Resource Rents, Genuine Savings and Sustainable Development: Revisiting the Evidence

Abstract

Economic theory on sustainable development suggests that resource-rich countries should reinvest the rents from natural resource extraction in other forms of capital to ensure that future consumption level of the economy can be greater than or at least equal to the level of their current consumption. Several seminal papers in the early 2000s indicated that the correlation between genuine savings and future consumption was weaker than theory predicted, at least when genuine savings were measured using the World Bank estimates. This paper revisits the issue and replicates two of these earlier studies to see whether the correlation has become stronger over time, on the back of policy changes in resource-rich countries and of revisions to the World Bank estimates. The results indicate that the correlation between genuine savings and future consumption growth may be stronger for poorer countries than for richer, and for sub-Saharan Africa, the theoretical predictions appear to hold.

1. Background

Genuine savings (GS) can be defined as a country’s net investment in all types of capital. This paper studies the link between countries’ GS and their consumption levels over time. The purpose of the study is to re-examine results from previous research, which found that the correlation between GS and consumption over time was weaker than predicted by green accounting theory.

Green accounting theory is concerned with the impact of natural resource depletion and environmental degradation on long-term welfare. According to an important version of this theory, countries should aim to follow a development path where the gains derived from exploiting natural resources and the ecosystem are reinvested in such a way that their future consumption can be greater than their present consumption. The extant literature predicts that with positive GS, future consumption will be greater than today’s, while with negative GS, it will be less.

This literature has contributed to considerable interest in empirical work on green accounting and GS, both in terms of case studies of individual countries (see, e.g., [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] for various countries in Sub-Saharan Africa and elsewhere) and cross-country comparisons (see, e.g., [16,17,18,19,20,21]). As part of the interest in the latter, the World Bank [22] began publishing data on estimated GS as part of its World Development Indicators database.

Soon after the first edition of the World Bank’s GS estimates, a series of seminal studies—notably by Ferreira and Vincent [18] and Ferreira, Hamilton and Vincent [19]—were conducted to see whether the connection between GS and future consumption was as green accounting theory predicted. These studies found that the correlation was far weaker than estimated. One likely explanation for this was that limitations in the World Bank’s estimates had weakened the link between the theory and the measured empirical outcomes. For example, Ferreira and Vincent [18] highlighted the weaknesses of the World Bank method in its calculation of the initial estimates of the GS. These shortcomings notably included the large number of natural capital types that were only partially covered or not covered at all (To give some key examples, the World Bank estimates exclude (1) changes in the quality of farmland and the availability of freshwater on it; (2) fisheries; the increased availability of farmland when forestland is converted into cropland; and (3) the net increase in forest capital when forest regeneration exceeds forest depletion); the problems with estimating the value of produced capital using the perpetual inventories method with a constant depreciation rate; the exclusion of new discoveries of natural resources; the effect of price changes on the value of reserves; and the inability to account for human capital losses.

Ferreira and Vincent [18] explained that their own findings were based on initial data, suggesting that the results they had generated could be improved over time with future updates of World Bank estimates. However, an additional explanation of those findings, discussed briefly (and fairly diplomatically) in Ferreira and Vincent [18], was that the capital stocks built up through the measured investments might not generate subsequent consumption streams, at least not that part of a country’s consumption measured in the World Bank data.

Obvious explanations for the discrepancy found by Ferreira and Vincent would include unrecorded capital flight; private investments that generated poor returns on paper because actual returns to private owners went unreported; or poor public investment decisions based mainly on political considerations, and which generated poor returns.

An additional explanation could be that, at least in richer countries, consumption may be reaching saturation levels where additional investment does not translate into increased consumption and where increased economic activity is less dependent on natural resources (see, e.g., [23,24]). If this is the case, the correlation between GS and future consumption should be higher in poorer countries than in richer countries.

Several studies have proposed extending the World Bank’s GS estimates by including relevant new items to make them more consistent with green accounting theory. For example, Biasi et al. [25] suggested adding degradation in water and land; McLaughlin et al. [26] proposed adding the present value of technological change; Fink and Ducoing [27] suggested adding negative resource incomes, fish incomes and technological change over time; and Yamaguchi [28] showed the need for GS estimates to account for change in neighbouring resource stocks. McGrath et al. [29,30] proposed further extension of the estimates to include changes in agricultural land value as well as in local air pollutants (sulphur dioxide, non-metallic volatile organic compounds, nitrogen oxides and ammonia) and non-greenhouse gases.

Boos [31], on the other hand, suggested modifying the GS estimates by, e.g., adding health expenses when calculating investment in human capital; covering a wider range of natural resources in calculating their depletion; excluding military investment from gross national investment; using five-year averages of resource rents to reduce the effects of the volatility of natural resource prices on GS estimates; and separating the forest from the rest of the non-renewable natural capital to avoid forest growth being interpreted as reinvestment of natural capital rents in further natural capital.

During the two decades since the release of the initial GS estimates, the World Bank has announced four major revisions, namely in 2006 [32], 2011 [33], 2018 [34], and 2021 [35]. It would be reasonable to assume that these updates have improved the estimates’ accuracy. Hence, it is of interest to revisit the findings by Ferreira and Vincent [18] in 2005 and Ferreira, Hamilton and Vincent [19] in 2008 to determine whether their results still hold.

Moreover, the debate around GS and green accounting has spurred several initiatives aimed at improving not only the management of natural resources per se, but also the rents derived from them—especially as regards developing countries, and especially those in sub-Saharan Africa. This provides further motivation to revisit the two earlier studies mentioned to see whether the correlation between GS and future consumption has strengthened over time. Moreover, if one considers how much attention is being devoted to improving resource management in sub-Saharan Africa, it is of particular interest to examine the correlation between GS and future consumption there. For this reason, the hypothesised links for this region are calculated separately for the current study.

This article proceeds as follows. The next section outlines the relevant sustainable development theory and establishes its connection with the World Bank’s GS estimates. Section 3 and Section 4 describe the econometric specification and data, respectively. Section 5 presents the results, while the last section presents a discussion of them.

2. Theory

2.1. Measuring Genuine Savings

The weak sustainability concept underlying green accounting theory assumes complete substitutability between physical capital, natural capital and human capital. Thus, when one form of capital, e.g., natural capital, is depreciated, the depreciation can be replaced by an increase in other forms of capital, i.e., physical or human capital, and production and consumption can be maintained if the overall capital stocks do not decline.

Based on the weak sustainability theory, Hartwick [36] defined the value of the net change in total capital stocks—physical, natural and human—at any given point in time as the sum of the changes in each of these three forms of capital. Hartwick’s rule states that, if this value is equal to (or greater than) zero, it means that a country is maintaining (or increasing) its level of capital so that it can sustain (or increase) its level of consumption [37,38].

The World Bank was inspired by the concept of weak sustainability and by the Hartwick rule to measure the GS as follows [18]:

$$GS=\underset{GrNI}{\underbrace{\underset{CNI}{\underbrace{\underset{CGI}{\underbrace{GNI+NITA}}-\delta K}}-\Sigma Rn,j-C{O}_{2}D}+IHC}$$

(1)

where GNI is gross domestic savings; NITA is net income and net current transfers from abroad; δ is the rate of depreciation of the produced capital stock (K); Rn,j is rent from depletion of natural capital j; CO₂D represents damages from carbon dioxide emissions; and IHC is investment in human capital measured as current (non-fixed-capital) expenditure on education. CGI is the conventional gross investment or gross savings, CNI is conventional net investment or net savings, and GrNI is green net investment or green net savings.

In line with Hartwick [36], the depletion of natural resources is included in the GS estimates by including energy rents (from the depletion of the three major fossil fuels—oil, natural gas and coal); mineral rents (including the depletion of a set of ten mineral resources, namely bauxite, copper, gold, iron, lead, nickel, phosphate, silver, tin and zinc) whose data are available; and forest rents (measured as a reduction in wood stock through the difference between forest growth and deforestation). Furthermore, the damages from carbon dioxide emissions (CO₂D) are assumed to be USD 20 per metric ton of carbon emitted.

Detailed descriptions and explanations of the assumptions made by the World Bank and the sources of data used in their initial estimates of GS can be found in [39,40,41].

2.2. Genuine Savings as a Predictor of Future Consumption

Although the theoretical model underlying the research by Ferreira and Vincent [18] and Ferreira, Hamilton and Vincent [19] is expressed slightly differently in the two studies, the theory underlying the model is the same. The relevant theory and its model were outlined in Weitzman [42], who showed that, under a number of restrictive assumptions, the change in average future consumption in an economy relative to its current consumption should be given by that economy’s net change in capital stocks. This net change has subsequently been referred to as the economy’s genuine savings rate. If we refer to this rate at time $t$ as $G\left(t\right)$ and the consumption at time $t$ as $C\left(t\right)$, Weitzman’s result can be written as

$$G\left(t\right)={\displaystyle \frac{{\int }_t^{\mathrm{\infty }}C\left(s\right)e^{-r(s-t)}ds}{{\int }_t^{\mathrm{\infty }}{e}^{-r(s-t)}ds}}-C(t)$$

(2)

where the first term on the right-hand side of the equation is an average of future consumption weighted by the discount rate $r$.

Weitzman’s seminal work has subsequently been revisited in several theoretical papers that have developed generalised results that hold under less restrictive conditions. Of particular interest here is the study by Hamilton and Hartwick [43], who show that

$$G\left(t\right)={\int }_t^{\mathrm{\infty }}{\displaystyle \frac{dC\left(s\right)}{ds}}{e}^{-{\int }_t^{u}r\left(u\right)du}ds$$

(3)

and Ferreira, Hamilton and Vincent [19], who bring in varying population growth $\gamma \left(t\right)$ and show that

$$g\left(t\right)={\int }_t^{\mathrm{\infty }}\left({\displaystyle \frac{dc\left(s\right)}{ds}}{\displaystyle \frac{d\gamma \left(s\right)}{ds}}w(s)\right)e^{-{\int }_t^s(r\left(u\right)-\gamma \left(u\right))du}ds$$

(4)

The lower-case letters (e.g., g in respect of G) denote per-capita values. Thus, $w\left(s\right)$ represents the economy’s per-capita overall capital stocks (W) at time $s$.

3. Econometric Specification

Shortening the time period from ∞ to $T$ gives us predictions that can be tested empirically. Writing the second and fourth equations in discrete form gives us the respective predictions that, for country $i$,

$$G_{it}={\displaystyle \frac{\sum _{s=t+1}^{t+T}{C}_{is}{(1+r)}^{-(s-t)}}{\sum _{s=t+1}^{t+T}{(1+r)}^{-(s-t)}}}-C_{it}$$

(5)

and

$$g_{it}=\sum _{s=t+1}^{t+T}\left({\displaystyle \frac{\left(\frac{C_{is+1}}{N_{is+1}}-\frac{C_{is}}{N_{is}}\right)+\left({\gamma }_{is+1}-{\gamma }_{is}\right)\frac{W_{is}}{N_{is}}}{\prod _{j=t+1}^s\left(1+{\rho }_{ij}-{\gamma }_{ij}\right)}}\right)=PV∆C_{it}+PV[\left(∆{\gamma }_{it}\right)w_{it}]$$

(6)

In Equations (5) and (6), $G_{it}$ represents various measures of net capital investment, ranging from gross physical investment to GS, while $g_{it}$ is the per-capita counterpart of $G_{it}$; $C_{it}$ is consumption, while $c_{it}$ is per-capita consumption; r is the discount rate; ${\rho }_{it}$ is the interest rate; ${\gamma }_{it}$ is the population growth rate; $W_{it}$ represents the produced and natural capital stocks and w_it their per-capita counterparts; PV is present value; and $N_{is}$ is the total population of country i in time s. These are all measured using data from the World Development Indicator (WDI) database.

Thus, if one calls the right-hand side of Equation (5) (the difference between average future and current consumption) ${∆}_{it}$, and one runs the regression

$${∆}_{it}={\beta }_0+{\beta }_1{g}_{it}+{ϵ}_{it}$$

(7)

One should get ${\beta }_0=0$ and ${\beta }_1=1$.

Similarly,

(a)

if one calls the term $PV∆C_{it}$ the present value of future consumption changes, one assumes constant population growth rates $\gamma$ in Equation (6), and one runs the regression

$$PV∆C_{it}={\beta }_0+{\beta }_1{g}_{it}+{ϵ}_{it}$$

(8)

(b)

if one assumes that population growth rates ${\gamma }_{it}$ vary over time in Equation (6) and one runs the regression

$$PV∆C_{it}+PV\left[\left(∆{\gamma }_{it}\right)w_{it}\right]={\beta }_0+{\beta }_1{g}_{it}+{ϵ}_{it}$$

(9)

(c)

if one includes the ratio of the population growth rate to the total population as an additional explanatory variable to control for omitted wealth components from the GS variable in Equations (8) and (9), and one runs the regressions

$$PV∆C_{it}={\beta }_0+{\beta }_1{g}_{it}+{\beta }_{2i}{\displaystyle \frac{{\gamma }_{it}}{N_{it}}}+{ϵ}_{it}$$

(10)

and

$$PV∆C_{it}+PV[\left(∆{\gamma }_{it}\right)w_{it}]={\beta }_0+{\beta }_1{g}_{it}+{\beta }_{2i}{\displaystyle \frac{{\gamma }_{it}}{N_{it}}}+{ϵ}_{it}$$

(11)

one should obtain ${\beta }_0=0$ and ${\beta }_1=1$ in all of these regressions, with the fit improving the closer the regression assumptions correspond to the theoretical model.

Both model versions used, respectively, in the studies in [18,19] give testable implications, provided one is willing to accept a shorter time horizon than theory requires. However, when actually running these regressions, neither Ferreira and Vincent [18] nor Ferreira, Hamilton and Vincent [19] found the predicted values for ${\beta }_0$ or ${\beta }_1$. It is, therefore, of interest to examine whether the subsequent improvements in the data set have led to results that are more in line with theory. Hence, these regressions are re-estimated here using more recent data.

Ferreira and Vincent [18] used the median of the lending and deposit interest rates to calculate a uniform discount rate of 3.5% for all countries. If one adopted the same approach and used the updated data instead, that rate would then be 2.7%. Ferreira, Hamilton and Vincent [19] also followed that approach, but they used country-specific discount rates while estimating the models. In the current study, the discount rates used in Ferreira and Vincent [18] and in Ferreira et al. [19], respectively, were employed to maintain comparability with the latter study’s results.

In Ferreira, Hamilton and Vincent [19], the labour force is used as a proxy of population, whereas Ferreira and Vincent [18] used the total population. The GS indicator used in estimating models (8)–(11) is defined as $GS=GrNI+\gamma w$, i.e., population-adjusted savings. In estimates of Equation (7), however, GS is calculated as in Equation (1).

Since CGI, CNI, GrNI, and GS are measures of savings which are determined at the same time as consumption, they were tested for endogeneity. In line with Ferreira and Vincent [18] and Ferreira, Hamilton and Vincent [19], the results showed that the p-values of both Wu–Hausman F-statistic and the Durbin χ² statistic were insignificant. The null hypothesis that CGI, CNI, GrNI, and GS were exogenous was rejected, therefore, and they were treated as endogenous.

In the replication of Ferreira and Vincent [18], the endogeneity issue was addressed by using lagged savings (CGI, CNI, GrNI, and GS, respectively) and the lagged proportion of the working-age population as instruments. The instrument set used to replicate Ferreira, Hamilton and Vincent [19] included lagged values of green savings, produced capital, the percentage of the population of working age, the population growth rate, and the time trend. Time dummy variables were employed to control for other unobserved factors. The first-stage regression statistics, which showed small and insignificant partial R² as well as F-statistics that were much larger than any of the critical values, validated the current study’s instruments. The results of overidentifying tests showed that the models had been correctly specified.

4. Data

A constraint in replicating both studies was that the names of the countries included in their sample was not disclosed. This constraint was overcome for the replications, as explained below.

Ferreira and Vincent [18] estimated Equation (7) using data from the World Bank’s WDI database, updated until 2001, covering 136 countries. Where T was equal to 10 years, their sample constituted only 93 countries; 43 were excluded because the database did not contain complete data for all needed variables to estimate the models. Out of these 93 countries, 22 were members of the Organisation for Economic Co-operation and Development (OECD) and 71 were not. Where T was equal to 20 years, their sample constituted only 83 countries.

For the current study, the relevant data set from the WDI database, as updated on 26 October 2023, was uploaded. The data set contains information on 217 countries. Countries that had complete data series for the period 1970–2001 were selected from this set to constitute the final sample of 93—the same number as in the Ferreira and Vincent [18] sample. Of these 93 countries, 22 were OECD members before 2001, also matching the number in the Ferreira and Vincent [18] sample. Thus, regression (7) estimated by Ferreira and Vincent [18] was replicated using data from the same countries and from the same period as their study, but employing the updated data. This entails that any differences between the current study’s results and those generated by Ferreira and Vincent [18] (

Table 1. Replication of Ferreira and Vincent (2005) [18].

Variable	Per Ferreira and Vincent (2005) [18]						Replication of Ferreira and Vincent (2005) [18], with Same Sample of Countries and Same Time Span But with Updated Data						Replication of Ferreira and Vincent (2005) [18] with Updated Data, More Countries and Longer Time Spans
Estimate number	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
Countries	93 world-wide	93 world-wide	93 world-wide	83 world-wide	22 OECD §	71 non-OECD	93 world-wide	93 world-wide	93 world-wide	83 world-wide	22 OECD	71 non-OECD	141 world-wide	141 world-wide	141 world-wide	141 world-wide	37 OECD	104 non-OECD
Country fixed effects (Yes/No)	No	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	Yes	Yes	Yes
Time horizon (T)	10 years	10 years	10 years	20 years	10 years	10 years	10 years	10 years	10 years	20 years	10 years	10 years	10 years	10 years	10 years	20 years	10 years	10 years
Discount rate	3.5%	3.5%	Country-specific	3.5%	3.5%	3.5%	3.5%	3.5%	Country-specific	3.5%	3.5%	3.5%	3.5%	3.5%	Country-specific	3.5%	3.5%	3.5%
Time period	Former 1970–2001	Former 1970–2001	Former 1970–2001	Former 1970–2001	Former 1970– 2001	Former 1970–2001	Updated 1970– 2001	Updated 1970–2001	Updated 1970–2001	Updated 1970–2001	Updated 1970–2001	Updated 1970–2001	Updated 1970–2022	Updated 1970–2022	Updated 1970–2022	Updated 1970–2022	Updated 1970–2022	Updated 1970– 2022
Estimated equation	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)	(7)
Savings measure:
Gross	0.263 ***	−0.002	−0.004	0.095	−0.274 ***	0.169 ***	−0.036 ***	−0.039 ***	−0.037 ***	−0.039 ***	−0.040 ***	0.089 ***	−0.047 ***	−0.081 ***	−0.045 ***	0.163 ***	−0.036	0.111 ***
	(0.007)	(0.025)	(0.025)	(0.064)	(0.067)	(0.018)	(0.011)	(0.013)	(0.014)	(0.018)	(0.015)	(0.022)	(0.012)	(0.011)	(0.012)	(0.013)	(0.163)	(0.013)
Net	0.551 ***	0.128 ***	−0.132 ***	0.214 ***	−0.001	0.282 ***	−0.094 ***	−0.102 ***	−0.095 ***	−0.102 ***	−0.002	0.201 ***	−0.112 ***	−0.188 ***	−0.111 ***	0.285 ***	−0.093	0.419 ***
	(0.015)	(0.035)	(0.036)	(0.068)	(0.078)	(0.027)	(0.012)	(0.020)	(0.033)	(0.043)	(0.321)	(0.041)	(0.037)	(0.016)	(0.015)	(0.024)	(0.148)	(0.127)
Green net	0.534 ***	0.129 ***	0.133 ***	0.250 ***	−0.029	0.349 ***	0.098 ***	0.105 ***	0.098 ***	0.206 ***	−0.016	0.374 ***	0.071 ***	0.083 ***	0.076 ***	0.389 ***	0.096	0.619 ***
	(0.016)	(0.034)	(0.035)	(0.055)	(0.073)	(0.028)	(0.018)	(0.028)	(0.044)	(0.019)	(0.874)	(0.093)	(0.012)	(0.013)	(0.034)	(0.095)	(0.815)	(0.205)
Genuine	0.416 ***	0.037	0.038	0.215 ***	−0.274 ***	0.322 ***	0.232 ***	0.250 ***	0.235 ***	0.353 ***	−0.253 ***	0.443 ***	0.113 ***	0.133 ***	0.140 ***	0.762 *	0.225	0.821 ***
	(0.011)	(0.034)	(0.034)	(0.065)	(0.078)	(0.026)	(0.015)	(0.041)	(0.075)	(0.089)	(0.126)	(0.088)	(0.017)	(0.018)	(0.029)	(0.079)	(0.724)	(0.341)

Note: Robust standard errors corrected for serial correlation are given in brackets. * Estimate is significantly different from 0 at the 10% level. *** Estimate is significantly different from 0 at the 1% level. ^§ Organisation for Economic Co-operation and Development.

in each case) should be due to changes in the data after the data sets were updated by the World Bank.

In the Ferreira, Hamilton and Vincent [19] study, they estimated Equations (7)–(11) using data from 64 developing countries from the WDI, updated until 2003, with a data range of 1970–2002. They assumed a time horizon (T) equal to only 20 years. In the current study’s replication, the 64 developing countries that matched the Ferreira, Hamilton and Vincent [19] sample were selected. Again, any differences between the current study’s results in estimating models (7) to (11) and those generated by Ferreira, Hamilton and Vincent [19] (

Table 2. Replication of Ferreira et al. (2008) [19].

Variable	Ferreira et al. (2008) [19]					Replication of Ferreira et al. (2008) [19] with Same Sample of Countries and Same Time Span But with Updated Data					Replication of Ferreira et al. (2008) [19] with Updated Data, More Countries and Longer Time Spans
Estimate Number	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Countries	64 non-OECD	64 non-OECD	64 non-OECD	64 non-OECD	64 non-OECD	64 non-OECD	64 non-OECD	64 non-OECD	64 non-OECD	64 non-OECD	104 non-OECD	104 non-OECD	104 non-OECD	104 non-OECD	104 non-OECD
Country fixed effects (Yes/No)	Yes	Yes	Yes	No	No	Yes	Yes	Yes	No	No	Yes	Yes	Yes	No	No
Time period	Former 1970–2002	Former 1970–2002	Former 1970–2002	Former 1970–2002	Former 1970– 2002	Updated 1970– 2002	Updated 1970–2002	Updated 1970–2002	Updated 1970–2002	Updated 1970–2002	Updated 1970–2022	Updated 1970–2022	Updated 1970–2022	Updated 1970–2022	Updated 1970–2022
Estimated equation	(7)	(8)	(9)	(10)	(11)	(7)	(8)	(9)	(10)	(11)	(7)	(8)	(9)	(10)	(11)
Savings measure:
Gross	−0.597 **	−0.642 *	−0.764 *	−0.084	−0.106	−0.139 ***	−0.236 ***	−0.389 ***	−0.031 ***	−0.0137 ***	−0.046 ***	−0.078 *	−0.081 ***	−0.008 ***	−0.010 *
	(0.268)	(0.365)	(0.415)	(0.255)	(0.258)	(0.035)	(0.045)	(0.096)	(0.015)	(0.017)	(0.022)	(0.013)	(0.029)	(0.002)	(0.002)
Net	−0.533 **	−0.610 *	−0.729 *	−0.200	−0.234	−0.102 ***	−0.092 ***	−0.100 ***	−0.080 ***	−0.095 ***	−0.050* **	−0.081 ***	−0.075 ***	−0.011 ***	−0.012 ***
	(0.274)	(0.364)	(0.412)	(0.316)	(0.324)	(0.022)	(0.011)	(0.036)	(0.021)	(0.021)	(0.011)	(0.027)	(0.018)	(0.004)	(0.007)
Green net	0.801 **	0.425 **	0.558 **	0.405 **	0.504 **	0.606 ***	0.395 ***	0.103 ***	0.283 ***	0.198 ***	0.278 ***	0.181 ***	0.279 *	0.148 ***	0.250 ***
	(0.362)	(0.203)	(0.274)	(0.178)	(0.197)	(0.202)	(0.097)	(0.025)	(0.071)	(0.098)	(0.089)	(0.088)	(0.069)	(0.073)	(0.083)
Genuine	0.788 ***	0.413 **	0.560 **	0.392 **	0.496 ***	0.553 ***	0.425 **	0.243 *	0.294 ***	0.335 ***	0.137 ***	0.299 *	0.188 ***	0.253 ***	0.462 ***
	(0.287)	(0.163)	(0.213)	(0.165)	(0.182)	(0.094)	(0.281)	(0.121)	(0.048)	(0.167)	(0.071)	(0.103)	(0.075)	(0.052)	(0.051)

Note: Robust standard errors corrected for serial correlation are given in brackets. * Estimate is significantly different from 0 at the 10% level. ** Estimate is significantly different from 0 at the 5% level. *** Estimate is significantly different from 0 at the 1% level.

in each case) should also only be due to changes in the data after their World Bank updates.

The replication of Ferreira, Hamilton and Vincent [19] focused on developing countries and on estimation procedures that not only accounted for changes in population growth rates, but that also adopted the present value of future consumption changes instead of the difference between average future consumption and current consumption as dependent variables. Moreover, the current study used country-specific interest rates as discount rates. It also employed a generalised two-stage least squares (2SLS) regression analysis method, which allows for full information estimations of a system of simultaneous equations but with an error component structure, as proposed by Balestra and Varadharajan-Krishnakumar [44] to reduce possible estimate bias.

After the pure replications of the Ferreira and Vincent [18] and Ferreira, Hamilton and Vincent [19] studies, the same models were estimated in a complementary way, using only data from sub-Saharan African countries.

5. Results

Regressions (7)–(11) from the previous studies were re-estimated and ${\beta }_1$ estimates (Table 1, Table 2 and

Table 3. Replication of Ferreira and Vincent (2005) [18] and Ferreira et al. (2008) [19] for sub-Saharan Africa.

Variable	Replication of Ferreira & Vincent (2005) [18]					Replication of Ferreira et al. (2008) [19]
Estimate Number	1	2	3	4	5	6	7	8	9	10
Country fixed effects (Yes/No)	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No
Time horizon (T)	10 years	10 years	10 years	20 years	10 years	20 years	20 years	20 years	20 years	20 years
Discount rate	3.5%	3.5%	Country-specific	3.5%	3.5%	Country-specific	Country-specific	Country-specific	Country-specific	Country-specific
Time period	Updated 1970–2022	Updated1970–2022	Updated 1970–2022	Updated1970–2022	Updated1970–2022	Updated1970–2022	Updated1970–2022	Updated1970–2022	Updated1970–2022	Updated1970–2022
Estimated equation	(7)	(7)	(7)	(7)	(7)	(7)	(8)	(9)	(10)	(11)
Savings measure:
Gross	−0.046 ***	−0.078 ***	−0.080 ***	−0.008 ***	−0.019 ***	−0.083 ***	−0.084 ***	−0.007 ***	−0.007 ***	−0.048
	(0.023)	(0.013)	(0.016)	(0.002)	(0.008)	(0.041)	(0.009)	(0.003)	(0.002)	(0.024)
Net	−0.050 ***	−0.081 ***	−0.075 ***	−0.011 ***	−0.010 ***	−0.057 **	−0.055 ***	−0.012 ***	−0.032 ***	−0.036 ***
	(0.011)	(0.018)	(0.031)	(0.006)	(0.005)	(0.012)	(0.027)	(0.006)	(0.016)	(0.017)
Green net	0.078 ***	0.081 ***	0.079 ***	0.548 ***	0.150 ***	0.376 ***	0.375 ***	0.446 ***	0.647 ***	0.771 ***
	(0.026)	(0.041)	(0.039)	(0.274)	(0.054)	(0.185)	(0.187)	(0.223)	(0.308)	(0.327)
Genuine	0.137 ***	0.199 ***	0.168 ***	0.753 ***	0.262 ***	0.482 ***	0.680 ***	0.550 ***	0.751 ***	0.794
	(0.047)	(0.091)	(0.011)	(0.371)	(0.125)	(0.230)	(0.295)	(2.683)	(0.366)	(0.397)

Note: Robust standard errors corrected for serial correlation are given in brackets. ** Estimate is significantly different from 0 at the 5% level. *** Estimate is significantly different from 0 at the 1% level.

) were reported. Thus, ${\beta }_1$ was estimated and reported for the four versions of savings indicators (CGI, CNI, GrNI and GS) derived in Equation (1).

Columns 7 to 18 in Table 1 contain the range of the current study’s estimates. For comparison purposes, the estimates in columns 1 to 6 are from Ferreira and Vincent [18]. The estimates in columns 7 and 13 are directly comparable with estimates in column 1, while the estimates in columns 8 and 14 are comparable with estimates in column 2, and so on. In estimates 13 to 18, updated data were used. Moreover, the time range was updated to consider all data available until 2021, while the data set itself covers 141 countries.

For the estimates reported in Table 1, the current study followed strictly the same estimation procedures as Ferreira and Vincent [18]. This included checking for stationarity for all time series by examining the autocorrelograms instead of formal testing, due to the shortage of observations in our sample. As is evident from Table 1, the results of the current study are largely similar to the results reported in Ferreira and Vincent [18]. Repeating the analysis for the same countries and the same time spans, but with revised data (columns 7–12 in Table 1), there is very little change compared to the original analysis (columns 1–6 in the same table). For the more limited savings measures, the fit with theory is, in most cases, even worse with the newer data than with the older data. With the most comprehensive savings measure, genuine savings, the fit does become better with the newer data, at least with the longer 20-year period of analysis, but remains far from the fit predicted by theory. Comparing OECD and non-OECD countries, the fit with theory is even worse for OECD countries, suggesting either that technological progress is more important there (in line with [18]) or that consumption is more saturated there.

Exploiting the additions to the dataset and bringing more countries and longer time spans into the analysis could, in principle, affect the outcome either way. The new countries added to the dataset presumably were excluded before because their economic statistics are worse than those in the original countries originally in the dataset, which should worsen the fit with theory further. On the other hand, the longer time spans in the updated dataset should improve the fit. Looking at the empirical results (columns 13–18 in Table 1), the outcomes are, indeed, mixed. The fit with theory is, in most cases, comparable to or worse than the results for the smaller data set. However, it deserves to be mentioned that when the analysis is restricted to non-OECD countries (column 18), the fit with theory improves, and for the most comprehensive genuine savings measure, we can in fact not reject the theoretical prediction that the coefficient is 1.

Table 2 displays the results of the estimation for developing countries, replicating the Ferreira, Hamilton and Vincent [19] study. Again, the current study’s estimates range from columns 6 to 15, with estimates in columns 1–5 being from Ferreira, Hamilton and Vincent [19] shown for comparison. Estimates 6 and 11 are directly comparable to estimate 1, while estimates 7 and 12 are comparable to estimate 2, and so on. Looking at these estimates, the picture is mixed. For the less comprehensive savings measures (conventional gross savings and net savings), the fit with theory improves somewhat with the better data and with the addition of more countries and longer time spans in the data set, but all the estimated coefficients are far from the value predicted by theory. However, for the more comprehensive savings measures (green net savings and genuine savings), the fit with theory is in almost all cases even worse than in the original study. Adding better data does not improve the fit with theory for any of the estimates for the original set of countries (columns 6–10 in Table 2), and bringing more countries and longer time spans into the analysis (columns 11–15) makes the fit even worse in almost all cases.

The general picture of the results in Table 1 and Table 2 is that the data of the World Bank’s GS framework still fail to predict the difference between average future consumption and current consumption accurately, as theoretically proposed. As the adjustment of savings indicators is extended from CGI to GS, the quality of the fit improves; however, as in the previous studies, the fit remains poor.

Table 3 presents the estimates for sub-Saharan African countries only. These estimates use all data available until 2022, which was the most recent data period recorded. Comparing the results for the regressions from Ferreira and Vincent [18] (i.e., comparing the results in columns 1–5 in Table 3 with those in Table 1), the fit with theory is in most cases even worse for sub-Saharan Africa than it is for the full sample or for the full developing country sample. The fit does become better, however, for the most comprehensive genuine savings measure and the longer twenty-year period of analysis (column 4), the only one of these estimates where the theoretical prediction cannot be rejected.

Comparing the results for the regressions from Ferreira et al. [19] (i.e., comparing the results in columns 6–10 in Table 3 with those in Table 2), for the less comprehensive savings measures, the fit with theory is just as poor as for the full developing country sample, but for the more comprehensive savings measures, the fit with theory is better than for the full sample. For several of the estimates using the full genuine savings measure, the theoretical prediction cannot be rejected.

The general picture of the results in Table 3 is, nonetheless, that the data of the World Bank’s GS framework do not accurately predict the difference between average future and average current consumption, nor do the data accurately predict the present value of changes in future consumption, as expected by the theory. However, as the adjustment of savings indicators is extended from CGI to GS, the quality of fit does improve considerably.

6. Discussion

The classic earlier studies showed that the World Bank data of the time did not provide results in line with theory; countries’ levels of GS were not good predictors of future consumption. At the time, the main explanation suggested for this was that the World Bank data were not comprehensive enough and did not capture the full picture. Another explanation that was suggested was that poor investment decisions might mean that, even when there was investment, it did not lead to the future income streams for the country that were theoretically predicted—whether due to capital flight, poor public investment decisions, or other reasons.

Revisiting and replicating these results almost 20 years later, it is notable how little has changed. Running the same regressions on the supposedly more accurate data that are available now produced no real difference in the results. Thus, countries’ levels of investment are still not good predictions of their future consumption levels. Poor data and poor investment decisions may both still be plausible explanations for this outcome. However, despite the current data being better than that of 2005 or 2008, it yielded little change in the results.

Economic theory predicts that the change in a country’s capital stocks should determine changes in its future consumption. As in the previous studies, our results in general showed a positive and significant correlation between savings and future consumption, with estimated coefficients that have greater magnitudes when the savings measures are extended to include broader capital measures. One noteworthy finding is, however, that the fit with theory is generally better for poorer countries than for the richer countries. In particular, for sub-Saharan Africa and for the most comprehensive savings measures, the fit with theory is relatively good. This result should not be overstated, as countries in sub-Saharan Africa generally have quite poor economic statistics, but it does suggest that more research in this area could be fruitful.

The worse fit with theory in richer countries could be due to, e.g., technical progress being a more important factor for consumption growth in richer countries, or a less clear-cut link between increased production and increased material consumption in the richer countries. Most of the studies that seek to combine estimates of genuine savings with estimates of technological progress have been conducted in richer countries, so it could be worthwhile to carry out similar studies in poorer countries to see if the results are different. It could also be the case that the link between increased economic capacity and increased material consumption is weaker in richer countries than in poorer countries because a greater share of the increased economic capacity is used for other purposes. This suggests that using more comprehensive welfare measures than material consumption in future GS studies could be fruitful. Both possibilities deserve further investigation.

Investment does, thus, seem to lead to higher future consumption, but not to the extent that the theory predicts. However, if—as our results suggest—the fit with theory is indeed better for poorer countries than for richer countries, using the results from GS theory as a guide for national investment decisions can still be useful for developing countries. A remaining challenge in these countries is then to ensure that the economic statistics are good enough to permit this.