Volatility Ambiguity, Consumption and Asset Prices

We formulate a stylized model that admits volatility ambiguity to the Lucas framework. The model specifies an economically motivated ambiguity penalty function that makes volatility ambiguity quantifiable with χ2-statistics, and allows for analytical solutions. The addition of volatility ambiguity greatly expands the range of possible equilibrium outcomes of the Lucas model with the well documented empirical regularity being the equilibrium outcome of a range of sensible combination of parameters. The paper shows that while return volatilities are much easier to estimate than expected returns and therefore have lower ambiguity than the ambiguity in mean returns, it nonetheless plays an important role in the equilibrium determination of asset prices.