\section{Introduction}
Economists are interested in identifying the socially optimal management strategy of common-pool resources. In many cases, the theoretically preferred policy is not politically feasible, and conservation policies are evaluated in conjunction with political feasibility \citep{walter2020,barragan-beaud2018,lipsey1956}. This paper evaluates a case where a first-best policy, a tax on externalities, is followed by a politically feasible but second-best alternative, a \ac{PES}. Econometric results show that the existence of the fee substantially reduces the expected gains from the second-best alternative. The joint outcome of the two policies is not the sum of the expected resource conservation of each policy, as estimated independently. Rather, the pumping tax decreases the total direct water conserved by the \ac{PES} by 32\%. This conservation reduction comes from the interaction of two effects from the pumping fee, each enrolled well in the program already reduced water usage by 62 \(\frac{\ac{AF}}{Year}\), and the added cost of pumping encouraged 29.52\% more wells to enroll. This case study is relevant to policy design, economic outcomes of policies must be estimated with consideration to the existing resource management efforts.

Groundwater resources have lacked clearly defined property rights resulting in externality costs of extraction. These include the cost to downstream surface water holders \citep{cobourn2015}, the common-pool resource management loss in a tragedy of the commons \citep{gisser1980,brownjr.1972}, local pumping externalities \citep{brozovic2010}, and added legal threat of neighbors when water rights could not be fulfilled. The estimates of these costs have historically been difficult to assess. Understanding and managing these costs is becoming progressively more important to economists and policymakers as arid regions face increased resource scarcity.

Theory and empirical research contribute to our understanding of the effectiveness of groundwater programs. The usual \emph{first-best} policies of pumping fees and quotas have been tried \citep{schuerhoff2013,drysdale2018,smith2017,smith2018}. A pumping fee can be economically efficient\footnote{When the rate is property set, and is assessed on the party with the lowest abatement costs.} because the creator of the externality bears the cost of the decision to pump water \citep{pigou1924}. The groundwater user is able to determine their own cost and benefits inclusive of social costs, which brings their private benefit in line with the socially optimal outcomes. A common hurdle to initiating a Pigouvian tax is that the interests of the existing industry are harmed by adding the tax \citep{jenkins2014}. Also, the policy outcomes of pumping fees sometimes fall short of expectations, with institutional enforcement, and political influences of competing interest groups identified as hindering conservation \citep{yang2003,schuerhoff2013}. Both the institutional rigidity and reduced conservation can be over-improved through collective action \citep{huang2013,cody2018,ostrom1990}. In the case study elaborated in this paper, groundwater users in the \ac{SLV}, were able to take collective action and employ a self-imposed pumping fee to mitigate externality costs of pumping. The result was a 33\% reduction in groundwater extraction \citep{smith2017}. 

The ability to self-organize is not a given, as is evidenced by the scarce case studies of a pumping fee adoption. It can be easier to induce political change by paying users to reduce an externality rather than charging them for generating the costs. One common and growing alternative following this method is a \ac{PES} \citep{wunder2008,engel2008}. The \ac{PES} of study is \ac{CREP}, which is a federal program that pays farmers to fallow land and to grow vegetation that improves local environmental quality. 

There are a number of studies that evaluate the factors that contribute to enrollment in \ac{CREP}. Payment rates are consistently found to drive enrollment \citep{monger2018,suter2004,suter2008}. Other enrollment factors are centered on opportunity costs, with land quality and urbanization effecting enrollment numbers \citep{parks1997,plantinga2001}. Some benefits identified in specific applications of \ac{CREP} include increasing the water table by 15\% \citep{manning2020}, decreasing water intensity by 1.29 \(\frac{\ac{AF}}{acre}\) \citep{rosenberg2020} and creating cooperative norms where neighboring wells reduce pumping rates by 9.6 \(\frac{\ac{AF}}{year}\) \citep{rouhirad2021}. Due to the distortions created in \emph{second-best} policy outcomes, some inefficiencies are identified. Such programs offer a lump sum payment for enrollment. As a result land is enrolled based on opportunity costs, rather than targeting land with a high return for water conservation\citep{wanhongyang2005}. For example, regions with high vacant land values due to growing urban development will require a higher \ac{CREP} payment to enter the program than equivalent parcels in rural areas, a factor unrelated to total water use of the parcel. A related program, \ac{CRP}, has been identified as suffering from a rebound effect where non-farmland is converted into farmland, leading to a 9\% slippage in conservation \citep{wu2000}.

The current analysis identifies how conservation outcomes of groundwater management programs change when alternative water conservation polices are in place. This is an important question to answer because almost all farmland in the United States will qualify for some form of \ac{PES} and the addition of a pumping fee or quota system should account for the combined policy outcome.

There are multiple mechanisms by which a pumping fee can change the water conservation outcomes of a \ac{PES}. Both direct and indirect consequences of the fee are examined using econometric methods. To highlight the different types of interactions between a \ac{PES} and pumping fee consider the model of \ac{PES} water conservation:
\begin{equation}
	Conservation = \sum_{w=1}^{W} \left( \theta_{w}\cdot I_{w}+\beta\left[1-\theta_{w}\right]\cdot\eta_{w}\right)
\end{equation}
Where \emph{w} is a well and \(w \in W\), \(I_{w}\) is the average water intensity of the well, \(\theta_{w}\) is a dummy variable indicating that a well is enrolled in the \ac{PES}, \(\beta\) is the change in pumping that results from a well being near a fallowed well, \(\eta_{w}\) is a dummy variable for a well being close to a well enrolled in the \ac{PES} program.
%\begin{equation}
%    \theta_{w}=
%    \begin{cases}
%	    1\text{ if } P_{PES}\cdot Area_{w} \ge\pi_{w}\  \\
%	    \text{else}=0  \\
%    \end{cases}
%\end{equation}
%Where \(P_{PES}\) is the price paid by the \ac{PES} program to retire an acre, \(Area_{w}\) is the area covered by a well and is assumed to be constant, and \(\pi_{w}\) is the total profit attributable to the operation of the well. 
%and is defined as \(\eta_{w}=\max\left(\theta_{f\left(w,d\right)}\right)\). \emph{f} is a subset of wells that are within a distance (\(d)\)) of well \emph{w}.

The \ac{PES} water conservation can be separated into direct and neighborhood spillover effects. The direct effect is captured in the term \(\theta_{w}I_{w}\) which is the amount of water saved by an enrolled well when it is shut off. The neighborhood effect is captured in \(\beta\left[1-\theta_{w}\right]\cdot\eta_{w}\), this is the change in water pumped by wells that are sufficiently near to a \ac{PES} well from both pro-social and water table consideration.

A marginal increase in the pumping fee influences each of these components through the equation:
%\begin{equation}
%	\frac{dConservation}{dFee} = \sum_{w=1}^{W} \left( \frac{d \theta_{w}}{d\ Fee}\cdot I_{w}+\frac{d\ I_{w}}{d\ Fee}\cdot \theta_{w}+\beta\left(\frac{\eta_{w}}{dFee}-\left[\theta_{w}\frac{\eta_{w}}{dFee}+\eta_{w}\frac{\theta_{w}}{dFee}\right]\right)\right)
%\end{equation}
\begin{equation}
\frac{dConservation}{dFee} = \sum_{w=1}^{W} \left[\theta_{w}\frac{dI_{w}}{dFee}+I_{w}\frac{d\theta_{w}}{dFee}+\beta\left(\left[1-\theta_{w}\right]\frac{\eta_{w}}{dFee}-\eta_{w}\frac{\theta_{w}}{dFee}\right)\right]
\end{equation}

Four total effects from the pumping fee on the \ac{PES} are identified. First, the fee changes the intensity of groundwater pumped by wells in the program prior to enrollment based on the term \(\theta_{w}\frac{dI_{w}}{dFee}\). Each well enrolled in the \ac{PES} reduces output to zero, but the existence of the fee lowers the baseline pumping rate. Therefore, each well added to the \ac{PES} conserves less water under a pumping fee policy. Second, the pumping fee changes which wells enroll in the \ac{PES} through the term \(I_{w}\frac{d\theta_{w}}{dFee}\). The fee makes some wells more or less profitable to operate. This in turn changes which wells select into the \ac{PES} program. When this term is positive more wells are enrolled because of the fee which counteracts the reduced water saving per well enrolled in the term \(\theta_{w}\frac{dI_{w}}{dFee}\). Third, the number of wells that respond to neighborhood spillover effects adjust. Changing which wells enroll in the program also changes which wells are near enough to a fallowed \ac{PES} well to induced shifts in pumping behavior, this effect is \(\beta\left[1-\theta_{w}\right]\frac{\eta_{w}}{dFee}\). Fourth, the addition of wells to the \ac{PES} removes any potential neighborhood spillover effects that the well would have responded to, which is shown in the term \(-\beta \eta_{w} \frac{\theta_{w}}{dFee}\).

These interactions are each evaluated empirically. First, the direct effect of the pumping rate of wells that eventually join \ac{CREP} and the magnitude of the neighborhood effect is found using a \ac{DID} study. An event study is developed that considers the institutional paths taken by farmers in the \ac{SLV}. In this setting, farmers self-organize and develop the self-imposed pumping fee. This fee began in 2011 and is treated as a natural experiment to develop a \ac{DID} estimate of the pumping effect replicating the work of \citep{smith2017} while distinguishing wells that join the \ac{PES} using \ac{CREP} as a separate treatment group. By 2014, farmland could begin active enrollment in \ac{CREP}. This is staggered treatment, so a weighted event study is used to estimate the amount of water conserved by the program \citep{sun2021}. A similar methodology is used to predict any neighborhood effects from \ac{CREP} enrollment as has been identified in Kansas \ac{CREP} \citep{rouhirad2021}.

Second, a probit model is used to determine if the fee changes which wells enroll in the \ac{PES} and how much additional water is conserved through this process. To identify an indirect effect on neighboring wells the results of the probit are used in a Monte Carlo simulation. The Monte Carlo simulates which wells may have been added to \ac{CREP} as a result of the fee. In each simulation the number of neighboring wells is calculated providing a metric to assess the additionality of the fee on the spillover effects. These results are combined to estimate the total change on the \ac{PES} water conservation that result from the pumping fee.
