Unemployment in an Interdependent World

aggregate value of imports is equal to the total aggregate value of exports. The multilateral
trade balance constraint for country i (or, balance of payments, BOPi) is given by:

2.6 General equilibrium

To obtain analytical results, the literature usually assumes quasi-linear preferences or the
existence of a freely-traded num´eraire good which is produced in every country under
conditions of perfect competition and where there are no labor market frictions. We are
not opting for such a short-cut, since this would relegate the effect of changes in market
sizes into the num´eraire sector. Another way towards a full-fledged analytical solution of
the model is to assume perfect symmetry in all respects which yields a recursive model
structure. Under these latter circumstances, the present model perfectly coincides with
Felbermayr, Prat, and Schmerer (2008) where the effects of trade liberalization on labor
market outcomes can be fully described analytically in closed-form and for a general
distribution function G(φ).

When countries are asymmetric, the Φ's depend, amongst other things, on all the
countries’ disposable incomes. The disposable incomes are in part determined by the
respective rates of unemployment, hence Φi = f (u1, u2, . . . , uN, . . .) . The wage and job
creation curves imply that u_i = g (b_i,c_i,m_i; Φ_i). Through Φ_i, country’ i's rate of unem-
ployment depends on all the other countries’ unemployment rates as well. This implies a
structural dependence of u_i on the whole world’s collection of institutional labor market
variables.

The proposed model is a generalized version of Krugman (1980). That model does not
lend itself to analytical solutions in the presence of asymmetries and trade costs, even in
the absence of firm heterogeneity or search frictions.¹⁷ Note that the underlying problem
in this type of model does not stem from the existence of external economies of scale; it
also does not vanish when the price of the final output good Pi is equalized by frictionless
international trade. Hence, in order to assess the properties of the model, we need to
resort to calibration and simulation.¹⁸

¹⁷See Anderson and van Wincoop (2003) for a recent example. Technically, in the generalized Krugman
(1980) model, labor market clearing conditions give rise to transcendental equations which do not possess
any analytical solution. Hence, wages cannot be solved for analytically.

¹⁸This is what many authors in the economic geography literature do; see, e.g., the surveys by Fujita,
Krugman, and Venables (1999) or Baldwin, Forslid, Martin, Ottaviano, and Robert-Nicoud (2003).

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