1. Discussion of “Has the Federal Reserve’s inflation target changed
Discussion of “Has the Federal Reserve’s inflation target changed?” by Zheng Liu, Dan Waggoner and Tao Zha Martin Ellison University of Oxford and CEPR
Bank of Korea, May 2008

2. A quick look at what went into this paper
Tao in Seoul
Tao in Atlanta
Bank of Korea, May 2008

3. Bridging two literatures
Erceg and Levin (2003), Favero and Rovelli (2003), Schorfheide (2005)
1. Small DSGE models  inflation target has changed
2. Loosely parameterised models  inflation target has not changed
Stock and Watson (2003), Sims and Zha (2006)
Q: Large DSGE models  ???
A: Large DSGE models  inflation target has not changed
Bank of Korea, May 2008

4. The research methodology
Schorfheide (2005):  
Replace private sector  with ACEL/Smets-Wouters apparatus
Leave monetary policy  unchanged
Bank of Korea, May 2008

5. Comments
Appropriate to model private sector behaviour in detail yet be so naïve about what policymaker does?
Monetary policy operates in a data-rich environment  estimated policy rule is simplification  spurious results?
Monetary policy evolves. Narrative evidence suggests policymakers did not understand concept of interest rate rule until about 1985  spurious results?
Problem compounded by RE assumption. Learning? Credibility?
Solution at hand: Explicitly model beliefs of policymaker
Sargent (1999), Primiceri (2006), Sargent, Williams and Zha (2006)
Bank of Korea, May 2008

6. Stochastic volatility
Results with SV following a 2-state Markov switching process
Can (approx.) check this by fitting Markov-switching SV models to 1-step ahead forecasts errors from non-switching model.
-60.0 4
-60.7 3
-61.2 2
SIC
Regimes
Linearity test: 258.9*** (χ36)
Modelling of SV looks okay.
Bank of Korea, May 2008

7. Number of regimes
Allowing all elements of VCV matrix to switch puts lot of strain on SIC 3 R π 2 H θ w I 1 C 4 Y
Number of regimes when SV restricted to only a couple of forecast errors:
Extra regimes in π and R  concern as key to results?
Bank of Korea, May 2008

8. SV in all forecast errors
What are the SV regimes?
SV in Y
forecast error
SV in R
forecast error
SV in all forecast errors
Y regimes  Great Moderation?  McConnell and Perez-Quiros (2000)
R regimes  NBR targetting?  Bernanke and Mihov (1995)
all regimes  ???  possibility of incorrect inference?
Bank of Korea, May 2008

9. Normalised 1-step ahead forecast errors in R
Regime
AR(1) coeff 1
0.09 2
0.58
High autocorrelation  even large DSGE model misspecified
Posterior converges to value minimising KLIC
SIC valid model selection tool in this case?
Misspecification in key part of model  concern?
Bank of Korea, May 2008

10. Final suggestion
Implicit idea: evidence for change in inflation target is due to misspecification of small DSGE models.
Large DSGE model  less misspecification  no evidence of change in inflation target
Suggests simple encompassing test:
Simulate from estimated large DSGE-SV model with no change in inflation target
Estimate small DSGE-SV model with change in inflation target from simulated data
If Liu, Waggoner and Zha are correct then ii) should suggest evidence of changes in inflation target. 
Bank of Korea, May 2008