Small Variance Value in Ramsey Policy NK Model

I am looking at the effects of alternative variants of Taylor rule such as lagged, forward looking and contemporaneous, and also inertial rule. I used 3 equation NK model and shock the system with 0.01 std error from the steady state value. I used ramsey_policy command in dynare and used the simple lost function as welfare objectives. I am wondering why the variance on my output is quite small is this something normal or shall worry that my specification is wrong. and also in my understanding the ramsey policy compute the overall welfare lost due to variance in output gap and inflation. Ramsey2.mod (1.5 KB)

I may be missing something, but why are you using Ramsey together with an interest rate rule? What is the instrument your planner is then using?

My research want to check welfare implication of different variants of Taylor Rule. I try to used OSR function before but I was to confuse with extremely high coefficient. What I wanted to used as objective of the planner is the quadratic lost function instead of the log utility function. Honestly this is the first time I am using this functions in my dissertation.

When you use Ramsey policies, the planner uses at least on instrument. Because the planner sets on variable, one equation needs to be left out. Usually in NK models that is the Taylor rule because the planner sets the interest rate. But in your model there is still a Taylor rule. So what is the instrument the planner uses?

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Prof. jpfeifer, I’m a little confused.

one equation needs to be left out. Usually in NK models that is the Taylor rule because the planner sets the interest rate. But in your model there is still a Taylor rule.

Your reply is exactly the same to my supervisor’s remark.

But in the following paper, authors actually INCLUDE the Taylor rule!
annotatedChang(2015).pdf (435.2 KB) (The JME paper we discussed few days before)
On page 13, equation (34), since authors relax/remove the assumption of pegged/fixed exchange rate, they seem to add the Taylor rule to complement into total equilibrium conditions when considering flexible exchange rate regime.

In parallel, annotatedChang2015_Appendix.pdf (266.1 KB) their appendix page 2 eqn (A23) is in the benchmark pegged/fixed exchange rate regime. When turning to flexible or full (flexible+capital control) models, they substitute it to the Taylor rule. See Flex.mod (5.4 KB) or Full.mod (5.5 KB) around line163-166 Eq.(23).


As a reference, their benchmark mod:Bench.mod (5.4 KB) line163-164, is (A23) in the Appendix.pdf.

This is strange, because a Taylor rule is a rule and not fully optimal Ramsey-policy. So I don’t understand what they are doing. Have you tried asking the authors?

Thank you for replying me!

I emailed questions about that paper to authors (Spiegel and Liu, they seem to be corresponding authors, and have coauthored several top papers on Ramsey Policies).

Unfortunately, never got feedback from them :sweat_smile: perhaps due to a special CoronaVirus period.

Hello, after reviewing your dialogue, I would like to complement just one remark on the following quote:

This is not unusual. I read SGU 2006 expanded version. On page 22 footnote 10, they did unconstrained OSR as well, finding a similar pattern:

Note the sentence “The associated welfare gain is about one thousandth of one percent…”. I experimented a 3D-diagram of welfare with inputs of \alpha_{\pi} and \alpha_y. The welfare surface is extremely flattened with varying \alpha_{\pi}.

And on page 15, they said: