Unemployment in an Interdependent World

1 δ          Pc

r+δ ^πij ^*j I = mr[θi] Lij ^*^j I⁺ Pi^fij ■                     (²¹)

For the marginal firm φ*j the discounted value of future operating profits has to be
large enough to cover the upfront costs of ramping up production (the hiring costs).
Empirical evidence strongly supports the view that only the most productive firms select
into foreign markets.¹⁵ Hence, we focus on parameter values where φ*j > φ*i for all
i,j. The ex ante probability of successful entry into the home market i is (1 — G[^*i]),
whereas the ex ante probability of exporting to country j conditional on successful entry
is Qij = (1 - G [^*j] ^)/(1 ^- G ^[^*i^]). Note that Q_ij can also be understood as the share of
active firms that sell both to the domestic and to the foreign market j . Appendix A1
shows how φ*i and φ*j are related.

Entry into existence. Following Melitz (2003), we define the average productivity of
a domestic firm serving the domestic market i and any of the foreign markets j as:

∞                ∞                    ∖ 1∕(σ-1)

(₁1 — G[φ∙j] Д '■ ^gtewi}      ■

Based on this definition we can write down the free entry condition as:

fePi = ∑ (1 - GMj]) '      ^δ∏ij∣≠<j] - _mPC_i]Lij∣≠<j] - Pifij) ■        <23)

where we have the costs of entering a market on the left hand side and the expected
profits on the right hand side. The profits of the firm are not yet known at the time of
the entry-decision because the productivity level is unknown. With probability 1 - G[^*i]
the productivity will be high enough to make production profitable in the home country
i. With probability 1 - G[φ*j] the productivity will be high enough so that even exporting
to country j is profitable. The term in brackets indicates how much a firm will earn in
these cases.

Equality in equation <23) is assured by the entry of new firms. As long as average
profits exceed the entry cost, new firms will enter the market, increasing competition,
thereby driving down profits until they have reached the entry cost <and vice versa if profits
are too low). The mass of available varieties in country i is given by MM_i = hQh Q_hiM_h,
where Mh is the mass of active producers in country h.

2.4 Stationarity conditions

Employment dynamics. As usual, we focus on a situation where flows into unem-
ployment and out of it are of equal size, hence η <1 - ui) = θimi [θi] ui. This provides

¹⁵For empirical evidence on selection into the export markets, see Bernard and Jensen (1995, 1999,
2004); Roberts and Tybout (1997); and Clerides, Lach, and Tybout (1998).

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