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Using information in returns, we identify the stochastic process of consumption. We find that aggregate consumption reacts over multiple quarters to innovations spanned by financial markets. This persistent component accounts for over a quarter of consumption variation. These shocks command a large and significant risk premium, driving a large share of stocks' and a small yet significant fraction of bonds' time-series variation. Nevertheless, we find no support for stochastic volatility of consumption driving time-varying risk premia. Finally, an otherwise standard recursive utility model based on our estimated process explains equity premium and risk-free rate puzzles with low-risk aversion.

We develop a transparent Bayesian framework to measure uncertainty in asset pricing models. By assigning a modified class of -priors to the risk prices of asset pricing factors, our method quantifies the trade-off between mean–variance efficiency and parsimony for asset pricing models to achieve high posterior probabilities. Model uncertainty is defined as the entropy of these model probabilities. We prove the model selection consistency property of our procedure, which is missing from the classic -priors. Acknowledging the possibility of omitting true asset pricing factors in real applications, we also characterize the maximum degree of contamination that the omitted factors can introduce to our model uncertainty measure. Empirically, we find that model uncertainty escalates during major market events and carries a significantly negative risk premium of approximately half the magnitude of the market. Positive shocks to model uncertainty predict persistent outflows from US equity funds and inflows to Treasury funds.

We propose a novel framework for analyzing linear asset pricing models: simple, robust, and applicable to high-dimensional problems. For a (potentially misspecified) stand-alone model, it provides reliable price of risk estimates for both tradable and nontradable factors, and detects those weakly identified. For competing factors and (possibly nonnested) models, the method automatically selects the best specification—if a dominant one exists—or provides a Bayesian model averaging–stochastic discount factor (BMA-SDF), if there is no clear winner. We analyze 2.25 quadrillion models generated by a large set of factors and find that the BMA-SDF outperforms existing models in- and out-of-sample.