Sorry, but I have to come back to this old post. I thought it would be quite straightforward to calculate some standard deviations from a model and compare them to those reported in a paper, but now I’m somewhat confused.
The standard deviation of a variable X should be sqrt(variance(X)) and this is also what Dynare reports in theoretical moments as std. dev…
There is also the concept of relative standard deviation, which to my knowledge is the ratio of the standard deviation to the mean. It is often reported in percentage terms, i.e., 100*sqrt(variance(X)) / mean(X). This is also suggested here Generate new statistics and tables
But in another part of the forum (How to get standard deviation in percentage - #3 by lm280299), where someone suggests to obtain the std. deviation in percentage by calculating
100*sqrt(variance(X)) / mean(X), jpfeifer responds
Regarding the transformation you suggest: up to first order and for small volatilities you are correct. You are basically performing a Taylor approximation of log(x) about the steady state xbar inside of the standard deviation
Why is this only correct up to first order and for small volatilities?
And furthermore, I also could not reconcile the standard deviations I got from BasicRBC.mod with those reported in the table on p.4 of “Stylized Facts” by Sims (see above). I see that when I calculate
sqrt(variance(X)/mean(X)) or alternatively, when I write the model in logs and then just take the sqrt(variance(X)), my results get closer to those reported by Sims, but they are still way off. Did anyone succeed in replicating the table from Sims?
And jpfeifer, how did you know that the values in the table are of logarithms of the levels? I couldn’t find this information in the text.
Thanks!