Throughout this research, the dynamics of population and economic growth are represented by the population growth rate and per capita GDP growth rate, respectively. Annual data on per capita GDP (in 2011 constant dollars, PPP-adjusted) and population, along with their respective growth rates, were obtained from the Penn World Table 10.0 database (Feenstra et al. 2015)². This database is widely regarded as a standard source for comparative economic growth studies. It includes annual data for 111 countries over the period 1960–2019³. During this period, the aggregate world population exhibited a clear trend.

As shown in Figure 1, the global population growth rate has been steadily declining, following a gradual and consistent trajectory with minimal fluctuations. This pattern aligns with the well-known stages of the demographic transition. However, significant disparities exist among countries regarding the timing and pace of their demographic transitions, which is the focus of this study.

The average growth rates of population and per capita GDP (Figure 2) over the analysis period are nearly identical, at 1.8% and 1.84%, respectively. However, the similarities end there. Average per capita GDP growth lacks a clear trend and has a standard deviation eight times larger than that of population growth. Furthermore, it exhibits erratic and volatile short-term behavior, with an average annual variation 40 times larger than that of population growth.

In this article, we propose a two-stage approach to examine the causal relationship between population growth and economic growth using panel data. In the first step, we employed a non-parametric methodology to group countries based on their homogeneous dynamics in population growth and economic development – two factors that influence the causal relationship between them. In the second stage, we tested causality by applying the procedure proposed by Dimitrescu and Hurling (2012).

Dimitrescu and Hurling (2012) extend Granger’s (1969) causality test, originally designed for time series, to panel data contexts, allowing for heterogeneous effects between observational units. This enables us to test for the presence of a causal relationship between population growth and GDP growth across different country clusters.

Dimitrescu and Hurling’s test relies on the cross-sectional average of individual Wald statistics associated with the standard Granger (1969) causality tests. The authors propose testing the null hypothesis of non-causality against the alternative hypothesis of causality. Under the null hypothesis, there is no causal relationship for any country in the panel. An advantage of this test is its ability to account for cross-sectional dependence, employing a block bootstrap procedure to correct empirical critical values. Accounting for this dependency is crucial, as ignoring it can lead to substantial bias and size distortions (Albaladalejo et al. 2022).

To address the nature of this cause-and-effect relationship, impulse-response functions are employed to illustrate the dynamic reaction of one variable to innovations in another. These functions are estimated using a GMM panel VAR approach for the groups of countries where Granger causality is found. Our impulse response analysis assumes that the error terms are orthogonal with unit variance. Thus, a shock occurs in only one variable at a time; since the variances of the error terms are one, a unit shock is simply an innovation of size one standard deviation.

To determine homogeneous groups of countries based on their dynamic patterns in population and economic growth, we employed the method suggested by Brida et al. (2020). This method involves conducting a hierarchical cluster analysis using a metric that enables the comparison of dynamic trajectories among different countries. To construct this metric, we utilized a symbolization process that transforms the original two-dimensional series defined by the dynamic trajectories of population growth rates and GDP per capita growth rates into a symbolic series that identifies shifts in economic regimes.

To describe the qualitative behavior of the joint evolution of economic and demographic growth, we introduced the notion of a regime (Brida et al. 2003; Brida and Punzo 2003). A regime is defined as a range of conditions characterizing the behavior of a system, specifically the joint dynamics of population and per capita output. We established two conditions: one sets a threshold for yearly population change, and the other sets a threshold for yearly change in the growth rate of per capita GDP. This results in the partitioning of the state space into four regions, each corresponding to a different relationship between demographic change and economic performance – in other words, different regimes. By taking the average change in per capita income and population during the analysis period for all countries, we obtain the following partition of the state space into four regions:

R ₁ ={(g_p, g_y): g_p ≥ μ_p, g_y ≤ μ_y}

R ₂ ={(g_p, g_y): g_p ≥ μ_p, g_y ≥ μ_y}

R ₃ ={(g_p, g_y): g_p ≤ μ_p, g_y ≥ μ_y}

R ₄ ={(g_p, g_y): g_p ≤ μ_p, g_y ≤ μ_y}

If we label each regime R_i by the symbol j, we can substitute the original bi-variate time series {(g_1p, g_1y), (g_2p, g_2y),…, (g_Tp, g_Ty)} by a sequence of symbols {s₁, s₂,…, s_T} such that s_t = j if and only if (g_p, g_y) belongs to R_j. This Symbolic Series summarizes the most relevant qualitative information on the dynamics of a country’s regime⁴.

When working with regime dynamics represented by symbolic sequences, we need to measure distances between symbolic sequences. Then, given two countries, i and j, with symbolic sequences and corresponding to countries i and j, we define the following distance:

where

Intuitively, the smaller the distance between two countries within the same regime, the more similarities they share. When two countries exhibit the exact same sequence of regimes, their distance is minimized to zero. The maximum possible distance is √T, occurring when two countries never coincide in the same regime in any given year.

After calculating all distances from the symbolic series of countries in the sample, we employed the Hierarchical Tree (HT) clustering technique to classify the countries in our study. To build this tree, we utilized the nearest neighbor single-link clustering algorithm, as described by Mantegna (1999) and Mantegna and Stanley (1999).

In this work, we chose to build country clusters solely based on the variables central to the analysis – population and GDP. This decision is motivated by three reasons. First, the impact of other factors that differentiate countries and influence GDP or population growth is already captured indirectly through population or GDP. Second, including additional controls at this stage would compromise comparability with the causality analysis between population and GDP dynamics in the second stage. Third, graphical analysis demonstrates that each of the three country clusters is reasonably homogeneous.

The MST enables the computation of the subdominant ultrametric distance matrix D* (Rammal et al. 1986), a prerequisite for building the Hierarchical Tree (HT). Figure 4 displays the dendrogram representing the HT obtained.

Given a predetermined number of groups for dividing the sample, the Hierarchical Tree (HT) illustrates how countries should be grouped. To determine the countries in each group, the final step involves applying a hierarchical clustering stopping rule to find the optimal number of groups. Using the Calinsky stopping rule (Calinski and Harabasz 1974) results in three well-differentiated clusters, encompassing 87 out of the 111 countries (approximately 80% of the sample).

The first group, termed ‘mature economies,’ consists of 32 countries and is the most homogeneous among the three. It exhibits the smallest sum of group distances in the minimum spanning tree (MST). This group includes all 24 initial members of the OECD, excluding Turkey⁵. The non-OECD countries in this group (Argentina, Barbados, Malta, Mauritius, Trinidad and Tobago, Romania, and Uruguay) are currently classified as upper-income or upper-middle-income countries.

In terms of regime dynamics, the common denominator in this group is that the countries almost strictly alternate between regimes R₃ and R₄ throughout the entire analysis period. Some countries in the group, such as Canada, Chile, and Trinidad and Tobago, experience a brief initial phase alternating between R₁ and R₂ (concentrated in R₂), lasting at most for the first decade and a half of the analysis period⁶. In summary, this group comprises countries that transitioned from high to low population growth before the analysis period or, in a few cases, at the beginning of the period (before the mid-1970s).

The second group, labeled ‘young economies,’ comprises 28 countries and exhibits the highest level of heterogeneity among the three groups. It includes 22 Sub-Saharan African countries, three Middle Eastern countries (Egypt, Jordan, and Syria), two Central American countries (Guatemala and Honduras), and Pakistan.

Following the pattern observed in the previous cluster, the defining characteristic of countries in this group is that, during the analysis period, they alternate almost entirely between regimes R₁ and R₂, mirroring the dynamics of the mature economies cluster. Among the 28 countries in this group, 16 have never visited regimes R₃ or R₄. Mauritania, Mozambique, and Syria are exceptions, where a short phase in R₃ and R₄ can be identified. Mauritania experienced this in the 1960s, Mozambique during the 1980s, and more recently, Syria in the last decade. The anomaly in Syria is attributed to population displacement resulting from the civil war that began in 2011.

Broadly speaking, countries in the third group, labeled ‘transition economies’,⁷ exhibit two distinct phases. In the first phase, countries alternate between regimes R₁ and R₂. In the second phase, they alternate between regimes R₃ and R₄. The timing of transitions between these phases varies, with extreme cases such as Korea shifting to the second phase as early as the late 1970s, while the Philippines did not transition until the 2000s. There is also variation in the proportion of years with above-average economic growth within each phase. For example, during the first period, this proportion is very low for Namibia, Venezuela, and Ecuador, but very high for Taiwan and Korea. The common denominator among the 26 countries in this group is that they transition from high to low population growth during the analysis period.

Many of these countries were able to capture the demographic dividend, as indicated by the duration spent in regimes R₂ and R₃ during the analysis period.

To assess the validity of the results from this stage, we examine the evolution of one of the proximate determinants of economic growth: human capital (see Figure 5). The graphical analysis below reveals the homogeneity of each of the three country clusters. The observed deviations are primarily associated with small countries, such as Jordan (indicated by the red series reaching the upper cluster), which do not alter the central findings of the paper. The figures demonstrate minimal overlap within the range of variation of this variable and a discernible order among the groups. The predominant commonality among the three groups is their shared temporal trend. In essence, this signals the robustness of our results.

Table 2 below presents the results of the Granger causality test conducted on the country panel. The findings indicate that, considering the complete sample, a bidirectional causal relationship exists between population growth and GDP per capita growth. The p-value associated with the test statistic suggests rejecting both null hypotheses, indicating that higher population growth contributes to increased GDP growth per capita, and vice versa.

When the analysis is disaggregated by country cluster, the results remain consistent. Once again, a bidirectional causality relationship is observed between population and GDP. An exception is found among countries in Cluster 1 (mature economies), where higher population growth does not correspond to higher GDP growth.

The results above have interesting implications. Countries in Cluster 1 lack incentives to promote population growth, as it does not translate into higher income. In contrast, countries in Clusters 2 (young economies) and 3 (transition economies) have clear incentives to do so. This suggests that countries in Cluster 1 may be experiencing an aging and declining population, while those in Clusters 2 and 3 experience accelerated population growth. This pattern aligns with global migratory flows: countries in Cluster 1 (high-income) exhibit reduced or even negative natural growth and receive constant migratory flows from countries in Clusters 2 and 3, where natural growth is higher.

Following the confirmation of a bidirectional causal relationship between population growth and GDP per capita growth, we investigated the nature of that causality using impulse-response functions. Figure 6 demonstrates that the series considered in the panel VAR model satisfy the stability condition (i.e., stationarity), as the eigenvalues fall within the unit circle.

The first row of Figure 7 illustrates the initial scenario for the entire panel, indicating that a shock in one variable (impulse) leads to an increase (response) in the other. This suggests a positive association between both variables – higher population growth is associated with higher GDP growth, and vice versa. However, this observed increase dissipates after a few periods and may even be statistically insignificant in some cases.

In mature economies, where higher population growth does not directly result in increased GDP growth, a positive shock in economic growth leads to a positive impact on population increase, but the effect dissipates after 6 to 8 years. In the case of young economies, the outcome remains consistent: there is a positive response in population growth when economic growth increases. However, the response to an increase in population is a decrease in GDP per capita (although this effect is not significant).

For the transition economies cluster, the results align with the full panel analysis: higher population growth is associated with higher GDP growth, and vice versa.

Our findings highlight significant qualitative disparities in the dynamics of population and economic growth across the clusters. In the first cluster, a positive causal link exists between GDP and population, while in the other two clusters, the causal relationship is bidirectional but exhibits distinct signs.

As a final robustness check, we demonstrate that the series in levels (population and GDP) exhibit a long-term relationship, indicating cointegration, even when they are not stationary. Table 3 presents the findings, revealing a long-term relationship between population and GDP for clusters 1, 2, and 3. This result remains robust across different panel cointegration testing methods, including Kao, Pedroni, and Westerlund.