Gali Chapter 3 and Walsh Chapter 5 comparison

I’ve difficulties to replicate the conclusion of Gali on technology shocks opening up a big and persistent output gap usign the same three equations model in the 5th Chapter of Walsh’s “Monetary Theory and Policy”.

The difference seems to me to boil down to a slighlty different dynamic IS:

x = x(+1)-sigma^-1*(rr-pip(+1)-(-(1-rho)u)); % Gali
x = x(+1)-sigma^-1
(rr-pip(+1))+u; % Walsh

What am I missing?
NKmodel.mod (600 Bytes)


I don’t have access to the chapter of Walsh. But isn’t u_t a cost push shock, not technology?

I will try to post a screenshot later. No, Walsh calls it productivity disturbance. Also, isn’t a cost-push shock factored in the Phillips curve?

Here’s the screenshot


From what I can see, the difference is whether you still have the natural rate of interest in the equation or you replace it.

sorry for being thick, but in the case of Gali it seems to me that the productivity shock enters with a negative sign, whereas for Welsh is clearly positive. Hence Gali signals a negative effect on the output gap.

If I look at Welsh, a positive shock u_t improves the output gap.

Which chapter/part of which Gali edition are you referring to? And which edition of Walsh?

Gali 2008 Chapter 3 (eq. 22 and 28) and Walsh 2003 second edition p. 244 (Chapter: A New-Keynesian Model for Monetary Analysis)

The two u in your notation are not comparable. In Gali it is indeed today’s productivity a_t, while in Walsh it is u_t=E_t y_{t+1}^f-y_t^f. If TFP today goes up and follows an AR1, then u_t=E_t y_{t+1}^f-y_t^f\propto \rho a_t-a_t=(\rho-1)a_t. So if TFP goes up today, u_t will be negative in Walsh

Thank you, that makes sense