The current theoretical analysis of labor market search and matching is dominated by two rather separate literatures. In the first of these one typically assumes firm wage posting. Wage dispersion may then result from either on-the-job worker search (Burdett and Mortensen (1998), Burdett and Coles (2003)), or from nonsequential search whereby workers find it advantageous to search for more than one firm simultaneously. Wilde (1977) and Burdett and Judd (1983) provide product market applications of the latter type of models; more recently, Acemoglu and Shimer (2000) (hereafter AS) and Mortensen (1998) have studied labor market applications. In AS, wage dispersion among identical workers can result from firms’ endogenous capital choices, whereby some firms invest more capital than others, and offer a higher wage, in return for greater probability of employing a worker.
The other main branch of this literature assumes bilateral matching and bargaining between individual firms and workers, and builds on the work of Mortensen and Pissarides and followers (e.g. Mortensen and Pissarides (1999), Pissarides (2000); see also Acemoglu and Shimer (1999)). This model framework assumes continuous time, unlimited decision horizon and sequential search. Firms’ capital choices and wages are here typically identical.
The current paper sets out to integrate these two strands of literature by extending the AS model to situations with (Nash) wage bargaining between individual firms and workers. Such bargaining by construction precludes the possibility that wages may differ for identical firms and workers. Equilibrium wage dispersion may still however arise when workers search nonsequentially and firms make endogenous capital choices prior to hiring and subsequent wage bargaining. Anticipating that the bargained wage splits net ex post output in given proportions between the firm and the worker, we show that firms may select different capital intensities. Nash bargaining over different total surpluses then results in different wages.
We study two versions of this model, differing in the more detailed assumptions about the technology for matching workers and firms. The first version, discussed in section 2, adopts the AS (and Burdett-Judd) matching technology whereby workers search one or two firms at random, and each firm may make several job offers. The second, studied in section 3, is less standard and assumes that initial worker search is directed in spreading workers’ search messages evenly out across active firms, and that firms make only one job offer for each job opening. Whenever the number of established firms then is at least as great as the number of search messages sent by workers, there is always full employment.
Under both matching technologies we demonstrate that for some (reasonably low) range of workers’ search costs, there exists an equilibrium distribution of productivities for established firms in the market, which corresponds to a distribution over workers’ wages, all workers searching at least one firm and some more than one. Under the AS search technology (model 1), such an equilibrium implies (as in AS) that workers search either one or two firms.
Under our alternative search technology, a wage dispersion equilibrium may imply that all workers search two firms or more. We also demonstrate that there always exists a low-wage equilibrium (LWE, similar to the “Diamond equilibrium” in AS) where each workers searches only one firm, firms face no effective competition for workers, and the wage distribution collapses to a single mass point. At an LWE, the wage (and firm productivity) always corresponds to the level at the lower support of the distribution, for the case where the distribution is spread out. As opposed to the wage-posting case, in an LWE workers earn positive rents by virtue of their ex post bargaining strength, and choose to enter the market given (small) positive search costs. While the lower support is the same in all equilibria, the distribution is more spread out under more competition (more workers obtain job offers from at least two firms).
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