We study a market with rationally inattentive consumers who are unsure of the terms of the offers made by firms, but can acquire information about the terms at a cost. In a symmetric equilibrium, the price set by firms is continuously increasing in the cost of information for consumers and decreasing in the number of firms operating. In addition, favorable a priori information about a firm leads it to set a higher price, and a new entrant can increase demand for incumbents. When consumers have heterogeneous costs of information, firms selling low-quality products may choose to set the highest prices.

In recent years, central banks have increasingly turned to forward guidance as a central tool of monetary policy. Standard monetary models imply that far future forward guidance has huge effects on current outcomes, and these effects grow with the horizon of the forward guidance. We present a model in which the power of forward guidance is highly sensitive to the assumption of complete markets. When agents face uninsurable income risk and borrowing constraints, a precautionary savings effect tempers their responses to changes in future interest rates. As a consequence, forward guidance has substantially less power to stimulate the economy.

We provide new time-varying estimates of the housing wealth effect back to the 1980s. We use three identification strategies: ordinary least squares with a rich set of controls, the Saiz housing supply elasticity instrument, and a new instrument that exploits systematic differences in city-level exposure to regional house price cycles. All three identification strategies indicate that housing wealth elasticities were if anything slightly smaller in the 2000s than in earlier time periods. This implies that the important role housing played in the boom and bust of the 2000s was due to larger price movements rather than an increase in the sensitivity of consumption to house prices. Full-sample estimates based on our new instrument are smaller than recent estimates, though they remain economically important. We find no significant evidence of a boom–bust asymmetry in the housing wealth elasticity. We show that these empirical results are consistent with the behaviour of the housing wealth elasticity in a standard life-cycle model with borrowing constraints, uninsurable income risk, illiquid housing, and long-term mortgages. In our model, the housing wealth elasticity is relatively insensitive to changes in the distribution of loan-to-value (LTV) for two reasons: first, low-leverage homeowners account for a substantial and stable part of the aggregate housing wealth elasticity; second, a rightward shift in the LTV distribution increases not only the number of highly sensitive constrained agents but also the number of underwater agents whose consumption is insensitive to house prices.