Governing the Commons?: Water and Power in Pakistan's Indus Basin

Surface irrigation is a common pool resource characterized by asymmetric appropriation opportunities across upstream and downstream water users. Large canal systems are also predominantly managed by the state. This paper studies water allocation under an irrigation bureaucracy subject to corruption and rent-seeking. Data on the landholdings and political influence of nearly a quarter million irrigators in Pakistan's vast Indus Basin watershed allow the construction of a novel index of lobbying power. Consistent with a model of misgovernance, the decline in water availability and land values from channel head to tail is accentuated along canals having greater lobbying power at the head than at the tail.

Surface irrigation is a common pool resource characterized by asymmetric appropriation opportunities across upstream and downstream water users. Large canal systems are also predominantly managed by the state. This paper studies water allocation under an irrigation bureaucracy subject to corruption and rent-seeking. Data on the landholdings and political influence of nearly a quarter million irrigators in Pakistan's vast Indus Basin watershed allow the construction of a novel index of lobbying power. Consistent with a model of misgovernance, the decline in water availability and land values from channel head to tail is accentuated along canals having greater lobbying power at the head than at the tail.

Introduction
Human efforts to control the flow of water for agriculture gave rise to the world's first great civilizations, 1 and today surface irrigation delivers lifeblood to tens of millions of farmers across the globe. Gravity-flow surface irrigation is also significant as a common pool resource. Because it is prohibitively costly to fully enforce off-take from a river or canal, irrigation water is subject to appropriation by upstream users ("headenders") at the expense of those downstream ("tailenders"), a version of the tragedy of the commons. 2 In Governing the Commons, Ostrom (1990) argued that non-state institutions often arise organically to avert such tragedies through collective action. Yet, private (free market) allocation of canal water in large-scale irrigation systems faces daunting economic and technical hurdles (Sampath 1992). Instead, extensive irrigation bureaucracies have been established to operate centralized systems for the allocation of water as it makes its way down from the rivers and main canals to the network of distributaries, minor and sub-minor canals, and, finally, to the watercourse outlets, where it is delivered to individual farms. While the dysfunction of state-managed irrigation has been well documented (e.g., Wade 1982 andChambers 1988), 3 we lack a falsifiable theory of commons regulation that accounts for the differing incentives within the bureaucratic hierarchy as well as between the regulator and the regulated.
In this paper we consider the interplay between bureaucratic management and common property users, or rather groups of users, in the context of the world's largest canal irrigation system, that of the Indus Basin watershed of Pakistan. On this vast system, de jure water allocations are based on a proportionality principle inherited from the British colonial administration: to each according to his cultivable area. De facto allocations, however, are determined by interactions between groups of farmers, organized by channel outlet, and the provincial irrigation department. As we will argue, this interaction is characterized by both corruption and rent-seeking. Corruption is of the "with theft" variety (Shleifer and Vishny, 1993), in that the farmers who pay the bribe and the local irrigation official who demands it both benefit; the losers are the farmers at the downstream outlets who receive less water than they are entitled to. Rent-seeking arises as coalitions of headenders and tailenders lobby the higher irrigation department office to intercede on their behalf, e.g., by replacing (or not replacing) the local official. In choosing how hard to lobby, we assume that the head coalition takes into account the bribes its members must pay, while the rational local official internalizes the rent-seeking induced by his own corruption.
Our theoretical model allows a role for political influence in the rent-seeking contest. Of critical importance for the contest outcome is the distribution of lobbying power (or efficacy) along a channel. We establish that, insofar as such influence is relatively greater at the head reaches than at the tail, "theft" will be greater, which is to say that more water will be diverted toward the head and away from the tail. Our model also has implications for the value of farmland, which is assumed to reflect not only the productive value of the canal water delivered but also the bribes that farmers may have to pay to ensure these deliveries.
Even though the bribe amount is increasing in the relative influence of headend landowners, thus depressing their land values, we show that the productive value of the greater off-take at the head more than makes up for this; thus, on balance, the head-tail land value differential increases with relative head influence. Finally, the assumption of competitive rent-seeking delivers a distinctive symmetry result: a one unit increase in lobbying influence of the head coalition has an equivalent impact on the head-tail differential in both water availability and land values as a one unit decrease in political influence of the tail coalition.
To test these implications, we have collected a truly unique data set on both landown-ership and influential positions held by every water-user in each of 3,923 watercourses (outlets) along 448 channels throughout Punjab province; in all, we have information on about 220,000 individual farmers. Knowledge of these two dimensions of influence, land and official position-holding, allows us to extend recent work equating political power with landownership (e.g., Anderson et al. 2015 and Baland and Robinson 2008). We construct a novel and intuitively appealing index of lobbying power that takes into account the interaction between irrigated lanholdings, a measure of an individual's economic stake, and personal influence aggregated across all members of each contending coalition. Landowners contribute to the index more than in proportion to their economic stake insofar as they hold an influential position (such as a local political office). Our empirical strategy exploits variation in canal discharge and land values across head and tail outlets along the same channel, thus purging channel-level unobservables that may be correlated with both lobbying influence and water availability.
The main contribution of this paper is to develop and empirically test a political-economy model of common pool resource management in the spirit of Krueger (1974). Past literature, by contrast, is largely prescriptive, focusing on the welfare costs of overexploitation and the optimal regulation of the resource by a benevolent social planner (e.g., Huang and Smith 2014 for the case of a fishery; Gisser 1983 and Timmins 2002 for the case of a groundwater aquifer). 4 We also contribute to a growing empirical literature concerned with bureaucratic incentives and corruption (Reinikka and Johnson and Libecap (1982), who consider the conflicting interests of heterogeneous fisherman in the formation of fishery regulation along the Texas coast. In their context, however, corruption within the regulatory enforcement agency does not appear to be an issue. 5 Reinikka and Svensson (2004) touch upon this issue by considering how communities interact with their local officials' school-fund disbursement decision. Importantly, however, there is no inter-community 3 The remainder of the paper is organized as follows. In the next section, we provide institutional background on the canal irrigation system in Pakistan, the basis upon which we build our theoretical arguments in section 3. Section 4 describes the data collection effort on the two aspects of political influence and on land values, as well as the measurement of canal discharge in the Indus Basin. In Section 5, we present empirical tests of the theory, consider alternative explanations for the results, and analyze their implications for wealth inequality. We conclude in Section 6.

Indus Basin irrigation system
The Indus Basin irrigation system, which accounts for 80% of Pakistan's agricultural production, lies mostly in its most populous province, Punjab, wherein it encompasses 37,000 kilometers of canals and irrigates about 8.5 million hectacres. From the Indus, Jhelum, Chenab, Ravi, and Sutlej Rivers, a dense network of main canals, branch canals, distributaries, minors, and sub-minors ramify out, ultimately feeding 58,000 individual watercourses in Punjab alone (See Figure 1 for a schematic of the canal hierarchy.). 6 Each watercourse outlet or mogha supplies irrigation to typically several dozen farmers according to a rotational system known as warabandi. The institution of warabandi (literally "fixed turns"), which traces its origins to British colonial rule and to the early development of irrigation in the Indus Basin, embodies a modified principle of equity: to each irrigator in proportion to his cultivated area. At each level of the canal hierarchy in this continuous gravity-flow irrigation system, "authorized discharge" is allocated in proportion to cultivable command area (CCA). At the main canal level, irrigation department staff operate a series competition for resources in their context and, hence, officials are not balancing opposing interests. Also related, Banerjee et al. (2001) explore the implications of rent-seeking within private sugar cooperatives in India, focusing on the conflict of interest between large and small growers. 6 On about a third of Punjab's irrigation system, canal management was devolved, in fits and starts, to locally elected farmers organizations beginning in the early 2000s (see Jacoby et al. 2018). This paper focuses on the remaining two-thirds of the system.  Figure 1: Channel schematic with discharge gauges of gates regulating flow into the off-taking distributaries according to a rotational schedule. However, since moghas are ungated, discharge into tertiary units, the watercourses, is determined by the width of the outlet; the greater the watercourse CCA, the greater the authorized outlet width and thus the greater the water in-take each week. Over the course of a week, proceeding from the head to the tail of the watercourse, each farmer takes his preassigned turn at using the entire flow to irrigate his field, with the length of turn proportional to the size of the field.
Although design discharge at any point along a channel accounts for seepage and conveyance losses and is therefore a declining function of distance to the head (see Figure 1 inset), tail outlets should, by virtue of their greater width, receive their full water entitlement. 7 In practice, however, this elaborately constructed allocation system does not guarantee equity.
If discharge at the distributary head is intermittent during the filling cycle (as is often the 7 Since there is no adjustment for seepage within a watercourse, farmers at the tail-end of a watercourse are at a disadvantage relative to those at the head even on paper (more on this below). 5 case; see Bandaragoda and Rehman 1995), or if the canal becomes over-silted, water may fail to reach the tail outlets. Canal maintenance, which consists largely of de-silting operations conducted during the January canal closures, is the responsibility of the irrigation department, giving it discretion over whether and how a canal gets dredged. 8 When a channel becomes silted up, water level rises at the head, increasing discharge there, while falling at the tail (Van Waijjen et al. 1997). Lack of canal maintenance, therefore, would typically favor farmers at the head outlets (Figure 1 inset), which may give rise to lobbying by farmers at tail outlets to increase maintenance and by those at head outlets to suppress it.
Maintenance suppression can thus be seen as one form of water theft.
More blatant forms of theft are well documented in the Indus Basin: Groups of farmers located in the upper reaches of the distribution canals may partly break their outlet or enlarge it in order to increase the discharge delivered to their fields...Farmers offer bribes to irrigation officials to avoid that the outlet be repaired and brought back to its official dimension, but also to avoid that the offense be taken to court. The outlet changes are typically made for a period of 6 months, after which it is repaired unless the farmers pay a new bribe. (Rinaudo 2002, p. 407-8). Uncooperative local staff may be transferred to another position. 9 But, such rent-seeking presents a trade-off: The change in outlet dimensions are made by the line agency staff on a temporary basis, and they are periodically re-negotiated... [This] seems to indicate that the irrigation agency staff regulates the competition between rent-seekers, and maintains the potential costs of tail-enders' opposition under a threshold guaranteeing the stability of their position.
In the next section, we develop a model that incorporates precisely this trade-off: too much corruption and the irrigation official risks losing his plum position.

Preliminaries
Assume a continuum of outlets along a channel indexed by n ∈ [0, N ], with n = 0 representing the first outlet at the head of the channel and n = N the last outlet at the tail of the channel.
Suppose that each outlet has the same command area, normalized to one, and hence the same de jure endowment of water w 0 . The de facto inflow of water to each outlet is given by the function w(n), which for the channel as a whole is constrained by 10 Agricultural output depends on water per acre cultivated, but with diminishing marginal product. 11 The demand schedule for water D(w) is, therefore, downward sloping (D < 0 for ∀w). Suppose further that D(w 0 ) > 0 and that surplus from off-take w is So, the de jure allocation has a positive marginal value and confers a collective surplus or total value of s 0 = s(w 0 ) to farmers on the outlet.
The efficient allocation of canal water along a channel maximizes subject to (1), which requires that D(w(n)) be equal across outlets. The de jure allocation, with w(n) = w 0 ∀ n, is thus efficient and deviations from equal per acre allocations, such as those discussed below, create deadweight losses. 12

Appropriation and corruption
Assume that canal water at each outlet is appropriated until its marginal value is zero subject to availability. Since water arrives first at the head of the channel, outlets at the head have first-mover advantage; some outlets at the tail must, therefore, get no water. Define outlet off-takeŵ such that D(ŵ) = 0 and the 'critical' outletn bynŵ = N w 0 (using equation 1).
Thus, all outlets n ∈ [0,n] off-takeŵ − w 0 in excess of their legal entitlement and receive surplusŝ = s(ŵ), whereas all outlets n ∈ (n, N ] receive no water and get zero surplus. Now consider the role of the local irrigation department official with the authority to enforce the de jure water allocation. While the official could, at some effort cost, set w <ŵ by restricting outlet tampering and other such violations, we assume that the amount of water theftŵ − w 0 is taken as given (the enforcement cost is prohibitive). Alternatively, we may suppose that the offical engages in Nash bargaining with each outlet over w, which yields the same result, i.e., w =ŵ. 13 In any case, the official accepts a bribe from each offending outlet to overlook the infraction. 14 If the official cannot commit to charging a particular bribe amount b to every outlet, then b would also be determined outlet-by-outlet in a Nash bargain and would thus only depend upon excess surplusŝ − s 0 . 15 However, in the more general case developed in the next two subsections, the official commits to a bribe amount and in so doing takes into account the channel-level impact of the corruption. What bribe will the official charge? A larger bribe, up to the maximum willingness to payŝ − s 0 , yields higher income to the official, but there is a potential downside. Before turning to the local official's trade-off, we must first consider rent-seeking.

Rent-seeking
Water theft creates groups of winners, namely farmers at head outlets, and losers, namely farmers at tail outlets. Define the head outlet coalition C H = {n|n ∈ [0,n]} and the tail outlet 13 In particular, w would be chosen to max where b is the bribe and η is an exogenous bargaining weight. The necessary condition for an optimum implies that s (w) = D(w) = 0.
14 "The distinction between a bribe, offered by farmers to get the [irrigation official] to do something he might not otherwise do, and extortion money, demanded by the officer in return for not inflicting a penalty, is often difficult to draw in practice." (Wade 1982, p. 297). 15 In the model of Mookherjee and Png (1995), which resembles ours inasmuch as it involves a triad of regulator, inspector, and polluter, bribes paid by the polluter to the inspector are determined in a Nash bargain. A crucial difference between their set-up and ours, however, is that they have only one polluter and thus no competition for rents between those subject to regulation. coalition C T = {n|n ∈ (n, N ]}, wheren is the last outlet that would receive water under the appropriation scenario described in the last subsection. Each coalition can exert political pressure on the higher-level irrigation department bureaucracy to obtain their preferred outcome. C H lobbies to maintain the water theft, which we take as the status quo, and C T lobbies to restore the de jure water allocation. To effectuate the latter outcome, we may think of the local official as being transferred to another posting and replaced, at least temporarily, by direct irrigation department oversight and enforcement. 16 Following Tullock (1980), then, we assume that the probability P of C H winning the rent-seeking contest depends on the effort level, e j , of both coalitions j = H, T as follows: 17 where the ι j represent the marginal influence of coalition j. When ι H = ι T , there is a power asymmetry along the channel.
Assuming a unitary marginal cost of effort, 18 expected net surplus for C H is Motives of the higher level office to provide for such a "clean" regime may include the need to respond to demands for political accountability. 17 The linearity of each player's effort in the probability function is a standard simplification in the literature on games of rent-seeking (see Nitzan 1994). 18 This assumption, applied to lobbying effort by both head and tail coalitions, is innocuous. High (low) marginal influence ι j is equivalent to low (high) marginal cost of effort.
where ∆ T = (N −n)s 0 . Although we abstract here from free-riding on rent-seeking effort within each coalition, political influence ι j can be seen, in part, as a measure of the efficacy of collective action (as in Acemoglu and Robinson's 2008 political contest model). Moreover, rent-seeking effort may consist of an array of activities that could differ between head and tail, especially given the nature of the status quo. For instance, C T may engage in protests (as in Reinniki and Svenson 2004) whereas C H may adopt actions ranging from "mutual backscratching" with bureaucratic officials to hiring private goon squads to block any effort at restoring the de jure allocation.
Each coalition chooses its rent-seeking effort taking that of the other coalition as given.
Assuming an interior solution, e T = Ωe H , where Ω = ∆ T /∆ H is the ratio of win-loss differentials. Thus, the Nash equilibrium win probability is This equilibrium probability of maintaining corruption depends on each coalition's net gains from winning the lobbying contest weighted by their marginal influence, and may be written more compactly asP where θ = ι H /ι T is a parameter representing the relative influence of the head coalition vis-à-vis the tail coalition. If θ = 1, then the two coalitions' influence is perfectly symmetric.

The local official's problem
Because the local official's position hinges on the outcome of the lobbying contest, he is effectively paid an efficiency wage. As long as he is retained he receives bribe incomenb; otherwise, he receives his outside option, which we normalize to zero. Bureaucratic career concerns thus generate a trade-off with regard to b, the amount of the bribe. 19 In particular, the expected income maximization problem is We can, therefore, view the local irrigation official as trading-off lower bribe income against greater net surplus to head outlets and, consequently, a higher equilibrium probability of retaining his position.
Given equation (8), it is straightforward to derive an explicit expression for the optimal bribe amount from the first-order conditions to problem (9): where r = (N −n)s 0 /nθ and ∆s =ŝ − s 0 . 20 Directly, we obtain (see Appendix for all proofs) which says that the greater the relative influence of the head coalition, the greater the bribe that head outlets have to pay. Intuitively, a more influential head coalition can be left with less net surplus (through a higher bribe) and still exert the same amount of effective lobbying power in favor of the status quo.
Although we do not observe bribes, lemma 1 helps deliver testable implications concerning water theft. Expected water availability at the head and tail are, respectively, w H (θ) ≡Pŵ+ Water theft is thus increasing in the relative influence of the head, a result not as obvious as it seems at first blush. While an increase in θ raises the probabilityP of C H success, it also increases the bribe that headenders must pay (lemma 1), which lowersP . Nevertheless,P (and hence τ ) rises on balance.

Land values
The market value of farmland reflects both the productive value of irrigation water and the cost of obtaining it. Put simply, bribes are capitalized into land values. Theoretical expressions for land values V j (ignoring discounting) at, respectively, tail (j = T ) and head In other words, abstracting from other sources of irrigation, tail-end land has value only insofar as it receives canal water (which occurs with probability 1 −P ), whereas the value of land at the head is negatively related to the size of the bribe.
Our focus is on the percentage land value differential between head and tail, or δ = log(V H /V T ), regarding which the model delivers So, as headend irrigators gain in political influence relative to tailend irrigators, the value of land at the head rises relative to the value of land at the tail. As with Proposition 1, this result is also not obvious because the higher probability of C H 's lobbying success and the higher bribe amount (see Lemma 1) have countervailing effects on δ. 21 21 The proof (see appendix) requires the assumption of a linear demand for water or at least thatŵ is sufficiently close to w 0 that demand is effectively linear over [w 0 ,ŵ].

13
Finally, since only relative political influence matters for lobbying success in our model, we have A 1 percent increase in head influence has an equivalent effect on water theft and land values as a 1 percent decrease in tail influence.
Before taking these propositions to the data, note that we have described a possible scenario in which an equitable allocation of water between head and tail is Pareto optimal and yet property rights are de facto assigned exclusively to the head. In a Coasean world with zero transactions costs, water would be transferred from head to tail in exchange for payment.
While there are many reasons to believe that such water contracts between head and tail patwaris, the latter responsible for maintaining the cadastre and recording land sales.
In addition, the survey firm visited one outlet at the head and tail of each selected channel to verify that the assessments were accurate.
Survey teams were able to cover all but one of the intended 470 channels (all but 13 of 4,294 outlets). However, 286 of the remaining 4,281 outlets were found to be permanently closed by 2016 for reasons including destruction in floods, population shifts, or perennial lack of water in the channel. 22 Of the closed outlets, 29 occurred on 4 channels on which every other outlet was also closed, leaving us with 465 open channels.
There are 103 open channels on which at least one selected outlet was closed, which is not a problem for us empirically, but in 15 cases the channel had no head outlets and in 2 cases no tail outlets. This leaves us 448 channels with both head and tail outlet data, which our empirical strategy requires (see Appendix Table C.1 for channel characteristics by division). That we lose only two channels to tail closure suggests that selection bias -i.e., less water theft on average in observed channels -is unlikely to be a serious issue.

Lobbying influence variables
Data are available on nearly a quarter-million irrigators on our final sample of 448 channels.
Rather than consider the distribution of individual landholdings, however, we aggregate across brothers to obtain total "family" landownership. In particular, we sum (canal irrigated) land owned on each outlet across individuals sharing the same father's name, yielding almost 150,000 family level observations. Given inheritance norms in Pakistan, patrimonial land is typically controlled by the sons. Using individual landholdings would imply that influence (as measured by economic stake) along a channel is diluted by a factor of N once landownership passes from a father to his N sons, which strikes us as extreme since, at a minimum, brothers are likely to cooperate on land-related matters and in many cases even designate one of their own as operator of their joint holdings. Figure 3 illustrates the distribution of family landholdings on all head outlets and all tail outlets pooled together.   Given that influential office-holding is so sparsely distributed along channels, its effects may prove difficult to detect in practice.

Land values and groundwater
Data on land values and groundwater conditions were collected at the head and the tail of each watercourse (tertiary canal), thus providing 2 observations per outlet on 3,922 outlets (1 outlet had missing land value data), for a total of 7,844 observations. Since watercourses are typically unlined and, in contrast to secondary channels (i.e., distributaries and minors), no allowance is made in their rotational schedules for the considerable seepage losses (Bandaragoda and Rehman 1995), land values should be lower at the tail of a watercourse than at the head. And, this is indeed what we find. Estimates in the first column of Table 1 show that land at the watercourse head is 15% more valuable per acre than land at the tail.
More reflective of canal water misappropriation, however, is that land at a head outlet of a secondary canal carries an 11% premium over land at a tail outlet of that same channel -typically such land is separated by little more than 10 km of canal (see Appendix Table   C.1). Specification (2) in Table 1 replaces the dummy variable for whether the outlet is at the head of the channel with the actual distance from the head, which of course attracts a coefficient of opposite sign. Since this refinement barely improves fit, we retain what will prove to be the simpler specification (1) in the sequel.
These inequities in the distribution of canal water are also reflected in groundwater conditions, which, in turn, affect land values. Depth to water table (DWT) is inversely related to the extent of aquifer recharge from nearby sources of surface water, especially irrigation canals. Results reported in the third column (first row) of Table 1 indicate that groundwater depth increases by a little more than 1% from head to tail of the average watercourse, attributable to both the inefficiency of conveying surface water through these tertiary channels as well as to the greater distance to good recharge (adjacent to the distributary or minor canal). On secondary canals, we estimate (second row) that water tables fall by about 3% from head to tail of the average channel. Once again, the mechanism is recharge, or lack thereof, due to the pervasive tail-end water deprivation that we document in the next sub-20

Canal water discharge
Punjab Irrigation Department's Program Monitoring and Implementation Unit (PMIU) has maintained daily records of authorized (designed) and actual canal discharge since 2006.
for j = H(ead), T (ail), where Q j id is daily discharge at position j of channel i andQ j id is the corresponding authorized daily discharge.
Tail shortage, DP R H it − DP R T it , is a measure of water theft, albeit a noisy one. As noted earlier, the extent to which tail outlets are deprived of water relative to their endowment (given discharge at the head) may also depend on exogenous factors such as flow variability into the channel. At any rate, tail shortage averages 0.053 (or 8.2% of mean tail DPR) across the 448 sample channels and across all years of discharge data ; the corresponding figure for all other irrigation channels in Punjab is 0.044 (6.3% of mean tail DPR). 24 Breaking this down by year, Figure 5 shows that, despite their selection on specific criteria, our sample channels track non-sample channels quite closely; in both sets of channels, tail shortage appears to be trending downward over time. An indicator for whether DP R T /DP R H < 0.5, a measure of extreme tail shortage in the channel, averages 0.073 in the sample across years, which is to say that, on about 7% of channels, tail outlets receive less than half the volume of irrigation relative to their allotment than head outlets.
where Z c is a vector of channel level controls, µ c is a channel-level fixed effect (absorbing the constant term) and ε pc is an idiosyncratic error. Notice that for β H = β T = λ = 0, the fixed effects estimatorβ 0 = 1 N C (Y Hc − Y T c ) is the average head-tail outcome differential 24 To maintain comparability, we exclude all 1,053 channels that were covered by the irrigation management reform that began in the mid-2000s (see Jacoby et al. 2018). 25 Although the corresponding average for non-sample channels is similar (0.080), Figure 5 indicates a substantial discrepancy for years prior to 2010. To reiterate, this is not an issue of sample representativeness. across all N C channels (see previous section). Equation (14) not only controls for all unobserved fixed channel-level characteristics (as in Table 1), but also for observed channel-level characteristics (Z c ) that may be correlated with head-tail outcome differences.

Clustering and inference
Continuing with our two observations per channel (Head/Tail) set-up, let us now ask whether the standard errors from the channel fixed effects estimation should be clustered on channels. Abadie et al. (2017) show that the answer to this question, rather than depending on whether clustering the standard errors "makes a difference," depends on whether there is clustering in sampling or in assignment. If either form of clustering is present and if there is treatment effect heterogeneity, only then should one cluster standard errors.
Clustering in sampling concerns how many clusters in the population are present in the sample. In our case, as noted, the term "sampling" of channels is really a misnomer. All channels in Punjab that met the selection criteria set out in Appendix B were chosen for analysis. Since there was no random selection within this universe, the cluster sampling probability is one. Clustering in assignment concerns the regressor of interest. Returning to the restricted version of equation (14) Y pc = β 0 H pc + µ c + ε pc , think of H pc as the treatment and consider the assignment process that determines its value within clusters (channels). In our case, trivially, Pr(H pc = 1) = 0.5 and hence the assignment process is the same across all clusters. Since the cluster sampling probability is one and there is no clustering in assignment of treatment, the fixed effects standard errors for regression equation (15) should not be adjusted for clustering on channels. 26 Thus far, we have assumed one observation per position on a channel, but our actual data are stacked at each channel-position. For example, in the case of DPR, there are multiple years of data at both head and tail of each channel. To account for this, we cluster our standard errors at the channel-position level.

Estimating the lobbying influence function
Letting N pc be the number of irrigators (or, rather, families) at position p of channel c, we posit an aggregate lobbying influence function for coalition C p of the form where L ipc is landholdings of irrigator i = 1, ..., N pc at position p of channel c and I ipc is an indicator for whether that same irrigator holds an influential office. The parameter γ reflects the importance of influential office-holding and the aggregator function G can be the mean operator G(x 1 , ..., x k ) =x or a percentile operator. In the former case, we have ι pc (0) =L pc , which is mean landownership at position p of channel c (see Figure 4). Here, of course, each irrigator contributes to ι pc in proportion to their landholdings. For γ > 0, irrigators with large landholdings, to the extent that they hold influential positions, contribute to ι pc more than in proportion to their landholdings. Conversely, an office-holder contributes little to the aggregate influence of his coalition unless he also has a significant economic stake in the outcome of the lobbying contest in the form of large landholdings.
If we indeed find a nonzeroγ, hypothesis testing proceeds as follows: First we test the symmetry hypothesis H 0 : β H = −β T , using a conventional Wald test as though γ were known with certainty. As discussed by Hansen (1999), the sampling variance of γ is not of first-order asymptotic importance. If we cannot reject symmetry, we then impose it so that 27 Finally, we test H 0 : β 1 = 0. In this case the test statistic is non-standard because of the non-identification of γ under H 0 , requiring a special bootstrap procedure.

Baseline results (γ = 0)
Before turning to estimation of the office-holding influence parameter γ, we consider the role of economic stake -irrigated landholdings on the channel -in isolation, focusing on the form of aggregator function G. In Table 2, we present results for equation (14) using the delivery performance ratio, Y pc = log DP R pc , and land values per acre, Y pc = log V pc , along with various G functions (mean, 80th, 90th, and 98th percentile) and γ set to zero. As mentioned, in the case of DPR (columns 1-4), we stack the 4 years (2011-2014) of kharif season data and cluster our standard errors on channel-position. 28 Thus, the estimates of β H and β T reflect the average impact of (log) influence at channel positions head and tail, respectively, on the percentage difference in DPR between head and tail of that channel. Land value estimates in columns 5-8 have the analogous interpretation. However, in this case, we stack outlets and, within outlets, the two watercourse-level observations (see subsection 4.1.2), with standard errors again clustered on channel-position.
As indicated in equation (14), all regressions include a set of channel-level controls (Z c ) 27 Under the null, we may first-difference equation (14) to obtain 28 We drop 74 channel-position-year observations with missing or unusable discharge data. Notes: Robust standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1), clustered on channel-position (head/tail). DPR data are from 2011-2014. All specifications control for channel fixed effects and include the following channel characteristics interacted with the head dummy (H): a constant term, the total number of outlets on channel, whether channel is on tail of its parent channel (versus at middle or head), whether channel is a distributary (versus minor or sub-minor), and a full set of 23 division dummies. In addition, specifications in col. 1-4 include year dummies and specifications in col. 5-8 include a position on watercourse dummy. Column headings refer to the form of the G function used to construct log ι j (γ) (see equation 16) with γ set to zero.  in the case of DPR, this symmetry test has considerable power, which is to say that nonrejection is noteworthy. In particular, we are able to strongly reject the joint null that β H = β T = 0. By this same metric, however, power is substantially lower in the case of land values, an issue revisited in the next subsection. 28

Main results
Next, we free up the γ parameter as described in subsection 5.1 under two alternative G functions, mean and 98th percentile, and the two definitions of influential positions (exclusive and inclusive of members of the army/police). In the case of DPR, results of the line search over a large range of γ values are not encouraging. For all four specifications, the γ that minimizes the sum of squared residuals is near zero and the estimated confidence intervals (see discussion below) are extremely wide and contain zero. Hence, there is no evidence that holding an influential position interacts with one's economic stake in determining canal water allocations; at least, we cannot detect such an effect in the discharge data. Given this finding and our inability to reject symmetry in Table 2, we re-run the log(DPR) regressions with the restriction β H = −β T ≡ β 1 imposed. As shown in Table 3, in each restricted specification we strongly reject the null that log θ = log(ι H /ι T ) has no effect on water allocation; more We turn next to land values, and here the results on influential positions are far more encouraging. Figure 6 displays Hansen's (1999) likelihood ratio statistic as a function of γ, whereγ is the estimate that minimizes the sum of squared residuals as defined in subsection  Full estimates of these four specifications are reported in Table 4 with and without the imposition of the symmetry condition β H = −β T . Despite the differences inγ, the estimates of β H and β T are quite similar across specifications and quite similar as well to those with γ = 0 in Table 2. A major difference, however, is that the estimates in Table 4 are far more precise, a consequence of the better fit of the augmented lobbying influence function 30  Notes: Robust standard errors in parentheses (*** p<0.01, ** p<0.05, * p<0.1), clustered on channel-head/tail. Sample size is 7,844. All specifications control for channel fixed effects and include the following channel characteristics interacted with the head dummy (H): a constant term, the total number of outlets on channel, whether channel is on tail of its parent channel (versus at middle or head), whether channel is a distributary (versus minor or sub-minor), and a full set of 23 division dummies. Position on watercourse dummy is also included in all specifications. Column headings refer to the form of the G function used to construct log ι j (γ) (see equation 16), whereγ is the estimate that minimizes the residual sum of squares. a Block-bootstrapped p-value of Hansen's (1999) F -statistic based on 1000 replications.
to the land value data. Even though this higher precision substantially improves the power of our symmetry test, we still fail to reject the null across all specifications. So, proposition 3 is again confirmed. Imposing symmetry, we may now formally address Proposition 2 (δ (θ) > 0) by testing H 0 : β 1 = 0. As noted, the standard Wald tests are invalid since γ is not identified under H 0 . We thus report block-bootstrapped p-values for these hypothesis tests as suggested by Hansen (1999), which yield similar strong rejections of the null. 29 The restricted DPR estimates in Table 3 and the corresponding estimates for land values in Table 4  the premium, bringing it down to 2.9 (2.8). 31,32 Given the primacy of agricultural land in 29 Indeed, the bootstrapped p-values are smaller than those of the conventional Wald test based on the cluster-robust variance-covariance matrix. Hansen's statistic essentially uses the likelihood ratio principle and hence cannot be adjusted for clustering. One additional caveat, albeit probably a minor one, is that Hansen assumes a balanced panel, whereas our data are unbalanced due to varying numbers of outlets per channel. It is unknown if Hansen's results extend to our case. 30 Standard errors in parentheses. Notice that, as a consequence of Jensen's inequality, the mean percentage head-tail differential in DPR is larger than the absolute differential as a percentage of mean tail DPR reported in subsection 4.2. 31 Recall that we are using a different γ for land values than for DPR (i.e., γ = 0.545 in the former case versus γ = 0 in the latter case), which is why the scales of log θ are different. 32 That the base head-tail land value differential of 11.4 log points is smaller than the corresponding DPR differential of 27.2 log points is consistent with the diminishing marginal product of water (concavity of s(w)).  Table 3 and the latter on column 8 of Table 4. Lower panels show histograms of log θ for the corresponding specifications. Bars in upper panels denote 95% confidence intervals. Short-dashed vertical lines denote one standard deviation above and below the mean of log θ (long-dashed vertical line).
the asset portfolio of most of rural Pakistan's households, these hypothetical reallocations of political power entail substantial redistributions of wealth along a channel.

Alternative explanations
One explanation of our findings is that the head-tail differential in lobbying influence as measured by log θ is picking up something besides relative influence. In our regressions, we control for several channel-level variables (Z c ), including administrative division dummies, that turn out to be highly correlated with head-tail differences in DPR and, to a lesser extent, with head-tail differences in land values. Nonetheless, we may be omitting some confounding variables. For instance, a large literature on collective action in commons management highlights the importance of heterogeneity among users (e.g., Ostrom 1990; Baland and Platteau 1997), though the effect of this inequality on cooperative outcomes is often theoretically ambiguous (Bardhan and Dayton-Johnson 2002). In the context of surface irrigation systems, Bardhan (2000) and Dayton-Johnson (2000) provide evidence that the landholdings Gini coefficient is negatively associated with cooperation in water allocation and channel maintenance. The question here is whether log θ merely reflects land inequality along a channel, vitiating our rent-seeking contest interpretation.
An immediate problem with the inequality story, however, is that, if there is a relationship between log θ and the channel-level Gini coefficient, it is likely to be a U-shaped one. High channel-level inequality should (mechanically) be associated either with high or with low relative influence of the head outlets; low channel-level inequality should be associated with more equal influence between head and tail outlets. This is exactly the pattern that we observe in the data (Appendix Figure C.3). Hence, it comes as no surprise that controlling for the channel-level Gini coefficient leaves our estimates of β 1 virtually unchanged, as seen in Table 5. Moreover, differences in the degree of land inequality on the channel as a whole D (w) < 0 ⇒ŵ/w 0 > s(ŵ)/s(w 0 ) ⇒ log(w H /w T ) > log(V H /V T ). Notes: See notes to Table 2. Compare columns 1 and 2 to, respectively, columns 1 and 4 of Table 3, column 3 to column 4 of Table 4, and column 4 to column 8 of Table 4. Gini coefficient of family landholdings is computed at the channel level (i.e., across head and tail outlets).
cannot explain variation in collective action or, rather, in its converse -water theft. This finding is consistent with our presumption that cooperation between head and tail outlets of a channel is practically nonexistent.
Another threat to our lobbying power interpretation revolves around the role of groundwater. As suggested above, the market premium on land at the head of a channel is partly attributable to better groundwater recharge at the head (due to more plentiful canal water supplies). Recovering this groundwater, however, requires costly private investments in tubewells. Only about a third of farmers in our data-set actually own a tubewell (or tubewells) and ownership is heavily skewed toward the larger landowners; around half of all tubewells are owned by the top 25% of farmers ranked by landholdings. Thus, one reason why the head-of-channel premium is higher along channels with larger average landholdings at the head might be that along these channels farmers at head outlets are better able to exploit existing groundwater potential than those at tail outlets. In other words, our relative influence variable log θ may be picking up differential groundwater access. To address this concern, which is obviously not relevant for DPR, we include the head-tail difference in tubewell density (total number of tubewells per acre CCA), ∆TW/acre, in the land value regressions (see Table 6). While this control attracts a significantly positive coefficient, so that relatively greater access to groundwater does seem to enhance the head-of-channel land value premium, 33 the lobbying power effect is undiminished.
A final issue is that head-tail differences in the size distribution of family landholdings may be correlated with head-tail differences in average land productivity, another example of the potential incompleteness of Z c . There are three necessary elements to the argument, each of which may be questioned: (1) substantial variation in average land quality between head and tail outlets of the same channel; (2) larger returns to consolidating landholdings in areas with higher average land productivity; (3) consolidation that mostly occurs through land purchases. Under these conditions, we could observe larger landholdings on higher productivity sections of the channel, thus reversing the arrow of causation relative to our interpretation of the land value regressions (but, of course, not of the DPR regressions).
On element (1), we reiterate that median channel length (the maximum distance between head and tail outlets) is only 9 kilometers, which limits the extent of spatial variation in land quality. On (2) (Table 6), its coefficient is insignificant, which suggests that returns to scale are not correlated with unobserved land productivity differentials. Moreover, the estimates of β 1 barely change. In sum, we find support for our contention that the arrow of causation runs from differential influence to land values, not the other way around.  log θ is quite close to zero). Here we consider the implications of rent-seeking for the overall concentration of wealth.

Implications for inequality
We calculate land wealth by multiplying owned area by average land value on the outlet for each of the roughly 220,000 individual farmers on the nearly 4,000 outlets. Figure 8 shows the Lorenz curve for land wealth at current land prices, indicating that the top 10% of landed households own about half of land wealth. 34 Next, we compute wealth at land prices that net out the effect of log θ. In other words, in this counterfactual experiment, land at head outlets with relatively high lobbying influence is assumed to be no more valuable than land at head outlets with relatively low lobbying influence, and likewise for land at tail outlets. As illustrated in Figure 8, the Lorenz curves for land wealth computed at current and at these counterfactual land prices virtually coincide.
Since eliminating the return to rent-seeking, therefore, has a negligible impact on the concentration of land wealth, we can conclude that variation in lobbying power does not exacerbate overall inequality (even as it may do so along particular channels). While the above-noted similarity of wealth distributions by location along a channel contributes to this result, a more fundamental explanation is that the returns to lobbying for a common pool resource are, in general, non-excludable. In our particular context, these rents accrue, not only to the rich and powerful on an outlet, but also to their poor and powerless neighbors.

Conclusions
While optimal exploitation of common pool resources has received considerable attention in economics, actual regulation of competing users on a commons has not. This paper begins to fill this lacuna by studying bureaucratic canal management in the Indus Basin watershed. Our theory of misgovernance views the irrigation administration as having to mediate between contending coalitions of water-users along each channel. Supporting this theory, we find that greater relative lobbying power -as measured by a novel index combining economic stake and influential position-holding -enhances a coalition's water allocation and thereby redistributes wealth in its favor.