In cooperation with O. Kitov**Introduction**In the beginning of 2009 we developed a model [1, 2] predicting the long-term price evolution for various subcategories of consumer and producer price indices as well as major commodities: gold, crude oil, metals, etc. The model was based on one prominent feature of the difference between consumer (producer) prices of individual components and the overall consumer (producer) price index. These differences are characterized by the presence of sustainable long-term (quasi-) linear trends. For many producer price indices, these trends are slightly nonlinear but still robust. They are observed in subcategories with varying weights in the CPI and PPI: meats [3], gold ores [4], durables and nondurables [5], jewelry and jewelry related products [6], and motor fuel [7].

**The model**

The model derived in [1, 2] implies that the difference between the overall CPI (same for the PPI), CPI (PPI), and a given individual price index iCPI (iPPI), can be described by a linear time function over time intervals of several years:

CPI(t) – iCPI(t) = A + Bt (1)

, where A and B are the regression coefficients, and t is the elapsed time. Therefore, the “distance” between the CPI and the studied index is a linear function of time, with a positive or negative slope B. Free term A compensates the difference related to the start levels for a given year. For example, the index of communication was started from the level of 100 in December 1997 when the overall CPI was already at the level of 161.8 (base period 1982-84 =100).

From Figure 1 (and many others published before), one can conclude that the presence of linear trends is a basic feature of the CPI and PPI. Another fundamental characteristic of the differences consists in the fact that all deviations from the trends were only short-term ones. This implies that any current or future deviations from the new trends in Figure 1, which have been under development since 2008, must be compensated promptly. This feature allows short-term (months) price predictions.

**Predicted vs. actual**

Originally, we presented a model for the price evolution for motor fuel and crude oil from March to December 2009. For the motor fuel index, we drew a straight line shown in the left panel of Figure 2. This line said that motor fuel price would be growing faster than the price of all goods and services. Specifically, we predicted that:

*In March 2009, the difference was at the level of +45, i.e. much higher than the level predicted by the new trend. As happened in the past with numerous individual price indices [9,10], such a strong deviation (one might call it “dynamic overshoot”) should be compensated in the near future. Without loss of generality, we have restricted the recovery to the trend by the end of 2009. As a result the index for motor fuel should growth by 90 units during the next 9 months, or by 10 units per month. Red filled circles represent the evolution of the difference from April to December 2009. In 2010, the difference may undergo an overshoot in the opposite direction with additional rise in the index for motor fuel.*

Translating indices into prices, the rise in the difference by 90 units (from 173 in March to 263 in December) means an increase in price by 50%. Therefore, it is very likely that the price for motor fuel in the beginning of 2010 will be 60% to 70% larger than in March 2009 due to the overshoot.

Translating indices into prices, the rise in the difference by 90 units (from 173 in March to 263 in December) means an increase in price by 50%. Therefore, it is very likely that the price for motor fuel in the beginning of 2010 will be 60% to 70% larger than in March 2009 due to the overshoot.

We have been also tracking the evolution of crude oil price, which obviously affects the price index of motor fuel. As Figure 1 demonstrates, these prices have no one-to-one correspondence and it might be instructive to model them separately. So, for oil price we used an alternative approach and assumed that the price trajectory would continue the pendulum-like motion observed since 2008. This implied the difference between the PPI and the index of crude petroleum should sink below the new trend and stop at the level of -120, which roughly corresponds to $120 per barrel.

From Figure 2, it is clear that the oil price differnce leads that of motor fuel by six to eight months. It is likely that the index of motor fuel will follow up the trajectory drawn by oil price and fluctuate around its trend with slightly larger amplitude. The predictive power of this assumption will be tested by the end of 2010. We are going to track and report on actual behavior. Our model needs further validation in both short- and long run.

**Discussion**

All in all, our prediction of the price index of motor fuel was based on a sound assumption and thus is accurate. The forces behind the observed long- and short-term behavior are not accessible yet but very powerful. We dare say they are fundamental and affect the economy to its deepest roots. These forces retain equilibrium among all economic agents and originate the sustainable trends in the differences between consumer (producer) price indices. At some point, the forces meet their limits and should be re-balanced in order not to harm the economy. As a result, the sustainable trends in the CPI and PPI turn.

**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.

2. Kitov, I., Kitov, O. (2009). Sustainable trends in producer price indices, Journal of Applied Research in Finance, vol. I(1(1)_ Summ), pp. 43-51.

3. Kitov, I., Kitov, O., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany

4. Kitov, I. (2009). Predicting gold ores price, MPRA Paper 15873, University Library of Munich, Germany

5. Kitov, I., Kitov, O. (2009). PPI of durable and nondurable goods: 1985-2016, MPRA Paper 15874, University Library of Munich, Germany,

6. Kitov, I. (2009). Predicting the price index for jewelry and jewelry products: 2009-2016, MPRA Paper 15875, University Library of Munich, Germany

7. Kitov, I., Kitov, O. (2009). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany

8. Bureau of Labor Statistics. (2010). Databases, Tables & Calculators by Subject, retrieved 30.03.2010 from www.bls.gov/data/

9. Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing

**Disclosure:**no positions