Comparison of dynamic models separating risk and intertemporal substitution

Abstract Different models have been proposed to separate the (elasticity of) intertemporal substitution from the risk attitude. Among those models, Epstein–Zin–Weil is the most famous, but there are others: Generalized Expected Discounted Utility (GEDU), Risk-Sensitive (RS), and Dynamic Quantile (DQ) preferences. This paper compares these four frameworks in terms of characteristics that are important for applications involving intertemporal decisions with risk, namely, the ability to separate intertemporal substitution from the risk attitude with observable data, dynamic consistency, monotonicity, and attitude toward long-run risk. We show that GEDU is able to separate EIS from risk, but it is neither dynamically consistent nor monotone. EZW is able to separate EIS from risk and it is dynamic consistent, but it is not monotone. RS is not able to separate EIS and risk with observable data, but it is dynamic consistent and monotone. The only model that retains all three properties—separation of intertemporal substitution and risk, dynamic consistency, and monotonicity—is the DQ model. Finally, all models, but GEDU, have aversion or indifference to long-run risk.