At the business cycle frequency
, a shock lowering the price of traditional capital causes labor's share to rise while a shock lowering the price of robot capital causes labor's share to fall.
Significantly more exceptions were found considering the lower boundary of business cycle frequency. Especially the cycles extracted with the use of the HP filter for many countries lasted longer than the most commonly accepted maximum length of 8 years.
In the case of most of the variables and countries two cycles within the business cycle frequency interval were indeed found.
The peak correlations between the components of money growth and inflation in Table 2A show no common pattern across countries at the business cycle frequency and are relatively small and mostly insignificant.
The filtered components allowed us to assess the role of money growth at the business cycle frequency and for longer-term cycles.
The frequencies below business cycle frequency
band correspond to the long-run, while the frequencies above business cycle frequency
band correspond to the short run.
This may also explain results reported in Table 2 where, while output leads unemployment in the business cycle frequency band, unemployment and output comove contemporaneously for periodicities ranging between one and 1.5 years.
Productivity leads output in most of the business cycle frequency band while it comoves contemporaneously with output at high frequencies.