Gamma discounters are short-termist

Weitzman (1998, 2001) proposed a simple “gamma discounting” method to characterize the term structure of discount rates today from the sole distribution of future spot interest rates. This rule which justifies using a smaller discount rate for longer maturities is now used for long-term policy evaluations in the UK, France, Norway, and potentially in the US. But we show that there is no social preference within the discounted expected utility framework that generically supports this pricing model and its underlying criterion, the expected net present value rule. Considering a standard Lucas tree economy, we characterize the term structure from a coherent joint distribution of future spot interest rates and future consumption levels. When future growth rates are positively serially correlated, efficient discount rates today are decreasing with maturity, and the gamma discounting rule yields discount rates that are larger than the efficient ones.