Monopoly Power and Distribution in Fragmented Markets: The Case of Groundwater

Evidence from Pakistan's Punjab indicates that monopoly power in the market for groundwater (irrigation water extracted using private tubewells) results in a substantial resource misallocation. But despite this substantial misallocation of groundwater, a welfare analysis shows that monopoly pricing of groundwater has limited effects on equity and efficiency. Policies aimed at eliminating monopoly pricing would do little to help the poorest farmers. Using data from Pakistan's Punjab, Jacoby, Murgai, and Rehman examine monopoly power in the market for groundwater - irrigation water extracted using private tubewells - a market characterized by barriers to entry and spatial fragmentation. Simple theory predicts that tubewell owners should price-discriminate in favor of their own share tenants. And this analysis of individual groundwater transactions over an 18-month period confirms such price discrimination. And among those studied, tubewell owners and their tenants use considerably more groundwater on their plots than do other farmers. Jacoby, Murgai, and Rehman also provide evidence that monopoly pricing of groundwater leads to compensating - albeit small - reallocations of canal water, which farmers exchange in a separate informal market. Despite the substantial misallocation of groundwater, a welfare analysis shows that monopoly pricing has limited effects on equity and efficiency. In the long run, a policy aimed at eliminating monopoly pricing would do little to help the poorest farmers. This paper - a product of Rural Development, Development Research Group - is part of a larger effort in the group to examine the role of policy and policy reform on rural development. The study was funded by the Bank's Research Support Budget under the research project Market Development and Allocative Efficiency: Irrigation Water in the Punjab.


I. Introduction
Markets in less developed economies often appear to deviate considerably from the competitive ideal. Two features of rural markets, in particular, underlie this observation: "fragmentation" due to high transportation or information costs, and entry barriers due to the interaction of credit constraints and indivisibilities in investment. Under such conditions, local monopoly can be widespread and persistent, with potentially large efficiency and distributional implications. 1 Yet, evidence of such monopoly power and especially of its welfare consequences is surprisingly sparse. 2 This paper uses data from Pakistan's Punjab to examine monopoly power in the market for irrigation water, specifically groundwater extracted by tubewells. Groundwater markets have flourished throughout South Asia, emerging over the past few decades along with the rapid development of private tubewells. 3 These markets are characterized by barriers to entry and extreme spatial fragmentation. Barriers to entry arise from the fact that one must own land above an aquifer before boring a tubewell and because of high installation costs. 4 Tubewell ownership in South Asia is, therefore, limited mostly to large landowners. 5 Heavy seepage losses involved in conveying groundwater through unlined field channels also severely restrict competition. These technological features of groundwater extraction and distribution have led several commentators to express concern over local monopolies, more colorfully termed "waterlords" (see Meinzen-Dick, 1996, andShah, 1993, for an overview of the debate and evidence).
Two features of groundwater markets in the Punjab provide unique and complementary tests for monopoly power. First, groundwater markets and tenancy contracts are interlinked. A monopolistic tubewell owner who sells groundwater both to his own share-tenants and to other cultivators would be expected to price discriminate between the two groups, charging a lower price to his own tenants for the simple reason that he shares their output. We use detailed data on daily groundwater transactions over an 18 month period to compare prices that the same tubewell owner charges to different customers, including his own tenants. Second, irrigation water is a production input not only for buyers but also for the tubewell owner himself, who typically cultivates adjacent land. Since the shadow price of groundwater to the owner is just the marginal extraction cost, he should use more of it per acre than a groundwater buyer facing a monopoly price. Comparing groundwater use across buyers, tubewell owners, and their tenants, at the plot level, therefore, provides a test for monopoly distortion that does not require estimates of shadow prices. The unique combination of price information and farm level quantity data allows an analysis of both the efficiency and equity implications of monopoly power; i.e., the deadweight loss and the transfer of surplus from buyers to sellers.
We also look for repercussions of monopoly pricing of groundwater in a closely related "market", that in which farmers exchange entitlements to canal water. The question we address is whether, given monopoly power, informal exchange of canal water fosters allocative efficiency. Since canal water is free at the margin, whereas groundwater is expensive to extract, farmers resort to tubewells mainly during periods of peak water demand. Thus, farmers may be able to alleviate the impact of monopoly pricing of groundwater by "borrowing" canal water during critical periods from tubewell owners and their tenants. We exp lore this possibility using weekly panel data on canal water endowments and use over three agricultural seasons. This paper brings together three disparate literatures. First, a large body of work has sought to measure market power in different industries using a variety of empirical strategies (see Bresnahan, 1989, for a survey). Our approach to inferring monopoly mark-ups is distinct, however, in that it does not rely upon measuring marginal cost or structurally estimating demand, both of which often require auxiliary restrictive assumptions. Second, this paper contributes to the voluminous literature on agricultural tenancy, specifically on the interlinkage of rural factor markets. Despite some theoretical analyses of interlinked sharecropping contracts (see Braverman and Stiglitz, 1982 and the survey by Bell, 1988), there is virtually no empirical work exploring the implications for factor market efficiency. Third, in examining the intertemporal exchange of canal water, this paper touches upon the role and functioning of informal markets.
These markets, characterized principally by the prominence of commitment problems and therefore by the reliance on self-enforcing contracts (see Greif, 1993, and Coate and Ravallion, 1993, and Ligon, Thomas, Worrall, 1996, in the context of risk-sharing), have also received scant empirical attention.
Our findings strongly support the existence of monopolistic price discrimination and a corroborating pattern of water misallocation within one watercourse in Pakistan. Evidence from canal water transactions, however, indicates that the impact of this misallocation on crop yields may be blunted somewhat by reallocations within the season. In any case, our welfare analysis shows that monopoly power in the groundwater market has only limited effects on efficiency and equity.
The rest of this paper is organized as follows. Section II describes the setting for this study and the data set in detail. We develop our theoretical predictions on pricing and use of groundwater in Section III, while Section IV models the institution of canal water trading in a general equilibrium framework. Section V presents the empirical analysis. We conclude in Section VI with the welfare analysis and the broader implications of our findings.

II. Institutional Setting and Data
The data for this study come from a survey of irrigation practices collected by the International Water Management Institute (IWMI) in the Fordwah-Eastern Sadiqia irrigation system of southern Punjab, Pakistan from 1993-95. In this agroclimatic zone, cotton and fodder are the main kharif (summer) season crops, with cotton by far the more important in terms of cultivated area. Wheat is the main crop in the rabi (winter) season, while sugarcane is cultivated year-round. The region receives low and erratic rainfall averaging 100-200 mm per year, mainly concentrated during the monsoon period from July to September. Farmers, therefore, rely heavily upon canal water and groundwater for agriculture.
In this paper, we focus on a single, but fairly typical, Punjabi watercourse, Fordwah-14R (Fd14R). A watercourse, or tertiary irrigation canal, is a natural unit of analysis for the study of water markets because, aside from its connection to the secondary canal, it is largely closed to import or export of water. 6 The eight watercourses covered by IWMI surveys were purposefully selected from the tail-end of the Fordwah-Eastern Sadiqia irrigation system, and hence have particularly unreliable canal supplies. We chose Fd14R because it has the most complete data.
In the Punjab, as in much of Pakistan and Northern India, canal water is distributed to each plot within a watercourse according to a rotational system, or warabandi. Fd14R is no exception. Each farmer is allotted a turn to use the entire water flow in the canal at a prespecified time each week. Access to water is limited to farmers with land in the watercourse command area, and the length of the water turn is proportional to landholding (though not necessarily cropped area), irrespective of the crops grown by the farmer. In Fd14R, the canal water entitlement is about 20 minutes per acre of landholding per week, viewed by farmers as about half of irrigation "requirements", although farmers in the tail-reach of the watercourse can lose much of their water to seepage (there is no allowance for this). Leasing or sharecropping in a plot of land entitles the cultivator to full use of the canal water allocation for that plot. In response to this rigid allocation scheme and the unreliability of actual water deliveries, 7 farmers have developed an informal system of canal water trading, discussed below.
The IWMI surveys cover every cultivator, landowner, and plot of land in the watercourse command area; thus, we have a "census" rather than a "sample", though we use the latter term for convenience. Since canal water turns are assigned to plots rather than to individuals, farmers who operate more than one plot (or set of contiguous plots) have more than one canal water turn.
Moreover, since the holdings of such farmers are often dispersed throughout the watercourse command, and hence may lie in different local groundwater "markets", it makes sense to conduct the analysis at the plot-level. As a result, while there are around 70 cultivators in Fd14R, there are up to 93 canal water turns (identified by 'warabandi id'), depending on the season. 8 A unique feature of this data set is that it includes information on every groundwater and canal water transaction between all warabandi ids in the watercourse command during a season.
A daily log was kept of canal water operations, including discharges and the exact timings of each turn at the canal, the amount of irrigation time exchanged, and the identity of the trading partners. A similar log was kept of the operations of each tubewell in the watercourse command, including hours of operation, and if water was sold, cash prices, any special transaction terms, and the identity of the buyer (these are described in more detail in section V). These data, along with daily rainfall measurements, provide a complete accounting of water ava ilability and use throughout the survey period.
In addition, an exhaustive mapping and crop survey of the watercourse command area identifies the location of each plot, what was grown on the plot, and the location of each tubewell. Figure 1 shows a diagram of FD14R pinpointing all 18 tubewells as of the end of the survey period. Most of the tubewells sit along the main watercourse channel to facilitate mixing of canal water and groundwater and to avoid using field channels with higher conveyance losses.
There are no tubewells in the tail-reach of the watercourse, at the far left of the map, because of the lack of adequate groundwater in this area.
All farmers in Fd14R trade canal turns. We present more detailed evidence on trading frequency in Section V. Typically, transfers of canal time involve one or two partners on closely neighboring plots; the greater the distance between farmers, the greater the number of intervening farmers whose turns must be shifted to accommodate the new timing. These transactions do not involve cash, at least not explicitly, nor is the receipt of water in one week necessarily followed by a reciprocal transfer of water the following week. Field interviews indicate an informal system of borrowing and lending depending on the relative irrigation demands of the participants. Over the long-term, there is a rough balance between the amounts given to and received from any one partner. 8 The number of warabandi ids vary across seasons primarily due to changes in tenancy arrangements between the rabi and kharif seasons. Most of the changes arise because plots that were rented out in the previous season are subsequently cultivated by the owner. There are a few cases in which a landowner rents out the plot to a different tenant.
At the end of the survey period, there were 18 diesel-powered tubewells in the watercourse command of Fd14R, 3 of which were installed during the 3 seasons covered in the survey. 17 of these sold water at least once during the survey period. Most (90%) of the warabandi ids used water from these wells, either as owners (23%), as share tenants of tubewell owners (14%), or as other buyers (78%). 9 Because of conveyance losses, most farmers use water from the nearest one or two tubewells. Farmers in the tail-reaches of the watercourse, where the closest tubewell is more than 650 meters away, may be excluded from groundwater use altogether; 6 of the 11 warabandi ids who never used groundwater are located in this area. Figure 2 shows the overall weekly pattern of irrigation supply from groundwater, canal water, and rainfall in Fd14R during the survey period (April 1994-October 1995. Notice that much more irrigation water is applied during the kharif season than during the rabi, even after controlling for rainfall which peaks during the July-August monsoon. Groundwater use is most intensive shortly after the monsoon, with the competing demands of cotton and sugarcane in the kharif, but there is also a brief flurry of tubewell activity in May coincident with cotton sowing.
Canal water supplies have no regular pattern, as diversions can occur at any time. An exception is the scheduled canal closure beginning in January for desiltation and maintenance. During these five weeks of the rabi season, wheat must be irrigated mainly with groundwater. Lastly, note that canal water supplies were relatively plentiful in kharif 1994 compared to kharif 1995, whereas the situation with rainfall was the reverse.

Environment
Our analysis of market power focuses on the ability of tubewell owners to price discriminate across two types of water buyers: their own tenants and everyone else in their market territory. Understanding why such price discrimination is profitable and what form it takes requires modeling the behavior of: 9 Owners typically use water from their own well, and share tenants typically purchase water from their landlords' wells. Occasionally, however, both sets of farmers also purchase water from other tubewell owners.
• Tubewell owners (O), who may cultivate some of their own plots adjacent to the tubewell and rent or sharecrop out others; • Tubewell tenants (T), i.e., share-tenants of tubewell owners; 10 • Other groundwater buyers (B), who may be share-tenants of other landlords, ownercultivators of nearby land, or renters.
We assume that groundwater is extracted at constant marginal cost, c, and that capacity constraints on groundwater pumping are never binding. The latter assumption is explored in Section V. There we also show that groundwater prices are essentially fixed over the course of the season. Given constant marginal cost and non-binding capacity constraints, the absence of peak-load pricing is perhaps unsurprising. Whatever the reason, this institutional feature is taken as given in our analysis. The model below is therefore static, with water prices, p, agreed upon at the beginning of each season.
Each farmer cultivates one unit of land with the same technology, given by a neoclassical production function, f. For the moment, f is assumed to depend only on the water input w and we ignore other sources of water (canal irrigation and rainfall), so that w refers only to groundwater.
We also abstract from production risk. Note that we do not specify a separate technology for each crop cultivated, so that a farmer may reduce his water use, not only by using less water on a given crop, but also by substituting away from water sensitive crops. After normalizing the price of output to unity, profit from farming is given by

Pricing groundwater to non-tenants
We assume that the tubewell owner acts as a single price monopolist toward buyers who do not have a tenancy contract with him. In other words, the owner's problem is to where the p subscript denotes partial derivative and 0 * < p w . In this case, there is no price discrimination across other buyers by tenancy status; share-tenants and renters (of other landlords), as well as owner-cultivators all have the same demand curve for groundwater and hence face the same price B p (we ignore incentive problems for now).
The implications of more elaborate pricing strategies toward other buyers are discussed below and investigated in the empirical work.

Pricing groundwater to tubewell tenants
Pricing to tenants of tubewell owners is complicated by the fact that the owner, as a landlord, receives a share of the tenant's output and also pays a share of the input costs, both of which depend on how much water the tenant uses. Denote the tenant's share of output by s, and assume that groundwater costs are also shared in this same proportion between tenant and landlord. This assumption is trivial in this single input model, but also happens to be consistent with the information in our production survey. We assume that s is a choice variable, even though in reality it rarely deviates from 0.5. 11 This is not necessarily a shortcoming of the In other words, the optimal contract maximizes the owner's income net of groundwater extraction costs, where income includes the owner's share of output as well as the tenant's share of the water cost. The owner also faces the tenant's incentive compatibility constraint, ICC, and the tenant's participation constraint, PC, where µ is the value of the tenant's outside option. 12 Note that ) ( * p w does not depend on s, because the tenant shares both its cost and benefit with the owner at the same rate.

The (interior) solution to (3) implies
Proof: see Appendix for part (a); part (b) trivial.
Part (a) just says that the tubewell tenant faces a two-part tariff (cf. Basu, 1987 Proposition 1 holds under the assumption that the tubewell owner acts as a single price monopolist toward his other buyers, which need not be true. The owner, for example, could demand a lump-sum fee from each buyer for the right to buy groundwater from his tubewell during the season, in which case the optimal strategy would be to set price equal to marginal cost and extract all the buyer's surplus through the fee. We have no indication from our data or from 12 The outside option may be to sharecrop land of someone who does not own a tubewell and earn ) ( B p sπ . In this case, which we do not pursue here, the groundwater pricing decision of each tubewell owner might impose an externality on all the other tubewell owners in the area. Namely, by setting a high B p a given owner lowers µ and allows some other owner to reduce his tenant's share.
field reports that such lump-sum payments occur in Fd14R, but under this scenario there would be no difference between the prices charged to tubewell tenants and to other buyers, even if owners have market power. Thus, failure to detect price discrimination is not necessarily evidence against local monopoly. A related point is that the tubewell owner may price discriminate among his non-tenant buyers by offering a lower price for bulk purchases.
Proposition 1 still holds in this case, since the average price charged to other buyers exceeds marginal cost, but the welfare implications are different than for the single-price monopoly. For this reason, we investigate in the empirical work whether tubewell owners offer their non-tenant customers quantity discounts.

Pricing groundwater with non-contractible inputs
The model presented thus far does not incorporate incentive problems that arise from the fact that some inputs, such as tenant effort, are prohibitively costly to observe and therefore cannot be specified in the tenancy contract. As we show next, accounting for non-contractible inputs (as in Braverman and Stiglitz, 1982) modifies some of the above conclusions.
Let output be now given by ) , , where e is tenant effort. Assume that effort and water are complements in production so that 0 > we f , 13 and that tenant utility is . Making the appropriate substitutions in (3) and solving for the optimal contract we obtain The optimal contract, in general, no longer involves marginal cost pricing of groundwater. In the presence of the unobserved input, extracting the tenant's surplus solely by reducing his share, as above, exacerbates the incentive problem. On the other hand, raising the price of groundwater to extract surplus is costly because it reduces water use and effort, and hence output. The owner trades off the use of these two instruments. It is even possible that the tenant is charged below marginal cost for groundwater; that is, if water and effort are sufficiently complementary.
It would seem that tenants should still pay less for groundwater than other buyers because the owner has another method to extract surplus from the tenant besides raising p. However, lemma 1 does not allow a direct comparison between T p and B p without further restrictions on the technology. We therefore assume that These assumptions lead to a linear (in p) demand for water and deliver Proof: see Appendix for part (a). 14 Part (b) follows from the fact that c p O = and the owner faces no incentive problem when cultivating his own land, whereas c p B > and the buyer may also face an incentive problem if he is a share-tenant.
Note that although the tubewell tenant is charged a lower price he does not necessarily use more groundwater than other buyers; it depends on the amount of effort supplied by the other buyers. If other buyers are on fixed rent contracts or cultivate their own land, they will supply more effort than the tenant of the tubewell owner and, if effort and water are strong enough complements, they could even demand more water. 15 The model also implies tha t a tubewell owner may price discriminate among buyers who are not his tenants. As just pointed out, renters and owner-cultivators have a higher demand for water than sharecroppers because they do not face an incentive problem (assuming complementarity of water use and effort). Therefore, among his other buyers, the tubewell 14 The proof assumes that the solution for B p is interior in the presence of the unobserved input, which means that ) , 0 ( * e f c w < , where * e is the chosen effort level when w=0 and s=1. 15 Shaban (1987) finds that rented and owned plots in rural India are cultivated equally intensively, suggesting the incentives of owners and renters are similar. owner should charge share-tenants less. 16 Recall that in the absence of non-contractible inputs there should be no price discrimination across these other buyers.
We would still expect the tubewell owner to charge share-tenants of other landlords a higher price than he charges his own tenants. Intuitively, the sole reason for giving a tenant of another landlord a discount is the complementarity between water and effort, which reduces water demanded by the tenant. But this complementarity cuts both ways: The higher the complementarity, the greater the incentive to price groundwater cheaply to one's own tenant to extract greater effort from him. 17 To sum up, both the model with and without non-contractible inputs imply price discrimination by the tubewell owner in favor of his tenant. Discrimination in favor of other share-tenants is also possible. In any case, owners of tubewells are predicted to use more water on their own land than any of their customers, with the possible exception of their own tenants.

IV. General Equilibrium: The Role of Canal Water Transactions
In the setting outlined thus far, unequal groundwater prices across users translate directly into allocative inefficiency. But a misallocation of groundwater does not necessarily imply an overall misallocation of irrigation, since canal water is the most important irrigation source.
Moreover, canal water use may respond to monopoly price differentials through the system of informal exchange described in Section II. In this section, we explore the implications of canal water trading for overall allocative efficiency.
The key observation is that the timing of irrigation matters. Because tubewells are expensive to operate, groundwater is used mainly as a supplement during periods of peak water demand. While over the course of a season a farmer may end up giving as much canal water as he receives, canal water trading may affect the timing of irrigation within a season. The basic intuition comes from imagining the social planner's problem of allocating canal water within a watercourse, taking the allocation of groundwater as given. Suppose that the social planner is working under the constraint that each farmer must receive the same total canal water volume over the course of the season. During peak periods of water demand, when tubewell owners and their tenants obtain more groundwater than other buyers, the social planner will want to reallocate canal water from the former group to the latter group of farmers. During periods of slack water demand, when groundwater is seldom used, other buyers must repay this "loan" of canal water. Although all farmers use the same amount of canal water during the season, those farmers facing high groundwater prices may still able to meet much of their irrigation needs during the critical periods and thereby differences in crop yields across farmers may be attenuated.
To formalize this argument, consider a simple two-period model of irrigation decisions within a season. Denote groundwater by x and canal water by z, and let z reflects the better quality of canal water. Since canal water is free at the margin, we assume that farmers decide how much groundwater to purchase only after receiving their canal water allocation. In each of the two periods, , irrigation contributes to crop growth according the period-specific production functions ) ( w f t , which are identical across farmers. We assume the productivity of water is higher in period H than in period L; i.e., Consider two farmers, i and j, each of whom receives with certainty a canal water allocation each period, e kt z , .
We can now trace out the marginal value curves for canal water, , below which a farmer will resort to purchasing is decreasing in k p ; the higher the price of groundwater the lower the supply of canal water must be to induce a farmer to purchase groundwater. At low canal volumes, farmers set (recall that k p is contractually fixed over the season), so that the marginal value curve is flat at k p , until canal volume exceeds , and the marginal value of canal water declines, since (the decline is linear in the case of a quadratic production function).
So far, there is no gain from intertemporal canal water exchange between the farmers, since they have identical endowments and technology. However, suppose that farmer i faces a lower groundwater price than fa rmer j ( Prior to any canal water trading, there are now two scenarios to consider: (1) neither farmer would use groundwater given their endowment ( ). 20 Suppose that technology and water endowments are such that scenario (1) holds in period L and scenario (2)  19 Such dependence is certainly not implausible in the case of irrigation, but it would greatly complicate the theoretical analysis. Since the return to current groundwater and canal water use would in this case depend on all future irrigation decisions, the model would have to be solved backwards from the end of the season. Incorporating dynamics aspects of irrigation is a topic for future research. 20 A third possible scenario is that both farmers would use groundwater ( ), but this leads to the same outcome as scenario (2). The equilibrium canal water allocation depends on the social norms or "rules" governing canal water transactions. As mentioned earlier, interviews with farmers in Fd14R reveal that these transactions are strictly exchanges of turns at the canal; no cash payments are involved. 21 If borrowing of canal water must balance lending over the course of a season, we have the . A different interpretation of the trading convention is that, though only in-kind transactions are permissible, the rate of intertemporal exchange is not necessarily one. In other words, there may exist an implicit "price" κ such that . Indeed, one might expect that canal water is considered more valuable in . Another possibility is that, field reports notwithstanding, there is in fact an informal cash market for canal water. We discuss the implications of these alternative rules momentarily, but for now we focus on the strictest interpretation of canal turn exchange. 22 Figure 3 illustrates the Pareto optimal allocation, i.e., the one which maximizes subject to the constraint imposed by the trading rule (see the Appendix). In period H, farmer i provides canal water to farmer j, but not enough to equate the two farmer's marginal values. In period L, farmer j returns the amount he borrowed, which drives farmer i's marginal value below that of farmer j. These "wedges" between marginal values in each period arise from the constraint that all transactions must be in-kind.
We can contrast the equilibrium depicted in Figure 3, with one in which the intertemporal exchange rate is not one. If 1 > κ , then the marginal value curves will be farther apart in period H than in period L and less water will be lent to farmer j than in the case where 1 = κ . The case of an unfettered cash market in canal water is even simpler. Farmer j would purchase canal water from farmer i in period H until the marginal values of the two farmers are equated. There would be no trade at all in period L. 23 In sum, regardless of the specific rules governing canal water transactions, the presence of this adjacent market mitigates the misallocation of irrigation water due to groundwater monopoly. In peak demand periods, more canal water is always directed to the farmers facing higher groundwater prices. As a result, differences in crop yield across tubewell owners/tenants and other buyers should not be as large as they otherwise would be. Of course, unless we know the parameters of the technology, we cannot directly quantify the efficiency enhancing role of canal water trading. The objective of the empirical work reported in the next section is therefore more modest: to assess whether such trading follows the pattern suggested by the theory and how much water is actually involved.

V. Empirical Results 24
Groundwater pricing Data are available on all 886 groundwater transactions that occurred in Fd14R over the 18 month period from the beginning of kharif 1994 to the end of kharif 1995. As mentioned earlier, this is primarily a cash market, and the price per hour of water pumped is recorded for each transaction along with any special terms. 25 While most transactions are straightforward purchases, the following special terms appear: (1) Only fuel costs charged to buyer (81 cases); (2) Buyer used own engine (54 cases); (3) Water given free of charge (9 cases); (4) Buyer used own fuel (7 cases). In the first three cases, the buyer is in effect getting a price discount.
In case (2), the buyer--typically, an owner of another tubewell--brings his own diesel engine (and fuel) to the owner's bore hole and is allowed to extract water for free to use on his nearby plot.
Tubewell tenants never receive these concessions and a given buyer may only get a discount season. In-kind exchange with 1 > κ implies that farmers facing higher groundwater prices would use less canal water over the season, because every hour of canal water that they borrow in peak periods must be repaid "with interest" in slack periods. A cash market for canal water would imply that those farmers facing higher groundwater prices would use more canal water. 24 Appendix Table A.1 provides an overview of all the different empirical analyses presented in this paper. 25 Payments are not necessarily immediate. In the case of tubewell tenants, the owner usually keeps track of what his tenant owes him and only asks for payment at the end of the season. Thus, there is a minor credit element in the price to tenants, meaning that their effective price is slightly lower than what is recorded in the data. occasionally, paying the full cash price most of the time. We include a dummy variable in the regressions for cases (2) and (4) to control for the element of "self-service". Finally, the transaction prices recorded for tubewell tenants already reflect the tenant's cost share (i.e., it is T sp rather than T p ). Therefore, we double the prices of half-share tenants and quadruple those of quarter-share tenants to get comparable prices for all buyers.
Each of the price regressions reported in Table 1 includes tubewell fixed effects to control for, among other things, variation in water quality and hourly volume (due to differences in pipe width), as well as season of transaction dummies. Specification (1) shows that tenants of tubewell owners pay significantly less for groundwater coming from their landlord's tubewell. A crucial question is whether this price discount is specific to tubewell tenants or rather applies to sharecroppers in general. Specification (2), therefore, controls for both the proportion of cultivated land sharecropped in and owned by the buyer (rented in land is the omitted category).
Evidently, only tubewell tenants, and not other tenants, receive lower prices, since the proportion of sharecropped land is not significant. The estimates also show that tubewell owners do not price discriminate among their other buyers according to tenancy status. Sharecroppers, ownercultivators, and renters all pay about the same for groundwater, and each pays more than tubewell tenants. The absence of price discrimination among these other buyers casts doubt on the importance of non-contractible inputs in explaining groundwater pricing.
Only eight of the tubewells in Fd14R (comprising 602 transactions) sell to both tenants and non-tenants and thus contribute to the estimation of the price differential in the tubewell fixed effects specifications. Allowing for different degrees of price discrimination across these eight tubewells, as in specification (3), uncovers considerable heterogeneity. In particular, five of the tubewells have highly significant tenant price differentials of between 9 and 22 Rupees/hour, while the other three tubewells do not seem to price discriminate at all.
Unfortunately, there are not enough tubewells to allow us to understand why pricing behavior differs; the watercourse map in Figure 1 reveals no obvious spatial characteristic of the nondiscriminating wells.
Spatial characteristics are potentially important though in explaining groundwater prices, and ignoring them could bias our results. First of all, because they farm the land of the tubewell owner, tubewell tenants tend to be closer to their source of groundwater than other buyers. In the simplest model of section III, without non-contractible inputs and with linear demand, the price to other buyers falls with distance, because the elasticity of demand rises with transport costs, whereas the price to tubewell tenants is fixed at c and hence should be independent of distance (the implications of the model with non-contractible inputs are less clear-cut). A second spatial consideration is position in the watercourse. Since farmers in the tail-end of the watercourse receive less canal water due to conveyance losses than farmers at the head, they should have a higher demand for groundwater and be willing to pay a higher price. Again, in the simple model, distance to the head of the watercourse should only affect the price charged to non-tenant buyers.
Specification (4) investigates these spatial issues by including distance between the plots of the buyer and the tubewell he purchases from, as well as distance to the head of the watercourse. Both distance variables are also interacted with tubewell tenancy status. Since distance between buyer and seller may be endogenous with respect to price--i.e., buyers choose which tubewell to purchase from (and hence distance) based on unobservable buyer-seller match characteristics that may be correlated with price--we estimate specification (4) by 2SLS, using the distance to the nearest tubewell as an instrument. None of the distance variables are statistically significant in Table 1 (neither are the unreported OLS estimates). This is not to say that distance is unimportant, as farmers clearly tend to buy from nearby tubewells. Rather, distance is evidently not an important determinant of groundwater demand conditional on the choice of tubewell. 26 We provide more evidence on this point in our analysis of quantity.
Returning to some of the other explanatory variables, the season of transaction dummies are insignificant in all specifications, indicating that prices were fairly stable over the sample period. We also check for peak-load pricing within seasons by including a measure of aggregate groundwater demand; namely, the total operating hours of all tubewells in the watercourse on the day of each transaction (much of which goes to the fields of tubewell owners). This variable has no significant impact on the price paid that day, which confirms the point made earlier that prices are fixed throughout the season. This finding is also consistent with the view that capacity constraints in groundwater extraction are inconsequential; sellers do not need to use price to ration quantity in periods of high demand. However, given the importance of this issue for our interpretation of the evidence, we explore tubewell capacity constraints in more detail next. 26 Another possibility is that the distance variables are picking up the density of neighboring tubewells and hence the degree of local competition. Thus, buyers farther away from their source of groundwater face less competition and a higher price, rather than a lower price as argued above. Unfortunately, the limited spatial variation in the data and the high correlations among spatial characteristics make it difficult to distinguish the impact of local competition.
A final issue to investigate is whether tubewell owners provide quantity discounts, which, as mentioned earlier, has implications for the welfare analysis. To each observation, we match the total hours of groundwater transacted between that buyer-seller pair over the course of the relevant season. The last specification in Table 1 includes this hours variable along with its interaction with the tenant dummy, since tubewell tenants should not receive quantity discounts, at least in the simplest model. We use the area of the plot as an instrument for hours, which is clearly endogenous in the price regression. A plot's area is positively correlated with how much groundwater is used on that plot over the season, and (to a lesser extent) with how much groundwater is purchased from a particular tubewell. The results lend only weak support to the quantity discount hypothesis; buyers who purchase more groundwater from a particular tubewell get a small price break, but it is not statistically significant even at the ten percent level.
Tubewell tenants, by contrast, get no discount, just as the theory (sans moral hazard) predicts.
Finally, note that in specification (5) the differences across tubewells in the extent of price discrimination become narrower.
To sum up, we find strong evidence of price discrimination in favor of tubewell tenants, a finding that persists even after controlling for distance between buyer and seller and for the total quantity transacted between them during the season. Although there is considerable heterogeneity across tubewells, a given owner charges an average of about 9 Rupees/hour more to other buyers than he does to his own tenant, which is quite a lot given that other buyers pay an average hourly price (adjusted for contract terms) of 32 Rupees/hour. It remains to be seen whether and by how much this price distortion affects resource allocation.

Do higher prices reflect greater 'reliability'?
Our interpretation of the price differentials in Table 1 as evidence of monopolistic behavior is based on the premise that the groundwater is a homogeneous commodity. While it is true that water is water regardless of who uses it, the timing of water delivery may matter. If it is important to a farmer that he receives water on certain days and capacity constraints are at least occasionally binding, then he would be willing to pay to avoid the possibility of being rationed out on those days. 27 Thus, a buyer may contract with a tubewell owner to be near the top of the water "queue" on full capacity days, in exchange for which privilege the buyer agrees to pay a higher fixed price. If tubewell tenants care less about reliability, 28 then they will pay lower prices than other buyers, which might explain the observed price differential.
To assess the relevance of this reliability hypothesis, we examine data on daily tubewell use for the same 18 month period used in our price analysis. If other buyers are favored in the daily queue over the tenants of tubewell owners, then we should see that the fraction of groundwater pumped by a given tubewell on a given day that goes to other buyers is higher when that tubewell is being operated at or near capacity, and the fraction going to tubewell tenants is lower. There are only a handful of days in our sample on which a tubewell operates at maximum capacity of 24 hours. However, on about five percent of the 1,069 tubewell operating days over this period, a tubewell was running for a total of 16 hours or more. Table 2 presents OLS regressions for both the proportion of daily pumping hours going to tubewell tenants and to other buyers (note that 44 percent of groundwater goes to tubewell owners themselves). The regressions include tubewell fixed effects. We use a three-piece linear spline in total daily hours with knots at 8 and 16 to capture nonlinearities (a four-piece spline yields identical conclusions). Also included in the regressions is the total number of users at the tubewell that day. This variable corrects fo r the possibility that the proportion of tenant (other buyer) hours might diminish (increase) in total hours merely because most tubewell owners in Fd14R have only one or two tenants, so that high output days tend to have more non-tenant users.
The evidence is not favorable to the reliability hypothesis. Although the point estimate indicates that the proportion of tenant hours is diminishing in total hours on days when the tubewell is operating at 16 or more hours, this coefficient is not nearly significant. Moreover, the corresponding coefficient in the regression for the proportion of other buyer hours is also negative (and also insignificant). If the reliability hypothesis were true, we should observe that 27 One reason for wanting groundwater on certain days is that farmers often mix it with canal water during their scheduled turn. During kharif 1994, nearly one-third of the days on which groundwater was used coincided with the farmer's canal turn.
other buyers receive relatively more groundwater on near full capacity days. Similarly, there is no significant relationship between total hours and distribution across the two groups at the intermediate level of tubewell use, 8-16 hours (42 percent of operating days). 29 In sum, it does not appear that price differentials between tubewell tenants and other buyers can be explained by differences in service reliability.

Use of groundwater
We analyze groundwater use per acre separately for the three seasons covered in our data, including all plots in the watercourse, even those that relied solely on canal water or were left entirely fallow (as these may be irrigated in preparation for sowing of the next season's crop).
Each regression includes indicators for whether the cultivator of that plot is a tubewell owner or a tenant of one during that season, the omitted category being a (non-tenant) buyer. Since farmers, particularly those with large plots, often use more than one tubewell to irrigate a single plot to minimize conveyance losses, we calculate volume share-weighted averages of the tubewell owner and tubewell tenant variables across all the tubewells used on that plot over the season. As in the price regressions, we also control for tenancy per se; i.e., the proportion of land sharecropped and owner-cultivated.
It is also important to control for canal water used during the season (rainfall does not vary across farmers). Since canal turns are actively traded in Fd14R, seasonal canal water use is not necessarily exogenous; unobserved water productivity shocks that influence groundwater demand may also influence canal water use. A natural excluded instrument in this case is the canal water endowment, since it is clearly uncorrelated with the productivity shock yet highly correlated with canal water use, given imperfect insurance of idiosyncratic canal water supply risk. Lastly, we include two potentially important spatial characteristics in the regressions: distance to the nearest tubewell and distance to the head of the watercourse. Although these two 29 The fact that total daily hours appears in the denominator of the dependent variable and as a regressor may create a division bias if total hours are measured with error. As a result, the coefficients on total hours may be biased downward. However, this bias would be present both in the tenant and other buyer regression and, for this reason, would not explain our findings. That is, if the reliability hypothesis were true, we should find a significantly negative coefficient on total hours for tenants and a positive coefficient for other buyers. Division bias might make the latter coefficient insignificantly different from zero (though hardly negative given the general accuracy of the data), but then it should make the former coefficient even more negative, which is not what we observe.
variables are highly correlated (rho is about 0.7), the latter should capture the extent of conveyance losses in the delivery of canal water, and possibly local tubewell density as well. Table 3 presents the groundwater use regression results. The main finding is that tubewell owners and their tenants use significantly more groundwater per acre than other buyers in all three seasons. The result for tubewell tenants is consistent with our earlier evidence that these tenants face lower prices than other buyers. Moreover, there is never a significant difference in groundwater use between tubewell owners and tenants. This implies that the two groups face roughly the same shadow price of groundwater, a key result that we use later. It is also important to note that sharecroppers who are not tubewell tenants and owner-cultivators who are not tubewell owners do not use significantly more groundwater than other farmers. This finding is again consistent with the results from the price regressions showing no price discrimination by tenancy status for buyers who are not tenants of the tubewell owner.
A Smith-Blundell test for the exogeneity of canal water only rejects for kharif 1995, so we report the two-stage tobit estimates in this case. But, after correcting the standard errors, even the impact of canal water use in kharif 1995 is not significant, though it is negative as should be expected. Evidently, there is not much variation across plots in the amount of canal water received over an entire season. As Figure 2 suggests, however, the situation is likely to be very different at the weekly frequency. We explore intraseasonal patterns of canal water trading in more detail below.
The two distance variables have negative coefficients in all three seasons, but are rarely significant. Again, these variables are highly correlated and the sample sizes are not large, which is why we do not also include interactions with the tenant and owner variables as in the price regressions. If distance to the head of the watercourse captures only conveyance losses in canal water delivery, then its coefficient should be positive, since farmers in the tail-end should have a higher demand for groundwater. Apparently, though, this variable is also picking up the absence of tubewells in the tail of the watercourse (see Figure 1), which is not fully captured by distance to the nearest tubewell.
One possible explanation for why tubewell owners use more groundwater than other buyers is that they are generally wealthier farmers who have greater access to inputs that are complementary to irrigation. Of course, this argument does not explain the results for tubewell tenants, but it is still worth taking seriously. To do so, we pool the data from the two kharif seasons, assuming all coefficients except the intercept terms are constant, and estimate a farmer fixed effects specification. The sample consists of 167 plots cultivated by 64 farmers, 15 of whom cultivate multiple plots (up to 6) in at least one season and all but two of whom appear in both seasons. One important caveat is that tubewell tenancy status varies within only seven farms (comprising 25 plots), so that the estimated coefficient on this variable may be unreliable.
The situation for tubewell ownership status is better, as it varies within 13 farms (46 plots). The linear regression results in the last column of Table 3 confirm our basic finding: 30 Tubewell owners and their tenants use more groundwater than other buyers. The tubewell tenant coefficient, in this case, is considerably larger than tubewell owner coefficient (though not significantly so), which may be a symptom of the aforementioned reliability problem. In any event, the main point is that the tubewell ownership effect is not merely due to the presence of unobserved farmer endowments that are correlated with groundwater use.
Finally, note that we do not control for crop composition in Table 3, since crop substitution is just one of the ways farmers may respond to higher groundwater prices. As mentio ned earlier, cotton and fodder are the main kharif crops, wheat and rabi fodder are grown during the rabi season, and sugarcane spans both seasons with a growing period from February through December. Of these crops, sugarcane is by far the most water intensive, with the bulk of its irrigation applied in the kharif season. The water "requirement" for cotton is almost twice as high as that for wheat (Strosser, 1997). We find some evidence that tubewell owners and their tenants devote a higher proportion of their land to sugarcane than do other groundwater buyers, while the evidence for cotton is less conclusive. In any case, it turns out that controlling for crop composition has little effect on the results in Table 3 (see Appendix Table A.2), except for a modest diminution of the tubewell tenant coefficients in both of the kharif seasons. 31 This result suggests that most of the response to monopoly pricing of groundwater occurs at the intensive margin; i.e., less water for a given crop.
Summing up this analysis, we find a large and significant difference between the groundwater use of tubewell owners and their tenants, taken together, and that of other buyers. 30 The exogeneity of canal water use could not be rejected, so we report the OLS estimates. We also do not deal with the censoring problem using a tobit estimator because of the small (and variable) number of plots per farmer. 31 The crop portfolio variables are not entirely accurate in rabi because the proportion of land devoted to sugarcane is not accounted for in that season; sugarcane may be irrigated in the rabi.
In kharif 1994, for example, the predicted effect of converting plots using some groundwater purchased by non-tenant buyers into plots using only groundwater purchased by tubewell tenants is to double groundwater use (from 489 to 964 m 3 /acre). Given that other sources of irrigation do not substitute for this discrepancy, there appears to be a substantial resource misallocation; whether the associated deadweight loss is also large is a question we address in the next section.

Canal water trading
For the analysis of canal water transactions, the natural unit of time is the week since each plot (i.e., warabandi id) is assigned one turn at the canal every week. Virtually all transactions take place around the time of the farmer's turn. For example, if a farmer wishes to augment his weekly allocation, he usually does so by extending his turn either earlier or later than scheduled, typically by asking the farmer who goes before or after him, as the case may be, for some extra time. More complicated trades occur, but rarely, between farmers separated by some distance, requiring each of the intervening farmers to shift the times of their canal turns.
Each week, in each of the three seasons, we have the minutes of canal water actually used by each warabandi id as well as the minutes entitled to under the official warabandi schedule.
Though recorded excha nges involve as little as one minute of irrigation time, farmers frequently trade away their entire weekly endowment. We convert canal time into water volume using information on the daily discharge at the head of the watercourse, and normalize by cropped area for each warabandi id. Canal water transactions occur in 47 percent of the weekly observations during kharif 1994, involving about 11 percent of total water volume in the watercourse in the average week; during rabi 1994-95, transactions occur in 46 percent of the id-weeks (12 percent of total water volume); and during kharif 1995 this number rises to 54 percent (16 percent of total volume).
The general equilibrium analysis of the previous section implies that farmers facing higher groundwater prices should be net recipients of canal water in peak periods of water demand, whereas tubewell owners and their tenants should be net givers in these periods. In the context of our model, "peak" periods are precisely those with high aggregate groundwater use.
Thus, within each season, we rank weeks according to the total amount of groundwater used in Fd14R based on the data that underlie Figure 2. Our first indicator, peak I, comprises 6 of the 22 weeks in kharif 1994, 5 of 25 weeks for rabi 1994-95 (excluding the canal closure period), and 7 of the 22 weeks in kharif 1995. A variable threshold insures the maximum contrast between peak and non-peak weeks. Peak II uses a much more stringent definition, consisting of only the two weeks of highest groundwater use each season. Table 4 reports OLS regressions for the net volume of canal water per acre received on each plot or warabandi id in each week (i.e., use minus endowment). Included in the regressions are warabandi id dummies, week dummies, and the tubewell ownership and tenancy indicators (volume share-weighted averages across all the tubewells used on the plot over the season) interacted with the peak period dummy. Standard errors are problematic because of cross-sectional dependence. Since farmers mostly trade with their nearest neighbors, there is negative contemporaneous correlation in the residuals of adjacent warabandi ids, but not necessarily across ids some distance apart. Driscoll and Kraay (1998) propose a standard error correction suitable for panel data that allows arbitrary spatial dependence across all crosssectional units as well as serial correlation within units. We report t-values based on these standard errors along with the usual robust t-values in Table 4; both sets are similar.
The results in Table 4 generally support the implications of the theory, though statistical significance is not overwhelming. Relative to other groundwater buyers, tubewell owners and their tenants trade away more of their canal water in peak periods than they do in non-peak periods, hence the negative coefficients on the interaction terms in all seasons. Peak I appears to be more relevant than peak II in kharif 1994 and rabi 1994-95, but not so in kharif 1995. We discuss the economic significance of these findings in the next section. 32

Rural institutions and resource allocation
This paper explores the role of two distinctive institutions, tenancy and informal markets, in the allocation of irrigation water. Sharecropping is often viewed as inefficient because of the moral hazard problem. Indeed, Shaban (1987) finds persuasive evidence from India that input 32 To address the question of which trading rule governs canal water transactions, we also regress the net volume of canal water received per acre over the whole season on the tubewell tenant and tubewell owner indicators. In none of the seasons is either coefficient significant, which implies that 1 = κ --i.e., there is no premium on peak period water. Given the standard errors, however, it would be difficult to detect a small premium if one existed. use is less intensive on sharecropped land than it is on owned land. By contrast, our findings suggest that in a monopolized input market, such as that for groundwater, interlinked tenancy contracts actually enhance efficiency. Tubewell tenants use about as much groundwater per acre as do their landlords, whose shadow price is presumably the marginal extraction cost, and both tubewell tenants and owners use more groundwater than do other farmers.
We also find that incentive problems do not influence groundwater pricing and use decisions. In a model with non-contractible effort, in which irrigation water and effort are complementary in production, tubewell owners should charge lower prices not only to their own tenants, but to the tenants of other landlords as well. However, we find neither groundwater price nor use differentials among other buyers according to their tenancy status. This result does not necessarily imply that moral hazard is absent; rather, it may only mean that the complementarity between irrigation water and effort is weak or nonexistent.
The second rural institution investigated in this paper is the informal market for canal water. The "informality" of this market derives from the fact that canal turns are borrowed without an explicit commitment to repay. Our empirical analysis is limited to the question of whether, given the observed groundwater price differentials between tenant and non-tenant buyers, canal water transactions bring the allocation of irrigation closer to Pareto optimality. The answer appears to be yes; canal water is transferred from tubewell owners and their tenants to other buyers during periods high of water productivity and repaid in periods of low productivity.
But, as discussed below, the practical impact of canal water trading is small.

Efficiency and equity implications of groundwater monopoly
Is the deadweight loss from groundwater monopoly large enough to warrant concern?
Our finding that tubewell owners and their tenants use the same amount of groundwater, coupled with the evidence against a role for non-contractible inputs, points to the two-part tariff model of proposition 1 in which tubewell tenants are charged marginal cost and other buyers are charged above marginal cost. In this case, there is no deadweight loss involved in the allocation of groundwater to the tubewell tenant, only in the allocation to other buyers.
We wish to compare the current situation in Fd14R with a scenario in which all groundwater is purchased at marginal cost, keeping in mind that some plots receive groundwater from multiple tubewells under different arrangements. Assuming a (locally) linear demand for groundwater and using c p T = , deadweight loss is given by where * w refers strictly to groundwater use. Table 1 provides an estimate of the average T B p p − , namely 9.3 Rupees/hour, which we then convert into volumetric terms. To get for each plot, we take the groundwater use differentials estimated in Table 3 for kharif 1994 and rabi 1994-95 and multiply them by the share of groundwater purchased as non-tenant buyers. The resulting annual deadweight loss for the watercourse as a whole comes to 9 percent of total groundwater expenditures (imputed at marginal cost for tubewell owners), and 19 percent of annual groundwater expenditures of non-tenant buyers. While these would seem to be nontrivial numbers, groundwater expenditures constitute only about 8 percent of total household income in rural Pakistan (around two-thirds of irrigation is supplied by canal water and rainfall), so any policy that removes the monopoly distortion can have only a limited impact on social welfare.
Our calculation ignores canal water trading, which the evidence suggests ameliorates deadweight loss. However, the estimates in Table 4 most favorable to this hypothesis, those for kharif 1994, imply that during six "peak" weeks only about 16 cubic meters per acre per week more of canal water are supplied to other buyers than on non-peak weeks, or about 100 cubic meters per acre for the whole season. This latter number is less than five percent of total irrigation water volume during kharif 1994 in Fd14R. The same calculation for kharif 1995 shows that trading reallocates less than two percent of seasonal irrigation. Though this may be a very valuable two percent, it is still hard to imagine that canal water trading appreciably reduces the deadweight loss from groundwater monopoly.
To assess the distributional implications of monopoly power, again consider the marginal cost pricing scenario. We calculate the implied surplus gain on each plot and then aggregate to the farm level for the kharif 1994 and rabi 1994-95 seasons. Also, using information on total groundwater sales by each tubewell owner over this period, we calculate the surplus loss to groundwater monopolists. For reasons that will become apparent below, all farmers with a productive stake in the watercourse, either as cultivators or as absentee landlords, are included in our calculations, for a total of 105 farmers. Our data set is unique in this regard in that it tells us not only who cultivates each plot of land, but also who owns each plot. 33 Consider first the distributional implications of marginal cost pricing in the "short-run", within which land prices, rents, and tenancy shares do not adjust. In this short-run, only tubewell owners and their non-tenant buyers are affected by the policy. Figure 4 plots, against the distribution of landholdings, the nonparametric (LOWESS) regression function of each farmer's annual net surplus gain as a proportion of his imputed household expenditures. 34 Note that since more than a quarter of the households in Fd14R are landless, there is a large cluster of observations at the minimum expenditure level. The story that emerges in the short-run is not consistent with the "water-lord" stereotype, in which a move to marginal cost pricing would benefit many poor farmers at the expense of a handful of wealthy tubewell owners. To be sure, net benefits decline relative to wealth and become negative as wealth increases, but the rate of decline is not dramatic. There are three factors militating against the water-lord scenario, at least in Fd14R. First, tubwell tenants do not gain at all from marginal cost pricing, and they tend to be small landowners or landless. Second, there are a few cases of tubewells jointly owned by two farmers, each with modest landholdings, and these farmers are net losers from the policy. Third, several tubewell owners with large landholdings are also buyers of groundwater on plots they rent or sharecrop in elsewhere in the watercourse, and so may even gain on net from marginal cost pricing.
In the long-run, the land tenancy market will adjust to marginal cost pricing. Rents on plots near monopolistic tubewells will increase, and the terms of share-tenancies on such plots will worsen, so as to just extract the entire surplus gain from the tenant. It is the surrounding landowners, therefore, not necessarily the current cultivators, who ultimately benefit from the 33 One caveat is that we have (and use) information on total landownership, both within and outside the watercourse, only for cultivating households, whereas for the 36 absentee landlord households we only know their landholdings within the watercourse. However, this may not create much of a bias in the distributional analysis because, while landholdings within the watercourse are similar for the 49 owner-cultivators and the 36 absentee landlords (medians are 5.2 and 4.8 acres, respectively), landholdings outside the watercourse are relatively small for the former group (median=0, mean=1.7 acres). Therefore, unless there is very strong selection on cultivator status, landholdings outside the watercourse should also be small for the absentee landlords.
elimination of their neighbors' monopoly power. The long-run curve in Figure 4 takes this into account by assigning all the benefits that formerly accrued to renters and sharecroppers over to the owners of those plots. Thus, landless households no longer benefit at all from the policy.
More generally, as tenancy terms adjust, benefits are shifted from small cultivators, who tend to rent or sharecrop in land, to households in the middle of the landowning distribution, many of whom are absentee landlords in Fd14R. In the long-run, then, a policy aimed at eliminating monopoly pricing would do little to help the poorest farmers.

Policies for groundwater markets
The above calculations provide the best-case scenario for what a policy intervention in the groundwater market can hope to achieve in terms of efficiency and equity. Practically speaking, however, neither the taxation nor the price regulation necessary to achieve marginal cost pricing are easily enforceable, so alternative interventions must be contemplated. In this context, it is important to realize that local groundwater markets resemble natural monopolies. Other solutions to the monopoly problem involve changes in the ownership structure of either land or tubewells. For example, if a tubewell owner could be encouraged to purchase all the land in the "command area" of his tubewell, then he would perfectly internalize the deadweight loss associated with monopoly pricing. Whether he then sharecrops out some of this land to tubewell tenants (as is common in Fd14R), or rents it out, he should charge only marginal cost for groundwater. Indeed, the puzzle is why trade in land does not entirely eliminate monopoly pricing of groundwater through buy-outs of landowners who do not also own tubewells. One answer might be that the land sales market has been slow to adjust to the relatively new technology of groundwater extraction spurred by the availability of inexpensive diesel engines in the 1980's; in fact, none of the tubewells in Fd14R were installed prior to 1987.
Another answer may be that the situation is complicated by the fact that tubewell command areas often overlap and so the efficient distribution of land ownership is unclear; in any case, the efficiency cost of groundwater monopoly is not that big, as we have seen.
The alternative to consolidating land ownership around a given tubewell is to divide tubewell ownership among several neighboring landowners (see Meinzen-Dick, 1996). Here, again, the question is why joint ownership has not happened already--only 3 of the 18 tubewells in Fd14R are jointly owned by two farmers. Evidently, there are significant costs to joint ownership, perhaps due to coordination problems or moral hazard. Interestingly, all three cases of joint ownership in Fd14R involve two brothers or father and son, between whom such costs are presumably low. Thus, before promoting joint ownership of tubewells (e.g., by targeting credit or subsidies to groups of farmers), more research is needed to understand the costs of sharing these investments and, specifically, on how these costs compare to the limited gains from eliminating monopoly pricing in the groundwater market.
All of this discussion may be obviated by the pace of recent developments. There were 15 tubewells in Fd14R at the start kharif 1994, and three more were installed during kharif 1995.
A field visit in early 2000 revealed an additional 9 tubewells, thus nearly doubling the existing number in about five years. It would be surprising if such a dramatic increase in the supply of groundwater does not alleviate the misallocation of 1994-95, but this remains to be seen. If so, monopoly power in the groundwater market would only be an ephemeral problem, a "growing pain" in the transition to a new technology.      Notes.--Dependent variable is net volume of canal water received in week per acre. All regressions include warabandi id dummies and week dummies. a Excludes period of canal closure (five weeks). b Definition I: 6 weeks with highest overall groundwater use for kharif '94, five weeks for rabi '94-95, and seven weeks for kharif '95. Definition II: 2 weeks with highest groundwater use in each season. c Robust (Huber-White) absolute t-values. d Absolute t-values adjusted for spatial dependence and serial correlation (lag window = 2). Groundwater prices Table 1 tubewell/warabandi id a day All groundwater transactions in 18 month survey period Reliability of supply Table 2 tubewell day All tubewell operating days in 18 month survey period Groundwater use Table 3 warabandi id season All warabandi id (plots) in watercourse Canal water transactions Table 4 warabandi id week/season All warabandi id (plots) in watercourse Deadweight loss ---watercourse annual All warabandi id (plots) in watercourse in 1994-95 Distributional implications  Notes.--See notes to Table 3.
a Refers to cotton in the kharif seasons and wheat in the rabi season. .014359