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ECONOMETRIC MODELLING OF TIME SERIES RELATIONSHIP
BETWEEN FERTILITY AND INCOME FOR THE RUSSIAN POPULATION:
METHODOLOGICAL ISSUES
Oksana Shubat
Anna Bagirova
Ural Federal University
620002, Ekaterinburg, Russia
Email: [email protected]
Email: [email protected]
KEYWORDS
Regression models, time series, modelling, fertility,
income
ABSTRACT
Finding determinants of demographic processes is a
highly topical issue in countries with negative
demographic trends. Our research was aimed at
studying the relationships between fertility and income
indicators in Russia. The period under review was 2000
to 2016. To explore the correlation between the time
series, we used the methodology of estimating trend
deviation. We applied analytical smoothing to model
trends, estimating regression models. To assess the
strength of relationship between the time series, we
analysed correlation between regressions’ residuals. The
results of our analysis showed no relationship between
people’s incomes and fertility rates. The research we
carried out into time series dynamics did not confirm
the results of other studies based on static data.
Accordingly, this raises questions about the
methodology for analyzing the relationship between
dynamic processes with a high volatility of input data.
Evidently to receive reliable and stable results, multi-
dimensional analysis methods should be integrated into
the study of relationships between dynamic time series,
including preliminary multi-dimensional data
classification. This will enable carrying out analysis on
homogenous territorial or temporal segments, which
would be more methodologically sound.
INTRODUCTION
Finding determinants of demographic processes is a
highly topical issue in countries with negative
demographic trends, including today’s Russia.
Birthrates in Russia are significantly below the simple
reproduction rate. In Soviet times, the Total Fertility
Rate (TFR) reached this level, starting to decline in the
1980s. In 2000, the TFR was at its lowest at 1.195, just
56.9% of the replacement fertility rate. Despite the
positive dynamic of the TFR in Russia from 2001, the
pace of change is very slow and the potential for growth
has been exhausted. The adverse demographic situation
in Russia is exacerbated by low life expectancy and
high mortality rates.
Given these factors, studying demographic processes
to seek out determinants and develop robust forecasts is
highly topical. Fertility is of utmost importance, since it
determines natural population growth. However, this
demographic process provokes the most vigorous
scientific and political debate in Russia – questions
related to fertility determinants and ways to regulate it
remain unresolved.
The issues of the nature of the relationship between
fertility indicators and population income levels have
been the subject of scientific research by economists
and demographers since the 18th century. The nature of
the relationship between fertility and people’s wealth
has been evaluated with respect to different research
subject groups.
The first group compares fertility indicators for
territories (countries, regions and so on) with different
levels of incomes. For example, figure 1 shows a scatter
plot of the relationship between GDP levels and TFR in
different countries for 2015 (Fertility rate 2017; GDP
per capita 2017). The values on the plot suggest an
inverse relationship between these variables.
Figure 1: Correlation between GDP per capita and TFR
in different countries (Fertility rate 2017; GDP per
capita 2017)
The second group evaluates families/women with
different levels of income within the same region. For
example, in their study, Maleva and Sinyavksaya
identified that for Russian women, growth in income
0
2
4
6
8
0 50000 100000
To
tal
Fer
tili
ty R
ate
GDP per capita, $
Proceedings 32nd European Conference on Modelling and Simulation ©ECMS Lars Nolle, Alexandra Burger, Christoph Tholen, Jens Werner, Jens Wellhausen (Editors) ISBN: 978-0-9932440-6-3/ ISBN: 978-0-9932440-7-0 (CD)
was accompanied by a decline in the average number of
children per woman (Maleva and Sinyavskaya 2007).
This is shown in Figure 2, presented in decile groups of
women, clustered by income.
Figure 2: Average number of children per woman in
groups of women, clustered by income (Maleva and
Sinyavskaya 2007)
Finally, the third group comprises specific territories
(countries, regions) whose populations display changing
incomes and fertility rates. Recall Adam Smith’s words
that “poverty… seems even to be favourable to
generation” (Smith 1827:33). However, contemporary
researchers are cautious about declaring an adverse
relationship between income levels and birth rates
(Maleva and Sinyavskaya 2007). This is connected to
the fact that, for example, countries with similar
economic dynamics may show varying rates of inverse
fertility dynamics. Moreover, low fertility is observed in
countries with different levels of income across the
population.
Stopping short of making sweeping statements about
declining fertility due to growing incomes, researchers
highlight two reasons for the presumed relationship.
Firstly, as people’s incomes grow, potential parents
start to assign more value to the quality, rather than
quantity, of children. This entails greater investment
(money, work, time) in the quality of children’s human
capital (Lee and Mason 2010; Becker et al. 1990).
Understanding that their resources are finite, parents are
forced to choose between quantity and quality of
children and, in the context of a developed economy,
choose to improve the latter.
The second reason is related to restrictions that
children place upon their parents, first and foremost on
mothers. They are connected to, inter alia, the so-called
“motherhood wage penalty” – a drop in earnings that
follows childbirth. When people’s incomes are high,
this decline becomes more pronounced (Van Bavel
2010; Begall and Mills 2012). Additional adverse
factors include fewer opportunities for professional self-
actualisation and impediments to working mothers’
career development. For countries with developed
economies and high levels of income, these factors
undermine reproductive intentions and consequently
lead to a decline in birth rates.
Despite the fact that such reasons may drive
declining fertility in high-income countries, incentives
that seek to mitigate them are often monetary. In
particular, there is an existing stereotype in
contemporary Russia, that sufficient material resourcing
boosts fertility. This belief led to the introduction of the
so-called maternity capital initiative in 2007, which
seeks to boost income levels and guarantees for women
who decide to have a second child.
As such, despite extensive evidence of a lack of a
positive relationship between income and fertility, in
Russia, economic factors of life continue to be seen as a
key determinant of fertility. This sees the
implementation of corresponding demographic policy
measures, at a high cost to the state.
On the other hand, we believe that such a clearly
mistaken view could hardly have been placed at the
heart of Russia’s demographic policy. One could thus
suppose that the real determinant of fertility is not
economic conditions per se, as the way they are
perceived by people, for instance, through expectations
of future economic and social stability. From this
standpoint, maternity capital, as a way to improve
fertility, may be viewed not as a means of genuine
improvement of material welfare, but attention on the
part of the authorities to family matters and an
orientation towards family values, which in turn raises
people’s confidence in the future and creates certain life
guarantees.
In light of this, our research was aimed at studying
the relationships between fertility and income indicators
in Russia, as well as people’s subjective assessments of
their welfare.
DATA AND METHODS
For our study we used data on annual dynamics for time
series of socio-demographic indicators. The data was
sourced from World Bank and Russian Federal State
Statistics Service resources. The period under review
was 2000 to 2016, which was chosen for two reasons:
firstly, the availability of corresponding open-source
data and secondly, the comparability of indicators as
regards the span of the time series.
The analysis covered the following variables:
- Total Fertility Rate (TFR). The average number of
children that would be born per woman if all women
lived to the end of their childbearing years and bore
children according to a given fertility rate at each age.
TFR is a more direct measure of the level of fertility
than the crude birth rate, since it refers to births per
woman (Total Fertility Rate 2017).
- GDP per capita (constant 2010 US$). Gross
domestic product divided by midyear population. Data
are in constant 2010 U.S. dollars (GDP per capita 2017).
- Consumer confidence index – general, as well as
for women and men separately. A generalised index,
which is calculated on the basis of five individual
indices: past and expected changes to personal material
welfare; past and expected changes to the economic
0
0.4
0.8
1.2
1.6
1 2 3 4 5 6 7 8 9 10
Aver
age
nu
mb
er o
f ch
ild
ren
per
wo
man
Decile groups of women,
clustered by income
situation in Russia; favourability of conditions for
capital purchases.
These indices are calculated on the basis of data
obtained in the course of representative polls (Consumer
confidence index 2017).
- Coefficient of income differentiation. Characterizes
the degree of social stratification and is defined as a
ratio between the average levels of money income of 10
percent of the population with the highest income and
10 percent of the population with the lowest income
(Coefficient Gini 2017).
- Coefficient Gini – index of income inequality.
Characterizes the level of deviation of the actual volume
of distribution of income of population from the line of
their even distribution. The value of coefficient may
vary from 0 to 1, and the higher the value of the
indicator, the less even is the distribution of income in
the society (Coefficient Gini 2017).
We chose these variables as we sought to include
both objective and subjective indicators of people's
incomes. Objective variables included statistical
indicators of levels and variability of income; subjective
ones covered sociological indicators connected to
people's assessments of the economic situation as a
whole and their material welfare in particular. As such,
we tested three hypotheses in our research:
1. Birth rates are correlated with people's incomes
(in this hypothesis GPD per capita was used as an
objective indicator of people's incomes);
2. Birth rates are correlated with people's subjective
perceptions as regards their income and material welfare
(in this hypothesis the consumer confidence index was
used as the subjective measure of welfare levels);
3. Birth rates are correlated with the level of income
inequality across the population (in this hypothesis, we
used the coefficient of income differentiation and the
index of income inequality as fertility determinants).
To explore the correlation between the time series,
we used two approaches. The first one is the
methodology of estimating trend deviation. We applied
analytical smoothing to model trends, estimating
regression models for the stated time series. We used
Ordinary Least Squares as the method for estimating the
unknown parameters in regression models. To assess the
strength of correlations between the time series, we used
the Pearson correlation (based on a study of correlations
between residuals in regression models). The second
approach entailed assessing a multiple regression
model, where time was one of the explanatory variables.
Including the time variable into the model allowed
assessing the specificity of the influence of income on
the level of fertility, while excluding trend effects.
To test the hypothesis about the possible influence
of income on fertility growth we assessed the models
and tested for a correlation between the studied
variables using synchronized data, and also data about
income levels with one and two-year lags. The idea was
that fertility changes after a change in income, but not
straightaway, with some lag (for example, 1-2 years).
RESULTS
Studying the fertility time series showed that over the
course of the considered period, the growth of this
indicator was well-approximated by a linear trend. The
main results of modelling the total fertility rate trend are
shown in tables 1-2 (model 1). As the presented data
show, the quality of the approximation for the model is
very high with a determination coefficient in excess of
95%. All parameters of the equation are statistically
significant and show that between 2000 and 2016 the
total fertility rate in Russia grew 0.039 points on
average.
Studying GDP per capita dynamics showed that this
dynamic is best approximated by a quadratic function.
Yet the largest part of the initial data (2000-2013) fits
the ascending arc of the parabola, while the three most
recent years (2014-2016) showed a slight decrease in
Russia’s GDP per capita. However we do not consider it
appropriate to speak of an established adverse trend
toward a decline in people’s incomes. The main results
of modeling the trend for GDP per capita are shown in
tables 1-2 (model 2).
Table 1: Model Summary
(dependent variable: model 1 – TFR; model 2 – GDP
per capita)
Mo
del
R S
qu
are
Ad
just
ed R
Sq
uar
e
Std
. E
rro
r
of
the
Est
imat
e
F
Sig
.
1 0.959 0.957 0.042 355.143 0.000
2 0.966 0.961 352.287 197.296 0.000
Table 2: Coefficients
(dependent variable: model 1 – TFR; model 2 – GDP
per capita)
Model
Unstandardized
Coefficients t Sig.
B Std. Error
1 Constant 1.094 0.023 47.145 0.000
Years 0.039 0.002 18.845 0.000
2
Constant 5259.955 289.748 18.154 0.000
Years 819.624 74.103 11.061 0.000
Years^2 -27.474 4.001 -6.866 0.000
Given the growth in both the TFR and income levels
over a long period of time (2000 to 2013), we tested the
hypothesis of an existing correlation between these two
factors in the course of subsequent analysis. During this
period, their dynamics were well approximated by a
linear trend; hence we used a multiple linear regression
model. TFR was the dependent variable in the model,
while GDP per capita and time were predictors. The
main parameters of the model are shown in tables 3-4
(model 1). As the presented data show, no relationship
between TFR and GDP per capita was established – the
parameters of the equation were not statistically
significant.
Table 3: Model Summary
(dependent variable: TFR;
predictors: model 1 – GDP per capita;
model 2 – GDP per capita with a 1-year lag;
model 3 – GDP per capita with a 2-years lag)
Mo
del
R S
qu
are
Ad
just
ed R
Sq
uar
e
Std
. E
rro
r
of
the
Est
imat
e
F
Sig
.
1 0.950 0.941 0.041 104.333 0.000
2 0.939 0.928 0.046 84.323 0.000
3 0.937 0.925 0.047 81.463
Table 4: Coefficients
(dependent variable: TFR;
predictors: model 1 – GDP per capita;
model 2 – GDP per capita with a 1-year lag;
model 3 – GDP per capita with a 2-years lag)
Model
Unstandardized
Coefficients t Sig.
B Std. Error
1
Constant 1.338 0.146 9.159 0.000
GDP per
capita
-4.160E-
005 0.000 -1.703 0.117
Years .057 0.011 5.372 0.000
2
Constant 1.183 0.152 7.798 0.000
GDP per
capita
-1.732E-
005 0.000 -.607 0.556
Years .047 0.013 3.592 0.004
3
Constant 1.104 0.144 7.650 0.000
GDP per
capita
-2.428E-
006 0.000 -0.080 0.938
Years .040 0.015 2.783 0.018
Similar analysis with account of a possible lag effect
also did not confirm any correlation (models 2 and 3 in
tables 3-4). An analysis based on a study of the
correlation of residuals in regression models also did not
uncover any relationship between TFR and GPD per
capita in Russia. Pearson correlation coefficients were
not high, nor statistically significant (table 5).
Table 5: Correlations between TFR and GDP per capita
(model 1 – GDP per capita; model 2 – GDP per capita
with a 1-year lag; model 3 – GDP per capita with a 2-
years lag)
Model Indicator Value
1
Pearson Correlation -0.457
Sig. (2-tailed) 0.101
N 14
2
Pearson Correlation -0.180
Sig. (2-tailed) 0.538
N 14
3
Pearson Correlation -0.024
Sig. (2-tailed) 0.935
N 14
To test the hypothesis about the possibility that
people’s subjective perceptions about income and
material welfare influence fertility we studied time
series for consumer confidence indices. We analysed
three indices – general, male and female. The analysis
we carried out showed that between 2000 and 2016
these indices did not show a single development trend.
Until 2007, consumer confidence grew rather stably,
however this gave way to a period of high volatility
with a trend toward sharp decline (figure 3).
Accordingly, given the uninterrupted growth in TFR
throughout this period, the hypothesis about a
correlation between fertility and subjective ideas about
income levels and material welfare was not confirmed.
Figure 3: Dynamic of indices of consumer confidence
for the Russian population
To test the hypothesis about income inequality
possibly affecting fertility we studied time series of the
coefficient of income differentiation and the index of
income inequality. The completed analysis showed that
between 2000 and 2016 both indicators did not have a
single growth trend (figure 4). Thus before 2007 the
level of inequality in people’s income distribution grew,
-30
-20
-10
0
2000 2004 2008 2012 2016
Years
Consumer confidence index (general)
Consumer confidence index (for women)
Consumer confidence index (for men)
followed by a short period of stabilization and then
decline. As such, given the uninterrupted growth in TFR
throughout the same period, the hypothesis that fertility
and income inequality are correlated has not been
confirmed.
Figure 4: Dynamics of indicators for income
differentiation of the Russian population
DISCUSSION
The results of our analysis showed no relationship
between people’s incomes and fertility rates. We note
that this is a departure from the results of many other
studies (Maleva and Sinyavskaya 2007; Jones et al.
2011). We believe there could be a number of reasons
behind this.
1. There is considerable differentiation between
Russian regions as regards fertility rates and people’s
incomes. Table 6 presents data from 2016 to illustrate
this variability.
Table 6: Differentiation of incomes and fertility by
Russian regions
Indicators Min Max
Ratio
of max
to min
TFR 1.32 3.35 2.54
Coefficient of income
differentiation 4.7 7.6 1.62
GDP per capita
(rubles) 116007 2047998 17.65
We note that such differentiation is observed over
the entire period we analysed. This highlights an
important methodological problem as regards the
appropriateness of using average values for analysis.
Indeed, given the volatility of input data for income and
fertility that characterize the overall situation in the
country, they can hardly be considered valid indicators.
This in turn may be why similar types of research
(fertility and income, fertility and GPD per capita),
which uses time series of nationwide indicators as
variables, often contradict one another.
One possible way out could be analysis conducted
for a single period but for different regions, or for
groups of people with different incomes. It is worth
noting that the results obtained in different studies of
this kind are also rather contradictory. For instance, the
aforementioned Maleva and Sinyavskaya noted a
negative correlation between income and the number of
children for Russian women (Maleva and Sinyavskaya
2007). At the same time, Konig identified that in
Hungary high earnings strengthened women’s
reproductive intentions (whereas in Germany, for
example, the correlation was much weaker) (Konig
2012). Moreover, analysis carried out using data from a
single period does not lend itself to talking about
reliability of results and their stability over time. In the
end, the situation for a particular year may be
determined by some one-off phenomenon and thus
cannot be seen as confirmation of an established cause-
and-effect relationship. The results of monitoring
research, repeated from time to time using a single
methodology, could provide such confirmation.
However, research of this type is not currently
undertaken in Russia.
It may be that given a high differentiation of
indicators, it would be more appropriate to study
relationships between different socio-economic and
demographic factors across similar types of regions,
rather than for the country as a whole. These regions
could be identified on the basis of, for example, cluster
analysis (using Ward’s method). Regions may be
clustered by income level or TFR, with subsequent time
series analysis inside each typified group. We have
partly used such an approach toward time series analysis
in our previous research (Shubat et al. 2016; Shubat et
al. 2017). The results we obtained, which showed a lack
of relationship between fertility and income, define the
expedience of differentiating groups beforehand. Each
cluster may have its own answer as to whether income
is a determinant of fertility for that group of regions.
2. There may be different determinants when birth
order is taken into account. For example, research by
Wood et al. across seven European countries identified
specific economic and institutional factors that
particularly influence the birth of second children
(Wood et al. 2016); a study by Anna Matysiak and Ivet
Szalma showed that the same demographic policy
measures may have different impact upon the birth of
the first or the second child (Matysiak and Szalma 2014)
and so on.
We believe that variability in determinants for
children of different birth order is even more likely in
Russia. We consider that there is a connection with
demographic policy measures aimed at stimulating
children of a particular birth order. For example, in
2007, Russia introduced financial incentives for second
children – maternity capital (Federal law 256-FZ 2006);
in 2011 and 2012 regions introduced payments for third
children, whereas from 2018 there is a significant
monthly payment aimed at stimulating the birth of first
children (Bill 333958-8 2017).
0.39
0.40
0.41
0.42
0.43
13
14
15
16
17
2000 2004 2008 2012 2016
Index of income inequality
Analysing the relationship between people's incomes
and children of different birth order may help to identify
a correlation between income and the birth of children
of specific order. The same could be fairly said for
groups of the population cut by income levels – such
correlations may exist in a specific group/ groups by
income to be levelled out by other determinants.
Unfortunately, this assumption is difficult to verify, as
Russian statistics on birth order are not collected.
3. Subjective, rather than objective factors may have
a greater influence on fertility. It is known that
reproductive behaviour is carried out against a
background of certain stereotypes as regards parenthood
and childbirth, which influence structural elements and
determine social norms on the number of children
(Newson 2005), the approach to parenting (Voroshilova.
2016), ideas about the advantages and disadvantages of
having children for future parents (Bagirova and Shubat
2014) and so on.
Subjective factors may include ideas about family
and children that exist in different religious doctrines.
Given Russia's multi-confessional landscape, this too
may play a significant role. Orthodox Christianity, the
most widespread religion in the country, does not
declare having and raising children as the goal of
marriage. Orthodoxy does not say that parents have to
give children a certain upbringing and education, create
for them cultural, material and social living conditions
that would allow them to flourish in later life.
Meanwhile, having children is encouraged in Islam and
in the Muslim tradition the role of the mother is a
woman's most important, sacred and invested
responsibility.
4. A high “cost of parenting”, which is traditionally
seen as the reason for reduced fertility in developed
countries, manifests itself quite peculiarly in Russia.
This may be due to the fact that unlike developed
countries with a positive correlation between income
and education (for example, this was shown by
Rodriguez-Pose and Tselios (Rodriguez-Pose and
Tselios 2009)), such a correlation began to manifest
weakly only in post-Soviet times. As such, the price of
parenting for developed countries, «paid» by mothers
with a high income and a higher education, is an issue
first of all for mothers with a high level of education,
which is not always backed by high income. In this case
the so-called subjective cost of maternity (unlike the
“objective” “so-called mommy tax, the lost lifetime
income a woman can expect by becoming a mother”
(Crittenden 2010)). This subjectively perceived cost of
motherhood is made up of different components – fewer
opportunities for professional self-actualisation, less
time for leisure, personal development, external
communication and so on. As such, a high “cost of
motherhood” in Russia may be a reason for low fertility
not for women with high income, but for educated
women.
CONCLUSIONS
The research we carried out into time series dynamics
did not confirm the results of other studies based on
static data on the relationship between fertility and
people’s incomes. Accordingly, this raises questions
about the methodology for analyzing the relationship
between dynamic processes with a high volatility of
input data. Evidently to receive reliable and stable
results, multi-dimensional analysis methods should be
integrated into the study of relationships between
dynamic time series, including preliminary multi-
dimensional data classification. This will enable
carrying out analysis on homogenous territorial or
temporal segments, which would be more
methodologically sound.
We note that the demographic policy measures that
are being currently implemented in Russia are
developed based on an assumed relationship between
people’s incomes and fertility. At the same time, there is
no unambiguous confirmation of a cause-and-effect
relationship. Moreover, there may be a different,
inverse, relationship between these indicators: a large
number of children may drive greater professional
engagement due to the need to provide for a family. The
role of latent factors also cannot be ruled out – for
example, the provision of housing, orientation toward
family values and so on, which may vary across
different groups of the population with different income
levels and be connected to fertility rates more than
income levels.
We believe there is opportunity to extend our
research by adapting the methodology for modelling
and carrying out multi-dimensional analysis to study
demographic processes in Russia. This is necessary to
find substantiated answers to questions about real
determinants of fertility in Russia. The search for such
determinants is particularly topical today, when experts
consider the potential for population growth and its
reproductive potential to be exhausted.
ACKNOWLEDGMENTS
The article is processed as one of the outputs of the
research project “Fertility and parenting in Russian
regions: models, invigoration strategies, forecasts“,
supported by the President of Russian Federation,
project no. NSh-3429.2018.6.
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AUTHOR BIOGRAPHIES
OKSANA SHUBAT is an Associate Professor of
Economics at Ural Federal University (Russia). She has
received her PhD in Accounting and Statistics in 2009.
Her research interests include demographic processes,
demographic dynamics and its impact on human
resources development and the development of human
capital (especially at the household-level). Her email
address is: [email protected] and her Web-page can
be found at http://urfu.ru/ru/about/personal-
pages/O.M.Shubat/
ANNA BAGIROVA is a professor of economics and
sociology at Ural Federal University (Russia). Her
research interests include demographical processes and
their determinants. She also explores issues of labour
economics and sociology of labour. She is a doctoral
supervisor and a member of International Sociological
Association. Her email address is: [email protected]
and her Web-page can be found at
http://urfu.ru/ru/about/personal-pages/a.p.bagirova/
