Questions to Measurement Equations and Estimation

Estimation ML/Bayesian estimation
1

Dear Dynare Team,

with the publication “Guide for specifying…” and the forum posts I was capable of transforming the data to match the variables of a log-linearized model by removing the trend via log difference and demeaning.

However, I would like to gain a better understanding of what I’m actually doing instead of solely replicating the necessary steps.

I hope, one of you can answer me the following questions:

  1. The observation equation for output is dy=y-y(-1). This makes sense to me since we have to match the GDP growth rate dy with the model variables (that is (log(y)-log(y(-1)).

However, I don’t understand why the observation equation for inflation is infobs=inf.

For inflation we also apply the log difference and demean it right? So we would also get the growth rate of Inflation. Why isn’t it infobs=inf-inf(-1) ? What is the difference between Output and Inflation?

  1. Is it correct that the interest rate is not trending and thus we only apply logs instead of log differences and demean it?

  2. If we want to estimate Bayesian irfs, do we usually estimate y,inf,i or is it common to estimate dy,infobs,iobs – again: what is the difference ?

I’ve read the Remark of Figure 10 in “An Introduction to Graphs in Dynare” but I don’t understand what output do we get for each of the two types

  1. Is the output of bayesian estimation (Graphs for Bayesian Irfs) given in basis points? E.g. inflation decreased by 30 basis points below steady state ?

Thank you very much for help and clarification!

Johanna

2
  1. Inflation is the log difference of the price level. That definition coincides with the one in the model already. In particular, inflation does not have a trend anymore.
  2. At least your model predicts the inflation rate not to have a trend. Empirically, that may be a different matter. There is some debate on whether interest and inflation rates are still integrated.
  3. Typically, we are interested in the economic responses of the actual model variables, not the auxiliary variables used to estimate the model.
  4. It all depends on your model setup and how you scaled your variables. Without more details it is impossible to know.