The Importance of Global Shocks for National Policymakers: Rising Challenges for Central Banks

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where ε^z_t and Sm equal the technology and the non-technology innovations,
respectively. Since GaH (1999) assumes that the unit root in productivity stems
exclusively from technology shocks, the matrix of long-run multipliers is lower triangular
( C ¹2(1) = 0 ). In order to estimate this approach on a global level, the following five-step
procedure is pursued. First, labor productivity figures for the G-7 plus euro zone are
calculated by subtracting the log of total employee hours from the log of GDP for each
country or region.⁶ Second, the obtained figures for labor productivity and total employee
hours are standardized on the basis of first differences with a mean of zero and a variance
of one. Third, global forces for labor productivity and hours worked are estimated by
deriving the first principal component (PC1) each. Accordingly, for labor productivity the
proportion of the total variance attributable to PC1 is 26.1% compared to 22.5% for PC2.
For total hours worked, PC1’s share is 38.3% (PC2: 22.7%). Fourth, we “re-construct”
the two first principal components in levels by setting each global factor zero in Q1 1984
and calculating the cumulative sum. Fifth, we apply a battery of unit root tests (Dickey-
Fuller; Phillips-Perron; Kwiatkowski, et. al., Elliot et. al.; Ng and Perron) for global
productivity and global hours worked. Accordingly, the majority of unit root tests
indicates that global productivity is integrated of order one. With respect to global hours
worked, the empirical evidence is more mixed, with some tests indicating integration of
order one or being stationary. Hence, concerning hours, equation (7) is estimated both in
levels and first differences. All lag criteria point lag to a length of one. After deriving the
global technology innovation, the following equation is estimated:

U_t — C oS + C1S t-1 + C 2S t_-2 + C 3S t-3 + C 4S t-4

with u_t as global structural shocks derived from our SFAVAR (cf. equation 5)
and s_t^z as global technology shock. Wald F-tests are done with the null hypothesis that

⁶ A series for total hours worked in the EMU is not available to our knowledge. We therefore construct the
EMU figure as the sum of hours worked in the following countries: Germany, France, Italy, Spain, the
Netherlands, Belgium, Ireland and Finland. On basis of PPP weights provided by the IMF, our measure
covers 89% of total EMU GDP in 2007.

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