Ambiguity and the Historical Equity Premium

This paper assesses the quantitative impact of ambiguity on historically observed financial asset returns and growth rates. The single agent, in a dynamic exchange economy, treats the conditional uncertainty about the consumption and dividends next period as ambiguous. We calibrate the agent's ambiguity aversion to match only the first moment of the risk‐free rate in data and measure the uncertainty each period conditional on the actual, observed history of (U.S.) macroeconomic growth outcomes. Ambiguity aversion accentuates the effect of conditional uncertainty endogenously in a dynamic way, depending on the history; for example, it increases during recessions. We show the model implied time series of asset returns substantially match the first and second conditional moments of observed return dynamics. In particular, we find the time‐series properties of our model generated equity premium, which may be regarded as an index measure of revealed uncertainty, relates closely to those of the macroeconomic uncertainty indices developed recently in Jurado, Ludvigson, and Ng, 2015 and Carriero, Clark, and Marcellino, forthcoming