We study the role of information in asset pricing models with long-run cash flow risk. When investors can distinguish short- from long-run consumption risks (full information), the model generates a sizable equity risk premium only if the equity term structure slopes up, contrary to the data. In general, the short- and long-run components are unidentified. We propose a sparsity-based bounded rationality model of long-run risk that is both parsimonious and fully identified from historical data. In contrast to full information, the model generates a sizable market risk premium simultaneously with a downward sloping equity term structure, as in the data.
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