Hi Johannes,

Your recent January article on detrending is great, but there are some additional issues that I thought would be educational to bring up for users (including myself!). As you acknowledge and cite references over, the detrending procedure will affect the MH estimate results; correlation across shocks, whether measurement error is used to identify a time series, etc, are not innocuous details. I think the article does a great job addressing the importance of these points, but the common error that comes up, at least for me, is that the hessian matrix (of the likelihood I assume) is not PSD.

I read a prior post that refers to this being a problem with the initial conditions, but I believe that often the main problem is more fundamental; sometimes, feeding in a first difference time series data set will work, whereas others will not, for a given model structure. For example, if I have a nonstationary model with trend growth in TFP, feeding in the log of y, k, c, etc, doesn’t work, whereas feeding in the difference of logs will work. In your paper, you emphasize the importance of making the system stationary by dividing by TFP, if there is no exogenous trend assumed (I have not tried this); but, if there is trend growth in TFP explicitly in the model, I would expect the difference of logs to work.

As another alternative, I tested the estimation under observable time series growth rates, i.e. setting dX=(X-X(-1))/X(-1), for a variable X. However, doing so led to the following error.

??? The left hand side is initialized and has an empty

range of indices.

However, the right hand side returned one or more

results.

I am attaching a sample code and .xls in case you are curious to see the details, but if you could also talk generally about the underlying problem for the two aforementioned errors, it would be highly educational. (In the xls file, H is normalized to 1, the rest are the difference of logs, i.e. X=log(X)-log(X(-1)) for the variables consumption, output, capital, energy, and pollution.)

kdata2.xls (24 KB)

benchmark.mod (2.14 KB)