Using log-differenced GDP in a non-linear model with stationary output variable

Estimation
1

Hi everyone,

I’m working with a non-linear NK DSGE model where the model’s output variable y_t is stationary.

My dataset contains Real GDP in levels (billions of USD, from FRED), which is obviously non-stationary.

I know I can’t just feed the model GDP in levels, so I was thinking of transforming it.

My question is:

  • Is it fine to take the log difference of Real GDP in the data (i.e. ln(Y_t) – ln(Y_{t-1})) and then use an observation equation in the .mod file:

y_obs = log(y) - log(y(-1));

so that the observed series matches the model variable’s transformation?

In other words, I’d be telling Dynare: “I took the levels of Real GDP, log-differenced them, and this corresponds to my model’s output growth.”

Is this approach correct for a non-linear model, or does it create problems for estimation?

Thanks in advance

2

That is the standard approach that most people use. However, you need to correctly handle the mean growth rate. In the data it will be positive but zero in the model. Most people therefore use demeaned growth rates.

4

Thank you so much Prof., that was really helpful. :slight_smile:

I just have a quick follow-up question:
Should the steady-state values of my observed variables match those of my model variables? For example, in the STEADY-STATE RESULTS: section of the output, should the steady-state value of y_obs be equal to that of y?

If they are not equal, would that imply that my observation/measurement equation is specified incorrectly?

Many thanks again,

5

Yes, those steady states need to be roughly equal. Any deviation between the two concepts will need to be explained by shocks.

1 Like
6

Thank you so much!