1. Fabrizio Zampolli BOK International Conference 2008 26-27 May
Discussion of “Optimal Monetary Policy under Uncertainty in DSGE Models: A Markov Jump-Linear-Quadratic Approach” by L.E.O. Svensson & N. Williams
Fabrizio Zampolli
BOK International Conference 2008
26-27 May
The views expressed here are solely the responsibility of the discussant and should not be construed as representing those of the ECB

2. What the paper does
Solve a quadratic optimal quadratic control problem under model uncertainty and learning:
Model incorporates regime switching according to a Markov chain with unobservable state
Adaptive optimal learning (AOP)
Bayesian optimal learning (BOP)
Contributions:
Learning in models with forward looking variables
LQ structure leads to improved tractability of AOP (not so for BOP)
Applications are based on a log-linearised versions of the standard New Keynesian model (DSGE)
Main finding: benefits from experimentation small

3. My comments What type of model uncertainty?
What are agents learning about?
Solving for optimal policy under commitment
The application: the estimated model of Lindé (2005)
Why monetary policy makers dislike experiments: one illustrative example
What type of model uncertainty is captured by the formulation adopted by the authors compared for example to others that have worked on similar topics?
What is the policymaker learning about? Are there alternatives? In particular alternatives that can simplify the computational algorithm somewhat?
One the things I asked myself when I read the paper is whether the exposition of the algorithm for the computation of adaptive optimal policy can be simplified to some extent. So this leads me to discuss

4. What type of model uncertainty? (1)
E.g. Cogley, Colacito & Sargent (2007):
2 models with known (estimated) & time-invariant parameters
PM learns about the probabilities of models being correct
Uncertainty is about which of two models is true (given that one of the models is the true DGP, always)
SW (2008): (One possible interpretation)
True model incorporates regime switching (so true model may exhibit time varying parameters, e.g. high/low productivity; rate of time preference, etc.)
Or, true models alternate periodically
Uncertainty is about which regime or model (‘mode’) prevails in a given period (given that a regime switching model is the true DGP)

5. What type of model uncertainty? (2)
If true model incorporates regime switching:
Are agents learning within the original non-linearised DSGE model? How?
Main issue: Is a log-linearised regime switching version of such a model a “good” approximation?
Does the approximation capture learning within the model?
Even if shocks are small and modes persistent, not clear that the transition from mode to mode is well approximated
How can we assess the approximation?
[e.g. (perhaps) measure of fit of RS log-linearised model to an artificial sample of data generated by the (calibrated) original RS DSGE model??]
If the true model incorporates regime switching, how does the private sector learns about them within the original DSGE model

6. What are agents learning about? (1)
Learning is about the probabilities of the prevailing regime (or ‘mode’) (additive shocks are unobservable)
But transition probabilities P are assumed to be known
learning within the model about P would be interesting
A possible alternative is to obtain an estimate of the state of the Markov chain and then apply algorithms to find optimal control based on observable state

7. What are agents learning about? (2)
For example, get state estimate by solving:
Control law depends on an estimate of the state rather than a vector of probabilities
Perhaps not much difference with SW approach, yet may make exposition and extensions somewhat simpler?

8. Solving for optimal policy under commitment (1)
If an estimate of the MC state is available then one can solve the optimal control problem under commitment in the following way (alternative to MM formulation):
timing can be generalised
it can probably be generalised to the case in which matrices are conditioned on p(t|t) (SW AOP learning) rather than best estimate of s(t)
Solve the optimal control problem for the economy based on beliefs

9. Solving for optimal policy under commitment (2)
We obtain a control rule:
and a set of value functions:
which capture all information about saddle path system
(replace this into the FOCs of a lagrangian formulation of the optimal control problem and you get the riccati equations)
Jumps can be solved as a function of predetermined and lagrange multipliers given knowledge or estimate of s(t)

10. Solving for optimal policy under commitment (3)
Define:
Model can be simulated under best estimate to determined jump variables
Model can be simulated under true (unobserved) MC realisation to get
(where jump variables and control computed in previous step)

11. The application: the estimated model of Lindé (2005)
It is hard to believe that Lindé’s model is structural in the sense of Lucas (1976)
Cogley & Sbordone (2008, AER forthcoming) show that the backward looking component in the Phillips curve disappears if one controls for trend inflation.
Benati (2008, QJE forthcoming): if you only focus on stable monetary regimes (EMU & IT) there is no backward looking component
 EMU & IT have virtually constant trend inflation

12. Why monetary policy makers do not like experiments: one illustrative example
Early work on experimentation were based on backward looking models: giving the private sector RE is important and may overturn results.
One example: Rosal & Spagat (2002):
Both CB & PS have priors on the slope of the PhC, but the PS is also learning about how ‘tough’ the CB is.
Optimal policy generates less information than under myopic policy
More structural uncertainty makes policymaker more conservative and less willing to experiment (“The ignorant should shut their eyes”)
Experimenting generates high volatility in both inflation expectations and inflation

13. Final remarks
In conclusion very interesting paper and relevant (and reassuring) findings.
It opens up a number of issues that, in my view, need further research, among which:
how to approximate DSGE models with regime switching and learning within the model
to check robustness of finding about experimentation by specifying alternative models, esp. ones that have an active role for private sector expectations formation mechanism
Improve tractability of BOP within LQ frameworks