Nominal prices in a two-sector model

General DSGE Modeling
1

Hi all,

I am trying to introduce nominal prices in a two-sector NK model setting. As it stands the model the model seems fine except that the nominal prices all return to their previous levels after a productivity shock, meaning that a period of low inflation is always followed by a period of high inflation and vice versa. My hunch is that a correct specification would give unit root nominal prices, but steady state reverting relative prices.

The consumer has CES preferences over two consumption goods, both produced by a continuum of monopolistically competitive intermediate producers and packed into a final consumption good by a perfectly competitive packer. Nominal prices are introduced by Rotemberg price adjustment costs.

Am i correct in thinking that the nominal prices should not return to their steady state values after a shock? If so, any hunch on where the miss-specification might lie?

Here is the mod file:
v4.mod (5.3 KB)

Thanks!

2

You are right that this is rather unusual. Have you tried dropping the price level from the model and only working with relative prices? The question is whether that works.
I also find it curious that the steady state of the price level is different from the initial value of 1. That suggests there is indeed a unique value to which it is pinned down.

3

Thanks for the quick reply! Working with only relative prices seems to have done the trick.

Here is the code for anyone interested:
v5.mod (5.3 KB)