Interdisciplinary study of the medium-term fertility trend in Latvia (1970-2022)

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The starting point for this study was the “Population Reproduction Strategy FAMILY — LATVIA — 2030 (2050)” [11] presented on November 9, 2022. Its main goal, which is clear from its title, is to ensure the population reproduction in Latvia in the near decades. Since the presentation of the Strategy, its priorities and forecasts have been widely discussed in the Latvian mass media [13; 16; 31] and by Latvian academic researchers, who have focused on the issues of reproduction of the population of Latvia both before and after the adoption of the Strategy [15; 34; 35] to examine the current global trends in fertility decline [9; 25; 27; 30; 33]. Thus, the decline in fertility is not a purely Latvian problem, and the scientific community, the public and the state all over the world, are concerned about it [1; 12; 17; 19; 20].

The article aims at considering the medium-term trend in fertility in Latvia in terms of the total fertility rate (the average number of children that could be born by one woman during her life if the birth rate in each age group remained at the level of the reference year [22]) with the mathematical and sociological methods. The main research question is whether the Strategy’s goals can be achieved in the near future. According to the summary, the “Population Reproduction Strategy FAMILY — LATVIA — 2030 (2050)” is “a targeted set of necessary measures designed to stop the decline in demographic indicators and contribute to the revival of the nation. The Strategy presents specific strategic directions of actions, support tools, programs and ways to increase the birth rate in the country” [11. P. 5]. As for specific figures of the total fertility rate in Latvia, the Strategy aims at achieving the fertility level of 1.77 by 2027, with an intermediate indicator of 1.72 in 2024, a base indicator of 1.61 in 2018 and a real indicator of 1.57 in 2021 [11. P. 5]. However, in 2022 the total fertility rate in Latvia was 1.47 [6]. Concerning the real demographic indicators, the Strategy’s goal — 1.77 by 2027 — seems unrealistic. The Latvian demographer Z. Vārpiņa has already called this Strategy “a letter to Santa Claus” [16]. In order to evaluate the possibility of increasing fertility in Latvia in the near future, we conducted the mathematical analysis [5; 7; 10; 32] of the fertility trend in Latvia for the medium-term period of 1970–2022, which consists of the so-called “Soviet era” and the period of the Latvian independence after the collapse of the Soviet Union [6].

The results of our review of publications on fertility trends in the contemporary world show that usually the analysis of these trends is rather descriptive [4; 8; 17; 18]. For instance, “the total fertility rate shows the most favorable situation in the 1980s and the lowest level of population reproduction in the second half of the 1990s” [4] (situation in Latvia); “after the Second World War, the birth rate in Latvia increased slightly and fluctuated around 19 newborns per 1000 inhabitants, but then decreased and fluctuated between 16–17 newborns in the 1950s” [18]; “the total fertility rate in Latvia increased to 1.74 in 2016, reaching its highest level since 1992, however, since 2017 it has gradually decreased and in 2021 it was 1.57, which is slightly higher compared to 2020–1.55; however, it is far from the number of children per woman required for a normal generational change” [8]; “fertility had fell continuously from 1992 to 2003, primarily due to educated women increasingly delaying their first child. The rise in fertility from 2005 confirmed that the preceding decline in fertility was actually a result of some women delaying their first child… As a result, women in their 30s overtook women in their 20s as having the highest rates of fertility and the total fertility rate increased and peaked at just over 2 babies per woman in 2007. From that peak in 2007, the fertility rate has fallen over the last decade and by 2018 it was back to approximately the historical low recorded in 2001” [17] (situation in Australia). Such a descriptive approach to the analysis of fertility trends, first, is rather superficial, without a detailed formalized analysis and an understanding of fertility in dynamics; second, does not allow to scientifically answer our research question. Therefore, we wanted to fill this methodological gap in fertility research with the mathematical and economic-sociological analysis of the fertility trend in Latvia in the medium-term period of 1970–2022 (53 years).

For a mathematical model of the nonlinear process of changes in fertility in Latvia in terms of the total fertility rate over several decades, i.e., for a formula for the total fertility rate function based on several dozen points, the authors used the polynomial interpolation method for approximation of the function [10]:

f(x) = a₀ + a₁x + a₂x² + … + a_nxⁿ,                                (1)

f (x) — approximating function; a₀, a₁, a₂, …, a_n — coefficients to be found (a₀ — value of the free term, indicates the value of y at x = 0, i.e., this is the initial level of fertility at the beginning of the period under study); x — independent variable (x value from data points).

The authors chose the polynomial type of interpolation as the most suitable approximation method, in which a function is approximated by a polynomial that passes through all given points; thereby, representing the behavior of the function over the range of interest [7]. To assess the influence and interpretation of a polynomial function, the authors used additional analysis of the function (In particular, differentiated the function, i.e., analyzed its derivatives at each point corresponding to each year of the period under study) [10] and visualization of the graph of the medium-term fertility trend in Latvia. Methodologically, even simple comparisons of fertility rates for specific years can show how fertility has changed over time. On the other hand, the derivative provides a more general and continuous way for the analysis of changes in variables (fertility rates) over the entire period under study, not limited to just specific years. Such an approach reveals more subtle trends and periods of change, which may be less obvious from simple comparisons of variables for specific years [5; 10]. The derivative can also help identify precise points in a trend change, such as the year fertility began to decline or rise.

For a function of type f(x) = a₀ + a₁x + a₂x² + … + a_nxⁿ (1), where n is the degree of the polynomial, and a₀, a₁, a₂ , …, a_n are coefficients, the derivatives will be calculated by differentiating each term separately with the rule of differentiation of the degree function xⁿ [10]:

dy/dx (xⁿ) = nx^n–1.                                                                      (2)

Since the polynomial function can have different slopes in different parts of its graph, calculating its derivative at each point x allows to understand how the value of the function y changes as the variable x changes [5; 10]. The smaller the absolute value of the derivative, the slower the fertility rate changes in a particular year within the time period under study. If the derivative is negative at a certain point, this means that as the value of x at that point increases, the value of the function y decreases; if it is positive, it increases.

The authors began the mathematical analysis of the fertility trend in Latvia for the medium-term period of 1970–2022 by approximating the function based on the polynomial interpolation method [5]. Thus, the following mathematical model of changes in fertility over the last half century was used on the data from [6]:

 y = 0,0097*x⁶–0,1751*x⁵ + 1,1776*x⁴–3,599*x³ +  4,8292*x²–2,393*x + 2,2168              (3)

y — fertility rate; x — the ordinal number of the year in a 53-year period (0 = 1970, 0.1, 0.2, …, 5.2 = 2022), reduced by 10 times to avoid a linear growth of the derivative due to large values ____of the ordinal year numbers [32].

The approximating mathematical model of changes in fertility rates in Latvia over the past half century is a polynomial function of the sixth degree, i.e., the relationship between variables (the total fertility rate and the ordinal number of the year within the period of 1970–2022) is complex and contains nonlinear effects. The determination coefficient R² is equal to 0.8463, which indicates a good quality of approximation: the share of variation over time in the total fertility rate explained by the approximating function is almost 85 %. The statistical significance of the R² was estimated by testing the null hypothesis of Fisher’s F–statistics: F_act=15,8 at a 5 % significance level, which is larger than the critical value F_cr=4.96. The null hypothesis about the inconsistency of the equation after the approximation was rejected [26]. The determination coefficient R² is statistically significant, and the resulting mathematical model can be used in further analysis.

From the approximating mathematical model of changes in fertility in Latvia over the last half century (3), we can make the following conclusion: since a degree function always has several extrema (maxima and minima) and bends in graph, the medium-term fertility trend in Latvia has a ‘wave’ nature: like all social processes, the medium-term fertility trend in Latvia is non-linear, i.e., there have been and will be ups and downs in fertility, which do not say anything about the general trend — downward or upward. These repeated fluctuations in fertility resemble economic cycles/cycles of economic activity [14] and characterize only short-term cyclical changes that periodically replace each other: an increase in fertility is followed by a decrease, then an increase again, then a decrease again, etc., regardless — by and large — of changes in political situation, economic conditions, climate and other factors — their influence on fertility indicators overlaps and ‘produces’ a result that does not go beyond the global longer-term, declining fertility trend.

However, we need a graph of functions, both initial and approximating, which allows to more accurately assess the nature of the medium-term fertility changes in Latvia, to visually assess the shape of dependence, highlight the features of the function (extrema and bends) and visually represent the general direction of the fertility trend in Latvia. In order to identify more subtle trends and periods of change in the fertility trend, we differentiated the function obtained after approximation (3; Fig. 1), i.e., defined the derivative of the function at each point x, indicating the ordinal number of the year during the entire 53-year period under study.

Figure 1. Changes in the total fertility rate, 1970–2022, Latvia
(y — total fertility rates, x — years, i.e., 0 = 1970, 0.1, 0.2, …, 5.2 = 2022)

Table 1 shows changes in the total fertility rate and the derivative of the fertility function in Latvia over the period of 1970–2022, providing an empirical interpretation (In relation to fertility) of changes in value of the derivative. The data in Table 1 (and Fig. 1) show the cyclical nature of the medium-term fertility trend in Latvia, with a generally decreasing slope — from 2.01 in 1970 to 1.47 in 2022. Furthermore, in the medium-term perspective of changes, there were periods of apparent contradiction — when fertility increased, and the derivative of the function (rate of change) was negative (for example, 1970–1971, 1983–1984), and the opposite also happened — fertility decreased, and the derivative of the function was positive (for example, 2003–2004, 2009–2010)

Table 1. Changes in the total fertility rate and in the derivative of fertility function, 1970–2022, Latvia

Year	Total fertility rate	Change compared to the previous year	Value of the derivative*	Percentage change in the derivative compared to the previous year**	Empirical interpretation
1	2	3	4	5	6
1970	2.01		–2.393		Previous growth in  fertility is slowing (In 1965–1.74)
1971	2.05	0.04	–1.5305	36
1972	2.03	–0.02	–0.8569	44
1973	1.96	–0.07	–0.347	59.5
1974	1.99	0.03	0.0225	106.5	Fertility growth slowed down and changed to decline
1975	1.96	–0.03	0.2729	1112.9
1976	1.93	–0.03	0.4236	55.2	Fertility decline continues but slows
1977	1.88	–0.05	0.4926	16.3
1978	1.86	–0.02	0.4958	0.6	Fertility decline stopped and changed to growth
1979	1.86	0	0.4478	–9.7
1980	1.88	0.02	0.3615	–19.3	Fertility growth continues but slows
1981	1.88	0	0.2483	–31.3
1982	1.97	0.09	0.1184	–52.3
1983	2.12	0.15	–0.0197	–116.6	Fertility growth stopped and changed to decline
1984	2.14	0.02	–0.1583	–703.6
1985	2.08	–0.06	–0.2913	–84	Fertility decline continues but slows (a short-term fertility rise in 1986–1987 did not change the general trend)
1986	2.21	0.13	–0.4135	–41.9
1987	2.21	0	–0.5208	–25.9
1988	2.16	–0.05	–0.61	–17.1
1989	2.04	–0.12	–0.6791	–11.3
1990	2.00	–0.04	–0.7266	–7
1991	1.86	–0.14	–0.752	–3.5
1992	1.74	–0.12	–0.7554	–0.5
1993	1.52	–0.22	–0.7375	2.4
1994	1.41	–0.11	–0.6997	5.1
1995	1.27	–0.14	–0.6439	8
1996	1.18	–0.09	–0.5722	11.1
1997	1.13	–0.05	–0.4872	14.9
1998	1.12	–0.01	–0.392	19.5
1999	1.18	0.06	–0.2894	26.2
2000	1.25	0.07	–0.1829	36.8
2001	1.22	–0.03	–0.0757	58.6	Fertility decline stopped and changed to growth
2002	1.25	0.03	0.0288	138
2003	1.32	0.07	0.1274	342.4	Fertility growth continues but slows (the short-term fertility decline in 2009– 2010 did not change the general trend)
2004	1.29	–0.03	0.217	70.3
2005	1.39	0.1	0.2946	35.8
2006	1.46	0.07	0.3575	21.4
2007	1.54	0.08	0.4034	12.8
2008	1.58	0.04	0.4305	6.7
2009	1.46	–0.12	0.4373	1.6
2010	1.36	–0.1	0.423	–3.3
2011	1.33	–0.03	0.3873	–8.4
2012	1.44	0.11	0.3306	–14.6
2013	1.52	0.08	0.2542	–23.1
2014	1.65	0.13	0.1602	–37
2015	1.7	0.05	0.0514	–67.9
2016	1.74	0.04	–0.0682	–232.7	Fertility growth stopped at the 1965 rate (1.74) and fertility began to decline
2017	1.69	–0.05	–0.1937	–184	Fertility decline continues but slows
2018	1.6	–0.09	–0.3189	–64.6
2019	1.61	0.01	–0.4367	–36.9
2020	1.55	–0.06	–0.5385	–23.3
2021	1.57	0.02	–0.6145	–14.1
2022	1.47	–0.1	–0.6535	–6.3

* Derivatives were calculated using Formula 3, taking into account, respectively, three or four decimal places
** Calculation of percentage changes is necessary to consider both absolute and relative differences between values  of the derivative and to reduce the effect of a purely mathematical relationship between values  of the function and its derivative associated with changes in the variable x

Such situations are a good example of how important not only values of the function but also its derivatives are for a more complete understanding of the dynamics of changes in fertility in the general trend. For example, the negative derivative in 1970–1971 under the rising fertility rates indicated that the previous growth in fertility (In 1965–1.74 [6]) was slowing down, and the negative derivative with an increase in fertility in 1983–1984 — that the growth of fertility stopped and changed to decline. In turn, the positive derivative in 2003–2004 (when fertility fell) indicates that fertility growth continued but slowed down, and the short-term decline in fertility in 2009–2010 (most likely due to the 2008 global financial crisis) did not change the general growing trend in 2003–2015. The behavior of the derivative of the fertility function in Latvia (Fig. 2) confirms a fairly uniform cyclicality in the development of fertility at least since 1973, i.e., before the social-economic and political changes in Latvia in the early 1990s.

Figure 2. The derivative (rate of change) of the fertility function, 1970–2022, Latvia

In Table 2, we identified the various phases of the demographic fertility cycles in Latvia, using an analogy with the phases of economic cycles — growth (expansion), peak or boom, decline (recession), bottom (depression) [29]. We also tried to predict the fertility trend in Latvia in the near future, focusing on the possibility of its increase.

According to the data in Table 2, there are indeed empirically based, demographic fertility cycles similar to economic cycles [14; 29] and even related to them [21; 23]. In the demographic perspective, historical process is a sequence of demographic cycles, and the mirror image of demographic cycles are cyclical changes in per capita consumption, that is, cycles of real wages or income [21]. Based on the results of our mathematical analysis, we can expect that the fertility decline in Latvia will continue for several more years until the bottom of the next demographic fertility cycle will be reached, followed by a reversal in the long-term declining fertility trend. However, the next growth will not reach the previous peak. Thus, the desired and even expected by the creators of the “Population Reproduction Strategy FAMILY — LATVIA — 2030 (2050)” increase in fertility in Latvia to the level of 1.77 by 2027 with an intermediate indicator of 1.72 in 2024 is unattainable in any social-economic and political conditions.

Table 2. Phases of the demographic fertility cycles, 1970–2022, Latvia

Time interval	Empirical interpretation of changes in the derivative value	Duration of phase	Name of phase
1970–1973	The growth in fertility slows (1.74 in 1965, 1.96 in 1973)	4 years	Growth  (expansion)
1974–1975	Fertility growth slowed down and changed to decline (1.99–1.96)	2 years	Peak (boom)
1976–1977	Fertility began to decline, with the rate of decline slowing (1.93–1.88)	2 years	Decline  (recession)
1978–1979	Fertility decline stopped and changed to growth (1.86 in 1978 and 1979)	2 years	Bottom  (depression)
Next demographic fertility cycle
1980–1982	Fertility growth continues but slows (1.88–1.97)	3 years	Growth  (expansion)
1983–1984	Fertility growth stopped and fertility began to decline (2.12–2.14)	2 years	Peak or boom
1985–2000	Fertility decline continues but slows (the shortterm rise in fertility in 1986–1987 — a result of M. Gorbachev’s anti-alcohol campaign which did not change the general trend) (2.08–1.25)	16 years	Decline  (recession)
2001–2002	Fertility decline stopped and changed to increase  (1.22–1.25)	2 years	Bottom  (depression)
Next demographic fertility cycle
2003–2015	Fertility growth continues but slows (1.32–1.70); a sharp short-term decline in 2009–2010 as a result of the 2008 global financial crisis (1.46–1.36)	13 years	Growth  (expansion)
2016	Growth stopped at the 1965 level (1.74), fertility began to decline	1 year	Peak or boom
2017–2022	Fertility decline continues but slows (1.69–1.47)	6 years	Decline  (recession)
The decline will continue for several more years until the bottom of the next cycle will be reached (this bottom will be lower than the previous one, i.e., below 1.22–1.25), and there will be a turn towards fertility growth as a part of the long-term declining trend. Thus, the next growth will not reach the previous peak, i.e., the next peak may be below 1.74

The main reason for the impossibility of increasing fertility in Latvia in the near future is value changes studied and interpreted by sociologists and demographers in Latvia and other countries. In the Soviet era, the ideal family model was a family with two children (both large families and childless ones were rare) [35], which ensured the fertility rates close to 2. Today, as the data of the comparative sociological “Study of factors affecting marriage, fertility and positive parent-child relationships” (2004 — N=1970; 2022 — N=2297), conducted by the University of Latvia, show, “family still has value (safety, health of loved ones), but the child is no longer the only and necessary means of realizing one’s life ambitions; the child is no longer at the center of the value system” [16] (Table 3). Thus, “with a decrease in the self-worth of children and families, one can expect that people will make less effort to achieve this value, i.e., they will be less willing to create families and have children” [24. P. 57]. The current tendency among the youth not to put in extra effort (to work) is also evidenced by the results of the international survey conducted by the Randstad Deutschland (N=35,000, 18–24-year-olds): 58 % would quit their job if it interfered with their enjoying life, and 38 % have already done this at least once. Many HR managers in Western (and not only Western) companies complain that young people do not want to take responsibility, do not want to work 5 days a week, and in every possible way avoid “overtime” [2].

Table 3. Hierarchies of values, Latvia [24. P. 57].

Values	Place in the hierarchy, 2004	Place in the hierarchy, 2022	Values
Family safety (safety of loved ones)	1	1	Family safety (safety of loved ones)
Health (no physical or mental illness)	2	2	Health (no physical or mental illness)
Children and family (as an intrinsic value)	3	3	Peace in the world (no wars and conflicts)
Inner harmony	4	4	Freedom (of action and thought)
Mature love	5	5	Inner harmony
Self-esteem	6	6	Self-esteem
Sincere friendship	7	7	Honesty
Freedom (of action and thought)	8	8	Intelligence
Intelligence	9	9	Country safety (protecting my people from enemies)
Honesty	10	10	Sincere friendship
Peace in the world (no wars and conflicts)	11	11	Mature love
Country safety (protecting my people from enemies)	24	22	Children and family (as an intrinsic value)

Researchers of the female childlessness in Lithuania, based on the results of the comparative survey of women of two generations, concluded that “the subjectively perceived causes of childlessness reveal different ways of experiencing childlessness… In terms of voluntary childlessness, the differences between two generations are great. Older women never say that they chose to remain childless, even though they admit never really wanting children; younger women are not afraid to declare they chose to be childfree and enjoy it” [30. P. 19–20]. Thus, “the value choice largely determines the pace and direction of the evolution of the contemporary society” [3. P. 247], including its demographic development. “Previously, it was believed that economic success was the decisive factor in improving people’s lives, achieving social dynamics and success in international cooperation” [28. P. 427]. Much later, the “programming role of culture” [3. P. 246] was recognized as “a way to transfer the accumulated social-historical experience (supra-biological programs of human life) to the organization of social life, its changes and generations… To change and transform into a new type, the society needed a change in its cultural code, worldview universals, then in technical and economic development and competition with other societies, which would determine the future fate of the new type of social organization” [28. C. 428–429].

We believe that the short-term ups and downs in fertility in Latvia are determined mainly by social-economic and political factors. For example, fertility increased in 1986–1987 due to M. Gorbachev’s anti-alcohol campaign and decreased in 2009–2010 due to the shock of the 2008 global financial crisis. Such short-term ups and downs do not imply fundamental changes in the current phase — growth or decline — of the demographic fertility cycle. More sustainable and long-term changes in the fertility trend are most likely determined not by social-economic or political factors, but by value system changes. Furthermore, the current cult of enjoying life does not support the childcare idea, which is the key factor for the steadily declining fertility rate — both in Latvia and in other countries of Europe and the world.

About the authors

V. Menshikov

Daugavpils University

Author for correspondence.
Email: vladimirs.mensikovs@du.lv
Vienibas St., 13, Daugavpils, Latvia, LV-5401

J. Kudins

Daugavpils University

Email: janis.kudins@du.lv
Vienibas St., 13, Daugavpils, Latvia, LV-5401

A. Kokarevica

Riga Stradins University

Email: anita.kokarevica@rsu.lv
Dziriema St., 16, Riga, Latvia, LV-1007

V. Komarova

Daugavpils University

Email: vera.komarova@du.lv
Vienibas St., 13, Daugavpils, Latvia, LV-5401

E. Cizo

Daugavpils University

Email: edmunds.cizo@du.lv
Vienibas St., 13, Daugavpils, Latvia, LV-5401

References

Supplementary files