Unemployment in an Interdependent World

3 Interdependence of labor market outcomes

3.1 Model calibration

We calibrate the model for three countries (hence, i = 1, 2, 3, j = 1, 2, 3 and N = 3),
which is the minimum number of countries in order to discuss the role of geography. We
choose parameter values such that all three countries are completely symmetric in the
initial steady-state and their equilibrium allocations replicate key empirical moments of
the United States for which both the search-and-matching and the Melitz (2003) model
have been calibrated by several authors. We set ν = 0 in our benchmark analysis (thereby
ruling out external economies of scale). Existence and uniqueness of this symmetric case
is shown in Felbermayr, Prat, and Schmerer (2008). Time is discrete and the time interval
is set to one month.

Productivity distribution. Following the literature,¹⁹ we assume that firms sample
their productivity from a Pareto distribution, so that the p.d.f. is g (φ) = γφ^γ^^-(1^+γ).
The shape parameter γ measures the rate of decay of the sampling distribution and φ > 0
is the minimum possible value of φ. We follow Bernard, Redding, and Schott (2007) and
set γ equal to 3.4. Without loss of generality, we may normalize φ = 0.5.

Matching function. The matching function is Cobb-Douglas m (θ_i)^{- α}i. We follow the
standard practice and set α_i = 0.5. In the absence of well-established estimates, we set
the bargaining power β_i = α_i.²⁰ To calibrate the scale parameter m, we use empirical
estimates of the job finding rate and labor market tightness. Constant returns to scale of
the matching function implies that the equilibrium tightness must be equal to the ratio of
these two rates. Shimer (2005) estimates the monthly rate at which workers find a job to
be equal to 0.45. Hall (2005) finds an average ratio of vacancies to unemployed workers
of 0.539 over the period going from 2000 to 2002. Accordingly, we match an equilibrium
tightness of 0.5 by setting the monthly job filling rate to 0.9. Reinserting these values
into the matching function, we find that m = 0.636.

Separation shocks. Job separations occur either because the firm leaves the market
or because the match itself is destroyed. We consider that the first type of shock arrives
at a Poisson rate of 0.916% per month. This implies that the annual gross rate of firm
turnover is equal to 22%²¹ , as suggested by the estimates in Bartelsman, Haltiwanger, and
Scarpetta (2004). The match-specific shocks account for the job separations which are left

¹⁹See for example Axtell (2001); Helpman, Melitz, and Yeaple (2004); or Bernard, Redding, and Schott
(2007). The assumption of Pareto distributed productivities is justified by the observation that the log-
density of firms’s log-sizes is well approximated by an affine function.

²⁰ The equality of the bargaining power and matching function elasticity is known as the “Hosios
condition” (Hosios, 1990) in the search-matching literature. Note, however, that in our case this condition
is not sufficient to ensure an efficient allocation because of the over-hiring externality.

²¹Along the steady state, the gross rate is 2 × 12 × 0.916 = 21.98.

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