1. By Soyoung Kim Korea University
Discussion on “Has the Federal Reserve’s Inflation Target Changed?” by Liu, Wagoner, and Zha
By Soyoung Kim
Korea University

2. Features of Empirical Model
Medium Scale DSGE Model with a variety of shocks and frictions
A la Smets and Wouters (2007) and Christiano,Eichenbaum, and Vigfusson (2004)
Has been able to fit the data well
Regime Switching in shock variances
Sims and Zha (2006) emphasized the importance of incorporating regime switching in shock variances, especially compared to regime switching in coefficients of the policy rule or private sector equations.
Regime Switching in Inflation Target
Schorfheide (2005), Favero and Rovelli (2003)…

3. The estimated model in this paper is one of the most complex models that appeared in the literature.
In addition, there are various computational innovations (i.e., Sims, Waggoner, and Zha’s method to compute marginal data densities, obtaining the estimates at the posterior mode…)
It shows the current state of art in constructing and estimating empirical macro model for monetary policy analysis that not only fits the data well but also incorporates important principles of economic agents.
It also provides various important insights on modeling monetary-macro models and explaining various empirical regularities.

4. Discussion on Model Features
Regime Switching in Shock Variances, but not in Other Coefficients of the Model (except for Inflation Target).
Is the specification warranted based on past studies?
Monetary Policy Rule Specification
Including monetary aggregate? (Sims and Zha, 2006)
Regime Switching in Inflation Target
How to represent changes in inflation target in the model?

5.    Regime Switching in Shock Variances, but not in other Coefficients of the Model
The paper tried to support this specification, mostly based on past studies.
Sims and Zha (2006): SVAR, Once regime switching in shock variances is properly accounted for, the data no longer favors regime switching in monetary policy or other parts of the economy.
Smets and Wouters (2007), Justiniano and Primiceri (2006): DSGE, estimated for two sub-samples, the pre-Volcker and the post-Volcker periods. Liu, Waggoner, and Zha interpreted that they found little evidence of changes in the monetary policy responses over two sub-sample periods.
Cogley and Sargent (2005), Stock and Watson (2003)…

6. Findings of Past Studies
The results of past studies do not seem to clearly support the model with heteroscedestic shock variances and constant model coefficients, especially in the context of the current model.
Smets and Wouters (2007), Justiniano and Primiceri (2006)
they compared two sub-sample periods, which may not be directly comparable to regime switching model.
there are some cases that the coefficients change substantially, including monetary policy responses.
Cogley and Sargent (2005) tend to support drifting coefficient specification.

7. Sims and Zha (2006) indeed supported constant coefficient model once regime switching in shock variances is allowed.
However, the conclusion is supported only when a large number of state is allowed. The current model allows only two states. Even Sims and Zha (2006) showed favorable evidence on regime switching in monetary policy coefficient when the number of state allowed is small (2, 3, and 4 state cases).

9. Some Reasons to Allow Changes in Model Coefficients
There are some arguments to allow regime switching in the coefficients of the model, especially when regime switching in shock variances is allowed.
When shock variances change, private sector may respond differently. For example, when shock variance is larger, more frequent price adjustment may be more profitable and the probability of price adjustments may be larger.
When shock variances change, policy authority may respond differently.

10. Specification of Monetary Policy Rule
Taylor-type rule is used, without any monetary aggregate.
Sims and Zha (2006) included a monetary aggregate in the monetary reaction function, and concluded as follows.
“Constraining the monetary aggregate not to appear in our monetary policy equation greatly worsens the model’s fit to the historical data, and we argue that it is likely that excluding the aggregate from the equation was a course of bias in earlier works.”
“including money improves the relative fit of models that allow variation in the policy rule.”
It may be interesting to consider regime switching in monetary policy rules that include a monetary aggregate (possibly with regime switching in inflation target).

11. Regime Switching in Inflation Target
Two states are allowed. But changes in inflation target might be better modeled as gradual changes (like Ireland, 2007), or allowing more number of states might be more appropriate.
Changes in inflation target can be a function of economic environment, which may be hard to be captured by the current specification of the model. For example, some studies (Blinder, 1982, Hetzel, 1998, Mayer, 1998) suggested that negative supply shock contributed to the increase in inflation target in the 1970s and others (Bomfim and Rudebusch, 2000, Orphanides and Wilcox, 2002) suggested that favorable supply shock helped the inflation target back down in the 1980s.

12. Regime Switching in Inflation Target
In addition, changes in inflation target might result changes in the steady states of the economy. Regime switching in model coefficients might be needed.
Overall, in order to model changes in inflation target properly, it may be worthwhile to think over why inflation target changes.

13. Conclusion
Overall, like his previous papers, Dr. Zha has made a great effort to construct realistic empirical macro model that fits the data very well.
I would like to give him a big applause to his great works and efforts.
I am looking forward to seeing his next model that is further improved in various dimensions.