Here we revisit our previous analysis of the difference between headline and core CPI in the USA [1]. Figures 1 and 2 illustrate the evolution of the difference which is apparently characterized by the presence of three distinct segments with linear trend and two short periods of change in the trends. Between 1960 and 1978, the difference is relatively stable and varies in a narrow range around +1 unit of index. Between 1979 and 1982, the curve falls to -2 and then suddenly changes its direction from downward to upward one.

Between 1982 and 1999, the core CPI was growing consistently faster and a gap of about 10 units was created through 1999. The curve between 1982 and 1999 is best represented by a straight line with small-amplitude deviations, the latter likely associated with measurement noise. The slope of the linear regression line presented in Figure 2 is -0.67 with R2=0.96. In other words, during these eighteen years the headline CPI was growing by 0.67 units of index faster than the core CPI.

If to assume that the evolution of both indices is driven by independent stochastic process like random walks, then the deviation between the indices would be a stochastic process itself. From Figure 2, it is more reasonable and reliable to assume, however, that there is a tight link between these variables, which provides the observed linear growth of the difference between them. For purely stochastic and independent variables such a linear behavior is highly unlikely. Because the CPI inflation is predefined by the labor force growth rate (Kitov, 2006ab) the evolution of the core CPI is also predefined.

There was another period of high volatility between 1999 and 2003 similar to that observed between 1979 and 1982. Between 2003 and 2008, the gap between the core CPI and CPI was closing in line with a faster growing CPI. In [1], we extrapolated the rate of convergence between the CPI and core CPI observed after 2003, as displayed in Figure 3, one can estimate the intercept time somewhere between 2009 and 2010. This linear trend of convergence is very robust with R2=0.86, as was the divergence trend between 1982 and 1999. The convergence is faster - approximately 1.6 units of index per year. This prediction was accurate in terms of the turn to a new positive trend but timing was slightly wrong. The turn started in the middle of 2008 with a severe fall in the difference down to -4. This early start of the transition to the new trend was accompanied by extraordinary volatility. After the difference reached the bottom at -4, it quickly (during six months) rebounded to +6. At this point we made (in this blog and several articles [2-4]) a new assumption that the difference would be freely falling since March 2009. Such behavior has been actually observed, as Figure 4 demonstrates. The return to the new linear trend may include a slight overshoot below the trend line in 2009 or early 2010.

What will happen after 2010? It is likely that the difference will fluctuate around the new trend, which characteristics have to be established yet.

Figure 1. The difference between the core CPI and headline CPI: update from October 2007 to August 2009.Between 1982 and 1999, the core CPI was growing consistently faster and a gap of about 10 units was created through 1999. The curve between 1982 and 1999 is best represented by a straight line with small-amplitude deviations, the latter likely associated with measurement noise. The slope of the linear regression line presented in Figure 2 is -0.67 with R2=0.96. In other words, during these eighteen years the headline CPI was growing by 0.67 units of index faster than the core CPI.

If to assume that the evolution of both indices is driven by independent stochastic process like random walks, then the deviation between the indices would be a stochastic process itself. From Figure 2, it is more reasonable and reliable to assume, however, that there is a tight link between these variables, which provides the observed linear growth of the difference between them. For purely stochastic and independent variables such a linear behavior is highly unlikely. Because the CPI inflation is predefined by the labor force growth rate (Kitov, 2006ab) the evolution of the core CPI is also predefined.

There was another period of high volatility between 1999 and 2003 similar to that observed between 1979 and 1982. Between 2003 and 2008, the gap between the core CPI and CPI was closing in line with a faster growing CPI. In [1], we extrapolated the rate of convergence between the CPI and core CPI observed after 2003, as displayed in Figure 3, one can estimate the intercept time somewhere between 2009 and 2010. This linear trend of convergence is very robust with R2=0.86, as was the divergence trend between 1982 and 1999. The convergence is faster - approximately 1.6 units of index per year. This prediction was accurate in terms of the turn to a new positive trend but timing was slightly wrong. The turn started in the middle of 2008 with a severe fall in the difference down to -4. This early start of the transition to the new trend was accompanied by extraordinary volatility. After the difference reached the bottom at -4, it quickly (during six months) rebounded to +6. At this point we made (in this blog and several articles [2-4]) a new assumption that the difference would be freely falling since March 2009. Such behavior has been actually observed, as Figure 4 demonstrates. The return to the new linear trend may include a slight overshoot below the trend line in 2009 or early 2010.

What will happen after 2010? It is likely that the difference will fluctuate around the new trend, which characteristics have to be established yet.

Figure 2. Linear regression of the difference between the core CPI and CPI.

Figure 3. Extrapolation of the trend in the differnce between core CPI and CPI beyond 2007 [1].

Figure 4. The return to the new linear trend. An overshoot below the trend line may happen in 2009 or early 2010. Then, the differnce will align around the new trend, which will emerge promptly.

[2] Kitov, I., Kitov, O., (2009). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15039/01/MPRA_paper_15039.pdf

[3] Kitov, I., Kitov, O., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/13587/,

http://mpra.ub.uni-muenchen.de/13587/01/MPRA_paper_13587.pdf

[4] Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, MPRA Paper 15194, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15194/01/MPRA_paper_15194.pdf

**References**

[1] Kitov, I., Kitov, O., (2008). Long-Term Linear Trends In Consumer Price Indices, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. III(2(4)_Summ), pp. 101-112. http://www.jaes.reprograph.ro/articles/Kitov.pdf[2] Kitov, I., Kitov, O., (2009). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15039/01/MPRA_paper_15039.pdf

[3] Kitov, I., Kitov, O., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/13587/,

http://mpra.ub.uni-muenchen.de/13587/01/MPRA_paper_13587.pdf

[4] Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, MPRA Paper 15194, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15194/01/MPRA_paper_15194.pdf

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