Spaces for Agreement: A Theory of Time-Stochastic Dominance

Abstract

Many investments involve both a long time-horizon and risky returns. Making investment decisions thus requires assumptions about time and risk preferences. Such assumptions are frequently contested, particularly in the public sector, and there is no immediate prospect of universal agreement. Motivated by these observations, we develop a theory and method of finding 'spaces for agreement'. These are combinations of classes of discount and utility function, for which one investment dominates another (or 'almost' does so), so that all decision-makers whose preferences can be represented by such combinations would agree on the option to be chosen. The theory is built on combining the insights of stochastic dominance on the one hand, and time dominance on the other, thus offering a nonparametric approach to inter-temporal, risky choice. We go on to apply the theory to the controversy over climate policy evaluation and show with the help of a popular simulation model that, in fact, even tough carbon emissions targets would be chosen by almost everyone, barring those with arguably 'extreme' preferences.

Is There Space for Agreement on Climate Change? A Non-Parametric Approach to Policy Evaluation

“…Having established rst-order TSD, we can proceed from here either by placing an additional restriction on the discount function, or on the utility function, It is evident from Proposition 2 that restricting the utility function by one degree corresponds to integrating D 1 1 (z, t) once more over the consequence space. If we want to pursue the further case of (v, u) ∈ V 2 × U 2 , representing a riskaverse planner with impatience decreasing over time, then we would integrate D 2 1 (z, t) once more with respect to time (see Dietz and Matei, 2013). Taking this to its logical conclusion, we can generalise TSD to the n th order with respect to time and the m th order with respect to risk.…”

“…Similarly, bounding the ratio of u (z) or u (z) amounts to restricting u (z) or u (z) respectively, such that extreme concavity (risk aversion) or convexity (risk seeking) of u(z) is ruled out, as are large changes in prudence with respect to z. Dietz and Matei (2013)…”

“…The one's strength is the other's weakness in this regard. Therefore, in a companion paper we unify Stochastic Dominance and Time Dominance to produce a theory of Time-Stochastic Dominance, which is able to handle choices between investments that are both inter-temporal and risky (Dietz and Matei, 2013). In this paper we present the theory in a stripped-down manner, highlighting the key theorems and providing cross-references to the proofs for the interested reader (Section 4).…”