9/29/09
CPI components in Japan: Medical care and education
9/25/09
Goldman Sachs on oil in 2009 and 2010
9/24/09
The Feds must bail out Lehman Brothers
Table 1.
....................vol............ price,$.......debt,$
LEH...... 689,000,000.......... 40...... 2.76E+10
C ..........11,000,000,000..... 10.......1.10E+11
AIG....... 134,000,000........ 870 ......1.17E+11
FRE...... 648,000,000......... 40 ........2.59E+10
FNM...... 1,110,000,000...... 45 .......5.00E+10
(see fictitious stock price estimates for Citigroup and AIG in Figures below)
The table shows that Lehman Brothers had smaller problems than Citigroup and AIG. So, it was was easier to bail out LEH from purely mathematical and financial point of view.
Also, the joint negative price of AIG, FRE and FNM is less than 200bn. It could be some (deliberate?) miscalculation of the >1000bn help package. The toxic debt might be bigger than the total debt associated with stock prices, but there should be unaccounted positive assets.
9/23/09
Beyond the bankruptcy – Fannie Mae, Freddie Mac, and Lehman Brothers
In several previous posts on bankruptcy, we have described the evolution of share prices for banks just before their bankruptcy or on their approach to negative prices: Colonial Bank (CNB), the CIT Group (CIT), American International Group (AIG), and Lehman Brothers (LEH). It was shown that the CNB sank below the edge of bankruptcy and CIT is on the brink with unclear future. AIG has been fluctuating around the waterline for a while, and LEH was definitely ready for a bankruptcy.
On the other hand, the CIT Group and AIG are bailed out, and thus, our model predicting share prices should fail to predict the artificially supported prices. Therefore, it would be instructive to estimate the fictitious evolution of share prices after the bankruptcies or alternative evolution after the bailouts. In this post we compare Lehman Brothers, Fannie Mae (FNM) and Freddie Mac (FRE). All three had a sharp fall in the second half of 2008.
Model and data
To predict share prices we use the 3C model [13]: a share price, sp(t), is described with the following empirical function:
sp(t) = A*CPI1(t+t1) + B*CPI2(t+t2) + C*(t2000) + D (1)
, where CPI1 and CPI2 are empirically determined CPI components; t is the calendar time; A, B, C, and D are empirical coefficients. Because the prices for goods and services (in the headline CPI) can lag or lead relevant share prices the time lags t1 and t2 are introduced. Both time lags can be positive or negative. In our model, we test all possible lags between 0 and +13 months. So, we chose the best from 34*33*14*14 ~ 200,000 possible models, with two extra degrees of freedom introduced by linear and free terms.
Results
When applied to the LEH time series between July 2003 and September 2008, the 3C model (1) gives the following empirical relationship:
LEH(t) = 10.40*FB(t4) + 5.84*DUR (t+2) + 67.96*(t2000) + 952; STDEV=$4.73 (2)
, where t is the calendar time, FB(t) is the (not seasonally adjusted consumer price) index for food leading the LEH by four months, and DUR(t+2) in the index of durable goods lagging two months behind the LEH. Figure 1 compares the stock price predicted according (2) with the observed one. This model differs from that in the previous post in two aspects. First, it uses DUR instead of the personal care index (PC). This is not a fundamental change, however. Each empirical model based on two components of the CPI includes one index, which is sensitive to the change in a given share price, and one index, which expresses the overall reaction of prices for goods and services induced by the change in the share price.
Then the difference between these two components maps the change in the price. Since there are many components of the CPI, which might represent the overall reaction of the CPI on the given price change, their exchange does not influence the model much. In the case of LEH, the defining component is the index for food (or food and beverages), and the reference component is the PC or DUR.
The empirical models for FNM and FER are as follows:
FNM(t) = 7.38*FB(t8) – 8.47*R (t+3) + 42.57*(t2000) + 2119; STDEV=$4.42 (3)
FRE(t) = 6.07*FB(t4)  3.42*O (t9) + 57.96*(t2000) + 1917.8; STDEV=$4.16 (4)
, where R is the index of recreation and O is the index for other goods and services in the CPI. Figures 2 and 3 compare the observed and predicted prices for FNM and FER, respectively.
Conclusion
We have predicted fictitious share prices of three companies. This prediction might be helpful for the assessment of future policy on Freddie Mac and Fannie Mae.
Figure 1. Comparison of the observed and predicted LHE’s share price. The latter is obtained using (2).
Figure 2. Comparison of the observed and predicted FNM’s share price. The latter is obtained using (3).
Figure 3. Comparison of the observed and predicted FRE’s share price. The latter is obtained using (4).
References
[1] Kitov, I., Kitov, O., (2009). Predicting share price of energy companies: JuneSeptember 2009, MPRA Paper 15863, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/15863/01/MPRA_paper_15863.pdf
[2] Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/15862/01/MPRA_paper_15862.pdf
[3] Kitov, I., Kitov, O., (2008). LongTerm Linear Trends In Consumer Price Indices, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(2(4)_Summ), pp. 101112.
9/22/09
Predicting bankruptcy : the case of Lehman Brothers
Predicting bank bankruptcy – the case of AIG
sp(t) = A*CPI1(t+t1) + B*CPI2(t+t2) + C*(t2000) + D (1)
where CPI1 and CPI2 are defining CPI components; t is the calendar time; A, B, C, and D are empirically determined coefficients. Because prices for good and services can lag or lead relevant share prices the time lags t1 and t2 are introduced. Both time lags can be positive or negative. In our model, we test all possible lags between 0 and +13 months. So, we chose the best from 34*33*14*14 ~ 200,000 possible models, with two extra degrees of freedom introduced by linear and free terms.
The full set includes 34 CPI components, which are tested as predictors for each share price. Among these components are major expenditure categories: the headline CPI (C), the core CPI, i.e. the headline CPI less food and energy (CC), food and beverages (F), housing (H), apparel (A), transportation (T), medical care (M), recreation (R), education (ED), communication (CO), and other goods and services (O). All components used in the model are not seasonally adjusted ones and retrieved from the Bureau of Labor Statistics.
When applied to AIG time series between July 2003 and August 2009, the 3C model (1) for AIG is as follows:
AIG(t) = 89.29*F(t) – 08.31*FB (t13) + 1031*(t2000) + 32666 (2)
, where t is the calendar time, F(t) is the (not seasonally adjusted consumer price) index for food and beverages and FB(t13) in the index of food without beverages leading AIG(t) by 13 months.
Figure 1 compares the stock price predicted according (2) with the observed one. There are two dives of the predicted price below zero – March and August 2009, the latter being of $123. With standard deviation of $102, the predicted price in August likely hints at unresolved problems with AIG. However, the negative price might also result from the uncertainty in F and FB measurements.
We will continue tracking AIG stock price and reporting our predictions.
Figure 1. Comparison of the observed and predicted AIG’s share price. The latter is obtained using (2).
Share price of select energy companies. Part 2
9/21/09
Share price of select energy companies
In the previous posts and articles [1,2] we introduced several models with varying number of CPI components. In our view, the best one, we call it 3C model, is seeking those two CPI components from 34 preselected ones, which minimize the difference between observed (monthly closing price adjusted for dividends and splits) and predicted prices for the period between July 2003 and August 2009. This model also includes free term (constant) and linear time term [36], which compensates well know linear (time) trends between various CPI components.
In the previous post we reported the empirical 3C model for COP:
COP(t)= 3.41CF(t+1)  7.17EC(t6) + 7.22*(t2000) + 145.76
where t is the calendar time, CF is the headline CPI less food, which lags behind COP by one months, and EC is the index for education and communication leading COP by six months. Standard deviation between the curves is $3.96 for the period between July 2003 and August 2009. Figure 1 displays the observed and predicted prices.
Figure 1. Observed and 3C predicted COP’s share price.
Below we present analytic models and figures for several energy companies without comments. One can judge the accuracy of the predictions and the similarity/difference between the companies.
Figure 2. Observed and 3C predicted Apache Corp.’s share price: APA(t) = 1.35*TPR(t+1) + 3.21*MCS(t7) + 47.20*(t2000)  973, where TPR is the index of private transportation, MCS is the index of medical care services. Standard deviation is $6.36.
Figure 3. Observed and 3C predicted Anadarko Petroleum Corp.’s share price: APC(t) = 3.31*EC(t+2) – 1.74*CSHF(t5) + 5.49*(t2000) + 58, where EC is the index of education and transportation, CSHF is the headline CPI less shelter and food. Standard deviation is $3.22.
References
[1] Kitov, I., Kitov, O., (2009). Predicting share price of energy companies: JuneSeptember 2009, MPRA Paper 15863, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/15863/01/MPRA_paper_15863.pdf
[2] Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/15862/01/MPRA_paper_15862.pdf
[3] Kitov, I., Kitov, O., (2008). LongTerm Linear Trends In Consumer Price Indices, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(2(4)_Summ), pp. 101112.
[4] Kitov, I., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/13587/01/MPRA_paper_13587.pdf
[5] 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.unimuenchen.de/15039/01/MPRA_paper_15039.pdf
[6] Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, MPRA Paper 15194, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/15194/01/MPRA_paper_15194.pdf
Predicting bank bankruptcy: Colonial Bank vs. CIT Group Inc.
This time our task is a more exciting and challenging one. Can our model describe the approach to bankruptcy? For a regular investor this question is of the top priority. The history of dramatic decline in share prices of financial companies in 2008 and 2009 dictates an inevitable choice – comparison of the Colonial Bank (CNB) and CIT Group (CIT), which both were beyond the edge of bankruptcy but with different outcome. In this study, all share prices are retrieved from YahooFinance.
Previously, we introduced and tested several models with varying number of defining CPI components. It was found that the best model includes two defining CPI components, free term (constant) and linear time term [46], which compensates well known the linear trends between the defining CPI components. For historical reasons we call it 3C model. In this study, we are seeking for those two CPI components from a full set of components, which minimize the (RMS) difference between observed and predicted prices.
The 3C model for a share price sp(t) is as follows:
sp(t) = A*CPI1(t+t1) + B*CPI2(t+t2) + C*(t2000) + D (1)
where CPI1 and CPI2 are defining CPI components; t is the calendar time; A, B, C, and D are empirically determined coefficients. Because prices for good and services can lag or lead relevant share prices the time lags t1 and t2 are introduced. Both time lags can be positive or negative. In our model, we test all possible lags between 0 and +13 months. So, we chose the best from 34*33*14*14 ~ 200,000 possible models, with two extra degrees of freedom introduced by linear and free terms.
The full set includes 34 CPI components, which are tested as predictors for each share price. Among these components are major expenditure categories: the headline CPI (C), the core CPI, i.e. the headline CPI less food and energy (CC), food and beverages (F), housing (H), apparel (A), transportation (T), medical care (M), recreation (R), education (ED), communication (CO), and other goods and services (O). All components used in the model are not seasonally adjusted ones and retrieved from the Bureau of Labor Statistics.
In [4] we have revealed and explained the presence of linear trends in the differences between various components of the CPI. It was also found that the trends exist during long but finite periods and then their slops turn to opposite signs. Accordingly, the evolution of the differences between CPI components since 1960 can be approximated by a piecewise linear function. When the trends turn, the coefficients in the link between CPI and share price also change. Because of this constraint we limit our modeling to the period between July 2003 and July 2009. The early date is a conservative estimate of the start of the current trend, and the latter one corresponds to the bankruptcy of Colonial Bank.
Here, we would like to emphasise that the usage of the differences instead of CPI components is caused by two crucial factors. First, we presume that the evolution of a share price depends only on the pricing power of goods and services associated with the company relative to other goods and services. Then, the difference in pricing powers of two companies should be directly mapped into the difference in the growth in relevant consumer price indices. Therefore, we assume that there exists a pair of CPI components, which reflect the best relative evolution of the share prices. Such a pair might not be always available among eight major expenditure categories. As a result, one needs two or more differences between CPI components to accurately predict the evolution of a share price.
Second factor consists in the presence of sustainable (linear and nonlinear) trends in the difference. This is the phenomenon we have described in [46]. Effectively, one can accurately decompose any share price using several CPI components. However, such decomposition does not allow forecasting without knowledge of the evolution of relevant CPI subcategories. The trends in the differences make it possible to predict at longer time horizons.
Now we apply the 3C model (1) to the CNB’s and CIT Group’s share prices. The (LSQR) bestfit empirical relationship is as follows:
CNB(t) = 1.58*F(t) – 1.39*O (t10) + 20.61*(t2000) + 633 (2)
CIT(t) = 4.14*F(t6) – 3.10*FB (t+4) + 43.18*(t2000) + 1776 (3)
Empirical relationship (2) implies that CNB’s share price evolve in sync with the index of food and beverages (F), but lags behind the index for other goods and services (O) 10 months. Therefore, the share price depends on past and contemporary values of the defining CPI components. Effectively, it allows predicting CNB price only in the past. Figure 1 displays the observed and predicted price as well as their residual.
Empirical relationship (3) shows that CIT’s share price leads by six months the index of food and beverages (F) and lags four months behind the index for food only (FB). Therefore, the share price depends on past and future values of the defining CPI components. Effectively, it allows predicting CIT price only in the past.
Comparing the time histories of CNB and CIT one can conclude that the former sank right below the zero price and thus this bank deserved the bankruptcy. CIT has been closing the negative zone but still is slightly above it. The next several readings of FB will answer the question – Was it worth to bail out CIT Group? In other words, will the predicted price sink below the zero line?
Figure 1. Upper panel: Comparison of the observed and predicted CNB’s share price. The latter is obtained using (2). Lower panel: the difference between the observed and predicted price.
Figure 2. Upper panel: Comparison of the observed and predicted CIT’s (adjusted for dividends and splits) share price. The latter is obtained using (3). Lower panel: the difference between the observed and predicted price.
References
[1] Kitov, I., (2009). ConocoPhillips and Exxon Mobil stock price, Journal of Applied Research in Finances, v. 1, issue 2 (in press).
[2] Kitov, I., Kitov, O., (2009). Predicting share price of energy companies: JuneSeptember 2009, MPRA Paper 15863, University Library of Munich, Germany.
[3] Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany
[4] Kitov, I., Kitov, O., (2008). LongTerm Linear Trends In Consumer Price Indices, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(2(4)_Summ), pp. 101112.
[5] Kitov, I., Kitov, O., (2009a). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany
[6] Kitov, I., Kitov, O., (2009b). Sustainable trends in producer price indices, Journal of Applied Research in Finance, v. 1, issue 1
9/20/09
The Phillips curve regains attention
9/17/09
CPI vs. core CPI: 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 smallamplitude 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 [24]) 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.
References
[1] Kitov, I., Kitov, O., (2008). LongTerm 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. 101112. 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.unimuenchen.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.unimuenchen.de/13587/,
http://mpra.ub.unimuenchen.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.unimuenchen.de/15194/01/MPRA_paper_15194.pdf
Price inflation: Q&A
Q1. What is it  price inflation?
In narrow sense, price inflation is a reaction of economic system to changing level of labor force. Inflation is the process which recovers personal income distribution to its natural and fixed (rigid) shape. As a monetary process, inflation is expressed in changing prices for goods and services (G&S), with the total cost of all these G&S exactly determined by real economic growth, if any, and inflation, as predefined by the change in labor force level.
In developed (capitalist) economies, prices for G&S have to interact and compete, i.e. to be governed by "invisible hand", in order to find some final (but not predetermined!) configuration, which corresponds to the total nominal cost of the G&S. This total cost (nominal GDP) is defined by real economic growth and inflation.
(Detailed explanation of price inflation as an economic phenomenon and process as well as relevant quantitative analysis are given in our papers.)
Q2. Is it possible to describe the link between inflation and labor force change using simple mathematical representation?
There exists a linear lagged relationship between inflation, Ï€(t), unemployment, UE(t), and the change rate of labor force, dLF(t)/LF(t):
Ï€(t+t1)= AdLF(t)/LF(t) + BUE(t+t2) + C
where A, B, and C are countryspecific empirical constant (this relationship is normalized to inflation); t1 and t2 are time lags between the change in labor force and the reaction of inflation and unemployment. These lags may reach several years and there is no general rule which variable reacts first.
Q3. Is inflation an economic ill, constantly threatening economic stability?
There is no statistical or any quantitative link between inflation and real economic growth except the one, which is related to population changes. There is a formal statistical and econometric prove available in our papers that real economic growth depends only on the attained level of real GDP per capita and the change rate of population of a countryspecific age. This defining age is nine years in the USA.
Q4. Is deflation harmful?
Since real economic growth and inflation are not directly related, the recession and deflation (like observed in Japan) have different sources. For example, the former process is approaching its end in Japan and real economic growth (per capita) is on its potential level (http://inflationusa.blogspot.com/2007/07/modellingevolutionofrealgdpin.html). The latter process will last the next 40 years with increasing amplitude (http://inflationusa.blogspot.com/2007/08/predictionofcpiinflationinjapan.html )
Q5. Is inflation unpredictable?
Inflation can be accurately predicted at various time horizons in developed countries. Examples are the USA, Japan, France, Germany, Canada, Austria, and the UK. The accuracy of inflation prediction is completely defined by the accuracy of labor force measurements, as follows from the relationship in Q2. There are some simple means to improve current labor force estimates.
Q6. Do central bankers control inflation and inflationary expectations through clear inflation targeting?
Because inflation is completely defined by the change rate of labor force Central Banks do not control inflation as it is. They can potentially control the balance between inflation and unemployment, which are linear lagged function of the change rate of labor force.
Quantitative prediction of the history of inflation in USA is a good example that the Fed does not control inflation. The history of inflation in France demonstrates that the suppression of money supply results in elevated unemployment. So, this is an example of negative affect of central bank in sense of high unemployment balancing low inflation.
9/16/09
ConocoPhillips share price revisited
The 3C model for COP is as follows:
COP(t)= 3.41CF(t+1)  7.17EC(t6) + 7.22*(t2000) + 145.76 (1)
where CF is the headline CPI less food. It does not differ from the model presented in the previous post except the time shifts are +1 (was +2) month and 6 (was 5) months now. This is due to the inclusion on the CPI readings for August. Figure 1 shows the predicted and observed curves. Standard deviation between the curves is $3.96 for the period between July 2003 and August 2009.
The 5C model does not include the linear time term, but two components extra to the 3C model play this role. The best 5C model also shows that the stock price leads all defining CPI components:
COP(t)= 1.53H(t+3) – 8.29R(t+1) – 4.90EC(t6) + 3.53C(t+1) + 518.4 (2)
There components from the four defining lag behind COP share price and only the EC leads by six months. Figure 2 presents the model. Standard deviation between the curves is only $3.03 for the period between July 2003 and August 2009, which is better than the accuracy of the 3C model.
Figure 2. Observed and 5C predicted COP’s share prices.
At first glance, the 5C prediction is better that the 3C one. However, this conclusion is not fully correct. As mentioned above, the extra two components chiefly represent the linear trend. Figure 2 illustrates the phenomenon. The difference between R and EC actually provides a linear trend with small fluctuations, which slightly suppress the residual of the 3C model. Among all pairs of CPI components 8.29R(t+1) – 4.90EC(t6) suppresses the model residual (noise) the most efficient. It is a positive side of the 5C model. It has a negative side as well. The difference may diverge from the linear trend in the next several months and will increase the residual and thus the accuracy of prediction instead of suppression. So, we do prefer using the 3C model for the prediction of share prices. Figure 4 depicts both residuals.
[1] Kitov, I., Kitov, O., (2009). Predicting share price of energy companies: JuneSeptember 2009, MPRA Paper 15863, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/15863/01/MPRA_paper_15863.pdf
[2] Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/15862/01/MPRA_paper_15862.pdf
[3] Kitov, I., Kitov, O., (2008). LongTerm Linear Trends In Consumer Price Indices, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(2(4)_Summ), pp. 101112.
[4] Kitov, I., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/13587/01/MPRA_paper_13587.pdf
[5] 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.unimuenchen.de/15039/01/MPRA_paper_15039.pdf
[6] Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, MPRA Paper 15194, University Library of Munich, Germany, http://mpra.ub.unimuenchen.de/15194/01/MPRA_paper_15194.pdf
Predicting Microsoft stock price
sp(t)= A1S1(t+t1) + A2S2(t+t2) + A3t +A4
where sp(t) is the stock price at time t, A1 through A4 are empirical coefficients, S1 and S2 are components of headline CPI, t1 and t2 are time difference (negative or positive) between the change in the stock price and relevant changes in the CPI components. Term A3t is introduced to compensate linear trends observed in the difference between the components.
For Microsoft, an accurate empirical model is as follows:
MSFT(t)= 3.61*R(t1) – 1.22*MSC(t11) + 23.5*(t2000) + 680.5.
where t is the calendar time, R(t1) is the index for recreation leading MSFT(t) by one month, MCS(t11) is the index for medical service leading the MSFT(t) by eleven months. The linear trend term 23.5*(t2000) compensates the trend term in the difference between R and MCS. Standard deviation between the curves is $1.75 for the period between July 2003 and August 2009.
Unemployment in Germany at 11% in 2011
The model stats, that unemployment in developed countries is a function of labor force change [25]. There is a general expectation of a good fit between these two variables for Germany. Figure 1 repeats the results of a simple manual trialanderror process for the period between 1965 and 2007. Since such procedure is based on visual fit only, no statistical estimates of the residual were made.
The resulting relationship between unemployment and labor force in Germany is as follows:
UE(t) = 2.5*dLF(t5)/LF(t5) + 0.08, after 1995 (1)
where UE(t) is the rate of unemployment in Germany at time t, LF(t5)is the level of labor force five years earlier. The observed unemployment needs a structural break to be introduced in 1995, which is easily explained by the reunification, i.e. 1990 plus the fiveyear lag. Free term in (1) underwent a significant increase, but the slope of 2.5 and the time lag of 5 years did not change, however. (It should be noted that the slope depends of definition of unemployment and labor force, i.e. on reporting agency.) One can read (1) in the following way – a 1% increase in labor force in Germany results in 2.5 % increase in unemployment five years later. When the labor force does not change, the level of unemployment is constant at 8%.
In order to test our model, we have borrowed unemployment estimates from the DEStatics (Federal Statistics Office). They are slightly different from those provided by the OECD, and are issued at monthly frequency. Figure 2 presents the measured and predicted unemployment rate for the period between 2000 and 2012. The predicted curve has slightly higher coefficient than that obtained from the OECD data (+3.2):
UE(t) = 3.2*dLF(t5)/LF(t5) + 0.08 (2),
References
Krugman, Cochrane, Altig ...
PPI of copper ores and grains: update. July and August 2009
In [47], we presented the evolution many commodities with varying weight in the PPI. But there are many more commodities of interest for producers, consumers and investors. In this article, we present the producer price indices of copper and grain. The evolution of the indices of these two commodities is independent, but both give a good example of the absence of clear sustainable trends. In other words, not every commodity price is predictable as an extension of a liner trend, as mentioned in [4]. However, in the shortterm, there is observed some inertia in the evolution of both prices. Therefore, one can predict the indices at a several month horizon. On July 27, we published selected results of our study for June 2009. This is a bimonthly update, which includes two new readings for July and August 2009. Both commodities demonstrate continuation of shortterm trends. Supposedly, these trends survive till the end of 2009.
Figure 1 displays the overall (commodity) PPI and the index of copper ores since 1988. The difference of these two indices has a remarkable history; no big change between 1988 and 2005, and then a sudden giant jump in the copper index. Fluctuations between 350 and 500 points lasted three years, and then the index dropped by ~300 units back to the PPI level. Despite the early start in 2005 the growth seems to be oil independent, the most recent fall looks to be driven by oil price and the overall economic slowdown. In July and August 2009, one can observe a sustainable increase in the cooper index likely associated with the rise in oil price. In the longrun, oil price should decline to the level of ~$25 in 2016. Therefore, copper price will likely not be growing to its peak in April 2008 (491.7), but will likely return to heights around 350. (Our model based on the presence of sustainable trends in the difference between the PPI and individual PPI is not applicable to copper ores.)
The producer price index for grains presents another difficult case. Figure 2 depicts the PPI and the index, and their difference between 1960 and 2009. There is no sustainable trend in the difference. Between 1974 and 2005, the difference demonstrated an overall growth with several spikes, the strongest one in 1996. The presence of a longterm positive trend in the difference is completely due to the growth in the PPI because the index of grains fluctuates around a constant level just slightly above 100 points. Lately, the grains index suffered the biggest rise and fall in absolute terms. The main increase started earlier in 2007 and stretched into 2008, with the peak in June 2008. Volatility of the difference during the past two years was so high that it is difficult to predict the next move of the price index of grains at a several year horizon. Seemingly, it has been repeating the trajectory of the index for crude oil in 2008 and 2009. If it is the case, one can expect that the index for grains will continue to oscillate around the constant level of ~100.
It is instructive to compare two major spikes in the grains index in 1996 and 2008 relative to the PPI. In order to avoid comparing absolute values, which undergo secular growth, the evolution of the difference between the PPI and the price index of grains normalized to the PPI. Figure 3 presents the normalized curves. The left panel shows that the spike in the grains PPI in July 1996 is similar in relative terms to that observed in 2008. The right panel tests this hypothesis: the spikes are synchronized  for the black line is shifted forward by 142 months. From this comparison, it is likely that decline in the grains index relative to the PPI will extend into the 2010s.
Conclusion
References
1. Kitov, I., Kitov, O., (2008). LongTerm Linear Trends In Consumer Price Indices, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(2(4)_Summ), pp. 101112.
2. Kitov, I., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany.
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., (2009). Sustainable trends in producer price indices, Journal of Applied Research in Finance, v. 1, (in press)
5. Kitov, I., Kitov, O., (2009). PPI of durable and nondurable goods: 19852016, MPRA Paper 15874, University Library of Munich, Germany
6. Kitov, I., (2009). Predicting gold ores price, MPRA Paper 15873, University Library of Munich, Germany
7. Kitov, I., (2009). Predicting the price index for jewelry and jewelry products: 20092016, MPRA Paper 15875, University Library of Munich, Germany
8. Kitov, I., Kitov, O., (2009). Predicting share price of energy companies: JuneSeptember 2009, MPRA Paper 15863, University Library of Munich, Germany
9. Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany
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