linearized vs. nonlinearized shock, unrealized news shock

[dt23]

Hi
these are 2 unrelated questions:

1. i saw in an old post that unrealized news shocks could not be modeled in 2006. is it possible to do so with the current version of dynare?
viewtopic.php?f=1&t=202&p=1091&hilit=news+shock#p1091

2. why does it make a difference if I enter a shock either in a linearized form or not.

The shock in the unlinearized system is (the secondline is the persistent shock):

Code: Select all

Y=Error_A_Per*L;
Error_A_Per   = Error_A_Aux*Error_A_Per(-1)^0.66;
Error_A_Aux =  exp(Error_A - 0.00125 );
var Error_A = 0.0025;

This is a lognomally distributed, persistent shock with expected value 1.

In the linearized system it is (the secondline is the persistent shock):

Code: Select all

Y=Error_A_Per*L;
Error_A_Per   = Error_A_Aux   +1;
Error_A_Aux =  Error_A +   0.66*Error_A_Aux(-1);
var Error_A = 0.0025;

This is a standart AR(1) shock with expected value 1.

I had expected that i woulndnt matter whether i use the first or the second specification, as log-linearizing the first gives the second.
Yet the Steady state values of the model I use change a little (1%) when i change the specifications and so do the IRFs.
Is that just due to rounding errors?

[SébastienVillemot]

Dynare does linearization, not log-linearization.

So it approximates your first system (by linearizing it); your second system is already linear so it solves for it exactly.

You get different results because the linearization of your first system is not equivalent to the second sytem.