“Do ethical considerations restrict the rate at which society consumes?”
In this paper, Campbell et al. look at sustainability, as a constraint rather than as an objective, in a risky economy where there is uncertainty over the return on capital. In this case the authors assume that social value does not remain constant but is not expected to decline over time either. They use a continuous-time model with two forms of capital, one safe and one risky, so that society faces a portfolio choice problem as well as a consumption-savings decision. They assume that society has a standard time-separable power utility function defined over aggregate consumption, and impose the sustainability constraint on this. Among their findings:
- The sustainability constraint does not distort portfolio choice, which is always the same whether or not the constraint binds;
- The sustainable rate of time preference lies between the riskless interest rate and the expected return on optimally invested wealth.
Sustainability in a Risky World
Authors: John Y. Campbell, Ian W. R. Martin
From: Harvard University, LSE
The welfare cost from using the wrong discount rate
Christian Gollier measures the welfare loss associated with using a single discount rate when performing a cost-benefit analysis to determine the optimal allocation of capital in the economy. Towards this goal he compares two models:
- A dynamic model in which investments with heterogeneous risk profiles and expected benefits are endogenously selected. At the beginning of each period, identical infinitely-lived agents must determine what share of their wealth should be consumed, and which investments should be implemented. The first-best investment rule entails a CCAPM discounting system in which the project-specific discount rate is a linear function of the project’s beta. Extreme events affect the common risk factor.
- A model where the representative agent uses a single discount rate to determine her investment strategy.
The welfare loss of using a single discount rate is equivalent to a permanent reduction in consumption that lies somewhere between 15% and 45%, depending upon which familiar discounting system is used.
The welfare cost of ignoring the beta
Author: Christian Gollier
From: Toulouse School of Economics
