The equity premium puzzle is an enduring challenge to our estimates of risk aversion. Indeed, as Rajnish Mehra and Edward Prescott have highlighted, the only way to reconcile a standard model with the observed long-term equity premium is to assume a risk aversion coefficient of 10, while micro-estimate hover around two. This puzzle has been resolved a little bit in various way, most prominently by taking into habit persistence and some other deviations of the standard CRRA or CARA utility functions. But all this still boils down to a risk aversion parameter that is linked by an identity to the intertemporal elasticity of substitution (it is the inverse). But we know how to disentangle the two.
Xiaohong Chen, Jack Favilukis and Sydney Ludvigson estimate a model with the recursive preferences of Larry Epstein and Stanley Zin and Philippe Weil. This is not obvious to do because to estimate the coefficient of risk aversion in this context, one needs a measure of claims to future consumption. Here this is overcome by estimating nonparametrically the continuation value of the consumption process from within the model. The result is that the elasticity of intertemporal substitution is above one, and the coefficient of risk aversion is somewhere between 17 and 60. These are huge numbers. But they still imply a rather modest and sometimes even negative risk premium.