RDP 2006-11: Component-smoothed Inflation: Estimating the Persistent Component of Inflation in Real Time 2. Literature Review

Reflecting the rise in the number of inflation-targeting central banks, there has also been an expansion in the number of articles on measuring underlying inflation since the 1990s. Wynne (1999) provides a useful summary of the various approaches to underlying inflation that have been adopted.

An important step in considering underlying inflation is defining what is meant by the term. One widespread view of underlying inflation is that it is the common component of inflation that is present in each individual price series and which monetary policy-makers ‘ought’ to be concerned about.^[1] That is, some component π^* where:

and i indexes individual components of the CPI. Diewert (1995) discusses this view and shows that a ‘neo-Edgeworthian’ measure which weights movements in each price series by their volatility would provide the optimal estimate of π^* . This approach, however, is at odds with the fact that headline CPIs, which are almost always the target of policy, are expenditure weighted. To address this concern, Laflèche (1997) proposes a ‘double weighted’ measure that multiplies the neo-Edgeworthian weights by expenditure weights as used in the CPI. In a similar vein, Cutler (2001) implements a persistence-weighted measure of core inflation following an idea first suggested by Blinder (1997). In this approach each component of the price index is weighted by its persistence rather than by its expenditure share.

Bryan and Cecchetti (1993), while still viewing underlying inflation as the common component of individual price series, approach the problem of extracting π^* by focusing on the possibility that ε_it may not be normally distributed. They show that, in such circumstances, trimmed means (of which the weighted median is a specific example) are a robust method of identifying the central tendency in headline inflation.

Although proceeding from the assumption of a common ‘monetary’ component of inflation, Quah and Vahey (1995) adopt a very different approach to identifying this component of inflation. They define underlying inflation to be the component of inflation that has no long-run effect on output and then calculate their measure using a bivariate structural VAR model including output growth and inflation growth. They do not make use of the information contained in the component price indices but just use the aggregate headline measure. Their method is subject to revision each period as the estimates of the VAR model are updated with new data.

Other approaches to determining underlying inflation consider it to be the systematic, trend, or otherwise persistent component of inflation. This approach was discussed in Cecchetti (1997) and Blinder (1997). Exclusion measures, for example, observe that price movements in fuel and food are particularly volatile and that a less volatile measure of inflation can be obtained by placing zero weight on movements in these items.

Cogley (2002) suggested smoothing headline inflation using an exponential smoother as a way to extract the trend component of inflation. While his measure had some appealing statistical properties, it has not received much attention. In part this may be because it was applied to aggregate inflation and was conceptually the same as a moving average of inflation or, indeed, year-ended inflation. And these measures typically tend to lag actual inflation by some quarters, which limits their usefulness in a policy-making context.

It is also possible to interpret trimmed means and weighted medians as a method for extracting the persistent components of inflation. The measures are, after all, just robust estimates of the underlying or central tendency in headline inflation that down-weight particularly large movements in individual components – provided one identifies large movements with temporary movements, this approach is analogous to removing temporary volatility while leaving persistent components relatively untouched.^[2] Furthermore, trimmed means are robust to relative price changes, provided those changes do not systematically affect the skewness of the price-change distribution.

Footnotes

Some papers consider this to be the purely monetary component of inflation that is unrelated to real factors such as supply shocks. This concept of ‘monetary inflation’ is expressed in the quantity theory of money. The paper by Quah and Vahey (1995), discussed below, provides a clear example of a focus on this concept of inflation. [1]

Because the trimmed mean and weighted median are non-linear functions of headline inflation it is not correct to say that they ignore the effect of all trimmed components. Rather, they limit the influence of outliers. For example, if the median is 2.5 per cent, it is insensitive to whether petrol prices rose by 5 per cent or 15 per cent in a particular period, but is not insensitive to the fact that petrol prices rose by more than the median. [2]