Log Linearising

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Log Linearising

Postby Tartaglia » Wed Mar 17, 2010 10:26 am

Hello everyone,

I am trying to log-linearise my model and I am not quite certain how this is implemented in Dynare. Looking at my first equation:
a=e^(tau)

To my understanding, in order to log-linearise this eqation I would need to do the following:
a'(â+1)=e'^(tau)(tau*ê+1)
where:
â= log a - log a'
ê= log e - log e'
the prime indicates the steady state value

How does this translate to Dynare? Michel had written in an earlier post:

F(X_t)=0 original equation

F(exp(lx_t))=0 log-linearised

where:

lx_t = log(X_t)

According to this, I would write my equation as:

exp(ln_a)=exp(tau*ln_e)
where ln_a= log(a)

Is this correct? How does this relate to the transformation above?
If this is correct, how would I correctly define this in the model. Would this be in the initval section where I declare the ss values as ln_a=log(a)? Does this interfere with the fact that my ss values of my endogenous variables for the linear case would be all zero?

Thank you for your help,
Tartaglia
Tartaglia
 
Posts: 10
Joined: Mon Dec 07, 2009 1:19 am

Re: Log Linearising

Postby Tartaglia » Thu Mar 18, 2010 9:05 am

Would it makes sense to declare the initial values of all ln_x variables as = 0 instead, that is instead of saying x=0, ln_x=0?
Tartaglia
 
Posts: 10
Joined: Mon Dec 07, 2009 1:19 am


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