Impact of transient shocks to productivity on long-term social discounting

The cost-benefit analysis of long-run climate mitigation projects and valuations of a social cost of carbon critically depend on the long-term social discount factor. Here, we consider the problem of the socially optimal risk-adjusted ‘Gamma discounting’ in the presence of strong exogeneous shocks to productivity of capital. We establish that the declining schedule of the long-term forward discount rates over time is very sensitive to the average frequency of shocks, $\lambda$, and the difference between the key model parameters: the intergenerational inequality aversion of a social planner $\eta$ and the shape parameter $a$ of the assumed Gamma distribution of productivity rates. We establish that for a relatively small intergenerational inequality aversion, $\eta \le a-1$, the lowest possible forward discount rate is equal to $\lambda$. Qualitatively, this important conclusion can be explained by a higher sensitivity of the discount factor to technological breakthroughs bringing back high productivity rates (positive shocks) than to disasters (negative shocks). However, if $\eta >a-1>0$, the socially optimal forward discount rate can decline further down, towards zero, with a growth of the time horizon. Thus, socioeconomic projections of long-term discount rates require account of potential advances in technology.