Estimating ‘gamma’ for tail-hedge discount rates when project returns are cointegrated with GDP

Martin Weitzman has suggested a method for calculating social discount rates for long-term investments when project returns are covariant with consumption or other macroeconomic variables, so-called ‘tail-hedge discounting’. This method relies on a parameter called ‘real project gamma’ that measures the proportion of project returns that is covariant with the macroeconomic variable. We compare two approaches for estimation of this gamma when the project returns and the macroeconomic variable are cointegrated. First, we use Weitzman’s own approach, and second a simple data transformation that keeps gamma within the zero to one interval. In a Monte-Carlo study, we show that the method of using a standardized series is better and robust under different data-generating processes. Both approaches are examined in a Monte-Carlo experiment and applied to Swedish time-series data from 1950–2011 for annual time-series data for rail freight (a measure of returns from rail investments) and GDP.