City size and the risk of being unemployed. Job pooling vs. job competition

We study the relationship between city size and the risk of being unemployed. We introduce a new mechanism, job pooling, as a source of agglomeration economies in a model of risk sharing with an imperfect labor market and risk-neutral agents. Despite competition across workers for jobs in the largest cities (job competition), workers tend to be located in large cities because tight labor markets yield income gains from the sharing of firms among workers that do not know ex ante the negotiated wage rates (job pooling). The covariance between the probability of being unemployed and firm-specific wage shocks decreases with the number of workers. This explains why larger cities exhibit a higher unemployment rate on average and weaker fluctuations. From French data, we find that the positive covariance between the unemployment rate and local wages decreases with city size. We also show that moving from an area in the first quartile of density to the last quartile translates into an increase in unemployment of 14%. In contrast, the elasticity of unemployment fluctuations with respect to employment density is negative: moving from an area in the first quartile of density to the last quartile translates to a decrease in our unemployment fluctuation index of 25%.