The introduction of firm-size into labor search models raises the question how wages are set when average and marginal product differ. We propose an alternative to the existing bargaining models by allowing firms to compete for labor. Fast growing firms do not only post more vacancies, they also post higher wages to attract more workers. Therefore, they fill each vacancy with higher probability, which is consistent with empirical regularities. Qualitatively the model also captures most other empirical regularities about firm size, job creation, and pay. In contrast to existing bargaining models that always induce inefficiencies on the intensive hiring margin, these factual implications of our model for firm dynamics are socially optimal. Social efficiency obtains on extensive and intensive margins of job creation and job destruction, both with idiosyncratic and with aggregate productivity shocks. Moreover, the planner solution allows for a tractable characterization which is useful for computational applications.
Search models of the labor market have traditionally treated the production side very simplistically: Each firm wants to hire one worker, which is usually equivalent to having several workers with constant marginal product (see e.g. the surveys by Mortensen and Pissarides (1999) and Rogerson, Shimer, and Wright (2005)). While successful in many dimensions, these models are silent about all aspects that relate to employer size, even though firm size and firm dynamics are important for both wages and employment. Larger firms are on average more productive and they tend to pay more (e.g., Brown and Medoff (1989), Oi and Idson (1999)). In percentage terms, older and larger firms grow less but also exit the market less (Evans (1987a, 1987b)). After controlling for worker characteristics, young and fast–growing firms pay higher wages (Brown and Medoff (2003), Belzil (2000)). And larger firms create and destroy more jobs (Davis, Haltiwanger, and Schuh (1996)), they are more sensitive to the business cycle than smaller firms (Moscarini and Postel-Vinay (2009a)), and therefore contribute to aggregate employment dynamics in very different ways. Abstracting from firm size not only precludes the analysis of firm-level hiring and growth, it also limits the ability of labor market models to account for business cycle behavior.