Blog - Investing Notes

July 6, 2006 - Which Shocks Mean More, Total CPI or Core CPI?

Our Real Earnings Yield (REY) Model uses a dampened inflation rate as a proxy for discount rate shocks to the stock market. In the discussion of that model, we note that "We have also tested whether the 'core' inflation rate (excluding the effects of food and energy prices) outperforms total inflation as a stock market indicator, with mixed but mostly degraded results." However, an April 2006 Federal Reserve Board report entitled "Core Inflation as a Predictor of Total Inflation" by Neil Khettry and Loretta Mester suggests reconsideration. In this entry, we re-test changes in total inflation versus changes in core inflation as shocks to the stock market. We conclude that:

First, some findings from the paper:

• Energy prices are ten times as volatile as the Consumer Price Index (CPI). Food prices, while more volatile than the CPI, are much less volatile than energy.
• The Core CPI is only 58% as volatile as total CPI, and CPI less energy is only 55% as volatile as total CPI.
• Core CPI is a better predictor of long-term total CPI than total CPI itself. However, total CPI slightly outperforms core CPI for forecasting total CPI over the next six to 12 months.
• Core CPI is a better predictor of long-term total CPI than either CPI less energy or the Federal Reserve Bank of Cleveland's weighted median CPI.
• Results on inflation prediction vary considerably across studies, depending on the forecasting model, time period and measures of inflation used.

To see whether these conclusions are meaningful for our use of changes in the inflation rate as discount rate shocks to the stock market, we compare three variations of the REY Model: (1) our existing model based on inflation derived from total CPI, but with volatility dampened mathematically to 60% of its observed value; (2) a revised model that uses inflation derived from Core CPI, dampened the same way as our existing model; and, (3) a revised model that uses inflation derived from Core CPI, but with no mathematical dampening.

The following chart shows the long-term outputs of all three model variations, along with the actual S&P 500 index, for 1990-2007. We develop inflation rate projections using the methodology described in our Inflation Forecast, using total or core inflation data as appropriate to the variation. Visual inspection suggests that changes in the dampened total inflation rate outperforms changes in dampened and undampened core inflation rate as a proxy for discount rate shocks for stocks over this period. In recent years, core inflation variations are notably optimistic.

The following table summarizes statistics for these long-term plots, showing that our existing model does outperform for three important measures of fit: correlation between the model variation and the actual S&P 500 index; average of differences between the model variation and the actual S&P 500 index; and, the standard deviation of differences between the model variation and the actual S&P 500 index. Results suggest that, while investors do de-rate inflation rate changes in deriving an investment discount rate, they do not de-rate by excluding variations in energy and food prices.

The next chart shows the short-term outputs of all three model variations, along with the actual S&P 500 index, for mid-2003 through 2007. Again, we develop inflation rate projections using the methodology described in our Inflation Forecast, using total or core inflation data as appropriate to the variation. Visual inspection shows the calming effect of core versus total inflation, even with mathematical dampening of the latter. The variation based on undampened core inflation appears to have about the same volatility as the stock market. The variation based on dampened core inflation is too steep, perhaps because of double-dampening.

The following table summarizes statistics for these short-term plots, showing that undampened core inflation competes well with our existing model over the past three years. However, given the closeness of the competition, the superiority of our existing model over the longer term and a judgment that ignoring inflation components is not the best way to dampen variability, we will stick with total CPI for inflation rate calculation in the REY Model.

Note that conclusions here regarding the long-term and short-term competitions between core inflation and total inflation are somewhat at odds with the Federal Reserve Board report, with core inflation outperforming short-term and underperforming long-term. The last finding of the paper, as listed above, applies.

In summary, changes in total inflation rate wins a close one over changes in core inflation rate as a proxy for stock market discount rate shocks.

See our REY Model and our Inflation Forecast for additional discussions.