analysis. Other authors have maintained analytical tractability by fixing expected wages
in a num´eraire sector that remains unaffected by labor market frictions and trade costs,
and which may additionally absorb all income effects due to quasilinear preferences.4 This
strategy blends the comparative advantage channel with Krugman/Melitz mechanisms.
Our paper does not follow this path: it allows for income effects to be fully operative
and focuses entirely on intra-sector reallocation (with intersectoral reallocation absent).
In order to see how our approach differs, it is useful to consider recent papers that use a
multi-sector structure.
Helpman and Itskhoki (2008) use a two-sector, two-country model, where one sector
produces varieties of differentiated goods under conditions of firm-level economies of scale,
monopolistic competition, iceberg trade costs and heterogeneous firms `a la Melitz (2003).
This sector also features search unemployment. The other (num´eraire) sector features a
linear production function, perfect competition, no trade costs, and no search frictions.
Families allocate members to sectors such that, in equilibrium, expected wage rates are
equalized. In most of the paper, Helpman and Itskhoki focus on a situation where con-
sumers’ preferences are quasi-linear in the num´eraire good. Countries are identical except
for labor market frictions, which are parameterized so that both economies are diversified.
In this setup, the less sclerotic country specializes on the differentiated good. Trade
liberalization triggers a reallocation of workers into the differentiated sector, thereby push-
ing up aggregate unemployment. However, there are additional effects due to increased
exit and entry of firms and changes in terms of trade, so that the net effect is ambiguous.
Helpman and Itskhoki show numerically that a reduction of search frictions in one country
leads to a hump-shaped response in this country’s unemployment rate but unambiguously
decreases the unemployment rate in the other country. It is unclear whether unemploy-
ment rates move in the same or in opposite directions; moreover, it is perfectly possible
that the more rigid country has the lower rate of unemployment.5 Helpman and Itskhoki
acknowledge that “the unemployment results depend on certain structural features of the
model” (p. 4).
Helpman, Itskhoki, and Redding (2008a,b) build on the paper by Helpman and It-
skhoki (2008), but assume that workers differ according to an exogenously given ability.
Firms engage into costly screening of their potential workers’ abilities before the wage
bargain. In that setup, a deterioration of home labor market institutions has an am-
biguous effect on home unemployment, with a slightly favorable prediction for a negative
relationship. Higher search costs lead to a decrease in labor market tightness which raises
unemployment, but also induces a decrease of the fraction of exporting firms, which lowers
unemployment. Concerning spill-overs, their model predicts that “... a rise in the foreign
country’s labor market frictions raises unemployment in the home country while a rise in
4 To our knowledge, in all papers that integrate search unemployment into general equilibrium trade
models authors assume that the destruction rates of matches (or firms) along the steady state are exoge-
nous. Relaxing this assumptions is an important direction for future research. One way to do this is to
depart from the standard Melitz (2003) model and to allow firm-level productivity to vary over time.
5 However, whenever the labor market rigidities are low and the differences in labor market institutions
are not large, a reduction in one country’s search frictions lowers unemployment in both.