Permanent Taylor rule shock

Hello everyone,
I need help with my mod file (attached). I am trying to simulate the effects of a permanent and surprise monetary policy shock in a deterministic New Keynesian model.

The problem is that I do not get the initial spike in interest rate one would see in a monetary tightening. Instead, the interest rate drops.

The shock works through the interest rate rule:

(1+int)/(1+int_t) = ((1+infl)/(1+infl_t))^varphi

int = interest rate
int_t = target interest rate
infl = inflation rate
infl_t = target inflation rate.

Before the shock, infl_t = infl_old (2%) (t = -infinity,…,-1)
After the shock, infl_t = infl_new (0%) (t = 0, … , infinity).
And int_t = (1+infl_t)/betta - 1, from the Euler equation.

In the mod file, I specified ‘infl_t’ and ‘int_t’ to be exogenous variables and ‘int’ to be endogenous. I use initval and endval having manually solved for the steady state values related to the two inflation rate targets.

Should I instead make ‘int’ an exogenous variable and use the ‘shocks’ command? But this is only for temporary shocks, isn’t it? I am really quite lost. What changes should I make?

Thanks in advance!
OMG.mod (2.68 KB)

I cannot really spot a mistake. Maybe your results are correct? There is an initial hike in interest rates that brings down inflation. Given that inflation is now quite low, the central bank can lower its interest rate (particularly given that the new natural rate is lower than before)

P.S.: Why is steady state capital and steady state output lower in a world with low inflation and thus no price dispersion?

Hi Johannes,

Thank you very much for your kind response! I’ve corrected the ‘endval’ values, i.e. output and capital are now higher in the zero inflation steady state (new mod file attached). Thank you for spotting that.

Below are the transition paths I get for nominal interest rate, output, and inflation. The transition is from 2% inflation to 0% inflation. The graphs below plot 20 quarters of transition, plus two quarters before and two quarters after. Both the interest rate and inflation rate fall immediately, while output jumps to the new steady state on the last period. (Other real variables do the same, i.e. jump to the new steady state on the last period).

Compare these with transition paths generated in similar permanent disinflation experiments done by Ascari and Ropele (paper attached), which I’m trying to mimic. The paths to the new steady state are smoother, and the interest rate rises initially. I am thinking my paths should look a little more like these.

My model is far simpler than Ascari and Ropele’s. Mine only has sticky prices, while theirs also have real rigidities. Could that be the reason? But I think my variables should behave similar to his during transition nonetheless. Which is why I’m guessing that the way I coded it is wrong. Should I add something to the ‘initval’ and ‘endval’ combo?

Thank you again!
OMG.mod (2.66 KB)
Ascari_Sacrifice ratio or welfare gain.pdf (597 KB)

When using simul(periods=20), you force the variables to have the endval value in the last period. Thus, the jump happens by construction. If your model is stationary, it will actually converge back to the endval values in infinite time. But not after only 20 periods. Thus, you need to increase periods.
It also seems that your model also does not feature much endogenous persistence, explaining why much action is in the first period after the transition.

And why should in your model the interest rate increase in the first period? The gap between inflation and its target

slightly increases. This in itself would increase the interest rate. But at the same time the target decreased by much more, leading to an overall fall. With more persistence in inflation, you might observe such an overall initial increase, but with the strong fall in inflation this is not going to happen.