Двестиграм (немедленно)

Я открыл новый блог Двестиграм (dvestigramm.blogspot.com) с лозунгом "немедленно" и собираюсь  ссыпать в него ссылки на понравившееся мне видео из youtube.  Совмещение собственных постов и ссылок на чужие не кажется мне правильным, хотя и увеличивает количество просмотров. 

Richard Feynman on Pseudoscience

История России в 20 веке в одной кривой изменения численности населения: Германия проиграла две войны, но, вероятно, убила СССР, убив его граждан

Реальный экономический рост и социальный прогресс в решающей степени зависят от притока нового населения трудоспособного возраста, то есть людей в возрасте 15-19 лет. Это не только механическое замещение старого (от 60 до 64 лет) работающего населения, но и внедрение новых идей товаров / услуг и методов работы, усвоенных в процессе школьного / университетского образования. История России в 20 веке является ярким примером влияния таких процессов демографической депопуляции на экономическую и социальную эволюцию. 

На рисунке 1 представлены кривые, описывающие ежегодное изменение численности населения в возрасте от 15 до 19 лет по данным ОЭСР. Исходные данные охватывают период с 1960 по 2018 год (красная линия). Чтобы восстановить временные ряды в прошлом и экстраполировать их в будущее, можно использовать популяции разного возраста и сдвигать их по разнице в возрасте. Например, мы берем население в возрасте от 5 до 9 лет, сдвигаем его на 10 лет вперед (зеленая линия) и получаем оценку на следующие 10 лет. Близость красной и зеленой кривых до 2018 года как раз подтверждает правильность такого подхода - отклонения намного меньше амплитуды кривых. Для оценки в прошлом мы сдвигаем оценку населения между 70 и 74 годами и получаем относительно точную оценку вплоть до 1910-х годов. Разница амплитуд в прошлом больше из-за потери популяции с возрастом, но можно также подогнать амплитуду, введя некоторый компенсационный коэффициент. Здесь мы этого не делаем. 

История российского населения (кривая синхронизирована с 17-летним возрастом - центром возрастной группы от 15 до 19 лет) пугает - есть несколько глубоких провалов в росте населения, которые должны были иметь крайне негативное влияние на страну и общество. Первый провал (отрицательный прирост населения) наблюдается между 1931 и 1938 годами, с минимальным значением в 1935 году. Этот пик определенно связан с Первой мировой войной и гражданской войной. Глубочайший провал 1935 года должен быть результатом наиболее интенсивной фазы гражданской войны 1917-1920 годов, но начало спада связано с началом Первой мировой войны. Любой пик депопуляции создает волны депопуляции в будущем как результат отсутствия населения, дающего жизнь следующему поколению. Такие волны наблюдаются у населения стран с наибольшими потерями в Первой и Второй Мировых Войнах. Для России восстановление молодого населения, начавшееся в 1940 году, было прервано началом Второй мировой войной, и падение годового прироста числа 17-летних (средний возраст для населения в возрасте 15-19 лет) началось в 1945 году, а самое резкое снижение наблюдалось в 1949 году. Этот провал не связан со глубоким спадом 1935 года, а только с ВОВ. Таким образом, эти два глубоких популяционных провала, разделенных 15 годами, вызвали череду волн депопуляции с периодом около 25 лет, что, вероятно, является возрастом пика рождаемости для населения в России.

 

Следующий спад наблюдался примерно в 1960 г. (отрицательный пик в 1961 г.), а амплитуда падения определяется синхронизированным действием депопуляции в 1930-е годы и отсутствием нормальной рождаемости во время Второй мировой войны. Обе волны депопуляции сделали спад очень глубоким, но по длительности он был не самым страшным. Следующее падение началось в середине 1970-х и продлилось до 1980-х годов. Это падение длилось не менее 15 лет, потому что волны 1930-х и 1940-х годов сошлись с интервалом 10 между пиками. Это был период, когда СССР был разрушен из-за серьезных экономических проблем, вызванных отсутствием «свежей крови», столь необходимой для реального роста и технического прогресса. Германия проиграла Первую и Вторую мировые войны, но потери населения в этих войнах были смертельными для развития СССР. 

В XXI веке глубокое и длительное (17-летнее) падение населения произошло в России в период от 2004 до 2018 года. Это прямое следствие падения между 1977 и 1988 годами, т.е. возникла структура, объединяющая две волны депопуляции: в Первую мировую и ВОВ. К счастью, в период действия этих негативных волн цены на нефть были высокими, и экономическая и социальная структура не пострадала в такой степени, как в 1980-е годы. Следующая волна депопуляции в России наступит в 2035-2040 годах.

Интересно, что появление либеральных идей хорошо коррелирует с падением численности населения. Во время роста населения консервативные идеи, вероятно, более привлекательны. 

 

Рисунок 1. Годовой прирост числа людей в возрасте от 15 до 19 лет, полученный из таблицы численности населения ОЭСР за период с 1960 по 2018 год.

The history of Russia in the 20th century in one population curve: Germany lost two wars but likely finally killed the USSR

Real economic growth and social progress critically depend on the influx of new working-age population, i.e. people of 15-19 years of age. This is not only mechanical replacement of old (above 60 to 64 years of age) working population but also the introduction of new goods/services ideas and methods of work learned in the school/university education process. The history of Russia in the 20^th century is an extreme example of the influence of such population/depopulation processes on the economic and social evolution. 

Figure 1 presents several curves describing the annual change in the population between 15 and 19 years of age as reported by the OECD. The original data cover the period between 1960 and 2018 (red line). In order to recover the time series in the past and to project them into the future, one can use populations of different ages and shift them by the age difference. For example, we take the population between 5 and 9 years of age, shift it by 10 years ahead (green line), and obtain an estimate for the next 10 years. The closeness of the red and green curves before 2018 just supports the accuracy of such an approach – the deviations are much smaller than the amplitude of the curves. In the past, we shift the population between 70 and 74 years and obtain a relatively accurate estimate down to the 1910s. The difference of amplitudes in the past is larger because of the population loss with age but one can also fit the amplitude by an introduction by some compensation factor. We do not do that here. 

The history of the Russian population (the curve is synchronized with 17 years of age as the center of the 15 to 19 years of age range) is shocking – there are several deep depopulation troughs, which must have an extremely negative influence on the country and society.  The first trough (i.g. negative population growth) is observed between 1931 and 1938 with the bottom around 1935. This peak is definitely related to WWI and the civil war. The bottom in 1935 should be the result of the most intensive phase in the civil war in 1917-1920, but the start of the trough is related to the beginning of WWI. Any depopulation peak creates depopulation waves in the future as a reflection of the absence of the population giving birth to the next generation in the 20 to 30 years after the depopulation event. One can see such waves in the populations of the countries with the largest losses in WWI and WWII.  For Russia, the population recovery which started in 1940 was killed by WWII, and the fall in the annual increase in the number of 17-year-olds started in 1945 with a sharp bottom in 1949. This trough is not related to the trough in 1935 but only to WWII. Therefore, these two dramatic depopulation events separated by 15 years started two sequences of depopulation waves with a period of around 25 years – which is likely the peak of the birth rate for the population in Russia.   

The next trough was observed around 1960 (the fall peaks in 1961) and the amplitude of the fall is defined by the synchronized action of the depopulation trough in the 1930s and the absence of a normal birth rate during WWII. Both depopulation waves made the trough very deep, but it was not the worst trough in terms of length. The next fall started in the mid-1970s and extended into the 1980s. This fall was more than 10 years long because the waves from the 1930s and the 1940s came together with a 10 spacing between their peaks. This was the period when the USSR was deconstructed because of severe economic problems driven by the absence of “fresh blood” so needed for real growth and technical progress. Germany lost WWI and WWII but the population wounds from these wars were deadly for the USSR. 

In the 21^st century, the deep and long (17-year-old) population fall came to Russia in 2004 and extended into the second half of the 2010s. This is the direct aftermath (wave) of the fall between 1977 and 1988, i.e. the two-depopulation-wave structure originated in WWI and WWII. Fortunately, the oil price was high during these negative waves period and economic and social structure did not suffer to the same extent as in the 1980s. The next depopulation trough will come to Russia in 2035-2040. Russia is rising.

It is interesting that the emergence of liberal ideas is well associated with the depopulation troughs. During population growth, the conservative ideas are likely more attractive.

Figure 1. The annual increment in the number of 15 to 19 year-olds as obtained from the OECD population table for the period between 1960 and 2018

the US recovery is highly likely severely overestimated

On January 31, 2021, I published an accurate estimate of the actual GDP fall in the USA  - 21.7%.  This estimate was based on a simple quantitative analysis that most of the money in the government 2.5 trillion bill was poured into the economy and counted as if it came from economic activity. In reality, this money was just (electronically) printed (e.g. compensation to employees was dropped severely as a reaction to the fall in economic activity). The estimate of actual GDP growth is simple if one extracts the bill money and actual fall in economic activity – 3.5% of the nominal GDP. The original 22% is likely overestimates but the fall is definitely below 15%.

One of the features revealing the great fraud was an outstanding growth in the personal income (PI), which was 1.05 of the GDP in Q2. This means that the economy generated more income than products and services. Figure 1 presents the ratio of PI and GDP, which includes also the 2021Q1. This makes me write this post. The new helicopter money injection in 2021Q1 has the same effect on the PI as in 2020Q2. This money has the same path to the GRP through “government social benefits to persons” and we not subtracted from the GDP.

The PI/GDP curve in Figure 1 is again above 1.0 indicating that the trick played in 2020 is in use again. The new 6.5% growth in 2021Q1 is overestimated by the volume of printed money – seems to be 2 trillion and thus the real GDP fell by around 4% in 2021Q1 and the nominal GDP by 7%. The most important message is that the US economy in a deep economic crisis in the first quarter. The recovery does not go well and the helicopter money allows hiding the actual fall by double counting. The last two quarters of 2020 demonstrated some optimism in an economic recovery but the Biden administration failed to support the recovery.  

Figure 1. PI/GDP ratio. 

Figure 2. Ratios revealing the printed money transfer from the government to personal income.

 

 

Open letter of French soldiers - "risk fo civil war".

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. 

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.

Figure 1. Left panel: The change in the shape of mean income dependence on age from 1962 to 2013 as measured by the Census Bureau in the March Supplements of the Current Population Survey. All curves are normalized to their respective peak values. Right panel: Comparison of mean income dependence on age as measured by the Census Bureau (CPS) and the Internal Revenue Service (IRS). The only year with data available from the IRS is 1998. Redline – function approximating the IPUMS curve between 18 and 55 years of age. Blueline - function approximating the IRS curve above 56 years of age. 

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)<X_max, 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, C_v, one can write the following equation:           

4/3πR³C_vdT(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 4/3πR³C_v we obtain: 

dT(t)/dt =  Ũ – D̃T(t)/R                                                                                                (2) 

where Ũ=3U/(C_v4πR³) is the specific power of the heating sources expressed in units of thermal capacity, and D̃ = 3D/C_v. 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 L_M, 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.