Unemployment cycles

non-active on-the-job search;
2. When the gains from sorting are arbitrarily high, there is a unique steady state with active on-the
job search.
3. For intermediate gains from sorting y ∈ [y l , y h ] (for given y) there are multiple equilibria.
Our results in this section illustrate the mechanism that gives rise to the strategic complementarity
and hence multiplicity. Firms trade off the expected quality or productivity of a job (which changes due
to the composition externality) against the duration. And workers trade off the matching probability
against the cost of searching. With active on-the-job search, there is more sorting and the value to
the firm of a job is higher, which creates incentives for vacancy posting. More vacancies in turn create
incentives for workers to actively search on-the-job since it is easier to find a job. Likewise, there
is also an equilibrium where workers do not actively search on-the-job, where the pool of searchers
has relatively few on-the-job searchers and is of relatively low match quality. For firms, the shorter
duration of jobs then dominates the impact of the composition externality, and as a result, they post
few vacancies. This in turn leads workers not to search actively. Our results from this section show
that too large or too small sorting or productivity gains from on-the-job search resolve the trade-offs
for firms an workers in an unambiguous way, leading to a unique equilibrium.
3.2 Steady State Equilibrium Properties
We now depict the equilibrium in the canonical Beveridge Curve diagram, i.e., the unemploymentvacancy
space. Since this is the convention, we continue to do so in the (u, v) space with corresponding
market tightness Θ = v u
. Since matching probabilities are a function of the effective market tightness
v
θ =
u+λ(Ω)γ = v s
, we then also report the effective Beveridge curve, in the (s, v) space.
From the flow equations (8)–(10), evaluated in steady state, we obtain the stock of the unemployed
and workers in low-productivity jobs:
u =
γ =
δ
δ + m(θ(Ω))
(14)
δm(θ(Ω))
[δ + m(θ(Ω))][δ + λ(Ω)m(θ(Ω))] . (15)
Equation (14) is the Beveridge curve, which through θ =
v
u+λγ
now not only depends on u and v but
also on γ. Even though the equilibrium system is expressed in terms of u, γ, θ, as is common practice
in this literature, we plot the system in terms of u, γ, v, where v is an immediate transformation of θ:
v = θ(u + λγ). This allows us to interpret the well-known Beveridge curve (BC). The BC is a steady
state relationship between vacancies and unemployment, in this setting, for a given stock of on-the-job
searchers γ, derived from the flow equation (14) in and out of unemployment. In our setting there is
also a second flow equation (15) in and out of low productivity jobs, which we label the γ-curve (γC)
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