Efficient Investments, Job Dynamics and Frictional Dispersion

When there are search frictions in the labor market, physical capital accumulation by firms interacts with job dynamics. To study this interaction, this paper integrates directed, on-the-job search (OJS) into the neoclassical theory of firm investments, analytically characterizes the social optimum and quantitatively evaluates the model. The constrained social optimum features a continuous ladder of capital stocks across jobs and, hence, of labor productivity among homogeneous workers. Workers who are employed from unemployment optimally start at the bottom of the ladder. There is a socially efficient tradeoff between reducing unemployment and increasing labor productivity. Firm investments move a worker up the ladder continuously and OJS makes a worker jump up on the ladder in discrete steps. OJS is socially efficient when the capital stock is low, despite that job-to-job transition destroys an existing job. OJS is front-loaded and stops after a finite number of job switches. In contrast, investments by firms continue throughout a worker's employment. Moreover, investments are partially delayed when the capital stock is low, and so investments can be hump-shaped over tenure and over the capital stock. Calibration exercises show that the social optimum generates large frictional dispersion in labor productivity, significant returns to tenure, and persistently large costs of job loss