Moment in Model vs. Data

Dear all,

I am a bit unsure if my model variables and simulated moments correspond to what I have derived in the data and would very much appreciate some help and clarification on this issue.

In my stochastic model, I use the log-approximation for all my variables, output Y, stock of debt and also an investment rate (investment/capital). In my data, I filter the log of the stock data (log(GDP) and the log(stock of debt)) with the HP-filter, whereas for the investment ratio I also filter out the trend with the same HP-filter, but without taking the logs of this ratio. But since in my model all variables are log-linearized, I wonder if the data series (and the moments I compute from these series) are compatible with the ones I get in my model. Could it be that I am doing a mistake here and compute growth rates of the investment rate in my model and only percentage point changes in my data?

Thank you a lot in advance!! :slight_smile: :slight_smile:

Hi, If the investment ratio is log linearised in your model, you should take the ratio in log in the data. An alternative would be to apply the log linearisation only on a subset of the model (GDP and debt in your example) replacing each variable X you want to log linearise by \exp(X) and then linearising the whole model (this is explained in other posts on the forum). Another alternative is to add measurement equations where you define the observed variables as the log of the variables in deviation to the associated steady state, x^{\text{obs}} = \log(X/X^{\ast}), and then linearise the whole model. Also note that is is possible to apply the HP-filter on the simulated data, or compute the unconditional moments of the theoretical filtered variables. The general principle is to apply the same transformations on the sample data and theoretical (simulated) data.

Best,
St├ęphane.