Non-identical quadruplets: four new estimates of the elasticity of marginal utility for the UK

Working Paper 121

Abstract

This paper reviews the empirical evidence on the value of the elasticity of marginal utility for the United Kingdom. This parameter is a key determinant of the social discount rate and also informs equity weighting in applied Cost Benefit Analysis.

Four different empirical methodologies are investigated: the equal-sacrifice income tax approach, the Euler-equation approach, the Frisch additive-preferences approach and the subjective-wellbeing approach. New estimates are presented using contemporaneous and historical data.

Combining the estimates using meta-analytical techniques yields a best-guess estimate of 1.5 for the elasticity of marginal utility. Critically the confidence intervals for this estimate exclude unity, which is HM Treasury’s current official estimate of the elasticity of marginal utility and the value used in the Stern Review (2007).

The paper illustrates the implications for the UK term structure of discount rates. We use extensions to the Ramsey rule reflecting uncertainty and auto-correlated consumption growth rates. Other things equal, our estimate of 1.5 for the elasticity of marginal utility would lead to a social discount rate of 4.5 per-cent for the short term. From this starting point, estimates of the term structure for the UK point to a long-run rate of 3.75%. This is a much higher and flatter term structure than currently recommended in the Treasury Green Book.

Using over 150 years of growth data, however, implies a term structure that starts at 3.6% and declines to 2.4% in the long-run. All these results raise conceptual and empirical questions about the current UK guidelines on social discounting.

Ben Groom and David Maddison