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.
To capture firm size phenomena, a series of recent work has introduced multi-worker firms with decreasing returns to labor into standard labor search models, considering among others the implications for wages and unemployment (e.g., Bertola and Caballero (1994), Smith (1999), Bertola and Garibaldi (2001), Acemoglu and Hawkins (2006), Cahuc, Marque, and Wasmer (2008), Mortensen (2009)), for labor market regulation (Koeniger and Prat (2007)), for business cycles (Elsby and Michaels (2010), Fujita and Nakajima (2009)) and for trade-based employment effects across countries (e.g., Helpman and Itskhoki (2010), Helpman, Itskhoki and Redding (2010a,b)). A central part of all labor market models concerns the wage formation, and all of these contributions rely on a combination of random search together bargaining without commitment over future wages. This bargaining framework based on Stole and Zwiebel (1996) and Smith (1999) might be viewed as the analogue of standard one-worker-one-firm bargaining for multi-worker settings. The validity of this wage setting assumption has never been analyzed; nonetheless, it dominates the current developments, possibly due to a lack of alternatives.
While these models are successful among many dimensions, the combination of bargaining without commitment under random search raises several concerns. Empirically, lack of commitment predicts that workers in growing firms see their wages decline over time, since workers receive part of the productivity and initially labor productivity is high but drops as more workers are hired. On the normative side a particular concern is that this setup introduces inefficiencies by assumption. If the marginal product of labor is decreasing, each individual firm hires too many workers (Stole and Zwiebel (1996), Smith (1999), Cahuc, Marque, and Wasmer (2008)): When a firm bargains with a worker, it understands that failure to agree with this worker will mean that it will have to renegotiate wages with the remaining workers next period and those workers will get a higher wage because they are in a steeper part of the production frontier. Therefore, the firms is willing to keep workers with negative marginal product since that reduces the wages to other workers.1 This arises within the particular match between the firm and its workers, before accounting for general equilibrium effects. Therefore, the overall equilibrium can never be efficient, and beneficial government interventions exist by assumption.
Note that this is very different from the standard one-worker-one-firm (or constant returns) setup, where each match (worker-firm-pair) takes decisions that are efficient for the matched parties: They stay together if marginal product is higher than the continuation values, and do not stay together otherwise. Whether this leads in equilibrium to efficient job creation and job destruction on the aggregate level depends on the exact bargaining parameter (Hosios (1990)). Therefore, applied work in this area has focused on the planner’s solution (see e.g. Merz (1995), Andolfatto (1996), Shimer (2005b)) or compared it with inefficient solutions (e.g. Hall (2005), Hagedorn and Manovskii (2008)) to see which seems to be closer to reality. The current multi-worker setup does not allow for such a horse race between efficient and inefficient outcomes, partly because we do not have plausible search models that justify an analysis of the planner’s problem.
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Efficient Firm Dynamics in a Frictional Labor Market
