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

6. Summary and discussion

This article has presented a synthesis of firm dynamics and on-the-job search. The result is an environment in which some of the key empirical regularities of the labor market can be understood jointly. Firms with concave revenue functions face idiosyncratic shocks that drive job creation and destruction (Davis and Haltiwanger, 1992). These in turn drive flows of workers in and out of unemployment (Blanchard and Diamond, 1990) and, through on-the-job search, directly from one employer to another (Fallick and Fleischman, 2004).
A set of novel contributions naturally emerges. First, the model admits an analytical characterization of equilibrium outcomes. This is a particular challenge posed by the presence of on-the-job search in the environment, since the rate of turnover faced by firms in general will depend on the firm’s position in an endogenous distribution of job values. We devise an environment in which this distribution can be derived analytically and, as a consequence, quit, layoff, hiring, and vacancy-filling rates can all be solved in closed form in steady-state equilibrium. We further show how these analytical results can be used to render feasible an analysis of out-of-steady-state transition dynamics.
Second, a host of new economic insights follow. Firms’ desire to manage their turnover costs gives rise to a novel manifestation of imperfect labor market competition. In contrast to the competitive limit, differences in marginal products across firms are closed only incrementally. Formally, there is endogenous, gradual mean reversion in marginal products. A consequence is that there is additional dispersion in marginal products across firms in equilibrium—there is endogenous misallocation—that arises from the interaction of firm dynamics and on-the-job search.
Third, the endogenous hierarchy of firms that emerges from the environment naturally captures several stylized facts of imperfect labor markets and establishment dynamics. Firms higher up in the distribution of marginal products pay higher wages, consistent with recent estimates of rent sharing. These firms also face lower quit rates; the resulting negative association between turnover and wages again mirrors leading estimates in the empirical literature. Turning to establishment dynamics, the model captures the empirical correlation between job and worker flows noted by Davis et al. (2012, 2013). Firms higher up in the hierarchy hire more intensively, and are less likely to lay off employees. Crucially, they also face lower quit rates, and are able to fill their vacancies more quickly. We show that the model generates cyclical fluctuations in labor market stocks and flows that resemble standard measures of their empirical behavior (Shimer, 2005). Strikingly, a quantitative assessment of the model reveals that, in all these dimensions, it generates moments in the region of their empirical counterparts.
Finally, the model is amenable to an array of extensions. Most importantly, we show how it is possible to accommodate a theory of partial offer matching into our multi-worker firm environment. An instructive implication is that the degree of misallocation among hiring firms due to on-the-job search is ameliorated by firms’ ability to match offers. In the limit in which firms can respond perfectly to each of the idiosyncratic outside offers of its employees, the distribution of marginal products among hiring firms becomes degenerate. In further extensions, we show how the model can accommodate richer structures of labor market frictions, such as convex hiring and vacancy costs, as well as firm entry, exit, and growth, while preserving much of its analytical tractability.
There remain several avenues for future research not taken up in our framework. Central to the tractability of our model are a lack of commitment in wage setting and, relatedly, the availability of what we term an “m-solution”. Although the model is able to account for many of the empirical features of wages—their procyclicality, and the presence of rent sharing, for example—a more satisfying understanding of the economics would also accommodate the implications of (limited) commitment in wage determination. Likewise, an m-solution is unlikely to be available in environments with more general technologies, shocks, frictions, and wage protocols. Our hope is that the present paper provides a first step toward a more complete synthesis of labor market frictions and firm dynamics.
The editor in charge of this paper was Dirk Krueger.