Valuation of natural capital under uncertain substitutability

Natural capital is complex to value notably because of the high uncertainties surrounding the substitutability of its future ecosystem services. We examine a Lucas economy in which a consumption good is produced by combining different inputs, one of them being an ecosystem service that is partially substitutable with other inputs. The growth rate of these inputs and the elasticity of substitution evolve in a stochastic way. We characterize the socially efficient ecological discount rates that should be used to value future ecosystem services at different time horizons. We show that the inverse of the elasticity of substitution can be interpreted as the CCAPM beta of natural capital. We also show that any increase in risk of this beta reduces the ecological discount rate. If our collective beliefs about the elasticity of substitution of ecosystem services are Gaussian, the ecological discount rates go to minus infinity for finite maturities. In that case, a marginal increase in natural capital has an infinite value. We provide a realistic calibration of the model that is coherent with observed asset prices by using the model of extreme events of Barro (2006). The bliss maturity for infinite discount factors is less than 100 years in this calibration.