Abstract We devise a tractable model of firm dynamics with on-the-job search. The model admits analytical solutions for equilibrium outcomes, including quit, layoff, hiring, and vacancy-filling rates, as well as the distributions of job values, a fundamental challenge posed by the environment. Optimal labor demand takes a novel form whereby hiring firms allow their marginal product to diffuse over an interval. The evolution of the marginal product over this interval endogenously exhibits gradual mean reversion, evoking a notion of imperfect labor market competition. This in turn contributes to dispersion in marginal products, giving rise to endogenous misallocation. Quantitatively, the model provides a parsimonious reconciliation of leading estimates of rent sharing, the negative association between wages and quits, the link between job and worker flows, and the cyclicality of labor market quantities and prices.

Replacement hiring plays a central role in establishment dynamics. US establishments frequently report no net change in their employment, often for years, despite facing substantial gross turnover. We devise a tractable model in which replacement hiring is driven by a novel structure of frictions, combining firm dynamics, on-the-job search, and investments into job creation that are sunk at the point of replacement. A key implication is the emergence of vacancy chains. Quantitatively, the model reconciles the incidence of replacement hiring with large cross-establishment dispersion in labor productivity and largely replicates the volatility and persistence of job creation and unemployment.