The price index of motor fuel

Couple years ago we introduced a concept of deterministic and sustainable trends in the differences of consumer (and later on - producer) price indices [1,2]. One of the best examples was the difference between the overall (often called “headline”) CPI and the index of motor oil [3], both indices were seasonally adjusted ones. A year ago we revisited this difference [4] and found our predictions in good agreement with observations. Essentially, this difference approached the new trend and we expected the following evolution along this new trend, which assumes that the price index of motor fuel will decrease relative to the CPI.

The model 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).

This post displays the evolution of the difference in 2010 (see Figure 1). All in all, the prediction was good enough: the earlier positive deviation from the trend is now compensated by a negative one. Currently, the difference is below the trend and we expect it to reach the trend in the beginning of 2011. This recovery should be accompanied by a drop in the price index of motor fuel and likely in the index of crude oil.

Figure 1. The difference between the headline CPI and the index for motor fuel. Solid diamonds represent the prediction given in March 2009 through December 2009 [1]. The total increase in the difference is +60 units of index or +35%: from 173 in March to 233 in December. Dashed line represents the new trend, which is a mirror reflection to that between 2001 and 2008 shown by solid black line. In 2010, the difference has been fluctuating around the trend and thus should return to the trend in the beginning of 2011.

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). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany

4. Kitov, I.. Kitov, O. (2010). "Crude oil and motor fuel: Fair price revisited," Quantitative Finance Papers 1005.0051, arXiv.org.

Bernanke and deflation

Deflation is the economic topic where the current  Chairman of the United States Federal Reserve Shalom Bernanke has got his nickname. We have been following the evolution of inflation in the USA for many years since predicted (2005)  that a deflationary period should start in 2012.  So, it is instructive to  compare the tools proposed by the Fed's chairman and actual situation. The most recent statement from the FRB on deflation was in the speech  on October 15.

... The significant moderation in price increases has been widespread across many categories of spending, as is evident from various measures that exclude the most extreme price movements in each period. For example, the so-called trimmed mean consumer price index (CPI) has risen by only 0.9 percent over the past 12 months, and a related measure, the median CPI, has increased by only 0.5 percent over the same period.2



... With long-run inflation expectations stable and with substantial resource slack continuing to restrain cost pressures, it seems likely that inflation trends will remain subdued for some time.

The longer-run inflation projections in the SEP indicate that FOMC participants generally judge the mandate-consistent inflation rate to be about 2 percent or a bit below. In contrast, as I noted earlier, recent readings on underlying inflation have been approximately 1 percent. Thus, in effect, inflation is running at rates that are too low relative to the levels that the Committee judges to be most consistent with the Federal Reserve's dual mandate in the longer run. In particular, at current rates of inflation, the constraint imposed by the zero lower bound on nominal interest rates is too tight (the short-term real interest rate is too high, given the state of the economy), and the risk of deflation is higher than desirable. Given that monetary policy works with a lag, the more relevant question is whether this situation is forecast to continue. In light of the recent decline in inflation, the degree of slack in the economy, and the relative stability of inflation expectations, it is reasonable to forecast that underlying inflation--setting aside the inevitable short-run volatility--will be less than the mandate-consistent inflation rate for some time. Of course, forecasts of inflation, as of other key economic variables, are uncertain and must be regularly updated with the arrival of new information.

and finally

Given the Committee's objectives, there would appear--all else being equal--to be a case for further action. However, as I indicated earlier, one of the implications of a low-inflation environment is that policy is more likely to be constrained by the fact that nominal interest rates cannot be reduced below zero. Indeed, the Federal Reserve reduced its target for the federal funds rate to a range of 0 to 25 basis points almost two years ago, in December 2008. Further policy accommodation is certainly possible even with the overnight interest rate at zero, but nonconventional policies have costs and limitations that must be taken into account in judging whether and how aggressively they should be used ...

So, the problem of approacing price deflation now is a big one. To implememnt a helicopter technology is not so easy.

Real GDP per capita in developed countries

Five years ago I published a paper [1] introducing the concept of constant annual increment in real GDP per capita, G(t), as observed in developed countries. In the long run, the GDP growth as a linear function of time:

G(t-t0)= G0+A(t-t0)

where G0 is the initial level of GDP per capita at time t0 in a given country, A is the country dependent increment measured in PPP dollars. Therefore, the rate of growth of real GDP per capita, dG/G, has a decelerating nonlinear trend:

dG/G = A/G

This assumption gives excellent statistical results and explains the evolution of real GDP per capita in developed countries, as also was confirmed in our 2008 paper [2].

Hence, the task now is to track the progress of the economies under study. The figure below presents several important cases, which demonstrate the accuracy of our concept. Since the increment is assumed to be constant, the mean value of the annual GDP increment should coincide with its linear trend (see the paper for details). In reality, the linear regression line is very close to the constant level. In many cases (e.g. France, Italy, Japan), it oscillates around the mean value over time with a small amplitude. The hypothesis of the constant increment looks sound.

Figure. The increment of real GDP per capita vs. real GDP per capita in select developed countries. Thick line – the mean increment. Two solid lines represent two linear trends (also represented by their equations) as associated with the original and population corrected GDP estimates. All data are borrowed from the Conference Board data base (http://www.conference-board.org/economics/database.cfm).

References
[1] Kitov, I., (2006). Real GDP per capita in developed countries, MPRA Paper 2738, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/2738.html

[2] Kitov, I., (2009). The Evolution of Real GDP Per Capita in Developed Countries, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. IV(1(8)_ Summ), pp. 221-234.

Journal of Applied Economic Sciences. Fall 2010

JAES 3(13). / Fall 2010

Contents

Mongi ARFAOUI, Ezzeddine ABAOUB. On the Determinants of International Financial Integration  in The Global Business Area …153

Melita CHARITOU, Petros LOIS, Adamos VLITTIS, Do Capital Markets Value Earnings and Cash Flows Alike?  International Empirical Evidence … 173

Madalina CONSTANTINESCU, Laura UNGUREANU, Laura STEFANESCU. Portfolio Optimal Choice under Volatility and Price Risk Impact  Applied to Derivative Transactions … 184

Georg ERBER, The Problem of Money Illusion in Economics … 196

Marco FIORAMANTI, Estimation and Decomposition of Total Factor Productivity Growth in the EU Manufacturing Sector: A Long Run Perspective … 217

George E. HALKOS, Marianna K. TRIGONI, Financial and Real Sector Interactions: The Case of Greece … 231

Cosmin FRATOSTITEANU, Guidelines for Promoting Science, Technology and Technical–Scientific Creativity, By Analyzing the Companies’ Performances, in the Context of the Globalized Economy …247

Drama Bedi Guy HERVE, Yao SHEN, Management of Stock Price and its Effect on Economic Growth:  Case Study of West African Financial Markets … 258

Bernard LANDAIS, The Monetary Origins of the Economic and Financial Crisis … 280

Piotr MISZTAL, Public Debt and Economic Growth in the European Union …292

Black Tuesday?

I assume that the closing S&P 500 level of 1183 in October 2010 and its following growth to 1225 in November 2010 is not good news for the US stock market. Figures 1 and 2 update the previous versions published in this blog in September. Both Figures demonstrate that the difference between the predicted and observed curves has been increasing since September.

This observation raises a question on the following events. Our concern about possible repetition of the 1987 fall, if the index would continue its deviation from the predicted trend into October 2010 is on again. So, I see a danger of a severe panic on the stock market. Because Tuesday is a common day for such events, I cannot exclude that one of Tuesdays in the nearest future will end in a return of the observed curves to the predicted one.

There is also a chance that the population estimates underlying the prediction become wrong since September 2010. The methods of population projection and updates used by the Census Bureau are also not well predicted.

Below we repeat a mandatory part with a bit of mathematics for the readers interested in details of our model. The model is also presented in our working paper [1] and monograph [2].

The original model links the S&P 500 annual returns, Rp(t), to the number of nine-year-olds, N9. In order to extend the prediction in time we use the number of three-year-olds, N3, as a proxy to N9 and obtain a forecast at a six-year horizon:

Rp(t+6) = 100dlnN3(t) - 0.23 (1)

where Rp(t+6)is the S&P 500 return six years ahead (in 2010 one can foresee the returns in 2016). Figure 1 depicts germane S&P 500 returns, both actual one and that predicted by relationship (1). Both curves are coinciding in practical terms.

Because of the observed linear growth in N3 one can replace it with linear trends for the period between 2008 and 2011, as Figure 2 shows. This model predicts that the S&P 500 stock market index will be gradually decreasing at an average rate of 37 points per month. All fluctuations in N3, as observed in Figure 1, are smoothed in this linear representation.

Figure 1. Observed and predicted S&P 500 returns. The last point for the observed series is October 31, 2010.

Figure 2. The observed monthly closing level of the S&P 500 stock market index and the trend predicted from the number of nine-year-olds. The slope is of -37 points per month. The same but positive slope was observed between February 2009 and April 2010. The last point in the observed series is October 31, 2010. The deviation between the predicted and observed curves has been increasing since September 2010.

Monographs

We have published three monographs this year. All three reflect the problems and topics, which have always been the main topic of this blog: Economics as Classical Mechanics. If one has been following the blog from the very beginning s/he could have a great deal of knowledge about our concept and results. Random readers might be interested in specific topics from inequality to stock pricing.

Our publisher, the LAP Lambert Academic Publishing, encourages us and we are also happy to request a favour of all readers to help the overall promotion of these monographs. We would appreciate very much if you could leave a short review and/or evaluate the books on amazon.com:

Mechanics of personal income distribution: The probability to get rich

Deterministic mechanics of pricing

mechanomics: Economics as Classical Mechanics

Thanks for your kind assistance

Ivan Kitov

Our brand-new monograph: Economics as Classical Mechanics

Finally, our book "mechanomics" or " Economics as Classical Mechancis" is published by the LAP Academic Publishing. We have collected all individual studies on macroeconomics issues published as working papers and journal articles and updated empirical relationships where possible.

The monograph is available on amazon.com:
http://www.amazon.com/mec-anomics-Economics-Classical-Mechanics/dp/3843361223/ref=sr_1_1?ie=UTF8&s=books&qid=1288264906&sr=8-1

Abstract

Macroeconomics is represented as a hard science like physics and, specifically, classical mechanics. Due to this similarity we have called our concept ?mec?anomics? highlighting its mechanistic entity. There exist statistically reliable deterministic links between measured macroeconomic variables. In the order of causality, the overall population and its age structure drives the evolution of real GDP which, in turn, determines the rate of participation in workforce. The level of labour force unambiguously defines the rate of price inflation and unemployment. The age structure also controls the S&P 500 returns. Statistically, the goodness-of-fit between measured and predicted macroeconomic time series is at the level of 0.9, with the residuals likely related to measurement errors. Tests for cointegration confirm the presence of long-term equilibrium relations. We have extended the sets of econometric tools by the method of boundary elements well-known in physics. As a bonus to the prolific concept of mec?anomics, we have modelled real GDP per capita during the transition from socialism to capitalism combining two physical processes: radioactive decay and saturation.