1 Introduction

The issue of cross-country differentials in development has been of great concern among economists and spawned a deep literature. Based on the work by Solow (1956), many prominent economists suggest that developing countries grow faster than developed ones (e.g., Barro and Sala-i-Martin, 1992; Mankiw et al., 1992; Sala-i-Martin, 1996). This convergence hypothesis, however, remained a lively debate as innovations bolster the support for convergence and provide evidence against it (Johnson & Papageorgiou, 2020). Recent studies claim that poor countries have been catching up to the rich since the mid-1990s (Kremer et al., 2022; Patel et al., 2021; Roy et al., 2016). However, such studies of economic convergence typically only consider variation in per capita income, even though economists agree that income alone is insufficient to approximate welfare (Hoekstra, 2019; Jorgenson, 2018; Nordhaus & Tobin, 1973). Even Simon Kuznets (1934), an architect of national income measures, famously said, ‘The welfare of a nation can scarcely be inferred from a measure of national income’.

There is a growing consensus that, in the long run, wealth matters more than income for welfare (Arrow et al., 2004; Boulding, 1950; Clark & Harley, 2020; Dasgupta et al., 2021; Stiglitz et al., 2009, p. 29). A prominent critique is that Gross Domestic Product (GDP), a flow variable indicating market dollars of output annually, does not account for the depreciation of capital assets. Perhaps most notably, GDP figures exclude the environmental damage of production. In contrast, Inclusive Wealth—a stock-based measure comprising all capital assets contributing to production and well-being—includes non-market depreciations. For this reason and more, it is often used as a forward-looking indicator or indicator of sustainable development (e.g., Kurniawan & Managi, 2019; Wang et al., 2022; Yamaguchi et al., 2016). When a country’s Inclusive Wealth per capita grows, the average citizen has more capital assets available to earn income and pursue well-being. As such, even though GDP is essential to short-run macroeconomics, it is unfit to address the sustainability of development (Dasgupta, 2021). Conversely, Inclusive Wealth is a more suitable measure for long run convergence. As Sir Partha Dasgupta puts it: ‘by economic progress we should mean growth in Inclusive Wealth’ (2021, p. 5).

Development in the short- and long run are not independent. Evidence suggests that impressive increases in per capita GDP come at the expense of the per capita Inclusive Wealth stock in many developing economies. A prime example is Laos (Lao PDR). Laos achieved annual per capita GDP growth of some 6% but a simultaneous annual decline of 1.5% in per capita Inclusive Wealth between 1990 and 2010 (UNU-IHDP-UNEP, 2015). Laos’s case is not unique. According to the United Nations University, one-third of all countries worldwide experienced a decline in per capita wealth despite achieving income growth in this period. This mismatch between income and wealth highlights a blind spot in convergence research. Income convergence suggests that the economic future is bright for billions of people. However, sustaining high national income levels will be impossible when countries liquidate wealth for present-day consumption. An impending divergence of standards of living may be imminent.

This study uses the Inclusive Wealth indicator (UNU-IHDP-UNEP, 2015) to investigate cross-country wealth convergence. Inclusive Wealth measures the social value of the productive base comprising stocks of produced, human, and natural capital for 140 countries between 1990 and 2010. The empirical strategy takes several approaches to estimate convergence. First, the paper tests so-called β-convergence. This idea asserts an inverse relationship between a country’s stock of wealth and its growth rate. I distinguish between unconditional or absolute convergence, which excludes structural determinants of development, and conditional convergence, which includes these so-called steady-state properties. The analysis employs a variety of techniques to address cross-sectional dependence and endogeneity. However, β-convergence is not a sufficient condition to bridge the gap in terms of development levels (Quah, 1993; Young et al., 2008). Therefore, I also analyze σ-convergence and stochastic convergence to understand better the convergence across the Inclusive Wealth cross-country distribution. Finally, I perform Blinder-Oaxaca decomposition, quantile regression, and club convergence analyses to demonstrate intra-distribution dynamics that remain unaccounted for in the previous analyses.

The study provides novel empirical evidence on cross-country convergence. Although the analysis confirms absolute/unconditional convergence of national income, results also reveal that absolute/unconditional divergence of per-capita Inclusive Wealth co-occurs. This discrepancy warrants caution against optimism. Many countries appear to earn income at the expense of their income-earning capacity. What empirical evidence I find of conditional wealth convergence comes with caveats. First, the evidence is not robust to bias-corrected estimation techniques that address endogeneity, finding conditional Inclusive Wealth divergence instead of convergence. Second, the speed of supposed conditional wealth convergence is much lower than conditional income convergence, suggesting that GDP convergence underestimates the duration of living standards reaching the steady state. Third, cross-country convergence dynamics are much better predicted by a country's capital stock composition than its size. Human and natural abundance drive divergence, hampering countries at the center of the per-capita wealth distribution. The Inclusive Wealth distribution is gradually becoming more dispersed with a more voluminous low-wealth club.

The remainder of this paper is organized as follows. Section 2 reviews the literature on cross-country convergence using non-income-based indicators. Section 3 provides a conceptual background on the relationships among Inclusive Wealth, income, and welfare. Section 4 describes the methodology and data. Section 5 presents and discusses the results of the analysis. Finally, Sect. 6 concludes.

2 Literature Review: Beyond GDP Metrics and Convergence

Aside from GDP, cross-country convergence studies employ composite indicators and sets of non-income-based variables to measure well-being. I briefly review the main findings of this literature.

In general, the result is that countries are converging slowly. Most studies employ the Human Development Index, which aggregates three categories—income, health, and education—into a 0 to 1 measure. Noorbakhsh's (2006) pioneering study tests β- and σ-convergence of HDI between 1975 and 2004 among 93 developing countries, finding that gaps decrease. Subsequent studies show that the speed of HDI convergence is "agonizingly slow" (Konya & Guisan, 2008), the income dimension is unrelated to education and health convergence (Gray Molina & Purser, 2010), and HDI convergence is not a smooth process (Mayer-Foulkes, 2010). More recently, Jordá and Sarabia's (2015) sophisticated convergence techniques corroborate all previous findings, firmly establishing the convergence of HDI and its components. Additionally, Ortega et al.'s (2016) heterogeneity analysis finds that not all countries converge toward the same final state but show patterns of club convergence.

The consistent findings of HDI convergence observed across diverse samples and employing various convergence techniques strongly indicate a pervasive trend of well-being convergence among different countries. However, HDI alone is ill-equipped to handle the complexity of measuring human well-being. The indicator is criticized for its arbitrary design, equal weights and substitutability of components, and variable selection, among other things (Kovacevic, 2010). Fortunately, the literature employs several alternative indicators of well-being.

Other studies examine cross-country convergence using a set of disaggregated quality-of-life variables or composite indices that consider more dimensions than income, education, and health. For example, Neumayer (2003) uses a wide range of quality-of-life variables to study β- and σ-convergence between 1960 and 1999 for a large panel of countries. His findings indicate a general trend of convergence, which is partially attributed to upper/lower bounds on some variables (e.g., infant mortality, literacy). Nevertheless, convergence is observed across the board; as he puts it: "convergence big-time". Kenny (2005) confirms this pattern, finding quality-of-life convergence even in decades when GDP did not converge.

Similarly, Peiro-Palomino et al. (2023) and Gligorić Matić et al. (2020) find cross-country convergence using the comprehensive Social Progress Index and Legatum Prosperity Index, which draw on dozens and hundreds of variables, respectively. Sinha Babu and Datta (2016) find convergence using four sustainable development indicators. Well-being convergence is even observed at the individual level. Ram (2021) estimates β- and σ-convergence of happiness across 132 countries from 2005 to 2018, while Apergis and Georgellis (2015) and Guriev and Melnikov find happiness convergence in smaller samples. The only limitation appears to be the unequal distribution of quality-of-life convergence across countries (Giannas et al., 1999; Paprotny, 2021).

Thus, on close examination, well-being convergence is strikingly uniform across samples spanning a century, an array of estimation techniques, scopes, and indicators. Collectively, the evidence portrays a favorable historical development.

What have we yet to uncover about 'beyond-GDP' convergence? The aforementioned studies largely comprise retrospective analyses. They implicitly explore the question, "How have historical inequalities evolved?". However, from a developmental standpoint, there is an opportunity to embark on a prospective analysis: "How are inequalities likely to evolve?". The Inclusive Wealth indicator is well-suited to address this question. Unlike estimations of actual living standards, this indicator monitors societies' capacity to achieve well-being and approximates a country's income-earning potential.

Thus, Inclusive Wealth offers valuable insights into the potential for well-being and income. Nevertheless, convergence studies employing prospective indicators remain scarce. This study endeavors to bridge this gap by examining cross-country Inclusive Wealth convergence.

3 Conceptualizing Income, Wealth, and Well-Being

As an alternative to Gross Domestic Product (GDP), some researchers consider Inclusive Wealth the preferred measure of economic progress (e.g., Dasgupta, 2021). There is a growing consensus that Inclusive Wealth is vital to understanding human’s ability to flourish (Arrow et al., 2004; Dasgupta et al., 2021; Stiglitz et al., 2009). It is designed to capture the available material means to support human well-being (Polasky et al., 2015; van den Bergh, 2022). Wealth aggregates the value of all capital assets (i.e., produced, human, and natural) that contribute to the welfare of society (Dasgupta, 2014; Hamilton & Hepburn, 2014). Increases in wealth indicate an improved capability to support a higher standard of living in the future (Hamilton & Hartwick, 2014). Hence, Inclusive Wealth is a forward-looking measure of potential future welfare in countries.

Figure 1 illustrates the links between wealth and well-being in a stylized economy. Wealth is the stock of produced, human, and natural capital assets that supply flows of resource inputs for production. In turn, the resulting output (income) is either reinvested to form new capital or used to satisfy present-day needs. Ideally, income contributes sufficiently to capital accumulation. When wealth grows, future generations have more resources and, therefore, an improved ability to earn income and raise their standard of living.

Fig. 1
figure 1

Wealth creation and its contribution to welfare in the capital-driven economy. This figure illustrates a stylized model of wealth creation. The productive base comprising natural, human, and produced capital creates output for consumption and reinvestment. Wealth also contributes to well-being directly. The illustration combines elements from two figures from the Inclusive Wealth Report (UNU-IHDP-UNEP, 2015, p. 18 and p. 203)

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Nevertheless, some economies accumulate wealth insufficiently and consume too much (Arrow et al., 2004). Instead of building capital assets, these countries liquidate assets to earn income. This matters for economic convergence because such a strategy is unsustainable in the long run. Consider Nauru, which had the highest GDP per capita in the world in the 1970s. This island nation has since exhausted its phosphate deposits and destroyed its agricultural potential. The island nation now ranks among the world's poorest in GDP per capita. Nauru's economic collapse signals that impressive income growth rates are merely transitory when driven by capital depletion. By extension, income convergence will not last when fueled by capital consumption. A decline in one type of capital asset can only contribute to ‘catch-up development’ when its revenues are converted sufficiently into other forms of wealth with equal or greater social value.Footnote 1 Hence, studying wealth convergence offers context to the existing literature on income convergence. Where income flows can gauge well-being today, wealth is a prospective measure of welfare—showing how income flows may develop in the future.

Some consider Inclusive Wealth and income complementary measures of economic performance (World Bank, 2021).Footnote 2 Like the balance sheet and income statement provide complementary information on firm performance, a country's national accounts are more comprehensive with both income flows and stock values of its assets. The rationale is that wealth alone cannot account for well-being. Consumption of goods and services (e.g., food, clothes) requires income flows. Without income, the stocks of natural, produced, and human capital assets can only provide for a limited array of material needs. As Stiglitz and Sen (2009, p. 29) put it, ‘income is an important gauge for standards of living, but in the end consumption and consumption possibilities over time matter. The time dimension brings in wealth.’

4 Data and Method

4.1 Data

4.1.1 Dependent Variables

The first dependent variable is per capita Inclusive Wealth provided by the Inclusive Wealth Report’s data appendix (UNU-IHDP-UNEP, 2015). Inclusive Wealth is developed by the United Nations Environment Program and the United Nations University—International Human Dimensions Program to measure a nation's capability to earn income and achieve well-being (Harley and Clark, 2020). As a forward-looking measure of development, it is designed to approximate whether a society can draw on its resources indefinitely to sustain its current level of development (Dasgupta et al., 2021). As such, Inclusive Wealth addresses several shortcomings of income-based measures of prosperity (Polasky et al., 2015).

Inclusive Wealth is defined as the aggregate value of all capital assets. Each capital stock is calculated by aggregating the value of a list of assets, each reflecting the asset’s lifetime potential to generate income. Shadow prices, which assign weights to each capital type, are constant within the time frame (UNU-IHDP-UNEP, 2015, p. 19).Footnote 3 For instance, the value of a particular natural resource is usually represented by the average market value of one unit of natural capital over the years 1990–2008. Therefore, the real dollar values of each capital stock are determined by its biophysical volume and are insensitive to price fluctuations. The original data provides values of each capital stock for 140 countries at five moments in time (1990, 1995, 2000, 2005, and 2010). Together, these countries cover 95% of the world's population.

The second dependent variable, GDP per capita, is used for benchmark analyses. The purpose is to juxtapose Inclusive Wealth convergence, which has not yet been studied, with the standard indicator for economic convergence. I employ the Penn World Table (PWT 10.1) 'real GDP at constant 2017 prices' data (Feenstra et al., 2015).

Furthermore, some analyses operationalize the dependent variable Inclusive Wealth as the change relative to the global mean by standardizing the natural log of per capita Inclusive Wealth per period (see Sect. 4.2.3).Footnote 4 To clarify, consider Fig. 2, which depicts the cross-country Inclusive Wealth distribution in 1990. The left y-axis shows the estimated kernel density distribution of per capita Inclusive Wealth. The right y-axis displays this dependent variable: countries’ change within the distribution between 1990 and 2010. A negative (positive) value shows a movement to the left (right) in the distribution.

Fig. 2
figure 2

Cross-country wealth distribution and relative country performance. The kernel density plot is derived from the per capita Inclusive Wealth log value. Each mark indicates a country. The left y-axis displays density, and countries’ change of position in the distribution between 1990 and 2010 is displayed on the right y-axis. Blue diamonds denote poor countries, natural capital-dependent countries are marked by green circles, and rich countries are marked by a red triangle. “Online Appendix A” discusses the method for country categorization

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4.1.2 Independent Variables

Although convergence analyses typically use a lagged dependent variable as the main independent variable, some analyses in the paper decompose Inclusive Wealth. Then, the independent variables are the natural logarithms of per capita human, produced, and natural capital. The rationale is that the individual capital stocks provide the inputs to create the output, which can be reinvested to accumulate Inclusive Wealth (see Fig. 1).

Human capital is the largest capital stock, followed by produced and natural capital. Natural capital shows the most cross-country variation. Oil states have the highest values, followed by well-endowed countries with low population density, such as Australia, Canada, and Iceland.

Natural capital consists of various types of renewable and non-renewable resources. Some countries’ non-renewable resource data are missing in the Inclusive Wealth report (e.g., Sierra Leone, Uganda, Rwanda, The Gambia). Depleting and reinvesting unreported mineral resources may give a false positive indication of Inclusive Wealth, leading to an amplification bias. A dummy addresses the issue.

4.1.3 Control Variables

Analyses of conditional convergence employ steady state control variables that measure sources of lasting development differentials across countries. Differences between steady states are considered permanent and deeply rooted in countries' institutions, culture, and geography. Kremer et al. (2022) show that the traditional set of steady-state control variables is not permanent but is converging.Footnote 5 Therefore, I instead utilize so-called deep determinants. This category of variables comprises hundreds or thousands of years old (time-invariant) factors determining today's development rates. The analysis includes population density in the year 1500 CE and the population in 1000 CE (Comin et al., 2010; Putterman & Weil, 2010), the presence of positive crops for the plow (Alesina et al., 2013), a head start in the state of technology in 1500 CE (i.e., distance to regional frontier), genetic diversity (Ashraf and Galore, 2013), the number of domesticable animals (Diamond, 2002), and the timing of the neolithic transition from hunter-gatherer to an agricultural society (Ashraf and Galore, 2013).Footnote 6 Details on all variables appear in Table 1; detailed information on the main variables is found in “Online Appendix B”.

Table 1 Descriptive statistics for selected variables
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4.2 Empirical Models

4.2.1 Parametric Convergence Analyses

The baseline analysis follows Barro and Sala-i-Martin’s (1992) OLS regression approach to study β-convergence. The dependent variable is the annualized log change in per capita Inclusive Wealth over a 5-year interval. Employing initial Inclusive Wealth per capita as the independent variable, I conduct regression analyses with two distinct specifications of this method. The first excludes the vector of steady-state control variables, indicating unconditional/absolute β-convergence, while the second includes the control variables, representing conditional β-convergence. Equation (1) describes the estimations:

$$\frac{{\ln IW_{t + 5} - \ln IW_{t} }}{T} = {\upalpha } + {\upbeta }_{1} \cdot \ln IW_{{{\text{it}}}} + \left[ {X_{{{\text{it}}}} } \right] + T_{t} + {\upvarepsilon }_{it}$$
(1)

where IW denotes per capita Inclusive Wealth and X the vector of steady-state controls for country i at time t.

I expand the baseline regression of conditional and unconditional convergence by accounting for cross-sectional dependence. This phenomenon can be caused by spatial autocorrelation, which is the tendency of spatially proximate countries to be more similar due to regional clustering of economic activity and spillover effects (Ertur & Koch, 2007). “Online Appendix D” reveals significant spatial autocorrelation of Inclusive Wealth and GDP. Consequently, I use a Spatial Autoregressive (SAR) estimation to model that spatial dependence. It introduces a spatial lag that measures spatial effects, rendering the coefficient for β-convergence more efficient. The model is tested with and without country-fixed effects (Lee & Yu, 2010).Footnote 7 The fixed effects account for all unobserved time-invariant determinants of the Inclusive Wealth growth rate, including the steady-state properties. Equation (2) describes the model:

$$\frac{{\ln IW_{t + 5} - \ln IW_{t} }}{T} = [a_{i} ] + \lambda MIW_{it} + {\upbeta }_{1} \cdot \ln IW_{{{\text{it}}}} + \left[ {X_{{{\text{it}}}} } \right] + T_{t} + u_{it}$$
(2)

where IW is Inclusive Wealth per capita for country i at time t. Xit is a vector of steady state control variables for the estimation without fixed effects, and Tt is the year fixed effects. M is the spatial weight matrix calculated using inverse distances between all countries. λ indicates the spatial lag of the dependent variable IW. “Online Appendix F” presents a sensitivity analysis that uses a contiguity spatial weight matrix in which only neighboring countries are spatially dependent.

The standard OLS and SAR methods are repeated using the natural log of GDP per capita as a dependent independent variable. Furthermore, I decompose the Inclusive Wealth analysis by considering human, produced, and natural capital as independent variables. Doing so targets the sources of convergence/divergence in the baseline regressions.

4.2.2 Non-parametric Convergence Analyses

Next, I estimate σ-convergence and stochastic convergence. Although cross-country convergence of growth rates (β-convergence) would suggest the catching up of poor countries, it is not a certainty (Quah, 1996; Young et al., 2008). Development gaps may even persist despite a robust inverse relationship between the level of economic prosperity and its growth rate. Relying solely on evidence of β-convergence is inadequate for inferring convergence across the distribution of wealth. Conversely, σ-convergence examines the statistical dispersion of that distribution and considers Inclusive Wealth levels. I estimate the σ for the natural log of Inclusive Wealth per capita, as shown by Eq. (3)Footnote 8:

$$\sigma = \left[ {\left( \frac{1}{n} \right)\sum \left( {\ln IW_{it} - \overline{\ln IW}_{t} } \right)^{2} } \right]^{0.5}$$
(3)

I calculate the σ per period. Its decrease indicates that the per capita Inclusive Wealth distribution is becoming less dispersed (i.e., convergence). Conversely, an increase indicates a divergence of cross-country Inclusive Wealth per capita.

Additionally, I conduct panel unit root tests to estimate stochastic convergence. Stochastic convergence differs from σ-convergence by evaluating the time series of individual countries, as opposed to dispersion across the panel. The test also considers level effects to find whether cross-country differences in Inclusive Wealth per capita are persistent. Panel unit root tests assess the stationarity of countries' time series. Stationarity implies reversion to a common mean (i.e., convergence). It means neither idiosyncratic country-specific factors nor shocks can explain long run Inclusive Wealth growth.

I use the Pesaran (IPS) (2007) and Fisher test (Choi, 2001) to assess stochastic convergence. The IPS approach is more dependable than the standard Levin-Li-Chu (LLC) approach because it handles cross-sectional dependence (implied by spatial autocorrelation), small samples, and heteroskedasticity. The Fisher test shares these properties while also dealing with serial correlation better. In the IPS and Fisher test, the null hypothesis is non-stationarity (i.e., no convergence), and the alternative hypothesis indicates that at least one country has a stationary time series. As such, stochastic convergence methods do not show how many countries converge or at what speed.

4.2.3 Estimation Heterogeneity of Convergence

Next, the study examines its intra-distribution dynamics to better understand the convergence mechanisms. I perform a Blinder-Oaxaca Decomposition analysis (Blinder, 1973; Oaxaca, 1973), which takes the difference in the estimated coefficient of the dependent variable between two groups and attributes the difference to a vector of explanatory variables. The analysis compares changes in position in the cross-country wealth distribution (dependent variable) between groups. Then, it shows how capital stocks and steady state control variables explain the difference in performance between groups. An unexplained component is calculated by creating a counterfactual. This element indicates what part of convergence or divergence is unaccounted for by the explanatory variables.

An essential condition is that the selection of units within groups is exogenous. The analysis would violate the independent selection assumption when comparing groups based on per capita wealth. Instead, group selection is based on the composition of wealth. Using Ahmad et al.’s (2018) categorization (see “Online Appendix A”), there are three types of countries: poor, rich, and natural capital-dependent. The color and symbol combinations in Fig. 2 display each country’s position in the distribution and change thereof and denote country type. I compare natural capital-dependent countries to rich countries and poor countries. A direct comparison between rich and poor would violate the independent selection assumption. The analysis reports robust standard errors and pools the groups.

Furthermore, I perform a quantile regression analysis to investigate variations in the drivers of convergence and divergence across different points of the wealth distribution. The analysis shows how top- and worst-performing countries are affected differently by the explanatory variables. The dependent variable of the approach is countries’ change in position in the wealth distribution. Results show the 0.1st, 0.25th, 0.5th, 0.75th, and 0.9th quantile, where 0.1st refers to the least-performing countries and 0.9th to the top-performing. The latter are not necessarily the wealthiest.

Finally, I test for club convergence following the common approach by Phillips and Sul (2007, 2009). Club convergence refers to the idea that there need not be a single universal convergence pattern. Instead, groups of countries that share similar characteristics converge in economic performance, leading to clusters of countries (i.e., "clubs"). Hence, countries within clubs may converge, while the clubs themselves could diverge. The Phillips and Sul (2007) is the current standard convergence club algorithm. The econometrics of the algorithm is too extensive for this section. However, it is covered in-depth in the original authors' work and reviewed by Tomal (2023).

5 Results

5.1 Parametric Techniques: β-Convergence Analyses

5.1.1 β-Convergence of GDP

I first test β-convergence of per capita GDP growth before considering the primary dependent variable (per capita Inclusive Wealth). I perform the standard unconditional and conditional convergence estimation (Eq. 1). Table 2 presents the results.

Table 2 Baseline results: β-convergence estimations for per capita gross domestic product growth
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Results show that the initial level of GDP per capita is negatively associated with per capita GDP growth, which is evidence of β-convergence of income. Resonating with recent evidence, the analyses confirm unconditional (Model 1) and conditional income convergence (Model 2) since the 1990s using the standard OLS approach. Including a spatial lag that addresses cross-sectional dependence (Models 3 and 4) greatly improve the models fit and renders the convergence coefficient more reliable. Hence, (conditional) convergence of GDP per capita appears robust. Model 5 adds country-fixed effects, which absorb all observed and unobserved time-invariant steady state variables. The coefficient for GDP per capita is substantially lower than other models, likely due to the inherent downward bias caused by endogeneity in dynamic fixed effects models (Nickell, 1981). “Online Appendix E” presents a bootstrapped-based bias-corrected fixed effects estimate, which addresses the Nickell-type bias and cross-sectional dependence without a spatial lag. The results find conditional GDP convergence, albeit with weaker statistical significance.

A caveat is that the models in Table 2 have low explanatory power and many insignificant steady state variables. The difference in R2 between Model 1 and Model 2 indicates that the steady state control variables do not explain much variation in GDP growth. To be complete, the sensitivity analysis in “Online Appendix C” considers an alternative set of control variables for conditional GDP convergence used by Kremer et al. (2022).Footnote 9 The results find a similar β-coefficient (− 0.025). Although the alternative specification contains some statistically significant steady state variables at the 5% and 10% levels, the explanatory power remains comparable to the original specification. However, the number of statistically significant control variables matches Kremer et al.'s specifications. Therefore, I conclude that conditional convergence of GDP is present between 1990 and 2010, albeit with low explanatory power.

5.1.2 β-Convergence of Inclusive Wealth

Table 3 presents the main results of the β-convergence estimation, reporting how per capita Inclusive Wealth growth is related to a country's level of per capita wealth. The main coefficient in Model 6 is positive, indicating unconditional Inclusive Wealth divergence. The findings imply that despite income convergence for 95% of the population, countries are also diverging in terms of Inclusive Wealth. Given that Inclusive Wealth forms the productive base used to earn future income, it suggests that countries' earning-capacity is drifting apart. Interestingly, this happens at the same rate of income convergence.

Table 3 Baseline results: β-convergence estimations for per capita Inclusive Wealth growth
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Models 7 and 9 invoke steady state control variables excluding and including a spatial lag of the dependent variable, respectively. The analyses find conditional convergence of Inclusive Wealth per capita at roughly half the speed of conditional GDP convergence. Model (10) includes country-fixed effects and a spatial lag, finding conditional Inclusive Wealth convergence. However, as before, these dynamic panel estimates are likely biased downward due to endogeneity. The bias-corrected fixed effects estimates (Table E1, “Online Appendix E”) indicate that conditional Inclusive Wealth convergence is not robust. Instead, the results suggest conditional divergence. The coefficient is substantially larger than 1, rendering conditional divergence of Inclusive Wealth plausible. Overall, the results suggest that developing countries will unlikely catch up to richer ones when considering Inclusive Wealth as a measure of economic progress.

Compared to the GDP estimates in Table 2, the explanatory power of the conditional convergence models for Inclusive Wealth (Table 3) is significantly improved. The steady state control variables explain more cross-country variation, indicating that Inclusive Wealth growth is better predicted by the standard growth specification than its GDP equivalent. The Pseudo R2 of 0.551 is quite high for a small sample (N = 91), considering the inherent measurement error of Inclusive Wealth and the noise associated with cross-country studies.

Table 4 presents results when Inclusive Wealth as an independent variable is decomposed into its components—human, produced, and natural capital. The analysis, therefore, attributes the source of unconditional wealth divergence and (supposed) conditional wealth convergence to specific capital stocks.Footnote 10 The main findings are that human capital has a positive coefficient, indicating a positive association between human capital and Inclusive Wealth growth. As levels of per capita Inclusive Wealth and human capital are highly correlated (0.89), ceteris paribus, developed countries accumulate wealth faster. The negative coefficient of natural capital indicates that natural resource abundance is associated with lower rates of Inclusive Wealth growth. Natural capital abundant countries are found at the center of the cross-country wealth distribution (Fig. 2), suggesting that poor and natural capital-dependent countries converge. Similarly, developed and natural capital-dependent countries diverge.Footnote 11 Finally, the coefficient for produced capital is mostly statistically insignificant.

Table 4 Decomposed results: β-convergence estimations for per capita Inclusive Wealth growth
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These findings indicate that the natural-to-human capital-ratio can explain much of the cross-country variation in Inclusive Wealth growth. A country with as much human and natural capital balances the positive and negative effects on Inclusive Wealth growth. 45 out of 140 countries have more natural than human capital, implying that, all else equal, their wealth composition contributes to negative wealth growth. Furthermore, the model predicts that two nearly identical countries with natural capital differentials will converge over time.

Additional analyses in “Online Appendix G” show that the statistically insignificant coefficient for produced capital hides heterogeneous effects. These are depicted in Fig. 3, showing the effect of produced capital on Inclusive Wealth growth moderated by the other capital stocks. The first panel illustrates how produced capital's effect is positive but downward sloping for human capital-abundant countries (green curve), indicating diminishing marginal returns to produced capital accumulation. Similarly, the second panel illustrates that natural capital decreases the effect of produced capital on Inclusive Wealth growth. As such, resource-rich countries appear less able to achieve Inclusive Wealth gains partly due to their inability to harness produced capital's beneficial effects.

Fig. 3
figure 3

Interaction plots of conditional β-convergence analyses. The figure plots the interaction effects in the decomposed model of conditional wealth convergence (see “Online Appendix G”). The first panel illustrates the slope of produced capital's effect on Inclusive Wealth growth for a high value of human capital (14), roughly the mean value of human capital (10), and a low value (6). The second panel illustrates the slopes of produced capital's effect on Inclusive Wealth growth for a high value of natural capital (14), the approximate mean (9), and a low value (4). The confidence intervals are at 95%

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I summarize the main findings as follows. Contrary to per capita GDP convergence, the analysis does not support β-convergence in per capita wealth. Instead, developed countries grow per-capita wealth faster than poorer countries. I verify these findings using a range of non-parametric convergence techniques next.

5.2 Non-parametric Techniques: σ-Convergence and Stochastic Convergence

Table 5 shows the estimates of σ-convergence of Inclusive Wealth per capita between 1990 and 2010 (Fig. 4). The positive coefficient indicates that the statistical dispersion of the natural log of Inclusive Wealth per capita increases during this period (i.e., σ-divergence). As the analyses do not account for steady-state control variables, the results support unconditional divergence of Inclusive Wealth. The baseline analysis is not an artifact of considering growth rates as dependent variables. Level effects support divergence as well. However, σ-divergence seems to slow down at the end of the sample period. It will be interesting to monitor the evolution of σ-divergence in the future.

Table 5 Σ convergence of Inclusive Wealth between 1990 and 2010
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Fig. 4
figure 4

σ-divergence of Inclusive Wealth over time. Graphs indicate σ of Inclusive Wealth per capita (ln) at five-year intervals. The second panel decomposes σ into three country types. See “Online Appendix A” for the categorization method

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Regarding cross-country heterogeneity, there is σ-convergence among developed countries, suggesting that wealth gaps among the wealthiest diffuse very slowly. σ-divergence is increasing gaps among poor and natural resource-rich countries, suggesting that some countries accumulate Inclusive Wealth faster while others stay behind.

Table 6 shows the Fisher and IPS panel unit root test results for stochastic convergence. It reports the inverse χ2 and \(\overline{t}\) statistics, respectively, and their accompanying p-values. The results reject the null hypothesis of no stochastic convergence, except for the IPS test that excludes a trend. In other words, the analysis demonstrates that at least one country in the panel converges stochastically.Footnote 12 The implication is that, for those countries, permanent or country-specific shocks affect long run relative Inclusive Wealth or GDP differentials only temporarily. However, the Fisher and IPS type tests neither inform us about the speed of convergence nor the share of countries that converge. Therefore, the results appear consistent with other techniques in the paper that find convergence among groups of countries but not across the entire distribution.

Table 6 Stochastic convergence: panel unit root tests between 1990 and 2010
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Drawing on non-parametric analyses, I conclude that statistical dispersion across countries in terms of Inclusive Wealth is increasing (σ-divergence) while there are some convergence intra-distribution dynamics. The following subsection explores these further.

5.3 Heterogeneity of Inclusive Wealth Convergence

This subsection considers heterogeneity in convergence dynamics across the distribution. Table 7 presents the results of the Blinder-Oaxaca Decomposition analysis. The independent variable is operationalized as countries’ change of position in the cross-country wealth distribution. Negative coefficients indicate a deterioration of per capita wealth relative to the global mean. Both analyses in the table compare two groups. The left column displays the comparison results between poor and natural capital-dependent countries, and the right column indicates results for rich and natural capital-dependent countries.

Table 7 The sources of divergence by country group: Blinder-Oaxaca decomposition
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The first column shows that poor countries outgrow natural capital-dependent countries. A representative poor country has improved its position in the distribution by 0.054 standard deviations between 1990 and 2010 relative to a representative natural capital-dependent country. Differences in explanatory variables account for most of the gap (0.039), which is fully explained by natural capital differences (0.040). Given that natural capital-dependent countries are generally wealthier (Fig. 2), the analysis implies that poor and natural capital-dependent countries converge. More concretely, natural capital differentials drive cross-country wealth convergence in the lower segment of the wealth distribution, matching evidence of stochastic convergence. However, part of the performance gap (0.014) is unexplained by endowments. Factors beyond the pool of explanatory variables hamper natural capital-dependent countries or benefit poor countries.

The second column in Table 7 shows that rich countries outperform natural capital-dependent countries. A representative rich country has improved its position in the distribution by 0.059 standard deviations between 1990 and 2010 relative to a representative natural capital-dependent country. Interestingly, the gap explained by endowments (0.071) exceeds the observed gap. Differences in capital endowment contribute roughly equally to the explained component. The lower levels of natural capital and higher levels of human- and produced capital in rich countries confer an economic advantage relative to natural capital-dependent countries. Additionally, the unexplained component signals an unobserved advantage for natural capital-dependent countries (− 0.012). If capital endowments and observed steady-state properties were identical between the two groups of countries, then natural capital-dependent economies would slowly catch up. It appears that variables beyond the regular pool benefit natural capital-dependent relative to rich countries.

The takeaway message is that poor and rich countries outperform natural capital-dependent economies by roughly the same margin. Ergo, poor and rich countries are neither converging nor diverging. However, there is convergence between the lower and the middle segment of the cross-country wealth distribution. Assuming the current trends persist, the normal distribution of cross-country per capita wealth gradually morphs into a bimodal distribution with a voluminous lower-wealth peak. An open question, however, is how some outliers with low human- and produced capital managed to outgrow their peers (e.g., China, Korea, Uruguay, Latvia).

Table 8 presents the quantile regression results following the best-fitting decomposed results from the decomposed Inclusive Wealth analysis with an interaction effect in “Online Appendix G”. The columns present coefficients from the worst-performing (Q10) to the best-performing (Q90) representative countries from left to right. The dependent variable is countries’ change in per capita wealth relative to the global mean. Each coefficient indicates the effect of an explanatory variable on distributional change. Results confirm that wealth composition is the main factor reshaping cross-country wealth distribution. They are as follows.

Table 8 Heterogeneity in convergence analysis: quantile regression of standardized inclusive wealth growth
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Natural capital is associated with lower relative performance regardless of the quantile; the effect is present even in top-performing countries.

The positive coefficient of the human capital shows that the larger the human capital stock, the better the country's performance relative to others. Human capital again emerges as a strong driver of convergence dynamics.

Produced capital’s positive coefficient shows that the larger the produced capital stock, the higher the rate of wealth growth.

The findings underline that capital endowments explain the general trend of divergence well. However, the explanatory power of the model decreases for higher quantiles. Thus, capital endowments and steady state control variables are better able to explain general divergence than idiosyncratic catch up experiences. Research on positive outliers is encouraged.

Table 9 presents the results of the club convergence analysis following Phillips and Sul's approach. First, the null hypothesis of conditional convergence for the entire sample is rejected. Then, the algorithm finds 14 convergence clubs of countries after merging adjacent clubs.Footnote 13 Results are read as follows: the null hypothesis is club convergence. A positive coefficient \(\hat{\beta }\) between 0 and 2 indicates conditional convergence, and a negative coefficient indicates divergence. Findings are that only 7 of 14 clubs show a statistically insignificant coefficient. There is club convergence which neither contributes to a pattern of divergence nor conditional convergence. The remaining clubs show patterns of conditional convergence but not convergence in terms of levels.Footnote 14 Hence, there is heterogeneity in Inclusive Wealth growth over the sample period, implying various steady states. However, clubs 1 through 4, containing 63 of the wealthiest countries, illustrated in red in Fig. 5, show little evidence of convergence. Their average growth rates continue to exceed nearly all other clubs. Thus, there is no overall convergence throughout the distribution. Any observed convergence dynamics typically concern the Inclusive Wealth distribution's middle- and lower segments.

Table 9 Club convergence of inclusive wealth
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Fig. 5
figure 5

Inclusive wealth growth across convergence clubs. Graphs indicate the average growth rate per convergence club established by the Phillips and Sul algorithm. Red lines indicate the four wealthy clubs. Black lines indicate all other clubs

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6 Conclusion

Although the recent studies on income convergence suggest that developing countries are catching up to the wealthy, this paper portrays a grimmer outlook. The analyses validate the presence of unconditional cross-country convergence in national income. However, they also reveal concurrent divergence in Inclusive Wealth. This discrepancy cautions against optimism. Many countries appear to be on an unsustainable path where they liquidate capital assets for income. They thus appear to mortgage their future productive capacity and well-being for present-day consumption needs. The implication is that the increase in living standards implied by income convergence is untenable. Conversely, the evidence presented in this paper suggests that global welfare inequalities are likely to increase rather than continue to decline.

The paper identifies two main drivers of Inclusive Wealth divergence. First, human capital abundance fosters wealth growth, disproportionally benefiting developed countries. Second, natural capital abundance hampers wealth growth, increasing the gap between developed and natural capital-abundant economies. Natural capital's hampering effect may imply that the wealth gap between poor and natural capital-dependent countries is shrinking. However, the underlying mechanism is that the latter group of countries is regressing. Although this is technically a case of convergence, it is neither catching up nor in the spirit of the original convergence hypothesis.

This research indicates that a country's wealth composition is a more accurate predictor of future wealth growth than its Inclusive Wealth stock size. The higher the human-to-natural capital ratio, the better the performance. The culmination of forces means the cross-country distribution of per capita Inclusive Wealth gradually morphs into a bimodal one, with more countries in the low wealth peak. This general trend, however, does not guarantee a grim future for all developing economies. It also hides some countries' exemplary growth experiences during the sample period. Despite lacking human- and produced capital, they successfully defy the trend and move toward the club of wealthy economies. These routes to success cannot be explained within the convergence framework.

I encourage future researchers to study these positive outliers and replicate the study when the time horizon of Inclusive Wealth data expands. The relatively short horizon, coupled with the inherent measurement error of the original data, has challenged addressing endogeneity. Once the T in the panel is sufficiently large, approaches such as system GMM become viable techniques for studying cross-country convergence. Given the variability of estimates, it is crucial to keep investing in better data.