estimates of the output gap adds another five so that these three variables already generate
an adjusted R2 of 0.88. The additional covariates used in (1) of Table 1 increase the
adjusted R2 to 93 percent. Hence, controlling for business cycle effects and fixed country
characteristics, labor market institution do not explain a large fraction of variance of the
unemployment rate since their entire cross-sectional variance is absorbed by the country
fixed effects.
In the next step, we include the trade-weighted average foreign unemployment rate
u*t and estimate versions of
uit = ρu*t + λ ∙ LMRit + ∏ ∙ pmrit + γ 1 ∙ gapit + γ2 ∙ gαp↑t + Fi + Tt + Sit + εit. (30)
The domestic unemployment rate is not used in the calculation of u*t. However, if shocks
to the unemployment rate exhibit correlation between countries, then estimation of (30)
via OLS would yield a biased value for ρ. To avoid this endogeneity bias, we instrument uit
by lagged foreign regulatory variables, LMR*t-1,pmr*t-1.38 The underlying assumption
is that past foreign regulation is exogenous to domestic contemporaneous labor market
outcomes.
Columns (2) and (3) show the most parsimonious specifications, using only uit along
with gapit , Fi , Tt , and Sit. The OLS estimate and the IV estimate are both positive; the
former is ρOLS = 0.072; the latter, being somewhat smaller, is ρIV = 0.067. The sign of the
bias ρOLS -ρIV is not surprising, since one would have expected that unemployment shocks
are correlated positively between countries so that OLS should overestimate. However,
the difference between the estimates is very small and will remain so in more complete
specifications. Note that adding u*t increases the adjusted R2 relative to a model with
gapit, Fi , Tt , and Sit as the only controls from 88 to 92 percent. Also note that the IV
strategy works well: invalidity of instruments or model specification is rejected with high
degrees of statistical significance.
Columns (4) and (5) add an array of labor market controls. They also include gap*t
in order to control for the direct effect of the foreign business cycle on domestic unem-
ployment. Qualitatively and quantitatively, results are comparable to those presented
in column (1). However, the measured coefficient ρ is somewhat larger now than in the
specification without controls. The sign of the endogeneity bias of ρ changes, but the dif-
ference between the OLS and the IV estimate is minor. Interestingly, while the coefficient
on gap*t is estimated with low precision, its sign is positive.
Columns (6) and (7) drop the insignificant labor market controls. Results do not
change much, but the overidentification test (while easily passed) becomes less convincing.
Hence, we prefer specification (5) over (7). It implies that an increase of the average
foreign unemployment rate by one percentage point increases the domestic unemployment
rate by about 0.09 percentage points. The average effect, therefore seems small. In
terms of the (different) underlying standard deviations of uit and u*t, the effect is 0.06
(0.088*3.144/4.294). However, this average effect may hide substantial variation across
countries.
38 This vector of instruments satisfies tests for instrument validity.
35