On the Dynamic Relationship between Household Debt and Income Inequality in South Africa

Abstract

This paper analyses the relationship between household debt and income inequality in South Africa for the period 1980–2021. We use two measures of inequality and estimate a vector error correction model (VECM) which includes household debt, inequality, and other macroeconomic variables. To test the robustness of our results, single equation models are used, which estimate household debt as a function of inequality and macroeconomic factors. We employ two measures of inequality, namely Gini coefficient and ratio of top and bottom income earners’ proportion of income. Furthermore, we use both household debt as a percentage of disposable income and household debt service costs as dependent variables in single equation regressions. The study finds a negative and significant relationship between household debt and income inequality in the long run, which contradicts the Rajan hypothesis in the South African case. Rather, we find that inequality in South Africa creates a bias in debt allocation towards high-income earners, whose incomes can easily absorb the extra debt (reduced ratio of debt to disposable income). There are therefore no socio-equity considerations in South African credit markets. We find growth in gross domestic product (GDP) per capita also has a moderating effect on the relationship between household debt and income inequality. High GDP per capita growth in the presence of high inequality reduces the impact of inequality on household debt and vice-versa. All other control variables take expected signs. These results are robust to changes in the inequality or household debt measures.

1. Introduction

Credit markets play a vital role in modern financial systems, granting economic agents access to financial resources required for investment and consumption smoothing across different sectors. Scholars argue that a deeper financial system improves market efficiency and fosters economic growth by enhancing capital allocation, facilitating risk management, mobilizing savings for investment, expanding credit access, and developing efficient payment systems (Apergis et al. 2007; Odhiambo 2009; Zhou and Dev 2020). These factors collectively contribute to a resilient and dynamic financial sector, driving economic development and prosperity. In this sense, financial development is therefore expected to result in improved welfare among economic agents. On the backdrop of such evidence, Rajan (2011) linked credit expansion in the United States of America (US) to rising inequalities.

In the case of South Africa, however, whilst both household debt and income inequality have soured, there has been no comprehensive empirical studies on their relationship. The few studies available on household debt in South Africa present an incoherent and incomplete analysis of the relationship between household debt and income inequality (Kereeditse and Mpundu 2021; Lombardi et al. 2017). This gap in the literature is surprising as South Africa is ranked as the most unequal country in the world. According to the Organisation for Economic Co-operation and Development (OECD), the nation’s Gini coefficient stands at an alarming 62% as of 2020. Additionally, there has been a discernible surge in household debt within the country in recent years.

Considering this background, our research aims to comprehensively explore the intricate correlation between household debt and income inequality within the South African context. As a departure from previous research, our study also delves into the ramifications of debt servicing costs for households, unemployment rates, gross domestic product (GDP) per capita, savings behavior, and housing prices. Our specific objectives therefore encompass several crucial aspects, including (1) investigating the impact of income inequality on household debt, (2) examining the determinants of household debt with a particular emphasis on inequality, and (3) exploring the moderating influence of economic growth. Additionally, our research contributes noteworthy insights to the existing literature by empirically examining the Rajan Hypothesis in the context of South Africa.

We hypothesize that the democratic government in South Africa could have utilized credit liberalization as a policy tool to stimulate consumption and address inequalities, aligning with practices witnessed in more advanced economies. This policy entails making borrowing money more accessible, which can involve actions such as lowering interest rates, easing lending requirements, or broadening credit availability. Our contention is that the democratic government could have utilized credit liberalization to boost consumption within the lower- and middle-income segments. This approach could have contributed to lessening income inequality by enhancing the purchasing capability of these groups.

The remainder of the paper is organized as follows: Section 2 provides a review of the literature on the relationship between household debt and income inequality. Section 3 outlines the methodology employed in the paper, while Section 4 presents the results of our analysis and discusses them in the context of the previous literature and the objectives of this study. Section 5 concludes the article.

2. Literature Review

We position this paper within the literature that links inequality to household debt or broader financial development. In the discussion below, we first provide a survey of the literature on inequality in South Africa. Subsequent to this, we review the literature that links inequality to household debt. Lastly, we provide some of the recent empirical literature on the links between inequality and broader financialization.

2.1. Inequalities in South Africa

In South Africa, the origins of inequality can be traced back to racial and class disparities that have been shaped by the legacies of colonialism and apartheid (Francis and Webster 2019; Wilson 2011). These disparities have been further reinforced by legislative actions, resulting in substantial gaps in wealth and income distribution (Francis and Webster 2019; Wilson 2011; Fortuin et al. 2022). Despite efforts to address poverty and inequality since the end of apartheid, there is a need for further investigation to evaluate the effectiveness of these measures (Wilson 2011). The International Monetary Fund (IMF 2020) identified three main drivers of inequality in South Africa, which includes (1) a lopsided income distribution, (2) unequal access to opportunities, and (3) regional disparities, while the rising unemployment and slow economic growth are also factors contributing to the perpetuation of inequality.

Leibbrandt et al. (2012) provides an analysis of post-apartheid inequality in South Africa. They show that inequality in the post-apartheid era was largely driven by skewed accrual of income to the higher-income group. They find disparities in incomes among different income groups in the job market as well as different races. Their study decomposes the sources of income inequality and finds that both access to labour market opportunities and disparities in labour incomes contribute to the aggregate inequality. Their findings are corroborated by Hundenborn et al. (2018), who investigates the drivers of inequality in South Africa between 1993 and 2014. Hundenborn et al. (2018) find labour market income disparities to be the main driver of income inequality. It is worth noting, however, that as measured by the Gini coefficient, inequality has declined albeit slowly for South Africa since 2008. In 2008 the Gini coefficient for South Africa peaked at 0.69 but decreased to 0.63 by 2021 while wealth inequality had a staggering 0.95 Gini coefficient (Orthofer 2016).

The financial sector in South Africa has continued to expand, and Aron and Muellbauer (2013) among others have argued for the role of credit market liberalization in increasing consumption. Lagoa and Barradas (2020) notes the expansion of financial services due to increased financialization in recent years. The South African financial sector is highly liquid and relatively deep compared to its African and other developing economy counterparts such that it has proved to be resilient in the face of external shocks. Thus, throughout both the apartheid era and the new democratic period, household debt has continued to grow to supplement consumption. Ssebagala (2017) among others bemoans over indebtedness among households in South Africa. This noticeable increase in over indebtedness and persistent low levels of savings among the low-income households point to greater credit risk, and possible increase in inequality. However, this growth in South African credit markets has been experienced within a tightly regulated system (Botha and Makina 2011), in which access to credit has largely been restricted for low-income households who lack assets for collateral.

Elsewhere, Bordo and Meissner (2012) and Rajan (2011) attribute inequality in the US and the United Kingdom (UK) to poor public education, which contributes to lack of access to employment opportunities. This could be the same case in South Africa, where the majority of African population were disadvantaged educationally during the apartheid period. In addition, the public education system has lagged widely compared to private schools due to lack of infrastructure, qualified personnel, and equipment. This has entrenched lower levels of skills amongst low-income groups, relegating them to lower paying employment opportunities. Furthermore, access to post school education has been identified as an important variable in driving inequality in South Africa (Branson et al. 2012). Branson et al. (2012) show that higher-income groups and individuals from some races tend to experience more schooling years compared to learners from low-income groups. Rogan and Reynolds (2016) also identify graduate unemployment as a factor in determining incomes. Graduate unemployment has been attributed to the mismatch between higher education pedagogy and skills required by industry. According to Rogan and Reynolds (2016) graduate unemployment in South Africa is driven by race, resulting in further racial inequalities.

However, in the post-apartheid era, the nature of observed response to the high inequality has been different from the US case as propounded in the Rajan hypothesis. Branson et al. (2012) and Leibbrandt et al. (2012) argue that social security support has been the main instrument used to counter income inequality in South Africa. The South African government responded to inequality through various types of social grants and interventions designed to provide equal access to opportunities. Legislation was formulated to promote equal access to opportunities and redress injustices of the apartheid era, including the Employment Equity Act of 1998 (as amended in 2013). However, despite concerted government efforts to reduce inequality, the Gini index continues to remain high.

2.2. Theoretical Literature on Inequality and Household Debt

Rajan (2011), put forth a significant perspective on the relationship between inequality and the development of the credit market in his book “Fault Lines”. He suggested that the surge in lending activity and the significant rise in housing prices were the underlying causes of the banking and financial crisis of 2008–2009. Rajan (2011) contended that the escalating income inequality in the US over the previous three decades had generated political pressure to address the issue through redistribution measures. In response to this pressure, policymakers in the US introduced housing finance subsidies to enhance access to mortgage credit for low-income households who would have otherwise been ineligible. The proposition is supported in various empirical studies including Destek and Koksel (2019), Chang et al. (2020), and El-Shagi et al. (2020). This supports the finance-inequality narrowing hypothesis, which contends that well-functioning financial markets reduce inequalities (Cong Nguyen et al. 2019). Moreover, the international literature on inequality and household debt is inconsistent as some empirical studies have concluded a positive relationship whilst on the other hand others have found the relationship to be negative (Berisha et al. 2021; De Vita and Luo 2021; Lombardi et al. 2017). Xu (2022), for instance, uses a systematic literature review and finds the Rajan hypothesis questionable. Their study argues for consideration of the variables used in empirical studies and how they are interpreted. In Xu’s (2022) study only one study supported the hypothesis.

The debate on inequality and household debt has grown into other jurisdictions (Bazillier and Hericourt 2017; Gu et al. 2019; Wood 2020; Rajan 2011). Bazillier and Hericourt (2017) review the literature on the linkages between inequality and household debt and raise two important issues. Firstly, the need to analyze how inequality impacts both demand and supply of credit. They caution that the causality between financialization and inequality could only reflect the two variables’ trends in the recent periods. Their second assertion concerns the presence of reverse causality between inequality and household debt, which has been confirmed by various studies (Lin and Tomaskovic-Devey 2013; Roberts and Kwon 2017). Therefore, it is worth drawing to the reader’s attention that household debt can also play a moderating function in the intersection between various types of inequality. For instance, consumer credit can temporarily ease off inequalities in current consumption (Rajan 2011); student loans can lessen inequalities in opportunity by enabling access to higher education; and workers frequently use their incomes to access mortgage debt in order to lessen the perceived wealth inequalities between households.

Bazillier and Hericourt (2017) distinguish between permanent and transitory income shocks and their impact on consumption and household debt. In line with Krueger and Perri (2006), they argue that within group income inequalities are more transitory, whereas between group inequalities derive from permanent income shocks. If consumers believe income shocks to be transitory, they can use credit markets to smooth out consumption. On the other hand, permanent income shocks induce households to adjust their consumption, which leaves household debt unchanged. It is this later assertion that is disputed by several other theories, which show that permanent income shocks have also been observed to be followed by increases in household credit (Bazillier and Hericourt 2017; De Vita and Luo 2021; Kumhof et al. 2015). Thus, apart from short-run volatility in incomes (transitory income shocks), the authors provide several other reasons that result in the responsiveness of household debt to increases in income inequality. Firstly, households do not adjust their consumption completely depending on the total welfare loss induced by the income shock, thus leaving room for debt. The second argument hinges on the ‘keeping up with the Joneses’ proposition, which asserts that household’s consumption does not only depend on current income but a certain benchmark level of consumption (Christen and Morgan 2005; Bazillier and Hericourt 2017; Hake and Poyntner 2022). Kumhof et al. (2015), also argue for households borrowing to smooth out consumption as a result of a loss in permanent income. In addition, the structure and growth of credit markets also has a role to play in determining credit supply to households in response to an increase in income inequality (Bazillier and Hericourt 2017).

2.3. Recent Empirical Literature on Inequality and Household Debt

Piao et al. (2023) employ a vector autoregressive (VAR) model in analyzing the relationship between income inequality, household debt, and consumption and find inequality to positively influence household debt. Their findings are further supported by Jestl (2022), who finds a positive relationship between income inequality and household debt for the European union (EURO). Hake and Poyntner (2022) investigate the impact of income inequality on household debt. Their findings suggest an increase in credit to high-income earners and decrease in credit for low-income earners in response to income inequality shocks. In addition, some studies have investigated the relationship between income inequality and other measures of financial development (Koh et al. 2020; Thornton and Tommaso 2020; Sotiropoulou et al. 2023). Whilst broader measures of financial development signal the importance of income inequality in driving financial depth, Xu (2022) argues that some measures may not be appropriate in explaining the finance-inequality conundrum. Instead, household debt and specifically mortgage debt is argued to be more appropriate in the analysis.

Some recent studies have argued for an asymmetric relationship between income inequality and household debt (Cheah et al. 2022; Wang 2023). Fasianos et al. (2016) used data from 1913 to 2008 and found evidence of an asymmetric cointegration between household debt and income inequality in the US, with household debt only responding to positive changes in income inequality. Berisha and Meszaros (2017) used ordinary least squares (OLS) regressions to understand the relationship between household debt, income inequality, and economic growth in the United States. Using household-level debt data over a period of 2000–2012 and local variation in inequality, Coibion et al. (2020) found that low-income households in high-inequality regions (zip-codes, counties, states) accumulated less debt relative to their income than low-income households in lower-inequality regions. Belabed et al. (2018) suggested that a substantial part of the increase in household debt and the decrease in the current account in the United States since the early 1980s can be explained by the interplay of rising (top-end) household income inequality and institutions, while Johnston et al. (2020) argued that variation in household debt can be explained by the intersection of two domestic institutions namely the labor market institutions that enable households to withstand negative employment/income shocks, and mortgage finance institutions that govern households’ credit access.

Other studies that examined the relationship between household debt and inequality includes Berisha et al. (2015) who tested for a cointegrating relationship between household debt and income inequality by estimating Johansen’s and Engle and Granger’s cointegration tests to determine if a cointegrating relationship exists between household debt flows and income inequality in the US. They found that increases in the stock market and household debt raise income inequality and that the relationship between the interest rate and income inequality is found to be negative and statistically significant. Lim (2019) examined the impact of changes in income inequality on household indebtedness using a heterogeneous panel vector autoregressive (VAR) model and found evidence in support of large cross-country heterogeneity in the responses of household leverage to income inequality shocks. The authors find that such heterogeneity stems from differences in the strength of financial regulations and supervision.

Shin analyzed data from the Survey of the Household Finance and Living Conditions in South Korea and found that wealth, employment status, family size, and education are significant contributors to income inequality. Bazillier et al. (2021) analyzed a country-level dataset over the period 1970–2017 and found that found that increases in income inequality leads to a rise in of household debt, particularly when inequality is measured by the ratio of top incomes to middle incomes, rather than the ratio of top incomes to bottom incomes. Cheah et al. (2022) used the nonlinear autoregressive distributed lag model to examine the potential asymmetries between household debt and income inequality within long-run and short-run relationships. They found that the association between income inequality and household debt is asymmetric in the long and short run. The authors showed that only decreases in income inequality had a significant and positive effect on household debt, while increases in income inequality did not have a significant effect.

The disproportionate impact on household debt between low-income earners and high-income earners has also received attention. In the UK, for instance, Berisha et al. (2021) opine that credit cycles have been characterized by an increase in debt among lower- and middle-income households whereas higher-income earners have tended to increase savings at the same time. Thus, increased debt uptake by low-income earners enables creditors (high-income earners) to increase their interest earnings and hence increase their savings and wealth. This scenario results in increased income inequality as the poor’s conditions worsen whereas the rich become richer. On the other hand, if a shock in inequality results in high credit up-take by low-income earners, their welfare worsens in comparison to high-income earners.

3. Materials and Methods

The study employs annual time series data for South Africa for the period from 1980 to 2021. However, the period sample of the data is constrained by availability of data for measures of inequality, which is also only available at annual frequency. The data used in the study has been provided together with the paper (see link under Supplementary Materials). The variables used to measure inequality in the study are the Gini coefficient and the ratio of top 10% to bottom 50% income proportions. The data for inequality is accessed from World Inequality Database (WID) data. Household debt is measured by the proportion of household debt to disposable income, and the data is obtained from the South African Reserve bank (SARB). In addition, we also use the debt service costs for households, the data of which we obtain from the SARB. We account for economic growth by employing gross domestic product per capita $(GDP\_cap)$. Other variables included are also obtained from the SARB and these include unemployment, national savings, and house prices. We transform GDP per capita and the Gini coefficient into logarithms and use the ratio of total savings to real GDP at market prices in our computations.

We pay attention to the issue of nonstationarity observed in macroeconomic and financial time series. Therefore, this paper firstly tests for stationarity of all variables before conducting estimations. Standard econometric procedure is followed where variables are tested for stationarity and cointegration before model estimations are undertaken. We employ the test proposed by Philips and Perron (1988) to test for unit roots in all the series.

3.1. Cointegration

Cointegration is tested using the Johansen (1988) cointegration test. Nonstationary time series are integrated if they display a long run equilibrium relationship. A nonstationary time series can be transformed through differencing to become stationary. A series that becomes stationary after first differencing is said to be integrated of order 1 or I (1). It is worth drawing the reader attention that new variables are tested for normality and stationarity, after they have been normalized by division. We employ the Johansen cointegration technique to test the presence of cointegration between the model vairables. Meniago et al. (2013) argues that this method is most suitable for multivariate time series analysis, and it tests the null hypothesis of no cointegration against the alternative hypothesis of the existence of cointegration. It uses two likelihood ratio (LR) test statistics, the trace statistic, and the maximum eigen value statistic to show the number of cointegrating vectors. Equations (1) and (2) show the derivation of the trace and max-eigen value statistics.

$$\lambda trace\left(r\right)=-Tln\Sigma ni=r+1(1-\lambda )$$

(1)

$$\lambda max(r,r+1)=-Tln(1-\lambda r+1)$$

(2)

where $\lambda$ are the estimated eigenvalues, $r$ is the rank of the long run matrix, $T$ is the number of observations, and $n$ is the number of endogenous variables.

3.2. VAR/VECM Model

Once the number of cointegrating vectors has been determined, the next step is to estimate vector error correction model (VECM), which depends on the stationarity properties of the data. The advantage of the VECM approach is that it is a multivariate method that can account for more than one cointegrating vectors (Meniago et al. 2013; Enders 2008). Therefore, this study uses the VECM approach.

The main purpose of a VECM is to estimate the long-run relationship and short-run dynamics of a multivariate equation. The higher the magnitude of the error correction term, the faster the adjustment to equilibrium (Uwubanmwen and Ajao 2012). Borrowing from (Verbeek 2008), the vector error correction model can be represented as follows:

$$\Delta Y_t=\mu +{\Gamma }_1\Delta Y_{t-1}+{\Gamma }_2\Delta Y_{t-2}+\cdots \dots .+{\Gamma }_{k-1}\Delta Y_{t-(k-1)}+\prod Y_{t-1}+\epsilon t$$

(3)

where $Y_t$ is a vector of I (1) variables and $\mu$ is a vector of intercepts. ${\Gamma }_1$_, ${\Gamma }_2$_, ${\Gamma }_{k-1}$ are vectors of parameters. $\prod$ is a long run matrix, which determines the long-run dynamics of $Y_t$. It can be shown that if $\prod$ has a reduced rank it can be written as a product of $\gamma$ and β′, where $\gamma$ is a $kxr$ matrix and β′ is an $rxk$matrix, both of rank $r$. Thus ∏ = γβ′. In Equation (3) ∏Y_t−1 becomes $\mathsf{\gamma }{\mathsf{\beta }}^{\prime }{Y}_{t-1}$, in which ${\mathsf{\beta }}^{\prime }{Y}_{t-1}$ represent the $r$ cointegrating relationships. The coefficients in the matrix $\gamma$ measure how the elements in $\Delta Y_t$ are adjusted to the $r$ equilibrium errors ${\mathsf{\beta }}^{\prime }{Y}_{t-1}$ and are referred to as the error correction terms (ECT)_. Assuming only one cointegrating vector, our study focuses on the following relationship:

$$\begin{array}{l}\Delta {HDEBT}_t={\alpha }_1+{\sum }_{l=1}^p{\beta }_1{\Delta HDEBT}_{t-l}+{\sum }_{l=1}^p{\beta }_2{\Delta LGINI}_{t-l}+{\sum }_{l=1}^p{\beta }_3{\Delta LGDP\_cap}_{t-l}+\\ {\sum }_{l=1}^p{\beta }_4{\Delta UNEMPL}_{t-l}+{\sum }_{l=1}^p{\beta }_5\Delta {HSE\_PRYC}_{t-l}+{\sum }_{l=1}^p{\beta }_6\Delta {SAVRATIO}_{t-l}+{\delta }_1{ECT}_{t-1}+{\epsilon }_t\end{array}$$

(4)

In Equation (4), ${\delta }_1$ is the coefficient of the error correction term, which shows how short-run deviations from the equilibrium will be corrected between the different periods. We expect the sign of ${\delta }_1$ to be negative and statistically significant. The variables are defined as follows: $HDEBT$ represents household debt as a percentage of disposable income; $LGINI$ is the logarithm of the Gini coefficient;${LGDP\_}_{cap}$ is the logarithm of GDP per capita; $UNEMPL$is the official unemployment rate; $HSE\_PRYC$ represents house prices; and $SAVRATIO$ is the ratio of national savings to real GDP at market prices.

In addition, for robustness testing, we also estimate a single equation model using Stock and Watson (1993)’s dynamic ordinary least squares, which provides long-run elasticities. This method is preferred due to its robustness in small samples. In Monte Carlo simulations, the method is shown to be more favorable compared to the Engle Granger two-step method or Philips and Hanson fully modified ordinary least squares method (Stock and Watson 1993). We further use the ratio between the proportion of income accruing to the top 10% and that of the bottom 50% ($TB50$) as an alternative measure of income inequality. We also use household/consumers’ debt service costs ($DSERV$) as an alternative measure of household debt.

4. Results

In this section, we present and discuss the results from our data analysis. In line with common quantitative analysis, we start by presenting the univariate characteristics of the series used in the study, the test for stationarity, and the test for cointegration. On the basis of both the stationarity and cointegration results, we estimate a VEC model. Furthermore, to check the robustness of our results, we estimate several models using the dynamic OLS method. Our results remain robust to these changes in estimation methods.

4.1. Descriptive Statistics

Table 1. Univariate characteristics of variables.

	HDEBT	UNEMPL	LGINI	LGDP_CAP	HSE_PRYC	SAVRATIO
Mean	0.56	21.95	−0.42	2.29	0.74	−0.04
Median	0.52	23.15	−0.42	2.31	0.74	0.04
Maximum	0.77	33.55	−0.27	2.44	1.22	0.48
Minimum	0.37	9.24	−0.54	2.05	0.41	−0.71
Std.Dev.	0.11	5.57	0.09	0.11	0.25	0.28
Skewness	0.31	−0.60	0.22	−0.51	0.10	−0.71
Kurtosis	1.72	2.84	1.46	2.06	1.42	2.94
Jarque-Bera (JB)	3.53	2.60	4.47	3.36	4.43	3.63
JBstatProbability	0.17	0.27	0.10	0.18	0.10	0.16
Sum	23.67	921.90	−17.68	96.45	31.19	−1.88
SumSq.Dev.	0.57	1274.03	0.40	0.57	2.74	3.21
Observations	42	42	42	42	42	42

The negative mean and median on the GINI coefficient indicate that we computed the logarithm of a decimal number. On the other side, the negative numbers on the savings ratio accounts for years during which national savings were negative. We compute the savings ratio as the ratio of national savings to real GDP at market prices. The variables enter the model with no further transformation.

shows the univariate characteristics of the variables used in the study. The total number of observations used in the study is 42 as indicated in the table. Whilst employing more observations for the model would have been desirable, unavailability of data for inequality either at higher frequency or for longer periods constrained the study to the period indicated. All variables depict normality as shown by the statistically insignificant Jarque–Bera test statistic (accompanied by the reported p-value below) and no outliers can be detected as variables have been normalized around the mean by taking logarithms where data was not already in percentage or decimal form. Skewness measures are small and near zero (0) which confirms the normal distribution assertion.

4.2. Stationarity Tests and Lag-Order Selection Criteria

Furthermore, analysing economic and financial time series requires an understanding of their stationarity properties. As alluded to earlier, we employ the Philips Perron test to test for unit roots among the time series. Our results shown in

Table A1. Stationarity Tests.

Variable	Philips Perron Statistics		Conclusion
	Level	1st Difference
$Lgdp\_cap$	4.39	−4.71 ***	I (1)
$Hdebt$	−1.53	−3.29 **	I (1)
$Dserv$c	−0.14	−4.31 ***	I (1)
$Gini$	−2.42	−4.88 ***	I (1)
$Tb50$	2.74	−4.97 ***	I (1)
$savratio$	−1.61	−5.94 ***	I (1)
$Hse\_pryc$	0.19	−3.43 ***	I (1)
$unempl$	−2.59	−6.31 ***	I (1)

*** and ** represents significant at 1% and 5% levels, respectively. The superscript $c$ shows the test included an intercept only. The null hypothesis for the test is that there is a unit root in the series.

in Appendix A reveal that all series employed in the model were of integration order one (I (1)). This means that they are non-stationary and have a unit root. To account for this, we need to use an error correction model (ECM). An ECM is a model that combines a regression model with an error correction term.

Table 2. VAR lag Order selection criteria.

Endogenous Variables: HDEBT LGINI LGDP_CAP UNEMPL HSE_PRYC SAVRATIO
Lag	LogL	LR	FPE	AIC	SC	HQ
1	408.60	NA	1.25 × 10−16	−19.61	−18.05 *	−19.05 *
2	449.49	55.95 *	1.08 × 10−16 *	−19.86	−16.75	−18.76
3	484.30	36.63	1.65 × 10−16	−19.80	−15.15	−18.14
4	525.54	30.38	2.95 × 10−16	−20.08 *	−13.87	−17.87

Meaning of abbreviations: LogL (log-likelihood value), LR (likelihood ratio test statistic), FPE (final prediction error), AIC (Akaike information criterion), SC (Schwarz information criterion), HQ (Hannan–Quinn information criterion). * refers to the number of selected lags.

and

Table 3. Cointegration Test.

Trace Statistic
Hypothesized		Trace	0.05	Prob. **
No. of CE(s)	Eigenvalue	Statistic	Critical Value	Critical Value
None *	0.70	133.28	95.75	0.000
$r\le 1$ *	0.55	85.95	69.81	0.002
$r\le 2$ *	0.44	55.16	47.86	0.009
$r\le 3$ *	0.41	32.18	29.80	0.026
$r\le 4$	0.20	11.40	15.49	0.188
Max-eigenvalue Statistic
Hypothesized		Max-Eigen	0.05	Prob. **
No. of CE(s)	Eigenvalue	Statistic	Critical Value	Critical Value
None *	0.70	47.33	40.08	0.006
$r\le 1$	0.54	30.79	33.88	0.111
$r\le 2$	0.45	22.98	27.58	0.174

Trace test indicates four cointegrating equation(s) at the 0.05 level. Max-eigenvalue test indicates one cointegrating equation(s) at the 0.05 level. * Implies rejection of the null hypothesis. Source: Author’s computations.

show the lag order selection criterion used for the underlying VAR and Johansen and Juselius (1990) cointegration test, respectively. We adopt the selection by the 8kaike information criterion (AIC), which identifies a maximum of four lags. Ozcicek and Mcmillin (1999) in their comparison of the performance of information criterion find the AIC to outperform the other criterion in selecting symmetric lag length orders. Therefore, the model is estimated using $(\mathit{n}-1)$ lags, which is a maximum of three lags.

4.3. Cointegration Test

The results from stationarity tests necessitate that we test for cointegration to determine whether the variables have a long-run relationship or otherwise. Table 3 presents the results of the Johansen cointegration test. The Trace statistic identifies four cointegrating equations whereas the maximum eigen value statistic identifies only one cointegration equation. We conclude that although individual time series depicts non-stationarity, a long-run relationship exists among the variables. This is in line with the theory on cointegration, which shows that it is possible for nonstationary time series to formulate a combination or relationship that is stationary (Murray 1994). Following the maximum eigenvalue result, we estimate a vector error correction model (VECM) using only one cointegrating equation. This is also guided by the specific relationship that we aimed to analyze.

4.4. Vector Error Correction Model Estimates

As indicated above, we estimated a VECM consisting of six variables, HDEBT UNEMPL LGINI LGDP_CAP HSE_PRYC and SAVRATIO. The error correction term (ECT) for the estimated model is −0.75 and is significant at the 1% level. This confirms the long-run relationship between household debt, unemployment, inequality, house prices, and savings in South Africa. Furthermore, the statistically significant ECT shows that 75% of the deviations from the equilibrium is corrected in the next period.

Table 4. VECM Results—Long-run elasticities.

$\mathit{H}\mathit{D}\mathit{E}\mathit{B}\mathit{T}$ (Dependent)	Coefficient	Standarderror	t-Value
$UNEMPL$	−0.012 ***	(0.003)	[−6.78]
$LGINI$	−1.562 ***	(0.168)	[−9.33]
$LGDP\_CAP$	2.125 ***	(0.152)	[13.94]
$HSE\_PRYC$	0.390 ***	(0.031)	[12.21]
$SAVRATIO$	0.013	(0.025)	[0.54]
$C$	4.849
$ECT$	−0.747 ***	(0.247)	[−3.02]

*** signify significance at 1%, 5% and 10% levels, respectively. Numbers in parenthesis [ ] are t-values and ( ) are standard errors.

presents the long-run elasticities and the error correction term for the model.

Our results show that in the long-run inequality and unemployment have negative impacts on household debt. The logarithm of the Gini (LGINI) coefficient has a coefficient of −1.56, with a t-value of 9.32, which shows significance at 1% level. A 1 percentage point increase in the Gini coefficient results in a −1.56 decrease in household debt. Inequality in South Africa therefore constrains the growth of household debt. This finding implies that there are no attempts to address socioeconomic inequalities using credit markets in the South African context. Credit markets function primarily on economic terms, where access to credit is not based on redressing inequities and inequalities of the past. Furthermore, the finding contradicts the Rajan hypothesis in the South African context, which suggest that credit markets respond to high inequality by increasing funds available to low-income groups.

High unemployment decreases household debt as expected. A 1 percentage point increase in UNEMPL results in an 18-basis points decrease in household debt. Unemployment impacts household access to debt negatively by lowering or removing future earning capacity of individuals. This in turn leaves individuals less qualified to access debt due to inability to make future repayments. Furthermore, unemployed individuals are unable to acquire assets that can be used as collateral in credit markets. High unemployment is also associated with periods of economics contraction such as recessions, during which households tend to be more precautionary and reduce their reliance on debt. In general, increasing unemployment reduces the number of people who can qualify for available credit instruments and can be perceived as a sign of economic hardships by current debt holders, who will also respond by cutting their debt stock.

We find both an increase in the GDP per capita and house prices to increase household debt. Specifically, a 1 percentage point increase in GDP per capita results in an over 200-basis points increase in household debt. This is expected from the literature as high economic growth increases confidence in the financial system, prospects of future earnings, and current income of households. Expectations of future income growth drive households to take more debt as they smooth out consumption over time. Higher house prices feed into the total amount of debt held by households as higher prices imply higher cost of debt. Therefore, increased house prices are expected to increase the proportion of household debt to disposable income.

Thus, our long-run results from the estimated VECM show that inequality and unemployment are negatively related to household debt in South Africa. On the other hand, GDP per capita and house prices have a positive relationship with income inequality.

4.5. Robustness Check Results (DOLS Technique)

In this section we present further analysis of the relationship between household debt and income inequality using Stock and Watson’s (1988) dynamic ordinary least squares (DOLS), a single equation modelling technique, which uses leads and lags of independent variables to account for serial correlation. Furthermore, our models are estimated using robust standard errors to correct for heteroskedasticity and serial correlation. Specifically, we use heteroskedasticity and autocorrelation consistent standard errors. In addition, we report on the normality test result for all models’ residual. Furthermore, to confirm the presents of a cointegrating relationship between the dependent variable and the independent variables, we employ Hanson’s (1992) instability test. We consider both household debt and debt service costs of households as measures of debt. On the other hand, we employ both the Gini coefficient and the ratio of top 10% to lower 50%’ proportions of total income as measures of inequality. The results provided in

Table 5. Long-run Estimates—DOLS Results.

$\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{e}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{n}\mathbf{t} \mathbf{V}\mathbf{a}\mathbf{r}\mathbf{i}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}$
	$\mathit{H}\mathit{D}\mathit{E}\mathit{B}\mathit{T}$	$\mathit{H}\mathit{D}\mathit{E}\mathit{B}\mathit{T}$	$\mathit{D}\mathit{S}\mathit{E}\mathit{R}\mathit{V}\mathit{E}$	$\mathit{D}\mathit{S}\mathit{E}\mathit{R}\mathit{V}$	$\mathit{H}\mathit{D}\mathit{E}\mathit{B}\mathit{T}$
$LGINI$	−0.822 *** [−2.11]		−0.533 *** [−6.66]
$TB50$		−0.031 *** [−7.98]		−0.081 *** [−8.12]	−0.010 ** [−2.03]
$LGDP\_CAP$	2.485 *** [5.96]	0.196 *** [7.21]	0.269 *** [3.75]	0.280 *** [4.02]	0.218 *** [7.66]
$UNEMPL$	−0.013 *** [−2.64]	−0.018 *** [−4.01]	0.000 [0.08]	−0.001 [−1.38]	−0.010 ** [−2.03]
$HSE\_PRYC$	0.306 *** [6.64]	0.149 *** [4.79]	0.039 *** [2.30]	0.005 *** [0.47]	0.218 *** [7.66]
$SAVRATIO$	−0.040 [−0.76]	−0.063 [−1.54]	−0.037 *** [−3.61]	−0.026 *** [−2.72]	−0.149 *** [−2.61]
$LGDP\_CAP*TB50$					0.224 ** [2.16]
$C$	−5.149 *** [−7.63]	−0.879 *** [−4.71]	−0.768 *** [−5.06]	−0.354 *** [−2.67]	−0.569 [−0.49]
$@TREND$	−0.010 *** [−2.41] **	−	−	−	−
Residual Normality	Yes	Yes	Yes	Yes	Yes
Cointegrated	0.29 (>0.2)	0.08 (>0.2)	0.26 (>0.2)	0.27 (>0.2)	0.27 (>0.2)

Cointegration method used for all single equation models is Hanson’s instability test. It tests the null hypothesis that the series are cointegrated against the alternative hypothesis that the series are not cointegrated. *** and ** signify significance at 1% and 5% levels, respectively. Numbers in parenthesis [ ] are t-values and in ( ) are p-values. Source: Authors’ Computations.

confirm our main findings above and show that inequality has a negative and significant impact on household debt in South Africa. In the first model for instance a 1 percentage point increase in Gini coefficient results in 82 basis points increase in household debt.

Our second measure of inequality is the debt service costs for private households. Increases in the debt service cost can signal a debt overhang for households. In our case an increase in the inequality also decreases debt service costs for households. We explain this to imply that an increase in top income earners’ incomes reduces overall debt uptake as they able to cover their expenses using current income. Furthermore, repayments of debt are accelerated due to higher incomes. However, on the other hand, decreasing the share of income for low-income earners reduces their access to credit hence resulting in lower aggregate debt service costs. This is in line with the assertion of Hundenborn et al. (2018) and Leibbrandt et al. (2012) that South African inequality is driven by labour market access. Unemployed individuals as confirmed by the negative coefficient on unemployment do not have access to credit and thus reduce lower quartile group’s income and aggregate debt service costs.

We also include a second measure of inequality in the form of the ratio between the proportion of income for the top 10% high-income earners and lower 50% income earners. Our results remain robust to these variable changes. Since we are using the proportion of household debt to disposable income ratio, we identify two main ways through which inequality decreases household debt, that is, by increasing disposable income or by decreasing household debt directly. The former channel implies that income inequality rewards high-income earners and results in an increase in the average disposable income. The later finding implies a decrease in the number of individuals relying on or accessing debt. Lower-income groups might be pushed out of credit markets due to diminishing incomes. On the other hand, higher-income earners desire less debt as the proportion of their income increases. Furthermore, with higher incomes, the higher-income groups are able to repay and cut on their debt, which reduces overall debt holding for all households.

To further understand the distinguishing features of this relationship, we formulate an interaction term between economic growth and income inequality. The coefficient of the interaction term is positive, whilst the coefficients of the two variables remain unchanged. Our interpretation of this is that economic growth has a moderating impact on the negative association between income inequality and household debt. Higher levels of economic growth in South Africa lower the overall negative impact of inequality on household debt. Therefore, higher economic growth tends to increase access to credit across the board, including among lower-income groups. Economic growth in South Africa improves access to debt and rewards both high-income earners and low-income earners. Furthermore, economic growth increases households’ disposable income, which in turn reduces the proportion of household debt to disposable income. Another way to understand this is that during periods of high economic growth, financial markets tend to become lax and increase provision of credit to lower-income groups. This can come through lowering of credit application requirements in anticipation of better economic times. The finding also implies low growth rates exacerbates the role of structural inequalities in allocation of credit.

These robustness estimations corroborate the results reported in Section 4.4 from the estimated VECM. We find income inequality to be negatively associated with household debt in South Africa. The results are robust to changes in both the measure of inequality and household debt.

4.6. Discussion of Results

Contrary to the Rajan Hypothesis, our research findings indicate a negative relationship between household debt and income inequality in South Africa. This relationship remains robust across different estimation techniques and measures of inequality. These results suggest that credit allocation in South Africa is primarily driven by economic factors rather than socio-equity considerations. Additionally, we observe that higher levels of unemployment negatively affect households’ access to credit, while an increase in the savings ratio is associated with lower household debt. Overall, these findings offer valuable insights into the complex dynamics between income inequality, household debt, and overall credit allocation.

On the backdrop of these results, we posit that the Rajan hypothesis is not applicable in the case of South Africa (Rajan 2011). In the Rajan hypothesis, rising inequality is observed to impact household debt positively. Rajan (2011) and Ahlquist and Ansell (2014) posit that increasing inequality coupled with stagnant incomes on lower-income groups leads to increasing credit uptake among low-income earners as they strive to maintain their consumption. The increasing debt can lead to fragility of the financial sector, hence the resultant global financial crisis (GFC) in 2008/2009. Our findings are also in contrast to Bordo and Meissner (2012), who do not find any evidence that link inequality to credit booms. Instead, we agree with Gu and Huang (2014) and Lim (2019), who emphasize the impact of heterogeneity in financial markets and regulation as the reason for huge disparities in the way household credit responds to changes in income inequality. They argue that the impact of inequality on household debt is largely felt in economies that have advanced financial systems, whereas those that are largely bank-based seem not affected. According to Lim (2019), economies with tighter regulations also tend to lessen the impact of inequality on household debt. This cannot be confirmed for South Africa however, where tighter regulation is accompanied by a negative association between income inequality and household debt.

The negative impact of inequality is achieved in two ways, firstly, through increasing the share of income for high-income earners. If income is increased, high-income earners will have more disposable income. Even if debt levels remain constant, this will lead to a lower ratio of household debt to disposable incomes. The other channel involves reduction in debt holdings by top income earners as they receive income, which has the same effect in reducing household debt to disposable income ratio. Secondly, inequality increases when incomes of the lower-income earners are further reduced, which further alienates them from debt markets and reduces the total stock of household debt. Inequality in South Africa therefore promotes unequal access to credit markets, which is skewed towards higher-income earners resulting in further entrenchment of an unequal society. There is no attempt to use credit markets in bridging the income gap between higher-income earners and lower-income earners.

As expected from the literature, we find economic growth to have a positive impact on growth of household debt in South Africa. Studies by Meniago et al. (2013) and Nomatye and Phiri (2017) confirm this positive relationship, which is also buttressed by Kereeditse and Mpundu (2021), who find consumption expenditure to have a positive impact on household debt in South Africa. However, our findings are contrary to Dumitrescu et al. (2022), who find economic growth to reduce household debt for OECD economies. Differences in the size of the economy, financial systems, and regulation should explain this contrast. Increases in unemployment decrease household debt as expected from the literature (Abd Samad et al. 2020; Dumitrescu et al. 2022). Unemployment reduces the number of borrowers who can qualify to borrow from the credit markets, thereby lowering credit applications.

Our results confirm findings from several studies that find house prices to increase household debt (Abd Samad et al. 2020; Dumitrescu et al. 2022). Increasing household debt raises the cost of purchasing houses by household and results in higher stock of debt as new buyers enter the housing market. Contrary to the findings of Meniago et al. (2013), we find the positive impact of house prices on household debt to be statistically significant. Furthermore, the growth in savings is found to have a negative impact on household debt. This finding is significant in three of the five models estimated in our robustness model. The result confirms the findings of Mongale et al. (2013) who established negative association between household saving and household debt in South Africa. Increased savings should imply an increase in household incomes, hence less reliance on debt. However, as noted by Mongale et al. (2013), lower levels of savings in South Africa leave households with little buffer to fall on during times of financial stress, which causes further dependence on debt.

Lastly, we identify some limitations of the study. Firstly, our study is by no means exhaustive in identifying the influences of household debt in South Africa. Other variables impacting household debt could not be captured in a single parsimonious model as we were paying more attention to the impact of income inequality on household debt. Secondly, we assume a linear relationship between household debt and inequality; further investigation could be made on linearity properties of this relationship in the South African case. Furthermore, our data is limited to annual frequency due to the lack of high-frequency data for income inequality. In the case where high frequency data is available, it can provide more information to aid analysis.

5. Conclusions and Policy Recommendations

This study analyses the relationship between household debt and income inequality in South Africa. Furthermore, we are able to test the Rajan hypothesis in the South African case. Our findings show a negative and significant relationship between household debt and income inequality. This finding, which is robust to changes in the estimation techniques and measures of inequality, contradicts the Rajan’s hypothesis and concludes that provision of credit in South Africa does not consider socio-equity differences. Rather, credit allocation is simply on the basis of economic reasons. Furthermore, we find a negative relationship between household debt and unemployment, showing that increases in unemployment dampen households’ access to credit. Increases in the savings ratio negatively impact household debt. In contrast, we find increases in national income per capita and house prices to positively impact household debt.

From both the VECM and DOLS analysis, we conclude that household debt in the South African context is not being driven by any socio-equity considerations as insinuated in the Rajan hypothesis. Instead, expansion of debt in South Africa is rather based on economic and business decisions (profit maximization). We recommend further investigation into different types of household debt and how they can be made affordable to both lower- and middle-income earners to promote economic activity and growth. The central bank can ease financial regulations during times of economic prosperity increase available credit and further promote growth if they can control the accompanying risk.

Further research in this area should explore various aspects following the conclusions drawn from this study. Specifically, given the observed negative and significant relationship between household debt and income inequality, it would be valuable to examine the underlying factors contributing to this unexpected result, potentially shedding light on the mechanisms through which credit allocation in South Africa diverges from socio-equity considerations. Additionally, investigating the intricacies of different types of household debt and their affordability for lower- and middle-income individuals could offer insights into ways to foster economic activity and growth while promoting financial inclusivity. Exploring the role of the central bank in adjusting financial regulations during periods of economic prosperity to enhance credit availability and manage associated risks could provide a comprehensive understanding of the dynamics between credit expansion, economic development, and risk mitigation in the South African context.