Linear models of DSGE models

General DSGE Modeling
1

Good morning,

I read some of the responses of yours about linear vs log linear but I need some clarifications to make sure that I am on the right track:

  1. If my FOC equations are all linear and variables are in levels, then whether I declared “model (linear)” or “model” without linear options, the variables are interpreted as absolute deviations from steady state and the only difference is the speed of computation. Right ?

  2. I was checking your code for Gali and Monacelli (2005) whereby you have used linear model option while the textbook (Gali book chapter 7) derivation is log-linear version.
    If I want to follow your methodology in estimating a linear version of the model to elude assigning steady state values, then it is sufficient to take the exponential for both sides of the log-linear equations or I have to derive the model again for a linear version ?

Thank you so much in advance,

2
  1. Yes, that is correct.
  2. I am not sure I understand that point. Dynare internally does keep track of whether the variables represent deviations or log deviations from steady state. All it cares about when specifying linear is that the variables defined with the var statement only appear linearly in the model.
3

Sorry to mix things up, I should have been clearer. I am referring to the attached code of yours where you have used “mode (linear)”. However, In the initial paper of Gali and Monacelli (2005), all the FOC equations are expressed in log-linear form and, therefore:

Have you transformed the log-linear equation to linear ones by taking the exponential of both sides in order to use “model (linear)” ? otherwise how come the code uses “model (linear)” when all equations are in log forms ?

Thank you so much !!

Gali_Monacelli_2005.mod (14.7 KB)

4

Again:

ake for example the loglinearized equation

y = a + n;

Here, y represents the log deviation of output from its steady state. That equation is clearly linear.

5

That’s awesome, many thanks