Just to follow up on this post, a simple test of the model would be to check if the ECEC (i.e. not normalised for compositional shifts) wages series is strongly correlated with the output gap. Output gap is easy enough – real potential GDP and real GDP are in FRED, and we convert this to a gap expressed in % of GDP:
Looks like a nice smooth correlation, and in fact the correlation coefficient is a very decent 0.51 for the annual data from 1991 to 2014. For the period 2003-2014 I’ve averaged the quarterly observations. But that’s just the classical effect, right? We need to compare the two indices. Here’s a plot with both series from 2002 to 2014 against the output gap.
It doesn’t look like I can replicate the result that the ECEC is more cyclical than the ECI, at least for the period 2002-2014. The correlation between the annual change in ECI and the output gap for that period is 0.83 and that for ECEC is 0.73. The covariance in ECEC is higher than ECI but both are really low (0.03 and 0.01).