Measurement equations, inflation and interest rates

Dear all,
dear Johannes,

I just wanted to ask you two quick questions regarding the measurement equations of inflation and interest rates.

  1. In Johannes’ “Guide to Specifying Observation Equations for the Estimation of DSGE Models”, you show how to demean the gross interest and inflation rates. Why is it for inflation (equation 39): ... - log[mean(Pi_data)] and for interest rates (equation 42): ... - mean[log( 1 + R_data/(4-100) )] Why is it not in both cases the log[mean(xxx_data)], since they are both gross rates?

  2. My model is entered nonlinearly into dynare, and inflation and the interest rate are gross rates. Let’s say I want to keep the mean in one of the observables, would I then just write the observation equation as:

inflation_data = log(inflation) This would mean I just feed in log inflation without demeaning it. This question is based on a post I read, where Johannes said that from his experience it is sometimes beneficial to feed in one undemeaned series. Or is not necessary to take the log in the mod file?

Many thanks for your help!


Hi Rob,

  1. This was an inconsistency on my behalf. Sorry for that. Usually, you want to make sure that the log deviations are mean 0. Due to Jensen’s Inequality, you should work with mean(log()) in both cases, not the log(mean()). Only the former will result in mean 0 variables due to the uncertainty correction. I have updated the document accordingly.
  2. Yes, that way you would keep the mean in the inflation rate (presuming it is measured as a quarterly/annual gross rate commensurate with the frequency of your model)

Hi Johannes,

Many thanks for your help and getting back to me! I will now start with the estimation of my model.