Simple two-good model: How to link the relative price to the inflation terms?

[mphilstudent]

Dear all,

I’m developing a toy model with two types of consumption goods, to later add more features and answer interesting questions. For now, it is just a standard NK model, but with two consumption goods instead of one. I define the model in terms of the relative price of good 1 and 2. When I run the model, I get reasonable results, but looking into the “Policy and transition functions”, I’m pretty sure there is a mistake. The relative price of good 1 and 2 shows up as a state variable and there are policy functions. In the standard NK model (Gali, ch.3), the price of the good does not show up in that table.

I think the problem is that I am defining the relative price and linking the inflation terms of good 1 and 2 with it (equation 2 in the .mod file). Instead of this equation, is there an equation I am missing?

two_good_nk_simple.mod (7.9 KB)

[jpfeifer]

If you were to take inflation and replace it by its definition p-p(-1), the lagged price level would also show up in Gali, Chapter 3.

[mphilstudent]

Yes, that is true, but the p(-1) would only have effect on p in the policy functions (this is output from the code on your GitHub):

Whereas when I run my code, the relative price shows up and has effect on multiple variables:

So I think there must be something wrong there? Because of this, I get some hump-shaped responses in my IRFs which I think doesn’t make sense…

[jpfeifer]

Then you need to check your computations. But your model is different from the standard model in that the relative price plays a role as opposed to just some inflation term.