The economic problems in France described in this blog are well supported by social problems best expressed in the open letter of ex-generals and high-ranked officiers. Not surprisingly, the letter has wide support in the population. Economic and economically driven social problems get into the most acute phase by the COVID-19 pandemic and a 10% real GDP fall. France is losing its international position (believe you or not but France is a permanent member of the UN Security Council) and own territory - the ex-generals (and a larger part of the population) state that there are areas within France where the French laws do not work. The French Revolution, which was also a greater civil war, was ignited by a few years of extreme hunger: "Qu'ils mangent de la brioche" was the apotheosis of the despotism. Nowadays, hunger is likely a minor issue in France, but the re-writing of the multi-century tradition, i.e. myths and pride, is not easy to digest. The long-term economic decay in France will continue as related by the EU's disproportionate developement.
5/1/21
Personal income growth - actually heating of a spherical body in a vacuum
1.
Physical intuition behind income growth and fall
Here,
a microeconomic model is presented, which has been developed to quantitatively
describe the dynamics of personal income growth and distribution [Kitov, 2005a].
The model is based on one principal assumption that each and every individual
above fifteen years of age has a personal capability to work. In essence, the
capability to work is equivalent to the capability to earn money. To get money
income, individuals have to use one or several means or tools from the full set
of options that may include paid job, government transfers, bank interest,
capital gain, inter-family transfers, and others. The U.S. Census Bureau questionnaire
[2006] lists tens of money income components. It is important to stress that
some principle sources of income are not included in the CB definition, which
results in the observed discrepancy between aggregate (gross) personal income
(GPI), as reported by the Bureau of Economic Analysis and the gross money
income calculated by the CB.
In this
section, we summarize the formulation of a theoretical model, originally
described in Kitov [2005a], and present it as a closed-form solution in
a simplified setting. Figure
1 illustrates a few general features any consistent model has to describe quantitatively.
In the left panel, we display the evolution of mean income curves from 1962 to
2013. The original income data are borrowed from the Integrated Public Use
Microdata Series (IPUMS) preparing and distributing data for the broader research
community [King et al., 2010]. These
are income microdata, i.e. each and
every person from the IPUMS tables is characterized (among other features) by
age, gender, race, gross income, and the population weight, which allows
projection of the individuals from the CPS population universe to the entire
population. Using age, income, and population weight we have calculated the age-dependent mean income for all years and then normalized them to their
respective peak values. The normalized curves better illustrate the growth in
the age of peak income – from below 40 in the earlier 1960s to 55 in the 2010s.
This is a sizeable change likely expressing the work of inherent mechanisms
driving the evolution of personal income distribution. One cannot neglect the
effect of increasing age when people reach their peak incomes – neither from a theoretical
nor from the practical point of view.
In the right panel of Figure 1, we
compare various mean income curves reported by two different organizations
responsible for income measurements: the Census Bureau (CPS) and the Internal
Revenue Service (IRS). The latter organization does not publish the age
distribution of income on a regular basis and only the year of 1998 is
available for such a comparison. The IRS mean income is calculated in 5-year
age cells [IRS, 2015], the CPS prepares historical datasets with a 5-year
granularity since 1993, and the annual estimates are available from the IPUMS
microdata. The annual curve has also been smoothed with a nine-year moving
average, MA(9). As in the left panel, all curves are normalized to their peak
values.
There are significant differences in
income sources and population coverage used by the CPS and IRS [Kitov, 2014]. Nevertheless,
between 40 and 60 years of age, all curves in the right panel of Figure 1 are
close to each other. With regard to the age of peak
income, the CPS and IRS give identical results to the extent the age
aggregation allows. The IPUMS curve has been smoothed and thus might have a
slightly biased peak age. Between 25 and 40 years of age, the difference in
normalized mean income is larger - likely because of the difference in income
sources. The same effect is observed in the eldest age groups, where taxable
incomes are not so often and the CPS curve is above the IRS one.
The closeness of the peak ages measured
by the IRS and CPS is important for model applicability and reliability. The
accuracy of income measurements, the coverage of population and income source,
the level of historical consistency in income definition and survey
methodology, the entire diversity of personal characteristics, and the length
of time series provided by the Census Bureau all these features make it
inevitable to use the CPS data for quantitative
modelling. The reverse side of this choice
is the necessity to defend the modelling results against
the accusation that the CPS data are not full and representative.
It is true that the CPS misses some
important sources of higher incomes, but Figure 1 stresses that the estimates
of key features are not different if the IRS sources are included and some CPS
income sources are excluded [Henry and Day, 2015, Ruser et al., 2004; Weinberg, 2004; U.S. Census Bureau, 2015b]. Besides,
the CB provides the best income estimates for the poorest population, where
incomes are just several dollars per year. Other organizations ignore small
incomes. As a result, the estimates of personal income inequality based on the
IRS data exclude half of the population, the poorest half. It is difficult to
consider such estimates as accurate and helpful for understanding the
mechanisms of the income distribution. The BEA income data are worthless for
quantitative analysis of individual incomes - no age, gender, race information
is available.
Astoundingly, the principal features observed
in Figure 1 can be accurately approximated by basic mathematical functions.
Moreover, these functions represent solutions of simple ordinary differential
equations. The solid red line in the right panel is calculated to fit the CPS mean
income curve. For this line, the equation is [1 - exp(-0.071(t-18))] + 0.09, where t is the age. The overall fit between the measured and
approximating curves is extremely good from 18 to 55 years of age before the
mean income curve starts to fall.
The approximating equation is a
well-known function often called the “exponential saturation function”. This
function represents a closed-form solution of a simple ordinary differential
equation dx(t)/dt=a-bx(t), where a>0 and b>0 are constants. The match between the observed and
approximating curves provides some hint on the forces behind income growth. The second term in the above equation represents the force counteracting the
unlimited growth of x(t). The
amplitude of the counteracting force is proportional to the attained level, and
that implies the finite value of x(t)<Xmax,
t →∞.
A standard example in general physics to illustrate the saturation process is associated with the heating of a metal ball by an internal source with constant power, U. The growth in temperature, T, is balanced by energy loss through the surface, and the energy flux through the surface is proportional to the attained temperature. Thermal conductivity can be treated as infinite in terms of the characteristic time of all other processes. For a ball of radius R and volumetric heat capacity, Cv, one can write the following equation:
4/3πR3CvdT(t)/dt = U – DT(t)4πR2 (1)
where D is a constant defining the efficiency of heat loss through the surface, which is similar to dissipation. By dividing both sides of (1) by 4/3πR3Cv we obtain:
dT(t)/dt = Ũ – D̃T(t)/R (2)
where Ũ=3U/(Cv4πR3) is the specific power of the heating sources expressed in units of thermal capacity, and D̃ = 3D/Cv. The solution of (2) is as follows:
T(t) = T0 + (ŨR/D̃)[1 - exp(-D̃t/R)] (3)
Relationship (3) implies that
temperature approaches its maximum value ŨR/D̃ along the saturation trajectory,
which we also observe in Figure 1. Instructively, the maximum possible
temperature is proportional to R.
This fact is helpful and important for a better understanding of our model and
income observations. We interpret temperature as income, which one can reach
using some physical capital, say, 4/3πR3, and personal efforts, say,
U. Then the saturation curve in Figure 1 becomes an obvious result.
Above the age of peak mean income in Figure 1, one observes an exponential fall. The Blue dotted line is defined by function exp[-0.052(t-56)]. It best matches the IRS curve above 56 years of age. The match between the observed curve and the exponent is extraordinary even in terms of the hard sciences. The exponential function is a solution of a familiar equation: dx(t)/dt=-bx(t). The only difference is in the absence of term a, but now the curve starts from 1.0. The evolution of mean income measured by the IRS above the critical age can be expressed by a differential equation formally identical to that describing free cooling of a preheated sphere, i.e. when heating source U=0 in (1).
Hence, the observed features of the mean
income behaviour are similar to those observed in simple physical experiments.
However, we need to describe the income trajectory for each and every person in a
given economy. It is natural to suggest that all individual incomes follow their own
saturation curves and their average value follows up some individual
trajectory. Then the distribution of parameters defining individual
trajectories, i.e. income analogues
of R and U, is completely constrained by observations. This is the intuition
behind our microeconomic model.
Originally, the idea of income modelling
with equation (2) came from geomechanics [Rodionov et al., 1982]. An identical equation describes the growth of
stress, σ(t), in an inhomogeneous
inclusion with characteristic size L
experiencing deformation at a constant rate ε̇
as induced by external forces. Solution (3) is important to predict the highest
possible level of stress at a given inclusion with size L. Unlike in the simple experiment with the heated sphere of radius R,
the sizes of inhomogeneous inclusions are distributed according to a power-law L3dn/d(lnL) =const, where n is the number of inclusion of size L in a unit volume. This distribution
defines the structural self-similarity of fractals.
Let us consider that deformation starts
at time t0 and all
stresses are zero before. Then stresses will rise at different rates for
different inclusion sizes. At time t,
there is some inclusion with size LM,
which reaches its highest possible stress balancing deformation and
dissipation. At all bigger inclusions,
stress is still growing. When the rate of deformation is high enough and there
are big enough inclusions the attained stress may exceed at some point the
critical stress of fracturing. Then a quake may occur. This is a transition to
a super-critical regime and the sizes of earthquakes are distributed by a power
law.
In economics, higher incomes are characterized by a similar distribution, but they are the net result of all forces and agents in the economy, which both vary with time. They do not represent a predefined structure as in geomechanics. Moreover, low and middle incomes are distributed according to an exponential law rather than a power one. So, we had to construct the basic distributions of defining parameters, which result in exponential distribution of low-middle incomes and power-law distribution above the Pareto threshold. The process of model development with explicit differential equations together with the selection of underlying distributions is described in the following Subsections.
4/30/21
Do we have criteria to estimate the income one deserves?
In the course of the equality and equity discussion, there are a few questions that make me feel uncomfortable. One of these questions the role of government in economic and social life it has to govern. The gender and race inequality in income are commonplace and the demand for equality seems to be absolutely justified.
To understand the income inequality problem, let's first take a look at real income inequality estimates and start with white (alone) males as published by the US Census Bureau. Figure 1 presents the age dependence of the Gini ratio in 2019. One can see that there is no equality in income distribution for the white males in any age group. The equality implies that the Gini ratio is equal to 0, but it is rather 0.5, i.e. income inequality is extremely high. The highest inequality (Gini=0.539) is observed in the youngest age group from 15 to 24 years of age. This group also has the lowerest mean income, as Figure 2 shows. Interestingly, the lowermost income inequality (Gini =0.405) is observed in the next to the youngest group - from 25 to 29 years of age. Then the income inequality grows with age to the age of the peak mean income - 57.5 years of age in 2019. The level and the age evolution of income inequality in the white-alone-male population does not ignite any visible discussion. It seems to be a fair one, i.e. the income distribution is considered as proportional to some widely accepted criteria (which I do not know except the one used in our income distribution model). In our previous post, we discussed the secular impoverishment in the youngest age group but it was not connected to the unfairness of income distribution as such. Therefore, the observed income inequality is not considered unfair when we talk about white males.
For the white females in Figure 3, the overall evolution of the Gini ratio is very similar, except it grows much faster in the mid-ages between 30 and 50. This reflects the fact that the white females have larger income inequality in the age interval when the mean income grows fast. Black males and females demonstrate similar Gini ratios with some small deviations. Therefore, within each of these four groups, we observe similar income inequality levels and evolution with age. It is highly likely that the same economic forces drive the distribution of income and these forces do not raise any questions about their unfairness. At least at the level of the unfairness of income differences observed between the groups - a major topic of discussion in the USA.
I wonder that the government servants have to be merciless robots to resolve the conflict between different gender/race (and age) groups. On one hand, any mechanical leveling of income will demolish the fair criteria of the current distribution of income in any of the groups. Essentially, the relatively fair income distribution mechanism has to be replaced with something artificial. One needs to defend such a new set of mechanisms to be accepted by all participants. On the other hand, income disparity between genders and races is obvious, has a clear historical background, and definitely needs urgent action. The real fight is ahead. However, the income distribution in and between the groups is a result of similar fights in the past when the capabilities and power distribution were different.
As a researcher, I would like to see the new criteria of the income distribution, i.e. who deserves what?
Figure 1. Gini ratio (published by the US Census Bureau. Table pinc01_1_2_3) in 2019. Dependence on age for white alone males.
Figure 2. Mean income of white (alone) males and females in 2019 as a function of age
4/29/21
Why liberals do not join the police 2
I wrote in the previous post:
The current police discussion in the USA reminds me of the excellent book by J.Haidt "The righteous mind" discussing the inherent difference between liberal and conservative moral foundations. This difference is well experimentally described in the book but what strikes my (conservative) mind is how liberal minds can serve the army and police. The liberal mind does not like authority and loyalty - the basis of hierarchy, order, honor, and duty. The police reformation (defund) discussion does not have a significant point - liberals have to reform the police from the inside, i.e. join the police and replace the rude policemen. However, they want the dirty part of the justice work to be done by somebody else and thus denying their own conviction that nobody has to be forced to do such a job. I do understand why liberals do not have overwhelming representation in the police force, but I do not understand how they are going to resolve actual social and criminal conflicts.
Now I have something to add. With the police crisis unfolding and the real depopulation of precincts, it seems that the idea behind the police defunding is much deeper than just to make the police weaker. I guess that the liberal mind sees the future force enforcement of the political power as applied to the society as driven by rules not be the law. As we observe now, the rules are adaptive and out of the legal field. The rules are developed ad hoc by the "derin devlet" and introduced through media (old Soviet joke - newspaper cannot tell lies). This procedure is now under successful testing in the "cancel culture" process. We will see actual force enforcement actions very soon.
On secular relative impoverishment of young people
The problem with young people's income deficiency attracts more and more attention from media and politicians. Almost every day one can find a publication in non-negligible (e.g. FT) media resources comparing the current young people generation with historical records. We have explained in this blog and many academic papers that this problem cannot be resolved in the situation with growing real GDP per capita.
Figure 1 describes the growth in average income in the USA for work experience between 4 and 10 years, i.e. for 19 to 25 years of age according to the CPS ASEC conducted by the Census Bureau every March for the BLS. (All data were retrieved from IPUMS USA, University of Minnesota, www.ipums.org.) Because of the growing nominal and real GDP, the curves in Figure 1 are normalized to the peak value for a given year and we observed how fast people can reach the peak income on average. In 1950, the mean income grew from 0.26 for 4 years of work experience to 0.70 for 10 years. The linear regression shows that extremely good fit (Rsq=0.991) and a linear growth rate of 0.073 relative units per year. In 2019, the rate was only 0.054 per year, and the change from 0.082 for 4 years of work experience to 0.40 for 10 years (Rsq.= 0.995). This observation indicates the progressive decay in the relative mean income for a given work experience. Figure 2 presents an example of such decay for 10 years of work experience from 1950 to 2019, i.e. during the last 70 years. The linear decay over decades implies that extremely strong natural economic forces drive this process. These forces are fully related to real GDP per capita linear growth.
We have developed an income
distribution and evolution model describing also these effects of the relative
decrease in the young people incomes - the mean income obviously means that all
young people of a given age have lower relative incomes. We also well
documented the process of full
similarity of the personal income distribution in various countries when compared according to
real GDP per capita. The linear fall in the mean income relative with time
is explained by the effect of the increasing age of the peak income, as Figure
3 shows. The peak age has been increasing as a square root of the real GDP per
capita since the beginning of the 20th century, where we have income
measurements. According to our model, the initial mean income growth is
approximately a linear function of time.
Real income measurements reveal the process
which underlies the relative impoverishment of the youngest cohorts. This is
not an economic problem in sense of natural forces driving this effect. One
cannot make younger people richer by economic measures. This is a social
problem, however. This social problem will deepen and expand with time if to
ignore the real economic forces behind it. These forces are fully related to real
economic growth.
Figure 1. Relative growth of the mean income depending on work experience between 4 and 10 years in 1950, 1980, and 2019.
Figure 2. The fall of the relative mean income of people with 10 years of work experience between 1950 and 2019.
Figure 3. Relative growth of the mean income depending on work experience in 1950, 1980, and 2019.
4/24/21
Will Green ruin Berlin?
I am waiting for the Greens victory and green Chancellor in Germany this fall. This would be a great social experiment when amateurs will run the biggest economy in Europe. The secret of German success was always in excellent engineering (industry) and order (social agreement). Both cornerstones will be deposed and the decay of the German economy will be dramatic with negative social consequences. I hope that Germany will compete in this race with the US - recognized leader of self-destruction.
4/22/21
МОК запретил вставать на колено во время Олимпийских Игр
Надеюсь чернокожие американцы откажутся от участия в этих ксенофобских и расистских соревнованиях, а остальные развитые страны их поддержат. Недопустимо ограничивать права угнетенных.
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