The rate of unemployment in the U.S. is 7.9%

After the 0.3% drop in September 2012, which provoked a fierce discussion on the accuracy and biases associated with the Census Bureau's surveys, the rate of unemployment has risen by 0.1% in October and the BLS reported 7.9%. This figure provides a strong support to the long term downward trend in unemployment and, in turn, a positive trend in employment. According to our version of Okun's law, we expect a healthy growth in real GDP by 3% per year.

Crude and steel - an unbreakable pair

The price of iron and steel is likely to fall in October-December 2012 following the drop in oil price.  We have been reporting on the trade-off between the (not seasonally adjusted) producer price index of crude oil (domestic production) and the PPI of iron and steel since 2009. It has been always a linear and lagged link between them.  Here we present data through September 2012.

We first reported that the PPI of crude oil had been likely evolving in sync with that of iron and steel, but with a lag of two months in September 2009.  In order to present both indices in a comparable form, the difference between a given index, iPPI (i.e. iron and steel or crude), and the overall PPI was normalized to the PPI: (iPPI(t)-PPI(t))/PPI(t). These normalized differences represent the evolution of the rate of deviation from the PPI over years.  

Figure 1 depicts the corresponding time histories of the normalized deviations from the PPI, including the most recent period through September 2012.  Even a simple visual inspection reveals the following feature: the (normalized deviation from the PPI of the) index of iron and steel lags by approximately two months behind the (normalized) index of crude oil.

Figure 1. The deviation of the iron and steel price index and the index of crude oil from the PPI, normalized to the PPI.

In order to reduce both deviations to the same scale we additionally normalized the curves in Figure 1 to their peak values between 2005 and 2012.

(iPPI(t)-PPI(t))/[PPI(t)*max{iPPI-PPI)}]

This scaling allows a direct shape comparison. In Figure 2, we display the normalized index of iron and steel shifted by two months ahead to synchronize its peak with that observed in the normalized index for crude petroleum. The scaled index of crude demonstrates short-term deviations from the index of iron and steel in the overall shape and timing of the peak and trough. Simple smoothing with a three-month moving average, MA(3), makes the curves resemblance even better. As an extra benefit of the resemblance, one can use the two-month lag to predict the future of the iron and steel price index.

Figure 2. Deviation of the iron and steel price index from the PPI, normalized to the PPI and the peak value after 2005 as compared to the deviations of the index for crude petroleum normalized in the same way. The normalized index for iron and steel is shifted two months ahead. One can expect the index of iron and steel to fall relative to the PPI in October-December 2012.  

Conclusion

The link between oil and iron has been unbreakable. Between 2006 and 2012, the deviation of the price index of iron and steel from the PPI in the USA repeats the trajectory of the deviation of the index of crude petroleum (domestic production) with a two-month lag. Therefore, the prediction of iron and steel price for at this horizon is a straightforward one. From Figure 2, one can expect the price of iron and steel to fall relative to the PPI in October-December 2012 in line with the observed fall in oil price.

Krugman: denial of denial of denial of economics

Paul Krugman   will never surrender.  He insists that the economic theory  does give a good explanation of the current  economic trajectory. However, a half of economic profession does not support him (and the other half).  When I and many other scientists working in physics) deny the economic theory this is a "denial of economics". When Krugman denies our denial - this is a denial of denial. When the other half of  economists deny Krugman's opinion - this is a denial of denial of denial of economics. They do not deny economics as we do.

Comparison of personal income distributions reported by the IRS and Census Bureau

We have discussed many times in this blog that personal incomes are not well defined and the lack of a comprehensive definition does not allow any accurate estimate of income inequality. Here we compare two data sets for 2001. The IRS reported 128,227,145 people with the cumulative income of $6.37E+12. The Census Bureau (CB) found 221,591,000 people with the total income of $6.45E+12, with the working age population of 243,946,000. All figures published by the CB are obtained as a projection of about 200,000 people covered by the Current Population Survey to the working age population as a whole using so called population controls and thus the higher incomes with just few representatives are subject to large biases. The Bureau of Economic Analysis (BEA) has estimated the personal income in 2001 as $8.89E+12. Therefore the IRS and the CB both reported only 72% of the gross personal income (GPI) as based on 53% and 87% of working age population, respectively. This BEA provides no personal income distribution (PID) and thus its data are worthless for the analysis of income inequality. The IRS and CB data sets are also not comprehensive since give two different and mainly independent slices of the personal income distribution. One might try to recover the overall PID from these data sets.

The IRS and CB provide PIDs in different income bins.  This excludes any direct comparison of the relevant PIDs.  The CB covers incomes between $0 and $250K with bins of $10K before and $50K above $100K. The IRS distribution spans the interval between $0 and $10M with the bin width varying from $1K to $5M. All incomes above $250K and $10M, respectively, are covered by open-end bins for which the width cannot be determined. We have calculated two probability density functions (PDF) for the IRS and CB by dividing their PIDs by the widths of income bins and total population. (We did not normalize to the total incomes because they are practically identical.) Figure 1 presents both PDFs. These curves represent the portion of total population in $1 bins as a function of income. Between $15K and $40K, the PDFs practically coincide. Below $15K, the probability density reported by the CB is higher, and above $40K the IRS curve is above the CB one. Both curves reveal a power law distribution above approximate $70K. This allows an extension of the CB curve above its limit of $250K with a power law function with the index of -3.34 as shown in Figure 2. From Figure 1, one can conclude that the excess of 93,000,000 of people in the CB’s PID is inherently related to low incomes. The IRS compensates the total income deficit associated with the lack of low-incomers by a larger portion of people with higher incomes. In that sense, the CB better covers the sources of low incomes and the IRS includes more accurate sources of incomes above $50,000.

In order to construct a comprehensive definition one should combine all sources on income over the whole income axis. The simplest way is to use the CB’s PID below and the IRS’ PID above some threshold. We have chosen the level of $75K because there are bins starting with this value for both the IRS and CB. The number of people reported by the IRS and CB with incomes above $75K is different: 19,452,000 and 15,218,000, respectively. The former number is more accurate since the IRS includes almost all sources of high incomes and we consider the joint (merged IRS/CB) distribution at high incomes to be that reported by the IRS. The extra 4,234,000 people with incomes above $75K might be counted in by the CB as having lower incomes. However, one cannot easily redistribute the CB’s PID by extracting these four millions. Therefore, we just added 4,234,000 to 221,591,000 reported by the CB in order to calculate the basis for the corresponding PDF. This is a crude approximation but it should not introduce a large bias in the lower income bins since it is less than 2% is added. At lower incomes, we use the CB’s PID. Figure 3 shows the new merged PID (black line) which includes 225,000,000 and $7,819B.  The total income in the merged distribution is closer (895) to the GPI.

 

Figure 1. PDFs for IRS and CB

Figure 2.  The high income PDFs for the IRS and CB. The actual CB PDF shown by red circles and is extended by a power law with the index of -3.34 as shown by yellow circles.  The highest two values reported by the IRS lie above the power law distribution and are shown by blue squares with red contour. The expected values are shown by yellow squares.  

 

Figure 3. The merged personal income distribution.  At lower incomes, we retained $5K bins instead of $10K in Figure 1. At higher incomes, the merged PID is parallel to that reported by IRS but is much lower because the normalization basis has been increased from 128M to 225M people.

When I'll buy the S&P 500 index

In April 2012, we predicted a drop in the S&P 500 to the level of 1300 by the end of May. Figure 1 shows the predicted behavior in April and May 2012, with the predicted segment shown by red line. We expected that the path observed in the previous rally would be repeated with the bottom points coinciding.  When this prediction realized, we invested, say, one unit at the average price 1320. The expected exit level was 1500 in October 2013.

Figure 1. The original S&P 500 curve (black line) and that shifted forward to match the 2009 trough (blue line). Red line – expected fall in the S&P 500: from 1400 in March to 1300 in May.

Figure 2 shows the evolution of the S&P 500 monthly closing price between May and August 2012. The S&P 500 closing level for August was 1430 and reached 1469 in the middle of September. This level provided a ten percent return over approximately 4 months. One can see that the observed level was far above the expected level (blue line). The return and the deviation from the expected level both made us think that this was the best time to exit. We sold the index on September 21 (1460) anticipating strong turbulence (economic, financial, and political) and an overall fall to 1375 at a few months horizon.  

Figure 2. Same as in Figure 1 with an extension between May and August.

Figure 3 shows the evolution of the S&P 500 monthly closing price in September-December 2012. The current level (October 26^th) is 1411. We used it as a closing price for October and put the November’s level down to 1375. One can see that the red line intersects the blue curve. The previous history of the black and red lines intersection with the blue one makes us think that the time to enter the market (S&P 500 index) is approaching. We’ll definitely buy at 1350 to 1375 which is an expected level by the end of 2012.  This level guarantees another 140 to 170 points (10% to 12%) by the end of 2013.

Figure 3. Same as in Figure 1 with an extension between September and November 2012.

TRENDS AND FLUCTUATIONS IN PRICE OF CRUDE OIL AND MOTOR FUEL

We have revealed long term sustainable trends in the difference between producer price index for oil and the overall PPI. In the long run, one can foresee the direction of oil price trend which is crucial for investments. Moreover, there are many short-term price fluctuations around the trend which have large amplitudes and thus allow active speculations.  

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].   

For major CPI and PPI subcategories, these trends last from five to twenty years and then turn to trends with opposite slopes. The transition to new trends lasted three years at most. We have not revealed any clear turns after 2009 and the current transition period might last longer. There are also several subcategories without slope changes since the start of the relevant measurement as reported by the Bureau of Labor Statistics [8]. All CPI and PPI time series (in this study we use seasonally adjusted CPIs and not seasonally adjusted PPIs) were retrieved from the BLS. The best example of such a one-leg trend since 1980 is the consumer price index of medical care. The index of communication has been linearly deviating from the headline CPI since 1998; before 1998 it had been reported as an indistinguishable part of the index of education and communication. 

In the short run, actual prices oscillate around the long-term trends with varying amplitudes. In a sense, the trends represent the lines of gravity centers for given prices and any large deviation from the trends must be compensated promptly. As a result, both short- and long-term predictions of commodity prices are feasible. In the long run, the prices follow up the trends. In the short-run, the next move in a given price depends on the current position relative to the corresponding trend.  When far from the trend, the price is more likely to start returning. When approaching the trend, the price may choose any direction for the further evolution, i.e. it should not inevitably go the other side of the trend. In this article, we focus on crude oil and motor fuel.

For the price index of motor fuel, we developed a similar model as based on the deviation from the core CPI, i.e. the headline CPI less food and energy.  Using this model, we predicted the evolution of oil price as well. The overall performance of the model between March and December 2009 was reported in [9]. Here we also revise the long-term prediction of crude petroleum and motor fuel price and make necessary corrections to the model as related to the observations since March 2009.  

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).  

Figure 1 displays examples of linear trends in the two differences related to the scope of this article. In the left panel, the evolution of the index of motor fuel relative to the headline CPI is shown. Notice that in the original paper [7] we referred the index of motor fuel to the core CPI, but the discrepancy between the headline and core CPI is negligible relative to the change in the index of motor fuel.  There are two distinct periods of linear dependence on time: from 1980 to 1999 and from 2001 to 2008. Apparently, there is one finished transition period between 1999 and 2001, where the trend with a positive slope (B=+4.2) changed to a negative one (B=-21.1), in both cases the determination coefficient being very high: R²~0.89. The first transition period is characterized by elevated price volatility.  Since 2008, the negative trend in the difference has been suffering a transition to a positive one, which is shown in Figure 1 by a dashed line. This transition is characterized by a much higher volatility and has been fading away since the end of 2009. Without prejudice, we have drawn the new trend as increasing from -110 in 2009 to -60 in 2016. (Notice that we made a different tentative assumption in [10] since we had no actual data after 2009.) This defines the long-term prediction of the motor fuel index and fits observations since 2010.  

In the right panel, the difference between the PPI and the index of crude petroleum (domestic production) is shown between 1985 and 2012. There are two distinct periods of linear dependence on time: from 1988 to 1999 and from 2001 to 2008. The slopes of regression lines in both periods are different from those for the index of motor fuel: +2.9 and -17.9, respectively. There was one transition period between 1999 and 2001, where the original positive trend was turned down. We expect the difference to grow (the oil price index has to rise slower than the PPI) from -80 in 2009 to +20 in 2016; the growth rate is ~14 point per year. 

 

Figure 1. Illustration of linear trends. Left panel: the difference between the headline CPI and the index of motor fuel between 1980 and 2012. Right panel: The difference between the overall PPI and the (producer price) index of crude petroleum (domestic production). In both panels: there are two quasi-linear segments with a turning period between 1998 and 2001. Since the end of 2008, both differences have been passing a transition. Linear trends with relevant linear regression lines and corresponding slopes are also shown.

From Figure 1, one can conclude that the presence of linear trends is a basic feature of the CPI and PPI components which is likely to be repeated in the future. 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. 

Simple visual inspection of the transition period in Figure 2 shows that the difference in timing and amplitude between motor fuel and crude oil is not too big.  The amplitude of oil price fluctuations is higher since 2007 and especially during 2011 and 2012. In turn, the fluctuations in motor fuel price were slightly higher between 2000 and 2007.

  

Figure 2. Comparison of two differences.   

Figure 3 presents both differences after 2007. Overall, the evolution of the difference between the CPI and the index of motor fuel follows the new trend since 2011.  One may expect that after a few months below the trend (say, through October –December 2012) the next move will return the difference above the trend, i.e. the price of motor fuel will fall a bit relative to the CPI. In the long run motor fuel will be losing its pricing power relative to the CPI. The oil price prediction for 2013 is similar.  The difference in Figure 3 will reach the new (dashed) trend line and the oil price has to fall below $80 per barrel. 

Figure 3. Left panel: The difference between the headline CPI and the index for motor fuel.  Right panel:  Evolution of the difference between the PPI and the index for crude petroleum (domestic production).  Notice oscillations around the new trends.  

The forces behind the observed long- and short-term behavior are not accessible yet but very powerful. We may assume that they are fundamental and affect the economy to its 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 trends in the CPI and PPI turn. 

Meanwhile, it is instructive to revise our long-term prediction of oil price shown in Figure 1. After a few minor adjustments to the initial and final levels of the PPI and the index of crude petroleum, Figure 4 depicts the revised prediction after 2010.  It is slightly different from our previous prediction with oil price in 2016 set between $30 and $60 per barrel. Short-term fluctuations cannot be predicted at a horizon of several years. However, the larger is a given deviation from the trend the larger is the returning force.

 

Figure 4. The evolution of crude oil price. Open circles represent the evolution of (monthly average) oil price for the period between 2001 and 2012.  Dashed lines – the upper and lower limits of the new trend between 2009 and 2016. According to the prediction, the price should fall to the level between $60 and $30 per barrel by 2017.  

Economists intentionally ignore 33,000,000 Americans when calculating income inequality

When discussing the increase in income inequality economists forget those people who have no income at all. According to the Census Bureau, there are tens of millions reporting no income every year and this number has been really growing since 1990 as Figure 1 shows. Notice also the dramatic fall in 1978, which was caused by a revision to income definition – more than 15,000,000 were added to income gainers in a few seconds.

The total population has been also growing by approximately 1% per year. Figure 2 depicts the ratio of the number if people without income and the total working age population (15 years of age and over).  This ratio has been growing since 1990 as well and there was no specific acceleration after 2007.  It is not clear why these people have been excluded by the Census Bureau from the reported measure of income inequality in the U.S. – the Gini ratio. Figure 3 displays three estimates of the Gini ratio. Black line presents the estimates published by the Census Bureau which are obtained for people with income only. Red line shows our estimates obtained from personal income distributions (PID) published by the Census Bureau.  The difference with the official figures between 1998 and 2011 is 0.011. This difference is likely related by the fact that we introduced a more accurate approximation of the PID in the lower and higher income bins. In any case, this difference is constant and negligible - one may correct any of the estimates by 0.011 and compensate the gap.  Therefore, we can use our method to estimate the Gini ratio and apply it to the PID including those without income.

When more than 30,000,000 people with zero income are added one should expect a dramatic increase in Gini ratio. Essentially, thirteen percent of working population adds to zero income what shifts the Lorenz curve further from the bisecting line. Blue line shows the estimates of Gini ratio for the whole working age population.  Unlike the red line, the blue line has been rising since 1990. The period after 2007 is characterized by an accelerated growth, which is obviously associated with the increasing number of zero-incomers. For people with income, the Gini ratio is rock solid over the whole period between 1967 and 2011 (with an almost negligible negative trend). Interestingly, there is no sign of the revision to income definition in 1977. Despite those 15,000,000 who were added in 1978 likely had negligible incomes they did not change the overall personal income distribution. This effect deserves a detailed investigation.

In terms physics, this is a mistake to neglect a substantial part of a closed system when calculating aggregate variables. Such aggregates are intrinsically biased and can not characterize the system and its behaviour.   Currently, the income inequality in the U.S. is much higher than the Census Bureau reports: the Gini ratio is rather 0.58.

Figure 1. The number of people without income according to the Census Bureau’s definition.

 

Figure 2. The portion of population without income

Figure 3. Three estimates of Gini ratio as described in the text.