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

FIGURE 3

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Steady-state equilibrium and comparative statics
Notes: Based on the model calibrated as described in Section 3. The figure illustrates the steady-state response to a 1% decline in aggregate labor productivity.

2.6. Equilibrium properties

The labor market equilibrium characterized in the preceding sections yields novel insights on labor market behavior. Here we highlight two distinctive features that emerge from the equilibrium: a novel form of imperfect labor market competition; and, relatedly, a novel form of misallocation. A set of instructive limiting economies underscores that the interaction of firm dynamics and on-the-job search is crucial to these new results.
Labor market competition. Proposition 3 reveals that, in steady state, the hiring rate η(m) is proportional to minus the elasticity of the quit rate—or, equivalently, the hazard function of the offer distribution of log marginal products, mf(m)/[1−F(m)]⁠. Intuitively, a firm’s hiring rate is thus determined by the intensity of offers at m⁠, f(m)⁠, relative to the intensity of offers at higher ms, as captured by 1−F(m)⁠. Offers at lower ms are not directly relevant, since all such offers are dominated by those issued by firms at m⁠.
In combination with Proposition 2, this result yields further intuitive insights. First, and most simply, since the quit rate is a constant (equal to sλ) in the natural wastage region, (26) confirms that the hiring rate is zero for m<mh⁠. Second, because δ(m) is strictly decreasing and concave in m in the hiring region, it follows that the hiring rate η(m) is strictly positive and increasing in m for m>mh⁠. Third, since the quit rate equals zero at the upper boundary, the hiring rate asymptotes to infinity at mu⁠, as in Figure 2A. Consequently, firms’ net employment growth, given by the difference between the hiring rate and the quit rate, η(m)−δ(m)⁠, takes the form depicted in Figure 4.