Income inequality: age-gender dependence

We have demonstrated the difference in mean income between men and women and the evolution of mean income over work experience (age). In this post we join both representation and display the evolution of mean income with work experience for each sex and for both sexes together. As before, we use personal income measurements published by the U.S. Census Bureau (CB). These data come from the CPS Annual Social and Economic Supplement of the Current Population Surveys (http://www.census.gov/cps/). It is worth noting that approximately 90% of working age population, i.e. 15 years of age and over, reports nonzero incomes. This portion is much higher than the rate of participation in labor force (~65% in the USA). Obviously the number of people with income is much higher than the number of employed. This makes consideration of income inequality based on wages slightly weird. There are many people having large incomes but not in the employment. Since employment is not the only way to get reasonable income why should we consider it as a crucial economic variable? In this sense, the rate of participation in labor force strongly varies across developed countries, with higher amplitudes than the rate of real GDP growth.


Figure 1 shows mean income as a function of work experience for male and female group separately since 1967. The male curves demonstrate a clear shift in the age of peak income, as was presented in the previous posts. The female mean income has a more stable shape and clear jump around 1987. It might be associated with new income definition introduced in 1987.

Figure 1. Mean income vs. work experience (i.e. age-15 years) for men and women since 1967.

Figure 2 displays the mean incomes presented in Figure 1 as normalized to the peak mean income for each year. The jump of the peak mean income from the age group between 35 and 44 years into the group between 45 and 54 years of age is well seen in the male curves. For women, the peak age is lower and one can observe the change from the group between 10 and 20 years of work experience to the group between 20 and 30 years. This is in line with the dependence of the peak age on mean income. With time the peak mean income will be drifting into elder age groups. Therefore, people with highest income become older over time. The youngest age group has been suffering relative decrease in the portion of total income, i.e. younger people are getting poorer in relative terms.

Figure 2. Same as in Figure 1 normalized by the peak mean income for given year.

Finally, Figure 3 displays the normalized mean income dependence on age for both sexes. The observed curves also show the increase in the work experience with peak income.

Figure 3. Same as in Figure 2 for the overall population with income.

Yahoo! share in January 2011

The model for Yahoo! (YHOO) is a weird example of the deterministic character of share price evolution. Our model for YHOO is stable over the past year but is defined by somewhat unexpected indices: the consumer price index of meat, poultry, fish and eggs (MEAT) and the index of motor vehicle parts and equipment (MVP). Both defining indices seem to have no relation to the internet services. On the other hand these CPIs are the most basic ones and are in the root of any economic activity.

The MEAT index leads the share price by 6 months and the MVP one - by 1 month. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between June 2010 and December 2010. The MEAT coefficient is positive and thus the increasing price of meats, poultry, fish and eggs causes the share price to grow. The MVP index has a negative coefficient and causes the share to fall. The slope of time trend is positive revealing the price tendency to increase over time. The best-fit 2-C model for YHOO(t) is as follows:

YHOO(t) = 0.49*MEAT(t-6) – 3.27*MVP(t-1) + 10.47(t-2000) + 145.67

where t is calendar time.

The predicted and observed curves are presented in Figure 2. The residual error is of $2.51 for the period between June 2003 and December 2010. The model provides a relatively good prediction of the share price in the past. Currently, the predicted price shows no tendency to rise. All in al, one should not expect the YHOO price to grow fast.

Figure 1. Evolution of the price of MEAT and MVP.

Figure 2. Observed and predicted YHOO share prices.

Wal-Mart share in 2011

Here we present a pricing model for Wal-Mart Stores (WMT), as based on the decomposition of a share price into a sum of two selected consumer price indices. This is a new model defined by the index of hospital and related services (HOSP) and the price index of miscellaneous personal services (MISS), as reported by the US BLS. The former CPI component leads the share price by 10 months and the latter one evolves in sync with the price. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between June 2010 and December 2010. Relevant coefficients are both positive. Therefore the growth in both indices causes the share price to increase. The slope of time trend is negative. The best-fit 2-C model for WMT(t) is as follows:

WMT(t) = 0.50*HOSP(t-10) + 1.42*MISS(t) - 28.39(t-2000) – 158.12

where t is calendar time. The predicted curve in Figure 2 evolves in sync with the observed price. The residual error is $1.99 for the period between June 2003 and December 2010, as Figure 3 presents. Since both defining components are on a steady rise one can expect the WMT price to grow in 2011.

Figure 1. Evolution of the price of HOSP and MISS.

Figure 2. Observed and predicted WMT share prices.

Figure 3. Residual error of the model.

Price model for H.J. Heinz Company

The model for H.J. Heinz Company (HNZ) is another example of the deterministic character of share price evolution. Our model is stable over the past year and is defined by the consumer price index of other food less beverages (FB) and the index of miscellaneous service (MISS). The former CPI component leads the share price by 4 months and the latter evolves in sync with the share price. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between January 2010 and December 2010. The FB coefficient is negative and thus the increasing food price leads to a decline in the share price four months later. The MISS index has a positive coefficient and causes the share price to grow. The slope of time trend is negative revealing the price tendency to decline over time. The best-fit 2-C model for HNZ(t) is as follows:

HNZ(t) = -1.21*FB(t-4) + 1.19*MISS(t) - 2.34(t-2000) – 64.78

where t is calendar time.

The predicted and observed curves are presented in Figure 2. The residual error is of $1.70 for the period between June 2003 and December 2010. The model provides and an excellent and very stable prediction of the share price in the past. Currently, the predicted price is lower than the observed one. One can expect a slight correction of the price down.

Figure 1. Evolution of the price index of FB and MISS.

Figure 2. Observed and predicted HNZ share prices. Black diamonds present the contemporary prediction to fit actual data.

Deterministic prediction of CVS share price

Deterministic prediction of share prices has been long considered as an impossible task in the current market paradigm. Stochastic approach to market prices has really won the hearts of market participants. This conclusion has been made in rash, however. Logically, no finite number of failures to describe and predict a measurable process is enough to prove that it has deterministic nature. People do fail to describe processes and events in scientific way, but this is the characteristic of people not processes. On the contrary, one (or several) example is enough to demonstrate that the link between share prices and CPIs is deterministic in principle, and thus, to demonstrate that the stochastic approach is not fully correct.

The model for CVS Caremark Corporation has been very stable over the past two years and helps to prove the deterministic character of share price setting. A very exciting feature of the CVS price model we developed two years ago is the possibility of prediction at a 4 months horizon. As with Avery Dennison Corporation we have been following the CVS share of since 2009, i.e. since we started to develop our concept of share pricing as related to consumer price indices.

The CVS model has not been changing much and is still defined by the consumer price index of other food at home (OFH) and that transportation services (TS). The former CPI component leads the share price by 4 months and the latter one - by 5 months. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between August 2009 and December 2010. Relevant coefficients are both negative. Therefore the growth in both indices causes the share price to fall with a several month delay. The slope of time trend is positive. The best-fit 2-C model for CVS(t) is as follows:

CVS(t) = -0.51*OFH(t-4) – 1.23*TS(t-5) + 12.15(t-2000) + 195.93

where t is calendar time.

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $1.88 for the period between June 2003 and December 2010. The model provides and an excellent and very stable prediction of the share price in the past. Moreover, it foresees a period of no growth in the first quarter of 2011. It is necessary to stress again that the model has been predicting the CVS share price since August 2009 with the same accuracy. The prediction for the first quarter of 2011 is the next step to validate the model.

Figure 1. Evolution of the price of OFH and TS.

Figure 2. Observed and predicted CVS share prices. Black diamonds present the contemporary prediction shifted 4 months ahead to fit actual data.

Avery Dennison in 2011Q1

We have been following the share of Avery Dennison Corporation since 2009. The model for AVY has not been changing much and is still defined by the index of food (F) and that of new and used motor vehicles (NUMV). The former CPI component leads the share price by 5 months and the latter one - by 3 months. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between August 2009 and December 2010. Relevant coefficients are both negative. Therefore the growth in both indices causes the share price to fall with a several month delay. The slope of time trend is also positive.

So, the best-fit 2-C model for AVY(t) is as follows:

AVY(t) = -4.10*F(t-5) – 2.95*NUMV(t-3) + 22.62(t-2000) + 754.97

where t is calendar time. The predicted curve in Figure 2 leads the observed price by 3 months with the residual error of $2.66 for the period between June 2003 and December 2010. The model does predict the share price in the past and foresees a period of no growth in the first quarter of 2011.

Figure 1. Evolution of the price of F and NUMV.

Figure 2. Observed and prdicted AVY share prices. Black diamonds present the contemporary prediction shifted 3 months ahead to fit actual data.

Figure 3. Residual error of the model.

Personal income inequality: age factor

Another traditional inequality topic is associated with age. We again use personal income measurements published by the U.S. Census Bureau (CB). These data come from the CPS Annual Social and Economic Supplement of the Current Population Surveys (http://www.census.gov/cps/). Figure 1 shows the age-dependent mean income since 1967. As mentioned in the previous post, mean income (as expressed in 2009 US$) in the age group between 15 and 24 years has been growing since 1974. The largest growth is observed in the elder age groups between 45 and 54 (marked 50) and between 55 and 64 (marked 60).

Figure 1. Age dependent mean income since 1967.

Figure 2 displays the same curves as in Figure 1 but normalized to the peak (among all age groups) mean income for each year. The overall picture is clear: peak mean income drift in the direction of larger ages. Extrapolating the curve “60” one can estimate that the peak mean income will be measured in this group in approximately 5 to 7 years. All these effects were well described by our model of personal income distribution.

Figure 2. Same as in Figure 1 normalized to the peak mean income for each year.