Published on: **Mar 4, 2016**

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- 1. Modeling Control of Population Dynamics in Russia: Preliminary Analysis Andrey A. Krasovskii1 , Dmitry A. Pisarenko2 1 Institute of Mathematics and Mechanics, S.Kovalevskoi 16, Ekaterinburg, 620219, Russia E-mail: akrasovskii@gmail.com 2 Altruix Software Development e. U. Tichtelgasse 23-1, Vienna, A-1120, Austria E-mail: dp@altruix.co Abstract In our study we analyze the dynamics of Russian population from 1970 to 2000 using a stylized mathematical model of fertility and mortality controlled by a central planner. The focus of our research is in the demographic catastrophe in Russia start- ing in 1986. Statistical analysis of the data indicates the sharp decline in population growth in the period 1986-1992 which could hardly be explained by natural factors. We assume that the demographic catastrophe could be the result of a change in the policy of central planner. We propose a method- ology, which uses theory of control of dynamic system in order to explain the trends of real data. In the proposed model, the dynamics of population growth is subject to con- trolled diﬀerential equations. The controls stand for investments into fertility growth and mortality retention and have diﬀerent regimes. To interpret these controls, we associate them with investments into factors, which indirectly (through statistically correlated economic, social, cultural, etc. processes) aﬀect these demographic indicators. The main results show that there are four periods corresponding to various control regimes from 1970 to 2001: 1. Period of sustainable fertility growth and moderate mortality growth from 1970 to 1985. 2. Period of dramatic decline in investments, and, consequently, decrease in fertility and rise in mortality from 1986 to 1991. 3. Period of “Catching up”: from 1991 to 1998 – attempts at recovery of fertility and mortality retention. 4. Period of “stagnation”: from 1998 to 2001 – constant investments in fertility and mortality retention. Keywords: population dynamics in Russia, data analysis, control design Materials relevant to the paper are available online: http://bit.ly/uUDSG5
- 2. 1. Introduction The aim of this paper is to propose a hypothesis that population growth in Russia could be controlled by central planner. We apply a control model to analyze the data on Russian population dynamics in the time period 1970-2001. This approach uses the methodology proposed for data analysis by means of mathematical models of control in [8], [5]. Unlike these papers we do not consider the optimal control problems in our study, but provide possible control policies which could impact the dynamics of demographic factors in such a way, that the resulting dynamics is determined by various control regimes. Similar analysis is done in the paper [6] for analysis of trends of mobile phone industry in Japan. We model the dynamics of fertility and mortality functions using controlled nonlinear diﬀerential equations. The available data in the analysis are given with respect to time, and no age distributions are available. For this reason we consider an aggregated time dependent model. This diﬀerentiates our research from most de- mographic studies, in which age distribution plays an important role in the analysis (see, i.e., [4] and [1]). The main thesis of our study is that mortality and fertility, and, consequently, population dynamics could be subject to control policy of a central planner. We interpret control as investments in factors which are highly correlated with mortality and fertility. We identify these factors by correlation analysis of data on twenty three indicators available for the period in question. Based on this analysis we choose social, health, and economic factors which have a coeﬃcient of correlation with considered demographic indicators higher than 0.88. Let us note that a similar type of control – investments in human capital – is modeled in the paper [9] to study dynamics of labor force in model of optimal economic growth. To verify the approach we make simulation of the proposed control model and compare outcome with real data. The main results are connected with proposition of four control regimes for four time periods. These periods are the same for fertility and mortality. The model helps to explain the so-called “demographic catastrophe” of 1986-1991 in Russia by the high decrease in investments during this period. It is also shown that in order to return the country to the pre-crisis fertility rates, much more investments are needed. Another interesting feature is the delay eﬀects in the dynamics of fertility and mortality. Namely, the decrease in investments plays its role in a long run, the growth rates could be negative even if investments are high at present. It seems that the model is reasonable and can be used for future studies including optimization approaches. The structure of the paper is the following. In Section 2. we present a formal mathematical model for the control design. We propose that for the fertility and mortality dynamics there are four control regimes leading to four periods of popu- lation growth. In Section 3. we provide comparison results of synthetic trajectories with real data. In Section 4. we present results of correlation analysis which justify that the fertility rate could be controlled by investments in diﬀerent social and cul- tural factors. In Section 5. the same analysis is presented for the possible policies on the mortality retention. In Section 6. we provide results of statistical analysis and data sources. Conclusions are presented in Section 7..
- 3. 2. The Control Design Our stylized model can be thought of as a control panel with two “knobs”: 1. Fertility. We assume the initial level of investments in fertility to be such that there is zero fertility growth. Depending on the increase or decrease in the investment policy, this level changes from positive to negative. Thus, one can imagine a control “knob”. The central planner can turn it to the left (fertility decreases), or to the right (fertility increases). He can also change the speed of the fertility growth (decay), by turning the knob faster or slower. 2. Mortality retention. We assume that there is a natural positive mortality rate, when there are no investments in mortality retention. One can mention that the longevity of ex- pected lifetime is connected with development of science, social and medical services subject to governmental investments. If there are no such investments, the mortality grows. Thus, we consider a second “knob”, which deﬁnes the level of the mortality retention. Turning the “knobs” increases/decreases the investment policy which indirectly (through various factors) inﬂuences the corresponding parameter. In this section we present the formal mathematical model of the possible control regimes. In our study the time t is divided in four intervals: t ⊂ [t0, t1] ∪ [t1, t2] ∪ [t2, t3] ∪ [t3, t4]. (1) 2.1. Modeling Control of Fertility We assume that the control policy could impact the fertility rate through the in- vestments in health, social and cultural sectors. In Section 4. correlation results for the main factors are given with comments. Thus, our idea is that there is a central planner who determines the policy. We restrict ourselves to a few control regimes hoping that it would help to construct in future an advanced model with optimization tasks. In our stylized model we start with the investments level at which the fertility rate is zero. For simplicity we denote this level by zero as it could be named “no stimulation” control. In the paper we consider only time-dependent population due to fact that avail- able data is given only with respect to time. This restriction does not allow us to apply age-distributed dynamics as in many studies of population mathematics. Assume that the fertility evolves according to the diﬀerential equation: df dt = u(t)f(t), f(t0) = f0, t0 ≤ t ≤ t4, (2) where f denotes fertility, u stands for control, and f0 is the value of fertility at initial time t0. Thus, the control determines the rate at which the fertility grows or declines each year. We ﬁx the initial time t0 = 0 at the ﬁrst year of our analysis (year 1970). Using equation (2) we model diﬀerent control regimes to catch the data trends. We propose four regimes for investments in fertility.
- 4. Regime of constant investments in fertility Based on the data analysis we assume that in the ﬁrst period the investment policy in fertility is constant u(t) = u1 = const, and provides sustainable growth. During this period, fertility is subject to exponential growth: f(t) = f0eu1(t)t , u1(t) = u1 = const, t0 ≤ t ≤ t1, (3) where t1 is the end of the ﬁrst period. During this period fertility grows to the value ˆf1 = f(t1). Regime of declining investments in fertility In the second period we assume that the investment policy is declining with constant rate α > 0, and the control dynamics is described by equations: df dt = u2(t)f(t), f(t1) = ˆf1, du2 dt = −α, u2(t1) = u1, t1 < t ≤ t2. (4) Here u2 = u2(t) is the control policy, α > 0 is the rate of cutting down the investments, and t2 is the end of the second period. Thus, during this period, the growth rate of fertility declines to n = u1 − α(t2 − t1). (5) The fertility becomes equal to ˆf2 = f(t2). Regime of increasing investments in fertility In the third period, the central planner tries to improve the fertility and chooses a policy contrary to the previous period. Namely, he invests more each year with some constant linear rate β > 0. Of course, it is more diﬃcult to increase the investments than to cut them, and 0 < β < α. The third period is described by the equation df dt = u3(t)f(t), f(t2) = ˆf2, du3 dt = β, u3(t2) = n, t2 < t ≤ t3. (6) where n is given by equation (5), u3 = u3(t) is the control policy, and t3 is the end of the third period. After the third period fertility rate is equal to n∗ = n − β(t3 − t2). (7) The fertility takes the value ˆf3 = f(t3).
- 5. Regime of ﬁxed investments in fertility In the fourth period the central plan- ner stops the increase in investments as the fertility reaches some positive growth rate. Namely, the central planner ﬁxes the investments policy on the level n∗ (7. df dt = u4(t)f(t), f(t3) = ˆf3, u4(t) = n∗ , t3 < t ≤ t4. (8) where n∗ is given by equation (7), u4 is the control policy, and t4 is the end of the third period. 2.2. Modeling Control of Mortality To model the mortality we assume that there is some ﬁxed mortality growth rate. If nothing is done to decrease this rate, the mortality grows exponentially with constant rate m > 0. Thus, the control policy can be deﬁned as the instrument for the mortality retention. We propose the following dynamics: dµ dt = (m − v(t))µ(t), µ(t0) = µ0, (9) where µ denotes mortality, v stands for the control, and µ0 is the initial value of mortality. Again, one can claim that control function is associated with investments in factors which help to prevent high rate of mortality. These factors are discussed in Section 5.. Similar to the case with fertility, we divide the control v = v(t) in four regimes. Switching between these regimes we obtain four periods of mortality dynamics. Regime of intensive investments in mortality retention In the ﬁrst regime the investments in mortality retention are constantly increased with the linear rate γ > 0. This period is described by the equation: dµ dt = (m − v1(t))µ(t), µ(t0) = µ0, dv1 dt = γ, v1(t0) = v0, t0 ≤ t ≤ t1, (10) where v1 = v1(t) stands for a control, µ0 is the initial value of mortality, and v0 is the initial value of mortality retention. At the end of this period the mortality equals ˆµ1 = µ(t1). The investments increase to the value: ˆv1 = v0 + γ(t1 − t0). (11) Regime of decreasing investments in mortality retention In this period the investments in mortality retention are constantly decreased with the rate δ > γ > 0. This period is subject to the equation:
- 6. dµ dt = (m − v2(t))µ(t), µ(t1) = ˆµ1, dv2 dt = −δ, v2(t1) = ˆv1, t1 < t ≤ t2. (12) where v2 = v2(t) stands for control, ˆv1 is given by (11). During this period the mortality rate grows to the value: ˆv2 = ˆv1 − δ(t2 − t1), (13) and mortality equals ˆµ2 = µ(t2) Regime of increasing investments in mortality retention In this period, the mortality retention is improved by increasing investments with the rate 0 < ε < γ. This period is described by the equation: dµ dt = (m − v3(t))µ(t), µ(t2) = ˆµ2, dv3 dt = ε, v3(t2) = ˆv2, t2 < t ≤ t3. (14) Here v3 = v3(t) stands for the control, ˆv2 is given by (13). After the third period investments policy have the value m∗ = ˆv3 = ˆv2 + ε(t3 − t2), (15) and mortality equals ˆµ3 = µ(t3) Regime of ﬁxed investments in mortality retention Similar to the fertility investments in the last period, control is ﬁxed on a positive level reached in the previous period. The dynamics is given by the equation: dµ dt = (m − v4(t))µ(t), µ(t4) = ˆµ3, v4(t) = m∗ , t3 < t ≤ t4. (16) m∗ is given by (15). 2.3. Modeling Population Dynamics To model the dynamics of total population we apply the following ODE: dN dt = (f(t) − µ(t))N(t), N(t0) = N0, t0 ≤ t ≤ t4, (17) where N is the number of people, N0 is the initial size of the population. Thus, population growth is subject to the natural growth rate times the current size of the population. Equation (17) is similar to the McKendrick equation for the age-distributed systems (see [4]). We integrate equation (17) starting with the initial value for population in 1970. Comparison results with real data are presented in the next section.
- 7. 3. Simulation and Veriﬁcation of the Model We simulate the control policy described in section 2. to construct the synthetic trajectories of fertility and mortality from 1970 to 2001. 3.1. Simulation Results The following values are used in modeling. Time periods: t0 = 0, t1 = 16, t2 = 21, t3 = 28, t4 = 31. Parameters of fertility control: f0 = 14.62, α = 0.045, β = 0.035. Parameters of mortality retention control: µ0 = 6.21, m = 0.06, γ = 0.0045, δ = 0.02, ε = 0.0115. Let us note that the time t0 stands for the ﬁrst year of analysis 1970. Diﬀerential equations proposed in Section 2. are integrated numerically with a small time step ∆t = 0.0001. The results of modeling controls of fertility and mortality retention are given in Figure 1. 3.2. Veriﬁcation of Results The comparison results for the synthetic trajectories of fertility and mortality and real data are presented in Figure 2. One can see that the synthetic trajectories follow the trends of real data adequately. We divide the entire period into 4 phases: 1. Stable fertility growth and moderate mortality growth from 1970 to 1986. 2. Dramatic decline in investments, and, consequently, decrease in fertility and rise in mortality from 1986 to 1991. 3. Catching up: From 1991 to 1998 – recovery of fertility and attempts at mortality retention. 4. Period of “stagnation”: from 1998 to 2001 – constant investments in fertility and mortality retention. Each of these phases is associated with diﬀerent positions of the fertility and mor- tality retention control “knobs”. The graph of population dynamics generated by synthetic trajectories of fertility and mortality according to equation (17) is depicted in the Figure 3. The results show that although the investments in fertility and mortality increase from 1991 to 1998, this is still not enough to change the situation to pre-1986 levels. Scenarios proposed by the model show that due to crisis in 1998 investments are ﬁxed on some positive levels. Although these investment levels are positive and even larger than pre-crisis levels (before 1986) in the case of fertility, still, they are not large enough to provide signiﬁcant improvements in population dynamics. Based on the model, one can make projections depending on the chosen control regimes. According to the model, it is clear that the increase in the investments could lead to high beneﬁts in population dynamics. 4. Interpretation of Fertility Control In this section we show, what parameters represent the fertility “knob” (control) in the real world. As the controlling body (central planner) one can think of Soviet Politburo (1970-1985) and the network of transnational corporations (see [10]). We take here all those parameters which – have a high correlation with fertility and
- 8. – the central planner has control of. Statistical results are given in Section 6.. These parameters are: 1. The rate of setting up new hospitals 2. The rate of setting up of new kindergartens 3. The rate of setting up of new polyclinics 4. Number of theater visits The central planner can inﬂuence all of these parameters by investing more or less money into the respective area (particularly in the central-planned Soviet Union at the end of 1980es). Imagine a woman, who thinks whether or not to get pregnant. If she is a rational economic agent, she considers the most: 1. the possibility of a healthy birth (the number of hospitals in her city), 2. the ability to pursue career with a child (the availability of kindergartens), and 3. the chance to get qualitative medical service for her and the child (availability of polyclinics). It is quite natural that statistical analysis shows that time series on these factors highly correlate with fertility. To interpret the high correlation of theater visits with fertility, we propose the following informal assumptions: 1. Humans are the more likely to have children, the higher degree of physical and mental wellbeing they are experiencing. 2. Physical wellbeing is biological health. 3. Spiritual wellbeing is determined by the ability to satisfy their mental demands, including the demand for intellectual entertainment. Number of theater visits can be an indicator of spiritual wellbeing of people. A person, who is physically healthy, but has no idea about how to live an interesting life is less likely to have good relationships with the opposite sex, and, consequentially, is less likely to give birth to children. If there are enough opportunities of intellectual entertainment (like theaters), the intellectual needs of people are satisﬁed to a higher degree, and they are more likely to engage in relationships with the opposite sex and give oﬀspring. 5. Interpretation of Mortality Retention Control The mortality retention “knob” in our research is represented in the reality by parameters, which can be divided in two groups: 1. Economic mortality factors. 2. Spiritual mortality factors. Statistical results are given in Section 6..
- 9. 5.1. Economic Mortality Factors We restrict our study to the following economic mortality factors: 1. Degree of income stratiﬁcation. 2. Level of industrial production. 3. Production of “kvass”. These variables can be controlled by the central planner. In the end of 1980es, Soviet economy faced the fall of industrial production (item (1) in the list above) without developing enough in other sectors. As a result, the majority of the popu- lation started to get poorer. In a sense, “poverty” means worse medical treatment (or no treatment at all) and increases the probability of getting sick, or die earlier (before expected lifetime). Decrease of the industrial production has two eﬀects on mortality. First, it leads to a “crisis” for individual: less money, worse food, worse medical treatment, more stress. Second eﬀect is a psychological one. People are happy when they produce something useful for others. When suddenly their work is not needed any more (they are ﬁred, or their factory is closed down), they either need to re-orient themselves in the new circumstances (which most people are not able to do in short term), or they experience constant distress. This increases the chances of getting ill and mortality. Thus, it is not a surprise that factors (1) and (2) correlate with mortality. The interesting statistical result is that production of “kvass” correlates well with mor- tality. “Kvass” is a light-alcoholic beverage: overall, the alcohol content is low (0.05 % - 1.0 %). One of reasons is that if its production falls, it may be substituted by stronger (less healthier) drinks like beer, wine and vodka which impact the health of the individual. On may also note an interesting citation from the article [7]: “Not so long ago Russians were drinking from 60 to 100 liters of kvass a year per capita. One might think that this fondness has a simple explanation: Kvass is invigorating and refreshing, quenches the thirst and has a good taste and aroma. But it should not be thought that these external qualities were all that attracted the attention of Russian doctors just at the time when the art of kvass brewing was starting to vanish with the development of capitalism in our country. At the turn of the century the Russian Society for Public Health took the manufacture of this ancient drink under its protection. The special production of “hospital kvass” an integral part of the diet, was organized in hospitals and inﬁrmaries”. 5.2. Spiritual Factors of Mortality We consider the following spiritual factors of mortality: 1. rate of homicides; 2. rate of suicides; 3. number of theatre visits; 4. number of books printed; 5. number of letters sent.
- 10. 5.3. Constructivist Nation-Builing as a Basis for Interpretation One can interpret the high correlation of the indicated spiritual factors with mor- tality along the lines of constructivist approach to nation-building as explained in [3]. Assuming that people are “social animals”, their well-being is determined by 1. the well-being of the individual and 2. the well-being of the people (nation) the individual belongs to. I.e. if the material and immaterial needs of the individual are satisﬁed, but the people as a whole experiences distress, the individual will feel distress as well. A nation is a social group, members of which have common 1. core values and 2. idea of the history. Inside the nation there are groups. For example, the Russian people consists of over 100 distinct nationalities. There are connections between 1. the diﬀerent groups inside the nation (“large” connections) and 2. between individuals (“molecular” connections). Every nation has a spiritual genotype – a set of core values. When the indi- viduals live according to these values (and design their economy and technology accordingly), they experience social well-being. If the individuals are forced to give up their original values, they experience distress. We cannot directly measure the degree of spiritual ill-being, but we can measure its eﬀects. There is an opinion that starting from 1985 (Gorbachev’s accession to power) Soviet government began 1. to impose (via mass-media) new values (individualism, proﬁt-orientation, ma- terialism, feminism) to Russian nation, 2. to discredit Soviet ones (idealism, collectivism) and 3. to blacken some achievements of Russian civilizations (falsify Russian/Soviet history). A detailed account of the ways, in which Russian culture was attacked by the Soviet/Russian elite can be found in [3]. 5.4. Rate of Homicides and Suicides: a Proxy for Psychological Assaults In the period 1991-2000 growth of mortality is highly correlated with the growth of murders and suicides. This growth could be explained by the transformation of the country, and by the impact of the media and the authorities, which led the people to distress. People may react diﬀerently to the same source of distress – by an increased probability of getting ill, or dying faster. Another feature of this period is a growth of crime and consequently number of murders.
- 11. 5.5. Books and Theatres: Intellectual Needs A human being has not only biological, but also intellectual needs. The degree, to which these needs are satisﬁed, could be represented by the time series for circulation of books and theatre visits. An informal explanation may look like this. Imagine a factory worker or clerk, who spends the largest part of his or her time doing boring things in a job. When people work hard without a clear purpose (as most employees do), they get tired and experience distress. Intellectual entertainment – like reading books and attending theater shows – cures these people from that distress. One can say that intellectual entertainment is the only thing that makes the living of people in boring jobs enjoyable. It drains boredom distress out of the organism. When this source of joy and energy is removed (books become inaccessible and theaters close down), these people cannot take out boredom distress out of their organisms any more, and that distress makes them more prone to sickness and death. 5.6. Number of Letters Sent: “Molecular” Connections Inside a Social Group There remains the number of letters and its high negative correlation with mortality. Above we assumed that a nation as a social group consisting of individuals, which are connected with each other through “molecular” bonds (telephone calls, letters, telegrams, e-mail, social media etc.). If nation’s elements (individuals) cease to communicate with each other, the nation disintegrates to a heap of isolated individuals. Those isolated individuals now perceive themselves as lost in the universe, facing troubles of the world completely alone. This imposes psychological pressure on them, which increases the probability that they get sick and die. One might argue that letters have been substituted by a diﬀerent communication medium, but this statement can be refuted by the following facts: – We can exclude pagers, cellular phones and Internet, since they almost didn’t exist in Russia in the late 1980es and early 1990es. – Time series of telegrams and phone calls indicate that their number fell as well in that time period. Their number would have risen, if they had substituted the letters. 6. Data Sources and Correlation Analysis Our investigation is based on diagrams taken from [2]. They, in turn, are derived from the following sources:
- 12. No. Source 1 Annual reports “Economy of the RSFSR”. Central Statistical Di- rectorate of the RSFSR, Goskomstat of RSFSR, Moscow. 2 “Russian statistial yearbook. Oﬃcial edition”. Goskomstat of Rus- sia, Moscow. 3 Statistical compendium “Healthcare in the Russian Federation”, Goskomstat of Russia, Moscow, 1993. 4 Statistical compendia “Demographic yearbook of Russia”, Goskomstat of Russia, Moscow. 5 Government report “On the state of health of the population of Russian Federation in 1992”, Ministry of healthcare of RF, Russian Academy of Medical Sciences and State Sanitary Inspec- torate, Moscow, 1993. 6 Government report “On the state of health of the population of Russian Federation in 1999”, Ministry of healthcare of RF and Russian Academy of Medical Sciences, Moscow, 2000. 7 Statistical compendium “Short-term economic metrics of Russian Federation”, Goskomstat of Russia, Moscow, April 2002. We use the R software for correlation analysis of data for mortality and fertility with data for other factors. In our analysis we used twenty three factors: 1. Rate of setting up of new kindergartens in RSFSR and RF,thousands of seats 2. Sales of vodka and distillery products (in natural units) in RSFSR and RF, millions of decalitres 3. Sales of wine in RSFSR and RF, millions of decalitres 4. Production of kvass in RSFSR and RF, millions of decalitres 5. Attendance of theatres in RSFSR and RF, millions of people 6. Production of ﬁctional ﬁlms in RSFSR and RF, pieces 7. Number of printed copies of journals in RSFSR and RF, millions of copies 8. Number of printed copies of books and brochures in RSFSR and RF, millions of copies 9. Income stratiﬁcation of the society in RSFSR and RF, ratio of the average income of the richest 10 % to the poorest 10 % 10. Volume of industrial production in RSFSR and RF (in comparable prices, 1980 = 100) 11. Number of people killed in car accidents on roads and streets of RSFSR and RF, thousands 12. Homicides and suicides, 1990-2010 13. Number of syphilis sickness cases of teenagers (15-17) in RSFSR and RF (num- ber of detected ill people per 100 000 of population) 14. Number of mail boxes, thousands 15. Number of letters sent in RSFSR and RF, billions 16. Number of telegrams sent in RSFSR and RF, millions 17. Number of provided inter-city and international phone calls, millions 18. Intensity of passenger transportation via public rail transport in RSFSR and RF, thousands of passenger-kilometers per kilometer of railroad track 19. Setting up of new new hospitals in RSFSR and RF, thousands of beds 20. Setting up of new new hospitals in RSFSR and RF, thousands of beds
- 13. 21. Consumption of meat and meat products per capita and year in RSFSR and Russia, kg 22. Consumption of milk and dairy products (converted to milk) per capita in RSFSR and Russia, kg 23. Setting up of new new polyclinics in RSFSR and RF, thousands visits per shift To identify factors highly correlated with fertility and mortality, we analyze data on time series for these indicators. We are interested in factors which have correlation coeﬃcient with fertility/mortality larger than 0, 88. 6.1. Factors Highly Correlated with Fertility Four factors have the highest correlation with fertility. These four factors are pre- sented by time series from 1980 to 2000 and are listed below: – Setting up hospitals, Thousands of beds – Visits to theatres, Millions of people – Setting up kindergartens, Thousands of places The results of correlation analysis are given on Figure 4. 6.2. Factors Highly Correlated with Mortality We specify the following factors highly correlated with mortality available in time series from 1980 to 2000: – Letters sent, Billions – Circulation of published books and brochures, Millions of copies – Visits to theatres, Millions of people – Production of “kvass”, Millions of decaliters – Volume of industrial production, Comparable prices The results are depicted in the Figure 5. In addition we present three factors highly correlated with mortality from 1990 to 2001: – Murders and suicides, Per 100000 people – Income stratiﬁcation, Diﬀerentiation coeﬃcient The results are presented in Figures 6-7. 7. Summary In this paper we – formulated the hypothesis that the population dynamics of Russia could have been controlled by a central planner, – provided a mathematical model for this hypothesis, – veriﬁed the model, and – explained how our hypothetical control policy may have been implemented in practice. Our ﬁndings raise questions, which open up several future research directions:
- 14. – We investigated central-planned control of Russian population dynamics. Is pop- ulation dynamics of other countries (except China, where this happens oﬃcially) being controlled as well? – We investigated how the imaginary central planner may have controlled the population dynamics. But we did not answer the question why it happened in that way (four control regimes)? What ultimate goal had the central planner in mind? Could it be a solution to an optimal control problem? – If population dynamics control seems reasonable for a particular country, may it be reasonable on a regional (e. g. EU) level? – We assumed that spiritual factors aﬀect fertility and mortality in Russia, and supported this view with correlation analysis. Is this a purely Russian singu- larity, or do spiritual factors aﬀect population dynamics in other cultures as well? – Can we measure the impact of spiritual factors in a better way, for example, by measuring the correlation between the number of Internet searches of certain phrases (and/or mentions in Twitter) and monthly (weekly, daily) mortality? – It is important to make comparison analysis with possible control policies ap- plied to several countries, and with traditional projections on fertility and mor- tality. 8. Acknowledgments The authors express their gratitude to “Sektor 5”, Co-working Spaces Vienna, for providing excellent working atmosphere.
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- 16. Figure1. Controls of fertility and mortality with respect to “zero” level. Figure2. Fertility and Mortality Rates. Comparison Results.
- 17. Figure3. Synthetic population dynamics. Figure4. Correlation Results for Fertility.
- 18. Figure5. Correlation Results for Mortality. Part 1. Figure6. Correlation Results for Mortality. Part 2.
- 19. Figure7. Correlation Results for Mortality. Part 3.