Reimagining cost recovery in Pakistan's irrigation system through willingness-to-pay estimates for irrigation water from a discrete choice experiment.

It is widely argued that farmers are unwilling to pay adequate fees for surface water irrigation to recover the costs associated with maintenance and improvement of delivery systems. In this paper, we use a discrete choice experiment to study farmer preferences for irrigation characteristics along two branch canals in Punjab Province in eastern Pakistan. We find that farmers are generally willing to pay well in excess of current surface water irrigation costs for increased surface water reliability and that the amount that farmers are willing to pay is an increasing function of their existing surface water supply as well as location along the main canal branch. This explicit translation of implicit willingness-to-pay (WTP) for water (via expenditure on groundwater pumping) to WTP for reliable surface water demonstrates the potential for greatly enhanced cost recovery in the Indus Basin Irrigation System via appropriate setting of water user fees, driven by the higher WTP of those currently receiving reliable supplies.

Farmers are typically willing to pay more for canal water than is assessed

Those farmers with most reliable supply are willing to pay the most

There is potential to develop self-reinforcing cost recovery in the Indus

1. Introduction

The network of millions of kilometers of channels that distribute the Indus River across the floodplain of Pakistan's Punjab and Sindh provinces is an engineering marvel, but one that has suffered from more than a century of wear and depreciation and decades of a policy of “build-neglect-rebuild” [World Bank, 2010]. Cost recovery for irrigation system maintenance is low, with the assessed water use charges or abiana themselves not reflecting the cost of service provision (on the order of 150 Rs./acre, approximately USD1.5/acre, depending on crop and season) [Khan, 2009] and with low levels of compliance [Briscoe and Qamar, 2005]. There is an ongoing process of irrigation management reform in Pakistan that, among other things, places responsibility for collection of abiana in the hands of local institutions [Bell et al., 2013]; establishment of these new institutions led in many cases to short-term increases in collection of abiana, but compliance typically declined again after only a few seasons [Memon, 2006; Asrar-Ulhaq, 2010]. These results suggest that farmers might be willing to pay for their water—but only if they can perceive a return to their investment. Given the slow (and still overall scant) adoption of the irrigation reform in Pakistan relative to the sheer size of the irrigation system, it is unlikely that farmers perceived much change in the wake of these short-term bumps in cost recovery.

The issue of poor cost recovery in irrigation systems is not unique to Pakistan. Neighboring states of India, Nepal, and Kazakhstan share similarly low water use fees, amounting to fractions of a US penny for every cubic meter received [Cornish et al., 2004; Ray, 2011], though across these countries, the investment in pumping costs (electric or diesel) to run shallow or deep tubewells is an indicator of an untapped capacity to afford payment [Cornish et al., 2004; Water Sector Task Force(WSTF), 2012]. Nor is the problem unique to the region or even to low or middle-income countries; among OECD countries, only Austria, Denmark, Finland, New Zealand, Sweden, and the UK can boast 100% cost recovery of operation, maintenance, and capital costs [OECD, 2013]. The issue is often political (as in the case of Brazil, where charges of $0.04/m3 were deemed to pose an unacceptably high production cost to farmers and capped [Formiga-Johnsson et al., 2006]), and politics is certainly a key factor in the case of Pakistan as well. Abiana rates were sufficient to capture operation and maintenance costs until the 1970s, at which time the Zulfiqar Ali Bhutto government declined to raise them, in what Khan [2009] describes as a “presumably…populist measure.” This decision not to increase the abiana rates set Pakistan within a heavy subsidization policy regime that continues to the present, and which provinces in Pakistan have taken only minor steps in the intervening years to address. In 2003, to deal with the problem of low recovery and underassessment of abiana, the government of Punjab introduced flat abiana rates (Rs. 85 for the Kharif (monsoon) season and Rs. 50 for the Rabi (dry) season per acre of cropped land). The government of Khyber Pakhtunkhwa (KPK) followed suit in 2008 with a flat rate of Rs. 150 per acre for food crops and Rs. 200 per acre for nonfood crops. These rates were revised in 2009 to Rs. 200 and Rs. 250, respectively. Currently, the abiana collected is sufficient for covering only about 1/4 of operations and maintenance costs of the irrigation system on average [Planning Commission Pakistan, 2012]; the costs of system improvements or investments can obviously not be covered from the same, as long as the heavy subsidization policy of the provincial governments remains in place.

Endemic as it may be across the world, the issue of cost recovery is particularly troubling for Pakistan, where further investments in new storage and infrastructure are stymied by interprovincial and interclass politics [Briscoe and Qamar, 2005; Kugelman, 2009], existing storage capacity is less than 150 m3 [Qureshi, 2011] (or 30 days [Kamal, 2009]) of water per capita, cropping intensities are often more than double the design intensities of the system [Meinzen-Dick, 1996], and the now-decaying infrastructure is fraught with issues of unreliable supply and waterlogging [Raza et al., 2009; Ul Hassan, 2009]. Identifying a means to sustainably maintain what is now the world's largest contiguous gravity-fed irrigation system [Khan, 2009] is of critical importance to maintaining Pakistan's agricultural economy, and we use the current study to challenge the notion that Pakistani farmers cannot or will not pay more for their water.

In this study, we present the results of a discrete choice experiment for irrigation water supply over the kharif (monsoon) season, undertaken in two sites in the Bahawalnagar Canal circle of Punjab Province, Pakistan, between January and June 2013. We use these results to demonstrate how willingness-to-pay for improved water reliability (i.e., an abiana payment) is typically much higher than current rates that range from about 85 to 200 Rs./acre, depending on season and crop [Planning Commission Pakistan, 2012], and is a multidimensional function of, among other possible factors, current surface water reliability, the salinity of the alternative groundwater, and the location of the farmers' distributary along the main branch, from head to tail. Finally, we draw on a key property of our observed results to suggest how a self-reinforcing, self-sustaining system of cost recovery might be designed for the system and outline some of the necessary empirical research to begin to bound and structure such a system. Throughout this study, we use the term “reliability” to mean the likelihood that water is received during an irrigation turn (see section 3 for measurement detail).

2. Study Area

To study farmer demand for improved surface water reliability, we utilize discrete choice experiments undertaken as part of a larger survey to collect information on current farm irrigation conditions conducted from January to June 2013. We focused our study on an irrigated area in Punjab Province that provides contrasts in the level of groundwater salinity, and thus the extent to which groundwater is chosen as a supplement to canal water availability. The Fordwah Eastern Sadiqia (FES) area is located near Bahawalnagar about 300 km south of Lahore in the Southeast corner of the Punjab (Figure 1). The culturable command area of the FES system is more than 300,000 ha. The climate of this area is (semi) arid with annual evaporation (∼2000 mm) far greater than annual rainfall (∼250 mm).

Figure 1

The Eastern Sadiqia irrigation system.

Fordwah and Eastern Sadiqia are the two canals that emerge from the Sutlej headworks. The Eastern Sadiqia Canal further divides into the Hakra branch canal and the Malik branch. The sites for the study were along the Hakra and Fordwah branch canals. Our high-salinity site was a region comprised 15 out of the 17 distributaries that originate from the Hakra branch canal. Groundwater in this canal command area is saline with a few pockets of useable water in the head reaches. The water table in the project area ranges from less than 1 m to about 25 m.

The low-salinity site was a region comprised 26 out of the 38 distributaries in the Fordwah canal command area. A clear indicator of good conditions for growing is the cultivation of rice in this area (as opposed to only cotton). Farmers with sufficient access typically supplement the supplies of surface water with low-salinity groundwater to cultivate rice. At present, more than one quarter of the canal command area is under rice cultivation. Irrigation water characteristics differ significantly across these two sites, with farmers in the Fordwah site typically enjoying higher-quality groundwater and using greater amounts of it, while Hakra farmers have access to more reliable surface water supply (Figure 2).

Figure 2

Frequency of reported irrigation supply attributes from study participants in Hakra and Fordwah sites. Average seasonal water costs per acre were Rs. 4598 in Hakra and Rs. 12,428 in Fordwah. Average groundwater share was 41.2% in Hakra and 80.8% in Fordwah. Average surface water reliability was 52.9% in Hakra and 43.5% in Fordwah.

2. 1. Cropping Patterns Across Study Sites

A portion of our questionnaire obtained data on participants' kharif season crops. For the high-salinity site in Hakra, cotton cropping was the dominant land use across farms with all levels of reliability in canal water receipt (Figure 3). Cropping in the low-salinity Fordwah site is more diversified, with three dominant crops of cotton, rice, and sugarcane. Rice cultivation dominates among respondents with comparatively high surface water reliability, giving way to cotton and to sugarcane among respondents reporting lower surface water reliability. Classifying participants by the main crop planted on their land, these four groups cover 94% (n = 561) of our sample (Table1) and provide some additional context for these cropping patterns. Spending on groundwater pumping in Hakra's cotton crop (where salinity is much higher) is lower overall compared to Fordwah's cotton crop, and yields are lower and more variable. At the Fordwah site, farmers focused on rice cropping spend the least on groundwater on average, with cotton farmers spending a greater amount and sugarcane farmers spending the most on irrigation water. Our questionnaire did not collect data on income or assets, but these data on yields and spending suggest a pattern of less wealthy farmers split among cotton and rice as a function of canal water reliability, and wealthier sugarcane farmers relying much more heavily on groundwater as an exclusive source for sugarcane cultivation.

Figure 3

Distribution of cropland by site and reliability of surface water. Estimates based on reported planted area by survey respondents. Width of bar is proportional to the number of respondents binned in current reliability class. Class i contains all respondents reporting reliability greater than i−1, up to and equal to i.

Table 1

Irrigation Characteristics Across Sample Sites by Primary Kharif Cropa

Group Code	Site	Primary Crop	Number of Farmers	Irrigation Costs per Acre (Rs.)	Yield (kg/acre)	CV of Yields
HC	Hakra	Cotton	278	4495 (4487)	828 (892)	1.077
FC	Fordwah	Cotton	67	12,481 (9059)	1015 (586)	0.577
FR	Fordwah	Rice	163	11,231 (11,836)	1488 (1292)	0.868
FS	Fordwah	Sugarcane	53	17,780 (13,639)	20,945 (9977)	0.476

Note: standard deviations are presented in parentheses. Total number of farmers reported represents 94% of overall sample. Remainder (30) were either excluded from analysis or do not focus on these three crops.

3. Empirical Methodology

To study preferences for improvements in surface water reliability, we employ stated choice modeling techniques. Choice modeling has become an increasingly important mode of studying economic behavior and demand patterns since this methodology allows the researcher to estimate marginal values for various attributes embodied in different goods or services, including nonmarket goods and services for which such marginal valuations are difficult or impossible to measure by examining revealed preferences. Choice experiments represent an alternative to analysis of revealed preference or contingent valuation exercises and avoid the weaknesses or pitfalls associated with both. While well-specified contingent valuation analysis can provide measures consistent with standard welfare economics, they can only compute welfare measures for unidimensional changes. Because choice experiments elicit valuations for a series of attributes bundled into a good, the results of such experiments can be used to estimate welfare changes for multidimensional changes [Hanley et al., 2001].

Choice experiments represent an empirical application and extension of the theoretical and conceptual work of Lancaster [1966], which posited that preference orderings rank different goods indirectly according to the characteristics or attributes that they possess. When faced with choices over heterogeneous alternatives, it is assumed the rational consumer will choose the vector (i.e., the bundle of attributes embodied in the good) that maximizes her (perceived) utility subject to a budget constraint. By observing consumers' choices we can make inferences regarding the marginal utility of one trait relative to the others. An advantage of choice experiments is that they can be designed to closely simulate real-world purchasing decisions. In these experimental settings, respondents are asked to choose among a series of alternative bundles of attributes. As a note, utility maximization is only one of a number of possible paradigms by which we can classify farmer behavior. Other paradigms include regret minimization, lexicographic preferences, etc. In what follows, we will follow the assumption of Thurstone [1927] and McFadden [1974] and assume that the process of utility maximization necessarily incorporates errors due to imperfect perception and optimization, as well as the inability of the econometrician to exactly measure all of the relevant variables [Maddala, 1983]. The utility function will, therefore, be a random function with both a deterministic component and a stochastic component.

Discrete choice experiments are not without shortcomings. Since choice experiments are hypothetical exercises, they are susceptible to hypothetical bias such that valuations may be inflated due to the lack of financial recourse for stated choices. Biases may be increasing in choice complexity, among less educated populations, or in situations in which the hypothetical choice is vastly different from real-world purchasing decisions that participants face. In order to reduce hypothetical bias, the choice experiment in this study was designed to closely simulate real-world irrigation scenarios that farmers in Pakistan face, and illustrations were used to increase comprehension and reduce overall complexity of choice tasks (see section 3.2). In addition, many of the questions preceding the actual choice experiment grounded farmers within their existing irrigation scenario to provide a reference point to which evaluations of the options in the discrete choice experiment could be anchored (Supplement A2 in supporting information).

3. 1. Utility Model Derivation

Suppose that individual faces alternatives contained in choice set during occasion. We can define an underlying latent variable that denotes the value function associated with individual choosing option during occasion. For a fixed budget constraint, random utility maximization implies individual will choose alternative so long as. The researcher does not directly observe, but instead directly observes the choice, denoted, where if and 0 otherwise.

We can write individual's latent value function as where is a vector of attributes for theth alternative, is a vector of taste parameters (i.e., a vector of weights mapping attribute levels into utility), and is a stochastic component of utility that is independent and identically distributed across individuals and alternative choices and takes a known distribution. This stochastic component of utility captures unobserved variations in tastes as well as errors in consumer's perceptions and optimization.

The probability of observing (i.e., the consumer chooses option given all other alternatives in) can be written as

We assume that the random component of utility follows a Gumbel (extreme value type I) distribution. Then, under the assumption that are identically and independently distributed, we can write our expression for the probability of observing alternative chosen over all other alternatives conditional upon the observed levels of the attribute vector for all alternatives in the choice set as which is the basic conditional Logit model and can be estimated using maximum likelihood.

Because farmers are heterogeneous, their preferences for surface water reliability may also be heterogeneous. Within the discrete choice literature, there are several ways for accounting for preference heterogeneity. A common method of evaluating preference heterogeneity is estimation of random parameters logit (RPL) models, also called mixed logit. The RPL is regarded as a highly flexible model that can approximate any random utility model and relaxes the limitations of the traditional multinomial logit by allowing random taste variation within a sample according to a specified distribution [McFadden and Train, 2000]. Following Train [2003], the probability that individual chooses alternative from the choice set in situation is given by where is a vector of taste parameters specific to individual, the matrix defines the parameters characterizing the distribution of the random parameters, the family (e.g., normal, lognormal, triangular, etc.) of which is specified by the researcher. For our purposes, we allow the coefficients corresponding to all attributes except price to vary normally. While the assumption of a fixed price coefficient artificially eliminates the possibility of heterogeneous preferences over irrigation costs, it is nevertheless a common assumption made in many random parameter logit applications. One reason for doing so is that allowing for random variation in price coefficients can result in positive marginal utility of price for some individuals if the range of the specified distribution is infinite or spans both positive and negative values. A positive marginal utility of irrigation cost would violate the standard axioms of downward sloping demand curves. Specifying a fixed price coefficient yields the convenient and intuitive result that the distribution of the derived attribute WTP is the same as the distribution of the random attribute coefficient, with mean and variance scaled by the fixed price coefficient [Revelt and Train, 1998; Hensher et al., 2005; Ubilava and Foster, 2009].

We also allow for the random parameters to be freely correlated, since there is an explicit correlation between, e.g., surface water reliability and groundwater share. In this case, the individual-specific taste parameter for theth attribute can be characterized as, where is the population average coefficient, captures individual taste variation, and is a lower triangular Cholesky decomposition matrix, where the variance-covariance matrix is computed as.

Given the utilitarian interpretation of our econometric specification, thevector of parameters defining tastes and preferences over the attributes can be interpreted as marginal utilities, and the ratio of two such marginal utilities is simply the marginal rate of substitution of one for the other. If one of the included attributes (say, theth attribute) is the price of the alternative, then can be interpreted as the marginal utility of price (or cost), the negative of which is the marginal utility of income (or money). The marginal rate of substitution of money for each of the corresponding attributes—that is, willingness-to-pay (WTP)—can be computed as

Clearly if there are relevant interaction terms, equation (5) must be modified to account for them. The marginal utility (disutility) for favorable (unfavorable) attributes will be positive (negative), indicating that the farmer is willing (unwilling) to substitute an increase in an attribute's expression for money.

3. 2. Choice Experiment Design

In our choice experiment, each choice task contains two alternatives with randomly varying attribute levels representing hypothetical (but plausible) bundles of irrigation characteristics, plus an option to retain their status quo method of irrigation. The attributes included in the two varying alternatives included groundwater salinity (zero, low, or high), surface water reliability (25, 50, 75, or 100% reliable), share of total irrigation water derived from groundwater sources (0, 20, 40, 60, or 80%), and total irrigation cost (4,000, 8,000, 12,000, 16,000, or 20,000 Rs.; Table2). Reliability, defined as the likelihood of receiving allocated water during an irrigation turn, is measured as the number of turns for which the complete water allocation was received, plus 0.5 times the number of turns for which a partial allocation was received, all divided by the total number of turns. Cost of irrigation is per season and includes both pumping cost of groundwater and surface water (with costs dominated by groundwater). This design was reached following initial focus-group discussions with farmers in the region regarding the criteria of principal relevance to them in thinking about irrigation water supply. One issue to note is the difficulty in disambiguating volumetric water receipt from reliability of surface water receipt. Specifying volumetric water receipt as an attribute of the supply interferes with the reliability attribute, while not specifying it leaves water volume implicit. Given the primary focus on reliability in our study, we opted to frame the choice as one made on irrigation water supply, for which the surface water component may be less than completely reliable (Supplement A2 in supporting information). Thus, the actual supply received is partially implicit in the surface water reliability; implications from this are discussed below, in the context of our results.

Table 2

Irrigation Attributes Included in Discrete Choice Experiment

Attribute	Levels Included in Hypothetical Alternatives
Groundwater salinity	Zero
	Low
	High
Surface water reliability (percent chance of receiving surface water during your turn)	25%
	50%
	75%
	100%
Share of total irrigation derived from groundwater sources (%)	0%
	20%
	40%
	60%
	80%
	100%
Total irrigation costs (Rs.)	4000
	8000
	12,000
	16,000
	20,000

In total, we employed 30 different choice sets, blocked in groups of 10, with each block being administered to one third of the overall sample in each of the two sites (Supplement A1 in supporting information). Each interview with a respondent began with a short household survey (Supplement A2 in supporting information) in which the status quo option was developed, and the respondent's irrigation conditions framed in the same terms as those of the choice experiment. Specifically, participants were asked to consider irrigation water supply over the kharif season for their whole farm (or if the farm is fed by more than one irrigation outlet, then to consider the outlet feeding the largest or most productive part of the farm). Participants were asked to estimate the size of the farm, the number of turns for which surface water was received, the amount of groundwater pumped, costs for fees or pumping, and the quality of their groundwater; from these quantities, enumerators assisted participants in framing their own “status quo” irrigation supply by calculating the attributes of surface water reliability, groundwater share, groundwater salinity, and total irrigation supply cost, on a per-area basis (Supplement 2 in supporting information). For each choice set, respondents were provided with a visual cue (Figure 4), with the results of their status quo calculation held alongside.

Figure 4

Example of illustrated choice card.

There is a vast literature that has explored the many issues pertinent to experimental design [e.g., Zwerina et al., 1996; Louviere et al., 2000; Ferrini and Scarpa, 2007; Kuhfeld, 2010]. While there are various criteria useful for judging experimental designs [e.g., Scarpa and Rose, 2008], we followed the conventional approach and specified a D-optimal experiment design with null priors. D-optimality implies minimization of the design's D-error, which is computed as the weighted determinant of the variance-covariance matrix of the design, where the weight is an exponential weight equal to the inverse of the number of parameters to be estimated.

A pretest was conducted in the Hakra site, but given the possibility that the coefficients for utility on groundwater may have differed across the two sites (i.e., been negative where salinity was high but positive where salinity was low), we decided not to perform any Bayesian updating of the design following the pretest—a decision that we acknowledge reduces the efficiency of our design compared to one in which perfect information is utilized. We included an additional subroutine within the design program to exclude solutions containing any choice sets in which one of the options clearly dominated the other. Initially, our experimental design only considered main effects, though we wanted to consider interaction effects in the analysis. Although it is often suggested that researchers should generally incorporate a priori assumptions about such interactions into the design of their experiment [e.g., Louviere et al., 2000], Lusk and Norwood [2005] have suggested that, so long as there are sufficient degrees of freedom, a main-effects-only design can reasonably be used to estimate nonlinear utility functions (though it should be noted that critics of their study claim their argument on the power of sample size to over come design shortcomings like a misspecified utility function are overstated). Given that each of the 591 respondents was asked to complete 10 choice sets, we have ample degrees of freedom to estimate higher-order effects. Additionally, studies dating back to Dawes and Corrigan [1974] have shown that 70–90% of the variation in the data can be attributed to main effects, so designing a choice experiment based on the prior assumption of a simple linear utility function may not be unrealistic. Furthermore, it should be noted that our choice experiment design accounted for separate parameters for each of the discrete levels for each of the attributes, where is the total number of levels that attribute can take. By incorporating household-specific responses in the status quo alternative, these variables largely became continuous, so we ultimately estimated only a single parameter for each attribute. Therefore, even our initial experimental design incorporated enough parameters for us to efficiently estimate both main and interaction effects.

4. Results

4. 1 Utility Model Estimation

The results of estimating our model of irrigation demand by equation (4) are shown in Table3. The first two sets of results show estimates of marginal utility under a main-effects-only specification, while the second two sets of results show estimates of marginal utility incorporating a series of interaction effects. Specifically, we allow for the groundwater share to interact with salinity levels and surface water reliability. For both of these sets, we report estimates assuming independent random coefficients and then relax this assumption and allow for freely correlated random coefficients. The reported estimates for the random parameters represent the sample means of the posterior individual mean coefficients for the random marginal utility coefficients, which provides information on the average absolute level of marginal utility attributable to a particular attribute. It should be noted that we do not directly estimate, that is, the vector of taste parameters for each individual, but rather we estimate, which reflects the best estimate of the individual's taste parameter conditional upon observed choices. The estimates for the distribution parameters (i.e., the estimated standard deviations for the random parameters) represent the sample means of the posterior individual standard deviations and provide information on the degree of heterogeneity in tastes and preferences for these attributes.

Table 3

Random Parameter Logit Estimates of Irrigation Demanda

	Main Effects Only				Main and Interaction Effects
	Uncorrelated Random Coefficients		Correlated Random Coefficients		Uncorrelated Random Coefficients		Correlated Random Coefficients
	Estimate	|Asy. Z|	Estimate	|Asy. Z|	Estimate	|Asy. Z|	Estimate	|Asy. Z|
Random Parameters in Utility Function
Zero salinity	3.0329	21.42	3.3687	20.06	2.5687	14.46	3.1327	14.95
Low salinity	1.4615	15.31	1.9132	15.46	1.0395	6.65	1.5764	8.79
Groundwater share	−0.0115	9.50	−0.0111	8.76	0.0097	2.49	0.0133	3.27
Surface water reliability	0.0369	24.45	0.0394	23.24	0.0576	23.17	0.0496	22.56
Nonrandom Parameters in Utility Function
Irrigation cost	−0.1154	15.96	−0.1185	15.90	−0.1292	17.17	−0.1317	17.13
Zero salinity x Groundwater share					0.0101	3.07	0.0053	1.51
Low salinity x Groundwater share					0.0803	2.24	0.0052	1.38
Surface water reliability x Groundwater share					−0.0005	11.87	−0.0005	11.70
Distribution of Random Parameters
SD(Zero salinity)	1.9178	14.84	2.55038	14.81	1.9023	14.28	2.5650	14.63
SD(Low salinity)	0.9718	9.62	1.43306	11.93	0.9424	9.33	1.4234	11.61
SD(Groundwater share)	0.0199	14.74	0.01999	12.40	0.0200	13.76	0.0202	13.15
SD(Surface water reliability)	0.0188	11.87	0.02015	6.44	0.0195	11.99	0.0214	11.70
Number of observations	5910		5910		5910		5910
Number of parameters	9		15		12		18
Log-likelihood	−4209.59		−4118.82		−4078.37		−4008.98
Pseudo R2	0.3512		0.3650		0.3712		0.3817
AIC	8437.19		8267.64		8180.75		8053.96
BIC	4248.67		4183.95		4130.48		4087.14

Note: presented models were estimated using maximum simulated likelihood using NLOGIT 5.0.

In the main-effects-only regressions, we see that most of the random coefficients have positive signs, while an increasing share of irrigation from groundwater sources reduces farmer utility. When we move from the main-effects-only model to one incorporating interaction effects, we see that the random main effect of groundwater share is no longer negative, but the interaction of this term with surface water reliability is negative. This implies that, other things equal, the marginal utility of groundwater share declines as surface water becomes more reliable. So, as improvements are made in surface water delivery infrastructure and surface water becomes more reliable, farmers will utilize more of this and extract less groundwater. The zero-salinity and low-salinity attributes are treated as binary variables in the choice experiment analysis, so the reported coefficients represent the marginal utility associated with moving from highly saline groundwater supply to one with zero or low salinity, respectively. Not surprisingly, there is much greater utility gained from moving from high to zero salinity groundwater supplies than from moving from high to low salinity groundwater supplies.

Based on various model selection criteria, including log likelihood, Akaike and Bayesian Information Criteria (AIC and BIC, respectively), and McFadden's Pseudo R2 (adjusted), the best model incorporates interaction effects as well as correlated random parameters. In what follows, we rely on these estimates to provide the basis for our ongoing analysis.

4. 2. Confounding Effects

Table4 reports the covariance matrix and Cholesky decomposition () matrix for the random coefficients in our preferred model accounting for main and interaction effects as well as allowing for freely correlated random coefficients. This table highlights the potential confounding of effects if the correlation between random parameters is not accounted for. The coefficients for zero and low salinity exhibit a very large negative correlation (−0.8235), suggesting that individuals that have a high marginal utility from moving from high to zero salinity tend to have significantly lower marginal utility for improvements from high to low salinity, and vice versa. This suggests that most farmers in the sample likely view these two characteristics as substitutes. Improvements in salinity, whether the ultimate result is no salinity or only low salinity, are considerable improvements over highly saline groundwater supplies. Failing to account for this negative correlation, however, understates the average marginal utility associated with the first-order effects of each of these two attributes. This is reflected in the increased coefficient estimates for these attributes in the far right set of estimates in Table3.

Table 4

Covariance Matrix and Cholesky Decomposition for Random Coefficientsa

	Zero Salinity	Low Salinity	Groundwater Share	Surface Water Reliability
Covariance Matrix
Zero salinity	6.5791 (14.63)
Low salinity	−2.9766 (11.75)	2.0261 (11.61)
Groundwater share	−0.0163 (3.83)	0.0052 (1.81)	0.0004 (13.15)
Surface water reliability	−0.0193 (3.54)	0.0067 (1.76)	0.0002 (2.64)	0.0004 (11.70)
Cholesky Decomposition Matrix (Γ)
Zero salinity	2.5650 (14.63)
Low salinity	−1.1605 (8.59)	0.8242 (9.12)
Groundwater share	−0.0064 (3.92)	−0.0026 (0.97)	0.0190 (12.05)
Surface water reliability	−0.0075 (3.50)	−0.0025 (0.83)	0.0059 (2.31)	0.0189 (9.72)

Note: absolute value of asymptotic Z value in parentheses.

The Cholesky decomposition matrix provides information about the degree of variation directly attributable to the different attributes. The first element is simply the standard deviation for the random coefficient associated with zero salinity. Subsequent diagonal elements represent the amount of variance attributable to random coefficients once the correlations with the other coefficients have been removed. The off-diagonal elements represent the amount of cross-coefficient correlation that was previously confounded with standard deviations for models not controlling for these correlations [Hensher et al., 2005]. For example, the amount of variance directly attributable to the low-salinity random coefficient is not 1.4234, as would be suggested based on just examining the standard deviations of the distribution, but is really 0.8242: there is a large negative portion that is due to correlation with the zero-salinity random coefficient that would otherwise be confounded within the standard deviation estimate if the correlation were not accounted for.

4. 3. Willingness-To-Pay (WTP) Estimation

Table5 reports the estimated WTP for the different attributes derived from our preferred model for the full sample (both sites), with 95% confidence intervals derived based on the parametric bootstrap procedure introduced in Krinsky and Robb [1986]. Where interactions are included, the interaction effects are estimated at the means of the relevant data for constructing these empirical distributions. Additionally, when farmers are making decisions about how much they implicitly value improvements in groundwater salinity, it is almost certainly in reference to a volume of groundwater. We assume that this reference is their existing volume of groundwater. To arrive at a measure of current groundwater volume, we assume a 1 ft3 s−1 flow rate (). Past reconnaissance surveys by the International Water Management Institute (IWMI) for the study region have established that around 80% of the tube wells use 5″ bore diameter pipe with a constant discharge of 1 ft3 s−1. The total volume for each farmer () is then calculated aswhere is the number of turns the farmer had with the groundwater pump, is the average length of each turn (in hours). The flow rate (given in cubic feet per second) is multiplied by 3600 to convert to cubic feet per hour. The WTP for improvements in salinity are therefore computed per million cubic feet of groundwater, where this figure is estimated at the mean of the data. As seen from the confidence intervals, the mean WTP for each of the irrigation system attributes is statistically different from zero at the 5% level. Perhaps not surprisingly, these results suggest that farmers are willing to pay a great deal for improvements in groundwater salinity. On average, farmers are willing to pay over Rs. 14,000 per million cubic feet for improvements from high to low salinity, or Rs. 25,000 per million cubic feet for an improvement from high to zero groundwater salinity. Taking the difference of these, we can infer that farmers would be willing to pay roughly Rs. 11,500 per million cubic feet for an improvement from low to zero groundwater salinity. This may suggest diminishing marginal returns to salinity improvements or may simply reflect farmers' interpretation that improvements from high to low salinity are larger in scope than improvements from low to zero salinity.

Table 5

Willingness to Pay for Irrigation Attributes (Rs.)a

Attribute	Lower 2.5%	Mean	Upper 2.5%
No salinityb	22,869.80	25,521.57	28,220.43
Low salinityb	11,910.12	14,029.53	16,127.87
Groundwater share	−66.62	−46.08	−27.34
Surface water reliability	202.48	227.36	253.22

Interaction effects have been estimated at the means of the relevant data.

Estimated per million cubic feet of groundwater.

Note that these estimates have been constructed based on the results of random parameters logit estimation incorporating both main and interaction effects and allowing for freely correlated random coefficients. Confidence intervals have been constructed based on the parametric bootstrap procedure introduced in Krinsky and Robb [1986] based on 1000 random draws from a multivariate normal distribution with means and variance-covariance matrix of the estimated model parameters.

Not all attributes have positive valuations. Farmers are, on average, unwilling to pay for an increased share of irrigation water from ground sources, since groundwater extraction is significantly more expensive than surface water, and furthermore prone to salinity. In fact, for each additional 1% increase in the share of total irrigation derived from groundwater sources, farmers would, on average, demand a roughly Rs. 50 discount. As a counterpoint, the results suggest that farmers are willing to pay for increasingly reliable surface water irrigation. Since more reliable surface water may be thought to generally imply less need to supplement with groundwater, this relationship is as expected. But it is interesting to note that the willingness-to-pay for incrementally more reliable surface water delivery is greater than the willingness-to-pay for a similar incremental reduction in the share of total irrigation derived from groundwater sources.

4. 4. Heterogeneity in WTP Across Farmers

Since random parameters Logit estimation introduces individual-level heterogeneity and allows us to estimate posterior mean marginal utility coefficients for each individual, we are also able to estimate the individual posterior mean WTP of the random marginal WTP of each individual. This reveals the wide heterogeneity in preferences for improvements in surface water reliability. Farmers' WTP for improvements to surface water reliability ranges from Rs. −150 (implying that farmers would demand a discount for increased surface water reliability) to nearly Rs. 700. It is interesting that some farmers would be unwilling to pay for more reliable surface water (discussed in further detail below). In an attempt to better understand this phenomenon, consider Figures 5 and 6, which plot the relationship between WTP for more reliable surface water and current surface water reliability and groundwater share, respectively.

Figure 5

Willingness to pay for improved surface water reliability as a function of current surface water reliability.

Figure 6

Willingness to pay for improved surface water reliability as a function of current groundwater share of total irrigation water.

4. 4. 1. WTP Over Surface Water Reliability and Groundwater Share

There is a clear pattern that farmers are willing to pay more for incremental improvements in surface water reliability if they already have more reliable surface water and use a larger proportion of surface water in their water supply. This is indeed surprising, since a priori one might expect that the greatest marginal utility from more reliable surface water supplies would accrue to those with currently limited surface water reliability. The implication of the data is that overall willingness-to-pay for surface water provision in a season is a concave-up function of reliability. Using the best fit line to the data in Figure 5 as a crude demonstration, the data suggest that farmers receiving their surface water 25% of the time would be willing to pay about 4000 Rs. per acre per season for it (estimated as the area under the curve from 0% to 25% surface water reliability; Figure 7). For farmers receiving water 75% of the time, this willingness-to-pay jumps to 15,500 Rs. per acre per season. This calculation effectively takes the significant spending on groundwater observed in the region, and translates it to a willingness-to-pay for equivalent service delivery via the surface water canal system, demonstrating the potential to assess fees to farmers that are orders of magnitude greater than current levels, conditional on the farmers perceiving the canal systems as a reliable supply for their seasonal irrigation needs.

Figure 7

Overall WTP for seasonal surface water supply as a function of existing surface water reliability.

The additional results implied by Figure 6—that farmers whose reliance on groundwater is greater are willing to pay less at the margin for improvements in surface water reliability—seem counter-intuitive but are actually in line with the results in Figure 5. Both sets of data imply that increased use of and reliance on surface water leads to higher valuation of surface water reliability at the margin.

Based on the results of Kolmogorov-Smirnov (KS), we find evidence that there are systematic differences in the levels of current surface water reliability between those who would and would not be willing to pay for additional improvements in surface water delivery: those that are willing to pay a positive amount for increased surface water reliability generally have access to more reliable surface water than those unwilling to pay for more reliable surface water (D+ = 0.2513, p value= 0.0546). Similarly, KS tests allow us to reject that the current groundwater share for those with negative mean WTP for improved surface water reliability is drawn from the same distribution as those with positive mean WTP for improved reliability against a two-sided alternative (D = 0.4464, p value= 0.0002). Characterizing these “unwilling to pay” farmers with our limited data on farmer characteristics, they tend to have fewer years of education than the overall sample (4.9 years, compared to 6.1 years), have slightly larger farms (16.6 acres, compared to 15.4 acres), and are disproportionately from Fordwah (67%, compared to 50%). Clearly there are systematic differences in current water delivery infrastructure between farmers with positive and negative valuations for improvements in surface water delivery. Figures 5 and 6 are, of course, only simple bivariate representations of the average relationship between these two variables, and do not take into consideration the potential influence of other covariates nor heterogeneity in the effects at different levels of WTP. To address these concerns, consider the simple linear regression equation where represents farmer's posterior mean WTP for improved surface water reliability conditional upon observed choices,, are a series of farmer-specific characteristics conditioning demand for improved surface water reliability, is an intercept term, and are slope coefficients corresponding to the farmer characteristics, and is an independently and identically distributed random disturbance term. Included in the vector of covariates are the farmers' age, education, farm size, current levels of groundwater salinity (factor variables for low and high salinity), current surface water reliability, total costs of groundwater irrigation, a binary variable equal to unity if the farm is located along the Fordwah branch (and zero otherwise, implying that the farm is located along the Hakra branch), a measure of the distributary's location, ranging from head (0) to tail (1), and an interaction term capturing branch-distributary location interactions. Results from estimating (6) using ordinary least squares (OLS) are reported in Table6.

Table 6

OLS Estimates of Determinants of WTP for Improved Surface Water Reliabilitya

	Coefficients	Robust Standard Errors
Constant	266.985***	35.219
Age	0.336	0.424
Education	0.971	1.142
Farm size	0.131	0.192
Low-salinity groundwater	−19.681	13.043
High-salinity groundwater	68.760***	19.545
Surface water reliability	1.126***	0.255
Cost of irrigation (Rs.)	−0.001**	0.001
Fordwah (=1)	−158.110***	27.036
Distributary location	−122.990***	41.555
Fordwah × distributary location	115.338**	49.132
Number of observations	591
R2	0.3188

Note: **, significant at 5% level; ***, significant at 1% level. The dependent variable is individuals' posterior mean WTP for improvements in surface water reliability, calculated as the individual posterior mean marginal utility of surface water reliability (conditional upon observed choices divided) by the sample constant marginal disutility of price. Standard errors have been adjusted to control for heteroskedasticity of an unknown form using White's [1980] consistent variance-covariance matrix estimator.

From these results, we are able to draw several interesting insights about the relationship between these household characteristics and demand for improved surface water delivery. First, consistent with the bivariate plot in Figure 5, WTP for improved surface water reliability is increasing in current surface water reliability. Even after controlling for the effects of the other covariates, farmers' willingness-to-pay (per season) for the next 1% increase in surface water reliability is, on average, an additional Rs. 1.13 greater than the willingness-to-pay for the previous 1% increase. That is to say, for example, a farmer receiving surface water 75% of the time during his turn is willing to pay on average about Rs. 57 more per season for the next 1% increase than the farmer receiving surface water 25% of the time during his turn, controlling for salinity and groundwater use.

How can it be the case that WTP for improved reliability at the margin is greatest when reliability is at its maximum? Relatedly, how can it be that cumulative demand for reliable water is concave upward (Figure 7)? Certainly, fitting our marginal WTP data to an inverted U-shaped curve could have forced a declining marginal WTP, but we argue that this would not be faithful to our data. We noted in discussing our design that it is difficult to disentangle the desire for more reliable water from the desire simply for more water and that our chosen design makes a compromise in defining the structure of the choice in this experiment. Here we suggest that the data reveal the implications of this imperfect disentanglement, suggesting that farmers enjoying the most reliable water value it the highest, and are perhaps most strongly aware of what they could do with more (consider that an increased allocation could loosely be thought of as reliability greater than 100%, just as cropping intensities and delivery performance ratios are interpretable above 100%).

This is not to say that we expect marginal utility of water reliability to always be high—at some point it would only make sense that a farmer would see no further value in more. We posit that in the current context the cumulative utility curve for reliable surface water is “S-shaped” (Figure 8). Consider in Figure 3 that farmers in Fordwah with low access to reliable surface water appear to disregard it, focusing instead on sugarcane cultivation via groundwater. As surface water reliability increases, farmers shift toward rice cultivation using surface water (this is true as well to a limited extent in Hakra). Our S-shaped cumulative demand curve would imply that some level of reliability is required before farmers will consider a use for it and begin to value it (here, the shift toward rice cultivation). With increasing reliability (and we acknowledge, overall availability), new cultivation possibilities open, leading to continued increases in WTP at the margin for more water. We suggest that this is where we sit in our sample, among farmers with the highest current reliability of water receipt. As new possibilities open, progressing perhaps through high-value crops such as fruits and vegetables at larger scales, the farmer reaches a point where no higher-value cropping systems are available and demand for water at the margin abates. Interpreted thusly, our data provide the very plausible suggestion that even those farmers receiving their full allocation of water could do with more; a clearer disambiguation of “more” from “more reliable” should be a topic of future research.

Figure 8

S-curve for cumulative willingness-to-pay for water, reflecting shifts in water usability.

4. 4. 2. WTP Over Farm Location

Given the interactions between canal branch and the distributary's location along the branch, it is difficult to see from these results exactly how WTP for improved surface water reliability changes as one moves from Fordwah to Hakra or as one moves along these branches from head to tail. Essentially, all other things equal, farmer located along the Hakra branch would be willing to pay an additional for an additional 1% improvement in surface water reliability, where defines the distributary's location along the irrigation branch. Likewise, other things equal, farmer located along the Hakra branch would be willing to pay an additional for improved reliability. Figure 9 demonstrates the WTP for increased surface water reliability in these two branches for various distributary locations. Interestingly, while the WTP for improved surface water reliability is higher among farmers in Hakra, regardless of the location of their distributary along the branch, there is a much more elastic demand: as the distributary moves toward the tail of the branch, the WTP for improved surface water reliability declines rather precipitously. Among farmers along the Fordwah branch, the WTP for improved surface water reliability is relatively constant, at just over Rs. 100 per additional percent of reliability. Disaggregated in this manner, it becomes clear that the WTP for reliability of around Rs. 227 from Table5 for the whole sample is really a composite of comparatively low WTP in Fordwah and comparatively high WTP in Hakra, as becomes even more clear as we examine differences by cropping pattern.

Figure 9

WTP for improved surface water reliability by distributary location, Hakra and Fordwah branches.

4. 4. 3. WTP Over Major Crops

Returning to the four major groups of farmers established in 2.3 (cotton farmers in Hakra; cotton, rice, and sugarcane farmers in Fordwah), we can identify some clear differences in willingness-to-pay for various aspects of irrigation water supply across cropping focus (Table7). Cotton farmers in Hakra place the greatest value on marginal improvements to surface water quality, followed by rice farmers in Fordwah, with sugarcane and cotton farmers in Fordwah exhibiting the lowest WTP. This pattern is mirrored in WTP for increased groundwater share, with cotton and sugarcane farmers in Fordwah exhibiting similar positive WTP for groundwater use, rice farmers in Fordwah exhibiting a negative WTP, and Hakra cotton farmers a further negative WTP. The cotton and sugarcane farmers in Fordwah are the only subsample in our study that exhibit positive valuation of an increased groundwater share, reflecting perhaps the unique positions they hold in being able to profitably make use of high-quality groundwater for cash crop production. Farmers in all Fordwah groups share an indistinguishably higher WTP (relative to Hakra) for reductions in salinity.

Table 7

Comparison of WTP Distributions Over Site and Cropping

Attribute	Group Code	Site	Primary Crop	Mean WTP (Rs.)	p Values for KS Tests (Two-Tailed Difference)
					Comparison Group
					FS	FR	FC
Surface water reliability	HC	Hakra	Cotton	301.25	1.31 × 10−11	6.83 × 10−17	6.68 × 10−13
	FC	Fordwah	Cotton	136.12	0.557	0.101
	FR	Fordwah	Rice	169.83	0.028
	FS	Fordwah	Sugarcane	128.17
Groundwater share	HC	Hakra	Cotton	−93.60	2.42 × 10−9	1.19 × 10−6	2.12 × 10−9
	FC	Fordwah	Cotton	26.30	0.781	0.014
	FR	Fordwah	Rice	−29.54	0.001
	FS	Fordwah	Sugarcane	45.53
Low-salinity groundwater	HC	Hakra	Cotton	11,458.94	1.89 × 10−6	2.24 × 10−17	1.92 × 10−9
	FC	Fordwah	Cotton	18,174.44	0.617	0.309
	FR	Fordwah	Rice	17,664.01	0.231
	FS	Fordwah	Sugarcane	18,310.68
Zero-salinity groundwater	HC	Hakra	Cotton	21,202.78	5.81 × 10−6	5.48 × 10−12	6.97 × 10−8
	FC	Fordwah	Cotton	34,388.94	0.936	0.123
	FR	Fordwah	Rice	31,949.62	0.160
	FS	Fordwah	Sugarcane	33,413.95

5. Policy Implications: Establishing a Self-Reinforcing, Self-Sustaining Cost Recovery System

The two most important implications of our results are that (i) farmers are willing to pay significantly more on average for water than they are paying, and (ii) the better that service provision is, the more they are willing to pay at the margin. Work by the Water Sector Task Force (WSTF) in Pakistan [WSTF, 2012] noted that the amount paid by farmers to pump groundwater acted as a de facto indicator of their willingness-to-pay above and beyond existing water charges; our work translates this spending on groundwater into an explicit measure of willingness-to-pay for surface water provision, and maps how this willingness varies as a function of the location of farmers' plots along the watercourse, the quality of groundwater they receive, their cropping focus, and the reliability of the water service they currently enjoy.

The notion that farmers cannot or will not pay for water is strong across agricultural domains all over the world. In Pakistan in particular, rates of payment and of cost recovery are among the lowest. In part, this could be attributable simply to the lack of consequence of nonpayment—access to surface water is not restricted for those who do not pay. A more complete interpretation would also attribute some of the problem to a lack of response to input—payment of fees does not lead to a perceptible change in water service provision. Our results clearly show that willingness-to-pay for reliable surface water is in general, much higher than current levies, and among those farmers with the greatest levels of reliability, orders of magnitude higher. Those farmers who are “unwilling to pay”—who would demand a discount for increased surface water reliability at the margin—are a part of a statistically distinct population of farmers with lower levels of existing surface water reliability. This observation supports the idea that some minimal level of reliability is a requirement for the willingness to contribute, and the notion that a system of phased-in increases to water charges, where the level of the fee is predicated on an achieved level of service provision across the system, might be necessary. The WSTF advocate such an approach in their recent findings [WSTF, 2012].

The observation that farmers receiving more reliable surface water are willing to pay more at the margin than their peers receiving less has very important implications. By design, those with more reliable supply sit toward the head-end of their respective watercourses, distributaries, or canals, and their willingness to contribute can, under certain conditions, lead to collateral benefits downstream. Any collateral improvement to supply reliability experienced downstream leads (by our observed result) to an increased willingness to contribute by those downstream farmers, and the potential opens up for a self-reinforcing system of cost recovery. Analysis of the conditions under which such a system might occur (appropriate levels for water use fees and patterns of maintenance and reinvestment) is a currently active research topic in our group.

6. Conclusions

This analysis is based on two select sites in Punjab Province, and is not broadly representative of the Indus Basin Irrigation System. Further, we have used a design that leaves overall supply of water partially implicit in surface water reliability, meaning that farmers' desire for “more reliable water” cannot be perfectly disentangled from their desire for “more water” overall. These caveats stated, the analysis provides explicit indication of a willingness to contribute to irrigation system maintenance and development that, while implicitly suggested by spending on groundwater pumping, runs counter to a strong political narrative shared not only by Pakistan but also by many other developing and developed nations across the world.

We estimate mean marginal (WTP) for improved surface water reliability in our two sites to be much higher than the current average rates of Rs. 85–200/acre, with farmers typically willing to pay more than this for each marginal (1%) improvement in reliability, and with this marginal willingness-to-pay the highest for those farmers who already experience high system reliability, are closest to the head reaches, and who use the least groundwater. These results alone do not provide a complete map for how best to set water user fees (abiana)—as abiana levels shift in tandem with surface water reliability and spending on groundwater pumping, farmer preferences may shift as well. However, they are indicative that members of the system (and in particular, those with the best ability to pay, at the head reaches) are willing to contribute much more to the system in exchange for water supply they can better rely upon.

In such a system, where the greatest willingness to contribute comes from those at the heads, with greatest ability to pay, there is potential for a system of cost recovery to be self-reinforcing, as long as there are benefits reaped from the contributions of those upstream that trickle to those further downstream. For large-scale irrigation systems, this property is a nontrivial function of investment strategy, efficiency and transparency in the organization responsible for maintaining and investing in the irrigation system. Further research into this process is necessary in order to better understand the potential for such cost recovery in the Indus Basin.