Conditional β-Convergence in APEC Economies, 1960–2020: Empirical Evidence from the Pooled Mean Group Estimator

Abstract

The aim of this research is to analyze the impact of conditional variables—physical capital, population, and Total Factor Productivity (TFP)—on the economic convergence of the member economies of the Asia-Pacific Economic Cooperation (APEC) Forum over the period 1960–2020. This study employs a causal and correlational methodological approach, utilizing the pooled mean group (PMG) estimator within a non-experimental design framework for quantitative analysis. This methodology facilitates the estimation of conditional β-convergence, ensuring the statistical significance of estimates even in heterogeneous data panels with variables of integration order I(0) and I(1). The results indicate that physical capital, population growth, and TFP have significantly influenced the growth rates of APEC economies, contributing to economic convergence within the region during the 1960–2020 period. This study offers significant contributions by analyzing the 21 APEC economies over a 60-year period, utilizing a PMG model to estimate conditional β-convergence, and conducting comprehensive evaluations of short- and long-term trends. Consequently, the research recommends implementing policies that prioritize innovation, strengthen capital, create employment opportunities, and enhance productivity to reduce inequalities and foster sustainable growth across APEC economies.

1. Introduction

Economic globalization, which accelerated in the late 20th century, prompted the creation of international organizations to boost the global economy. One such organization, the Asia-Pacific Economic Cooperation (APEC), was founded in 1989 to capitalize on the growing interdependence of regional economies. APEC’s main objective is to promote widespread prosperity in the region through inclusive, sustainable, and innovative economic growth (Ávila, 2015).

APEC economies have shown notable dynamism. Between 1990 and 2020, while global per capita growth averaged 1.5% annually, APEC’s Gross Domestic Product (GDP) per capita grew by 2.28% per year (World Bank, 2022). The diversity of APEC economies is evident in their unique cultural, geographical, and social traits, as well as in the variations in their economic growth patterns. Though APEC economies have outpaced the global average, growth has occurred unevenly, with rapid expansions concentrated in certain economies over time.

The hypothesis of economic convergence, as discussed by Mankiw (2014), posits that under certain production levels and technological conditions, poorer economies will, over time, reach the level of wealth of richer economies. Empirical analyses in the literature both support this prediction, as demonstrated by DeLong (1988), Barro and Sala-i-Martin (1992a, 1992b, 1992c), and Barro (2015), and challenge it, as noted by Dowrick and Nguyen (1989), and Rodriguez et al. (2014).

The research aims to analyze the impact of conditional variables—physical capital, population, and Total Factor Productivity (TFP)—on the economic convergence of APEC member economies from 1960 to 2020. Consequently, this study focuses on economic convergence among APEC members by analyzing empirical data on regional economic growth levels and their specific determinants. To achieve this goal, the conditional β-convergence estimation is carried out using the pooled mean group estimator methodology proposed by Pesaran et al. (1999).

Analyzing convergence among different economies on a global scale is essential, as it involves examining the dynamics of economic cooperation and integration, as well as evaluating the performance of organizations and institutions that facilitate and support these processes. From a national perspective, the study of convergence is equally relevant, as it provides an indirect evaluation of development strategies and the effectiveness of implemented public policies. In this context, the present research contributes to the existing literature in several aspects: (a) conducting a comprehensive analysis of the APEC region’s economies over a 60-year period; (b) applying a dynamic PMG model to estimate conditional β-convergence; (c) focusing on three critical drivers of economic growth—physical capital, population, and TFP—to examine convergence; (d) providing nuanced insights into short- and long-term convergence processes within the region; (e) presenting empirical evidence that underscores the pivotal role of physical capital in short-term growth and TFP in long-term growth; and (f) emphasizing the need for tailored policies that promote innovation, enhance capital, create jobs, and boost productivity to reduce inequalities and ensure sustainable growth across APEC economies.

This document is organized into five main sections. The first section presents the introduction. The second section provides a theoretical framework related to conditional β-convergence. The third section describes the methodological approach used to measure conditional β-convergence. The fourth section discusses the results and contrasts them with findings from previous studies on the topic. Finally, the fifth section shows the conclusions derived from the research.

2. Conditional β-Convergence: A Theoretical Retrospective

The theory of economic growth can be traced back to early economic thought, particularly within the physiocratic and mercantilist traditions, which aimed to explain the accumulation of wealth. This focus is expressed in Adam Smith’s seminal work, The Wealth of Nations (Coyle, 2017).

Subsequent economic schools introduced key concepts, including the principles of diminishing returns, the framework of general equilibrium, and the model of the production function, which shaped modern growth theories (Barro & Sala-i-Martin, 2012). These ideas helped model growth dynamics and identify main drivers, including investment, labor, technological progress, and factor mobility (Weil, 2006).

According to Sarmiento (2009), growth models can be classified into two main categories: (a) demand-driven models, which draw on the works of Keynes (1936), Harrod (1939), Domar (1946), Kaldor (1963), and Thirlwall (1972); and (b) supply-driven models, further divided into three subgroups: (1) models that incorporate exogenous technological progress and savings, such as those proposed by Swan (1956) and Solow (1956); (2) models with endogenous savings rates, exemplified by the works of Koopmans (1965) and Cass (1965); and (3) models that integrate endogenous technological progress, as developed by Romer (1987), Lucas (1988), and Aghion and Howitt (1992).

As one of the foundational models in neoclassical growth theory, the Solow–Swan model (1956) offers a key framework for understanding economic growth driven by exogenous technological progress. Built on fundamental assumptions, such as a production function with constant returns to scale, diminishing marginal returns, and adherence to the Inada conditions, the model describes a closed economy without public spending (Barro & Sala-i-Martin, 2012). In this context, per capita income is determined by the accumulation of physical and human capital, along with factors such as savings, technological progress, depreciation, and population growth (Mankiw et al., 1992).

Mankiw (2014) argues that neoclassical (exogenous) growth models predict that diminishing returns to capital lead economies toward a stationary state. This stationary state represents the highest level of production an economy can achieve, determined by its savings rate and technological progress (Esquivel, 1999). As factors of production become scarce, the Inada conditions state that their marginal productivity increases, enabling less-developed economies to grow faster than more developed ones. This forms the basis of the economic convergence hypothesis, which asserts that poorer economies will eventually catch up with wealthier ones, given certain levels of production factors and technology (Barro & Sala-i-Martin, 2012).

Although early analyses of economic convergence were pioneered by Easterlin (1960) and Borts and Stein (1965), the seminal works of Abramovitz (1986), Baumol (1986), DeLong (1988), and Dowrick and Nguyen (1989) provided the first rigorous evaluation of the convergence hypothesis. These studies tested the hypothesis by examining the relationship between GDP per capita growth and initial income levels. An inverse relationship indicates economic convergence, while a positive one suggests divergence. This approach became known as absolute beta (β) convergence (Durlauf et al., 2015; Rabanal, 2017; Sala-i-Martin, 2000).

While Dowrick and Nguyen (1989), DeLong (1988), and Abramovitz (1986) identified evidence of divergence, Baumol (1986) observed signs of convergence, although his findings were later questioned. In this context, Barro (1991) and Barro and Sala-i-Martin (1991) argued that the convergence hypothesis had not been thoroughly evaluated, emphasizing the need for a more nuanced approach. The neoclassical model, while predicting that economies converge toward a steady state, acknowledges that this state varies between economies. These variations arise from differences in institutional capacity, cultural factors, and technological progress, meaning that each economy achieves its own unique stationary state. Addressing this complexity, Sala-i-Martin (2000) introduced the concept of conditional β-convergence, which allows for convergence within individual contexts by accounting for variables that shape each economy’s specific stationary state. Unlike absolute β-convergence, conditional β-convergence recognizes these contextual factors, providing a more realistic framework for understanding economic convergence (Barro & Sala-i-Martin, 2012).

Understanding income convergence is essential for assessing globalization, institutional roles, and the effectiveness of public policies. Key studies on international convergence include works by Barro (1991, 2015), Crespo et al. (2022), Kremer et al. (2022), Martínez (2021), Rodriguez et al. (2014), Singh (2022), and Smith (2024). In the context of APEC, notable contributions come from Carmignani (2006), Engelbrecht and Kelsen (1999), Ibrahim and Shah-Habibullah (2013), Michelis and Neaime (2004), Morrison and Pedrosa (2007), and Vu (2015).

The importance of convergence analysis in shaping national development strategies is emphasized by Esquivel (1999). Notable contributions in this field include works by Adabar (2001), A. Díaz et al. (2017), Gömleksiz et al. (2017), Kumo (2011), León (2013), and Ochoa (2010). In the case of APEC, important studies have been conducted by Barro (2016), Caballero et al. (2019), and J. Díaz et al. (2009).

3. A Methodological Approach for Measuring Conditional β-Convergence

This section outlines the methodological framework for conditional β-convergence, as developed by Barro and Sala-i-Martin (1991, 1992a, 1992b, 1992c). It also explains how conditional β-convergence is operationalized in this study using the pooled mean group (PMG) approach.

3.1. Absolute and Conditional β-Convergence

β-convergence analysis evaluates whether the gap between less-developed and more-advanced economies narrows over time (Rabanal, 2012). Empirically, it indicates that less-developed economies grow at a faster rate than their advanced counterparts (Rodríguez & Mendoza, 2015). Thus, β-convergence measures the speed at which a less-developed economy catches up with a more-advanced one (Rodríguez et al., 2016). According to Sala-i-Martin (2000), the mathematical formulation of absolute β-convergence is expressed as follows:

ϒ_it = α_it − βlog(y_i, _t0) + u_it

(1)

where ϒ_it is the growth rate of GDP per capita of the economy (i) between period 0 and t (dependent variable); log(y_i, _t0) represents the per capita income level of each economy, which serves as the explanatory variable; α_it is a parameter assumed to be uniform across all economies, indicating a similar level of the steady state; u_it is a random variable with zero mean, constant variance, and a distribution independent of log(y_i, _t0); and β represents the speed of convergence between the economies and serves as the parameter to be determined (Dávalos et al., 2015; Navarro et al., 2018).

Cass (1965) explains that a negative β coefficient indicates convergence, whereas a positive coefficient signifies divergence. Absolute β-convergence, in this context, reflects an inverse relationship between per capita income growth rates and initial income levels. Likewise, Rodríguez et al. (2012) highlight that absolute β-convergence assumes income levels converge without accounting for the factors that influence the steady state of each economy.

Equation (1) reflects the theoretical implications of the neoclassical growth model but fails to align with empirical evidence. Although the assumption that all economies converge to the same stationary state—sharing uniform rates of technological progress, preferences, and savings levels—may provide a convenient mathematical framework, it is outdated and unrealistic. Empirical evidence indicates that international economies are heterogeneous in their economic, sociocultural, and institutional characteristics. Consequently, we should not expect the poorest economies to grow faster than the richest. Rather, the fastest-growing economies are those furthest from their own stationary state (Barro & Sala-i-Martin, 2012). This implies that the absolute convergence equation is mis-specified, leading to a bias in the estimation of β and resulting in incorrect inferences.

To address this limitation, Barro and Sala-i-Martin (1991, 1992a, 1992b, 1992c) introduced the conditional β-convergence methodology. Conditional convergence shares the components of absolute convergence but uses multiple regression. By adding variables to the growth rate analysis, it estimates a proxy value of each economy’s stationary state. Furthermore, this approach accounts for the heterogeneity among economies, providing a more accurate estimate of their individual stationary states (Gómez-Zaldivar et al., 2010). The inclusion of these variables modifies Equation (1), resulting in the conditional convergence equation (Sala-i-Martin, 2000)

ϒ_it = α_it − βlog(y_i, _t0) + φX_it0 + u_it

(2)

The term ϒ_it (dependent variable) represents the growth rate of the GDP per capita of the economy (i) between periods 0 and t. The parameter α_it and the disturbance term u_it follow the same logic as in Equation (1). X_it0 is a vector of variables determining the stationary state position of each analyzed economy (i).

The key difference between absolute and conditional convergence lies in the treatment of excluded variables. If the variable vector X_it0 is essential for determining the stationary state, it is likely correlated with the economy’s income level (y_i, _t0). In Equation (1), X_it0 is part of the error term (u_it), causing a correlation between u_it and the explanatory variable of the income level (y_i, _t0) in the absolute convergence equation (Barro & Sala-i-Martin, 2012).

In Equation (2), economic convergence is indicated by a negative β coefficient after including the variables (X_it0) that condition each economy’s stationary state. In conditional convergence estimates, the variable vector (X_it0) is essential for determining stationary state levels, making the selection of these variables crucial for accurate analysis (Barro, 2016).

3.2. Conditional β-Convergence with PMG

The literature review reveals that most studies on conditional β-convergence estimation employ static econometric estimators (Barro, 2015, 2016; Caballero et al., 2019; Carmignani, 2006; Durlauf et al., 2015; Gómez-Zaldivar et al., 2010; Ibrahim & Shah-Habibullah, 2013; Michelis & Neaime, 2004; Osorio, 2019; Vu, 2015).

The main limitation of conditional β-convergence estimates is the issue of stationarity, as income convergence analyses rely on GDP growth, typically stationary at level I(0). The problem arises because econometric studies suggest that regressions using static estimators, whether with fixed or dynamic effects, involving variables with integration orders I(0) and I(1), are spurious. This limitation is overcome by the PMG estimation.

Economic convergence studies often span extended periods, which static estimators may fail to capture. The PMG estimator addresses this by incorporating lags and trends, crucial for analyzing temporal dependencies. It also provides estimates that reveal the variable behavior in both the short- and long-term, offering a more accurate understanding of the phenomenon under study.

Given these considerations, the most suitable methodology for analyzing conditional β-convergence among APEC economies from 1960 to 2020 is the dynamic regression approach through the PMG estimator proposed by Pesaran et al. (1999).

3.3. Equation of the Model

This study analyses the economies within APEC, which exhibit significant heterogeneity in cultural, economic, and institutional factors due to their diverse historical trajectories. The PMG estimation occurs in two simultaneous stages. First, the long-term equation is addressed, following the approach by Pesaran et al. (1999). The empirical application of the PMG model is based on the following assumptions:

$${\mathrm{Y}}_{\mathrm{i}\mathrm{t}}={\mathsf{\theta }}_{0\mathrm{i}}+{\mathsf{\theta }}_1{\mathrm{l}\mathrm{n}\mathrm{X}1}_{\mathrm{i}\mathrm{t}}+{\mathsf{\theta }}_2{\mathrm{l}\mathrm{n}\mathrm{r}\mathrm{k}\mathrm{n}\mathrm{a}}_{\mathrm{i}\mathrm{t}}+{\mathsf{\theta }}_3{\mathrm{l}\mathrm{n}\mathrm{e}\mathrm{m}\mathrm{p}}_{\mathrm{i}\mathrm{t}}+{\mathsf{\theta }}_4{\mathrm{c}\mathrm{t}\mathrm{f}\mathrm{p}\mathrm{c}\mathrm{r}\mathrm{e}}_{\mathrm{i}\mathrm{t}}+{\mathrm{U}}_{\mathrm{i}\mathrm{t}}$$

(3)

where i represents the APEC economies; t is the period in time; $\mathsf{\theta }$ is the vector of long-term coefficients; Y is the growth rate of the logarithm of the GDP per capita at purchasing power parity prices (dependent variable); lnX1 is the logarithm of the GDP per capita at purchasing power parity prices (X₁); lnrkna is the natural logarithm of capital services at constant national prices, where the base year corresponds to 2017 (X₂); lnemp is the natural logarithm of the number of people hired (X₃); ctfpcrec is the growth rate of Total Factor Productivity (TFP) at purchasing power parity prices (X₄); and U is the disturbance term, a random variable that satisfies the following conditions: it has a zero mean, is independent of Y, and exhibits constant variance (see

Table A1. Variables and indicators of the conditional β-convergence model.

Nomenclature	Variable	Indicator	Source
Y	GDP growth per capita	Growth rate of log GDP per capita at purchasing power parity prices.	University of Groningen (2024).
X1	Gross Domestic Product per capita	Log of GDP per capita at purchasing power parity prices.	University of Groningen (2024).
lnrkna	Physical capital	Logarithm of capital services at purchasing power parity prices.	University of Groningen (2024).
lnemp	Population	Logarithm of the number of people hired.	University of Groningen (2024).
ctfpcrec	Total Productivity of Production Factors	Growth rate of Total Factor Productivity at purchasing power parity prices.	University of Groningen (2024).

Source: designed by the author.

).

In the second stage, the PMG model estimation is complemented by reparametrizing common factors among the groups, as outlined by Pesaran et al. (1999):

$$\begin{array}{ll}\Delta {\mathrm{Y}}_{\mathrm{i}\mathrm{t}}={\mathsf{\varphi }}_{\mathrm{i}}{\mathrm{Y}}_{\mathrm{i}\mathrm{t}-1}& +\mathrm{l}\mathrm{n}{\mathrm{X}1}_{\mathrm{i}\mathrm{t}}{\mathsf{\beta }}_1+{\mathrm{l}\mathrm{n}\mathrm{r}\mathrm{k}\mathrm{n}\mathrm{a}}_{\mathrm{i}\mathrm{t}}{\mathsf{\beta }}_2+{\mathrm{l}\mathrm{n}\mathrm{e}\mathrm{m}\mathrm{p}}_{\mathrm{i}\mathrm{t}}{\mathsf{\beta }}_3+{\mathrm{c}\mathrm{t}\mathrm{f}\mathrm{p}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{c}}_{\mathrm{i}\mathrm{t}}{\mathsf{\beta }}_4+{\displaystyle \sum _{\mathrm{J}=1}^{\mathrm{p}-1}}{\mathsf{\lambda }}_{\mathrm{i}\mathrm{j}}^{\ast }\Delta {\mathrm{Y}}_{\mathrm{i},-\mathrm{j}}\\ & +{\displaystyle \sum _{\mathrm{J}=0}^{\mathrm{q}-1}}{\Delta \mathrm{X}1}_{\mathrm{i},-\mathrm{j}}{\mathsf{\delta }}_{\mathrm{i}\mathrm{j}}^{\ast }+{\displaystyle \sum _{\mathrm{J}=0}^{\mathrm{q}-1}}\Delta {\mathrm{l}\mathrm{n}\mathrm{r}\mathrm{k}\mathrm{n}\mathrm{a}}_{\mathrm{i},-\mathrm{j}}{\mathsf{\delta }}_{\mathrm{i}\mathrm{j}}^{\ast }+{\displaystyle \sum _{\mathrm{J}=0}^{\mathrm{q}-1}}\Delta {\mathrm{l}\mathrm{n}\mathrm{e}\mathrm{m}\mathrm{p}}_{\mathrm{i},-\mathrm{j}}{\mathsf{\delta }}_{\mathrm{i}\mathrm{j}}^{\ast }\\ & +{\displaystyle \sum _{\mathrm{J}=0}^{\mathrm{q}-1}}\Delta {\mathrm{c}\mathrm{t}\mathrm{f}\mathrm{p}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{c}}_{\mathrm{i},-\mathrm{j}}{\mathsf{\delta }}_{\mathrm{i}\mathrm{j}}^{\ast }+{\mathsf{\mu }}_{\mathrm{i}}\mathsf{\iota }+{\mathsf{\epsilon }}_{\mathrm{i}\mathrm{t}}\end{array}$$

(4)

where ϕ_i is the error correction speed parameter of the fitting term; Y_it is the vector of T × 1 of the observations of the growth rate of the logarithm of the GDP per capita; lnX1_it is the T × k matrix of observations on the regressors of the logarithm of the GDP per capita; lnrkna_it is the T × k matrix of observations on the regressors of the logarithm of capital services; lnemp_it is the T × k matrix of observations on the regressors of the natural logarithm of the number of people hired; ctfpcrec_it is the T × k matrix of observations on the regressors of the growth rate of TFP; $\iota$ = (1, …, 1) is a vector T × 1 of 1s; Y_i,−j, X1_i,−j, lnrkna_i,−j, lnemp_i,−j, and ctfpcrec_i,−j are j-lagged values of the period of Y_it, X1_it, lnrkna_it and lnemp_it, and ctfpcrec_it; λ_it are scalars; $\mathsf{\delta }$ are vectors of coefficients k × 1; and ${\mathsf{\epsilon }}_{\mathrm{i}\mathrm{t}}$ is the error term (see Table A1).

4. Conditional β-Convergence in APEC Economies: Evidence from 1960 to 2020

This section outlines the findings on conditional β-convergence among APEC economies during the 1960–2020 period. Unlike absolute β-convergence, conditional β-convergence does not assume that all economies share the same stationary state. Instead, it uses a vector of conditioning variables tailored to each economy’s characteristics, allowing for the estimation of a unique stationary state for each economy under study. Given the 60-year temporal scope of the analysis, it is crucial not only to assess the impact of explanatory variables but also to determine whether a long-term equilibrium relationship exists among the variables.

4.1. Statistical Testing of the Model

The methodological framework begins with a cross-sectional dependence test to analyze whether the unobserved components of the regressors are correlated with the error term. The Pesaran CD test (2004) is applied to verify the existence of cross-sectional dependence.

Table 1. Cross-sectional dependence test CD (Pesaran, 2004).

Variable	Statisticians	Values
Y	CD	37.96
	p-value	0
lnX1	CD	78.1
	p-value	0
lnrkna	CD	81.65
	p-value	0
lnemp	CD	80.85
	p-value	0
ctfpcrec	CD	12.29
	p-value	0

Source: designed by the author using Stata MP 16.1.

presents the results of the cross-sectional dependence test for the estimation of conditional β-convergence, both for the dependent variable and the explanatory variables. The p-value for all the variables in the analysis is observed to be 0.000. Since this value is less than 0.05, the null hypothesis (Ho: there is transversal independence) is rejected, concluding the existence of cross-sectional dependence among the variables.

The results in Table 1 indicate the presence of cross-sectional dependence, demonstrating a strong correlation between the heterogeneity of the regressors and the error term. This necessitates the application of a second-generation unit root test. In this case, we use the test proposed by Pesaran (2003) to determine whether the variables are stationary. The null hypothesis of the test states that the series are non-stationary (possess a unit root), so we look for p-values below 0.05.

Table 2. Pesaran (2003) test results. Second generation unit root.

t-Bar	p-Value	t-Bar	p-Value	t-Bar	p-Value	t-Bar	p-Value	t-Bar	p-Value
Y		lnX1		lnrkna		lnemp		ctfpcrec
−4.640	0.000	−1.330	0.976	−3.700	1.000	−1.600	0.789	−2.080	1.000
ΔY		ΔlnX1		Δlnrkna		Δlnemp		Δctfpcrec
−4.360	0.000	−5.140	0.000	−2.840	0.002	−5.310	0.000	−5.200	0.000

Source: designed by the author using Stata MP 16.1.

summarizes the results of the test for each variable, both at level and in their first difference.

Regarding the explanatory variables (lnX1, lnrkna, lnemp, ctfpcrec) they are all stationary (they do not possess a unit root) in their first difference. Therefore, the null hypothesis of non-stationarity is rejected according to the second-generation unit root test proposed by Pesaran (2003), indicating that the variables are of integration order I(1). In the case of the dependent variable Y (the GDP per capita growth rate), the Pesaran test (2003) indicates that the variable is stationary at level (i.e., it does not follow a random walk process), implying that its stationary process is of order I(0). This finding is significant for the research because, empirically, values related to GDP growth tend to be stationary at the same level due to the stability of the growth rates of the indicator over time (Heston et al., 2002).

The literature review on absolute and conditional β-convergence estimations reveals that most studies use static panel data econometric estimators. These studies typically do not account for variables with different integration orders from I(1). The dependent variable in β-convergence estimations is the growth rate of the logarithm of GDP per capita, which is generally stationary at level, indicating it is I(0).

The fact that the economic growth variable (Y) indicator is stationary at level I(0) necessitates the use of an econometric regression that accommodates variables of different orders of integration, in this case, I(0) and I(1). Given these circumstances, the PMG estimator proposed by Pesaran et al. (1999) was chosen to estimate the conditional β-convergence.

By employing the pooled mean groups estimator, the coefficient of the error correction mechanism, denoted as ${\mathsf{\varphi }}_1$, is calculated. The expected result—a negative value less than one—determines that the variables of the model are cointegrated and that there is an equilibrium relationship in the long-term (Marín et al., 2023). Since cointegration is part of the PMG estimation process, the next step involves directly obtaining the conditional β-convergence.

4.2. The Results in APEC Economies with the PMG Estimator

Table 3. Conditional β-convergence model in the economies of the APEC, 1960–2020.

Variables	Coefficients	p-Value
Long-term
lnX1 (L2)	−0.0813	0.001
lnrkna (L2)	0.0445	0.002
lnemp (L3)	−0.0274	0.013
ctfpcrec (L4)	0.0516	0.046
Short-term
lnX1 (D1)	0.0417	0
lnrkna (D1)	0.0428	0.006
lnemp (D1)	−0.054	0.022
ctfpcrec (D1)	−0.0142	0.012
Error Correction (∅)	−0.277	0
Const	0.3554	0

Source: designed by the author using Stata MP 16.1.

presents the results of the conditional β-convergence estimation for the APEC economies over the period 1960–2020. Notably, the p-values for both the short-term and long-term parameters of the study variables are statistically significant at the 95% confidence level. According to the methodological approach proposed by Pesaran et al. (1999), it is essential first to verify the error correction mechanism, which illustrates how the variables adjust towards a long-term equilibrium relationship. If the error correction mechanism ranges between 0 and −1, it indicates a smooth and gradual adjustment towards the long-term equilibrium (Pesaran et al., 1999).

The results of the conditional β-convergence model for the period 1960–2020 show an error correction mechanism value of −0.2770. In temporal terms, this suggests that the variables return to equilibrium in the long-term after approximately 3.61 years. Since the value of the error correction mechanism is negative and less than one, it can be concluded that the variables used in the model exhibit a long-term equilibrium relationship. Therefore, cointegration is inferred between them, ensuring the statistical validity of the results.

To analyze conditional β-convergence, it is necessary to evaluate the behavior of the coefficient (β) obtained from the estimation of the explanatory variable, the logarithm of per capita income (X₁). Upon examination, it is observed that the coefficient is positive in the short-term (0.0417), while it is negative in the long-term (−0.0813). This indicates that there is evidence of economic divergence in the short-term, whereas the model demonstrates conditional economic β-convergence in the long-term.

The finding of short-term economic divergence is noteworthy, as it aligns with the observations of Moncayo (2004) and Crespo et al. (2022), who note that such divergence tends to be more prevalent over shorter time periods. This tendency is attributed to the susceptibility of low-income economies to shocks and cyclical economic fluctuations, often due to them having less efficient mechanisms to mitigate these impacts. In line with the presented model, it appears that the APEC economies are exhibiting this pattern. In the long-term analysis, the negative sign indicates that the economies of the APEC have exhibited conditional β-convergence. This suggests that as these economies adjust and structurally adapt to economic dynamics, per capita income differences tend to diminish over time.

The results regarding conditional β-convergence highlight that, although current economic shocks affect low-income APEC economies more significantly, a long-term structural adjustment has occurred. This adjustment has enabled poorer economies to narrow the per capita income gap with high-income economies. In other words, the economies comprising APEC demonstrated conditional β-convergence during the period 1960–2020.

The application of conditional β-convergence helps identify the role of conditioning variables in determining growth levels. In line with the literature on the neoclassical growth model, the explanation of the convergence hypothesis emphasizes the importance of physical capital accumulation. Therefore, the capital services indicator (rkna) was included among the conditioning variables to represent the contribution of capital stock to economic production.

The lnrkna coefficient exhibits a positive sign in both the short- and long-term, indicating a direct relationship between capital accumulation and economic growth, consistent with theoretical formulations on the subject (Solow, 1956; Swan, 1956; Martínez, 2021). Since the variable is expressed in logarithmic form, the coefficient indicates that for unit changes in capital services, the level of per capita income will respond with changes in the same direction at a rate of 0.0428 in the short-term and 0.0445 in the long-term. The impact of capital services on the growth of the GDP per capita in the APEC economies remained consistent in both the short- and long-term throughout the study period.

Following the economic growth literature, the model was conditioned not only with a physical capital variable but also with a variable representing population behavior, specifically the logarithm of the number of employed individuals (lnemp) (Jackson, 2022). The parameter for population exhibits a negative sign in both the short- and long-term, suggesting an inverse relationship between the number of workers and economic growth. In the short-term, an increase in the number of workers by one unit leads to a per capita income decrease of 0.0540. In the long-term, an increase in the number of workers by one unit leads to a 0.0274 decrease in per capita income. This inverse relationship between the GDP per capita and the working population is explained by the fact that the GDP per capita is calculated by dividing the GDP by the total population. Therefore, when the population grows, the proportion of the product per person decreases (Coyle, 2017; Crespo et al., 2022; Singh, 2022).

The variable that complements the conditional convergence analysis is related to TFP. The indicator used in the model is the growth rate of the level of TFP at purchasing power parity prices (ctfpcrec). The behavior of the ctfpcrec indicator is differentiated; in the short-term, it shows an inverse relationship with the growth rate of the logarithm of the GDP per capita, while in the long-term, the relationship is positive. This result aligns with findings from studies related to the endogenous growth model. According to the research of Lucas (1988) and Gramkow and Porcile (2022), allocating more resources to activities aimed at increasing productivity, such as research and technology development, initially leads to a reduction in total production in the short-term due to resources no longer being utilized as factors of production. However, in the long-term, the impact is positive because improvements in productivity enhance the ability to convert the factors of production into products.

In summary, the estimation of conditional β-convergence for the APEC economies from 1960 to 2020 indicates that although short-term economic shocks primarily affect low-income economies, a long-term structural adjustment has led to a reduction in the per capita income gap between the poorest and richest economies. This suggests that the analyzed economies exhibit conditional β-convergence over the long-term, portraying the APEC region as a “club” where income disparities among member economies are diminishing.

Regarding the conditioning variables (physical capital, population, and TFP) their roles in influencing GDP per capita growth rates differ between the short- and long-term. In the short-term, the physical capital variable (capital services, lnrkna) has the greatest impact on the growth of the APEC economies. However, in the long-term, the coefficient for TFP (ctfpcrec) is higher than that for physical capital. This implies that, over time, TFP has a greater impact than production factors, aligning with the perspectives of Acemoglu and Molina (2021), Aghion and Howitt (1992), Cass (1965), Koopmans (1965), Malik et al. (2021), Magazzino et al. (2022), Romer (1987), Smith (2024), Solow (1956), and Villanueva (2024). This is also consistent with the findings of Feronica et al. (2024), which indicate that all APEC economies that have reached a high-income level first underwent a transformation in their productive structure. This process involved a reduction in the relative importance of physical capital in favor of technological development.

The estimation of conditional β-convergence using a PMG estimator enabled the evaluation of the long-term impact of per capita income levels on the growth rates of economies. The results indicate that the poorest economies have narrowed the gap in per capita income levels with high-income economies over time. Additionally, the analysis of conditional convergence highlights the roles of physical capital, population, and TFP in economic growth. It is observed that while physical capital is a crucial factor in short-term growth, TFP becomes more influential in the long-term, significantly impacting the growth of per capita income levels in APEC economies from 1960 to 2020.

5. Conclusions

The theoretical perspective of convergence provides an ideal analytical framework for studying the disparity between economies and assessing whether regional growth benefits lower-income economies. The convergence hypothesis does not imply that poorer economies will inevitably catch up with higher-income ones. Instead, it suggests that, given relatively similar and equitable structural conditions, low-income economies will experience faster growth rates than higher-income ones, leading to a reduction in per capita income disparities. If these structural conditions are maintained in the long-term, the poorest economies could eventually catch up with the wealthiest.

Conditional β-convergence is a technique that evaluates economic convergence using a set of determining variables that influence economic growth. Unlike absolute β-convergence, it does not assume that all economies tend toward the same stationary state. Instead, it enriches the analysis by allowing inferences to be drawn from the behavior of the conditioning variables.

In methodological terms, the fundamental contribution of this article is the proposal to estimate conditional β-convergence using the pooled mean group (PMG) estimator. This approach maintains the statistical relevance of the estimations even in heterogeneous data panels with variables of integration orders I(0) and I(1). This is crucial because, empirically, it is rare for the GDP growth rate or the logarithm of the GDP to exhibit stationary behavior in their first difference. Therefore, using the PMG estimator for conditional β-convergence helps avoid spurious regressions. Additionally, the PMG estimator provides a better approach to incorporating a time perspective, which is particularly beneficial for economic convergence estimates that typically cover extensive time frames.

To condition the data, three variables were added to the regression of the GDP per capita growth rate as a function of the initial level of the GDP per capita. These variables were selected based on the Solow–Swan model and the empirical literature on convergence. They include physical capital, represented by capital services; population, represented by the number of workers; and Total Factor Productivity, represented by the TFP growth rate (Barro & Sala-i-Martin, 2012; Solow, 1956; Weil, 2006).

Regarding economic convergence, the results indicate that short-term economic shocks affect low-income APEC economies more significantly. Nonetheless, in the long-term, the coefficient (β) has a value of −0.0812, reflecting an inverse relationship. Interpreted through the PMG estimator, these findings suggest that as economies adjust and structurally adapt to economic dynamics, the disparities in per capita income levels between rich and poor economies tend to decrease over time. Therefore, the APEC economies exhibited conditional β-convergence during the period 1960–2020.

In general terms, the coefficients obtained for the conditioning variables demonstrate different dynamics in the short- and long-term. In the short-term, the physical capital indicator has the greatest impact on the growth of the APEC economies. However, in the long-term, TFP is the most influential indicator on the GDP per capita growth. This finding aligns with the arguments of Acemoglu and Molina (2021), Aghion and Howitt (1992), Cass (1965), Feronica et al. (2024), Koopmans (1965), Malik et al. (2021), Romer (1987), Solow (1956), and Villanueva (2024).

The substantial long-term influence of TFP on economic growth holds significant implications. Based on the empirical data of the variables, it can be inferred that among APEC members, economies that have achieved a high-income status have undergone a transformative process in their productive structure. This transformation involved a reduction in the relative significance of physical capital in favor of technological advancement. These results highlight the importance of promoting innovation, strengthening capital, creating employment opportunities, education, and the development of advanced productive capacities. To achieve this, it is essential to implement policies tailored to the specific characteristics of each economy, with a comprehensive approach that fosters regional cooperation, technology transfer, and regulatory harmonization. These measures, along with sustainable structural reforms, will not only reduce inequalities but also ensure inclusive and sustainable growth throughout the APEC region.

Based on the results of this research, the following future lines of study are proposed: (a) incorporating additional economic and institutional variables into analytical frameworks, (b) examining causal relationships among the variables studied, and (c) broadening the scope of the analysis to include other regions for inter-regional comparisons.