Consumption insurance over the business cycle

How do business cycle fluctuations affect the ability of households to smooth consumption against idiosyncratic shocks? To answer this question, we first document that, in U.S.\ micro-data, individual consumption reacts more to income changes in booms. Standard incomplete markets models, in contrast, where individuals borrow and save to smooth consumption, predict a lower sensitivity of consumption to individual income changes during times of high output. This motivates us to consider an alternative environment where financial frictions are endogenous and arise from lack of contract enforcement, whose business cycle properties have so far not been studied. We show analytically that this model is consistent with a wide variety of cyclical patterns of insurance. In a quantitative application with unemployment risk, we show that the response of individual consumption to job losses differs strongly between times of high and low output, and identify the conditions under which it is procyclical, as in the data.