We use the Bayesian method introduced by Gallant and McCulloch (2009) to estimate consumption-based asset pricing models featuring smooth ambiguity preferences. We rely on semi-nonparametric estimation of a flexible auxiliary model in our structural estimation. Based on the market and aggregate consumption data, our estimation provides statistical support for asset pricing models with smooth ambiguity. Statistical model comparison shows that models with ambiguity, learning, and time-varying volatility are preferred to the long-run risk model. We also analyze asset pricing implications of the estimated models. Received April 12, 2016; editorial decision September 11, 2018 by Editor Stijn Van Nieuwerburgh.