an infinity of steady states with Taylor rules

[superztt]

Hi, I am new to Dynare. I have a problem in getting the steady state with a monetary policy of Taylor rule.

When I set the monetary policy in constant money supply, I got a steady state solution. However, it said "Impossible to find the steady state" when I changed to a Taylor rule. My understanding is when switch the monetary policies, Taylor rule in the steady state is the same as Euler equation is the steady state. Compared to the constant money supply, does it mean there is one less steady state condition? Since less conditions than unknowns, the stead state is indeterminate. Or the nominal price can be inflated to any arbitrage level.

Did I understand correctly?
What are the ways to resolve the problem, beside use logarithm to get the deviation?
Cheers!

[jpfeifer]

As always, post the mod-file.

[superztt]

Hi jpfeifer,

I have attached the mod file. When I set the monetary policy as a Taylor rule, there is a problem in finding the steady state. When I use a constant money supply, it works. So I was wondering if it is because the taylor rule at the steady state is equivalent to euler equation. Anyway, what is the problem on earth? How to deal with it? Thanks!

[jpfeifer]

Could it be that you are trying to use the steady state operator to compute something that cannot be set endogenously?
Take inflation: every percentage point higher steady state inflation will increase the steady state nominal interest accordingly. But any consistent combination of both (via the link the Fisher equation provides) is feasible. You need to pin down one of them by setting the value. The model cannot do this for you.

[superztt]

Thank you, jpfeifer! At the steady state, there is no inflation. But I see you point, the stock level of money supply, as well as the price level can be any arbitrage number. That's probably why Dynare returns '' an Infinite of steady state", whereas constant money supply monetary policy explicitly fixes those levels.

But Taylor rule is still influential in numerous models. So I was wondering how do people usually deal with it in Dynare?

[jpfeifer]

I am just saying: fix the steady state inflation to a particular value in steady state instead of using the steady_state-operator to compute it endogeously. An example is the Gali 2008 textbook. You can find a mod-file for this on my homepage. It has a Taylor rule and works.

[superztt]

Is setting the steady state inflation at a certain value in the Initval the way to fix it exogenously?

If so, is it the same to give the price level or nominal wage a particular initial value in the Initval in my model? But still couldn't find the steady state. Then I am thinking if it is the problem of the setup of Taylor rule or monetary policy. Because when I set one country with Taylor rule while the other adopts a peg, there occurs the failure of finding steady state. When I set both countries with Taylor rules independently, the problem becomes "The rank condition ISN'T verified!". Moreover, it's fine with the constant money supply.

[jpfeifer]

No. Usually, you have a Taylor Rule of the form

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R/Rbar=(pi/pi_bar)^phi_pi

You set pi_bar in the parameter initialization instead of trying to use steady_state(pi). The reason is that steady state inflation is not endogenously determined. Given the value for pi_bar, you use

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#R_bar=1/beta*pi_bar

to set the nominal interest rate.

Regarding the peg problem, there often occur problems in open economy model with closing the model. First make sure the model solves for the individual countries. Then, after this works, close the model by linking the two economies using a peg.

[superztt]

I changed steady_state(... ) to ...bar. Appears there is some progress. I got the steady state. But I ran into "Blanchard Kahn conditions are not satisfied: indeterminacy"

My Taylor rule is like R = (1/beta)*(p /p (-1))^5* (p/pbar)^0.001;
1/beta is the correspondence of R_bar. Instead of targeting inflation, it targets the price level. I set pbar in the parameter initialization. There would be less eigenvalues above than the number of forward looking variables.

However, if I set R = (1/beta)* (p/pbar)^0.001, the problem disappears.

What is the problem? Cheers!

[jpfeifer]

This sounds a lot like an economic problem. I am not familiar with Taylor rules that implement price level targeting. You might want to check the literature about determinacy and existence of an equilibrium in this case. It seems that, in contrast to inflation targeting, the feedback must not be too strong.

[superztt]

It seems more like an economic problem. But I still encountered the problem of Blanchard Kahn conditions, even if I set the Taylor rule in an inflation fashion. R = (1/beta)*(p /p (-1))^5. So here R_bar=1/beta , Pi_bar=1. Indeed, I changed the index from far below one to far above one, it still doesn't work. Is a strong feedback from inflation to policy rate supposed to yield the determinacy? Thank you!

[jpfeifer]

I am not sure about your notation. Is p the price level? If yes, then there must be indeterminacy. p itself is a variable here and its level is not determined. Only

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pi=p /p (-1)

is determined. See my Guide to Observation Equations.