An Empirical Exploration of Population Dynamics and Economic Performance

Emiliano Alvarez; Juan Gabriel Brida; Gaston Cayssials; Verónica Segarra

doi:10.3897/popecon.9.e127348

Abstract

The purpose of this study is to conduct a descriptive and exploratory analysis of the complex relationships between population dynamics and economic performance. The paper introduces a methodology that enables a model-free topological and hierarchical description of the interaction between economic growth and population. For the empirical analysis, time series data on GDP and population from 111 countries over the period 1961–2019 is used. Using the concept of regimes, we classify countries based on the regime changes they experience throughout the analysis period. This classification allows us to identify groups of countries exhibiting similar behavioral patterns and clearly distinguish between these groups. Once these internally homogeneous groups are obtained, we characterize them by considering additional variables identified in the literature as proximate determinants of growth. Finally, we repeat the exercise with 30-year time windows to examine the emergence and evolution of each group and assess the potential for convergence or divergence among them. The study finds that the relationships between population dynamics and economic performance are non-linear, with the sign, intensity, and direction changing over time. This highlights the need for periodic policy evaluation and revision.

Keywords

time series analysis, Minimal Spanning Tree, Hierarchical Tree, population dynamics, economic performance

JEL codes: C10; C14; J10; O40

Introduction

The study of the relationship between economic and population growth has a long-standing tradition in economics. Population has played a central role in the analysis of economic growth since Adam Smith’s assertion (Smith 1793, p. 12) that a nation’s wealth should be measured by per capita income rather than aggregate income. Shortly afterward, Malthus (1798) introduced his “Population Principle,” which postulated that population and aggregate income dynamics are inextricably linked through a bidirectional causal relationship. Malthus’s vision became highly influential in the development of economic theory, leading to the consideration of population dynamics in studies of economic growth by subsequent economists. Despite this, no clear consensus has emerged on whether population growth is beneficial, neutral, or detrimental to economic growth. Additionally, there is a lack of consensus on the effects of economic growth on population dynamics, a direction of causality that has received comparatively less attention in the literature.

Although the global population growth rate has declined over the past 60 years, consistent with the stylized facts of demographic transition, this process has not been uniform across countries. Different economies have experienced or are experiencing this transition at various times and with differing levels of intensity. Population growth rates exceeding 3% in many countries coexist with others where population levels are stable or declining. The potential effects of both rapid and slow or no population growth on economic growth, as well as their magnitude and the mechanisms through which they operate, remain largely uncertain. The empirical literature on the relationship between economic growth and demographic change has primarily focused on testing for cointegration between the two variables and examining their causal relationships. To contextualize our research, we provide a brief overview of this literature below. The present study examines the hierarchical structure and dynamic relationships between economic and population growth for a group of countries using a non-parametric approach. This method’s main advantage is that it enables the analysis and comparison of the interplay between population growth and economic growth without relying on a predetermined model. The cluster analysis further allows for the grouping of countries based on the similarity of their dynamic behavior.

This study has several objectives. Firstly, it introduces a methodology that provides a model-free topological and hierarchical description of the interaction between economic growth and population – an approach not previously explored in the literature to our knowledge. Secondly, while we do not delve into the underlying mechanisms at play (such as causes, effects, or propagation mechanisms), the proposed methodology indirectly indicates dynamic interdependence in the trajectories of economic growth and population change among countries. Additionally, it provides evidence that challenges single-model approaches for explaining the interdependence between demographic change and economic growth. The findings support the understanding of this relationship as non-linear and potentially non-monotonic.

The paper is organized as follows. The second section provides a review of the empirical literature on the relationship between economic growth and demographic change. The third section details the data and describes the set of tools used for conducting an empirical analysis of comparative economic growth without the imposition of an a priori model. Here, we explain the methodology for constructing minimum spanning trees and hierarchical trees. We introduce the concept of regime analysis and symbolic time series, and we define a distance metric within this framework to assess the proximity between countries. These tools enable us to identify and analyze the global structure, taxonomy, and hierarchy within our sample of countries, which we explore in the fourth section. Finally, the fifth section presents our final conclusions.

Literature review

The relationship between economic growth and population has long been a topic of debate among policymakers, economists, demographers, and social scientists. Empirical research has found evidence of both negative and positive relationships between population growth and GDP per capita growth, as well as cases of independent relationships. Each of these findings, although seemingly contradictory, is supported by theoretical arguments, adding to the controversy surrounding the issue.

A rapidly growing population can lead to fewer resources per person, reduced physical capital per worker, and a higher proportion of dependents, placing greater demands on social protection infrastructure and resulting in lower economic growth. The neoclassical growth model (Solow, 1956) aligns with these views, linking economic growth to the population growth rate. The model predicts a negative relationship between population growth rate and per capita income: in the long run, higher population growth leads to lower steady-state per capita output. In the short term, an increase in the population growth rate results in reduced per capita output growth during the transition to a new equilibrium. This model does not distinguish between population and the labor force, implicitly assuming they grow at the same rate or that the population structure remains stable. Consequently, under this model, decreasing marginal returns lead to stable per capita output, and sustained economic growth can only occur through continuous technological progress.

In contrast, some endogenous growth models (Romer 1986, 1990) propose a positive relationship between population growth and economic growth. In these models, the population is not just a proxy for the labor force but a source of scientists and innovators. A larger population can lead to greater technological progress, driven by increased numbers of innovators and heightened demand for new products. This demand stimulates changes in human capital that enhance productivity (Kuznets 1967; Kremer 1993; Simon 1989). These models differ from earlier approaches by incorporating “scale effects,” which can be contentious but suggest that population size can positively impact economic growth.

Other theoretical approaches build on the classical perspective of treating population as an endogenously determined variable. Researchers such as Hansen and Prescott (2002), Irmen (2004), Mierau and Turnovsky (2014), Corchón (2016), and more recently Bucci et al. (2019), have developed models in which the relationship between population growth and economic growth is non-monotonic, with effects that vary in magnitude, sign, and direction.

In the empirical literature on the relationship between economic growth and demographic change, there is significant emphasis on testing for cointegration between the two variables and examining their causal relationships. The earliest empirical efforts to assess the impact of population change on economic growth involved correlation analysis. For instance, Coale and Hoover (1958) analyzed the case of India and found a negative relationship between population growth and economic growth, concluding that rapid population growth posed an obstacle to economic progress. However, when Coale (1977) examined Mexico during the period 1955-1975, he arrived at the opposite conclusion.

Barlow (1994) analyzed 6-year periods for 86 countries and found no significant correlation between population growth and economic growth. When fertility rates were factored into the analysis, the authors identified a significant negative relationship between population change and economic growth. Further analysis by income level showed that while the negative correlation was present in both low- and high-income countries, it was significant only for the former. Additionally, a positive correlation emerged between fertility rates lagged by one generation and economic growth.

From the late 1960s, many empirical studies employed cross-sectional analysis, often using “Barro regressions.” Studies by Kuznets (1967), Thirlwall (1972), Simon (1989), and Crenshaw and Christenson (1997), among others, did not find evidence supporting a negative relationship. Their estimations yielded positive coefficients, though these were not statistically significant.

Kelley and Schmidt (1995) conducted an influential study using fixed-effects modeling (FEM) and random-effects modeling (REM) on data from 89 countries with populations exceeding one million, covering the periods 1960-1970, 1970-1980, and 1980-1990. Their models incorporated population-related variables, such as education and population density, as well as economic factors like savings and investment. Their analysis found no evidence that population growth had a significant impact on per capita income during the 1960s and 1970s.

The publication of the Penn Tables by the Maddison Project, particularly Maddison (1995), marked a significant milestone in studying the links between population and economic growth. By offering standardized per capita GDP statistics across various countries, it greatly facilitated comparative analyses of the interaction between population dynamics and economic growth.

By the late 1980s, the first studies employing cointegration and Granger causality analysis (Granger 1969; Engle and Granger 1987) emerged to explore the relationship between population and economic growth. Pioneering contributions in this area include Jung and Quddus (1986) and Kapuria-Foreman (1995). Their findings, however, diverged notably. While Jung and Quddus (1986) did not identify evidence of a causal relationship, Kapuria-Foreman (1995) found significant causal relationships from population growth to economic growth in most of the countries analyzed.

Darrat and Al-Yousif (1999) expanded Kapuria-Foreman’s analysis to 20 developing countries over the period 1950-1996, discovering varying causal relationships based on the country. In 14 of the sampled countries, rapid population growth was associated with higher long-term per capita income, with the labor market participation rate playing a significant role in determining productive capacity. These results challenge the notion that limiting population growth would lead to higher living standards. However, their findings were not uniform across all cases. In all 20 countries, causality between population and economic growth was detected, but the direction varied: in half the countries, causality ran from population to economic growth, while in the other half, it was either bidirectional or ran in the opposite direction.

A significant number of studies have focused on individual countries, particularly developing nations with large populations, where concerns about the potential negative impact of population changes on income growth are prevalent. Dawson and Tiffin (1998), in particular, found no evidence of causality between population growth and economic growth in China from 1950 to 1999. In contrast, Li and Zhang (2007) identified a negative causal relationship from population growth to economic growth, validating concerns about population growth hindering economic performance. Hasan (2010) also reported a negative causal relationship but in the opposite direction, indicating that economic growth slows population growth.

Choudhry and Elhorst (2010) examined the period from 1961 to 2003, distinguishing between short- and long-term effects. Their findings indicated a causal relationship in the short term, but no evidence of causality in the long term. Yao et al. (2013) studied the period from 1952 to 2007 and supported the view that population growth could impede economic growth. Liu and Hu (2013) conducted a panel analysis using data from 28 Chinese provinces between 1983 and 2008. They incorporated additional variables to account for China’s population control policies, such as “one couple, one child” and “1.5 children,” as well as factors like working-age population, mortality rate, net migration, and government expenditure. Their results revealed a negative correlation between birth rate and economic growth, and a positive correlation between education level, the proportion of the working-age population, and economic growth. Similar evidence was found in the study by Furuoka (2018), which also characterized these relationships as bidirectional.

India has also been the subject of various studies, including those by Dawson and Tiffin (1998), Mahmud (2015), and Azam et al. (2020). Dawson and Tiffin (1998) found no evidence of causality between economic and population growth. In contrast, Mahmud (2015) identified a positive relationship between the two variables, while Azam et al. (2020) also found a positive relationship but in the opposite direction, with population growth causing economic growth in the Granger sense. Nakibullah (1998) analyzed Bangladesh and found a causal relationship from population growth to economic growth during the period from 1960 to 1990. For Malaysia, Mulok et al. (2011) concluded that population growth neither hinders nor promotes economic growth. Garza-Rodriguez et al. (2016) studied Mexico from 1960 to 2012 and found a bidirectional causal relationship between economic and population growth.

Another common approach in academic literature is to consider regions by pooling sets of developing countries based on their geographic location. The findings in this area are varied. Bloom et al. (2000) analyzed 70 countries from 1965 to 1990 and found evidence of a unidirectional causal relationship from population growth to economic growth. Thornton (2001), studying seven Latin American countries from 1900 to 1994, found no long-term relationship between population growth and per capita GDP growth. Tsen and Furuoka (2005) painted a more complex picture in their study of 10 Asian countries from 1950 to 2000, showing four distinct outcomes depending on the country: causality from population growth to economic growth, causality from economic growth to population growth, bidirectional causality, and no causal relationship at all. Song (2013), examining 13 Asian countries from 1965 to 2000, pointed to a causal relationship from population growth to economic growth. Similarly, Diep and Hoai (2016), analyzing 10 Southeast Asian countries from 1990 to 2013, reached the same conclusion. Mahmoudinia et al. (2020), studying a sample of 57 Islamic countries from 1980 to 2018, found evidence of a bidirectional causal relationship.

A recent body of research (Chang et al. (2017)) has shifted its focus to developed countries, exploring concerns about the implications of aging populations and the slow or negative population growth observed in mature economies for economic growth. It analyzed 21 countries from 1870 to 2013, revealing varied results. For Finland, France, Portugal, and Sweden, the study identified a unidirectional causal relationship from population growth to economic growth. Conversely, in Canada, Germany, Japan, Norway, and Switzerland, the causal relationship ran from economic growth to population growth. Austria and Italy showed bidirectional causality between these variables.

The study found no evidence of Granger causality between population and economic growth in Belgium, Denmark, the Netherlands, the UK, the US, and New Zealand. Notably, causality directions were not static; when the analysis period was split into two sub-periods (1871–1951 and 1952–2013), many countries displayed changes in causality direction over time.

Aksoy et al. (2019), examining 21 OECD countries between 1970 and 2014, concluded that slow population growth leads to lower GDP per capita growth. The table below summarizes the surveyed empirical literature on the links between demographic and economic growth, detailing the analysis period, sample, methods used, and main findings.

As Table 1 shows, using different econometric tools and data structures (time series, panel data, and cross-section), the studies described attempt to detect the magnitude and direction of the effects between population growth and per capita income growth. Their analyses focus on different periods, consider different groups of developed and/or developing countries (in some cases, single countries) and control for a variety of factors (education, health, institutional quality, geography). In particular, the vast majority of the studies surveyed resort to the Granger test and cointegration analysis. Using this approach, Kapuria-Foreman (1995) for the Philippines, Guatemala, and Turkey; Thornton (2001) for seven Latin American countries; Tsen and Furuoka (2005) for Taiwan and Indonesia; and Chang et al. (2017) for Belgium, Denmark, the Netherlands, the UK, the USA, and New Zealand found no evidence of causality. According to them, economic growth neither affects nor is affected by population growth. Analyses by Kapuria-Foreman (1995) for Nepal, Syria, and Mexico; Yao et al. (2013), Tsen and Furuoka (2005), and Rahman et al. (2017) for China; Furuoka (2018) for Thailand; Mahmud (2015) and Azam et al. (2020) for India; Ali et al. (2013) for Pakistan; Chang et al. (2017) for Finland, France, and Portugal; Aksoy et al. (2019) for 21 OECD countries; Gatsi and Owusu Appiah (2020) for Ghana; and Lianos et al. (2022) for the United States and the United Kingdom report a unidirectional causal relationship between population and economic growth: population affects economic growth, but not vice versa. A unidirectional causal relationship, but in the opposite direction – with economic growth affecting population – is reported by Kapuria-Foreman (1995) for Sri Lanka, Bolivia, Peru, and Thailand; Hasan (2010) for India; Tsen and Furuoka (2005) for Hong Kong and Malaysia; Chang et al. (2017) for Sweden, Canada, Germany, Japan, Norway, and Sweden; and Lianos et al. (2022) for France and Italy. Finally, some studies find evidence of a bidirectional causal relationship, with population affecting and being affected by economic growth. This is the result of Kapuria-Foreman (1995) for China, India, Argentina, and Chile; Furuoka (2018) for China; Chang et al. (2017) for Austria and Italy; Garza-Rodriguez et al. (2016) for Mexico; Chirwa and Odhiambo (2019) for Zambia; and Lianos et al. (2022) for Germany.

Table 1.

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Empirical literature surveyed

Author	Period	Sample	Estimation Method	Findings
Jung and Quddus (1986)	1950–1980	44 countries	Granger Causality test	p ⇒ + y
				p ⇒ − y
				y ⇒ + p
				y ⇒ − p
				Non causality
Kelley and Schmidt, (1995)	1960–1970	86 countries	FEM, REM	Non impact p to y
	1970–1980
	1980–1990
Kapuria-Foreman (1995)	1961–1991	Nepal	Granger Causality test	p ⇒ + y
	1961–1990	India		p + ⇔ − ** y
	1953–1989	China		p – ⇔ + ** y
	1951–1990	Ghana		y ⇒ − p
	1953–1989	Sri Lanka		y ⇒ − p
	1961–1991	Bolivia		Non Causality
	1949–1991	Philippines		Non Causality
	1952–1991	Guatemala		p ⇒ + ** y
	1961–1990	Syria		y ⇒ − p
	1961–1990	Peru		y ⇒ − * p
	1951–1990	Thailand		Non Causality
	1958–1990	Turkey		p – ⇔ + ** y
	1961–1990	Chile		p – ⇔ + ** y
	1952–1990	Argentina		Non causality
	1948–1986	Mexico		p ⇒ + ** y
Nakibullah (1998)	1960–1990	Bangladesh	VAR	y ⇒ + p
Dawson and Tiffin (1998)	1950–1993	India	Cointegration (Johansen)	Non Causality
Darrat and Al-Yousif (1999)	1950–1996	20 countries	Cointegration, VEC	p ⇒ + * y
Bloom et al. (2000)	1965–1990	70 countries	OLS	p ⇒ y
Thornton (2001)	1900–1994	Argentina, Brazil	Granger Test, VAR	Non Causality
	1925–1994	Chile, Venezuela
	1921–1994	Colombia
	1913–1994	Mexico, Peru
Li and Zhang (2007)	1978–1998	China	VI – GMM	p ⇒ − y
Ukpolo (2002)	1950–2000	Ivory Coast, Ghana, Kenya, Nigeria, South Africa, Sudan	VEC	p ⇔ − y
Hasan (2002)	1973–1997	Bangladesh	Cointegration, VEC	y ⇔ − p
Tsen and Furuoka (2005)	1950–2000	Japon, Korea, Thailand	Cointegration (Johansen), VAR	p ⇔ y
		China, Singapore, Philippines		p ⇒ y
		Honk Kong, Malaysia		y ⇒ p
		Taiwan, Indonesia		Non Causality
An and Jeon (2006)	1960–2000	25 OCDE countries	Cross-country regression, kernel non parametric	relationship, U-inverted
Faria et al. (2006)	1950–2000	125 countries	OLS, (logy) (logy)2	Africa – Asia. U-inverted. Europe: y ⇒ − p
Yao et al. (2007)	1954–2005	Taiwan	Cointegration (Johansen), VAR, Toda – Yamamoto	until 2000 p ⇒ + y, until 2005 insignificant
Li and Zhang (2007)	1978–1998	China	VI – GMM	p ⇒ (−) y
Savaş (2008)	1989–2007	Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan, Uzbekistan	ARDL	p ⇔ + y
Azomahou and Mishra (2008)	1960–2000	110 countries	GAM non parametric
Furuoka (2009)	1961–2003	Thailand	Cointegration (Johansen), VEC	p ⇒ y
Furuoka and Munir (2011)	1960–2007	Singapore	Cointegration (Johansen), VEC	y ⇔ + p
Hasan 2010	1952–1998	China	VAR VEC	y ⇒ − p
Choudhry and Elhorst (2010)	1961–2003		OLS	Effect positive (growth differential pop of working age – total pop)
		China		46%
		India		39%
		Pakistan		25%
Mulok et al. (2011)	1960–2009	Malaysia	Cointegration (Johansen), VAR, Toda – Yamamoto	Non Causality
Yao et al. (2013)	1952–2007	China	Cointegration, VECM	p ⇒ − y
Huang and Xie (2013)	1980–2007	Panel 90 countries	simultaneous ADL	p ⇒ − y
Furuoka (2013)	1960–2007	Indonesia	Cointegration non lineal, Breitung	A long-term equilibrium relationship exists
Mahmud (2015)	1980–2013	India	Cointegration (Johansen), VEC	y ⇒ + p
Musa (2015)	1980–2013	India	Cointegration (Johansen), VEC	p ⇒ + * y
Tartiyus et al. (2015)	1980–2010	Nigeria	Cointegration (Johansen), VEC	p ⇔ y
Sethy and Sahoo (2015)	1970–2010	India	Cointegration (Johansen), VEC	y ⇒ (+) p
Furuoka (2018)	1961–2014	China	ARDL	p ⇔ y
Ali et al. (2013)	1975–2008	Pakistan	ARDL	p ⇒ + y
Garza-Rodriguez et al. (2016)	1962–2012	Mexico	VEC	p ⇔ y
Diep and Hoai (2016)	1990–2013	7 countries South East Asia	Panel Regression Model, Structural Equation Models	p ⇔ y
Sibe et al. (2016)	1960–2013	30 most populous countries	VEC	p ⇔ + y
Fumitaka (2016)	1960–2011	India, Japan, South Korea, Sri Lanka, Malaysia, Pakistan, Singapore, Bangladesh, China, Indonesia	VEC – IRF. Impulse Response	p ⇒ + y
Rahman et al. (2017)	1960–2013	USA, UK, Canada, China, India, Brazil	Panel cointegration, VEC	p ⇒ + y
Diwani (2017)	1990–2013	India	ARIMA	p ⇒ y
Akinbode et al. (2017)	1970–2014	Nigeria	MCE – IRF	p ⇒ + y
Furuoka (2018)	1961–2014	China	ARDL	p ⇔ y
Alvarez-Diaz et al. (2018)	1960–2010	21 countries UE	ARDL	p ⇔ y
Karim and Amin (2018)	1980–2015	India, Pakistan, Bangladesh, Sri Lanka, Nepal	Panel Cointegration. VEC	Non causality
Ahmed (2018)	1990–2015	13 West African countries	ARDL. Panel Causality. Dimitrescu – Hurlin	p ⇒ − y
Ahmed (2018)	1981–2015	Nigeria	ARDL. Panel Causality. Dimitrescu – Hurlin	p ⇒ − y
Chirwa and Odhiambo (2019)	1970–2015	Zambia	ADL Cointegration (Johansen)	p ⇔ y
Aksoy et al. (2019)	1970–2014	21 OECD countries	Panel VAR	p ⇒ + y
Rizk (2019)	1971–2015	Egypt	Cointegration, VEC	p ⇒ + y
Hosen (2019)	1970–2017	10 high income countries	Cointegration, VEC	p ⇒ − y
		10 upper middle income countries		p ⇒ − y
		10 middle-income countries		p ⇒ + y
		10 low income countries		p ⇒ + y
Mahmoudinia et al. (2020)	1980–2018	57 Islamic countries	Cointegration (Johansen), VEC	p ⇒ + y
Sebikabu et al. (2020)	1974–2013	Rwanda	ARDL	Effect positive (p ⇒ y)
Bawazir et al. (2020)	1996–2016	10 Middle East	OLS	positive effect
Gatsi and Owusu Appiah (2020)	1987–2017	Ghana	ARDL	p ⇒ − y
Azam et al. (2020)	1980–2020	India	ARDL	p ⇒ + y
Alemu (2020)	1980–2020	Ethiopia	ARDL	p ⇒ + y
Lianos et al. (2022)	1820–1938	USA, UK	Toda – Yamamoto	p ⇒ + y
	1950–2016	Germany	Sims Granger causality test	p ⇔ +y
	1950–2016	France, Italy	Sims Granger causality test	y ⇒ + p

The regression analyses reviewed, particularly those including cointegration testing, tend to assume a linear model, partly because their underlying model (usually Solow’s model) posits a linear relationship. The goal of these studies is to test for the existence of a linear long-term relationship between population and per capita output growth rates. However, there is a smaller group of studies that address the dynamic interplay between demographic change and economic growth using non-parametric approaches, often finding evidence of non-linear causal relationships between the variables. This is the case, for example, with An and Jeon (2006) and Azomahou and Mishra (2008). The former analyzes 25 OECD countries during the period 1960-2000.¹

Their results portray a dynamic relationship between these two variables that changes over time. Initially, demographic change has a positive effect on economic growth, but the magnitude of the effect decreases over time and turns negative toward the end of the period. In other words, the relationship between the variables follows an inverted U-shape. The authors explain this phenomenon as an artifact of the three stages of demographic transitions: 1) high fertility/high mortality, 2) high fertility/low mortality, and 3) low fertility/low mortality.

Another example of a non-parametric approach is Azomahou and Mishra (2008), who also analyze the period 1960–2000 but cover a wider set of countries. Their panel includes 110 countries: 24 OECD members and 86 developing countries. Their estimations provide evidence of a non-linear relationship between the two variables, as well as of “direct” and “feedback” effects of population structure on growth. Furthermore, they affirm that “a highly non-linear demographic structure characterizes age-structured population and economic growth, and that the non-linearity can be a potential source of growth fluctuations in OECD and non-OECD countries.”

Most of the empirical literature reviewed consists of linear regression models coupled with Granger causality tests. The linearity assumption is rarely discussed, and Granger causality tests are often misinterpreted. This is particularly true with respect to the policy recommendations suggested by the analyses. The fact that the results of several empirical studies on the same country, using similar econometric techniques, differ so radically is an indication of a possible non-linear underlying cointegration relationship that cannot be captured by Granger causality analysis. If the sign of the causal relationship can change, policy recommendations may be incorrect. Granger causality analysis is useful for forecasting, but the conclusions that can be drawn about the causal mechanism are limited. The Granger test should be a starting point for a more in-depth analysis of the causal relationship between economic and population growth. The conclusions that can be drawn about the causal mechanism, beyond temporal precedence, and the possibilities for policy manipulation are constrained.

Many of the studies using panel data models fail to check for homogeneity in the effect of explanatory variables across different countries. Zooming out from the details, the overall picture that emerges suggests that a single model is inadequate to explain the dynamic relationships between demographic change and economic growth across all countries and/or over long periods. This observation forms the starting point of our work. We seek to explore a novel path within the empirical literature that examines the dynamic relations between demographic change and economic growth, without imposing constraints on the form of these relationships or assuming homogeneity in the effects across countries. More specifically, we investigate the possibility of multiple patterns in the dynamic relationships between these two variables coexisting at the same time.

With this goal in mind, we aim to identify groups of countries, each internally homogeneous in terms of the dynamic relations between demographic change and economic growth, and at the same time clearly distinct from other groups. In short, this exercise highlights the advantages of a non-parametric methodology over the econometric approach. Note also that the proposed methodology considers both variables together, by analyzing the regime dynamics – essentially the qualitative dynamics of the two variables that represent structural changes. This method, which groups countries based on the dynamics of both variables, is an example of clustering multidimensional time series. It is fundamentally different from statistical grouping criteria that rely solely on each of the two variables independently.

Regimes, regime shifts and complex systems

The problem we aim to analyze involves the dynamics of two variables (population and economic output), where each economy is represented by a two-dimensional time series. To compare these dynamics and identify homogeneous groups with similar patterns, we need to introduce an appropriate metric. Since the units of measurement for each variable differ, and we do not know the relationship between them, we encounter a problem akin to the “Cartesian axis travel speed” issue in physics (Mantegna and Stanley 1999). As a result, Euclidean or similar metrics cannot be used. Therefore, we will frame this problem within the context of complex systems, introducing dynamical regimes and focusing our analysis on regime shift dynamics.

Recently, an interdisciplinary literature analyzing catastrophic regime shifts has emerged (see Cooper et al. 2020; Brida et al. 2011b, and references therein), suggesting that dynamical systems and complexity theory are becoming increasingly central to a wide range of disciplines. To study complex dynamical systems, researchers collect data or build models to identify which variables and parameters are useful in determining regimes and their boundaries. In many cases, it is crucial to know the distance to the boundary of a regime in order to detect a potential regime shift and, if necessary, to trigger one. Although the problems, data, and variables used may differ between disciplines, the models are based on the same fundamental principles.

In the economic literature, the term “regime” is used to describe a distinct way of behavior in an economy, which can be qualitatively distinguished from other regimes. One regime is defined to differentiate it from another, and it is meaningful to think in terms of multiple regimes. Intuitively, an economic regime refers to a set of rules that govern the economy as a system and determine its qualitative behavior (whether static or dynamic). According to Böhm and Punzo (2001), “a regime is a class of (dynamic) behaviors that are sufficiently similar from a qualitative point of view that they can be considered (generated) by variants of the same basic model.”

In terms of modeling, we can define a regime indirectly by defining a regime shift, which occurs when there is a change in the nature of the equation representing the functional form of the model. Regime shifts are associated with qualitative changes in the dynamics produced by variations in the model that governs an economy. These changes are essentially discontinuities or jumps.

The term complex economic dynamics is used in the literature to distinguish economic models whose trajectories exhibit irregular fluctuations and phase shifts, where by phase shift we mean the possibility that different types of qualitative dynamic behavior can be exhibited in different regions of state space, and this means that the laws governing change in the model change.

R. Day introduced multiphase economic dynamics and regime shifts in economic models to formalize the concept that ‘quite different forces or relationships govern behavior in different states’ (Day 1995). But what exactly is a regime, particularly in dynamic, complex, or catastrophic contexts? “A regime is a dynamic model with its own associated multidimensional domain, in which state variables exhibit characteristic behaviors or structures. Those structures can be defined either by inherent dynamic behavior (e.g., a basin of attraction) or by the observable manifestation of them (e.g., an oligotrophic lake vs. a eutrophic one). The state space of a system can encompass multiple regimes of a variety of basin sizes and attraction strength, which in some disciplines is referred to as resilience” (Brida et al. 2011, p. 2). A regime shift occurs when a system crosses regime boundaries due to exogenous or endogenous mechanisms, resulting in the occupation of a new regime.

How can we detect and characterize different regimes in complex problems involving multiple regimes? Various heuristics can be applied to define these regimes. One approach involves observing the phenomenon and identifying qualitatively different behaviors. For instance, the behavior of an economy with respect to inflation varies notably between deflation, moderate inflation, high inflation, and hyperinflation. In mathematical models, regimes are often constructed using Markov partitions (Adler 1998). When working with data, partitioning the state space with statistical indices is another effective criterion. For a more comprehensive discussion on identifying and representing problems with multiple regimes, see Brida et al. (2003).

Once the regimes are defined, we have a division of the state space into regions, each of which has qualitatively different dynamics. This gives rise to a dual dynamic: one within each regime and the other of regime change. This regime changes dynamics (which somehow captures the complexity of the system under study) – since it is defined in a discrete domain (the set of regimes) – can be represented by coding and symbolic dynamics (Brida and Punzo 2003). Returning to the problem we want to analyze, in this exercise we will identify the regimes using a statistical criterion, dividing the state space into four regions based on a statistical index (median) for each of the variables, population growing and GDP per capita levels.

Data and methodology

Data

This study represents population and economic performance dynamics through the evolution of the population growth rate and per capita GDP level. Annual data for per capita GDP (adjusted by Purchasing Power Parity, base year 2017), population, and corresponding growth rates were obtained from the Penn World Table 10.0 (PWT), a standard source for comparative economic growth studies (Feenstra et al. 2015).² The dataset includes annual data for 111 countries spanning the period 1961–2019.³ Over the analyzed period, at the aggregate level, both the population growth rate and per capita GDP show clear trends.

As shown in Figure 1, the global population is increasing, but at a decelerating rate. This indicates a slow and steady evolution, with a clear trend and minimal fluctuations in the growth rate, consistent with the well-documented characteristics of the demographic transition model. In contrast, the evolution of GDP per capita shows a clear upward trend. However, this trend averages out substantial differences between countries in the timing and pace of their demographic transitions. Understanding these differences is the focus of this study.

Figure 1.

Economic performance and population growth over the period analyzed. Notes: on the vertical axis, on the left, the level of GDP per capita (million dollars, PPP, year 2011) and, on the right, the rate of population growth percentage, both at the median, for the sample of countries analyzed. Source: qwn calculations based on PWT 10.0.

Methodology

In this section, we describe the methodology used to compare and analyze the behavior of countries based on variables related to economic performance and demographic change. Our approach establishes a taxonomy and hierarchical ordering of countries, enabling us to evaluate the similarity of their trajectories. We construct the taxonomy using a nearest neighbor clustering procedure, which classifies time series according to their proximity as defined by a distance function. For the joint analysis of demographic change and economic performance, we apply a metric specifically designed for symbolic sequences to capture relevant patterns.

The methodology involves the following steps: compute the distance matrix, build the Minimum Spanning Tree (MST), compute the subdominant ultrametric distance matrix, construct the Hierarchical Tree (HT), and apply a hierarchical clustering stopping rule to determine the number of clusters in the sample. We begin by constructing the distance matrix D, DN×N, where N is the number of countries and the dij element is the distance between country i and country j. Next, we use Kruskal’s algorithm (Kruskal 1956) to construct the MST by sorting all edges by their weight, selecting the smallest edge, and including it in the tree if it does not form a cycle. This process repeats until the MST includes V-1 edges. The resulting MST is a connected, edge-weighted graph of the 111 countries that highlights the 110 most significant distances, aiding in the identification of similar and dissimilar country dynamics based on the chosen variables.

The MST arranges countries based on the most significant connections between them. Any two countries in the MST are connected through one or more vertices, representing the minimum distance path between them.

The third step involves deriving the subdominant ultrametric distance matrix D * (Rammal et al., 1986). Each element d*ij, in this matrix represents the longest step (maximum distance) along the shortest path between countries i and j in the MST, defined formally as d*ij = max(dkl), where k and l are all nodes connecting i and j (including i and j).

Once the value of d*ij is calculated for all country pairs, we have the necessary elements to build the hierarchical tree (HT).

The HT indicates how to group countries for a specified number of clusters. For example, if you wish to divide the countries into eight groups, the HT specifies the allocation of countries to each group. To identify the statistically optimal number of clusters, we use the pseudo−T2 criterion (Duda and Hart 1973) and the Calinski-Harabasz index (Calinski and Harabasz 1974). Further details about the clustering process can be found in Brida et al. (2011a), Segarra et al. (2020), and Prakash et al. (2021), among others.

Symbolic Series and Regimes

To describe the qualitative behavior of the joint evolution of income and demographic growth, we introduce the concept of a regime (Brida et al., 2003; Brida and Punzo, 2003). A regime refers to a set of conditions that define the behavior of a system, characterizing the joint dynamics of population growth and per capita output. These conditions divide the state space of population growth rate and per capita production into distinct regions, each representing a different explanatory model of demographic and economic performance.

We define two conditions: one sets a threshold for yearly population growth, and the other sets a threshold for per capita GDP. The state space is partitioned using median values for each variable, resulting in a uniform division. Although we initially considered using mean values for this partitioning, the results were similar, and median values offer clearer interpretations. Figure 2 illustrates the population growth rate and per capita income for the 111 countries at the beginning and end of the analysis period, with lines marking the median thresholds that define the four regimes.

Figure 2.

Data partition in state space for the set of 111 countries at the start (left: year 1961) and end (right: year 2020) of the analyzed period. Notes: the partition is determined by the thresholds of the medians (in red) of the population growth rate and the per capita GDP level. The graph includes the mean of both variables (in green) to show the skewed distribution of these variables. The point cloud is defined by all countries in 1961 in the left graph and in 2020 in the right graph. Source: own calculations based on PTW 10.0.

Each region corresponds to a unique relationship between demographic change and economic performance. Consequently, a country transitioning from one region to another indicates a structural shift in how population and per capita output are related (a regime switch). Our analysis emphasizes the dynamics of these regimes, focusing on the sequence of regime transitions that countries experience over the study period.

Given the skewness of the variables, we opt to partition the state space using medians. In our analysis, each regime is defined by partitioning the state space into four regions, delineated by the annual median of each variable. This results in four distinct regions, each representing a different relationship between demographic change and economic performance. By calculating the median of per capita income (M_y) and population growth rate (Mg_p) for all countries, we obtain the following partition of the state space of each year⁴:

R ₁ = {(g_p,y) : g_p ≥ Mg_p, y ≤ M_y}. (1)

Region R1 is characterized by low GDP per capita levels (below the median) and high population growth (above the median), which could be associated with economies trapped in so-called “poverty traps,” such as Senegal or Kenya.

R ₂ = {(g_p,y) : g_p ≥ Mg_p, y ≥ M_y}. (2)

In Region 2, we observe a virtuous relationship between economic performance and population growth, with GDP per capita levels in the top 50% and a growing population. We refer to this regime as ‘demographic dividend capture,’ as seen in countries like Korea.

R ₃ = {(g_p,y) : g_p ≤ Mg_p, y ≥ M_y}. (3)

Regime 3 is characterized by a slowly growing population and GDP per capita levels above the median, typical of OECD countries.

R ₄ = {(g_p,y) : g_p ≤ Mg_p, y ≤ M_y}. (4)

Finally, Regime 4 corresponds to a poor economy with a slowly growing population. This regime represents an economy that has completed the demographic transition but failed to capture the ‘demographic dividend.’ An example of this would be a country such as Bangladesh.

As depicted in Figure 3, a wide range of dynamic behaviors can be observed. The dynamics of regimes vary significantly. For instance, Spain remains in the R3 regime for most of the period, with a brief transit through R2, without visiting the other regimes. In contrast, China transitions between the R1 and R4 regimes. Countries like Fiji and Tunisia display more erratic behavior, moving through all four regimes.

Figure 3.

Dynamics of regimes in Spain, China, Fiji and Tunisia, in the period 1961-2019. Notes: each point of each graph represents a pair (g_p,y) corresponding to each of the four countries in each year between 1961 and 2019. Source: own calculations based on PTW 10.0.

Framing the problem in terms of multiple regimes through which countries move over time grants us the flexibility to account for different sequences of dynamic relationships between population and economic performance. An important regime sequence to consider is R1 → R2 → R3, which reflects the stylized facts of the demographic transition theory. In this ideal sequence, countries successfully capture the demographic dividend.⁵ By incorporating the demographic transition theory as a specific case within the broader framework of regime sequences, our approach allows us to assess the extent to which countries conform to this stylized pattern.

Simultaneously, a sequence of transitions from R1 → R4 indicates an economy that has completed its demographic transition but has not captured the demographic dividend. Table 2 provides an initial characterization of regime dynamics by showing the percentage of time each country or economy spends in each regime over the analysis period.

Table 2.

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Percentage of time each country or economy spends in each regime during the period of analysis

Country	R ₁	R ₂	R ₃	R ₄	Country	R ₁	R ₂	R ₃	R ₄	Country	R ₁	R ₂	R ₃	R ₄
ARG	0	0	88	12	GAB	0	71	29	0	MYS	7	93	0	0
AUS	0	27	73	0	GBR	0	0	100	0	NAM	51	39	10	0
AUT	0	0	100	0	GHA	71	20	2	7	NER	83	0	0	17
BDI	69	0	0	31	GIN	61	0	8	31	NGA	97	3	0	0
BEN	97	0	0	3	GMB	100	0	0	0	NIC	29	44	0	27
BFA	66	0	0	34	GNB	63	0	0	37	NOR	0	0	100	0
BGD	54	0	0	46	GNA	31	37	0	32	NPL	47	0	0	53
BOL	75	0	0	25	GRC	0	0	100	0	NZL	0	3	97	0
BRA	12	25	63	0	GTM	90	0	0	10	PAK	100	0	0	0
BRB	0	0	100	0	HKG	0	27	73	0	PAN	0	92	8	0
BWA	27	51	5	17	HND	100	0	0	0	PER	47	20	0	33
CAF	59	0	0	41	HTI	53	0	0	47	PHL	100	0	0	0
CAN	0	0	100	0	IDN	27	0	0	73	PRT	0	0	100	0
CHE	0	3	97	0	IRL	0	17	83	0	PRY	92	3	0	5
CHL	0	10	90	0	IRN	29	34	31	7	ROU	2	0	76	22
CHN	19	0	12	69	ISL	0	7	93	0	RWA	85	0	0	15
CIV	100	0	0	0	ISR	0	80	20	0	SEN	97	3	0	0
CMR	83	0	0	17	ITA	0	0	100		SGP	0	53	47	0
COD	97	0	0	3	JAM	0	3	36	61	SLV	25	0	0	75
COG	97	0	0	3	JOR	86	14	0	0	SWE	0	0	100	0
COL	0	41	59	0	JPN	0	0	100	0	SYC	0	29	71	0
COM	95	0	0	5	KEN	100	0	0	0	TCD	71	0	0	29
CPV	41	0	0	59	KOR	15	0	73	12	TGO	97	0	0	3
CRI	0	75	25	0	LKA	12	3	7	78	THA	31	0	51	19
CYP	0	20	80	0	LSO	51	0	0	49	TTO	0	3	97	0
DEU	0	0	100	0	LUX	0	24	76	0	GTM	42	58	0	0
DNK	0	0	100	0	MAR	41	0	0	59	TUN	17	24	31	29
DOM	24	10	61	5	MDG	86	0	0	14	TUR	0	44	56	0
DZA	7	71	22	0	MEX	0	46	54	0	TWN	3	15	82	0
ECU	44	56	0	0	MLI	51	0	0	49	TZA	97	0	0	3
EGY	85	1	0	14	MLT	0	0	86	14	UGA	100	0	0	0
ESP	0	8	92	0	MOZ	75	0	0	25	URY	0	0	100	0
ETH	73	0	0	27	MRT	78	5	10	7	USA	0	0	100	0
FIN	0	0	100	0	MOZ	75	0	0	25	VEN	0	86	3	10
FJI	10	10	46	34	MRT	78	5	10	7	ZAF	0	78	22	0
FRA	0	0	100	0	MUS	0	8	92	0	ZMB	88	12	0	0
GAB	0	71	29	0	MWI	90	0	0	10	ZWE	66	3	2	29

The first observation is the diversity of behaviors within the sample of countries, evident from the range of regimes they visit and the time spent in each. Some countries alternate between R3 and R4, never visiting R1 or R2, while others do the opposite, alternating between R1 and R2 and never entering R3 or R4. A third group of countries transitions through all four regimes. In short, the sample does not exhibit a single, uniform pattern but rather a multitude of distinct pathways.

However, this initial approach to understanding regime dynamics has a significant limitation: it overlooks the sequence in which countries transition between regimes, which is crucial for understanding regime dynamics comprehensively. Specifically, it fails to capture information on regime transitions. To address this limitation, we employ symbolic series to represent regime dynamics. This method reduces the information space of our problem while retaining essential details about regime transitions.

If we label each regime Ri by the symbol i, we can substitute the original bi-variate time series {(gp1,y1),(gp2,y2),...,(gpT,yT)} by a sequence of symbols {s1,s2,...,sT} such that st = j if and only if (gpt,yt) belongs to Rj. This Symbolic Series that summarizes the most relevant qualitative information on the dynamics of a country’s regime.⁶

To group the 111 countries based on their different economic-demographic performance, we use the non-parametric approach described in the previous section. The steps include computing the distance matrix, building the MST, computing the subdominant ultrametric distance matrix, constructing the HT, and applying a hierarchical clustering stopping rule to determine the number of clusters in the sample.

As previously discussed, the joint analysis of demographic change and economic performance requires a metric different from the standard Euclidean distance. Since we are working with regime dynamics represented by symbolic sequences, it is necessary to measure the distances between these symbolic sequences.

To detect clusters of countries with similar regime dynamics, we use the discrete distance measure, a common approach for symbolic time series analysis. For any given pair of countries, we first compute the yearly distance by comparing their regime status. The distance is assigned a value of zero if both countries are in the same regime and a value of one if they are in different regimes. In the second step, we sum these yearly distances over the entire period to determine the total distance between the two countries.

Given two symbolic series ${s_{i t}}_{t = 1}^{t = T}$ and ${s_{j t}}_{t = 1}^{t = T}$ corresponding to countries i and j, we define the following distance:

$d (i, j) = \sum_{t = 1}^{T} f (s_{i t}, s_{j t}),$ (5)

where $f (s_{i}, s_{j}) = {\begin{matrix} 0 if s_{i t} = s_{j t} \\ 1 if s_{i t} \neq s_{j t} \end{matrix} \forall i \neq j, t = 1, \dots, T .$ (6)

Intuitively, the more frequently two countries share the same regime, the smaller their distance will be. If two countries have identical sequences of regimes throughout the analysis period, they achieve the minimum possible distance, which is zero. Conversely, the maximum possible distance, denoted as T, occurs when two countries never share the same regime in any year.

To construct the MST, we employ Kruskal’s algorithm. The MST for this study, built with 111 nodes and 110 edges, emphasizes the most significant distances for each country. The graph provides an arrangement of countries that identifies the strongest connections within the sample. Each connection between two nodes represents the shortest path linking those countries, illustrating shared or differing regime dynamics.

Figure 4 shows the resulting tree.⁷ Note that all the computational elaborations in the present exercise are based in packages of the R-software. In this visualization: Node A (highlighted in blue) groups countries that maintained a consistent regime throughout the analysis period. This cluster includes developed economies such as the United States (USA), Uruguay (URY), Sweden (SWE), Portugal (PRT), Norway (NOR), Netherlands (NLD), Italy (ITA), Japan (JPN), Greece (GRC), the United Kingdom (GBR), France (FRA), Finland (FIN), Denmark (DNK), Germany (DEU), Canada (CAN), Barbados (BRB), Austria (AUT), and Belgium (BEL).

Figure 4.

Minimum Spanning Tree. The two clusters and the outliers are showed in the MST. Notes: each country is represented by a node in the MST. The first cluster is highlighted in green. See Appendix, Table A1 for country codes. Source: authors’ own elaboration.

Node D (marked in orange) represents another cluster that includes Uganda (UGA), the Philippines (PHL), Pakistan (PAK), Kenya (KEN), Honduras (HND), Côte d’Ivoire (CIV), and Gambia (GMB). These countries predominantly shared the R1 regime during the analysis period.

Nodes highlighted in red indicate countries with distinct regime dynamics, differing from those in Nodes A and D.

Given a predetermined number of groups for dividing the sample, the HT indicates how countries should be grouped. For instance, if the goal is to partition the sample into eight groups, the HT can be used to identify which countries belong to each group. The final step involves applying a hierarchical clustering stopping rule to determine the optimal number of groups.

In hierarchical cluster analysis, the output is typically a hierarchical tree that begins by grouping individual cases. However, we often seek a specific cluster solution, meaning we want to cut the hierarchical tree at a particular level to obtain a single classification of cases into a fixed number of categories. In the cluster analysis conducted using a hierarchical classification method, two groups of countries are identified. The stopping rules employed are the Pseudo-F (Calinski and Harabasz 1974) and the Pseudo-t test (Duda and Hart 1973).

There are various methods to determine where to stop the clustering process. These methods often start with one cluster and then evaluate whether splitting it into two improves a measure of fit (such as a loss function), continuing this process for each subsequent solution. The Calinski-Harabasz pseudo-F index is one such measure. It compares the sum of squared distances within the partitions to that of the unpartitioned data, adjusting for the number of clusters and the number of cases (Calinski and Harabasz 1974). Similarly, the Duda-Hart index compares the sum of squares in the next pair of clusters to be combined, both before and after the merge (Duda et al. 2000).

Both tests indicate that the optimal number of clusters is two. These two well-differentiated clusters contain 103 of the 111 countries, or approximately 90% of the countries in the sample.

Cluster analysis stopping rules are used to determine the optimal number of clusters. A stopping-rule value is computed for each cluster solution at each level of the hierarchy. For both rules used in this analysis, larger values indicate more distinct clustering. In Figure 5, the hierarchical tree (HT) resulting from the analysis shows that Cluster 1 (in green) includes 51 rich countries with low population growth, while Cluster 2 (in orange) consists of 52 poorer countries with higher population growth. By analyzing the ultrametric distance at which countries branch in the tree (shown on the y-axis), it can be observed that Cluster 1 is slightly more homogeneous. The HT also reveals the presence of 8 countries with dynamics that are more differentiated from the rest.

Figure 5.

Hierarchical Tree. Notes: in the hierarchical tree, two clusters of homogeneous countries (1961-2020) are identified based on their population dynamics and economic performance. Table A1 in Appendix contains country codes. Source: authors’ own elaboration.

The first cluster, referred to as mature economies, includes 51 countries and is the most homogeneous, with the smallest sum of group distances in the Minimum Spanning Tree (MST). This cluster comprises Argentina, Australia, Austria, Belgium, Brazil, Barbados, Canada, Switzerland, Chile, Colombia, Costa Rica, Cyprus, Germany, Denmark, the Dominican Republic, Algeria, Spain, Finland, France, Gabon, the United Kingdom, Greece, China, Hong Kong, Ireland, Iceland, Israel, Italy, Japan, the Republic of Korea, Luxembourg, Mexico, Malta, Mauritius, Malaysia, the Netherlands, Norway, New Zealand, Panama, Portugal, Romania, Singapore, Sweden, Seychelles, Thailand, Trinidad and Tobago, Turkey, Taiwan, Uruguay, the United States, Venezuela, and South Africa. These countries are currently classified as upper-income or upper-middle-income nations.

In terms of regime dynamics, the common feature in this group is that they do not visit the R1 and R4 regimes throughout the entire analysis period. Most countries in this group remain in the R3 regime for the majority of the time. Some countries experience a brief initial phase alternating between R1 and R2 (with R2 being dominant), lasting at most for the first decade and a half of the analysis period.⁸ In summary, this group consists of middle- and high-income countries that, during the analysis period, exhibited low or declining population growth in the early years.

The second group, which we call young economies, contains 52 countries and is less homogeneous than the previous one. It includes Burundi, Benin, Burkina Faso, Bangladesh, Bolivia, Central African Republic, China, Côte d’Ivoire, Cameroon, Democratic Republic of the Congo, Republic of the Congo, Comoros, Cabo Verde, Ecuador, Egypt, Ethiopia, Ghana, Guinea, Gambia, Guinea-Bissau, Guatemala, Honduras, Haiti, Indonesia, India, Jordan, Kenya, Sri Lanka, Lesotho, Morocco, Madagascar, Mali, Mozambique, Mauritania, Malawi, Namibia, Niger, Nigeria, Nepal, Pakistan, Philippines, Paraguay, Rwanda, Senegal, Syrian Arab Republic, Chad, Togo, Tanzania, Uganda, Zambia, and Zimbabwe.

As with the previous cluster, the defining characteristic of the countries in this group is that, during the period of analysis, they alternate almost entirely between regimes R1 and R4, mirroring the dynamics of the mature economies cluster. The countries in this cluster do not visit the R3 regime and only briefly enter the R2 regime. These countries are mostly lower-middle-income or low-income, with high population growth. They are either still in the intermediate stages of demographic transition or have completed the transition but have not yet reaped the demographic dividend.

Table 3 provides key descriptive statistics for each cluster and for the overall sample. Figure 6 illustrates the geographic distribution of the clusters.

Table 3.

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Descriptive statistics for each cluster and the sample

	GDP				Population
	Mean	Median	Min	Max	Mean	Median	Min	Max	N
Cluster 1	21.784	17.520	251	112.942	1.19%	1.04%	-18.05%	4.33%	51
Cluster 2	2.746	2.138	428	13.988	2.46%	2.59%	-6.54%	13.34%	52
All countries	11.800	5.485	251	112.942	1.85%	1.93%	-18.05%	13.34%	111

Figure 6.

Cluster obtained: geographical location. Notes: cluster 1 is shown in green, Cluster 2 is shown in orange and the outliers are shown in red. Source: authors’ own elaboration.

As indicated in Table 3, 104 of the 111 analyzed countries are grouped into two clusters. The remaining countries are considered outliers, exhibiting dynamics that differ significantly from the rest. It is important to note that the existence of only two distinct typological groups – each with very different population dynamics and economic growth patterns – stems from the homogeneous qualitative regime dynamics within each cluster, which can be clearly differentiated from the other cluster.

The proposed methodology separates the dynamics of the two variables into two distinct forms: one within each regime and another associated with regime transitions. It is the latter dynamic, representing structural change, that is emphasized in this analysis. Therefore, the results suggest that we have two distinct groups, each homogeneous in terms of regime dynamics.

To conclude this section, we characterize the two groups based on a set of variables that the literature considers closely related to the two dimensions of our regime dynamics analysis. Specifically, these variables are interconnected within a dynamic system that reflects both dimensions of our study. First, we consider the Economic Complexity Index (ECI), which serves as an indicator of the knowledge embedded in a country’s productive structure (Hausmann and Hidalgo 2011). This structure is seen as a reflection of the capacities and networks of factors and inputs available to the country for production (Utkovski et al. 2018).

Second, we include the Human Development Index (HDI), which reflects the living conditions of a population in terms of life expectancy, education, and income. Finally, we also consider a measure of human capital accumulation in each country.

Figure 6 shows the geographical distribution of the countries in each cluster, revealing that many neighboring countries are grouped within the same cluster (e.g., European countries and several in the Americas).

Figure 7 illustrates the differences in the dynamics of each variable for each cluster. While both clusters share the same overall trend, the intensity varies. The evolution of the average real per capita GDP shows that Cluster 2 consistently lags behind Cluster 1, with the divergence widening over time. Although both clusters exhibit increasing economic performance, the gap between them becomes more pronounced. Conversely, while both clusters show declining population growth rates, the cluster of poorer countries maintains higher rates, and this gap also shows no signs of narrowing.

Figure 7.

Economic performance and population growth. Notes: evolution of the median for each variable by cluster and for the entire sample. Source: authors’ own elaboration.

As shown in Figures 8 and 9, the evolution of the ECI and the HDI follows a similar trend, maintaining a nearly constant gap over the period. However, as illustrated in Figure 10, this pattern does not hold for the evolution of human capital.

Figure 8.

Economic Complexity Index. Notes: we use freely available data on the Economic Complexity Index from the MIT Economic Complexity Observatory. Source: authors’ own elaboration. Available on: http://atlas.media.mit.edu.

Figure 9.

Human Development Index. Notes: Human Development Index evolution (average) per group. Source: UN (2020). Human Development Index (HDI) and authors’ own elaboration. Available on: http://hdr.undp.org/en/indicators/137506

Figure 10.

Human Capital Index. Notes: Human Capital per capita evolution (average) per group. Source: PWT 10.0, Human capital index, based on years of schooling and returns to education and authors’ own elaboration.

In summary, we grouped countries based on their regime dynamics as represented by symbolic series constructed from population growth rates and per capita GDP. We found that these groups could be clearly differentiated using other variables not included in the symbolization but considered fundamental in the literature. This suggests that symbolizing just two variables significantly reduced the complexity of a dynamic system involving multiple variables, while still preserving valuable information that allowed us to characterize the entire system.

To complete this stage of the analysis, we repeated the exercise using the growth rates of population and GDP per capita, rather than their levels. This approach partitions the state space based on the median of both rates for each period. Applying the same clustering methodology, we found that the results were quite similar. In summary, the clusters are distinguished not only by their population growth and economic performance but also by their economic growth dynamics.

Cluster dynamics, global distance and convergence

In the previous analysis, we gathered insights into the dynamics over the entire period. As noted earlier, the clusters exhibit distinctly different dynamics throughout the period, with notable qualitative differences between them. In this section, we examine the evolution of the clusters over time. Our aim is to investigate whether the size and composition of the clusters remained stable and, ultimately, to assess whether there was a trend toward convergence, meaning whether the clusters displayed increasingly similar dynamics or diverged further apart.

To conduct this analysis, we divided the period into 27 overlapping 30-year windows and repeated the previous clustering procedure for each window.

The results indicate that the number of clusters remained consistent with the earlier analysis. The composition of each cluster was relatively stable, with only a few countries changing clusters over time. For instance, Nicaragua, Ecuador, and Namibia were initially part of Cluster 1 in the first windows, shifted to Cluster 2 during the intermediate windows, and eventually moved out of both clusters.

In terms of homogeneity within each group, there is a clear trend toward increasingly similar trajectories among countries within the same group. As the analysis progresses across the different time windows, the sub-cluster of countries exhibiting identical dynamics grows in size.

To assess whether the countries in the sample, considered collectively, moved closer together or diverged over the period of analysis, a measure of global distance is necessary. Using the methodology outlined by Onnela et al. (2002), the sum of all the distances in the MST represents the tree’s diameter and provides insight into the overall proximity of the countries to one another.

The evolution of this global distance across the trees for each time window is shown in Figure 11. The figure indicates a slight tendency for distances to shorten, suggesting that the dynamics of the countries in the sample became more similar over time.

Figure 11.

Evolution of the diameter of the MST for windows of 30 years. Source: authors’ own elaboration.

The observed decreasing trend in the MST’s diameter does not indicate convergence between the clusters. Instead, it reflects the increasing compactness within each cluster, as the trajectories of countries within each group become more similar.

Final conclusions

The relationship between economic and population growth has been a longstanding topic of study in economics. However, there is no theoretical consensus on the scope and mechanisms through which population growth and economic growth influence each other. Empirical evidence further complicates this issue, as findings from numerous studies remain contradictory and inconclusive. Given this diversity of outcomes reported in the literature, we opted for a descriptive and exploratory analysis to investigate the links between economic and population growth.

In our paper, we introduce a methodology that facilitates a model-free topological and hierarchical description of the relationship between economic growth and population dynamics. While we do not explore the underlying mechanisms at play, such as causes, effects, or propagation pathways, the proposed methodology indirectly points to the presence of dynamic interdependence in the trajectories of economic growth and population change across countries. Additionally, it provides evidence against single-model approaches for explaining the complex interdependence between demographic changes and economic growth.

By applying clustering techniques and introducing the concept of regime dynamics, we aim to identify groups of countries that are internally homogeneous in their dynamic relationships between demographic change and economic growth, while remaining clearly distinct from other groups.

Our findings reveal evidence of multiple coexisting patterns in the dynamic relations between these variables. Specifically, we identify two well-differentiated groups of countries, each displaying a unique dynamic pattern: mature economies and young economies.

The first group, consisting predominantly of OECD countries, is characterized by low population growth and strong economic performance. In contrast, the group of young economies, primarily located in Central Africa, exhibits above-average population growth paired with poor economic growth.

The methodology we use also allows for the inclusion of additional variables such as the Economic Complexity Index (ECI), the Human Development Index (HDI), and human capital accumulation. This has enabled us to identify key characteristics of the productive structure and living standards shared by countries within the same cluster. The analysis reveals clear differences between the clusters in terms of the evolution of these variables, which serves to reinforce the conclusions from the previous analysis.

When analyzing the overall dynamics of the countries in the sample, we observe a slight tendency for their trajectories to converge. However, this convergence is not due to a blending of dynamics between the clusters, but rather to increased homogeneity within each cluster. Over time, each cluster becomes more compact, and the trajectories of countries within the same cluster become increasingly similar.

Our findings – on the variety of ways in which population dynamics are linked to economic performance, and how these relationships evolve – have important implications for the design and evaluation of public policies. Given that the relationships between these variables are likely non-linear, and that their sign, intensity, and direction can change over time, it is crucial to periodically evaluate and revise policies to account for these dynamics.

Finally, we would like to highlight some limitations of the analysis and suggest directions for future research. One key limitation is that our analysis does not differentiate between natural population growth and the impact of net immigration. This distinction is important because the dynamic effects of these two sources of population change on economic output are likely to differ. Incorporating this distinction into future research is therefore a crucial next step.

Additionally, it is important to reiterate that this study is exploratory and descriptive in nature. As such, it does not allow for conclusions regarding causal relationships, nor does it provide insights into the sign or magnitude of any potential effects.

A promising direction for future research would be to conduct a cointegration and causality analysis using panel data, based on the groups identified in this study (countries with similar dynamics in terms of population growth and economic performance). This would involve testing for potential shifts in the relationship between population and economic growth at specific points in time. Prior to this, it would be essential to analyze the hypothesis of linearity and compare the results with those found in the existing empirical literature.

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Information about the authors

Emiliano Alvarez – member of economic dynamics research group, Department of Quantitative Methods, Faculty of Economics and Administration, University of the Republic. Montevideo, 11200, Uruguay. Email: emiliano.alvarez@fcea.edu.uy

Juan Gabriel Brida – member of economic dynamics research group, Department of Quantitative Methods, Faculty of Economics and Administration, University of the Republic. Montevideo, 11200, Uruguay. Email: elbrida@gmail.com

Gaston Cayssials – member of economic dynamics research group, Department of Quantitative Methods, Faculty of Economics and Administration, University of the Republic. Montevideo, 11200, Uruguay. Email: gacayssials@gmail.com

Verónica Segarra – member of economic dynamics research group, Department of Quantitative Methods, Faculty of Economics and Administration, University of the Republic. Montevideo, 11200, Uruguay. Email: verosegarras@gmail.com

Appendix

Table A1.

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Country Codes

Code	Country	Code	Counry	Code	Country
ARG	Argentina	GAB	Gabon	NAM	Namibia
AUS	Australia	GBR	United Kingdom	NER	Niger
AUT	Austria	GHA	Ghana	NGA	Nigeria
BDI	Burundi	GIN	Guinea	NIC	Nicaragua
BEL	Belgium	GMB	Gambia	NLD	Netherlands
BEN	Benin	GNB	Guinea-Bissau	NOR	Norway
BFA	Burkina Faso	GNQ	Equatorial Guinea	NPL	Nepal
BGD	Bangladesh	GRC	Greece	NZL	New Zealand
BOL	Bolivia	GTM	Guatemala	PAK	Pakistan
BRA	Brazil	HKG	China, Hong Kong SAR	PAN	Panama
BRB	Barbados	HND	Honduras	PER	Peru
BWA	Botswana	HTI	Haiti	PHL	Philippines
CAF	Central African Republic	IDN	Indonesia	PRT	Portugal
CAN	Canada	IND	India	PRY	Paraguay
CHE	Switzerland	IRL	Ireland	ROU	Romania
CHL	Chile	IRN	Iran	RWA	Rwanda
CHN	China	ISL	Iceland	SEN	Senegal
CIV	Côte d’Ivoire	ISR	Israel	SGP	Singapore
CMR	Cameroon	ITA	Italy	SLV	El Salvador
COD	D.R. of the Congo	JAM	Jamaica	SWE	Sweden
COG	Congo	JOR	Jordan	SYC	Seychelles
COL	Colombia	JPN	Japan	SYR	Syrian Arab Republic
COM	Comoros	KEN	Kenya	TCD	Chad
CPV	Cabo Verde	KOR	Republic of Korea	TGO	Togo
CRI	Costa Rica	LKA	Sri Lanka	THA	Thailand
CYP	Cyprus	LSO	Lesotho	TTO	Trinidad and Tobago
DEU	Germany	LUX	Luxembourg	TUN	Tunisia
DNK	Denmark	MAR	Morocco	TUR	Turkey
DOM	Dominican Republic	MDG	Madagascar	TWN	Taiwan
DZA	Algeria	MEX	Mexico	TZA	Tanzania
ECU	Ecuador	MLI	Mali	UGA	Uganda
EGY	Egypt	MLT	Malta	URY	Uruguay
ESP	Spain	MOZ	Mozambique	USA	United States
ETH	Ethiopia	MRT	Mauritania	VEN	Venezuela
FIN	Finland	MUS	Mauritius	ZAF	South Africa
FJI	Fiji	MWI	Malawi	ZMB	Zambia
FRA	France	MYS	Malaysia	ZWE	Zimbabwe

1 In the case of Germany the period of analysis is 1970-2000.

2 Available for download at www.ggdc.net/pwt.

3 We aimed to strike a balance between including as many countries as possible while at the same time covering a period long enough to ensure the robustness of our methods.

4 The results we got are contingent on the specific thresholds we relied upon. For future research, it would be interesting to explore alternative partitions of the state space and compare the results with the ones obtained here.

5 Given that our framework considers overall population growth without differentiating the effects of birth rates and mortality rates, it’s not possible to ascribe the demographic dividend to a single specific regime. That said, in a regime sequence of the type R1 → R2 → R3, the demographic dividend would be captured somewhere between.

6 See Brida et al. (2003) and Brida and Punzo (2003) for a more detailed exposition of regime dynamics and its symbolic representation. In Brida et al. (2011a) can be found an empirical analysis on convergence clubs that apply the same approach as the one used in our paper.

7 The Figure shows 86 nodes because some countries had the same regime throughout the analysis period and therefore the distance between them was zero. These nodes are represented in the MST by the letters A, B, C, and D.

8 Three countries in the group, Australia, Ireland, and Luxembourg have some years alternating between R2 and R3 in the final 15 years of the analysis. One possible explanation: the relatively high influx of immigrants during those years. In fact, as a percentage of their population, these are the countries that received the most immigrants in the group during the last two decades.