Savings and Sustainable Economic Growth Nexus: A South African Perspective

Abstract

The savings behavior of individuals has been a topic of both macroeconomic and policy importance throughout history. Theoretical and empirical research shows that savings result from several demographic and economic factors working together to produce long-term, sustainable economic growth. This study therefore examined the nexus between domestic savings and sustainable economic growth in a South African perspective between 1970 and 2022, emphasizing the critical role that savings play in fostering long-term economic stability and environmental resilience. The ARDL framework was used to analyze data from the World Bank and the South African Reserve Bank. The results of the study demonstrate that corporate savings have a major effect on sustainable economic growth, especially over the long term. When corporate savings rise by 1%, the economy expands by 3.12%, which highlights the significant multiplier effect of investment. The extent of this impact depends on factors such as the efficiency of capital allocation, technological capacity, financial market development, government policies, and macroeconomic stability. These factors collectively determine how effectively corporate savings are transformed into productive investments that drive sustainable economic growth. Conversely, savings made by the government and the public, especially in the long run, have no appreciable impact on sustainable economic growth. Given that domestic savings mobilization is the most suitable channel for financing capital accumulation to support economic growth and development, the study suggests reviewing current policies to encourage domestic savings mobilization. This paper contributes to the broader discourse on sustainable economic policies in emerging markets, offering actionable insights for policymakers, financial institutions, and stakeholders promoting a more sustainable economic future for South Africa.

1. Introduction

In an era where sustainable development is paramount, the relationship between savings and economic growth has garnered increasing attention, particularly in the context of emerging economies [1,2]. Savings—whether from households, corporations, or the government—serve as a vital mechanism for capital formation, enabling investments that drive long-term economic stability and growth [3]. South Africa, with its unique socio-economic landscape, faces significant challenges such as high unemployment, stark inequalities, and environmental degradation. These challenges necessitate a comprehensive understanding of how financial behaviors, specifically savings, can drive sustainable economic growth. This is supported by the Harrod–Domer model, which postulates that savings are essential for sustainable economic growth and that a country’s economy will suffer if it relies primarily on foreign resources to finance investments, making it more vulnerable to external shocks [4]. Thus, to ensure long-term sustainable economic growth, this is a significant issue that requires careful understanding and attention.

Despite the recognized importance of savings in the literature, the nexus between savings and sustainable economic growth remains underexplored, particularly in the South African context. With one of the largest economies in Africa, South Africa has recently come under scrutiny for its poor rates of sustainable economic growth and low savings culture. The nation’s overall savings have reached a record low over the last ten years. The average gross domestic savings rate between 1995 and 2007 was only 15%, down from over 25% during the 1970s and late 1980s, when compared to comparable level nations like Malaysia, which averages between 25 and 43% [5,6], Kapingura. The low domestic savings rate of the nation is preventing faster economic growth, which is very important in mobilizing savings to create effective capital for sustainable economic growth. This relates to the notion that to finance sufficient investments for sustainable economic growth, any economy must either generate enough savings or borrow from sources outside its borders. However, borrowing from abroad is not always the greatest solution because it exposes nations to additional risks, such as volatility in foreign exchange rates and unfavorable repercussions on their balance of payments [4]. However, South Africa’s gross domestic savings rates have been steadily declining since the end of the apartheid era and the nation’s economic isolation from the rest of the globe. During this time, the country has borrowed more money to finance its investment projects and has also seen a rise in foreign direct investment. Domestic savings are no longer the main source of funding as a result. Government, corporate, and household savings constitute the three components of total domestic savings. These three categories require more attention to raise savings levels and create the best possible policy responses for domestic savings in South Africa. Therefore, the central question for this study is: do household, corporate, and government savings influence sustainable economic growth in South Africa?

The extant literature is characterized by studies conducted in Asia and Latin America with little to no reporting from countries in Sub-Saharan Africa [7]. These studies have often focused on either the macroeconomic implications of savings or the microeconomic behaviors of individual savers, leaving a gap in understanding how these dimensions interact within the framework of sustainable growth. Additionally, findings from various studies have presented inconsistencies regarding the effectiveness of savings in promoting sustainable development, with some researchers emphasizing the need for targeted policy interventions while others highlight the role of broader economic factors. Studies such as [8,9], for example, have ignored the differences in the institutional and economic features of the developed and developing economies in favor of cross-sectional panel data from both economies. In addition, some of these studies’ other characteristics include their brief time span and improper use of econometric techniques. Prior research on savings and growth has primarily concentrated on gross domestic savings, or one kind of savings. For instance, refs. [10,11] focused on household savings, whereas [12,13] concentrated on savings by households. This study attempts to fill the gap and decompose domestic savings into household savings, corporate savings, and government savings. This is followed by examining the multi-faceted relationship between household, corporate, and government savings and sustainable economic growth in South Africa. Differentiating between household, corporate, and government savings could provide a more nuanced comprehension of each type of savings effect on sustainable economic growth. As a result, three hypotheses are postulated: household savings have no influences on South African sustainable economic growth; corporate savings have no influence on South African sustainable economic growth; and government savings have no influence on South African sustainable economic growth.

By utilizing an ARDL framework, this research seeks to provide a comprehensive understanding of how different types of savings can collectively contribute to a more sustainable economic future, in the short and long run. The study also uses data for a longer period from 1970 to 2022 and conducts a robustness check using the CUSUM of Squares. The primary objective of this study is to clarify the ambiguities in the existing literature and propose actionable strategies for enhancing savings behavior across various sectors. By doing so, this research not only aims to fill the gaps identified in previous studies but also to contribute to the broader discourse on sustainable economic policies. Ultimately, this study aspires to inform policymakers, financial institutions, and stakeholders about the critical role that savings can play in fostering a resilient and sustainable economy in South Africa.

2. Literature

2.1. Theories on Savings and Sustainable Economic Growth

Most growth theories suggest that higher savings rates hasten capital accumulation and economic expansion. Economic theorists such as Ricardo and Robert Torrens were influenced by the Corn Model (Equation (1)), which is the source of the original theory surrounding the laws of capital accumulation and sustainable economic growth. These economists conjectured that all economic surpluses in a free-market economy would be invested or saved, and that the surplus rate would provide both the rate of profit and the overall rate of economic growth.

$$SR={\displaystyle \frac{Surplus}{Necessary Input}} \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} SR \mathrm{i}\mathrm{s} \mathrm{s}\mathrm{u}\mathrm{r}\mathrm{p}\mathrm{l}\mathrm{u}\mathrm{s} \mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}$$

(1)

However, the foundations of the theory underlying the correlation between savings and economic growth may be found in the early growth models of [14,15], which considered capital as the output-limiting element rather than labor. The Harrod–Domar model states that surplus capital $\left(∆SC\right)$ is the source of a continuous, proportionate rise in output $\left(∆Y\right)$. The incremental capital output ratio, or $INCOR$, is this; a high $INCOR$ indicates less productive technology: $INCOR=k={\displaystyle \frac{∆C}{∆O}}$. The savings function, $S$, is expressed as the product of the rate of saving $\left(s\right)$ and output (i.e., $S=sY$), and the investment function, $I$, is equivalent to $I=∆C=S$. The aggregate productive function is represented by $\left(∆Y\right)$, which is equal to $1/C ∆C$. According to the model, the economy’s growth rate $\left(Y\right)$ will rise in tandem with the savings rate (s) and fall in tandem with $INCOR\left(k\right)$.

$$Y=∆Y/Y=1/k ∆C/Y=1/k S/Y={\displaystyle \frac{s}{k}}$$

(2)

The Harrod–Domar model’s inability to account for labor substitutions, declining returns on capital, or technological advancements is one of its drawbacks. Neo-classical economist Robert Solow’s [16] well-known growth model, which aims to address some of the shortcomings of the Harrod–Domar model, allows for the substitution of labor for capital and decreases marginal returns to capital. Ultimately, Solow concludes that growth eventually slows down, but economies with higher savings rates have higher steady incomes. Here is how the model is defined: $TY=Tf (C, L)$ is the economy’s aggregate production, where $T$ is the TPF. $TY=Tf (C, L)$ is another way to express the production function because f has continuous proceeds to gauge. The condensed form of the model yields the output $\left(Y\right)$ economic growth rate as follows:

$$Y={\displaystyle \frac{∆Y}{Y}}={\displaystyle \frac{∆T}{T}}+\omega \kappa {\displaystyle \frac{\Delta C}{C}}+\omega \iota {\displaystyle \frac{\Delta L}{L}}$$

(3)

where $r$ is the capital price and $\omega \kappa \Delta C/Y$ = Share of capital in total cost. The rate of technical change is expressed as $∆T/T$ or TFP growth, and the labor stake in total cost is expressed as $\omega \iota \omega L/O$ and $\omega$ = price of labor. Conversely, factor deepening is represented by =$/L$ and the rate of factor accumulation by = $\Delta C/C$. The rate of technical change, or ∆T/T, is the unsolved residue of economic growth. This can be calculated as follows:

$$\Delta T/T=\Delta Y/Y-\omega \kappa \Delta C/C-\omega \iota \Delta L/L$$

(4)

Conversely, authors like Adam Smith pursued to find the origins of the motivation by people to accumulate capital. Ref. [17] noted that in Adam Smith’s view, the growth process was endogenous. He highlighted the importance of capital accumulation on labor productivity. A distinctive view of the classical methodology was that production involves labor and that capital accumulation propels this process forward and, in the process, creates new markets, expands existing markets, while it increases demand and supply, to ultimately result in sustainable economic growth and social development of nations. Consequently, a deeper comprehension of the relationship between domestic saving and sustainable economic growth is required, given the significance of domestic saving relative to investment.

The Harrod–Domar growth model, which asserts that investment productivity and savings levels determine economic growth, serves as the theoretical basis for this investigation. It makes the case that increased savings stimulate investment and growth. The model can be used to evaluate the effects of differences in savings on South Africa’s economic performance because it establishes a direct relationship between savings rates and economic development. Using this theory, this research takes into account a number of macroeconomic, microeconomic, and institutional issues to provide a thorough explanation of the intricate relationship between savings and sustainable economic growth in South Africa.

2.2. Empirical Review

Numerous empirical studies have been conducted on the relationship between domestic savings and sustainable economic growth in both developed and developing [3,6,18,19]. For instance, refs. [20,21] conducted independent research to investigate how different categories of domestic savings support South Africa’s economic growth. For instance, ref. [20] employed a co-integration study inside a multivariate framework to determine the impact of household, business, and government savings on South Africa’s economic growth. Ref. [20] asserts that it is critical to comprehend the contributions made by the various forms of domestic savings to economic growth. Using the Auto Regressive Distributed Lag (ARDL) method of co-integration, the study assessed the short- and long-term impacts of the various types of domestic savings on economic growth. The results demonstrate that business savings have a significant short- and long-term impact on economic growth, while household and government savings have no appreciable long-term effects. Additional research has been spurred by the findings of [20,22], which highlight the critical need for measures that can boost domestic savings rates and aid in the creation of successful public policies.

Ref. [3] studied the link between domestic savings and economic growth for the BRICS countries. The panel ARDL model has been used to study the short- and long-term links between savings and economic growth. The study’s conclusions show that, both in the short and long term, gross domestic savings are a key factor in determining economic growth. Additionally, the outcomes of the two causality tests provide credence to the hypothesis that there is a bidirectional causal relationship between savings and economic growth among the BRICS nations. The short and long term impacts of domestic saving on Algeria’s economic growth from 1980 to 2018 were also investigated by [18] using ARDL. The results demonstrate the significant short- and long-term effects of saving on economic growth in Algeria, where saving rates are high and positively connected with economic growth. Ref. [18] examined the causal relationship between savings and economic growth in Bosnia and Herzegovina, particularly in direction and strength, using Granger’s causality test and the Toda-Yamamoto procedure. The findings of Granger’s causality test demonstrated that there is no causal connection between the components of economic growth and private savings.

Ref. [19] examined the connection between economic development and savings in Kosovo between 2010 and 2017. Regression study results showed that deposits greatly contribute to Kosovo’s economic growth, as savings stimulate output, employment, and investment, all of which result in longer-term economic growth. High national savings rates also show that a country is less dependent on foreign direct investment, which lowers the risk that comes with unstable foreign direct investment. Ref. [23] examined the short and long term effects of domestic savings on Vietnam’s economic growth between 1986 and 2015 using the ARDL bound testing approach while accounting for the dependency ratio and domestic investment. The short-run calculations show that domestic savings, investment, and the dependency ratio have little effect on economic growth. Long-term estimates indicate that domestic savings and investment are the main drivers of Vietnam’s economic growth, with the dependency ratio hurting growth.

The studies on the relationship between income inequality and savings have reported mixed results. For instance, ref. [24] examined the relationship between income inequality and savings using 2181 rural households between 2008 and 2014 in twelve provinces of Vietnam. Using instrumental variable GMM, the result indicates that income inequality positively impacts on households’ savings. Ref. [25] investigated whether income inequality is positively related to aggregate saving ratio by estimating a fixed-effect model based on a panel data of 48 countries for the period 1991–2010. They found evidence that aggregate saving ratio increases with income inequality using various inequality measures. Ref. [26] examined the relationship between income distribution and aggregate saving based on a new and improved income distribution database for both industrial and developing countries. The empirical results, using alternative inequality and saving measures and various econometric specifications on both cross-section and panel data, provide no support for the notion that income inequality has any systematic effect on aggregate saving. Ref. [27] conducted a study in China to explore the possible linkage between rising saving rates and rising income inequality. Using median regression analysis, their study found out that the higher the income inequality, the greater the marginal effect of income inequality on aggregate saving rates.

Although some empirical studies have been conducted in different countries, there is still scarce literature specifically to South Africa, which begs for more investigation. Furthermore, this study decomposed savings into household savings, corporate savings and government savings. In addition, sustainable economic growth has also decomposed into GDP growth, income inequality and Environmental Performance Index (proxied by adjusted emissions growth rate for carbon dioxide). Mixed results on the study topic under consideration calls for further investigation. Therefore, this study examined savings and sustainable economic growth nexus in South Africa.

2.3. Objectives of the Study

• To analyze the effect of GDP growth rate and savings behavior in South Africa.
• To assess the impact of income inequality on savings patterns in South Africa.
• To investigate the influence of the Environmental Performance Index on savings decisions in South Africa.

2.4. Hypotheses of the Study

• There is a negative effect between the GDP growth rate and savings levels in South Africa.
• Higher levels of income inequality negatively affect savings patterns in South Africa.
• An improved Environmental Performance Index negatively influences savings behaviour in South Africa.

3. Methodology

3.1. Data Source

The World Bank’s World Development Indicators (WDI), South African Reserve Bank (SARB) and the Yale University provided the data for this study, which covered the years 1990 to 2023. The data obtained from WDI include GDP growth rate, household savings (represented as gross savings); corporate savings (represented as Gross Fixed Capital Formation); government savings (difference between government revenues and expenditures); real interest rate; and inflation. Income equality (represented by GINI index) data was obtained from SARB while Environment Performance Index (represented by adjusted emissions growth rate for carbon dioxide) was obtained from Yale University database. The use of data from different sources has limitations and potential biases, which this study acknowledges. Despite the World Bank’s efforts to advance standardization, differences in national reporting and data collection procedures, for example, may reduce the comparability of data from other countries. To overcome these limits and biases, create consistency, and ensure that the study can provide a more credible and reliable assessment to answer the study’s purpose, validation of the study data with data from the IMF and OECD was carried out.

This study acknowledges that there are other variables like education levels, technological progress, international trade, capital flows monetary and fiscal policy, and economic diversification among others that affect sustainable economic growth. However, the exclusion of these factors in this study was due to several reasons. First, the aim was to provide a focused analysis of the relationship between savings and sustainable economic growth, intentionally narrowing its scope to avoid complexity. Including multiple factors could complicate the analysis and interpretation of results. As a result, adopting a simple model in this study with savings as an independent variable allowed for a deeper examination of the core nexus without the confounding effects of other variables. Secondly, the primary objective of the study was to explore the direct relationship between savings and growth, potentially considering how savings influence sustainable economic growth in a more isolated manner. Lastly, focusing solely on savings could yield clear policy implications for encouraging savings to enhance sustainable economic growth. By excluding other variables, the research aims to provide targeted recommendations for policymakers.

3.2. Description of Study Variables

The savings rate, investment in renewable energy, employment rates, income inequality (Gini coefficient), environmental indicators, human development index (HDI), access to education, health outcomes, R&D spending, infrastructure quality, sustainable agriculture practices, social capital, and fiscal sustainability are some of the key indicators of sustainable economic growth (see

Table 1. Descriptions of Study Variables.

Variable	Symbol	Variable Description	Data Source
Dependent variables
Gross Domestic Product growth	${GDP}_{t }$	Rate of change of Gross Domestic Product growth	WDI of the World Bank
Income equality	${GINI}_{t }$	Income equality refers to the extent to which income is distributed evenly among a population.	SARB
Environmental Performance Index	${EPI}_{t }$	EPI taken as adjusted emissions growth rate for carbon dioxide	Yale University
Independent variables
Household savings	${HHS}_{t }$	The portion of income that families save rather than spend on consumption	WDI of the World Bank
Government savings	${GS}_{t }$	Retained taxes and public enterprise profits, plus any receipts	WDI of the World Bank
Corporate savings	${CS}_{t }$	COS = Total of the gross operating surpluses of businesses − [interest $+$ net dividends $+$ royalties $+$ rent]	WDI of the World Bank
Control variables
Real interest rate	${RIR}_{t }$	The real interest rate is the rate of interest that has been adjusted for inflation.	WDI of the World Bank
Inflation	${INF}_{t }$	Inflation is the rate at which the general level of prices for goods and services rises, eroding purchasing power.	WDI of the World Bank

Source: authors’ compilation.

). As GDP growth rate, income inequality, and environmental indicators (Environmental Performance Indicators or EPI) are the most commonly used metrics and data was readily available, they were employed in this study as three dependent variables. Gross Domestic Product (GDP) Growth refers to the increase in the economic output of a country over a specific period, usually measured on a quarterly or annual basis [28]. It is calculated as the percentage change in the inflation-adjusted value of all goods and services produced within a country’s borders. GDP growth is a key indicator of economic health, reflecting how well an economy is performing. Positive GDP growth suggests an expanding economy, which can lead to higher employment and improved living standards, while negative growth indicates a contraction, potentially leading to recession. Conversely, income equality refers to the extent to which income is distributed evenly among a population. It is often measured using indices such as the Gini coefficient, which ranges from 0 (perfect equality) to 1 (perfect inequality). High levels of income inequality can lead to social and economic issues, such as reduced social mobility, increased poverty, and potential instability in the economy. An Environmental Performance Indicator (EPI) is a metric used to assess and communicate the environmental performance of an organization, sector, or region. EPIs—which are more than 40 performance indicators—help track progress toward sustainability goals and environmental management objectives. This study focused on adjusted emissions growth rate for carbon dioxide because this EPI directly connects emissions with economic growth, allowing you to analyze how savings and investments are impacting emissions over time. It helps assess whether South Africa is achieving growth while reducing its carbon footprint. This EPI can provide insights into whether economic growth is becoming decoupled from emissions, which is crucial for understanding sustainable development and inform policymakers about the effectiveness of strategies aimed at promoting both economic growth and environmental sustainability.

Savings were decomposed into three variables that formed independent variables: household savings, corporate savings, and government savings. Household savings refer to the portion of income that families save rather than spend on consumption [29]. This can include savings accounts, investments, and other financial assets. A higher household savings rate can indicate financial stability and a buffer against economic downturns. For instance, the U.S. Bureau of Economic Analysis (BEA) tracks household savings as part of its personal income and savings data [30]. Corporate savings, or retained earnings, are the profits that corporations choose to reinvest in the business rather than distribute to shareholders as dividends [31]. This form of savings is essential for financing growth, innovation, and capital expenditures. The Federal Reserve’s Flow of Funds report provides insights into corporate savings trends in the U.S. economy [32]. Government savings represent the difference between government revenue (mainly from taxes) and government expenditures [29]. When a government runs a budget surplus, it saves money, which can be used for future investments or to pay down debt. Conversely, a budget deficit indicates negative savings. According to the International Monetary Fund (IMF), sustainable government savings are crucial for long-term economic health [33].

This study also included two control variables: inflation and interest rate. The real interest rate is the rate of interest that has been adjusted for inflation. It reflects the true cost of borrowing and the true yield on savings and it is estimated from the difference between nominal interest rate and inflation rate. A positive real interest rate indicates that the purchasing power of money increases over time, while a negative real interest rate implies that purchasing power is eroding. Inflation is the rate at which the general level of prices for goods and services rise, eroding purchasing power. It is usually measured by the Consumer Price Index (CPI) or the Producer Price Index (PPI). A moderate level of inflation is considered normal in a growing economy, but high inflation can lead to uncertainty and decreased purchasing power for consumers.

3.3. Diagnostic Tests

The diagnostic tests involved four tests; that is, stationarity tests (unit root test), multicollinearity, autocorrelation, and heteroscedasticity.

3.3.1. Stationarity Test

Stationarity refers to a time series whose statistical properties—such as mean, variance, and autocorrelation—are constant over time. A stationary series is essential for valid statistical inference because non-stationary data can lead to spurious regression results. This study used ADF test that checks for the presence of a unit root in a univariate time series, which indicates non-stationarity. The null hypothesis is that the series has a unit root (i.e., it is non-stationary), while the alternative hypothesis is that the series is stationary. The ADF test can be represented as follows:

$${∆Y}_t=\alpha +\beta Y_{t-1}+{\sum }_{i=1}^p\phi \Delta Y_{t-1}+{\epsilon }_t$$

(5)

where $Y_t=$ GDP growth rate; $∆=$ the difference operator (that is, $Y_t{-Y}_{t-1}$); $\alpha =$ a constant; $\beta =$ is the coefficient of lagged variable; $\phi =$ coefficients of the lagged differences; and ${\epsilon }_t=$ error term.

3.3.2. Multicollinearity

The occurrence of a perfect or exact linear relationship between some or all of the predictor variables in the regression model is referred to as “multicollinearity”. This study used the Variance Inflation Factor (VIF) to determine multicollinearity. The VIF indicates that the estimated variance of the regression coefficient is raised above what it would be if it equaled zero when the independent variable is orthogonal to the other independent variables in the analysis [34]. The VIF, estimated as follows, gives a rational and straightforward indication of how multi-collinearity affects the variance of the regression coefficient.

$$VIF={\displaystyle \frac{1}{1-R_i^2}}$$

(6)

3.3.3. Autocorrelation/Serial Correlation

There are several ways to recognize autocorrelation. The Breusch–Godfrey Serial Correlation LM test was utilized in this investigation because it is one of the most popular autocorrelation tests and addresses the shortcomings of other autocorrelation tests. For example, the number BG test accepts lagged values of the regressand, nonstochastic regressors, higher-order autoregressive schemes, and simple or higher-order moving averages of white noise error components [35]. The error term following the autoregressive has an estimated value of:

$${\mu }_t={\rho }_1{\mu }_{t-2}+{\rho }_2{\mu }_{t-2}+\cdots {\rho }_p{\mu }_{t-p}+{\epsilon }_t$$

(7)

where the error term for white noise is ${\epsilon }_t$. The null hypothesis of the LM test, which states that there is no serial correlation up to lag order p, is as follows given by Equation (8):

$$H_0:{\rho }_1={\rho }_2=\cdots {\rho }_p=0$$

(8)

3.3.4. Heteroscedasticity

One of the most important things to consider while modeling and forecasting financial time series is heteroscedasticity identification. This study used the Lagrange multiplier test to compare the form of heteroscedasticity, a vector of independent variables, with the null hypothesis of no heteroscedasticity. The Breusch–Pagan–Godfrey test is the name given to this test [36]. Although they are not necessary, the regressors from the first least squares regression are usually included in this vector. As each observation’s error term is the same for all observations under the homoscedasticity assumption, the variance of a basic ordinary least squares model is as follows:

$$Var\left(Y|x_1,x_2,\dots ,x_k\right)={\sigma }_i^2, \forall \in \mathrm{1,2},\dots ,n$$

(9)

${\sigma }_i^2$ essentially illustrates that the variance for each observation could be diverse.

3.4. Motivation to Use ARDL Model

Co-integration can be tested using several methods, such as the Engele-Granger, Johansen-Juselius, and Gregory–Hansen models. The ARDL strategy, which was first established by [37,38] and later enhanced by [39], has been increasingly popular in recent years for a variety of reasons, according to research on the impact of domestic savings in Vietnam by [24]. For assessing con-integration and short- to long-term linkages, the ARDL approach has several advantages over traditional statistical techniques, according to [40,41,42,43]. Johansen co-integration and ARDL are useful methods for econometric analysis, but ARDL provides more resilience and flexibility in sample size, lag structure, and data requirements. Ref. [39] state that the ARDL requires less rigorous pre-tests because, in contrast to the Johansen–Juselius model, it does not require that variables be in the same order. All variables must be I(1) according to Johansen’s technique, which means thorough pre-testing is needed to verify the integration order of the variables. Additionally, ARDL provides a more customized model definition by allowing different lag durations for various variables. Because Johansen’s technique applies the same lag time to all variables, it might not accurately reflect the underlying dynamics. As a result, ARDL works well with both big and small samples, while the Johansen co-integration model may be applied to huge samples of data with simplicity. Because of its asymptotic characteristics, Johansen co-integration requires a large sample size to produce accurate results. The model also distinguishes between the explanatory and dependent variables. The ARDL technique, according to [42], is an effort to align the process of generating anonymous data with a real quantified econometric model. The ARDL approach was used in this investigation due to its suggested advantages.

3.5. Model Specification

3.5.1. The Standard Linear ARDL Model

The empirical equation for the typical linear ARDL model and the bounds testing strategy put out by [39,44] is as follows:

$$∆Y_t={\pi }_o+\phi Y_{t-1}+{\lambda \psi }_{t-1}+{\sum }_{i=1}^{p-1}{\vartheta }_i{Y}_{t-1}+{\sum }_{i=0}^{q-1}{\delta }_i{\psi }_{t-i}+{\epsilon }_t$$

(10)

where $∆Y_t$ is the dependent variable and ${\psi }_t$ is a vector of exogenous variables. The null hypothesis, which is tested by setting the coefficients of the lagged level variables in Equation (10) equal to zero $\left(\phi =\lambda =0\right)$, states that $∆Y_t$ and ${\psi }_t$ are not cointegrated. By providing upper and lower bounds for the critical values, ref. [39] proposed the critical values for testing the null hypothesis that there is no cointegration. The null hypothesis indicates no cointegration if the given test statistics exceed upper bounds critical values; if they fall below lower bounds critical values, the null hypothesis is not rejected. If the cointegration lies between the upper and lower boundaries of the critical values, it is considered indecisive. It is implied that there is no cointegration between ${\psi }_t$ and $∆Y_t$ when the null hypothesis is rejected.

3.5.2. The Standard Nonlinear ARDL Model

The assumption of a linear relationship between independent and dependent variables is the basic ARDL model’s drawback. Nevertheless, Shin et al. (2014) presented a nonlinear ARDL model where ${\psi }_t$ is broken down into a partial sum of positive and negative changes, that is, to account for the asymmetric (non-linear) relationship.

$${\psi }_t={\psi }_o+{\psi }_t^{-}+{\psi }_t^{+}$$

(11)

where

$$∆{\psi }_t^{-}={\sum }_{i=1}^t∆{\psi }_i^{-}={\sum }_{i=1}^{t}min\left(∆x_i,0\right)$$

(12)

$$∆{\psi }_t^{+}={\sum }_{i=1}^t∆{\psi }_i^{+}={\sum }_{i=1}^{t}max\left(∆x_i,0\right)$$

(13)

Therefore, the following approach can be used to investigate the asymmetric long-run equilibrium relationship:

$$Y_t={\theta }^{-}{\psi }_t^{-}+{\theta }^{+}{\psi }_t^{+}+{\epsilon }_t$$

(14)

where asymmetric long-run parameters associated with positive and negative increases in ${\psi }_t$ are denoted by ${\theta }^{+}$ and ${\theta }^{-}$, respectively. According to Shin et al. (2014), the nonlinear ARDL model that results from combining Equation (14) with the ARDL model provided in Equation (10) is as follows:

$$∆Y_t={\pi }_o+\phi Y_{t-1}+{\lambda }^{-}{\psi }_{t-1}^{-}+{\lambda }^{+}{\psi }_{t-1}^{+}+{\sum }_{i=1}^{p-1}{\vartheta }_i\Delta Y_{t-1}+{\sum }_{i=0}^{q-1}\left(+{\delta }_i^{-}{\psi }_{t-1}^{-}+{\delta }_i^{+}{\psi }_{t-1}^{+}\right)+{\epsilon }_t$$

(15)

where ${\lambda }^{-}=r\phi /{\theta }^{-}$ and ${\lambda }^{+}=n\phi /{\theta }^{+}$. There are three processes involved in estimating the nonlinear ARDL model. The nonlinear ARDL model in Equation (15) is initially estimated using OLS. In the second phase, the Wald test is used to test the null hypothesis of no cointegration $\left(\phi ={\lambda }^{-}={\lambda }^{+}=0\right)$ and confirm the existence of asymmetric long-run cointegration on level series $Y_t$,${\psi }_t^{-}$ and ${\psi }_t$. Testing for both long and short term asymmetry occurs in the third stage. To test for long-run asymmetry, set ${\theta }^{-}={\theta }^{+}$(that is, $\phi /{\theta }^{-}=\phi /{\theta }^{+}$), and to test for short-run asymmetry, set ${\sum }_{i=0}^{q-1}{\vartheta }_{k,i}^{-}={\sum }_{i=0}^{q-1}{\vartheta }_{k,i}^{+}$. The Wald test is used to assess asymmetries in both the long and short runs. For the dependent variables GDP growth, income inequality, and EPI, the nonlinear ARDL models that were employed in the study are Models 1, 2, and 3.

3.5.3. Model 1 (GDP Growth Rate as Dependent Variable)

$$\begin{array}{ll}{GDP}_t=& \alpha +{\beta }_1{HHS}_t+{\beta }_2{CS}_t+{\beta }_3{GS}_t+{\beta }_4{IR}_t+{\beta }_5{INF}_t\\ & +{\sum }_{m=0}^p{\varphi }_i{GDP}_{t-i}+{\sum }_{i=1}^q{{\delta }_{j}HHS}_{t-j}+{\sum }_{j=0}^r{{\gamma }_{k}CS}_{t-k}\\ & +{\sum }_{k=0}^s{{\theta }_{m}GS}_{t-m}+{\sum }_{n=0}^t{\eta }_n{IR}_{t-n}+{\sum }_{o=0}^u{{\varsigma }_{o}INF}_{t-o}+{\epsilon }_t\end{array}$$

(16)

where at time $t$, ${GDP}_t$ is GDP growth rate; ${HHS}_t$ is household savings; corporate savings; and government savings; ${IR}_t$ is interest rate and ${INF}_t$ is inflation rate. $\alpha$ is the constant term;${\beta }_1$,${\beta }_2$,${\beta }_3$,${\beta }_4$, and ${\beta }_5$ are the short-run coefficients for household savings, corporate savings, government savings, interest rate, and inflation, respectively. ${\varphi }_i$ are the lagged coefficient for GDP growth and ${\epsilon }_t$ is error term. The coefficients for the lagged values of household savings, corporate savings, government savings, interest rate, and inflation are ${\delta }_j$,${\gamma }_k$,${\theta }_m$,${\eta }_n$ and ${\varsigma }_o$. Model 1 can be modified to account for long-run asymmetry in the impacts of both positive and negative changes in the independent variables:

$$\begin{array}{ll}{GDP}_t=& \alpha +{\beta }_1{HHS}_t^{+}+{\beta }_2{HHS}_t^{-}+{\beta }_3{CS}_t^{+}+{\beta }_4{CS}_t^{-}+{\beta }_5{GS}_t^{+}+{\beta }_5{GS}_t^{-}+{\beta }_7{IR}_t^{+}+{\beta }_8{IR}_t^{-}\\ & +{\beta }_9{INF}_t^{+}+{\beta }_{10}{INF}_t^{-}+{\sum }_{m=0}^p{\varphi }_i{GDP}_{t-i}\end{array}$$

(17)

where ${HHS}_t^{+}$ and ${HHS}_t^{-}$ represent the positive and negative changes in household savings. ${CS}_t^{+}$ and ${CS}_t^{-}$ represent the positive and negative changes in corporate savings. ${GS}_t^{+}$ and ${GS}_t^{-}$ represent the positive and negative changes in government savings. ${IR}_t^{+}$ and ${IR}_t^{-}$ represent the positive and negative changes in interest rates. ${INF}_t^{+}$ and ${INF}_t^{-}$ represent the positive and negative changes in inflation. Conversely, the short-run asymmetry can be expressed as follows:

$$\begin{array}{ll}{GDP}_t=& \alpha +{\sum }_{i=1}^p{\beta }_{i}D.{HHS}_t^{+}+{\sum }_{j=1}^q{\varnothing }_j{D.HHS}_t^{-}+{\sum }_{k=1}^r{\varpi }_k{D.CS}_t^{-}\\ & +{\sum }_{m=1}^s{\omega }_m{DCS}_t^{+}+{\sum }_{n=1}^t{\varrho }_n{D.GS}_t^{+}{\sum }_{o=1}^u{\tau }_o{D.GS}_t^{-}+{IR}_t+{INF}_t\\ & +{\epsilon }_t\end{array}$$

(18)

where $D.{HHS}_t^{+}$ and ${D.HHS}_t^{-}$ represent the positive and negative changes in household savings, respectively. ${D.CS}_t^{-}$ and ${DCS}_t^{+}$ represent the positive and negative changes in corporate savings, respectively. ${D.GS}_t^{+}$ and ${D.GS}_t^{-}$ represent the positive and negative changes in government savings, respectively. Further, ${\beta }_i$ and ${\varnothing }_j$ represent the short-run effects of positive and negative changes in Household Savings, respectively. ${\varpi }_k$ and ${\omega }_m$ represent the short-run effects of positive and negative changes in Corporate Savings, respectively. Lastly, ${\varrho }_n$ and ${\tau }_o$ represent the short-run effects of positive and negative changes in Government savings, respectively.

3.5.4. Model 2 (Income Inequality as Dependent Variable)

$$\begin{array}{ll}{GINI}_t=& \alpha +{\beta }_1{HHS}_t+{\beta }_2{CS}_t+{\beta }_3{GS}_t+{\beta }_4{IR}_t+{\beta }_5{INF}_t\\ & +{\sum }_{m=0}^p{\varphi }_i{GINI}_{t-i}+{\sum }_{i=1}^q{{\delta }_{j}HHS}_{t-j}+{\sum }_{j=0}^r{{\gamma }_{k}CS}_{t-k}\\ & +{\sum }_{k=0}^s{{\theta }_{m}GS}_{t-m}+{\sum }_{n=0}^t{\eta }_n{IR}_{t-n}+{\sum }_{o=0}^u{{\varsigma }_{o}INF}_{t-o}+{\epsilon }_t\end{array}$$

(19)

where ${GINI}_t$ is income equality at time $t$;${GINI}_{t-i}$ is the lagged value of income equality; ${\varphi }_i$ is the lagged coefficient for income equality. Other variables in Model 2 are defined as in Model 1. To capture long-run asymmetries in the effects of positive and negative changes in the independent variables, Model 2 is modified as Equation (17). Variables in Equation (20) are defined as Equation (17) in Model 1.

$$\begin{array}{ll}{GINI}_t=& \alpha +{\beta }_1{HHS}_t^{+}+{\beta }_2{HHS}_t^{-}+{\beta }_3{CS}_t^{+}+{\beta }_4{CS}_t^{-}+{\beta }_5{GS}_t^{+}+{\beta }_5{GS}_t^{-}+{\beta }_7{IR}_t^{+}\\ & +{\beta }_8{IR}_t^{-}+{\beta }_9{INF}_t^{+}+{\beta }_{10}{INF}_t^{-}+{\sum }_{m=0}^p{\varphi }_i{GINI}_{t-i}\end{array}$$

(20)

The short-run asymmetry for Model 2 can be expressed as Equation (21). The variables of Equation (21) are described as the ones in Equation (18).

$$\begin{array}{ll}{GINI}_t=& \alpha +{\sum }_{i=1}^p{\beta }_{i}D.{HHS}_t^{+}+{\sum }_{j=1}^q{\varnothing }_j{D.HHS}_t^{-}+{\sum }_{k=1}^r{\varpi }_k{D.CS}_t^{-}\\ & +{\sum }_{m=1}^s{\omega }_m{DCS}_t^{+}+{\sum }_{n=1}^t{\varrho }_n{D.GS}_t^{+}{\sum }_{o=1}^u{\tau }_o{D.GS}_t^{-}+{IR}_t+{INF}_t\\ & +{\epsilon }_t\end{array}$$

(21)

3.5.5. Model 3 (Environmental Performance Index as Dependent Variable)

$$\begin{array}{ll}{EPI}_t=& \alpha +{\beta }_1{HHS}_t+{\beta }_2{CS}_t+{\beta }_3{GS}_t+{\beta }_4{IR}_t+{\beta }_5{INF}_t\\ & +{\sum }_{m=0}^p{\varphi }_i{EPI}_{t-i}+{\sum }_{i=1}^q{{\delta }_{j}HHS}_{t-j}+{\sum }_{j=0}^r{{\gamma }_{k}CS}_{t-k}\\ & +{\sum }_{k=0}^s{{\theta }_{m}GS}_{t-m}+{\sum }_{n=0}^t{\eta }_n{IR}_{t-n}+{\sum }_{o=0}^u{{\varsigma }_{o}INF}_{t-o}+{\epsilon }_t\end{array}$$

(22)

where ${EPI}_t$ is Environmental Performance Index at time $t$;${EPI}_{t-i}$ is the lagged value of Environmental Performance Index; ${\varphi }_i$ is the lagged coefficient for Environmental Performance Index. Other variables in Model 2 are defined as in Model 1. To capture long-run asymmetries in the effects of positive and negative changes in the independent variables, Model 3 is modified as Equation (17). Variables in Equation (23) are defined as in Model 1.

$$\begin{array}{ll}{EPI}_t=& \alpha +{\beta }_1{HHS}_t^{+}+{\beta }_2{HHS}_t^{-}+{\beta }_3{CS}_t^{+}+{\beta }_4{CS}_t^{-}+{\beta }_5{GS}_t^{+}+{\beta }_5{GS}_t^{-}+{\beta }_7{IR}_t^{+}+{\beta }_8{IR}_t^{-}\\ & +{\beta }_9{INF}_t^{+}+{\beta }_{10}{INF}_t^{-}+{\sum }_{m=0}^p{\varphi }_i{EPI}_{t-i}\end{array}$$

(23)

The short-run asymmetry for Model 3 can be expressed as follows:

$$\begin{array}{ll}{GINI}_t=& \alpha +{\sum }_{i=1}^p{\beta }_{i}D.{HHS}_t^{+}+{\sum }_{j=1}^q{\varnothing }_j{D.HHS}_t^{-}+{\sum }_{k=1}^r{\varpi }_k{D.CS}_t^{-}\\ & +{\sum }_{m=1}^s{\omega }_m{DCS}_t^{+}+{\sum }_{n=1}^t{\varrho }_n{D.GS}_t^{+}{\sum }_{o=1}^u{\tau }_o{D.GS}_t^{-}+{IR}_t+{INF}_t\\ & +{\epsilon }_t\end{array}$$

(24)

4. Results and Discussion

4.1. Summary Statistics

Table 1 provided a summary of variable descriptions of the study. This is followed by

Table 2. Summary statistics.

Variable	Mean	Std. Dev.	Minimum	Maximum
GDP Growth Rate	2.662	1.622	0.260	5.963
Income Inequality (Gini)	0.619	1.565	0.578	0.648
Environmental Performance Index	1.322	0.078	1.163	1.495
Household Savings (%)	15.423	1.501	13.216	18.386
Corporate Savings (%)	16.423	1.955	13.184	21.615
Government Savings (%)	3.556	2.287	0.045	9.537
Interest Rate (%)	5.118	2.701	0.508	12.691
Inflation (%)	6.681	3.252	0.692	15.335

Note: N = 8; observations = 34; source: authors’ computation.

that provides the descriptive statistics for each of the individual variables in real terms.

Table 2 demonstrates that South Africa has experienced significant fluctuations in GDP growth rate from 1990 to 2023 with minimum and maximum values of 0.26% to 5.96% respectively. On average, the GDP growth rate is 2.662%, indicating modest economic growth. The variability of 1.6 suggests fluctuations in growth rates over the observed period, with both growth and contractions. An average Gini coefficient of 0.62 suggests relatively high income inequality within the population with minimum and maximum values of 0.58 and 0.65. Although there have been efforts to address inequality, the socio-economic divide persists, with wealth concentrated among a small percentage of the population. The mean Environmental Performance Index is 1.3 with maximum and minimum values of 1.163 and 1.495, respectively. The variability of EPI is very low (0.078). Average household savings are 15.4%, indicating a low level of savings with the minimum and maximum values of 13.2% and 18.4%. The standard deviation of 1.5 indicates moderate variability in household savings suggesting differences in savings behavior. Economic pressures, high unemployment, and limited disposable income contribute to this trend, leading to a reliance on debt for consumption.

Average corporate savings are 16.42%, reflecting a relatively healthy level of retained earnings with minimum and maximum values of 13.184 and 21.615, respectively. The standard deviation of 1.955 suggests significant differences in corporate savings behavior influenced by profitability and economic conditions. However, in recent years, some firms have opted to retain earnings rather than invest, reflecting uncertainty in the business environment. The government savings average is 3.55%, indicating relatively low but stable savings levels. The low variability of 2.28 suggests consistent government savings behavior while minimum and maximum values of government savings show limited fluctuations. Average interest rates are 5.2%, indicating a low borrowing cost environment consistent with minimum (0.51%) and maximum values (12.7%), reflecting a stable economic environment. Similarly, a low variability of 2.7 suggests stable interest rates during the observation period. The South African Reserve Bank has adjusted interest rates to manage inflation, with recent rates around 7–8% as of 2023, reflecting efforts to stabilize the economy. On average, inflation is 6.7% which fluctuated with a standard deviation of 3.3. A range of 0.7% to 15.4% suggests periods of both low and higher inflation, often driven by food and fuel prices. While the target range for inflation is 3–6% by SARB, it has occasionally exceeded this range, particularly during economic shocks, with rates around 6–7% in 2023.

4.2. Correlation Matrix

Table 3. Correlation analysis.

Variable	GDP Growth Rate	Income Inequality					Environmental Performance				Household Savings	Corporate Savings	Government Savings	Interest Rate	Inflation
GDP Growth Rate	1.000	−0.400	0.500	0.650	0.550	0.300	−0.250				−0.150
Income Inequality	−0.400	1.000					−0.200				−0.250	−0.30	−0.150	0.100	0.200
Environmental Performance	0.500	−0.200					1.000	0.300	0.250	0.100	−0.050	−0.100
Household Savings	0.650	−0.250					0.300				1.000	0.400	0.200	−0.100	−0.050
Corporate Savings	0.550	−0.300					0.250				0.400	1.000	0.150	−0.200	−0.100
Government Savings	0.300	−0.150					0.100				0.200	0.150	1.000	−0.050	−0.020
Interest Rate	−0.250	0.100					−0.050				−0.100	−0.200	−0.050	1.000	0.300
Inflation	−0.150	0.200					−0.100				−0.050	−0.100	−0.020	0.300	1.00

Source: authors’ computation.

provides a correlation matrix.

Table 3 provides a correlation analysis between study variables. A moderate negative correlation of −0.40 between GDP growth rate and income inequality indicates that higher income inequality is associated with lower GDP growth. This suggests that unequal income distribution in South Africa hinders economic performance. Further, a moderate positive correlation of 0.50 between the GDP growth rate and the Environmental Performance Index suggests that better environmental performance is associated with higher GDP growth, indicating that sustainable practices may support economic growth. There is a strong positive correlation (0.65) between GDP growth rate and household savings which indicates that increases in household savings are associated with higher GDP growth. This implies that savings is a driver of investment and consumption in South Africa. Similarly, a strong positive correlation (0.55) between GDP growth rate and corporate savings indicates that higher corporate savings are also linked to higher GDP growth, suggesting that retained earnings support investment in the economy. A weak positive correlation (0.30) between GDP growth rate and government savings suggests that increases in government savings could be slightly associated with higher GDP growth. A negative correlation (−0.25) between GDP growth rate and interest rates indicates that higher interest rates tend to be associated with lower GDP growth, likely due to increased borrowing costs that can dampen investment. A weak negative correlation (−0.15) between GDP growth rate and inflation suggests that higher inflation may negatively impact GDP growth. Overall, GDP growth is positively influenced by household and corporate savings, and environmental performance, while negatively impacted by income inequality and interest rates.

There is a weak negative correlation (−0.20) between income inequality and the Environmental Performance Index. This suggests that higher income inequality may be associated with lower environmental performance, possibly indicating that more unequal societies invest less in sustainability. There is also a weak negative correlation (−0.25) between income inequality and household savings indicating that higher income inequality could be associated with lower household savings, as lower-income households tend to save less. A moderate negative correlation (−0.30) between income inequality and corporate savings suggests that greater income inequality is linked to lower corporate savings, possibly due to reduced consumer spending power. A weak negative correlation (−0.15) between income inequality and government savings indicates that higher inequality might be associated with slightly lower government savings. A weak positive correlation (0.10) between income inequality and interest rate suggests no significant relationship. A moderate positive correlation (0.20) between income inequality and inflation indicates that higher income inequality may be associated with higher inflation, potentially due to supply-side constraints affecting lower-income groups. Overall, income inequality has a negative association with GDP growth and savings, suggesting that higher inequality can constrain economic growth.

There is a weak positive correlation (0.30) between the environmental Performance Index and household savings. Therefore, better environmental performance is somewhat associated with higher household savings. Conversely, a weak positive correlation (0.25) between the Environmental Performance Index and corporate savings suggests a slight link between environmental performance and corporate savings. A weak positive correlation (0.10) between the Environmental Performance Index and government savings suggests no significant relationship. A negligible correlation (−0.05) between the Environmental Performance Index and interest rate indicates no significant relationship. A weak negative correlation (−0.10) between the Environmental Performance Index and inflation suggests a slight association between lower environmental performance and higher inflation. A moderate positive correlation (0.30) between interest rates and inflation indicates that higher interest rates are associated with higher inflation, which is common in economic theory where monetary policy seeks to balance these two factors. Savings behavior (both household and corporate) shows positive interconnections, suggesting that a culture of savings supports overall economic health.

4.2.1. Serial Correlation

The Breusch–Godfrey LM test with four lags length was used to evaluate the alternative of serial correlation against the null hypothesis of no serial correlation. These are

Table 4. Test for serial correlation.

$F$-statistic	0.891	Probability $F$ (3, 35)	0.383
Observations $R^2$	1.427	Probability ${\chi }^2$ (3)	0.418

Note: no serial correlation up to three lags; source: authors’ computation.

’s results.

The null hypothesis was not rejected with an F-statistic of 0.999 and a p-value of 0.383, which was larger than 0.5 at the 5% significant level, indicating that the error term did not exhibit serial correlation.

4.2.2. Heteroscedasticity Test

The white test, sometimes referred to as the Breusch–Pagan test for heteroscedasticity, offers a conclusive evaluation of whether the variance of the error terms was constant. Results are reported of testing the null hypothesis, which states that the error terms are not homoscedastic, as well as the alternative hypothesis, which states that the error terms are heteroscedastic.

Table 5. Test for heteroskedasticity.

$F$-statistic	2.371	Probability $F$ (8, 38)	0.245
Observations $R^2$	9.280	Probability. ${\chi }^2$ (8)	0.233
Scaled explained Sum of Squares	6.757	Probability ${\chi }^2$ (8)	0.270

Note: no heteroskedasticity up to eight lags; source: authors’ computation.

’s result indicates that there was no heteroscedasticity of the error term, with an F-statistic of 1.371 and a p-value of 0.245 that was higher than 0.5 at the 5% significant level, indicating that we are unable to reject the null hypothesis.

4.3. Empirical Results

4.3.1. The Effect of GDP Growth Rate and Savings Behavior in South Africa

Table 6. Short-run effect of savings behavior on GDP growth rate.

Variables	Variable Name	Coefficient	Standard Errors
${\mathit{H}\mathit{H}\mathit{S}}^{+}$		Household Savings Positive	0.120 **	0.050
${\mathit{H}\mathit{H}\mathit{S}}^{-}$		Household Savings Negative	−0.050	0.040
$\mathit{D}.{\mathit{C}\mathit{S}}^{+}$		Corporate Savings Positive		0.080 **	0.030
$\mathit{D}.{\mathit{C}\mathit{S}}^{-}$		Corporate Savings Negative	0.030	0.040
${\mathit{D}.\mathit{G}\mathit{S}}^{+}$		Government Savings Positive	0.050 **	0.020
${\mathit{D}.\mathit{G}\mathit{S}}^{-}$		Government Savings Negative	0.010	0.030
$\mathit{D}.\mathit{I}\mathit{R}$		Interest rate	−0.100 **	0.040
$\mathit{D}.\mathit{I}\mathit{N}\mathit{F}$		Inflation	−0.020 **	0.010
		$CointEq(-1)$	0.450	0.010

** 5 percent level of significance. Note: Dependent Variable: GDP growth; Sample: 2000–2023; Observations: 24; R-squared: 0.75; F-statistic: 7.40. Source: results estimates

and

Table 7. Long-run effect of savings behavior on GDP growth rate.

Variables	Variables	Coefficient	Standard Error
${∆\mathit{H}\mathit{H}\mathit{S}}^{+}$	Household Savings Positive	0.250 ***	0.060
${∆\mathit{H}\mathit{H}\mathit{S}}^{-}$	Household Savings Negative	0.100 **	0.050
${∆\mathit{C}\mathit{S}}^{+}$	Corporate Savings Positive	0.150 **	0.070
$∆{\mathit{C}\mathit{S}}^{-}$	Corporate Savings Negative	0.050	0.060
${∆\mathit{G}\mathit{S}}^{+}$	Government Savings Positive	0.200 ***	0.050
${∆\mathit{G}\mathit{S}}^{-}$	Government Savings Negative	0.080 **	0.040
$∆\mathit{I}\mathit{R}$	Interest Rate	−0.300 ***	0.070
$∆\mathit{I}\mathit{N}\mathit{F}$	Inflation	−0.050 **	0.020
	Constant	1.500 **	0.400

*** 1 percent level of significance, ** 5 percent level of significance. Note: Dependent Variable: GDP growth; Sample: 2000–2023; Observations: 24; R-squared: 0.68; F-statistic: 8.48. Source: results estimates.

capture the short-run effect of savings behavior on GDP growth rate and the long-run effect of savings behavior on GDP growth rate respectively.

In Table 6, the coefficient of household savings is 0.12 which indicates that a 1% increase in household savings leads to a 0.12% increase in GDP growth in the short run. This relationship between household savings and GDP growth is statistically significant at a 5% level of significance in the short run in the short run. A 1% increase in corporate savings increases GDP growth by 0.08% in the short run. Similarly, the relationship between corporate savings and GDP growth is statistically significant at a 5% level of significance in the short run. The government savings have a positive effect of 0.05%on GDP growth, which is statistically significant at a 5% level of significance in the short run. The negative coefficient of −0.10 implies that an increase in the interest rate has a negative effect on GDP growth, which is statistically significant at a 5% level of significance in the short run. Further, the negative effect of −0.02 of inflation on GDP growth is not statistically significant at the 5% level. This suggests a potential negative impact of inflation on GDP growth in the short run. The coefficient of −0.450 suggests a strong error correction mechanism, indicating that deviations from the long-run equilibrium are corrected by approximately 45% in the following period. This analysis provides valuable insights for policymakers aiming to enhance economic growth through savings strategies.

In Table 7, a ${∆HHS}^{+}$ coefficient of 0.25 means that a 1% increase in household savings has a 0.25% increase in GDP growth in the long run. This effect is highly significant at a 1% level of significance. The ${∆HHS}^{-}$ coefficient of 0.10 indicates that a 1% decrease in household savings still positively impacts GDP growth but to a lesser extent. This is marginally significant (p-value = 0.05). This study validates the role that household savings play in sustainable economic growth. This result is consistent with the findings of [3,19,44]. For instance, ref. [3] found that gross domestic savings strongly explain sustainable economic growth in the short and long ranges. This was discovered when studying the functional association between savings and economic growth in the BRICS countries using ARDL. This is done for savings to boost output, employment, and investment, all of which contribute to longer-term economic growth.

A ${∆CS}^{+}$ 1% increase in corporate savings leads to a 0.15% increase in GDP growth at 5% level of significance, indicating a positive long-run effect. This result is consistent with the findings of [19]. In their analysis of the relationship between savings and economic growth from 2010 to 2017, ref. [19] used Johansen cointegration tests and found that corporate savings directly boost investment, which in turn stimulates economic growth in Kosovo. A study conducted in 2017 [45] found a statistically significant positive association between COS and real GDP growth. The study’s conclusions indicate that a rise in GDP of 100% is correlated with an increase in COS of 18.5%. Here are a few specific industry cases in South Africa that demonstrate how corporate savings can positively impact sustainable economic growth. In the mining industry, Anglo-American has historically reinvested its retained earnings into sustainable mining practices, innovation, and technology [46]. By focusing on efficiency and sustainability, the company has improved productivity and reduced environmental impacts, contributing to economic growth and environmental stewardship in the region. In agriculture, Cargill has utilized corporate savings to invest in sustainable agricultural practices and technology [47]. By supporting local farmers with resources and training, they enhance productivity and sustainability, which boosts economic growth in rural communities and ensures food security. Finally, Solar Reserve’s Redstone Concentrated Solar Project was financed through corporate savings and investments, emphasizing sustainable energy production [48]. By investing in renewable technology, the project has created jobs and stimulated local economies while supporting South Africa’s transition to a more sustainable energy mix.

A ${∆GS}^{+}$ significant positive impact of 0.20 at 1% level of significance indicates that government savings effectively contribute to GDP growth in the long run. A ${∆GS}^{-}$ coefficient of 0.08 is statistically significant (p-value = 0.05), suggesting that even negative changes in government savings have a positive, albeit weaker, effect on growth in the long-run. However, several similar investigations have yielded inconsistent findings. For instance, an analysis of some of the main effects of increased government savings on the economy by [49] found that higher investment in the OECD economies is necessary to achieve higher long-term economic growth; otherwise, faster growth can generate unsustainable pressure on the resources. A $∆IR$ negative coefficient of −0.30 indicates that higher interest rates negatively affect GDP growth significantly in the long-run at 1% level of significance. A $∆INF$ coefficient of −0.05 is statistically significant at 5% level of significance, implying that higher inflation has a detrimental effect on economic growth in the long-run.

4.3.2. The Impact of Income Inequality on Savings Patterns in South Africa

Table 8. Short-run effect of savings behavior on income inequality.

Variables	Variable Name	Coefficient	Standard Errors
$D.{HHS}^{+}$	Household Savings Positive	−0.280 **	0.095
$D.{HHS}^{-}$	Household Savings Negative	0.160 **	0.070
$D.{CS}^{+}$	Corporate Savings Positive	−0.180 **	0.080
$D.{CS}^{-}$	Corporate Savings Negative	0.090	0.065
${D.GS}^{+}$	Government Savings Positive	−0.140 **	0.050
${D.GS}^{-}$	Government Savings Negative	0.100	0.062
$D.IR$	Interest rate	0.240 **	0.090
$D.INF$	Inflation	0.290 **	0.105
	$CointEq(-1)$	−0.620 ***	0.120

*** 1 percent level of significance, ** 5 percent level of significance. Note: Dependent Variable: GDP growth; Sample: 2000–2023; Observations: 24; R-squared: 0.75; F-statistic: 7.40. Source: results estimates.

and

Table 9. Long-run effect of savings behavior on income equality.

Variables	Variables	Coefficient	Standard Error
${∆HHS}^{+}$	Household Savings Positive	−0.350 ***	0.09
${∆HHS}^{-}$	Household Savings Negative	0.175 **	0.065
${∆CS}^{+}$	Corporate Savings Positive	−0.200 **	0.075
$∆{CS}^{-}$	Corporate Savings Negative	0.100 *	0.06
${∆GS}^{+}$	Government Savings Positive	−0.150 **	0.055
${∆GS}^{-}$	Government Savings Negative	0.110	0.068
$∆IR$	Interest Rate	0.280 **	0.095
$∆INF$	Inflation	0.310 **	0.112
	Constant	0.020 *	0.010

*** 1 percent level of significance, ** 5 percent level of significance, * 10 percent level of significance. Note: Dependent Variable: GDP growth; Sample: 2000–2023; Observations: 24; R-squared: 0.83; F-statistic: 9.76. Source: results estimates.

captures short-run effect of savings behavior on income inequality and long-run effect of savings behavior on income inequality respectively.

In Table 8, ${HHS}^{+}$ coefficient of −0.280 indicates that a 1-unit increase in household savings reduces income inequality with a factor of 0.280 in the short run. The ${HHS}^{-}$ coefficient of 0.160 suggests that a 1-unit decrease in household savings increases income inequality with a factor of 0.160 in the short run. A $D.{CS}^{+}$ coefficient of −0.180 implies that increases in corporate savings have a significant negative effect on income inequality with a factor of 0.180 in the short run. A $D.{CS}^{-}$ coefficient of 0.090 indicates a smaller positive effect on inequality when corporate savings decrease with a factor of 0.090 in the short run. The ${D.GS}^{+}$ coefficient of −0.140 shows that increases in government savings correlate with lower income inequality with a factor of 0.140 in the short run. A ${D.GS}^{-}$ coefficient of 0.100 suggests that decreases in government savings may contribute to higher inequality, albeit with less significance with a factor of 0.100 in the short run. The $D.IR$ coefficient of 0.240 indicates that higher interest rates are associated with increased income inequality in the short run with a factor of 0.240 in the short run. A $D.INF$ coefficient of 0.290 implies that rising inflation correlates positively with income inequality with a factor of 0.290 in the short run. The $CointEq(-1)$ coefficient of −0.620 suggests a strong error correction mechanism, indicating that deviations from the long-run equilibrium are corrected by approximately 62% in the following period. The differing effects of positive and negative changes in savings underscore the complex dynamics at play and can inform policy recommendations aimed at reducing inequality.

In Table 9, The ${∆HHS}^{+}$ coefficient of −0.350 indicates that a 1-unit increase in household savings is associated with a reduction in income inequality by a factor of 0.35 in the long-run, suggesting that saving behavior has a beneficial impact on equity. The ${∆HHS}^{-}$ coefficient of 0.175 suggests that a 1-unit decrease in household savings tends to increase income inequality by a factor of 0.175 in the long-run. A ${∆CS}^{+}$ coefficient of −0.200 implies that increases in corporate savings lead to a decrease in income inequality by a factor of 0.200 in the long-run, indicating potential reinvestment in labor or social initiatives. A $∆{CS}^{-}$ coefficient of 0.100 suggests a smaller but positive impact on inequality when corporate savings decrease by a factor of 0.100 in the long run. The ${∆GS}^{+}$ coefficient of −0.150 indicates that higher government savings contribute to reduced income inequality, likely through public investments or social programs by a factor of 0.150 in the long-run. A ${∆GS}^{-}$ coefficient of 0.110 indicates that lower government savings could lead to increased inequality by a factor of 0.110 in the long run. The $∆IR$ coefficient of 0.280 shows that higher interest rates are associated with increased income inequality by a factor of 0.280 in the long run, potentially due to higher borrowing costs for lower-income households. The $∆INF$ coefficient of 0.310 suggests that rising inflation is positively correlated with income inequality by a factor of 0.310 in the long-run, indicating that inflation disproportionately affects lower-income households. These results illustrate the dynamics of savings and economic factors on income inequality. The coefficients provide insights into how positive and negative changes in savings can have differing impacts, emphasizing the need for targeted economic policies to address inequality effectively.

4.3.3. Influence of the EPI on Savings Decisions in South Africa

Table 10. Short-run effect of savings behavior on EPI.

Variables	Variable Name	Coefficient	Standard Errors
$D.{HHS}^{+}$	Household Saving	0.120 **	0.050
$D.{HHS}^{-}$	Lagged household savings	−0.050	0.045
$D.{CS}^{+}$	Corporate savings	0.180 **	0.060
$D.{CS}^{-}$	Lagged corporate savings	−0.100 *	0.055
${D.GS}^{+}$	Government savings	0.090	0.055
${D.GS}^{-}$	Lagged government savings	−0.150 **	0.050
$D.IR$	Interest rate	0.050 **	0.025
$D.INF$	Inflation	0.040 **	0.020
	$CointEq(-1)$	0.200 ***	0.050

*** 1 percent level of significance, ** 5 percent level of significance, * 10 percent level of significance. Note: Dependent Variable: GDP growth; Sample: 2000–2023; Observations: 24; R-squared: 0.78; F-statistic: 8.19; EPI = Adjusted Emissions Growth Rate for Carbon Dioxide. Source: results estimates.

and

Table 11. Long-run effect of savings behavior on EPI.

Symbol	Variables	Coefficient	Standard Error
${∆HHS}^{+}$	Household Savings Positive	0.150 **	0.045
${∆HHS}^{-}$	Household Savings Negative	0.038 **	0.038
${∆CS}^{+}$	Corporate Savings Positive	0.200 ***	0.050
$∆{CS}^{-}$	Corporate Savings Negative	−0.050	0.040
${∆GS}^{+}$	Government Savings Positive	0.100 *	0.055
${∆GS}^{-}$	Government Savings Negative	0.075 **	0.042
$∆IR$	Interest Rate	0.030 **	0.015
$∆INF$	Inflation	−0.050 **	0.020
	Constant	1.500 **	0.400

*** 1 percent level of significance, ** 5 percent level of significance, * 10 percent level of significance. Note: Dependent Variable: GDP growth; Sample: 2000–2023; Observations: 24; R-squared: 0.82; F-statistic: 9.71. Source: results estimates.

captures short-run effect of savings behavior on EPI and long-run effect of savings behavior on EPI respectively.

In Table 10, positive changes in household savings are associated with a significant increase (by a factor of 0.12) in emissions growth rate for carbon dioxide at 5% level of significance in the short run. However, negative changes in household savings have no significant effect (−0.050, p = 0.268) on in emissions growth rate for carbon dioxide at 5% level of significance, suggesting short-run asymmetry. Conversely, positive changes in corporate savings lead to a significant increase in emissions growth rate for carbon dioxide at 5% level of significance in the short run, while negative changes in corporate savings have a marginally significant negative effect on emissions growth rate for carbon dioxide at 5% level of significance, indicating some degree of short-run asymmetry. Positive changes in government savings are not associated with a significant increase in emissions growth rate for carbon dioxide at 5% level of significance in the short run. Negative changes show a significant decrease in emissions growth carbon dioxide at 5% level of significance, indicating strong short-run asymmetry. Furthermore, a rise in interest rates correlates with a significant increase in emissions growth rate for carbon dioxide while inflation also has a positive and significant effect on emissions growth at 5% level of significance in the short run. The $CointEq(-1)$ coefficient of −0.200 suggests a strong error correction mechanism, indicating that deviations from the long-run equilibrium are corrected by approximately 20% in the following period.

In Table 11, positive changes in household savings lead to a significant increase in emissions growth rate for carbon dioxide at a 5% level of significance in the long run. Negative changes in household savings result in a significant decrease in emissions growth at a 5% level of significance in the long-run, indicating a long-run asymmetry. The positive changes in corporate savings have a substantial positive impact on emissions growth rate for carbon dioxide at 5% level of significance in the long run. The corporate savings effect of negative changes (−0.05) is not statistically significant at a 5% level of significance in the long-run. Positive changes in government savings are associated with a 0.10 increase in the emissions growth rate for carbon dioxide but are marginally significant at a 10% level of significance in the long run. Negative changes have a significant negative impact on the emissions growth rate for carbon dioxide at a 5% level of significance, also indicating long-run asymmetry. A rise in interest rates correlates with an increase in emissions growth at a 5% level of significance while inflation has a positive and significant effect on the emissions growth rate for carbon dioxide at a 5% level of significance in the long run.

4.4. Discussion of Results

4.4.1. The Effect of GDP Growth Rate and Savings Behavior in South Africa

The results of this study indicate that household, corporate, and government savings significantly contribute to GDP growth in the short and long-run, while higher interest rates negatively affect growth. This research’s findings support several conventional growth theories, such as [16,50]. It is important to stress that these findings are consistent with the different growth theories covered in the theoretical study. The results of the analysis assist us in identifying areas in which greater focus is needed to increase domestic savings, which in turn can stimulate greater investments and quicken sustainable economic growth. Increased investments are only possible when savings are greater. According to the analysis, less government spending increases national savings and encourages private-sector investment. Over time, higher investment levels may raise the potential and actual output levels of the economy.

The effect of savings on sustainable economic growth has been the subject of further investigation [51,52,53]. The results of the studies demonstrated that while saving and sustainable economic growth have a substantial link, experts continue to disagree about the exact causal relationship between the two variables. Higher savings typically occur before and after more robust economic expansion, according to [16]. A study by [54] suggests that higher capital production results from increased saving, which contributes to the understanding of how savings affect economic growth. The analysis also showed an increase in investment, which aided in the growth of the country’s GDP. Solow’s claims were followed by several scholars, including [55,56], who noted that higher savings growth precedes higher economic growth. More studies by scholars including [54,57,58] revealed that higher economic growth comes before and is a cause of higher savings.

It should be mentioned that the research’s findings support several conventional growth theories, such as [16,50]. According to these growth models, increasing savings increases growth by increasing the amount of domestic capital available. This accelerates the accumulation of physical capital, which is considered to be the main engine of sustainable economic growth. In light of this, it may be said that domestic savings are an essential marker and requirement for higher rates of sustainable economic growth. Several economists have conducted additional research, which has shown that the relationship between savings and growth is probably overstated. This supports the theory that savings drive growth instead of the other way around, as demonstrated by [54,59,60].

4.4.2. The Impact of Income Inequality on Savings Patterns in South Africa

The results of this study indicate that household and corporate savings positively influence income equality in the short and long run. This suggests that higher household savings may facilitate better access to resources, such as education and healthcare, which can contribute to a more equitable income distribution. When households save, they may invest in opportunities that enhance their earning potential, thereby reducing inequality over time. Further, positive influence of savings on income inequality suggests that when corporations save and reinvest their profits (rather than distributing them solely as dividends), it can lead to job creation and wage growth, benefiting a wider segment of the population. These results are consistent with [24,25,61]. For example, [24] found that income inequality positively impacts on households’ savings. This result is inconsistent with [26,27,62]. Similarly, ref. [25] examined 48 countries for the period 1991–2010 and demonstrated that aggregate saving ratio increases with income inequality using various inequality measures. Ref. [26] examined analytically and empirically the links between income distribution and aggregate saving and found out that there is no support for the notion that income inequality has any systematic effect on aggregate saving. The results also suggest that increases in government savings correlate with lower income inequality, in the short and long run. This finding suggests that higher government savings may come at the expense of public spending on social services, infrastructure, and welfare programs that help reduce income inequality. If the government saves excessively without adequately investing in programs that promote equity, it could exacerbate disparities in income. The interest rates have negative effects on income equality in the short and long run. Moderate inflation appears to have a slight positive impact, though the evidence is not as strong. These findings underscore the importance of savings behaviors and economic policies in shaping income distribution, suggesting that promoting household and corporate savings could be beneficial for improving income equality.

4.4.3. Influence of the EPI on Savings Decisions in South Africa

This results for long-run NARDL model provides valuable insights into how savings behaviors and macroeconomic factors contribute to emissions growth rate of carbon dioxide over time. Understanding these dynamics can help inform policymakers aiming to mitigate emissions while considering the economic implications of saving and spending behaviors. For instance, both household and government savings exhibit long-run asymmetry, where increases in savings tend to boost emissions, while decreases in savings lead to reductions. This indicates that in the short and long-run, an increase in household savings is associated with a significant increase in emissions growth [63,64]. This suggests that as households save more, there may be associated economic activities (like increased consumption or investment) that lead to higher emissions [65]. Similarly, a substantial long-run positive effect of corporate savings on emissions growth means that higher corporate savings lead to a significant increase in emissions growth. This could imply that corporations investing more (through savings) may engage in activities that boost emissions, such as expanding production or increasing energy consumption [66,67]. Corporate behavior, however, the strong positive effect of corporate savings on emissions growth emphasizes the need to consider how corporate investments and savings decisions affect environmental outcomes. Conversely, interest rates and inflation are significant factors affecting emissions in the long run. For instance, a positive and statistically significant effect of interest rate on emission suggests that higher interest rates are associated with increased emissions growth. This may imply that rising interest rates encourage certain economic behaviors that elevate emissions, perhaps by affecting investment decisions or consumption patterns. This coefficient of inflation is statistically significant at 5% level of significance, indicating that in the long run, higher inflation rates are linked to an increase in emissions growth. Inflation can influence purchasing power and consumption habits, potentially leading to higher emissions.

4.4.4. Model Stability Test

The CUSUM and the CUSUM of squares conversations have been used in this work to test the stability of this model. The red dotted lines in both figures indicate the bounds of the 5% significance level. It is clear that the model fulfills both the CUSUM Test (Figure 1) and CUSUM of squares test (Figure 2) conditions at the 5% significance level because the model’s blue line stays inside the red dotted lines. The calculated ARDL long-run model was therefore shown to be both structurally and dynamically stable by the stability test results.

5. Conclusions and Policy Recommendation

5.1. Conclusions

It is necessary to comprehend how to increase domestic savings rates to contribute to the continuing discourse about sustainable economic growth in South Africa. South Africa has to raise its domestic savings rates to lay the groundwork for future economic growth, given its current over-reliance on foreign funding. The study used the ARDL bond test to look at how domestic savings impact sustainable economic growth. The diagnostic tests of the ARDL model were adequate. The HHS and COS coefficients were significant at 95% and 90% confidence levels, respectively, whereas the GOS coefficient was significant at 90%. The empirical results about the correlation between domestic savings and sustainable economic growth in South Africa underscore the significance of saving for the advancement of the nation. Given that families and GOS make up such a small portion of national savings, it should come as no surprise that COS has the biggest influence on economic growth. The model passed the stability diagnostics as well, but the CUSUM stability test showed some shocks from the CUSUM of squares test. The model derived from this research validates savings as the primary catalyst for sustainable economic expansion, with an $R^2$ of 0.999. The significance of savings for national growth is demonstrated by an empirical analysis of the relationships between domestic savings and sustainable economic growth in South Africa. It should come as no surprise that COS has the largest influence on sustainable economic growth given the negligible contributions that GOS and households make to national savings.

5.2. Policy Recommendation

5.2.1. Analyzing the Effect of GDP Growth Rate and Savings Behavior

One potential policy is the promotion of national savings incentives that specifically target individuals and businesses. This could involve creating tax benefits for contributions to savings accounts, particularly for low- and middle-income households [68]. By encouraging higher savings rates, the policy aims to facilitate increased capital formation, crucial for driving investments and ultimately fostering GDP growth [10]. This result demonstrates that higher savings rates can lead to enhanced economic stability and development, as they provide a buffer against economic shocks [69]. Moreover, by directing savings into sustainable investment vehicles, such as green bonds, the policy can also align financial growth with environmental objectives, creating a dual benefit for both the economy and the planet.

5.2.2. Assessing the Impact of Income Inequality on Savings Patterns

South Africa is one of the countries with very high-income inequality. As a result, a critical approach to addressing income inequality is the implementation of a progressive taxation system combined with effective redistribution programs [70]. By raising tax rates on higher income brackets and redistributing these funds towards savings programs for lower-income households, the policy can increase disposable income for those most in need. Studies show that income redistribution can significantly improve savings behavior among lower-income populations, thereby fostering economic growth [71]. This approach not only aims to reduce the wealth gap but also promotes financial security for disadvantaged groups, enhancing their capacity to save. Additionally, the funds generated from progressive taxation can be allocated to educational programs that emphasize financial literacy and sustainable practices, further bridging the economic divide while promoting environmental awareness.

5.2.3. Investigating the Influence of the Environmental Performance Index on Savings Decisions

Incorporating the Environmental Performance Index (EPI) metrics into financial literacy programs represents a proactive policy to shape consumer behavior toward sustainability [66]. By educating the public about the correlation between environmental performance and financial savings, the policy encourages individuals to make informed decisions that favor sustainable investments. This can lead to a shift in market dynamics, with increased consumer demand for environmentally responsible products and services, ultimately benefiting both the economy and the environment [48]. Furthermore, as awareness of EPI metrics grows, individuals and businesses may allocate their savings toward initiatives that improve environmental outcomes, creating a virtuous cycle where financial decisions support ecological sustainability.

These policies collectively aim to create a more resilient and equitable economic landscape in South Africa. By promoting savings behavior linked to GDP growth, addressing income inequality through progressive taxation, and fostering environmental consciousness via financial literacy, South Africa can enhance its economic stability while committing to sustainable development. In this way, the interconnectedness of economic and environmental considerations can be effectively harnessed to achieve a more prosperous and sustainable future.

5.3. Areas for Future Research

The findings of the research have inspired the researcher to recommend future research that will focus on a more in-depth analysis of COS and explore more innovative ways to enhance and encourage greater savings by the sector. This is especially important because of the significant contribution towards the national savings relation. It is also an uncommon phenomenon in emerging markets that normally reflects HHS to be the dominant contributor.