Price Level in Gertler/Karadi (2013)

Hi everyone,

I understand that the price level in standard NK models is typically indeterminate, and only its growth rate (i.e., the inflation rate) is determined.

My question concerns the model in Gertler/Karadi 2013 (pdf here: https://www.ijcb.org/journal/ijcb13q0a1.pdf) and the determinacy of the price level in that model. In the model, the real rate of return Rb on a government bond seems to implicitly define the price level P as a function of the real bond price q (see screenshot below). The nominal side of the model features standard pricing frictions and a Taylor rule.

Now, when solving for steady state, I can obtain values for steady-state Rb and steady-state q (from other model equations). Does this imply that the bond return in equation (6) pins down the steady-state price level? Am I right in concluding that the price level is determinate in GK13?

Thanks for any help!

image

I am not entirely sure, but my hunch is that the answer is no. q_t is the nominal price of the bond. It should permanently move if the price level moves. Only the ratio on the right should be stationary, but the individual components may not be. But they definitely need to be cointegrated.

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