The Matching Multiplier and the Amplification of Recessions

Recessions are thought to be larger than the shocks that cause them, and the incidence of recessions is unequally distributed across workers. This paper shows empirically that the unequal incidence of recessions is a core channel through which aggregate shocks are amplified. I show that the aggregate marginal propensity to consume (MPC) is larger when income shocks disproportionately hit high-MPC individuals, and I define the Matching Multiplier as the increase in the output multiplier originating from the matching of workers to jobs with different income elasticities – a greater matching multiplier translates into more powerful amplification in a range of business cycle models. Using administrative data from the United States, I document that the earnings of individuals with a higher marginal propensity to consume are more exposed to recessions. I show that this covariance between worker MPCs and the elasticity of their earnings to GDP is large enough to increase shock amplification by 40 percent over a benchmark in which all workers are equally exposed. Using local labor market variation, I validate this amplification mechanism by showing that areas with higher matching multipliers experience larger employment fluctuations over the business cycle. Lastly, I derive a generalization of the matching multiplier in an incomplete markets model and show numerically that this mechanism is quantitatively similar within this structural framework.