Log-linearization question

[kgarb]

Hello all,

This isn't a dynare question, but I'm having problems figuring out exactly how log-linearizations happen in a lot of these papers. Looking specifically at Fernandez-Villaverde and Rubio-Ramirez (2006), I'm not sure how they get to equation (5) on page 28. See the attached PDF for more details on my problem in understanding how exactly they do the log-linearization.

Thank you for your help.

[jpfeifer]

Easy. Your have to subtract the steady state from both sides. You have an equation of the type

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a_t+b_t=c_t

Your Taylor approximation is

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a*(1+hat a_t)+b*(1+hat b_t)=c*(1+hat c_t)

As in steady state

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a+b=c

you can subtract this from the above equation to get

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a*(hat a_t)+b*(hat b_t)=c*(hat c_t)

[kgarb]

Thanks!