\section{Background}

\subsection{Subdistrict One}
The \acf{SLV} is an agricultural region located in south-central Colorado. Farming practices started in 1630 with industrial farming becoming common by 1880 \citep{hearne1988}. The \ac{SLV} expanded rapidly at the turn of the twentieth century, with developments in rotary well technology spurring an explosion in groundwater use by 1940 \citep{cody2015}. Today 26\% of direct employment continues to come from the agricultural sector, median incomes are  \$47,599 which is 37\% lower than the Colorado average \citep{slvdev2024}.

The valley has a multifaceted water system with the Rio Grande River providing surface water, an unconfined aquifer providing strong feedback to the river, and a lower confined aquifer supplying hydrologic pressure. Transmissivity in the region varies but ranges from 700-30,200 \(\frac{feet^2}{day}\) in the unconfined aquifer and 13,400 to 16,800 \(\frac{feet^2}{day}\) in the confined aquifer \citep{bexfield2010}. This connectivity makes the groundwater a common-pool resource creating a tragedy of the commons \citep{hardin1968}. From both a geologic and technical level, the linkages between groundwater and surface water were not well understood at the time farmers increased drilling rates in the 1940s. This type of uncertainty can lead to institutional misallocation of resources which are difficult to correct \citep{libecap2011}. Sunk capital in wells provided an incentive to continue groundwater extraction under drought conditions in the 1950s and 1960s \citep{loos2022,cody2015}. This came to a head in 1969 when the State of Colorado passed the \emph{Water Rights Administration and Determination Act of 1969}, placing groundwater use more directly under prior apportion orders \citep{cody2015}. Out of this, the conservation districts of Colorado were formed to manage agricultural water usage in six Colorado hydrologic basins. The \ac{SLV} falls into the \acl{RGWCD}.

With the backdrop of this institutional development, a drought in the early 2000s created historically large declines in aquifer storage volumes (See \cref{FIG:STOR}). During this era, other wells in Colorado were required to retire due to pumping deemed out of priority \citep{loos2022}. Facing this legal uncertainty and increasing externalities from pumping, \ac{SBD1} of the \ac{RGWCD} was formed in 2006. The number of farmers in the \ac{SLV}, and their joint interest in preserving agricultural productivity, contributed to the ability to manage the groundwater common-pool resource collectively \citep{ostrom1990,walker1990,smith2018,cody2015}. 

%\FloatBarrier
\begin{figure}
		\includegraphics[width=0.97\textwidth]{GW_LEVEL}
	\caption{Storage levels of closed basin relative to 2000}
	\label{FIG:STOR}
\end{figure}

Members in the subdistrict voted for enfranchisement under the authority of \ac{RGWCD}. Six total subdistricts have formed in the \ac{SLV}, each addressing water management locally. However, the region encompassing \ac{SBD1} was deemed to create the most injurious depletions to downstream rights holders. Given the limited resources of the \ac{RGWCD}, \ac{SBD1} was given priority over other subdistricts, becoming the first subdistrict to implement a water management plan.

Leveraging the flexibility afforded to the subdistrict as a self-governed institution, different policies have been tried to reduce depletions. One policy that has met with interest from economists is a pumping fee. By charging groundwater users an additional cost above the electrical costs of pumping, the external costs can be internalized, allowing the socially optimal pumping rate to be achieved through pricing \citep{pigou1924}. Empirical evidence finds that the subdistrict pumping fee was able to reduce groundwater use by 33\% and promote institutional social norms that encourage water conservation \citep{smith2017,smith2018}. 

Aquifer levels have declined since the policy's inception, despite the reduced water use from the pumping fees. Climate factors have been identified as contributing to these declines \citep{grabenstein2022,sbd12023,sbd12022a}. The pumping fee has been raised four times to address this issue and currently is set at \$500 per \ac{AF}, suggesting that the 63\% decline in groundwater pumping from 2011 levels has been insufficient to meet aquifer goals \citep{sbd12022a}.

The subdistrict has taken a holistic approach to policy management, employing a range of regulatory options. The focus of the present paper is involvement in \cref{CREP}, a program that pays users to retire cropland (refer to \cref{bckgndcrep}). A related program was a temporary fallowing program that provided rental rates to fallow farms for a four-year window. By retiring land for four years, the farmers were able to receive a payment and had the flexibility to rotate which acreage was fallowed. This program was only offered for the 2020 and 2021 irrigation years. The subdistrict is active in purchasing wells and surface water rights in order to retire or provide augmentation. They have also used funds to purchase land on the outskirts of the subdistrict and acquiring the associated water rights. Such mixing of policies and repeated treatment can make isolating policy effects difficult and lead to reversals of cause-and-effect interpretation \citep{besley2000,callaway2021}. Much of the policy changes can be treated as exogenous since the unexpected drought was outside human control. With proper econometric methods, such dynamic policy interactions provide a rich pool of knowledge to assess groundwater management. 

\subsection{CREP}
\label{bckgndcrep}
The \acf{CREP} is a program offered by the \acf{FSA}, which creates incentives to apply conservation practices on agricultural land within environmentally sensitive regions. \ac{CREP} is an offshoot of the \acf{CRP} program which provides more moderate incentives but covers a large portion of the country. \citep{fsa2023}

Each local \ac{CREP} program has goals and requirements that are tailored to the region, with the Colorado Rio Grande \ac{CREP} program having additional entry requirements over \ac{CRP} or \ac{CREP} \citep{sbd12013}. The \ac{CREP} program as applied to the \ac{SLV} pays farmers to fallow land\footnote{The program allows for various forms of "fallowing" including planting cover crop or reintroducing wetland.}, requiring that no crops are planted over the contract term. The payment includes a sign-up bonus of \$300 per acre, with a yearly payment of \$288 \(\frac{acre}{year}\) over 15 years \citep{rgwcd2014,fsa2023a,sbd12011,rgwcd2023}\footnote{Federal, state, and local payments when land is not in the bonus payment region.}. The \ac{FSA} pays \$200 \(\frac{acre}{year}\) of this total with the caveat that a minimum of 20\% of funding must come from the State of Colorado or the subdistrict \citep{rgwcd2014}. The subdistrict funding of \ac{CREP} comes from self-imposed acreage fees that adjust to meet demand \citep{sbd12011}. As part of the fallowing incentive structure, the subdistrict provided resources to develop an additional \ac{CREP} contract option. Unlike other \ac{CREP} programs, \ac{SLV} participants can enter a permanent retirement contract \citep{sbd12011}. The subdistrict pays a one-time bonus of \(\frac{\$100}{acre}\) and a yearly bonus of \(\frac{\$22}{acre-year}\) for entering a permanent retirement contract\footnote{Amount above the 15-year contract, but the subdistrict supports both contract types.}\textsuperscript{,}\footnote{Payment only continues for 15 years, even if the contract is for permanent retirement.}. 

There is a set of criteria for eligibility in \ac{CREP}. Three of the most restrictive being that all land must be in \ac{SBD1} \citep{sbd12013a}, the covered area must have been irrigated with at least half a \ac{AF} per acre for at least four of the six years between 2008 and 2013, and half a \ac{AF} per acre must have been applied to the land within two years of submitting the application \citep{rgwcd2015}\footnote{Other restrictions include the land must be capable of being irrigated and the cropland must have water rights.}. Notably, for the proceeding analysis, the subdistrict pumping fee discussed in \cite{smith2017} was set at \$45 in 2011 and raised to \$75 per \ac{AF} in 2012. The groundwater use of farms during the four-year window with a low pumping fee can be used to meet the \ac{CREP} eligibility requirements, allowing farms with low water use in 2012-2013 to enter the program. 

The sign-up period began in 2013, placing the 2011 irrigation year within two years of sign-ups. 2011 happened to be the highest groundwater use year on record for \ac{SLV} farmers (see \cref{fig:AVPUMP}). While the \ac{SBD1} farmers began reducing water relative to other \ac{SLV} farms in 2011, the overall water use rate was high. For this reason, the pumping choices made in response to the \ac{SBD1} pumping fee do not significantly affect entry into \ac{CREP} based on either minimum irrigation requirements. 

Within the subdistrict, the main goals of \ac{CREP} are to enroll 40,000 acres of cropland and reduce irrigated water use by 60,060 \ac{AF} per year\footnote{Other goals are included in \cref{A_CREP_GOALS} (\cite{sbd12013a}).}. Since 2013, the subdistrict has enrolled 10,868 acres of farmland. Engineering estimates of water consumption reduction due to \ac{CREP} are 14,775 \ac{AF} per year in 2023\footnote{14,666 in 2022 and 17,365 in 2021.} \citep{sbd12023,sbd12022,sbd12021}. Prior to the subdistrict pumping fee, wells that were enrolled in \ac{CREP} averaged 17,365 \ac{AF} per year in total pumping. 

\subsection{Evidence of \ac{CREP} Outcome Changes}
The existence of the pumping fee changes the incentives of farmers choosing to enter the \ac{CREP} program. The pumping fee has an effect on the amount of land enrolled in \ac{CREP}, and the amount of water saved per acre enrolled. The direction of these factors is ambiguous without further empirical analysis.

The first adjustment is made along the intensity of groundwater use, which lowers the amount of water saved by \ac{CREP}.  The marginal cost of pumping increases because of the pumping fee. Increasing the cost of using groundwater reduces the quantity of groundwater applied by farmers\footnote{This is strictly non-increasing and could remain zero.}. Since all wells in the subdistrict decreased water use prior to the CREP program, \ac{CREP} induces less water conservation per well than if the pumping fee did not exist. Taking one extreme, if the pumping fee was high enough then all wells would be shut off, so the gains from \ac{CREP} would be zero. This implies that the marginal abatement cost of \ac{CREP} increases from the fee. Each enrolled well will cost the same amount as before the pumping fee, but the amount of water per retired well is lower.

The fee can also interact in \ac{CREP} by changing the economics of entering the program. In other settings, \ac{PES} programs have been found to suffer from selection bias, with agents choosing to enter the program if they already meet the conservation standards \citep{daniels2010,martinpersson2013}. The design of the pumping fee is to alter groundwater extraction rates. By doing so, the fee increases the number of wells that would be in compliance with \ac{CREP}\footnote{Or close to compliance.} which may select into the program. In other groundwater management settings, the gains from the program were found to raise the value of farmland unevenly based on the hydraulic connectivity \citep{edwards2016}. This provides a mechanism by which the pumping fee has unevenly encouraged enrollment in \ac{CREP} based on spatial characteristics. This further reduces the per well intensity savings but will likely increase the amount of farmland enrolled in \ac{CREP}. This factor can increase overall water savings by inducing more enrollment but increase abatement costs through selection of wells that would have pumped less than the average subdistrict well.

An evaluation of crop choice in the \ac{SLV} suggests that heterogeneous land attributes are significant in selecting into \ac{CREP}. \cref{FIG:CROP} shows the average acreage of crops grown by three user groups; farmland outside \ac{SBD1} ('\emph{Other} wells'), farmland in \ac{SBD1} \emph{Sbd.1}, and farmland that is enrolled in \emph{\ac{CREP}}. The crop choice is broken out into three periods: before the pumping fee (\emph{Pre-Policy}), after the pumping fee but before \ac{CREP} starts (\emph{post-2011}), and after \ac{CREP} begins (\emph{post-2014}). Wells that are entered into \ac{CREP} grow substantially more small grains and alfalfa compared to wells in \ac{SBD1}. These crops have been identified as seeing the largest intensive adjustments to the pumping fee \citep{smith2017}. This suggests that heterogeneous farm conditions lead to a selection of some farms into \ac{CREP}.


% \FloatBarrier
\begin{figure}
	\subfloat[Crops of Other Wells]{
	\begin{minipage}[c][0.32\linewidth]{0.32\textwidth}
		\centering
		\includegraphics[width=1\textwidth]{OTHER_CROP.jpeg}
	\end{minipage}}
	\hfill
	\subfloat[Crops of Sbd.1 Wells]{
	\begin{minipage}[c][0.32\linewidth]{0.32\textwidth}
		\centering
		\includegraphics[width=1\textwidth]{SBD1_CROP.jpeg}
	\end{minipage}}
	\hfill
	\subfloat[Crops of \ac{CREP} Wells]{
	\begin{minipage}[c][0.32\linewidth]{0.32\textwidth}
		\centering
		\includegraphics[width=1\textwidth]{CREP_CROP.jpeg}
	\end{minipage}}
  
 	\caption{Crop variations by groups (average acreage per well)}\label{FIG:CROP}
 \end{figure}
 % \FloatBarrier

The well intensity margin also appears to be in play. The average pumping rate of wells in each of these three groups is provided in \cref{fig:AVPUMP}. \ac{CREP} wells and subdistrict wells have a nearly identical average prior to the pumping fee, suggesting the parallel trend assumption is valid. After the pumping fee starts, \ac{SBD1} wells, and wells that eventually join \ac{CREP} deviate from the control group, reducing average pumping. However, the \ac{CREP} wells reduce output even more than the subdistrict average while following the same yearly trend. The disproportionate response of \ac{CREP} wells is indicative of selection into \ac{CREP} by land that was most impacted by the pumping fee.

% \FloatBarrier
\begingroup
\begin{figure}[h]
	\includegraphics[width=\linewidth]{Pumping_Rates.jpeg}
	\caption{Adjustments in average pumping by well group}
	\label{fig:AVPUMP}
\end{figure}
\endgroup

This preliminary evidence is used to inform the following empirical analysis. The intensive margin of \ac{CREP} wells is explored before and after the pumping fee using a \ac{DID} specification. Next, a probit model is applied to predict the likelihood of a well joining \ac{CREP} based on their response to the pumping fee. These can be used together to estimate the direct effect of \ac{CREP} on water savings and program abatement costs.
