Explaining the Decline of Natural Wealth per Capita: A Three-Pillar ESG Analysis of the World Bank Wealth Accounts

1. Introduction

Comprehensive wealth accounting defines an economy as sustainable when the value of its total capital stock, produced, human and natural, is not declining per head, and the change in that stock is therefore the operational measure of whether a country is investing in or liquidating its future (Dasgupta, 2009; Polasky et al., 2015). Three decades of measurement work have made the concept operational: wealth accounts have been compiled, extended to omitted assets and adapted to technological progress and ageing populations (Ahmad et al., 2018; Yamaguchi, 2014; Biasi et al., 2019). The picture is consistent: natural capital per capita is falling across most of the world.

What this literature has not produced is an account of why. The change in the natural asset base is treated as an accounting outcome, obtained by subtracting depletion from investment within a savings identity, rather than as a phenomenon with determinants to be estimated (Boos, 2015; Engelbrecht, 2016). A quarter of a century of estimates therefore exists without an explanation of the variation it contains.

A second literature applies environmental, social and governance frameworks at country rather than firm level, and has grown rapidly around the World Bank Sovereign ESG Data Portal. Its dependent variables, however, are almost invariably flows: emissions, energy consumption, the ecological footprint (Ibrahim & Ajide, 2022; Jahanger et al., 2023; Kılıçaslan et al., 2025). These measure the rate at which damage is done rather than the stock it draws down, and the distinction matters, since a country can reduce emissions while converting forest to cropland. That literature also aggregates the three pillars into composite scores with conventional weights, a practice whose interpretive difficulties are documented but persistent (Cook & Davíðsdóttir, 2021; Hoekstra, 2020).

The two literatures therefore speak past one another. One measures environmental wealth without explaining it; the other explains environmental pressure without measuring wealth. This paper occupies the gap between them and asks a single question: which environmental, social and governance conditions are associated with a country adding to, rather than drawing down, its stock of natural assets?

The originality of the answer lies as much in the architecture as in the variable. The dependent variable is the annual change in renewable natural capital per capita, drawn from the Changing Wealth of Nations accounts within the Sovereign ESG portal, for 149 to 151 countries between 1995 and 2020. It is explained three times, through three parallel equations differing only in the pillar of origin of their regressors, so that environmental, social and governance determinants are estimated as distinct and directly comparable effects rather than compressed into an index with arbitrary weights. Each equation is then developed along three routes: panel econometrics across six estimators, with the Mundlak test separating the between and within dimensions that applied work routinely conflates; a competition among six clustering algorithms ranked on eleven internal validity indices, since these criteria disagree systematically by algorithm family (Zhao et al., 2023); and six supervised learners deployed not to predict but to validate the specification through permutation importance, Shapley values and partial dependence. The design yields nine analytical modules on one outcome, entirely reproducible from public data, and speaks directly to the monitoring of sustainability criteria for which the change in natural capital per capita is the operational indicator.

The paper is organised as follows. Section 2 locates the study between two literatures that have developed in parallel, comprehensive wealth accounting and country-level ESG analysis, and identifies the gap between them. Section 3 describes the data and the three analytical routes. Section 4 to 12 form the empirical core: for each ESG pillar in turn — environmental, social and governance — a panel analysis across six estimators, a comparison of six clustering algorithms on eleven internal validity indices, and a machine learning module used to validate the econometric specification rather than to predict. Section 13 draws the nine modules together, Section 14 sets out the limitations, Section 15 the policy implications and Section 16 concludes. Appendices A to I report, in the same order, the full diagnostics, robustness and instrumental variable results for each of the nine modules, and Appendix J lists every variable, acronym and source code used.

2. Literature Review

The question this paper asks — which environmental, social and governance conditions are associated with a country adding to rather than drawing down its stock of natural assets — sits between two research programmes developed in parallel.

The first is comprehensive wealth accounting, built on the proposition that an economy is sustainable if its total capital stock, produced, human and natural, is not declining per head (Dasgupta, 2009; Dasgupta, 2010; Hanley et al., 2015). Its empirical branch has documented the composition of national wealth and how often countries fail that criterion (Ahmad et al., 2018; Yamaguchi, 2014; Managi et al., 2024), extended the accounts to water and soil depletion (Biasi et al., 2019), tested sensitivity to discount rates and technological progress (Yamaguchi & Managi, 2019), and applied the framework to individual economies (Agarwal & Sawhney, 2021; Kumar & Mizunoya, 2022). Since boundary extensions proceed asset by asset and are not always comparable (Halkos et al., 2018; Polasky et al., 2015; Roman & Thiry, 2016), the measured base excludes the atmosphere, groundwater and several unpriced ecosystem functions. What this literature does not do is estimate the determinants of what it measures: the change in the asset base is treated as an accounting outcome of a savings identity rather than as a phenomenon with causes to be identified.

The second programme applies ESG frameworks at country level, but its dependent variables are almost invariably flows — emissions, energy consumption, the ecological footprint (Kwilinski et al., 2026; Saba et al., 2024; Wen et al., 2024). These measure the rate at which damage is done rather than the stock it draws down: a country can cut emissions while converting forest to cropland. That literature also aggregates the three pillars into composites with conventional weights, despite an established critique of arbitrary weighting (Ciacci et al., 2020; Cook & Davíðsdóttir, 2021; Hoekstra, 2020). The two also treat time asymmetrically: wealth accounting is longitudinal in principle but often cross-sectional in application, while ESG work estimates panel relationships without asking whether the identifying variation is temporal or cross-sectional — a distinction that matters, since a fixed-effects coefficient on a variable with two per cent within-country variation does not measure what its interpretation claims.

What is known about the determinants. Within each pillar there is evidence, though directed at other outcomes. Land use change has been studied ecologically, through valuations pricing ecosystem services and tracking their loss under conversion (Pacheco et al., 2018; Souliotis & Voulvoulis, 2025; Zank et al., 2016); these are confined to single countries or biomes and unconnected to national accounts. Climatic variables enter as drivers of ecological change rather than as exogenous instruments, so the identification that meteorological exogeneity offers is unexploited. The resource curse literature relates institutions to extraction, rents, emissions and the ecological footprint (Abou Houran & Mehmood, 2023; Jahanger et al., 2023; Sun et al., 2023; Zhang et al., 2023), but its outcomes are again flows, and it treats institutional quality as a level without separating it from its trajectory. The measurement critique of the Worldwide Governance Indicators is relevant: the six are too correlated to be distinct dimensions (Langbein & Knack, 2010; Muno, 2012; Kaufmann et al., 2010). Social evidence is thinnest: population enters as a control, its role in the denominator of per capita wealth never isolated from behaviour. Two strands supply mechanisms tested below. A high renewable share signals traditional biomass dependence rather than energy transition (Alsaleh & Abdul-Rahim, 2023; Naimoğlu & Shahbaz, 2025), and Gulf migration produces population growth unattainable through fertility. Neither has been brought to bear on natural capital accumulation.

Method. Three methodological literatures inform the design. The first concerns the two dimensions of a panel. The correlated random effects formulation makes the between-country and within-country relationships separate objects and tests their equality, yet applied practice reports a single preferred estimator and treats the rest as robustness, concealing rather than examining the divergence. The recent literature on shift-share instruments is also relevant, having clarified when such instruments identify a causal effect and when they do not (Goldsmith-Pinkham et al., 2020; Borusyak et al., 2022; Borusyak et al., 2025). The second concerns supervised learning, which has entered cross-country environmental research rapidly and is used predominantly for prediction and feature ranking (Chang et al., 2024; Espoir et al., 2026; Saba & Ngepah, 2022). A smaller strand uses Shapley values and partial dependence for interpretation, though to describe a fitted model rather than to test an econometric one; using a flexible learner to validate a linear specification remains uncommon. Cluster analysis lies between the two. Algorithms are usually chosen by convention, with k-means adopted by default and k selected on one index, although internal validity criteria disagree systematically by algorithm family (Deist et al., 2018; Zhao et al., 2023). Comparing several algorithms across the full set of criteria is the practice followed here. See Table 1.

3. Data and Methodology

Every variable is drawn from a single source, the Sovereign ESG Data Portal of the World Bank, which assembles country-level indicators under the three pillars of the ESG framework. No proprietary data are used, so the estimates can be reproduced in full from a public download.

The dependent variable is taken from the Changing Wealth of Nations accounts distributed within that portal. Renewable natural capital per capita is measured in real chained 2019 US dollars and comprises eight components: agricultural land, timber, non-timber forest services, forest recreation and protection, hydropower, fisheries and mangroves. Each is valued as the discounted present value of the rents it is expected to generate, and the basis for treating the total as an element of national wealth is set out in the comprehensive wealth literature (Dasgupta, 2009; Polasky et al., 2015). The accounts exclude the atmosphere, groundwater and ecosystem functions for which no defensible shadow price exists (Biasi et al., 2019; Hoekstra, 2020), so the dependent variable describes the measured base against which sustainability is officially assessed.

The dependent variable is the annual first difference of the natural logarithm of that series, in percentage points. In wealth accounting this quantity is the net investment of a nation in its renewable natural asset base, positive when the base grows faster than population and negative when it is being liquidated per head (Hanley et al., 2015; Ahmad et al., 2018). A specification in levels was rejected because the first-order autocorrelation of the level is 0.999.

The three regressor blocks correspond to the three pillars, each with seven indicators. The environmental block covers land allocation, extraction intensity, climatic stress and the energy mix: 3,611 country-year observations, 149 countries, 1996–2020. The social block covers demographic and labour market conditions: 3,293 observations, 151 countries, 1997–2020. The governance block gives 2,629 observations on 151 countries over 2003–2020, the later start reflecting the biennial publication of the Worldwide Governance Indicators before 2002. Because those six indicators correlate between 0.73 and 0.95 and cannot be treated as distinct dimensions (Langbein & Knack, 2010; Muno, 2012), they are replaced by their first two principal components, accounting for 87.7 and 5.3 per cent of their joint variance. All three panels are close to balanced.

Each pillar equation is developed along three converging routes, applied identically so that differences between pillars are attributable to the variables rather than the treatment.

The first is panel econometrics. Six estimators are reported for every equation: pooled OLS, weighted least squares, random effects, two-way fixed effects, between and correlated random effects in the Mundlak formulation. Reporting all six is a requirement of identification rather than a ritual of robustness, since the regressors differ sharply in the share of their variation that is temporal, and the Mundlak test on the group means establishes whether the between and within relationships coincide. Standard errors are clustered by country and inference on the leading coefficients is re-assessed by a wild cluster bootstrap-t with Rademacher weights and the null imposed over 1,999 replications. Shift-share instruments are constructed where simultaneity is plausible, following recent guidance on that design (Goldsmith-Pinkham et al., 2020; Borusyak et al., 2025), and dynamic specifications are estimated by least squares with dummy variables and by the Anderson–Hsiao procedure.

The second is unsupervised classification, conducted on country averages. Six algorithms — k-means, hierarchical clustering with Ward linkage, a Gaussian mixture, fuzzy c-means, density-based clustering and an unsupervised random forest built on a permuted synthetic contrast — are compared on eleven internal validity indices and ranked by their mean rank across all eleven, since these criteria disagree systematically according to the family of algorithm being evaluated (Zhao et al., 2023).

The third is supervised learning used for validation rather than prediction. Six learners are compared out of sample on the same variation the panel estimator uses, with folds grouped by country, and the best nonlinear model is then interrogated through permutation importance, Shapley additive explanations and partial dependence, to establish whether an algorithm with no knowledge of the estimated coefficients recovers the same ordering and the same directions (Deist et al., 2018). See Figure 1.

4. Panel Analysis: The E–Environment Component

The dependent variable is the annual rate of change of renewable natural capital per capita, computed as the first difference of its logarithm and expressed in percentage points. The series is taken from the Changing Wealth of Nations accounts within the World Bank Sovereign ESG Data Portal and measured in real chained 2019 US dollars. In wealth accounting it is by construction a nation’s net investment in its renewable natural asset base. Levels were rejected: their first-order autocorrelation is 0.999.

Seven environmental regressors come from the same source: annual changes in forest area and agricultural land, net forest and total resource depletion as shares of gross national income, the drought index, log population density and the renewable share of final energy. The sample covers 149 countries over 1996–2020, 3,611 observations. See Figure 2.

The median country holds renewable natural capital worth roughly 7,100 chained 2019 dollars per inhabitant in 1995 and 4,993 in 2020, a contraction of 29.7 per cent, while its share of comprehensive wealth halves from 23.3 to 12.4 per cent. The mean annual rate of change is −1.40 per cent, 77.1 per cent of observations are negative, and 131 of 149 economies record a negative average. Disinvestment from the natural asset base is therefore the modal condition of the world economy, coexisting with the accumulation of produced and human capital — precisely the configuration the weak sustainability criterion is designed to detect. The variance structure determines what each estimator can learn. The dependent variable carries 86.0 per cent of its variation within countries, so fixed-effects estimates are identified on genuine annual adjustment. The regressors divide sharply: the changes in agricultural land and forest area and the drought index vary mostly over time, while the depletion measures, the renewable energy share and population density vary mostly across countries, the last at 0.011. Reporting six estimators is a requirement of identification, not a ritual of robustness. See Table 2.

Three coefficients survive a wild cluster bootstrap-t with the null imposed and a Bonferroni correction, and the discussion is confined to those. The largest, the change in agricultural land, is close to 1.34 in every estimator exploiting within variation, but requires qualification: agricultural land is itself 62.1 per cent of renewable natural capital, so cultivated expansion mechanically raises the valuation. Excluding that component cuts the coefficient to 0.229, still significant at five per cent — five sixths accounting, one sixth a genuine spillover. The drought index is the more informative result, being the only regressor with a strong claim to exogeneity. Positive and significant at one per cent in all six estimators, it more than doubles under the same redefinition, from 0.457 to 1.113, implying that aggregates dominated by cultivated land understate the erosion of natural wealth under drought. The third result is a sign reversal that motivates the design of the whole study. See Figure 3.

Across countries the relationship is negative, at −0.010; within countries it is positive, at +0.027, both significant at one per cent. The two dimensions measure different things. A high renewable share across 149 countries is predominantly a marker of traditional biomass use in low-income economies, which also have the fastest population growth and the most intense pressure on forests and soils, so the between coefficient captures development and demography. Within a country a rising renewable share reflects substitution of modern generation for fossil and biomass inputs, relieving pressure on the land. The Mundlak test on the group means confirms this at 71.00, and the income split shows the within effect is driven by the poorer half. The lesson is a caution against composite scores aggregating such variables with fixed weights, since a pooled coefficient would average two opposite mechanisms into a number describing neither.

The remaining four coefficients do not survive the bootstrap. The specification tests support the strategy: country effects are jointly significant, Hausman and Mundlak favour correlated random effects, serial correlation is absent, and the cross-sectional dependence detected by the Pesaran test does not disturb the surviving coefficients under Driscoll–Kraay errors. The dynamic coefficient is negative and insignificant, so accumulation carries no inertia and the static estimates can be read as complete. Appendices A.3 to A.6 report the diagnostics, the instrumental variable estimates and eight alternative specifications.

The block explains 19.1 per cent of the within-country and 34.3 per cent of the between-country variation — modest, appropriately so, since the annual change in a valuation driven by commodity prices and discount rates is not a quantity a few environmental indicators can explain in large part. It establishes that climatic conditions matter most for the non-agricultural components of natural wealth, that land conversion operates predominantly as an accounting channel whose magnitude can be quantified, and that the energy mix relates to accumulation in opposite directions across and within countries.

5. Clustering Analysis: The E–Environment Component

The panel estimates describe average relationships across a sample in which countries differ enormously in how they use their natural assets. The clustering asks whether that heterogeneity is continuous or whether countries fall into a small number of recognisable environmental configurations. Each of the 149 economies is described by its 1996–2020 average of the dependent variable and the seven environmental regressors, all standardised so that no variable dominates the distance metric. The exercise makes no use of the estimated coefficients, so any agreement with the econometrics is informative rather than mechanical, and averaging over twenty-five years removes the temporal dimension, so the classification describes permanent configurations rather than trajectories. Six algorithms are compared: k-means, hierarchical clustering with Ward linkage, a Gaussian mixture, fuzzy c-means, DBSCAN, and an unsupervised random forest whose leaf co-occurrence proximities are converted into distances. They are evaluated on eleven internal validity indices covering explained variance, the information criteria, silhouette width, cluster diameter and separation, the point-biserial correlation, Dunn, entropy, Herfindahl and Calinski–Harabasz. The number of clusters is fixed beforehand so that all six face the same problem, and the choice is not unambiguous. The silhouette peaks at k = 2, but that solution merely separates rich from poor economies. From k = 3 it is essentially flat, between 0.236 and 0.253, while the marginal reduction in within-cluster deviance falls only slightly from k = 3 to k = 4, by 116 against 119, before dropping to 82 at k = 5. Four clusters are retained on the elbow criterion and on interpretability, with the silhouette accepting rather than driving the decision. See Table 3.

The first panel covers the indices that reward compact and well-explained partitions, and on all five of them the ordering is the same: k-means first, hierarchical second, random forest last. The second panel covers the indices that evaluate the geometry of the solution and the balance of the size distribution, and there the ordering changes substantially. See Table 4.

Panel B: indices of separation and of the size distribution. Higher values are preferred for minimum separation, the Dunn index and the entropy, lower values for the maximum diameter, the Herfindahl–Hirschman index and the point-biserial correlation.

No algorithm dominates on every index, which is why the comparison rests on a mean rank. K-means is first on six of eleven, including explained variance, the silhouette and both information criteria, and its mean rank of 2.50 places it ahead of hierarchical clustering at 2.77; the two agree on most memberships. Density-based clustering shows the characteristic profile of its family, leading on separation and Dunn because it isolates a dense core and treats the periphery as noise, at the cost of nineteen unassigned countries and an explained variance of 0.192. The unsupervised random forest ranks last, with a silhouette of 0.034: its proximity metric detects dependence structures rather than compact groups. The disagreement between indices is systematic rather than random, following the algorithm family — partitional methods score on compactness, density-based on separation — and the information criteria here duplicate the explained variance rather than complementing it, so their agreement is not independent confirmation. K-means is retained. The four groups that emerge are readily interpretable and the differences between them are large. See Figure 4.

The largest group, with 77 members, contains the European economies, Japan and the middle-income countries of the former Soviet bloc and the Caribbean. It is the only group in which forest area is expanding and agricultural land contracting, with resource rents at 1.06 per cent of national income and the lowest renewable energy share at 21.6 per cent. It loses renewable natural capital per capita at 0.65 per cent a year, less than half the sample mean: these stabilising economies have completed the land-use transition.

The second, with 45 members, comprises the agricultural frontier economies of sub-Saharan Africa, South-East Asia and Central America, where cultivated land is expanding, forest contracting and the renewable share high at 60.7 per cent, reflecting traditional biomass. It loses 1.95 per cent a year. The third is small and extreme: twelve forest-rent economies — the Congo basin, Liberia, Ethiopia, Gabon, Angola — with total depletion at 19.9 per cent of national income, losing 2.49 per cent. The fourth, with fifteen members, is defined by aridity rather than extraction: its drought index is 1.69 standard deviations below the mean, the largest deviation of any cluster on any variable, and it contains the Gulf states, Iraq, Iran, Egypt and Kazakhstan, recording the fastest loss at 2.85 per cent.

This connects the classification to the econometrics. The panel estimates identified the drought index as the coefficient with the strongest claim to exogeneity; the clustering, uninformed by those estimates, isolates aridity as the sharpest discriminant in the sample and identifies that group as the one losing natural wealth fastest. Two methods sharing no assumptions converge on the same variable. The ordering, from −0.65 to −2.85 per cent, spans a range wider than any single coefficient can generate, suggesting configurations matter more than marginal effects. The partition is moderate — average silhouette 0.253, eight negative widths — so the groups are real but their boundaries gradual. Details are in Appendix B.

6. Machine Learning Validation: The E–Environment Component

The third module applies supervised learning to the environmental equation, and its purpose requires stating explicitly, because it is not the one for which these algorithms are ordinarily used. The objective is not to predict the growth of renewable natural capital per capita. Prediction would be of limited interest, since the wealth accounts are published with a lag and their future values are not a policy target. The objective is validation: to establish whether the linear fixed-effects specification of Section 4 has left structure in the data unexploited, and whether a flexible learner allowed to search freely for that structure attributes explanatory weight to the same variables, and in the same direction, as the econometric model.

The exercise is conducted on exactly the variation the fixed-effects estimator uses. The dependent variable and the seven regressors are first residualised on country and year effects by iterated demeaning, so that the learners face the same within-country, within-year information as the panel estimator and any difference in performance is attributable to functional form rather than to the treatment of heterogeneity. Six algorithms are compared: linear regression, a linear support vector machine, k-nearest neighbours with twenty-five neighbours and distance weighting, a decision tree of depth six, a random forest of six hundred trees, and gradient boosting with six hundred stages and a learning rate of 0.03. Validation uses ten-fold cross-validation with folds constructed by country, so that all observations of a given economy fall in the same fold and no learner can exploit the persistence of a country’s characteristics to predict its own future observations. The grouping is a precaution rather than a necessity in this sample, since repeating the comparison with conventional random folds leaves the ordering of the models unchanged, but it is the conservative choice and it is what makes the comparison a genuine test of generalisation to economies the learner has never seen.

Table 5. Comparison of six supervised learners on the residualised environmental equation, 3,611 observations, ten-fold cross-validation grouped by country.

Model	Cross-validated R2	RMSE	MAE	Correlation	In-sample R2	Overfitting gap
Linear regression	0.1842	2.851	1.457	0.429	0.191	0.007
Linear SVM	0.1791	2.860	1.422	0.424	0.181	0.002
Random forest	0.1399	2.927	1.519	0.376	0.493	0.353
K-nearest neighbours	0.1226	2.957	1.579	0.350	1.000	0.877
Boosting	0.1144	2.970	1.562	0.363	0.538	0.423
Decision tree	0.0936	3.005	1.575	0.323	0.185	0.092

Note. The overfitting gap is the difference between the in-sample and the cross-validated coefficient of determination.

Table 5. Comparison of six supervised learners on the residualised environmental equation, 3,611 observations, ten-fold cross-validation grouped by country.

Model	Cross-validated R2	RMSE	MAE	Correlation	In-sample R2	Overfitting gap
Linear regression	0.1842	2.851	1.457	0.429	0.191	0.007
Linear SVM	0.1791	2.860	1.422	0.424	0.181	0.002
Random forest	0.1399	2.927	1.519	0.376	0.493	0.353
K-nearest neighbours	0.1226	2.957	1.579	0.350	1.000	0.877
Boosting	0.1144	2.970	1.562	0.363	0.538	0.423
Decision tree	0.0936	3.005	1.575	0.323	0.185	0.092

Note. The overfitting gap is the difference between the in-sample and the cross-validated coefficient of determination.

The ordering is unambiguous and is the opposite of what a prediction-oriented exercise would hope for. Linear regression achieves the highest cross-validated coefficient of determination at 0.1842, followed closely by the linear support vector machine at 0.1791. The random forest reaches 0.1399, k-nearest neighbours 0.1226, boosting 0.1144 and the single tree 0.0936. The final two columns explain why. The flexible learners fit the training data far better than the linear model, with in-sample coefficients of 0.493 for the random forest and 0.538 for boosting against 0.191 for the linear specification, and k-nearest neighbours with distance weighting interpolates the training data exactly, but none of this additional fit generalises to countries not seen during training. The gap between in-sample and out-of-sample performance is 0.007 for linear regression and between 0.35 and 0.88 for the flexible learners.

The conclusion is a validation result of the strongest kind available in this design. When six learners of very different inductive bias are given the same information, the linear specification is not merely competitive but best, which means the econometric model of Section 4 is not discarding systematic structure that a more flexible functional form could recover. Two direct tests confirm the reading. Adding all twenty-one pairwise interactions to the linear model reduces cross-validated performance from 0.1842 to 0.1794, and adding the seven squared terms leaves it essentially unchanged at 0.1843; including both together reduces it further to 0.1758. Neither non-linearity nor interaction is present in a form that survives out-of-sample validation.

Establishing that flexibility does not help is only half of the validation. The second half asks whether a flexible learner, when allowed to allocate explanatory weight freely, allocates it to the same variables as the panel estimator. The random forest is used for this purpose, being the best performing of the non-linear learners, and its attribution is computed through permutation importance and through Shapley additive explanations. Figure 5.

The agreement is close. The three regressors that survived the bootstrap in Section 4 are those to which the random forest assigns most weight, in the same order: the change in agricultural land takes 45.2 per cent of the total mean absolute SHAP value, the drought index 23.2 per cent and the renewable energy share 8.1 per cent, together 76.5 per cent of the attributed explanation. The four that failed the bootstrap receive between 4.7 and 7.1 per cent each, close to what an uninformative variable receives among seven. The Spearman correlation between the SHAP ranking and the ranking by absolute standardised coefficient is 0.750, and 0.857 for permutation importance. Direction agrees where the econometric model makes a claim. For the three significant regressors the correlation between a variable and its SHAP contribution is positive throughout, at 0.951, 0.847 and 0.511, matching the fixed-effects signs. Three of the four insignificant regressors disagree in direction, which is uninformative rather than contradictory, since a coefficient indistinguishable from zero has no sign to match. Partial dependence gives the same answer differently. The curve for agricultural land is almost a straight line, a linear fit accounting for 96.7 per cent of its variation with a slope of 1.50 against a coefficient of 1.34; the drought index yields 0.914 and a slope of 0.385 against 0.457. Only the renewable energy share shows appreciable curvature, at 0.540: flat over the lower range and rising thereafter, consistent with a threshold below which substitution of modern generation has little effect on land pressure. This is the one respect in which the module refines rather than confirms the specification. Three limitations follow from what the exercise is. Attribution is not identification: a SHAP value measures how a variable moves a fitted prediction, not the outcome under intervention. The learners receive the same seven regressors, so no omitted variable can be revealed. And residualisation removes the cross-country variation, so the sign reversal on the renewable energy share is invisible here by construction. Remaining diagnostics are in Appendix C.

7. Panel Analysis: The S–Social Component

The second equation retains the dependent variable of Section 4, the annual rate of change of renewable natural capital per capita, and replaces the environmental regressors with the social block of the Sovereign ESG framework. Seven indicators are used: the rate of population growth, the total fertility rate, the annual change in life expectancy at birth, the labour force participation rate, the ratio of female to male participation, the annual change in the share of the population with access to electricity, and the share of parliamentary seats held by women. The estimation sample covers 151 countries between 1997 and 2020, for 3,293 country-year observations. Collinearity is low, with variance inflation factors between 1.01 and 1.92; the correlation of 0.59 between fertility and population growth is the highest in the block and is well within tolerance.

One feature of this equation requires treatment before any coefficient is interpreted, and it is the social analogue of the accounting problem addressed in Section 4.6. The dependent variable is a per capita magnitude, so population growth enters it through the denominator by construction: the growth of renewable natural capital per capita is identically the growth of the total stock minus the rate of population growth. A coefficient of −1 on population growth is therefore what the accounting identity predicts before any behavioural mechanism is considered. Population growth nonetheless belongs to the social pillar in the World Bank classification and cannot simply be omitted, so the strategy adopted here is to include it, to test whether its estimated coefficient departs from the identity value, and to re-estimate the entire equation with the growth of the total stock as the dependent variable, in which specification population growth has no mechanical role at all. See Table 6.

The coefficient on population growth is the most stable estimate in this study. It ranges from −0.818 to −0.995 across the six estimators and is significant at the one per cent level in every one of them, and in four of the six the confidence interval contains −1. This is precisely the identity value, and it is the first indication that the relationship is arithmetic rather than behavioural. The between estimator, at −0.994 with a standard error of 0.054, is indistinguishable from the identity to two decimal places.

The decisive test is the change of dependent variable, and its result is unambiguous. See Figure 6.

Over the estimation sample the mean growth of renewable natural capital per capita is −1.37 per cent a year, that of the total stock +0.07 per cent, and mean population growth 1.43 per cent. The per capita decline is therefore demographic: the world’s renewable asset base has been approximately constant in aggregate, and 89 of the 151 countries record a non-negative average change in the total stock against only 20 in per capita terms. Re-estimating on total growth moves the coefficient on population growth from −0.913 to +0.087 (p = 0.306), and in the cross-section the slope reverses outright, from −0.877 to +0.123. Countries with faster population growth are not depleting their asset base more rapidly; they are dividing a roughly constant base among more people. The decline documented in Section 4 is thus not primarily a story of environmental mismanagement but of demography operating on a stock that is not growing. Two qualifications apply: the valuation is a discounted rent, so a constant total may conceal offsetting movements in quantities and prices, and the accounts omit the atmosphere and subsoil water.

One social variable survives the change of dependent variable. The fertility coefficient is 0.537 on both definitions (p = 0.008), so it is not an artefact of the denominator, and decomposing by component locates the mechanism: 0.975 on agricultural land (p = 0.0003) and −0.033, insignificant, on everything else. Higher fertility is associated with the expansion of cultivated land and nothing else, a Boserupian pattern in which the accounts register the conversion of one natural asset into another as an increase. The remaining five regressors are weak.

The diagnostics differ sharply from the environmental block. Country effects are jointly insignificant (F = 0.709, p = 0.997), the Hausman test does not reject random effects, and the Mundlak test is borderline at 0.058, because population growth absorbs the heterogeneity the country effects would otherwise capture. The between estimator explains 82.0 per cent of the cross-country variation against 34.3 per cent for the environmental block, and only 5.5 per cent within. The dynamic coefficient, −0.201, indicates mean reversion. Instrumentation is informative here because fertility is a candidate for simultaneity: a shift-share instrument with a first-stage F of 155.6 returns 0.540 against 0.537, with a Wu–Hausman p-value of 0.991. Applied to population growth the same design is weak (F = 6.2) and would instrument an identity; it is reported in Appendix D.

8. Clustering Analysis: The S–Social Component

The social equation of Section 7 reached a conclusion that is arithmetic in nature: the decline of renewable natural capital per capita is almost entirely the effect of population growth operating on a stock that is roughly constant in aggregate. That conclusion holds on average, and the natural follow-up question is whether the demographic configurations producing it are homogeneous across the world or whether distinct national types can be identified. This is the question the clustering module addresses. As in Section 5 the unit of analysis is the country, described by the average over 1997–2020 of the dependent variable and of the seven social regressors, all standardised before clustering; and as in Section 5 the exercise makes no use of the estimated coefficients, so any agreement with the econometric results is informative rather than mechanical.

Before the results are read, one restriction of the design should be recalled from Section 5. Averaging over twenty-four years removes the temporal dimension, so the classification describes permanent national configurations rather than trajectories. In the social block this restriction is more consequential than in the environmental one, because several of the variables are moving systematically over the period: fertility falls in most developing economies, life expectancy rises almost everywhere, and access to electricity expands. A country is therefore placed according to its average position along a transition that it is traversing, not according to where it now stands. The classification should be read as a typology of demographic regimes over the last quarter of a century, and the groups identified below would be drawn differently on data from 2020 alone.

The same six algorithms are compared on the same eleven internal validity indices. The number of clusters is fixed at four, and here the criteria agree rather than conflict. The average silhouette width attains its maximum over the whole range from two to ten precisely at k = 4, at 0.344, and falls sharply thereafter, to 0.220 at k = 6. Explained variance reaches 0.515 and the marginal reduction in within-cluster deviance, having fallen from 178.5 at k = 3 to 76.5 at k = 4, declines only gradually afterwards. The absence of the tension that characterised the environmental block is itself a result: the social variables partition the world more cleanly than the environmental ones, and the average silhouette of the retained solution, at 0.344, exceeds the 0.253. See Table 7.

K-means is again the preferred algorithm, and by a wider margin than in the environmental block: its mean rank of 2.18 rests on first place in eight of the eleven indices, including explained variance, the silhouette, both information criteria, the maximum diameter and the point-biserial correlation. Hierarchical clustering follows at 2.45 and produces a broadly similar partition. Two differences from Section 5 deserve note. The unsupervised random forest performs considerably better here, moving from last place with a silhouette of 0.034 to fourth with 0.272, which suggests that the social variables contain the kind of dependence structure its proximity metric is designed to detect. Model-based clustering performs considerably worse, falling to fifth with a silhouette of 0.128, because the Gaussian mixture with unrestricted covariance fits elongated overlapping components to what are in fact compact groups of unequal size. The second panel of indices, reported in Appendix E, confirms that density-based clustering again buys separation at the price of coverage, leaving 42 countries unassigned. See Table 8.

The four groups are more sharply differentiated than their environmental counterparts, and the ordering of their rates of natural capital accumulation is far wider. See Figure 7.

The largest group, with 79 members, comprises Europe, North America, China, the former Soviet republics and the Southern Cone. Fertility averages 1.84 births per woman and population growth 0.54 per cent, and these economies lose renewable natural capital per capita at 0.62 per cent a year, the slowest rate in the classification: demographically settled. The second group, with 40 members, is sub-Saharan Africa almost in its entirety — fertility 4.94, population growth 2.51 per cent, the highest female participation of the four — and loses 2.07 per cent a year. The third, with 26 members, spans North Africa, the Middle East, South Asia and parts of Central America, and is defined not by fertility but by the exclusion of women from the labour market, with participation 1.50 standard deviations below the sample mean. It loses 1.95 per cent a year, almost identical to the African group: two very different social configurations produce the same environmental outcome. The fourth group has six members — Bahrain, the United Arab Emirates, Qatar, Kuwait, Oman and the Maldives — and is the most extreme observation in the paper. Population growth averages 4.69 per cent a year while fertility, at 2.27, is below the sample average, a combination possible only through immigration, and natural capital per capita falls at 5.08 per cent a year. Were the decline driven by environmental behaviour, the most extreme group should be distinguished by extraction or land conversion; instead it is distinguished by migration. The clustering, given no information about the accounting identity of Section 7, recovers it as the defining feature of the extreme case. The ordering, from −0.62 to −5.08 per cent, spans a range four times wider than the environmental classification, and almost all of it is demographic. A reader treating the ranking as a league table of environmental performance would be reading population growth rates — the sense in which composite ESG scores can invert the meaning of what they aggregate. The average silhouette is 0.344, with four negative widths. Details are in Appendix E.

9. Machine Learning Validation: The S–Social Component

The validation module is applied to the social equation in the same form as in Section 6 and with the same purpose, which is not prediction but the assessment of whether the linear panel specification has exhausted the information in the data and whether a flexible learner independently attributes explanatory weight to the same variables. The dependent variable and the seven social regressors are residualised on country and year effects before estimation, so that the learners face exactly the variation the fixed-effects estimator uses, and cross-validation is performed on ten folds constructed by country. The same six algorithms are compared.

The social equation, however, poses a question the environmental one did not, and the module is organised around it. Section 7 established that the coefficient on population growth is an accounting identity and that the substantive content of the block reduces to the fertility rate. The exercise is therefore run twice, once with the growth of renewable natural capital per capita as the dependent variable and once with the growth of the total stock, in which the identity is absent. Comparing the two runs isolates how much of the apparent explanatory power of the social block is arithmetic. See Table 9.

The pattern of Section 6 recurs and is if anything sharper. The two linear models occupy the first two places, separated by 0.0004 and effectively tied, while the three tree-based learners and the nearest-neighbour method fall behind. Gradient boosting achieves a negative cross-validated coefficient of determination, which means that predicting the sample mean for every observation would have been more accurate than the model it fitted. The overfitting gaps are large: 0.395 for the random forest and 0.485 for boosting, against 0.002 and 0.004 for the two linear specifications. Extending the linear model does not help either, and here it actively harms: adding the twenty-one pairwise interactions reduces cross-validated performance from 0.0516 to 0.0130 and adding the seven squared terms reduces it to 0.0360. Flexibility of any kind is penalised.

The absolute level of these figures should be read against the panel results rather than against Section 6. The two-way fixed-effects estimator reported a within-country coefficient of determination of 0.055 for the social block, and the best learner recovers 0.052 out of sample. The econometric model was therefore already extracting essentially all the systematic within-country signal available, and there is none left for a flexible functional form to find. That is the validation result, and it holds even though the amount of signal is small.

The attribution exercise, conducted with the random forest as the best performing non-linear learner, is where the two runs diverge instructively. See Figure 8.

With the per capita dependent variable, population growth receives 38.3 per cent of the total mean absolute SHAP value, three times any other regressor, while the remaining six divide the residual almost equally, between 9.1 and 12.8 per cent. The learner has recovered the accounting identity: given seven variables and no prior information, it concentrates the explanation on the one entering the dependent variable by construction. Fertility, the only substantive survivor of the econometric analysis, receives 9.9 per cent, indistinguishable from variables the panel found insignificant.

With the total dependent variable population growth falls to 15.6 per cent, close to the 14.3 per cent equal division would imply, and fertility rises to first at 18.6 per cent. The ordering now matches the econometric one but is close to uninformative: every regressor lies between 10.9 and 18.6 per cent, and the model explains almost nothing, with a cross-validated coefficient of 0.0006 for the linear specification and −0.020 for the random forest.

This qualifies the fertility result of Section 7. That coefficient remains significant, robust to the bootstrap and unchanged under instrumentation, but carries almost no predictive content: knowing a country’s fertility rate and six other social indicators does not predict whether its asset base will grow next year. Significance and out-of-sample relevance are separate properties, and the explanatory power of the per capita equation, at 0.052, is mostly arithmetic.

Three restrictions bound this negative conclusion. Residualisation removes the cross-country dimension, where the block was strongest (between R² 0.820 against 0.055 within); the specification is contemporaneous, whereas demographic pressure on land operates with long lags; and the dependent variable is an annual change in a discounted valuation dominated by prices no social indicator could anticipate. Where Section 6 confirmed and refined, this module confirms the specification but subtracts from the interpretation — which is what a validation exercise capable of more than one answer should do. Details are in Appendix F.

10. Panel Analysis: The G–Governance Component

The third equation retains the dependent variable of Section 4 and Section 7 and replaces the regressors with the governance block. The construction of that block requires a decision that the previous two did not, because the governance pillar of the Sovereign ESG framework is dominated by the six Worldwide Governance Indicators, and those six are not distinct measures in any statistical sense. Their pairwise correlations in this sample range from 0.73 to 0.95 with a mean of 0.85, and entering them together produces variance inflation factors up to 23.1, at which point the individual coefficients are not identified and their signs are arbitrary. See Figure 9.

The first principal component of the six accounts for 87.7 per cent of their joint variance and loads almost uniformly on all of them, between 0.374 and 0.428, so it is a general index of institutional quality rather than a contrast among its dimensions. The second component accounts for a further 5.3 per cent and is dominated by political stability, on which it loads at 0.900, against negative loadings on government effectiveness and regulatory quality; it therefore measures the extent to which a country’s stability exceeds its administrative capacity. The remaining four components together account for 7.0 per cent and are not interpretable.

The governance block is built accordingly, with seven regressors. Institutional quality is the first principal component, centred at the sample mean, and its square is included to allow the relationship to be non-monotonic, following a long-standing conjecture that environmental outcomes improve with institutions only beyond a threshold. The annual change in institutional quality is included separately, because a reform episode is a different object from a level of institutional development and, as the variance decomposition shows, it is the only governance variable with substantial year-to-year movement. The second principal component enters as the stability–effectiveness contrast. The remaining three regressors are the growth rate of GDP, the annual change in internet penetration and agriculture value added as a share of GDP. Variance inflation factors in this specification lie between 1.03 and 2.33. The sample covers 151 countries from 2003 to 2020, for 2,629 observations; the later start reflects the biennial publication of the WGI before 2002. See Table 10.

The first thing to record is the weakness of the equation in the temporal dimension. The two-way fixed-effects specification explains 0.47 per cent of the within-country variation in the accumulation of renewable natural capital per capita, against 19.1 per cent for the environmental block and 5.5 per cent for the social one. No coefficient survives the wild cluster bootstrap with the Bonferroni correction: the closest is the squared institutional quality term at a bootstrap p-value of 0.009 against a threshold of 0.00714, and the change in internet penetration at 0.028. Governance, measured annually and read within countries, does not explain the year-to-year accumulation of natural wealth. This is a negative result and it is reported as such rather than rescued by selective emphasis.

The between dimension tells a different story, and the difference is systematic rather than accidental. The between estimator explains 21.6 per cent of the cross-country variation, and two of its coefficients are significant at the one and five per cent levels respectively. Institutional quality carries 0.167, so an improvement of one standard deviation of the index, equal to 2.26 points, is associated with a rate of accumulation higher by 0.38 percentage points a year. The change in institutional quality carries 9.096, by far the largest coefficient in this study, but its magnitude reflects units: the variable is an annual change whose standard deviation across country means is 0.037, so a one standard deviation difference corresponds to 0.34 percentage points a year, and a country in the top decile of institutional improvement accumulates natural capital roughly 0.8 percentage points a year faster than one in the bottom decile. See Figure 10.

The contrast between the two panels is the substantive content of this section. Across countries the cumulative institutional trajectory over eighteen years is positively associated with the accumulation of natural wealth, with a slope of 0.231 percentage points per unit of improvement; within countries the same variable measured annually carries a slope indistinguishable from zero. The Mundlak test rejects equality of the two dimensions at 43.37, and the group-mean term on the change in institutional quality is 9.620 (p < 0.001) against a within counterpart of −0.434.

The natural reading is that institutions operate over horizons far longer than a year: improving the rule of law in a given year does not preserve more forest that year, while two decades of steady improvement leave a materially different rate of accumulation. The data cannot distinguish this from the alternative in which institutional quality marks something else, since the between dimension offers no protection against omitted permanent characteristics. The section therefore reports an association across countries and a null within them, and claims no mechanism. The squared term changes sign between dimensions, implying concavity across countries and convexity within, but it is fragile and no weight is placed on it.

The three blocks can now be compared on the same dependent variable. The environmental equation explains 19.1 per cent of the within-country variation and 34.3 per cent of the between; the social equation 5.5 and 82.0; the governance equation 0.5 and 21.6. A composite averaging the three with fixed weights would combine a variable identifying annual variation, one identifying an accounting identity and one identifying neither.

Instrumenting institutional quality returns −1.292 with a standard error of 1.342 and a Wu–Hausman p-value of 0.361: the instrument reaches only the annual component that the fixed-effects results show to be uninformative, a limitation of the design rather than a finding. Country effects are jointly significant, the Hausman and Mundlak tests reject, serial correlation is marginal, and the dynamic coefficients are negative and insignificant, so the absence of persistence found elsewhere holds here too. Details are in Appendix G.

11. Clustering Analysis: The G–Governance Component

The governance equation of Section 10 produced a result that the clustering module is well placed to examine further. Within countries, annual movements in governance explain essentially nothing about the accumulation of renewable natural capital, with a fixed-effects coefficient of determination of 0.005; across countries, the institutional trajectory over the period is associated with the rate of accumulation, and the Mundlak test rejects the equality of the two relationships decisively. Since clustering operates entirely on the cross-sectional dimension, it works precisely where the governance block has content, and the question it answers is whether the association identified econometrically corresponds to identifiable national types.

The design follows Section 5 and Section 8. Each of the 151 countries is described by the average over 2003–2020 of the dependent variable and of six governance variables: institutional quality as the first principal component of the six Worldwide Governance Indicators, its annual change, the stability–effectiveness contrast, the growth rate of GDP, the annual change in internet penetration and agriculture value added as a share of GDP. The squared institutional term used in the panel specification is omitted here, since a monotone transformation of a variable already present adds nothing to a distance metric. All variables are standardised, and the exercise makes no use of the estimated coefficients.

The number of clusters is again fixed at four, and the tension observed in the environmental block reappears in the same form. The average silhouette attains its maximum at k = 2, at 0.256, where the partition simply separates high-income from low-income economies; it then falls to 0.202 at k = 3 and recovers to 0.217 at k = 4 and 0.219 at k = 5, remaining essentially flat thereafter. The marginal reduction in within-cluster deviance falls from 119.7 at k = 3 to 81.3 at k = 4 and 57.3 at k = 5, placing the elbow at four. Explained variance at that solution is 0.453. As in Section 5 the choice rests on the elbow and on interpretability rather than on the silhouette, and the tension is recorded rather than concealed. See Table 11.

K-means obtains its clearest victory of the three blocks, with a mean rank of 1.91 built on first place in seven of the eleven indices, including explained variance, the silhouette, both information criteria, the maximum diameter and the Calinski–Harabasz statistic. Density-based clustering fails here in a way it did not in the other two blocks: its silhouette of 0.029 indicates a partition barely distinguishable from an arbitrary one, and it leaves 49 of the 151 countries unassigned, or 32.5 per cent. The reason is visible in the data rather than in the algorithm. Governance variables are close to continuously distributed across countries, with no dense regions separated by empty ones, so a method that defines clusters as regions of high density has little to find. This is itself informative about the object being classified: institutional quality is a gradient, not a set of discrete regimes. See Table 12.

The four groups are of comparable size, with a Herfindahl index of 0.266 and an entropy of 1.353, both the most balanced of the three blocks, and they divide the world along two axes rather than one. Figure 11.

The first group, with 34 members, comprises the advanced economies of Western Europe, North America, Australasia and Japan: institutional quality 1.27 standard deviations above the sample mean, agriculture at 2.3 per cent of value added. These high-capacity economies lose renewable natural capital per capita at 0.80 per cent a year. The second, with 47 members, is the mirror image — institutional quality 1.99 points below the mean, agriculture at 23.5 per cent — covering most of low-income sub-Saharan Africa with parts of Central Asia and Melanesia, and losing 2.10 per cent a year.

The remaining two are the interesting ones, because they sit at almost the same institutional level and differ sharply in outcome. The third, with 46 members, has institutional quality of 0.11 and is distinguished by improvement, with a cumulative change of +0.72 index points; it contains the Central and Eastern European accession states, the Balkans, the Caucasus, Vietnam and much of Andean South America, and loses only 0.27 per cent a year, the best outcome in the classification. The fourth, with 24 members, has institutional quality of −0.26, indistinguishable from the third, but a cumulative change of −0.28, and contains the Gulf states, Iran, Gabon, Jordan, Bolivia and Guatemala. It loses 3.11 per cent a year.

Two groups at the same institutional level, differing only in the direction of institutional travel, therefore differ in accumulation by 2.84 percentage points a year. The clustering recovers, from the cross-sectional structure alone and without any coefficient, the distinction Section 10 identified between level and change — as a property of the joint distribution rather than an average partial effect, which is weaker causally and stronger descriptively.

Two qualifications restrain this. All six migration-driven Gulf economies of Section 8 fall in the fourth cluster and constitute a quarter of its members; excluding them raises its mean from −3.11 to −2.42, so the demographic and institutional explanations overlap without either being redundant. And the partition is the weakest of the three blocks, with an average silhouette of 0.217 and the fourth group the least cohesive of all twelve clusters at 0.105. The advanced economies also record the only negative institutional trajectory among the three non-drifting groups, at −0.55, reflecting the decline registered for several Western democracies; whether that is an artefact of perception-based indices this study cannot settle. Details are in Appendix H.

12. Machine Learning Validation: The G–Governance Component

The validation module is applied to the governance equation with the same six algorithms, the same grouped cross-validation and the same purpose as in Section 6 and Section 9. The governance block, however, differs from the other two in a way that dictates the design of this section. Section 10 established that the equation has almost no temporal content, explaining 0.47 per cent of the within-country variation, and that what content it has lies in the cross-section, where the between estimator reaches 21.6 per cent and the Mundlak test rejects the equality of the two dimensions with a p-value below 0.001. Running the learners only on the residualised data would therefore test the specification exactly where the econometrics has already reported nothing. The module is consequently run twice: once on the within-transformed observations, as in the previous two blocks, and once on the 151 country means, which is the cross-sectional counterpart of the between estimator.

The asymmetry between the two runs is worth stating before the results, because it is what makes this block instructive rather than merely weak. In the environmental equation the informative dimension was temporal and the module could be run in the standard way; in the social equation the informative dimension was also temporal, though most of what it contained was an accounting identity; here it is cross-sectional. A validation exercise that applied the same residualisation to all three blocks without asking where the information lies would have concluded that the governance block is empty, when in fact it is empty only in the dimension that residualisation preserves. This is a general point about applying supervised learning to panel data: the transformation that makes the comparison fair with respect to unobserved heterogeneity also determines which of the two dimensions the learner is allowed to see, and that choice should follow the econometrics rather than convention. See Table 13.

The within columns confirm what Section 10 reported and add nothing to it. Five of the six learners return a negative cross-validated coefficient of determination, meaning that predicting the sample mean would have been more accurate than the fitted model, and the best performance, achieved by linear regression, is 0.0013. There is no signal in the annual movement of governance indicators to be recovered by any functional form, and the sharply positive overfitting gaps of the flexible learners, at 0.42 for the random forest and 0.56 for boosting, show them fitting noise. The conclusion is the same as the econometric one, reached by an independent route: governance measured annually does not explain the year-to-year accumulation of natural wealth.

The between columns produce the one exception to a pattern that has otherwise held throughout this study. See Figure 12.

In the cross-section the random forest attains a cross-validated coefficient of 0.2172 and boosting 0.2039, against 0.1291 for the linear support vector machine and 0.1090 for linear regression. This is the first and only occasion in the paper on which flexible learners outperform the linear specification out of sample, and the margin is substantial: the random forest doubles the explanatory power of the linear model. The result is not an artefact of a favourable fold assignment. Repeating the comparison across ten random partitions returns a mean of 0.288 for the random forest, with a standard deviation of 0.015, against 0.107 for the linear model with a standard deviation of 0.018, and the random forest is ahead in ten splits out of ten.

Two cautions apply before this is interpreted. The cross-section contains 151 observations, so cross-validated estimates are considerably noisier than those computed on thousands of country-year observations, and the in-sample gaps remain large, at 0.41 for the random forest and 0.79 for boosting. And the nonlinearity being exploited is not of the kind an econometrician would ordinarily add to a specification: extending the linear model with all twenty-one pairwise interactions reduces cross-validated performance from 0.109 to 0.017, and adding the seven squared terms reduces it to 0.027. Whatever structure the forest is finding, it is neither multiplicative interaction nor quadratic curvature, and the natural candidates are thresholds and local effects confined to subsets of countries — which is consistent with the taxonomy of Section 11, where four groups with distinct institutional profiles were identified and two of them differed in outcome by nearly three percentage points at almost identical institutional levels.

The attribution exercise then asks whether the forest, given the country means and no information about the econometric estimates, allocates explanatory weight in a way that matches the between coefficients. See Figure 13.

Directional agreement in the between dimension is close to complete: six of seven regressors have a SHAP direction matching the sign of the corresponding between coefficient. The three strongest correlations belong to the three variables the between estimator identified — the change in institutional quality at +0.887, its level at +0.857 and GDP growth at −0.737. The one disagreement concerns agriculture value added, whose between coefficient is zero to three decimals, so there is no sign to match.

The distribution of importance is nonetheless flat. The five leading regressors receive between 17.1 and 19.2 per cent of the total mean absolute SHAP value, close to the 14.3 per cent equal division would imply, and the rank correlation with the ordering by standardised between coefficient is accordingly low at 0.214. The learner agrees about direction and disagrees about hierarchy, which is what happens when correlated variables carry overlapping information: the forest distributes credit among them, the regression assigns it to whichever enters the linear projection most strongly. The within-dimension attribution is reported for symmetry and is uninformative, deriving from a model with negative cross-validated performance.

Partial dependence confirms the linear reading of the relationships that matter, with linear fits of 0.964 for the change in institutional quality, 0.815 for its level and 0.808 for GDP growth. The individual relationships are approximately linear, which sharpens the puzzle: the advantage of the random forest comes not from curvature in any single dimension but from the joint structure.

Three applications of the same procedure have now produced three verdicts. In the environmental equation the linear specification won and the module added a refinement; in the social equation it won and the module subtracted from the interpretation; here it loses in the dimension that matters, suggesting the econometric model is missing something. The governance block is the only one where flexibility helps, pointing to a configurational rather than marginal relationship, consistent with Section 11 and offered as interpretation rather than finding. Details are in Appendix I.

13. Discussion

The nine modules answer the same question about the same dependent variable and disagree in ways that are informative rather than contradictory. Table 14 summarises what each has established.

Read across the rows, the table shows that the three pillars occupy different positions on the same map. The environmental block is the only one that explains annual movement to any appreciable degree, because drought and land conversion are events rather than characteristics. The social block explains the cross-country ranking almost completely, at 82.0 per cent, but does so mainly through an accounting identity. The governance block explains a fifth of the ranking and none of the movement. A composite ESG score that averaged the three with fixed weights would combine a variable identifying annual variation, one identifying an identity and one identifying neither, and would report the average as a single measure of environmental performance.

Read down the columns, the methods do different work in each block, which is the strongest evidence that the design is not triangulating a foregone conclusion. Clustering converges with the econometrics twice and independently: aridity in the environmental block and the level-versus-trajectory distinction in the governance block are recovered from the cross-sectional structure alone. The machine learning module returns three different verdicts — confirming and refining, confirming and subtracting, signalling an omission — where a ratifying exercise would have returned three of the first kind.

The table also carries a lesson about where each method applies. The three do not see the same information: the panel estimators exploit both dimensions, which is why six are reported; the clustering sees only country averages; the learners see whichever dimension is preserved by the transformation. The governance block makes the consequence explicit. Residualising on country and year effects, the standard way to make a learning comparison fair with respect to unobserved heterogeneity, would have shown that block to be empty, while the same comparison on country means reveals a relationship that six learners recover and a flexible one recovers better. The choice of transformation is a decision about which question is asked, and should follow the variance decomposition rather than convention.

Two substantive conclusions follow. The first is that the global decline in natural wealth per capita is predominantly demographic rather than environmental: the aggregate stock is roughly constant over twenty-five years, and the per capita fall is arithmetic. This does not make the decline benign, since a stock that cannot grow while population does is a stock whose contribution to per capita wealth must fall, but it relocates the policy problem from environmental management to the question of whether the natural asset base can be made to grow at all.

The second is that institutional trajectory matters more than institutional level, a result that emerges independently from the between estimator, from the clustering and from the attribution exercise, and that the fixed-effects estimator cannot see. Whether the relationship is causal remains open: the between dimension offers no protection against omitted permanent characteristics, the shift-share instruments reach only the annual component, and the governance cluster losing wealth fastest overlaps by a quarter with the demographic outlier group of Section 8. What can be said is that the association is robust to three methods that share no assumptions.

Three limitations bound all of this. The estimates are associations, not causal effects: only the drought index has a strong claim to exogeneity, and the instrumental variable exercises confirm the fixed-effects results rather than establishing identification. The dependent variable is a discounted valuation, so a constant total may conceal offsetting movements in physical quantities and in prices, and the accounts omit the atmosphere, groundwater and several ecosystem functions. And the classifications average over twenty-five years, so they describe permanent national configurations rather than trajectories, a restriction that bears most heavily on the social block, where fertility and life expectancy move systematically across the period.

14. Limitations

Four sets of limitations bound what the preceding sections establish, set out in order of their consequence for interpretation.

The first concerns identification. The estimates are structural associations, not causal effects. Of the twenty-one regressors used across the three equations, only the drought index has a strong claim to exogeneity, being constructed from precipitation and evapotranspiration and not plausibly influenced by national wealth accounts. The shift-share instruments have first-stage F statistics between 6.2 and 155.6, but relevance is not sufficient, and the identifying assumptions of this design must be defended on the exposure shares rather than on the shocks (Goldsmith-Pinkham et al., 2020; Borusyak et al., 2025). In the governance block the instrument reaches only the annual component of institutional quality, which the results show to be uninformative, so it cannot speak to the cross-country association actually reported. Where a coefficient is significant, the claim is that it is a robust feature of the conditional expectation, not that intervening would move the outcome.

The second concerns the dependent variable. Renewable natural capital is a discounted valuation of expected rents, so a constant aggregate may conceal offsetting movements in quantities and prices, and the sensitivity of wealth-based measures to discount rates and to technological progress is a known weakness (Boos, 2015; Pearson et al., 2013; Engelbrecht, 2016). The accounts exclude the atmosphere, groundwater and ecosystem functions lacking a defensible shadow price, a boundary problem only partly addressed by asset-by-asset extensions (Biasi et al., 2019; Hoekstra, 2020). Agricultural land carries 62.1 per cent of the total, so the aggregate is dominated by an asset responding to agricultural support as well as to ecological condition (Ghauri et al., 2022), and Section 4.6 shows five sixths of the land-use effect to be accounting rather than economics.

The third concerns the classification and validation modules. The clustering averages over the period and describes permanent configurations rather than trajectories, a restriction bearing most heavily on the social block, where fertility, life expectancy and electricity access move systematically. Internal validity indices disagree by algorithm family, so the choice of k-means rests on a mean rank, and a different weighting of the eleven could favour another algorithm (Zhao et al., 2023). Hyperparameters were fixed rather than tuned within the cross-validation loop, so the finding that linear specifications win out of sample is defended in its weaker form: on conventional settings, flexibility does not help. The between-dimension comparison in the governance block rests on 151 observations, where cross-validated estimates are considerably noisier.

The fourth concerns coverage and measurement. The governance equation begins in 2003 because the Worldwide Governance Indicators were published biennially before 2002, and those indicators are contested as measures of distinct dimensions, being built largely from perception surveys whose correlations are too high to separate (Langbein & Knack, 2010; Kaufmann et al., 2010; Huque & Jongruck, 2018). The block therefore measures general institutional development rather than any named component. The income-based splits are descriptive rather than tests of heterogeneity, and the study covers 149 to 151 countries, excluding economies for which the wealth accounts are not compiled (Li, 2024).

15. Policy Implications

The results carry implications for three audiences, and separating them matters because the same finding points in different directions depending on the instrument available.

For the design of sovereign sustainability metrics, the implication is that composite ESG scores should not rank countries on environmental wealth. The three pillars explain very different parts of the same variation: 19.1 per cent of the within-country variation for the environmental block, 5.5 per cent but 82.0 per cent of the cross-country variation for the social block, and 0.5 and 21.6 per cent for the governance block. A fixed-weight average would combine an indicator of annual environmental events, an accounting identity and a slow-moving institutional characteristic, and report their mean as a measure of performance; the difficulty of interpreting composites built from heterogeneous series is well documented (Cook & Davíðsdóttir, 2021; Halkos et al., 2018). The sign reversal on the renewable energy share makes the point concretely: a high renewable share indicates traditional biomass dependence across countries and modern substitution within them, so a composite treating it as favourable inverts its meaning for the poorest economies (Olaniyi & Odhiambo, 2025; Naimoğlu & Shahbaz, 2025). Metrics guiding sovereign capital allocation should report the pillars separately and distinguish an indicator’s level from its trajectory.

For environmental and land policy the most robust finding is climatic. The drought index is the only regressor with a credible claim to exogeneity, is positive and significant in all six estimators, and more than doubles when agricultural land is excluded, rising from 0.457 to 1.113. The erosion of natural wealth under water stress is therefore understated by aggregates dominated by cultivated land, whose valuation is partly insulated by agricultural support. Monitoring frameworks tracking natural capital in aggregate will register drought effects late and incompletely, and disaggregated reporting by asset class is a low-cost correction, consistent with the case for spatially explicit accounting (Ahmed & Jahan, 2026; Maher et al., 2020). The land-use results point the same way: agricultural expansion raises measured natural capital while converting forest and wetland assets, so a rising aggregate may conceal a change in composition that a sustainability criterion should register.

For development policy the implication is more uncomfortable and should be stated carefully. The global decline in natural wealth per capita is almost entirely demographic: the aggregate stock is roughly constant while population grows, and the coefficient on population growth is indistinguishable from the value implied by the accounting identity. This is not an argument for population policy, and nothing here supports one; the role of population growth in wealth-based criteria is a recognised property of the accounting framework rather than a behavioural finding (Ferreira et al., 2008; Yamaguchi, 2014). It is an argument about arithmetic. If per capita natural wealth is the benchmark and the stock cannot be made to grow, the criterion will be failed by any country whose population is rising, regardless of its environmental management. Either the asset base must grow, through restoration, protection and extension of the accounting boundary to unpriced assets, or the criterion should be supplemented by measures separating stewardship from demography. The governance results suggest where effort might go: countries whose institutions improved accumulated natural capital 2.84 percentage points a year faster than countries at the same institutional level whose institutions deteriorated, and the direction of institutional change proved more informative than its level in all three methods, consistent with evidence that institutions condition the environmental consequences of resource dependence (Jahanger et al., 2023; Ameer & Ahmad, 2024).

16. Conclusions

This paper has taken the annual change in renewable natural capital per capita, which comprehensive wealth accounting defines as the net environmental investment of a nation, and estimated its determinants within an environmental, social and governance framework. The dependent variable and every regressor are drawn from the Sovereign ESG Data Portal of the World Bank, and the analysis covers 149 to 151 countries between 1995 and 2020. Three equations sharing that dependent variable and differing only in the pillar of origin of their regressors were each developed along three routes — panel econometrics across six estimators, a comparison of six clustering algorithms on eleven internal validity indices, and a comparison of six supervised learners used for specification validation rather than prediction — producing nine analytical modules on a single outcome.

Four findings emerge. The first is descriptive and reframes the others: median renewable natural capital per capita fell by 29.7 per cent over the period and its share of comprehensive wealth halved, yet the aggregate stock was roughly constant, so the per capita decline is demographic arithmetic rather than a record of environmental mismanagement. The second is that climatic conditions are the most robust environmental determinant, that the drought coefficient more than doubles when agricultural land is removed from the dependent variable, and that aridity independently defines the group of countries losing natural wealth fastest in the environmental classification. The third is that the direction of institutional change matters more than the institutional level: the between coefficient on the annual change in institutional quality is large and significant while its within counterpart is indistinguishable from zero, and the clustering recovers the same distinction from the cross-sectional structure alone. The fourth is methodological: relationships in this field differ systematically between the two dimensions of a panel, the Mundlak test rejects their equality in all three blocks, and the renewable energy share carries opposite signs across and within countries.

The design is the paper’s second contribution. Estimating the three pillars as separate and directly comparable equations, rather than aggregating them into a composite index with fixed weights, revealed that they explain different parts of the same variation, and applying the same three methods to each revealed that the methods do different work in each block. The machine learning module confirmed and refined the environmental specification, confirmed but qualified the social one by showing that its surviving coefficient carries little predictive content, and signalled an omission in the governance one by outperforming the linear model across countries. A validation procedure that could only ratify would have returned three identical verdicts.

Three directions follow. The threshold structure suggested by the renewable energy relationship and by the superior cross-sectional performance of the random forest in the governance block invites a formal threshold or finite mixture specification, which a larger cross-section could support. Extending the accounting boundary to groundwater and atmospheric assets would test whether the flat aggregate survives a fuller measure. And applying the same design to subnational wealth accounts, where the demographic denominator behaves differently, would separate stewardship from demography more cleanly than a cross-country panel allows.