Do labor market institutions matter for business cycles?∗ - European ...

3 CROSS SECTIONAL EVIDENCE 9
thus, slice the multivariate distribution to take into account macroeconomic conditions. Note
also, that since rank correlations are computed, we allow for non-linear relationship between
business cycle statistics and LMI. 8 .
Formally, let S i denote the statistical factor i and let B j denote the business cycle statistic
j, while M is the principal component of the macroeconomic variables, then the Spearman’s
partial rank correlation coefficient can be expressed as:
r Si B j |M =
r Si B j
− (r Bj ,M)(r M,Si )
(1 − rBj ,M) 2 (1 − r M,Si ) 2 1 2
where r Si B j
is the Spearman correlation coefficient between statistical factor i and business
cycle statistic j. Table 3 reports the p-values associated with testing whether an observed
value of r Si B j |M is significantly different from zero using a small sample Wald-Mann test.
In Figure 3 we present partial rank correlations when we use different ways to detrend the
data. In particular, we detrend the data with either HP (for λ = 1600), or BP filters (keeping
cyclical movements of 6-32 quarters).
Independently of the filtered used to detrend the cycle, the overall index of rigidity does
not affect the volatility of the cycle, it only reduces significantly the correlation between
the real wage and labor productivity. The wage setting factor significantly increases the
volatility of the real wage and decreases significantly the correlation between output and
inflation 9 .
3.3.2 Economic factors
Given the natural interpretation of our statistical factors, we have considered identifying
factors using economic intuition. To this end we have considered separately the effects of the
RR index and renamed it economic factor 1 (henceforth EF1); we have extracted a common
factor from the indicators that characterize the strength of unions (EF2); another from
indicators such as COOD, GOVINT, LEVEL, EXT and MIN_W, characterizing the wage
bargaining (EF3) and one from the series of indicators of employment protection, EPL, EPR
and EPT (EF4). Table 4 presents the correlation of the economic factors with the original
indexes. Notice that the economic factors correspond closely to the statistical factors except
8 Spearman’s correlation (unlike Pearson’s correlation) is successful in small samples like ours, since normality
is violated, and is robust to outliers. Moreover, since we can apply the method conditioning on more
than one series, we have also investigated whether extracting more components from the macroeconomic
variables, and conditioning on more macroeconomic factors would change the results. The results we present
are robust to this change.
9 These results continue to hold when we use the average value of the LMI indices between 1970 and 2009
instead of their initial values to compute the principal components of the LMI indicators. They are available
from the authors upon request.