Consumption Response Heterogeneity and Dynamics with an Inattention Region

A theory in which the timing of consumer expectation adjustments is endogenously state-dependent and stochastic is proposed. These expectation adjustments generate highly heterogenous consumption responses to income windfalls: many households do not respond, those who do over-react, the marginal propensity to consume depends on windfall size and is asymmetric. We document these features in the Bank of England survey of consumers and find that they simultaneously rule out most previous explanations for these effects, including consumption adjustment cost and liquidity constraints. At the aggregate level, consumption is less sensitive to expansionary policies during recessions and its excess smoothness varies significantly over the business cycle with consumers attention, a feature that we document in US data.