Firm dynamics and random search over the business cycle

I build a tractable random search model with firm dynamics, on-the-job search, and aggregate shocks. Multi-worker firms make recruitment decisions, choose whether to enter or exit the market, and design wage contracts. Tractability is obtained by showing that, under a set of assumptions on the recruitment technology, the decisions of workers and firms can be expressed in terms of the firms' current productivity. I introduce a numerical solution method to accommodate aggregate shocks in this environment and show that the model can replicate salient features of both firm-level data on productivity and employment and aggregate time series describing the business cycle. I use this framework to quantify the drivers of worker reallocation over the recent business cycle in Britain.