by Jeffrey C. Fuhrer
No. 3, January 2005 - June 2005

Motivation for the Research
In recent years, much of the development of Phillips curves has centered on two issues: (1) the emergence of real marginal cost (versus an output gap measure) as the preferred driving variable in the specification, on both theoretical and empirical grounds; and (2) the incorporation of frictions into optimizing rational expectations models. The frictions have been ad hoc in that they are not micro-founded. Still, the prevailing view is that, after allowing for just a little friction, the baseline model works well.

This paper explores the validity of this emerging consensus on price-setting models.

Research Approach
The author demonstrates analytically the propositions about inherited persistence for the forward- looking model; analyzes the case of the hybrid model; considers some extensions, including a model with explicit monetary policy; and considers the implications of possible recent changes in the persistence of inflation. Finally, he examines reduced-form properties in the data that will lead to structural models that embody a small coefficient on the driving process and a relatively large variance of the inflation shock.

Key Findings

• Regardless of the persistence in the driving process, very little of that persistence is inherited by inflation in the conventional New Keynesian Phillips Curve (NKPC). This result runs counter to the common intuition that inflation in the NKPC directly inherits the persistence of the driving process, which, in the case of real marginal cost (or proxies thereof ), is quite considerable.
  
  
• In part, the lack of inherited persistence derives from the presence of a large inflation shock whose variance is typically one to five times as large as the shock that perturbs the driving process.
  
  
• The lack of persistence also derives from a rather small estimated coefficient—on the order of .001 to .05—on the driving process. The paper presents a battery of new estimates of this key coefficient, which are uniformly small and insignificant.
  
  
• The predominant source of inflation persistence in the NKPC is the lagged inflation term. The amount of persistence imparted by the lag is quite sensitive to its size, with significant differences in persistence implied by an increase in the weight on past inflation from 0.3 to 0.6.
  
  
• As several papers have noted, the persistence of inflation appears to have declined in recent years. If that is true, this paper suggests that the reason for the decline in persistence is unlikely to be related to a decline in the persistence of the driving process.

Implications
The findings of this paper suggest that the optimizing foundations in the standard specifications are nearly unrelated to the dynamics observed in the data for inflation and real marginal cost. That is, lagged inflation is not a second-order add-on to the optimizing model; it is the model. One may motivate price-setting behavior from these optimizing foundations, but in practice, they tell us little about why inflation behaves the way it does.

Because monetary policy in the standard models acts through its effect on output and marginal cost, it becomes more difficult to attribute recent changes in inflation persistence to changes in monetary policy. This does not necessarily imply that monetary policy has had no such effects, but it does suggest that the current crop of models will have difficulty in attributing such changes to monetary policy.

The conclusions also imply that in order to understand inflation dynamics, we will need to identify the economic source of the large inflation shock in the specification. In turn, the findings in this paper imply either that this identified shock is itself highly autocorrelated or that we require a micro-founded mechanism that generates substantial intrinsic persistence in inflation.

Full text of Working Paper 05-8