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!!