### Discussion Paper

## Abstract

Arguments about the appropriate discount rate often start by assuming a Utilitarian social welfare function with isoelastic utility, in which the consumption discount rate is a function of the (constant) elasticity of marginal utility along with the (much discussed) utility discount rate. In this model, the elasticity of marginal utility simultaneously reflects preferences for intertemporal substitution, aversion to risk, and aversion to (spatial) inequality. While these three concepts are necessarily identical in the standard model, this need not be so: well-known models already enable risk to be separated from intertemporal substitution. Separating the three concepts might have important implications for the appropriate discount rate, and hence also for long-term policy. This paper investigates these issues in the context of climate-change economics, by surveying the attitudes of over 3000 people to risk, income inequality over space and income inequality over time. The results suggest that individuals do not see the three concepts as identical, and indeed that preferences over risk, inequality and time are only weakly correlated. As such, relying on empirical evidence of risk or inequality preferences may not necessarily be an appropriate guide to specifying the elasticity of intertemporal substitution.

Paper submitted to the special issue “Discounting the Long-Run Future and Sustain¬able Development”

## Comments and Questions

Good stuff.

However, I would think that inequity aversion is different within and between societies. The cursory evidence is that income redistribution is stronger within societies than between countries.

And yes, we need a practical social welfare function that makes the necessary distinction before this can be put ...[more]

... into practice.

The referee for our paper in the special issue also the issue of the multiple roles of the curvature of the utility function. Formulating our response, it struck me that there is no reason why consumption smoothing over time should be the same between and within generations.

I have two comments on the empirical methodology:

1. My first comment is on the recruitment of the sample and the generalizability of the results. The authors use a non-random internet sample for their study. They do take the extra step of discussing possible drawbacks of this approach. ...[more]

... I think this should be mentioned both in the introduction and abstract of the paper because there is always the chance that the reader will take the estimates at face value (especially the reader that does not go through every single detail of the paper).

2. My second comment is on the use of an ordered probit model in section 4.6. I would suggest using a grouped data regression model instead (also known as interval regression). The difference between a grouped data regression and an ordered probit regression model is that the threshold values are known in the former model. Since that is true, there is information on the scale of the latent variable in the data. Indeed, the measures for risk aversion, inequality aversion and intertemporal substitution are measured in ranges. This model can be easily fit in Limdep or Stata.