Markup shock in NK Model


I am trying to introduce a markup / cost-push shock into a basic New Keynesian model with price stickiness as laid out in chapter 10 of McCandless’ “The ABC’s of RBC’s”. The model is log-linearized and, asides from the markup, has three shocks: technological, intertemporal preference, and money growth. The way I am introducing this shock is as follows: If psi is the elasticity of substitution between intermediate goods, I let alpha = psi/(psi-1), and after some algebra, I obtain a phillips curve where alpha is added to the marginal cost expresion. I then let alpha follow an AR(1) process. Thus, when alpha increases unexpectedly, inflation increases by the change in alpha times ((1-rho)(1-betarho))/rho. Is this a correct way of introducing the markup shock?

I have attached the mod file. Thanks in advance. nk_markup.mod (2.2 KB)

Without knowing the model in more detail, it is hard to tell. But it sounds reasonable.