Our theoretical model gives rise to a gravity-type relation between bilateral trade
volumes and explanatory variables related to countries’ market sizes and bilateral trade
costs.34 The model also predicts that the effect of labor market regulations of some
country j on country i′ s rate of unemployment is conditioned by the amount of bilateral
trade between the two countries. However, when computing trade-weighted averages of
foreign variables to gauge the influence, e.g., of foreign labor market institutions, we need
to make sure that the weights are strictly exogenous. Hence, we proxy the amount of
bilateral trade between i and j by
where P OPit denotes population of country i, DISTij is the great circle distance between
the two countries’ most populated cities; α1, α2, and δ are parameters. ωij∙t varies with
time as population changes. It mimics the simplest possible gravity formulation, but
substitutes population for GDP which is potentially endogenous.35 Standard gravity
predictions suggest that α1 = α2 = 1. Overman, Redding, and Venables (2003) state that
δ , “the elasticity of trade volumes with respect to distance is usually estimated to be in
the interval 0.9 to 1.5.” In a meta analysis of 1,467 estimates from 103 papers, Disdier and
Head (2008) find that the mean effect is about 0.9, with 90% of estimates lying between
0.28 and 1.55. Hence, we choose δ = 1 as our benchmark case, but conduct robustness
checks with respect to the assumptions on α1, α2, and δ.
ω ijt =
POP⅞1 POPjα
DISTiδ
ij
(29)
We calculate ωij∙t for all 168 countries for which population and distance data is avail-
able (i.e., not only the 20 OECD countries for which we have reliable labor market data).
There are several possible ways to normalize the data; the choice of normalization has in-
terpretational consequences but should not affect our qualitative findings. In our preferred
setting, we normalize the weights such that ^1=81 ωijt = 1 for all 168 countries. Then, we
construct the trade-weighted average of foreign unemployment rates, u*t = ∑2=1 ωijtUjt,
where country i′s rate of unemployment is excluded by definition (ω iit = 0) and the sum-
mation only involves the 20 OECD countries for which high-quality unemployment rates
are available. Similarly, we construct the trade-weighted average tax wedge of all countries
other than i as b*t = ∑2°1 ωijtbjt (and similarly for all other labor market variables LMRit,
denoted by LMR*t), and the average foreign output gap as gap*it = ∑j°1 ωijtgapjt. Note
that this strategy implies that the foreign variables have smaller sample means than the
domestic ones.
covariation between uit and bit . In a similar empirical study without spill-over effects, Felbermayr, Prat,
and Schmerer (2009) treat bit as endogenous but do not find evidence for endogeneity bias.
34See Helpman, Melitz, and Rubinstein (2008) for a derivation of a gravity model in the presence of
firm heterogeneity.
35We have also worked with predicted bilateral trade volumes obtained by regressing observed bilateral
trade on exogenous variables such as population, distance, and other typical covariates such as common
language, contiguity, joint membership of countries in currency unions or free trade areas, etc., using
Poisson Pseudo maximum likelihood methods following Santos Silva and Tenreyro (2006, 2008). Results
are qualitatively and quantitatively comparable. We prefer our specification as bilateral trade volumes
may be endogenous to unemployment rates so that weights obtained from this procedure may lead to
inconsistent estimates.
33