Important progress has been made in economists' understanding of the Beveridge curve, from its measurement to its expression in canonical labor market models. Yet enduring puzzles remain. Chief among these are the empirical role of vacancies in the recruitment process; the amplitude, comovement, and persistence of cyclical unemployment–vacancy dynamics; and the sources of lateral shifts in the Beveridge curve. The synthesis of these themes identifies several priorities for ongoing research, including the role of entry costs into vacancy creation in shaping Beveridge dynamics; the cyclicality of search intensity, both off and on the job, and its relation to participation and job-to-job transitions; the theory and measurement of mismatch; and the sources of hysteresis in unemployment flows. (JEL E24, J63, J64)

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.