We extend existing methodology for estimating shadow prices for exhaustible natural resources to renewable resources with common pool characteristics, using groundwater in irrigated agriculture as an example. The resource's shadow price is defined in terms of a perfect foresight open loop Nash equilibrium. Furthermore, we introduce a new estimation approach and derive shadow groundwater scarcity rents by estimating a stochastic restricted distance function using duality results between distance and cost functions. This approach is appropriate when price information is not available or when cost, profit, or revenue functions representations are precluded because of violations of the required behavior assumptions. We use our results to study policy implications for groundwater management.