Hi jpfeifer,

Thank you so much for your help!

You are totally right. The steady state of hours worked “constelab” is specified as a estimate with a normal prior distribution centring around 0. That might already take into account the fact that hours worked are demeaned.

I have three follow up questions:

1, regarding the strategy of “demean”, take “hour worked” in SW(2007) for example, my thought is: to map the data of hours worked with hours variable (in log deviation) in the model, we may want to first take the mean of data series and then do log difference, as in the following equation:

[100*log(h_t^data) – 100*log( MEAN(h_t^data) ) ] = h_t^{hat}

where “h_t^data” refers to the data series, “MEAN(h_t^data)” is to take mean of the raw data series of hours worked directly. “h_t^{hat}” denotes the variable (in log deviation) in the linearized model.

However, I saw many studies, including SW(2007), demean in different way: “demeaning” is specified as in this equation:

[ 100*log(h_t^data) –MEAN(100*log(h_t^data) ) ] = h_t^{hat}

that is to take mean after taking “log” and scaling by 100, and then demean. It seems this approach is more appealing, but I have a hard time to understand why.

Could you help to understand why the second approach make more sense?

2, In SW(2007), hours worked is the only variable whose steady state is estimated, i.e. “constelab”. Why the variables “hours worked” is so special? Why do they want to make the steady state of hour worked “constelab” stochastic?

3, In SW(2007), I checked that the steady state value of hour worked “constelab” affects the model dynamics only through the measurement equation “labobs = lab + constelab”. How important is it to estimate the steady state of hour worked “constelab”? How important it is for this estimate to determine the estimation results and the induced model dynamics?

Thanks for your time!

Best

Andy