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In chapter 2 of Gali's book, he uses the equation (25):enter image description here

and combine the "driving processes for technology and preference parameters", inflation can be written as :

enter image description here I wonder how this new inflation equation is derived, and does the phrase "driving processes for technology and preference parameters" refer to the AR(1) process of technology and preference? like the following equation: enter image description here

zt is the preference shifter in utility function.

enter image description here

at is the technology level in production funtion.

enter image description here

vt is the monetary shock in interest rate rule.

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