Osr gives different results for different opt_algo

Optimal Policy
1

Osr gives different results for different opt_algo's. Is this to be expected? For example…

osr(opt_algo=8)
OPTIMAL VALUE OF THE PARAMETERS:
phi_pi             8942.9
phi_y            0.115428

osr(opt_algo=9)
OPTIMAL VALUE OF THE PARAMETERS:
phi_pi            38.9066
phi_y           -0.233414

Or the results should be somehow similar?

2

The OSR-problem may have multiple local optima. Thus, this is not unexpected.

3

Oh, I see, so you can’t really pin down optimal values for phi_pi and phi_y. It depends on the optimizer…

Maybe one just have to indicate which optimizer used in a paper he or she writes involving osr analysis…yeah? And if referee ask why not some other optimzer…you say it is just a discretionary choice from many options?

4

No, when dealing with local optima, you should strive to find the global one. When running different optimizers and different starting values, you can still compare the results and use the one with the highest objective function value.

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5

Preference shocks cause lower damage to welfare, output volatility, and inflation volatility—relative to some other shocks. However, phi_pi, phi_y are largest in osr results when I have only preference shocks active in the model. Not sure how to explain that. Is that also related to the local optimum narrative, if I may ask?

I was thinking lower volatility of output gap and inflation, and lower welfare loss (due to preference shock) would mean that the CB has to optimally react less strongly compared to when there is higher volatility of output gap, inflation, and larger welfare loss (due to productivity shock). osr results say otherwise…like the algorithm may be stuck in a bad local minimum?

6

I am not sure what you mean. Preference shocks can be harmless if they can be fully stabilized. But that implies such stabilization, typically that the central bank reacts strongly with the interest rate.

7

Hi Prof Pfeifer, may I clarify…
When all shocks (including preference shocks) are non-zero in the model, dynare’s osr gives phi_pi = 3.4 as optimal (opt_algo = 4)

When only productivity shock is non-zero (all other shocks are zero), osr gives phi_pi = 2.5 as optimal (opt_algo = 4)

When only cost-push shock is non-zero (all other shocks are zero), osr gives phi_pi = 2.6 as optimal (opt_algo = 4)

My question
When only preference shock is non-zero (all other shocks are zero), osr gives phi_pi = 622.501 as optimal (opt_algo = 4).

Why such a large value of phi_pi in the case of preference shocks?. In the model, preference shocks do not generate the largest volatility in output gap and inflation rate.

8

You are confusing the description of off-equilibrium behavior implied by the central bank and the equilibrium itself.
Stabilizing preference shocks means keeping output constant. That requires discouraging agents from increasing their consumption despite their preference to do so. What the central bank does here is to threaten to increase interest rates like crazy if inflation goes up by a tiny bit. As a consequence, households will not increase consumption in equilibrium.

9

Oh I see, thanks!. Is the large value of phi_pi in the case of preference shocks something specific to my model (and parameters) or it is something true in general?

10

It always depends on the model.