Firm Dynamics, On-the-Job Search, and Labor Market Fluctuations

G(m)=ς0F(m)ς0+sλ[1−F(m)].
(34)
Lemma 3 reveals that the hiring region induced by the interaction of firm dynamics and on-the-job search is present even in the absence of idiosyncratic shocks and endogenous job destruction. Importantly, this hiring region, and the accompanying dispersion in marginal products, would not emerge in the absence of on-the-job search (⁠s=0)⁠. A striking implication, then, is that on-the-job search in fact gives rise to all equilibrium misallocation in this case. We argue in what follows that Lemma 3 presents a stark point of contrast to existing canonical models of on-the-job search.17
On one hand, the hiring region shares interesting parallels with a large literature inspired by Burdett and Mortensen (1998). This emphasizes how ex ante wage posting and firms’ turnover concerns generate “residual” wage dispersion among identical workers. By contrast, in our model ex post wage bargaining and firms’ turnover concerns give rise instead to “residual” dispersion in marginal products, and thereby in wages. Both results can be traced to notions of imperfect labor market competition associated with on-the-job search and labor market frictions, as well as to the nature of wage setting. In Burdett and Mortensen (1998), wage dispersion arises from firms having to commit ex ante to wage payments that cannot respond to workers’ current or future outside options. In the present model, marginal product dispersion arises from firms being unable to commit to wages, and managing turnover instead via hiring decisions. For the special case of no idiosyncratic shocks in Lemma 3, the worker distribution of marginal products in (34) becomes exactly analogous to the worker distribution of wages in Burdett and Mortensen (1998), yielding a stable job ladder whereby workers move toward higher-wage, more productive firms.
On the other hand, a crucial message of Lemma 3 is that these models have fundamentally different implications for misallocation. Wage posting models in the mold of Burdett and Mortensen (1998) invoke linear technologies. When extended to incorporate productive heterogeneity (Bontemps et al., 2000), an extreme implication is that allocative efficiency requires all workers to be employed in the most-productive firm. On-the-job search is thus a force toward resolution of misallocation in these models, since it accelerates worker transitions toward more productive firms.
The paradox of Lemma 3 is that this last implication is turned on its head. In Lemma 3, heterogeneity in marginal products emerges as an equilibrium outcome, rather than by assumption. And the presence of on-the-job search is the primitive force that gives rise to equilibrium misallocation, rather than solely being an equilibrium response to it.
The key difference is the presence of diminishing returns. This provides an economic margin by which differences in firm marginal productivity can be resolved. Indeed, in the absence of on-the-job search, marginal products are equalized: s→0 implies mu→mh⁠. Instead, in the presence of on-the-job search, firms allow their marginal products to vary as a means to manage turnover, generating equilibrium misallocation. Thus, the interaction of frictions with neoclassical forces that militate toward equality of marginal products fundamentally alters the economic role of on-the-job search in misallocation.
Lemma 3 makes this point starkly, by abstracting from idiosyncratic shocks and endogenous job destruction. Returning to the general case, though, Proposition 2 and Lemma 2 imply that on-the-job search will at least give rise to greater misallocation among hiring firms. It follows that there must be configurations of the parameters of the model such that this effect dominates, and on-the-job search can raise misallocation overall.