RDP 2006-10: The Performance of Trimmed Mean Measures of Underlying Inflation 2. Background on Underlying Inflation

There are a number of different views as to what constitutes underlying inflation. At a theoretical level, it is sometimes said to correspond to the ‘monetary’ component of inflation. At a more practical level it is frequently described as either the ‘persistent’ or ‘generalised’ component of inflation. Behind both of these latter notions is the idea that in any month or quarter, there can be significant noise in the CPI (or other standard price indices) which may not be indicative of the underlying trend in inflation. The noise in short-horizon movements in the CPI reflects a range of relative price movements due to price changes in commodity markets, supply shocks, weather effects, infrequent resetting of prices or taxes, and so on. Of course, not all changes in relative prices are noise, but much of this high-frequency movement in the CPI will indeed be relatively temporary.

Our approach in this paper is an empirical one, but to help motivate the work in Section 5, we begin by presenting a simple framework for thinking about candidate measures of underlying inflation. We denote the unobservable true rate of underlying inflation in each month or quarter by π^*. We can view any candidate measure of underlying inflation (π_i) as equal to the actual unobservable underlying rate, plus an idiosyncratic (or noise) term:

We can think of monthly or quarterly headline inflation, π_CPI as being one of the candidate measures of underlying inflation and also represented in this way. The idiosyncratic term for any candidate measure should have an expected value close to zero, and the variance of this term will be inversely related to the usefulness of the measure.

Based on this framework, there are several criteria we could use to assess different candidate measures of underlying inflation.^[5] First, if the true level of underlying inflation is likely to be fairly persistent and to evolve only slowly based on variables such as inflation expectations and the output gap, we would expect a good measure of underlying inflation to also be relatively smooth. Thus, a volatile measure is unlikely to be a good estimate of underlying inflation. Hence, we might consider the size of month-to-month or quarter-to-quarter changes in short-horizon inflation rates as a simple measure of how much noise there is in a particular proxy for underlying inflation.^[6] We implement this in Section 5.1.

Another criterion by which measures of underlying inflation are often judged is how closely they mirror movements in some measure of the longer-run trend in CPI inflation. This test can be done in two dimensions: in terms of long-run average inflation rates for different measures, and the ability to match movements in some measure of trend inflation over time.

Comparisons of long-run average rates of growth are typically done relative to the long-run rate of growth of the headline CPI. Although institutional arrangements differ across countries, most central banks share the explicit or implicit goal of ensuring low and stable inflation, usually as measured by the CPI (or the CPI excluding effects from factors such as mortgage interest charges or large tax changes). Hence for practical policy purposes, we would expect that a candidate measure of underlying inflation should have a similar long-run mean to the target variable. Accordingly, in Section 5.2 we calculate the long-run mean rates of inflation in our various underlying measures, and compare them with average headline inflation.

An assessment of the ability of underlying measures to match movements in trend inflation requires the choice of a reference measure for the longer-run trend. This is somewhat arbitrary, but researchers such as Bryan and Cecchetti (1994) have proposed a two- or three-year-centred moving average of monthly headline CPI inflation rates. In Section 5.3, we calculate the root mean squared error (RMSE) of the candidate measures versus similar measures of trend inflation.

Finally, an additional criterion that is frequently suggested, including in the quote from Blinder (1997) in our introduction, is that a good measure of underlying inflation should have some predictive power for inflation: we implement this in Section 5.4. However, it is important to consider what types of predictive power one should expect to see. In particular, we do not expect that there exist measures of underlying inflation that lead headline inflation in any deep sense or that there are any significant lead or lag relationships between headline inflation and various candidate measures of underlying inflation.^[7] That is, like most other researchers in this area, we view the search for good measures of underlying inflation as a search for measures which have a high signal-to-noise ratio for current underlying inflation, rather than for leading indicators of inflation: analysts looking for the latter are likely to find it more fruitful to estimate forecasting models based on the variables that drive inflation.

Accordingly, we think it is more plausible to think that any predictability is more a statistical, and fairly short-term, phenomenon. We view true unobservable underlying inflation as being a relatively persistent variable, typically changing only slowly as the fundamental drivers of inflation evolve. So unobservable underlying inflation in period t should be a very good predictor of itself in period t+1. And, as is represented in Equation (1), headline inflation in period t+1 will be given by unobservable underlying inflation in period t+1 plus an error term. So a good estimate of period t underlying inflation should be a reasonably good predictor of headline inflation in period t+1. However, this will be somewhat dependent on the variance of e_CPI: if headline inflation is extremely noisy then even a very good measure of underlying inflation will have trouble forecasting it. In summary, we do not expect that measures of underlying inflation should necessarily have any predictive power for headline inflation at any deep level: rather because true underlying inflation is fairly persistent, a good estimate of underlying inflation will also be persistent and will have some predictive power for other measures of near-term inflation.

Similar insights hold for Granger causality tests involving the CPI and various candidates for underlying inflation. Suppose we have two noisy measures of underlying inflation that each contain some independent information about true unobservable underlying inflation. In general, if underlying inflation is quite persistent and we have a sufficiently long data sample, we would expect both to Granger cause each other.^[8] In reality, the sample period may not be long enough to observe Granger causality in both directions. If so, it is likely that the presence or absence of Granger causality between the two measures of underlying inflation will depend on how close each is to true underlying inflation (that is, on the relative variance of the e_i terms). If one measure tends to be a significantly better proxy for underlying inflation than the other, then we would expect Granger causality to be more likely to go from the former to the latter than vice versa. But if one measure is a sufficiently poor proxy for underlying inflation then we might not observe Granger causality in either direction. In particular, if CPI inflation is a particularly noisy measure of underlying inflation, in small samples we might find that it is not Granger caused by even very good measures of underlying inflation.

Footnotes

Another approach, which we do not follow, would be to assess how different measures of underlying inflation accord with various economic relationships, such as Phillips curve models of inflation. However, it would be surprising if measures that do well against the criteria in this paper did not also perform well in other contexts. [5]

Of course, we would not overstate the benefits of smoothness. A long moving average, or indeed a constant, will be extremely smooth but neither is likely to be an optimal estimate of underlying inflation. However, a greater degree of smoothness in exclusion or trimmed mean measures is presumably a positive thing, especially given that – unlike measures such as moving averages – they are not subject to any intertemporal smoothing in their construction. [6]

It seems unlikely that there exist a significant number of expenditure items which are true leading indicators of the overall trend in inflation. One way to shed light on this is to calculate correlations between inflation in individual expenditure items and some measure of underlying inflation. For Australia, there are some items for which the highest correlation is leading or lagging rather than contemporaneous. However, one would expect to find some sample variation in such correlations. When we divide the sample and ask if the leads or lags are stable, we find that many of the apparent lead or lag relationships from the first half of the sample disappear (and some even change sign) in the second half. [7]

Our argument is clearly at odds with a significant amount of earlier work (see, for example, Marques, Neves and Sarmento 2003) which maintains that Granger causality should go only from underlying measures to headline inflation. Our point of departure is that we do not assume that there is any candidate measure that is so close to true unobservable underlying inflation as to have essentially no error term, and we allow for the possibility that the noise in the headline measure may be so large that its error term dominates any regression involving headline inflation. [8]