\section{Neighborhood Effect Estimates at Various Radii}
\label{A:RAD}
The neighborhood pumping effect of \ac{CREP} enrollment for various radii are estimated in \cref{REGRAD}\footnote{The year number is the time after a \ac{CREP} is first enrolled at the specified distance. For example, if a well is enrolled in \ac{CREP} in 2015, wells that are within a half mile of the \ac{CREP} well are in \(Year=0\) in 2015, \(Year=5\) in 2020, and \(Year=-5\) in 2010.}. This provides a robustness check of the radius selected. The values are reported as an event study, showing how the coefficients vary over time. 
\input{Tables/REG_DIFF_RAD.tex}
The results of \cref{REGRAD} suggest that the neighborhood effect is sensitive to the radius of impact selected. The half mile radius shows the most consistent policy effect, with a statistically significant decline in well extraction in the first year of the program. Generally, this effect peaks two years after the policy begins, and then dampens in magnitude and statistical significance after this point.

It is somewhat surprising that the smaller quarter mile radius has a less consistent policy effect, with only the peak period of the policy effect (two years after enrollment) showing a significant negative neighborhood effect. This can be explained in a few ways. 

From a data perspective, doubling the radius of impact includes four times the area\footnote{\(4=\frac{\pi\cdot (2r)^{2}}{\pi\cdot r^{2}}\)}. The small radius therefore reduces the data set of the neighborhood effect by more than half. This lower data availability results in more noise in the estimate, preventing the effect from being picked up. 

There are also causal explanations of this result. For example, cones of depressions around a well are present at close distances. At the quarter mile radius, the reduction in pumping of \ac{CREP} wells will raise the water table by more than wells at one half mile. As a result, the cost of pumping groundwater decreases more for close wells, creating an incentive to increase pumping. This generates an incentive counter to the pro-social generalized pumping reductions seen at farther distances. On net, very close wells may reduce extraction rates by less than more distant wells, with closer wells pumping about the same as before \ac{CREP} enrollment but with a lower operating cost.

A second causal explanation is that using too small of a radius shifts treated wells into the control group. If the neighborhood pumping effect is approximately constant across the effected radius, then using a small radius will bias the results towards zero. For example, if the driver of decreased pumping is having a line of sight to the \ac{CREP} well, then a well within a quarter mile will reduce pumping at a similar rate as a well at a half mile. In that case, going from a half mile radius down to a quarter mile radius shifts approximately four-fifths of treated wells to the control group. In turn, this attributes some of policy impact to year fixed effects and the results lose significance. Due to these factors, the lower magnitude of neighborhood effects at the quarter mile radius is not viewed as a major concern in the model outcomes. 

At the one-mile radius, the average neighborhood effect appears to be close to a random process, which is expected when the radius of impact is identified correctly. There are four years at the two-mile radius where the results are significant, and generally positive.  Most years are not significant, these results are attributed partially to random variation. However, as can be seen in \cref{FIG:MAP}, nearly all wells in \ac{SBD1} are within two miles of a \ac{CREP} well. As a result, the two-mile year interaction coefficients represent the pumping change relative to a small set of wells that are at the far edges of \ac{SBD1} or at the center.