Generalized entropy and model uncertainty

I provide a model uncertainty foundation to the power certainty equivalent of Epstein-Zin-Weil risk sensitive preferences (EZ), enabling the analysis of these preferences using detection probabilities (DEPs) and worst case models. This completes the connection between these preferences and the model uncertainty of Hansen and Sargent (2007) (HS) that was previously limited to the special case of unit elasticity of intertemporal substitution. The connection between EZ and HS rests on a powerlike extension of entropy and its associated statistics from Tsallis (1988) and I show that the same additional margin of pessimism that implies this connection can close the gap to the empirical Sharpe ratio in a more general specification. For the specific cases of EZ and HS preferences, I find that calibrations that match detection error probabilities yield comparable asset pricing implications across models. Surprisingly, I find that the low levels of risk aversion with EZ preferences that match asset pricing facts are associated with a high level of model uncertainty in the long run risk environment of Bansal and Yaron (2004).