A. Krasovskii, D. Pisarenko, Modeling Control of Population Dynamics in Russia: Preliminary Analysis

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: [email protected] Altruix Software Development e. U.

Tichtelgasse 23-1, Vienna, A-1120, AustriaE-mail: [email protected]

Abstract In our study we analyze the dynamics of Russian population from1970 to 2000 using a stylized mathematical model of fertility and mortalitycontrolled 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 inpopulation growth in the period 1986-1992 which could hardly be explainedby natural factors. We assume that the demographic catastrophe could bethe 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 explainthe 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 fertilitygrowth and mortality retention and have different regimes. To interpret thesecontrols, 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 arefour periods corresponding to various control regimes from 1970 to 2001:

1. Period of sustainable fertility growth and moderate mortality growthfrom 1970 to 1985.

2. Period of dramatic decline in investments, and, consequently, decreasein fertility and rise in mortality from 1986 to 1991.

3. Period of “Catching up”: from 1991 to 1998 – attempts at recovery offertility and mortality retention.

4. Period of “stagnation”: from 1998 to 2001 – constant investments infertility and mortality retention.

Keywords: population dynamics in Russia, data analysis, control design

? Materials relevant to the paper are available online: http://bit.ly/uUDSG5

1. Introduction

The aim of this paper is to propose a hypothesis that population growth in Russiacould be controlled by central planner. We apply a control model to analyze thedata on Russian population dynamics in the time period 1970-2001. This approachuses the methodology proposed for data analysis by means of mathematical modelsof control in [8], [5]. Unlike these papers we do not consider the optimal controlproblems in our study, but provide possible control policies which could impactthe dynamics of demographic factors in such a way, that the resulting dynamics isdetermined by various control regimes. Similar analysis is done in the paper [6] foranalysis of trends of mobile phone industry in Japan.

We model the dynamics of fertility and mortality functions using controllednonlinear differential equations. The available data in the analysis are given withrespect to time, and no age distributions are available. For this reason we consideran 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. Weinterpret control as investments in factors which are highly correlated with mortalityand fertility. We identify these factors by correlation analysis of data on twenty threeindicators available for the period in question. Based on this analysis we choosesocial, health, and economic factors which have a coefficient of correlation withconsidered 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 optimaleconomic growth.

To verify the approach we make simulation of the proposed control model andcompare outcome with real data. The main results are connected with propositionof four control regimes for four time periods. These periods are the same for fertilityand 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 isalso shown that in order to return the country to the pre-crisis fertility rates, muchmore investments are needed. Another interesting feature is the delay effects in thedynamics of fertility and mortality. Namely, the decrease in investments plays itsrole in a long run, the growth rates could be negative even if investments are highat present. It seems that the model is reasonable and can be used for future studiesincluding optimization approaches.

The structure of the paper is the following. In Section 2. we present a formalmathematical model for the control design. We propose that for the fertility andmortality dynamics there are four control regimes leading to four periods of popu-lation growth. In Section 3. we provide comparison results of synthetic trajectorieswith real data. In Section 4. we present results of correlation analysis which justifythat 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 policieson the mortality retention. In Section 6. we provide results of statistical analysisand data sources. Conclusions are presented in Section 7..

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 iszero fertility growth. Depending on the increase or decrease in the investmentpolicy, this level changes from positive to negative. Thus, one can imagine acontrol “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 fertilitygrowth (decay), by turning the knob faster or slower.

2. Mortality retention.We assume that there is a natural positive mortality rate, when there are noinvestments in mortality retention. One can mention that the longevity of ex-pected lifetime is connected with development of science, social and medicalservices subject to governmental investments. If there are no such investments,the mortality grows. Thus, we consider a second “knob”, which defines the levelof the mortality retention.

Turning the “knobs” increases/decreases the investment policy which indirectly(through various factors) influences the corresponding parameter. In this section wepresent 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 resultsfor the main factors are given with comments. Thus, our idea is that there is acentral planner who determines the policy. We restrict ourselves to a few controlregimes hoping that it would help to construct in future an advanced model withoptimization tasks.

In our stylized model we start with the investments level at which the fertilityrate is zero. For simplicity we denote this level by zero as it could be named “nostimulation” 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 toapply 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 atinitial time t0. Thus, the control determines the rate at which the fertility grows ordeclines 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 datatrends.

We propose four regimes for investments in fertility.

Regime of constant investments in fertility Based on the data analysis weassume 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 subjectto 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 thevalue f̂1 = f(t1).

Regime of declining investments in fertility In the second period we assumethat the investment policy is declining with constant rate α > 0, and the controldynamics is described by equations:

df

dt= u2(t)f(t), f(t1) = f̂1,

du2dt

= −α, u2(t1) = u1,

t1 < t ≤ t2. (4)

Here u2 = u2(t) is the control policy, α > 0 is the rate of cutting down theinvestments, and t2 is the end of the second period. Thus, during this period, thegrowth rate of fertility declines to

n = u1 − α(t2 − t1). (5)

The fertility becomes equal to f̂2 = f(t2).

Regime of increasing investments in fertility In the third period, the centralplanner tries to improve the fertility and chooses a policy contrary to the previousperiod. 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, and0 < β < α. The third period is described by the equation

df

dt= u3(t)f(t), f(t2) = f̂2,

du3dt

= 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 theend of the third period.

After the third period fertility rate is equal to

n∗ = n− β(t3 − t2). (7)

The fertility takes the value f̂3 = f(t3).

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 growthrate. Namely, the central planner fixes the investments policy on the level n∗ (7.

df

dt= u4(t)f(t), f(t3) = f̂3,

u4(t) = n∗, t3 < t ≤ t4. (8)

where n∗ is given by equation (7), u4 is the control policy, and t4 is the end ofthe 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 withconstant rate m > 0. Thus, the control policy can be defined as the instrument forthe 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 valueof mortality.

Again, one can claim that control function is associated with investments infactors which help to prevent high rate of mortality. These factors are discussed inSection 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 regimethe investments in mortality retention are constantly increased with the linear rateγ > 0. This period is described by the equation:

dµ

dt= (m− v1(t))µ(t), µ(t0) = µ0,

dv1dt

= γ, v1(t0) = v0,

t0 ≤ t ≤ t1, (10)

where v1 = v1(t) stands for a control, µ0 is the initial value of mortality, and v0is the initial value of mortality retention.

At the end of this period the mortality equals µ̂1 = µ(t1). The investmentsincrease to the value:

v̂1 = v0 + γ(t1 − t0). (11)

Regime of decreasing investments in mortality retention In this period theinvestments in mortality retention are constantly decreased with the rate δ > γ > 0.This period is subject to the equation:

dµ

dt= (m− v2(t))µ(t), µ(t1) = µ̂1,

dv2dt

= −δ, v2(t1) = v̂1,

t1 < t ≤ t2. (12)

where v2 = v2(t) stands for control, v̂1 is given by (11).During this period the mortality rate grows to the value:

v̂2 = v̂1 − δ(t2 − t1), (13)

and mortality equals µ̂2 = µ(t2)

Regime of increasing investments in mortality retention In this period, themortality 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) = µ̂2,

dv3dt

= ε, v3(t2) = v̂2,

t2 < t ≤ t3. (14)

Here v3 = v3(t) stands for the control, v̂2 is given by (13).After the third period investments policy have the value

m∗ = v̂3 = v̂2 + ε(t3 − t2), (15)

and mortality equals µ̂3 = µ(t3)

Regime of fixed investments in mortality retention Similar to the fertilityinvestments in the last period, control is fixed on a positive level reached in theprevious period. The dynamics is given by the equation:

dµ

dt= (m− v4(t))µ(t), µ(t4) = µ̂3,

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 forthe age-distributed systems (see [4]). We integrate equation (17) starting with theinitial value for population in 1970. Comparison results with real data are presentedin the next section.

3. Simulation and Verification of the Model

We simulate the control policy described in section 2. to construct the synthetictrajectories 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 analysis1970. Differential equations proposed in Section 2. are integrated numerically witha small time step ∆t = 0.0001.

The results of modeling controls of fertility and mortality retention are given inFigure 1.

3.2. Verification of Results

The comparison results for the synthetic trajectories of fertility and mortality andreal data are presented in Figure 2. One can see that the synthetic trajectoriesfollow 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 fertilityand mortality according to equation (17) is depicted in the Figure 3.

The results show that although the investments in fertility and mortality increasefrom 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 arefixed on some positive levels. Although these investment levels are positive and evenlarger than pre-crisis levels (before 1986) in the case of fertility, still, they are notlarge enough to provide significant improvements in population dynamics. Basedon 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 leadto 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 SovietPolitburo (1970-1985) and the network of transnational corporations (see [10]).

We take here all those parameters which

– have a high correlation with fertility and

– 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 orless money into the respective area (particularly in the central-planned Soviet Unionat the end of 1980es).

Imagine a woman, who thinks whether or not to get pregnant. If she is a rationaleconomic 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 (availabilityof polyclinics).

It is quite natural that statistical analysis shows that time series on these factorshighly correlate with fertility.

To interpret the high correlation of theater visits with fertility, we propose thefollowing informal assumptions:

1. Humans are the more likely to have children, the higher degree of physical andmental 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. Aperson, who is physically healthy, but has no idea about how to live an interesting lifeis 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 morelikely 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 byparameters, which can be divided in two groups:

1. Economic mortality factors.

2. Spiritual mortality factors.

Statistical results are given in Section 6..

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 leadsto a “crisis” for individual: less money, worse food, worse medical treatment, morestress. Second effect is a psychological one. People are happy when they producesomething useful for others. When suddenly their work is not needed any more (theyare fired, or their factory is closed down), they either need to re-orient themselvesin 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 andmortality.

Thus, it is not a surprise that factors (1) and (2) correlate with mortality. Theinteresting 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 bystronger (less healthier) drinks like beer, wine and vodka which impact the healthof 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 yearper capita. One might think that this fondness has a simple explanation: Kvass isinvigorating 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 theattention of Russian doctors just at the time when the art of kvass brewing wasstarting to vanish with the development of capitalism in our country. At the turnof the century the Russian Society for Public Health took the manufacture of thisancient drink under its protection. The special production of “hospital kvass” anintegral 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.

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 and2. 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 thepeople 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 and2. idea of the history.

Inside the nation there are groups. For example, the Russian people consists ofover 100 distinct nationalities.

There are connections between

1. the different groups inside the nation (“large” connections) and2. 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 technologyaccordingly), they experience social well-being.

If the individuals are forced to give up their original values, they experiencedistress.

We cannot directly measure the degree of spiritual ill-being, but we can measureits 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) and3. to blacken some achievements of Russian civilizations (falsify Russian/Soviet

history).

A detailed account of the ways, in which Russian culture was attacked by theSoviet/Russian elite can be found in [3].

5.4. Rate of Homicides and Suicides: a Proxy for PsychologicalAssaults

In the period 1991-2000 growth of mortality is highly correlated with the growth ofmurders and suicides.

This growth could be explained by the transformation of the country, and by theimpact of the media and the authorities, which led the people to distress. Peoplemay react differently to the same source of distress – by an increased probability ofgetting ill, or dying faster.

Another feature of this period is a growth of crime and consequently number ofmurders.

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 timeseries 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. Whenpeople work hard without a clear purpose (as most employees do), they get tired andexperience distress. Intellectual entertainment – like reading books and attendingtheater shows – cures these people from that distress.

One can say that intellectual entertainment is the only thing that makes theliving of people in boring jobs enjoyable. It drains boredom distress out of theorganism.

When this source of joy and energy is removed (books become inaccessible andtheaters close down), these people cannot take out boredom distress out of theirorganisms any more, and that distress makes them more prone to sickness anddeath.

5.6. Number of Letters Sent: “Molecular” Connections Inside a SocialGroup

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, whichare 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, thenation disintegrates to a heap of isolated individuals. Those isolated individuals nowperceive themselves as lost in the universe, facing troubles of the world completelyalone. This imposes psychological pressure on them, which increases the probabilitythat they get sick and die.

One might argue that letters have been substituted by a different communicationmedium, but this statement can be refuted by the following facts:

– We can exclude pagers, cellular phones and Internet, since they almost didn’texist in Russia in the late 1980es and early 1990es.

– Time series of telegrams and phone calls indicate that their number fell as wellin that time period. Their number would have risen, if they had substituted theletters.

6. Data Sources and Correlation Analysis

Our investigation is based on diagrams taken from [2]. They, in turn, are derivedfrom the following sources:

No. Source1 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 ofRussian Federation in 1999”, Ministry of healthcare of RF andRussian Academy of Medical Sciences, Moscow, 2000.

7 Statistical compendium “Short-term economic metrics of RussianFederation”, Goskomstat of Russia, Moscow, April 2002.

We use the R software for correlation analysis of data for mortality and fertilitywith 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 seats2. Sales of vodka and distillery products (in natural units) in RSFSR and RF,

millions of decalitres3. Sales of wine in RSFSR and RF, millions of decalitres4. Production of kvass in RSFSR and RF, millions of decalitres5. Attendance of theatres in RSFSR and RF, millions of people6. Production of fictional films in RSFSR and RF, pieces7. Number of printed copies of journals in RSFSR and RF, millions of copies8. Number of printed copies of books and brochures in RSFSR and RF, millions

of copies9. 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, thousands12. Homicides and suicides, 1990-201013. 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, thousands15. Number of letters sent in RSFSR and RF, billions16. Number of telegrams sent in RSFSR and RF, millions17. Number of provided inter-city and international phone calls, millions18. Intensity of passenger transportation via public rail transport in RSFSR and

RF, thousands of passenger-kilometers per kilometer of railroad track19. Setting up of new new hospitals in RSFSR and RF, thousands of beds20. Setting up of new new hospitals in RSFSR and RF, thousands of beds

21. Consumption of meat and meat products per capita and year in RSFSR andRussia, kg

22. Consumption of milk and dairy products (converted to milk) per capita inRSFSR 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 analyzedata on time series for these indicators. We are interested in factors which havecorrelation 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 timeseries 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 havebeen 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:

– 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 thepopulation dynamics. But we did not answer the question why it happened inthat way (four control regimes)? What ultimate goal had the central planner inmind? Could it be a solution to an optimal control problem?

– If population dynamics control seems reasonable for a particular country, mayit be reasonable on a regional (e. g. EU) level?

– We assumed that spiritual factors affect fertility and mortality in Russia, andsupported this view with correlation analysis. Is this a purely Russian singu-larity, or do spiritual factors affect population dynamics in other cultures aswell?

– Can we measure the impact of spiritual factors in a better way, for example, bymeasuring the correlation between the number of Internet searches of certainphrases (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, forproviding excellent working atmosphere.

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Figure1. Controls of fertility and mortality with respect to “zero” level.

Figure2. Fertility and Mortality Rates. Comparison Results.

Figure3. Synthetic population dynamics.

Figure4. Correlation Results for Fertility.

Figure5. Correlation Results for Mortality. Part 1.

Figure6. Correlation Results for Mortality. Part 2.

Figure7. Correlation Results for Mortality. Part 3.