Directed Search on the Job, Heterogeneity, and Aggregate Fluctuations

In models of search on the job (e.g. Kenneth Burdett and Dale Mortensen 1998, Burdett and Melvyn Coles 2003, Alain Delacroix and Shouyong Shi 2006), employed and unemployed workers search the labor market for job openings. Workers who are unemployed are willing to accept any job that makes them better off than enjoying leisure and continuing to search. Workers who are employed are willing to accept any job that offers themmore than their current job does. On the other side of the market, firms are indifferent between opening jobs that offer different wages, as firms that offer higher wages can fill their jobs faster and retain their workers for a longer period of time. The extent of search frictions determines how quickly workers move up in the wage-offer distribution and how the wage-offer distribution itself looks like. Overall, models of search on the job provide an equilibrium theory of workers’ transitions between employment, unemployment and across employers, and, simultaneously, a theory of wage inequality. Because of these properties, models of search on the job are a useful tool for studying the labor market. Under the standard assumption of random search, these models are difficult to solve outside of the steady state because agents need to forecast the evolution of the infinite-dimensional wage distribution in order to solve their individual problems. For example, firms need to forecast the evolution of the wage distribution in order to compute the probability of filling a vacancy. Similarly, workers need to compute the evolution of the wage distribution in order to compare the value of a particular job offer with the value of their current employment position. Because of this technical property, models of random search on the job are difficult to use for studying the aggregate dynamics of the labor market. For example, these models are