of irrigation water. High yields and production

efficiency levels are driven by fertilizer application, which may be detrimental to soil quality and

future yields. The next focus of this paper will be the question of how to address the problem of

water overutilization. The input-specific water efficiency measures directly lead to estimates of

minimum feasible water use and maximum possible water savings for each farmer, ceteris

paribus. Excess water usage can thus be reduced while maintaining the same amount of rice

yield. Table 6 presents summary statistics for maximum potential amount of water savings

across all farmers in the Krishna Basin.

Overall, part I of this analysis showed that overall technical efficiency levels of the

farmers sampled were high. This result may not be particularly revealing because efficiency

  20  

levels are compared to the highest producing farmer. It is possible that the efficiency levels of

all farmers do not vary drastically, thus leading to similar (and high) TE estimates. The input-

specific efficiency levels are slightly more revealing. The input efficiency levels of water are

low on average, while the input efficiency levels of fertilizer are high. This paper differs from

previous studies on efficiency levels of inputs in rice production because of the comparison of

water and fertilizer efficiencies. The input-specific technical efficiency estimates imply that

there are huge potential water savings across these farms, holding output constant. The main

difficulty is to implement a methodology that will allow farmers to utilize water at more efficient

levels. One potential solution is a volumetric pricing scheme, which may prompt farmers to

produce at the point where marginal cost equals marginal benefit. This potential pricing scheme

will be discussed in the next section.

Part II: a hypothetical volumetric pricing scheme for water

Many policy analysts have proposed that irrigation-pricing schemes will help improve

irrigation water efficiency. There are various factors that must properly be assessed before

implementation of water pricing can be feasible. One important component that must be

understood comprehensively is farmer preferences for irrigation-pricing methods, and their

potential for compliance to new pricing schemes. Veettil et al. (2011) explored the price

sensitivity of farmers towards irrigation water pricing across various types of pricing

mechanisms in the Krishna River Basin of India. Using a discrete choice model, the authors

identified four types of transferability levels, two duration lengths, and four types of water-

pricing methods (WPMs). The water pricing methods include area pricing, crop pricing, quota

pricing, and single-rate volumetric pricing. Area pricing, the status quo, was the most inefficient

pricing option. Volumetric pricing, which prices water per volumetric unit, was the most

  21  

efficient option as it allowed farmers to buy water depending on their quantity demanded. Each

pricing mechanism had four price levels and degrees of transferability, reflecting the mobility

and interchangeability of water rights. Area pricing was associated with no transferability, while

volumetric pricing involved a full water-market.

After interviewing a sample of farmers living in the state of Karnataka, the authors

presented results on the price elasticity of farmers across each pricing mechanism. They found

that the price of water and preferences for area water pricing were negatively correlated. Under

volumetric pricing, irrigation water demand is elastic beyond a threshold price level, and affects

farmer consumption behavior when water cost is above 10% of their income. With respect to

issues of policy implementation, the authors find that membership in a local water users

association (WUA) increases farmer preferences for volumetric pricing. Since volumetric water

pricing requires local level administration that can facilitate water metering and volume

measurement, water users associations allow farmers to have direct involvement with irrigation

management in the area. The authors showed that farmers in the region prefer volumetric pricing

if pricing were above current price levels.

Measurements of farmers’ average price elasticity of demand for water help to

understand how farmers will respond to changes in prices under a volumetric pricing system.

Recognizing the increasing necessity for a national policy surrounding water usage and

allocation in the agricultural sector of Spain, Varela-Ortega et al. (1998) employ a mathematical

programming model to simulate how farmers will respond to different water pricing scenarios.

They do so by characterizing farmer’s behavior for a set of 17 representative farms from six

irrigation districts. Using a constrained linear optimization model that sets up a scenario where

farmers maximize profit subject to financial, technical, economic, and policy constraints, the

  22  

authors approximate the farmers’ water demand curve and price elasticities. One major finding

from the study is that in general, farmers’ demand for water is inelastic at lower prices, and may

be elastic, depending on the region, at higher prices. Districts that tend to be more developed

also had a price elasticity of demand for water that was less elastic. The authors found that

reducing total water usage had major impacts on farmers’ incomes, however. To mitigate the

problem, the authors propose a bonus system, where farmers were given a bonus if they saved

more than 20% of their water allotment right. The bonus-pricing scheme allowed for the highest

amount of water savings with the least amount of income loss to farmers.

The literature shows that water quantity responses to price may vary depending on the

region of study, and the type of pricing mechanism. The next few sections will utilize study

results from the previous literature and the collected data from IWMI to propose a hypothetical

demand curve, marginal values of water, and potential percentages of irrigation water savings for

rice farmers in the Krishna basin.

Motivation

In order to propose a new water pricing mechanism, we must first derive irrigation water

demand across all farmers in the basin. This is a difficult task, because constructing a theoretical

water demand function is constrained by the availability of information, the characteristics of the

geographic location, and governmental policy. There are two primary approaches to deriving

water demand in agricultural economics. The first method is to econometrically estimate water

demand, requiring an availability of data that reflects water quantity responses to changes in

price. The second method of demand estimation is through linear programming methods, most

commonly by estimating shadow prices through constrained optimization. Studies that use linear

  23  

programming to measure demand for irrigation water in agriculture assume a known production

technology, and measure the shadow price of water at each level of water constraint to derive the

demand for water. One limitation of linear programming is the assumption of Leontief

production functions. Leontief production functions imply that an increase in one input, ceteris

paribus, will not help increase total yield. This may be a limiting assumption in the context of

rice agriculture because the increase of fertilizer or pesticide usage may in fact increase yields,

regardless of water or labor increases.

Econometric estimation of irrigation water demand is also limited, especially with respect

to the quality and quantity of data collection. Acquiring varying prices of water may sometimes

be impossible because irrigation water in many developing nations is heavily subsidized. In the

case of farmers in the Krishna basin who were surveyed in this study, each farmer paid a fixed

price of 400 Rs per acre of land. Farmers thus paid a zero-marginal price per volume of water

utilized, leading to overutilization, as displayed in Part I of the study. Overall, estimating the

price elasticity of water demand using econometric modeling is not possible with fixed prices,

constraining our understanding of irrigation water demand of farmers in our sample.

One alternative is to use information from existing academic studies conducted on

irrigation water demand in other nations. Irrigation water demand, however, is largely dependent

on local conditions. Price variability is also typically very small for water, potentially leading to

imprecise elasticity estimates. A study conducted in California’s San Joaquin Valley, using

panel data and instrumental variables estimation, found that the price elasticity of agricultural

water demand is approximately -0.79 (Schoengold et al, 2006). The authors in this study use

econometric analysis to decompose water use by both crop and irrigation technology, and

includes the direct effect of improved water management. Their results show a surprisingly high

  24  

price elasticity of water, suggesting that farmers in developed nations are also relatively price

sensitive towards irrigation water prices.

Farmers from developed nations such as the U.S., however, are exposed to more

sophisticated irrigation infrastructure, better water quality, and higher farm incomes. Using

elasticity estimates from developed nations may result in grossly biased estimates, because

farmers in developing nations tend to have higher price elasticities of water due to more

restrictive income constraints. Thang and Singh (2006) find that farmers in Vietnam and India

face many constraints within the production major crops, including rice. One constraint that

small and marginal farmers face includes limited access to credit. Lack of adequate

infrastructure, credit constraints, and limited access to inputs all suggest that farmers in

developing nations have higher price elasticities of water.

Another limitation to estimating price elasticities of water for farmers in developing

nations is that a large majority of farms in developing nations utilize subsidized unmetered

water, leading to an absence of price-quantity data. If price elasticity estimates cannot be

acquired through the existing data, as in the case of this study, the second-best option is to find

previous studies that measured price elasticity estimates of irrigation water from a similar region.

Somanathan and Ravindranath (2006) conducted one such study in the Andhra Pradesh and

Karnataka states of India, measuring the price of irrigation water per cubic meter, and its price

elasticity of demand. The authors conducted the survey in six mandals, and randomly chose five

hamlets from each mandal. They then interviewed all the farmers in each hamlet. Since large

samples are generally difficult to obtain in developing nations, the authors used and compared

two methods to elicit the marginal value of irrigation water: one obtained directly from data on

sale prices of water from farmers with pumps to farmers without pumps, and another based on

  25  

the price differential between un-irrigated and irrigated land. Since irrigation water is heavily

subsidized, the purpose of using differential land prices is to obtain a more market-based

marginal value of water; this may consequently be more effective at eliciting preferences for

irrigation water.

The authors also obtain an estimate for the price elasticity of demand for irrigation water

by approximating the demand curve. Since irrigation water is not traded in a purely competitive

market, the authors assume that water used by buyers and sellers (those who own the water

pumps) are purely limited by water supply. The authors regress water quantity on water prices,

using owner’s water use during the growing season as an instrument for water price, and find a

price elasticity of demand for irrigation water of -1.03. Their results indicate that irrigation

water demand in the Upper Papagni watershed is relatively price elastic. They also obtain

marginal value of water estimates using two methodologies: first, they estimate price as rupees

paid to the seller divided by the quantity of water supplied; and next, they estimate revealed

preferences for irrigation water by regressing the price of land on irrigation and soil type dummy

variables to estimate the price differential between irrigated and un-irrigated land. The first

method resulted in a price of 0.58 Re/m3 of water, while the second resulted in a price of 0.31

Re/m3, with an average yearly irrigation water quantity of 38,000 m3/hectare, or 15,378.05

m3/acre.

Methodology and Results

For the purposes of this study, I will use price elasticity results from Somanathan and

Ravindranath’s study to estimate an approximate demand scenario for the farmers in the Krishna

River basin. Since their results suggest a relatively high elasticity of demand for irrigation water,

  26  

one assumption is that the price elasticity of demand for farmers is approximately constant at all

price levels. This may not be accurate, especially given findings that elasticity levels may be

elevated at higher prices, and this may be due to its impact on incomes. I will use the constant

elasticity assumption as a starting point, and will later present potential alternate scenarios that

incorporate qualitative findings from the literature. These alternate scenarios will be discussed in

the sensitivity analysis.  

  Somanathan and Ravindranath estimate the price elasticity of demand for irrigation water

to be approximately -1. Assuming an irrigation water demand curve with a constant price

elasticity of demand, the initial problem is that the constant elasticity demand curve does not

theoretically include a zero price. The following shows the derivation of the constant elasticity

demand curve, with a price elasticity of -1:  

𝜀! = −1 =𝑃𝑄 ∗

𝑑𝑄𝑑𝑃  

      𝑙𝑛𝑄 = −𝑙𝑛𝑃 + 𝐶                   (9)  

𝐶 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡  

A price-quantity combination must be plugged into the equation to determine the constant value

in the above equation. The problem is that the marginal cost of water for farmers in the Krishna

basin is currently zero, with a fixed cost of 400 Rs/acre. This implies that farmers currently pay

a zero marginal price for irrigation water – it is impossible to plug in a zero price into the

equation. The second-best option is to use an approximation. One approximate price-quantity

combination is derived from dividing the total current cost of irrigation water (average of

1,719.15 Rs/farm), by the total amount of water utilized for each farmer (average of 24,500

m3/farm). Averaging this value across all farmers leads to an average marginal cost of water of

  27  

0.072 Re/m3, and an average quantity of water utilized of 24,500 m3. Plugging this price-

quantity combination leads to the following equation:

𝑄 = 𝑒! !"# ! 𝑒! = 𝑒! !"# ! ∗ 7818.05         (10)  

Using the estimated price-quantity combination bypasses the zero-price problem to customize

the demand curve for farmers in the study region. The purpose of constructing this demand

function is not to achieve 100% accuracy, but to reflect the potential amounts of savings from

volumetric irrigation water pricing. Graph 1 shows a graph of the potential demand curve

constructed from equation 10.

The primary purpose of constructing a hypothetical demand curve is to approximate

potential water savings with incremental increases in price. The maximum amount of water

savings possible is on average 21,500 m3 per farm, or 5,002 m3 per acre, given the same amount

of yield. This measure was determined using the input-efficiency calculations from Part I (see

Table 4). This is a very large amount of potential water savings, and is likely to be highly

inaccurate. Another problem is that using large quantities of water also aids in controlling the

impact of weeds on rice yields. Studies indicate that flooding to depths of 10 cm during rice

cultivation prevents the germination of weeds. This method is combined with herbicides and

hand pulling to control weeds in the crop. The IPM reports that uncontrolled weed growth was

the cause of yields losses of 45-75% in Asia. For the farmers in the Krishna basin, the average

rice paddy water depth is 6.5 cm. Researchers from IWMI, Hyderabad confirm that farmers in

the Krishna basin control weed through hand weeding, which is conducted 2-3 times during the

cropping season. Hand weeding in rice cultivation is the most common method in developing

nations. The main restriction is that hand weeding requires considerable manual labor. For some

farmers, manual labor is scarce and expensive to hire, while herbicides are detrimental to soil

  28  

and human health. Therefore, the best way to control weed is through integrated management,

because there is no weed method that can control all weeds (IWM).

Maximum water savings calculated for each farmer are unrealistic, especially given

estimation inaccuracies and weed management requirements. I will thus only explore water

savings of up to 50%. Equation 10, the constant elasticity demand curve, leads to calculations of

potential prices and corresponding quantities demanded. Table 8 (Scenario 1) shows these

potential price-quantity combinations, and corresponding percentages of water savings4 per acre

of land. At an approximately 100% increase in price per m3 of irrigation water (0.15 Rs/m3), the

percentage of water savings of total potential water savings is approximately 30%. This leads to

a more than 50% increase in total costs for farmers, from 400 Rs/acre to 622 Rs/acre. Given the

relatively low levels of total revenue for farmers in the region (at an average of 21,806.25 Rs per

farm), pricing schemes that attempt to achieve high levels of water savings may be detrimental

for farmers. For water savings that reach 50%, the price increases to 0.27 Rs/m3, leading to a

115% increase in costs of water per acre. This is a substantial cost increase for subsistence

farmers, and may cause production shutdowns.

To rectify high irrigation costs for farmers, the Indian government has historically

provided subsidies for irrigation and electricity. A USITC briefing (2011) reports that

agricultural policies in India subsidize between 70 to 90 percent of irrigation and electricity

costs. Since the purpose of a volumetric pricing scheme is to incentivize water savings, the extra

costs from instituting volumetric pricing can be effectively returned to the farmer through other

forms of block grants. These grants will be determined at fixed amounts independent of water

utilization volume; these fixed block grants will not alter water efficiency incentives. The grants

                                                                                                               4  The  percentage  savings  is  a  percentage  of  the  maximum  quantity  of  potential  water  savings,  (21,500  m3)  given  the  same  level  of  yield.      

  29  

will serve to help farmers with their overall operations. For example, the government can

subsidize total operational costs given that the farmer follows the rules with respect to paying for

water per volume (m3) utilized. With volumetric pricing, the government can help farmers

achieve more water savings at a near revenue-neutral level of water pricing, thus mitigating the

decrease in income for farmers as a result of the policy.

A main hypothesis of this study is that the reason for irrigation water over-extraction is

its zero-marginal cost. If water is purely a fixed price, then there is no incentive for farmers to

reduce their water use for the benefit of other players. Any marginal cost that water suppliers

impose will help reduce water extraction, helping all players who utilize water from the river

basin. The hypothetical results from Table 8 show the potential efficiency gains from charging a

positive price per volumetric unit of water utilized. Implementing volumetric pricing based on

the hypothetical irrigation water demand curves shows that raising the initial price of 0.07 by

0.08 and 0.19 Rs/m3 leads to water savings of 30% and 50%, respectively. The major

assumption from this section is that the government can only induce savings if water is charged

at a price that leads to higher costs than current levels.

It is possible that charging a price that is greater than zero and less than 0.072 Re/m3 will

still lead to positive water savings. Another possibility is that the demand curve for irrigation

water does not have a constant elasticity. These different scenarios may lead to substantially

different projections of water savings. The sensitivity of the various parameters in the irrigation

water demand curve must therefore be tested to understand the potential range of water savings

percentages as a result of incrementally increasing volumetric water prices. The following

section is a detailed sensitivity analysis of the estimated demand curve using Somanathan and

Ravindranath’s price elasticity estimates.

  30  

Sensitivity Analysis

This section will explore the following alternate scenarios for the irrigation water demand

curve. One possibility is that volumetric water pricing will induce water savings even at total

costs lower than the current cost level (average 1,719.15 Rs/farm). The lowest cost-quantity

ratio of all 240 farmers is approximately 0.050 Rs/m3. Using the price-quantity combination of

0.05 Rs/m3 and 21,500 m3 leads to equation 11. Table 9 (Scenario 2) presents price-quantity

combinations, and associated water savings percentages and costs per acre, using the minimum

cost-quantity ratio (of all 240 farmers).

𝑄 = 𝑒!!"#  (!) ∗ 6670.16 (11)

Raising the price of water by 0.7 Rs/m3 has a potential water savings of approximately 35%, with

a cost increase of approximately 17%. To reach water savings of 50%, prices must increase to

0.19 Rs/m3, which is a cost increase of about 150%. These are slightly different results from the

original estimated irrigation water demand curve (reflected in Table 8), and this may be due to

the different starting price. Results from both demand curves (Tables 8 and 9) suggest that to

achieve water savings of 30-35%, costs per acre for each farmer must increase by 15-50%. To

achieve water savings of 50%, costs must increase from 50-100%. Although the range of

projected cost increases is wide, the incremental increases in price per cubic meter of irrigation

water leads to substantial water savings.

The two potential irrigation water demand curves assume a relatively high elasticity of -

1, however. If the elasticity of irrigation water is in reality, more inelastic, then potential water

savings may be substantially lower. Equation 12 shows the potential constant elasticity demand

curve using the elasticity estimate of -0.8, in order to assess the possibility of a more inelastic

  31  

irrigation water demand5. Table 10 (Scenario 3) presents the corresponding price-quantity

combinations, percentage water savings, and total costs per acre with given price.

𝑄 = 𝑒!!.!∗!"#  (!) ∗ 9824.54 (12)

Table 10 shows potential water savings given incremental increases in price. With an increase in

price of from 0.07 to 0.14 Rs/m3, farmers will save approximately 25% of their total potential

water savings volume, with a cost increase of around 63%. This is still a substantial amount of

water savings, even with a more inelastic price elasticity estimate. To achieve water savings of

30% of total potential water savings volume, price per cubic meter of irrigation water must

increase to approximately 0.18 Rs/m3; for water savings of 50%, price must increase to 0.38

Rs/m3. These water savings targets are associated with cost increases per acre of 87% and 204%,

respectively. Using a more inelastic estimate of the price elasticity of irrigation water demand

thus leads to less water savings per incremental increase in price per cubic meters of water

volume, and higher associated costs with water savings targets of 30% and 50%.

The three scenarios tested thus far suggest that costs associated with increasing

volumetric water pricing are sensitive to the assumptions on irrigation price elasticity and the

initial price-quantity combination (required to derive the demand equation). Nevertheless, all

three models show that incrementally increasing price will lead to substantial water savings. The

models reveal that increasing price of irrigation water per cubic meter by 0.07-0.08 Rs/m3 leads

to water savings of 25% to 37% of total potential water savings for the rice farmers in the

Krishna basin, with a cost increase of 12% to 63% per acre. Therefore, the three constant

elasticity irrigation water demand models imply a high potential for water savings with small

increases in volumetric prices.

                                                                                                               5  Rounded  up  from  elasticity  estimate  of  -­‐0.79  (Schoengold  et  al.,  2006).      

  32  

The final scenario follows Varela-Ortega’s (1998) conclusion that demand is inelastic at

lower prices, and more elastic at higher prices. A linear demand curve may more accurately

portray the farmers’ irrigation water demand, since demand becomes gradually more elastic as

prices increase. The problem with a linear demand curve is that the price elasticity of demand

for irrigation water is extremely inelastic at low prices. This may be unrealistic since farmers in

the Krishna basin generally have low incomes, which leads to higher sensitivities to price

changes. Somanathan and Ravindranath, as mentioned earlier, found that the price elasticity of

irrigation water for farmers in India is -1.03 at a price level of approximately 0.31 Rs/m3. This

serves as a valuable benchmark for price elasticities of irrigation water. Their study was

conducted in a similar watershed in Andhra Pradesh and Karnataka, using survey data from a

randomized sample of farmers in the watershed. Assuming that a zero price leads to the current

average water use, in cubic meters per acre, a linear demand curve can be approximated if we

assume that the price elasticity of irrigation water is approximately -1 at a price level of 0.3

Rs/m3.

Graph 5 shows this simple hypothetical linear demand curve using information from

Somanathan and Ravindranath’s paper, and Table 11 (Scenario 4) presents price-quantity

combinations, water savings percentages, costs, and elasticity values. As presented in Table 11,

a price level of 0.15 Rs/m3 leads to approximately 30% water savings, with a cost increase of

about 60% (as compared to 400 Rs/acre under the area-pricing scheme). To achieve water

savings of 50%, prices must be between 0.20 and 0.25 Rs/m3, leading to cost increases of 100%

to 115%.

The predictions from the linear demand curve are surprisingly close to the water savings

and cost increase results from the constant elasticity demand curves. Scenario 1, 3 and 4

  33  

suggest that a price level increase to 0.14-0.15 Rs/m3 will lead to water savings of 25-37% and

cost increases of 50-63%. All four scenarios show that water savings of 50% requires price

increases of approximately 0.15-0.30 Rs/m3. Although the projections in cost increases vary

across scenarios, all four models show a high potential for water savings with very small

increases in price per cubic meter of irrigation water. As discussed, any increase in cost for

farmers could be returned to them in the form of block grants that are independent from

irrigation water usage. These grants will allow the policy of volumetric water pricing to be

nearly cost-neutral.

The design of an alternate irrigation water pricing system, coupled with block grants,

serve to ameliorate prospects of inadequate food production due to decreases in water supply in

the future. Two major forces of water supply decreases are population increases and climate

change. The next section uses recent forecasts of climate change impacts on water supply in

India to understand the implications for rice production in the Krishna basin, including water

efficiency requirements across farmers. I will also discuss the volumetric price levels that will

accommodate projected decreases in water due to climate change.

Part III: climate change and policy implications

Climate Change

Climate change has the potential to decrease fresh water levels and increase the

incidence of extreme weather events. Since agriculture is vital to developing economies, nations

such as India are more vulnerable to climate change impacts in the future. One hypothesis of this

study is that marginal cost pricing mechanisms may increase input efficiency levels, eliminate

waste, and help farmers adapt to increasing water shortages as a result of rising temperatures.

Rates of current agricultural production in developing nations have led to many studies that

  34  

predict the future impact of climate change on crop yields. Guiteras (2007) studied the economic

impact of climate change on Indian agriculture in particular, using a 40-year district-level panel

data set covering over 200 districts to estimate the approximate change in crop yields due to

projected climate changes in the short, medium, and long run. His results show that climate

change projections over the years 2010-2039 will reduce crop yields by 4.5 to 9 percent. If

farmers do not adapt to climate change in the long run, the potential long-run impacts of climate

change are large, causing a reduction of yields by 25 percent or more between 2070-2099.

Fertilizer usage is also affected by temperature increases. Guiteras finds that an increase of one

degree Celsius decreases fertilizer use by 4.5 percent.

Predictions on climate change adaptations and welfare effects are complex, largely due

to weather fluctuations, farmer adaptation behaviors, and differences in environmental conditions

due to geographic locations (soil, pollution, etc.). Climate change exacerbates the rate at which

mountain ice caps melt, leading to a higher chance for droughts and floods. A report on the

impact of climate change in India reported that glaciers that supply water to Indian water basins

are receding at an average rate of 10-15 meters per year (NIC, 2009). However, recent findings

by scientists found that glaciers in the western Himalayas along the Karakoram Range have

overall resisted global warming. Extreme weather events, coupled with lowering reservoir levels

overall, have large implications for rice yields. Based on estimates made by the World Bank

(2008), a 2.3-3.4 °C increase in temperature and a 4-8% increase in rainfall (modest to harsh

climate change scenarios) may cause incomes of small farmers to decrease by as much as 20%.

The threat of climate change on expected yields and farm practices heightens the necessity for

further policy research on irrigation water allocation.

  35  

This study explores water-pricing options beyond the status quo that may potentially

mitigate the harmful effects of decreasing water supply driven by population growths and

climate change on rice yields in India. The goal is to target farmer behavior, designing an

incentive-based pricing mechanism that will help farmers to adapt to lower water supply in the

future. Pricing based on volume, rather than area, may lead to more optimal water allocation

schemes. Less irrigation water would be wasted because farmers will attribute value to each

incremental increase in water usage. Water pricing that leads to more optimal water allocation

will also lead to a more sustainable solution in the face of rising water stress. Current projections

of water supply decreases in India help highlight the potential for volumetric pricing to

incentivize water savings. The IPCC projected gross per capita water availability in India to

decline from about 1,820 m3/year in 2001 to as little as 1,140 m3/year in 2050 (Bates et al.,

2008). This suggests that future water supply in India will decline by approximately 37%.

Results from Part II, Scenario 1, indicate that prices must be raised to approximately 0.20 Rs/m3

in order to achieve 37% water savings, increasing total costs per acre by around 80% (as

compared to the current 400 Rs/acre cost of irrigation water). Given that much of this extra cost

could be returned to the farmers in the form of block grants, volumetric pricing may have the

potential to effectively reduce water usage. Volumetric pricing is clearly not the only potential

method of reducing water usage. Other possible effective ways of reducing water usage is

improvements in irrigation technology, the widespread adoption of conservation irrigation

methodologies, and crop switching to less water-intensive staple crops (e.g. wheat).

The decline of 37% does not include the additional impact of climate change, however.

The IPCC projects that climate change and population growth in India will lead to a per capita

water supply of lower than 1,000 m3 by 2025 (Bates et al., 2008). Water supply may decrease by

  36  

as much as 45% in the next fifteen years. Scenario 1 shows that irrigation water prices may need

to increase to 0.28-0.30 Rs/m3 to accommodate these drastic decreases in water supply. Results

from my rice production model in Part I suggest that these supply decreases are still lower than

total potential water savings for each farmer. There is thus considerable room for farming

adaptation with changes in water pricing policy, given the looming threat of climate change.

These changes may help bring about more sustainable food production for developing nations in

the future.

Other future policy interventions that can help mitigate the impact of climate change on

agriculture yields include weather-based crop insurance, educational programs on fertilizer

application, high yield variety seeds, and new methods of implantation including machine

transplanting. The sample from the Krishna River Basin has an extremely small number of

farmers using alternative methods of rice cultivation. Future studies based on large samples may

help with regards to finding the most effective of methodologies that can effectively increase

yield.

Policy Context

Water pricing mechanisms have large implications for government policy. For many

pricing schemes, the divide between theory and application is huge. Although theory dictates

that volumetric pricing will generate the maximum amount of economic surplus, implementation

costs may ultimately negate this argument. Volumetric pricing theoretically requires marginal

cost pricing, setting the price to be equivalent to the marginal cost of supplying the last unit of

water. Marginal cost pricing leads to the first-best efficient allocation, but does not incorporate

fixed costs such as capital depreciation, installing meters and pumps, building reservoirs and

  37  

canals, and interest payment on the investment. This pricing mechanism may not be able to fully

recover costs, especially in the case of high fixed costs. Another problem that is commonly cited

is that volumetric pricing ignores equity issues, potentially forcing low-income, less-efficient

producers out of the market. Agricultural policy in some developing nations throughout has

placed higher importance on equity rather than efficiency, stressing how wealth is distributed

across the population. Many claim that water prices are ineffective at tackling the issue of

income inequality, and higher prices resulting from volumetric pricing may prove extremely

detrimental to lower income groups (Johansson et al., 2002; Tsur et al., 2005). In this analysis,

block grants provided to farmers that are independent of the volume of water usage serve to

rectify the equity issues of volumetric water pricing. Since these block grants are not based on

the amount of irrigation water utilized, water prices will more accurately reflect marginal values,

and pricing could be served as an effective tool to limit over-extraction.

There still remains the problem of high infrastructure costs and limited government

funding availability. Alternative methods of water pricing have been proposed to tackle the cost

recovery objective. One methodology is block pricing, which involves varying the water price

when water extraction for a certain time period exceeds set levels of volume. Block pricing sets

water prices to be below operation and maintenance (O&M) costs in the first block, and raises

prices to higher rates at second, third, and later blocks in order to sufficiently cover O&M costs.

The problem with this method is that it is difficult to determine the correct volumes for each

block, and may not fully recover O&M costs. This is especially a problem if the volume limit

for the first block is large. This pricing methodology may also increase the disincentive for

farms to expand; larger farms may have increasing returns to scale, and may be more efficient in

supplying staple goods such as rice.

  38  

Another mechanism that may reconcile the conflict between full cost recovery and water

reduction is the two-part tariff, which combines volumetric pricing and a fixed cost. This may

lead to extremely high prices for low-income farmers, however, and is associated with high

implementation costs (World Bank, 2005). The installation and maintenance of water pumps

and meters involves an extremely large investment and requires administrative costs that may not

be completely feasible for local governments to sustain. One alternative is to charge a water

price per output produced, pushing prices and allocation to the first-best efficient level, which

was proposed by Tsur et al. (2005). Another alternative is the implementation of a water market.

The ability to create a functioning, competitive water market requires water rights to be tradable,

causing administrative and logistical complications. Water market implementation requires

high-level stakeholder involvement and a sophisticated judicial body that can oversee trading

activities and resolve disputes. In the Suriana-Riudecanyes irrigation district of Spain, water

users association (WUA) members trade water use rights to gain access to the six million m3 of

water utilized per year (Maass and Anderson, 1973). Overall, the institution of water markets

requires a considerable degree of transparency and active user participation, with implementation

costs that may be too high for developing nations.

To mitigate the cost recovery problems associated with volumetric pricing, the Chinese

government implemented an integrated circuit card automated irrigation charge collection system

for groundwater irrigation in Shandong. The farmer extracts irrigation water by inserting the card

into a server; after irrigation is complete, the farmer receives a receipt that states the total amount

of water used and the price paid per unit. All the water payment servers are connected to the

Internet, decreasing administrative costs. Due to the implementation of this IC card system,

Shandong saves approximately five billion m3 of water per year, while ensuring nearly 100

  39  

percent collection rates (World Bank, 2005). Cost saving technologies such as the IC card

system may help in reducing the implementation costs associated with initiating volumetric

irrigation water pricing in other developing nations such as India. One problem is that India has

considerably less electricity and Internet connectivity and infrastructure than China. The only

way for an IC system to be established in India is therefore through complete financial support

by the government.

Conclusion

Initial results from data on rice farmers in the Krishna Basin collected by N.S. Praveen

Kumar show that output-oriented technical efficiency levels are surprisingly high, attaining an

average of around 91% efficiency. Water efficiency levels are much lower, however, reaching

an average efficiency level of approximately 17%. Further analysis shows that fertilizer

efficiency levels are extremely high, close to 100%, and thus help drive technical efficiency

levels for farmers in the region. Given issues of fresh water scarcity in the future for rice farmers

in Andhra Pradesh and surrounding regions, driven by droughts caused by climate change, there

is an increasing urgency for policy oriented towards a more efficient water allocation

mechanism.

One method I propose in this paper is using a volumetric water-pricing scheme, based

on irrigation water demand. Due to limited time and data, a study by Somanathan and

Ravindranath (2006) provides a reference point for irrigation water price-elasticities. I use their

elasticity estimate to construct theoretical demand curves in order to identify potential water

savings levels from small increases in price per m3 of irrigation water. The theoretical demand

curves constructed include constant elasticity demand curves and a linear demand curve, as

  40  

shown in Part II of this analysis. Irrigation water savings predictions from the linear demand

curve and the constant elasticity demand curve are close in value. Scenarios 1, 3 and 4 in Part II

show that a price level increase to approximately 0.14-0.15 Rs/m3 will lead to average water

savings of 25-37% and cost increases of 50-63%. All four of the theoretical demand curves

constructed showed that water savings of approximately 50% requires price increases of

approximately 0.15-0.30 Rs/m3. Based on IPCC projections of population effects on the future

supply of water in India by the year 2050, water prices under demand Scenario 1 in Part II must

be increased to approximately 0.20 Rs/m3 to achieve the 37% water savings required to maintain

similar levels of yields. With the additional impact of climate change, by the year 2025,

Scenario 1 indicates that irrigation water prices may need to increase to approximately 0.28-0.30

Rs/m3 to accommodate potentially huge decreases in water supply. To rectify potential equity

problems associated with this pricing scheme, block grants that are determined independent of

water usage are proposed.

Extensions to this study include identifying potential effects of other pricing

mechanisms, including quota pricing, block pricing, and output pricing. These studies must

balance the potential problems of equity, growing water stress due to population growth and

climate change, and cost recovery. Another interesting extension mentioned in this study is to

analyze the impact of canal location on water efficiency and yields. Finally, a study that

explores the behavioral aspects of switching from a zero price-level to a non-zero price level, and

its effects on quantity demanded for irrigation water, will be useful for future studies on the

impact of volumetric pricing on farmer incomes.

  41  

Appendix

Table 1: Summary statistics of farmer survey data collected by N.S. Praveen Kumar (IWMI) in the Krishna River Basin; number of observations = 240  

Variable Mean Std. Dev. Min Max Unit Description

yield 29.08 2.26 24 32 bag 1 bag=75 kg tot_water 24.50 19.4 3.560 109.0 1000 cu.m. total annual water use per farm tot_fert 2919 465 1750 3895 Rs cost of fertilizer utilized

tot_labor 6100 856 4000 8500 Rs cost of labor utilized tot_pest 937.9 325 290.0 1900 Rs cost of pesticides utilized

tot_other 6062 728 4132 6930 Rs cost of other inputs (seeds, machine use, etc.) age 41.22 11.2 20 70 year age of farmer

education 7.748 3.45 0 15 year education of farmer owned 4.298 3.33 1 19 acre acres of land owned by farmer

Derivation of elasticity of supply of fertilizer, and input efficiency levels of fertilizer:

𝜁!" =!"!!"!

∗ !!!!= !"#!!

!"#!!= 𝛽! + 𝛽!"𝑙𝑛𝑥!"

!!!!!! + 2𝛽!!𝑙𝑛𝑓!  ;    𝑓 = 𝑓𝑒𝑟𝑡𝑖𝑙𝑖𝑧𝑒𝑟 (13)

𝐼𝐸!! = exp!!!"± !!"

! !!!!!!!

!!!!   ; 𝑖 = 1,… , 𝐼!!  𝑓𝑎𝑟𝑚𝑒𝑟 (14)

  42  

Table 2: Coefficient estimates of potential stochastic production frontier models6  VARIABLES (1) (2) (3) (4) labor (l) -0.0926* 5.356** -5.770 -6.202 (0.0473) (2.428) (3.609) (5.896) fertilizer (f) 0.0121 -4.393 -6.229 -5.143 (0.0243) (2.735) (3.884) (4.466) pesticide (p) -0.0459*** 0.150 2.968** 2.811 (0.0123) (0.281) (1.372) (1.744) water (w) 0.00913 0.261 2.172 1.772* (0.00624) (0.186) (2.034) (1.031) other (o) -0.318*** -0.317*** -7.584*** -6.816** (0.0633) (0.0635) (2.792) (2.853) labor*fertilizer 0.292 0.271 (0.204) (0.222) labor*pesticide -0.123 -0.0600 (0.0897) (0.0898) labor*other 0.708*** 0.653** (0.222) (0.279) labor*water -0.114 -0.0890 (0.107) (0.0675) fertilizer*other 0.555 0.364* (0.371) (0.215) fertilizer*water -0.0678** -0.0579*** (0.0276) (0.0224) pesticide*other -0.260** -0.190 (0.130) (0.134) pesticide*water 0.0202 0.0129 (0.0133) (0.0142) other*water -0.0895 -0.0413 (0.114) (0.0576) labor2 -0.314** 0.0123 (0.141) (0.238) fertilizer2 0.277 0.0370 (0.172) (0.165) pesticide2 -0.0138 -0.0645** (0.0210) (0.0266) water2 -0.00764 -0.00779* (0.00552) (0.00417) Constant 7.076*** -1.768 59.45 57.42 (0.882) (15.26) (40.09) (39.63) 𝜎!! -6.572*** -8.098*** -9.744*** -10.81*** (0.687) (0.748) (1.832) (1.088) 𝜎!! -4.762*** -4.358*** -4.262*** -4.256*** (0.412) (0.149) (0.138) (0.0995) Observations 235

*** p<0.01, ** p<0.05, * p<0.1                                                                                                                6  All terms are logged values; interaction terms are logged individually before interacting. The interaction term between log(f) and log(p) was not included due to convergence issues when running the model in Stata.

  43  

Table 3: Distribution of output-oriented technical efficiency (TE) levels across all farmers Percentiles TE

Summary Statistics

1% 0.7737

Mean 0.9103 5% 0.7985

Std. Dev. 0.0626

10% 0.8167

Skewness -0.3772 25% 0.8697

Kurtosis 2.107

50% 0.9141

75% 0.9668

90% 0.9890 95% 0.9937 99% 0.9954

Graph 1: Histogram of TE levels of n=240 farmers in the Krishna River Basin.

Table 4: Distribution of input-oriented efficiency (IE) levels of irrigation water across all farmers Percentiles IE (water)

Summary Statistics

1% 0.0046

Mean 0.1692 5% 0.0092

Std. Dev. 0.1392

10% 0.0192

Skewness 0.8131 25% 0.0527

Kurtosis 2.820

50% 0.1296

75% 0.2749

90% 0.3812 95% 0.4340 99% 0.5173

0

0

010

10

1020

20

2030

30

3040

40

40Density

Dens

ity

Density.92

.92

.92.94

.94

.94.96

.96

.96.98

.98

.98Technical Efficiency (TE)

Technical Efficiency (TE)

Technical Efficiency (TE)

  44  

Graph 2: Histogram of water IE levels of n=240 farmers in the Krishna River Basin

Table 5: Distribution of input-oriented efficiency (IE) levels of fertilizer across all farmers Percentiles IE (fertilizer)

Summary Statistics

1% 0.9889

Mean 0.9946 5% 0.9908

Std. Dev. 0.0019

10% 0.9919

Skewness -0.9470 25% 0.9935

Kurtosis 3.571

50% 0.9949

75% 0.9961

90% 0.9967 95% 0.9969 99% 0.9974

Graph 3: Histogram of fertilizer IE levels of n=240 farmers in the Krishna River Basin

0

0

01

1

12

2

23

3

34

4

45

5

5Density

Dens

ity

Density0

0

0.2

.2

.2.4

.4

.4.6

.6

.6Input Efficiency Levels for Water (IE_water)

Input Efficiency Levels for Water (IE_water)

Input Efficiency Levels for Water (IE_water)

0

0

050

50

50100

100

100150

150

150200

200

200250

250

250Density

Dens

ity

Density.988

.988

.988.99

.99

.99.992

.992

.992.994

.994

.994.996

.996

.996.998

.998

.998Input Efficiency Levels of Fertilizer (IE_fert)

Input Efficiency Levels of Fertilizer (IE_fert)

Input Efficiency Levels of Fertilizer (IE_fert)

  45  

Table 6: Distribution of maximum quantity of potential water savings across all farmers Percentiles Water Savings (100 m3)

Summary Statistics (1000 m3)

1% 2.55

Mean 21.50 5% 3.81

Std. Dev. 19.20

10% 4.50

Skewness 1.97 25% 8.75

Kurtosis 7.30

50% 15.90

75% 28.00

90% 44.50 95% 62.20 99% 90.60

Table 7: Regression results of IE_water on catchment area dummy variables Variables IE of Water head 0.0183 (0.0221) end 0.0520** (0.0222) Constant 0.145*** (0.0158) Observations 235 R-squared 0.024

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.  

Table 8: Potential price-quantity scheme for irrigation water, with resulting water savings percentages and costs

(per acre) Price (Rs/m3) Quantity (m3/acre) Water Savings (%) Total Cost (Rs/acre)

0.08 5447.87 5.78% 435.83 0.09 5176.21 11.22% 465.86 0.10 4944.70 15.84% 494.47 0.11 4744.20 19.85% 521.86 0.12 4568.27 23.37% 548.19 0.13 4412.19 26.49% 573.59 0.14 4272.45 29.28% 598.14 0.15 4146.33 31.80% 621.95 0.16 4031.73 34.09% 645.08 0.17 3926.96 36.19% 667.58 0.18 3830.68 38.11% 689.52 0.19 3741.78 39.89% 710.94 0.20 3659.35 41.54% 731.87 0.21 3582.63 43.07% 752.35 0.22 3510.97 44.50% 772.41 0.23 3443.84 45.85% 792.08 0.24 3380.77 47.11% 811.39 0.25 3321.36 48.29% 830.34 0.26 3265.27 49.42% 848.97 0.27 3212.19 50.48% 867.29

  46  

Graph 4: Hypothetical constant elasticity demand curve for irrigation water in the Krishna basin (elasticity = -1)

Table 9: Potential price-quantity scheme for irrigation water, with resulting water savings percentages and costs

(per acre), using the minimum cost-quantity ratio. Price (Rs/m3) Quantity (m3/acre) Water Savings (%) Total Cost (Rs/acre)

0.05 5700.50 0.73% 285.02 0.06 5266.53 9.41% 315.99 0.07 4925.50 16.23% 344.78 0.08 4647.98 21.77% 371.84 0.09 4416.20 26.41% 397.46 0.1 4218.68 30.36% 421.87

0.11 4047.63 33.78% 445.24 0.12 3897.53 36.78% 467.70 0.13 3764.37 39.44% 489.37 0.14 3645.14 41.82% 510.32 0.15 3537.54 43.97% 530.63 0.16 3439.76 45.93% 550.36 0.17 3350.38 47.71% 569.56 0.18 3268.24 49.36% 588.28 0.19 3192.39 50.87% 606.55

0

0

0.2

.2

.2.4

.4

.4.6

.6

.6.8

.8

.81

1

1Price (Rs/meters cubed)

Price

(Rs/

met

ers

cube

d)

Price (Rs/meters cubed)0

0

050000

50000

50000100000

100000

100000150000

150000

150000Quantity (meters cubed/acre)

Quantity (meters cubed/acre)

Quantity (meters cubed/acre)

  47  

Table 10: Potential price-quantity scheme for irrigation water, with resulting water savings percentages and costs (per acre), using price elasticity -0.8

Price (Rs/m3) Quantity (m3/acre) Water Savings (%) Total Cost (Rs/acre) 0.08 5497.49 4.79% 439.80 0.10 5087.38 12.99% 508.74 0.12 4775.11 19.23% 573.01 0.14 4526.10 24.21% 633.65 0.16 4320.91 28.31% 691.35 0.18 4147.66 31.78% 746.58 0.20 3998.58 34.76% 799.72 0.22 3868.34 37.36% 851.03 0.24 3753.14 39.66% 900.75 0.26 3650.21 41.72% 949.05 0.28 3557.42 43.58% 996.08 0.30 3473.16 45.26% 1041.95 0.32 3396.15 46.80% 1086.77 0.34 3325.37 48.21% 1130.62 0.36 3259.98 49.52% 1173.59 0.38 3199.31 50.73% 1215.74

Graph 5: Hypothetical linear demand curve for irrigation water in the Krishna basin, using elasticity and price

values determined by Somanathan and Ravindranath.

0

0

0.2

.2

.2.4

.4

.4.6

.6

.6Price (Rs/meters cubed)

Price

(Rs/

met

ers

cube

d)

Price (Rs/meters cubed)0

0

02000

2000

20004000

4000

40006000

6000

6000Quantity (meters cubed per acre)

Quantity (meters cubed per acre)

Quantity (meters cubed per acre)

  48  

Table 10: Potential price-quantity scheme for irrigation water, with resulting water savings percentages and costs (per acre)

Price (Rs/m3) Quantity (m3/acre) Water Savings (%) Total Cost (Rs/acre) Elasticity of Demand 0.00 5737.26 0.00% 0.00 0.00 0.05 5259.15 9.56% 262.96 0.09 0.10 4781.05 19.12% 478.10 0.20 0.15 4302.94 28.67% 645.44 0.33 0.20 3824.84 38.23% 764.97 0.50 0.25 3346.73 47.79% 836.68 0.71 0.30 2868.63 57.35% 860.59 1.00 0.35 2390.52 66.91% 836.68 1.40 0.40 1912.42 76.47% 764.97 2.00 0.45 1434.31 86.02% 645.44 3.00 0.50 956.21 95.58% 478.10 5.00

  49  

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