By Fabrice Collard, Sujoy Mukerji, Kevin Sheppard and Jean-Marc Tallon
This paper assesses the quantitative impact of ambiguity on the historically observed equity premium. We consider a Lucas-tree pure-exchange economy with a single agent where we introduce two key non-standard assumptions. First, the agent’s beliefs about the dividend/consumption process is ambiguous. Second, the agent’s preferences are sensitive to this ambiguity. We further extend the model to allow for uncertainty about the magnitude of the persistence of the latent state. The agent’s beliefs are ambiguous due to the uncertainty about the conditional mean of the probability distribution on consumption and dividends in the next period. This results in an endogenously volatile and (counter-) cyclical equity premium. We calibrate the level of ambiguity aversion to match only the first moment of the risk-free rate in data, and ambiguity to match the uncertainty conditional on the historical growth path, and evaluate the model using moderate levels of risk aversion. We find that this simple modification of Lucas-tree model accounts for a large part of the historical equity premium, both in terms of its level and variation over time.
Ambiguity is largely neglected in the macro and finance literature, but it can obviously have an impact on risk premia (broadly defined). This paper show that ambiguity can in fact be a very important contributor to the equity premium puzzle.