Labor hours index as observable

Hi everyone

Given the absence of data for the country with which I am working, I found an index of hours worked and another of the working population, both with 2013 = 100. I made the quotient of the series (seasonally adjusted) and obtained a stationary series with a mean around of 1. My model is log-linearized, and I wonder if I could use that quotient (demeaned) as an observable variable, so that,
quotient = index_labor / index_working_age_pop
quotient - mean = Lhat
or if I have to get logarithms, that is,
100 * (log (quotient) - mean) = Lhat
the latter seems reasonable because of the variance of the series, but Iā€™m not sure if I can do this.
Thanks in advance.

Hi ManuelTorres,

as your model is log-linear, you should match your variable (which is a concept of %-deviations from ss) with a %-deviation from the mean in the data. Hence, I would suggest to specify the observation equation as
\log(Q_t)-\log(\bar{Q})=\hat{L}_t, where Q_t=\text{quotient} and \bar{Q}=\text{mean}(Q).

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