Determinants of Financial Stability and Development in South Africa: Insights from a Quantile ARDL Model of the South African Financial Cycle

2.1. Data and variables

To represent the South African financial cycle, the following variables are used. Total domestic credit as percentage of GDP (CR), real house price index (HP), real all share price index (SHARE). The variables are selected because they are widely used in both global financial cycle literature and the South African literature on financial to represent financial cycles. The primary theoretical motivation for using these variables is that they drive financial market development, and they are strongly correlated with each other. Moreover, their peaks tend to coincide with system-wide fluctuations in the financial system. The practical consideration for these variables in the case of South Africa is that they represent the three largest financial sectors in the country: the credit sector which includes banks and insurers, the housing sector, and the equity market. In the country these sectors set the tone for the behavior of the overall financial system.

There are two important caveats regarding the use of these variables in the study. First, they are used to construct the financial cycle. This implies that they are aggregated into a single index, in the study the principal component analysis (PCA) is used to archive this task. For the purpose of this exercise, the variables are standardized using their mean and standard deviation. Second, the variables are also as explanatory variables in the QARDL of the estimated cycle. For this purpose, these variables are not standardized. However, in order to address the issue of multicollinearity, the lags of the variables and other explanatory variables were used. Accordingly, the Akaike Information Criteria is used to determine the optimal lag to be included in the QARDL. After determined the number of lags to be included, each variable is transformed to its optimal lag using the transformation (y=x[_- N-l], where y is the new transformed variable, x is the original variable, N is the current observation, and l is the optimal lag. The main motivation for including the credit, house prices, and share prices, in the QARDL is to uncover how the magnitude and direction of impact they have on the cycle, which cannot be robustly done in the PCA.

Other explanatory variables the real effective exchange rate (EXCH), GDP, inflation rate (INF), broad money supply (M3), the repo rate (REPO), and the macroprudential policy index (MPI). The inclusion of these variables in the model is justified by their significant roles in shaping the dynamics of the financial cycle and economic conditions in South Africa. Exchange rates are included because they capture the effects of the foreign exchange market, which are particularly relevant in South Africa due to its free-floating exchange rate system. This system makes the South African financial system more vulnerable to external shocks, such as fluctuations in global commodity prices and changes in international investor sentiment (Mlachila et al., 2013). Exchange rate volatility can directly impact inflation, external debt, and trade balances, all of which influence the broader economy and financial stability (Borio et al., 2012). GDP is incorporated as a key indicator because there is substantial evidence suggesting that the business cycle and the financial cycle are closely related, typically moving in tandem in a procyclical manner. In other words, periods of strong economic growth are often associated with financial booms, while economic downturns tend to coincide with financial contractions. Therefore, GDP serves as an essential driver in understanding both the short-term fluctuations and long-term trends within the financial cycle.

The inflation rate is included due to the significant threats that an unstable price environment poses to the financial system. High inflation can erode purchasing power, destabilize currency values, and increase uncertainty, which may prompt financial market volatility and disrupt investment decisions (Cecchetti et al., 2000). On the other hand, deflation can lead to reduced consumer demand, rising debt burdens, and greater risks of financial crises. Thus, inflation is a critical variable in analyzing financial cycles and their impact on economic stability. Monetary policy variables, such as interest rates, are essential in understanding the cost of borrowing, which directly affects financial activities such as lending, investment, and consumption (Bernanke & Gertler, 1995). Changes in the policy rate influence the level of credit in the economy and can exacerbate or dampen financial cycle fluctuations. As such, the repo rate, a key policy tool in South Africa, is included to reflect the central bank’s stance on liquidity and borrowing costs. Finally, macroprudential policy is included because it specifically targets the stabilization of the financial cycle. The goal of macroprudential measures is to mitigate systemic risks and enhance the resilience of the financial system, especially during periods of financial instability (Borio, 2011). By addressing imbalances and vulnerabilities within the financial sector, macroprudential policies aim to prevent the amplification of financial cycles and their detrimental effects on the broader economy. This makes the inclusion of the macroprudential policy index (MPI) crucial to understanding how regulatory actions influence the financial cycle. In addition to these key variables, the real effective exchange rate (EXCH), broad money supply (M3), and other monetary variables help provide a comprehensive picture of the financial cycle's drivers and the interactions between domestic and external economic conditions.

The data used in this study spans from 2000 to 2024 on a monthly basis. This period was specifically chosen for several reasons. First, it coincides with South Africa’s adoption of a flexible inflation targeting framework, which has shaped monetary policy decisions since its implementation. Second, the focus on macroprudential policy and financial stability concerns began around 2002, following the banking crisis in the country, marking a critical point in the evolution of financial regulation. The chosen period is also sufficiently long to capture both short-run and long-run effects of the financial cycle. The data for the variables CR, HP, REPO, EXCH, INF were obtained from the Bank for International Settlements statistics. The variables for GDP and Share Prices (SHARE) were collected from the SARB statical time series database. The MPI was sourced from the International Monetary Fund Integrated Macroprudential Policy database. These data sources provide reliable and consistent indicators crucial for understanding the dynamics of the South African financial cycle during this period.

The study applies the quantile ARDL model to examine the short-run and long-term impact of the exchange rate, gross domestic product, inflation rate, total domestic credit, house prices, share prices, money supply, repo rate, and macroprudential policy index on the South African financial cycle. The South African financial cycle has multiple phases, including expansions, contractions, peaks, and troughs which the model captures as per quantiles. The model was chosen because of its robustness to non-normal errors, as well as its ability to account for outliers, heterogeneity, and skewness in the dependent variable (Hashmi et al., 2022; Anwa et al., 2021; Sharif et al., 2020). Additionally, the model facilitates the examination of both short-run and long-run effects of independent variables on the dependent variable across different quantiles (Hashmi et al., 2023). It provides more reliable results when the sample size is small and, like the ARDL model, is particularly useful when the variables are integrated of either order zero I(0) or one I(1) (Mensi et al., 2019).

We start the following OLS specification as benchmark for estimating the impact of the afore-mentioned explanatory variables:

$$\ln CYCLE=\mathrm{ }{\beta }_0+{\beta }_{1}lnEXCH+{\beta }_{2}lnGDP+{\beta }_{3}lnINF+{\beta }_{4}lnCR+{\beta }_{5}lnHP+{\beta }_{6}lnSHARE+{\beta }_{7}lnM3+{\beta }_{8}lnREPO+{\beta }_{9}lnMPI+{ϵ}_t$$

(1)

Where $\ln$refers to the natural logarithm of variables. The QARDL model is not particularly robust when variables are integration order two (I). Therefore, for examining the order of integration of variables the Augmented Dickey-Fuller (ADF) unit root test is conducted. After the order of integration is determined, we proceed further and use the QARDL. The model estimated in the study is similar to Hashmi et al. (2022). An extension of the ARDL model into QARDL model leads to the following which is the standardized version of the OLS model in equation 1:

$$Q_{CYCLE}=\alpha {\left(\tau \right)}_0+{\sum }_{i=1}^{n3}{b}_i\left(\tau \right)∆{LnY}_{t-1}+{\sum }_{i=1}^{n2}{c}_i\left(\tau \right)∆Ln{X}_{t-1}+{\sum }_{i=1}^{n3}{d}_i\left(\tau \right)∆Ln{Z}_{t-1}+{\beta }_1\left(\tau \right)Ln{Y}_{t-1}+{\beta }_2\left(\tau \right)Ln{X}_{t-1}+{\beta }_3\left(\tau \right)Ln{Z}_{t-1}+{ϵ}_t$$

(2)

Where Y is the vector of financial explanatory variables, i.e., CR, HP, and SHARE which maintain the lag of dependent variable. X is a vector of real variables containing EXCH, GDP and INF. Z is a vector of policy variables which contains M3, REPO, and MPI. The parameter $\tau$ is the quantile measurement. In order to empirically investigate the impact of the above variables on the financial cycle, the study utilizes the following quantiles: $\tau \in \left\{\mathrm{0.05,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,0.95}\right\}$. A Wald test is used to assess the short-run and long-run symmetry of parameters. For the short run, the symmetry is tested using the following null hypothesis:

${\mathit{H}}_0^{\mathit{s}}:\mathit{ }\cdot \mathrm{b}\mathrm{i}\left(0.05\right)=\mathrm{b}\mathrm{i}\left(0.1\right)=\dots =\mathrm{b}\mathrm{i}\left(0.95\right)$

${\mathit{H}}_0^{\mathit{s}}:\mathit{ }\cdot \mathrm{c}\mathrm{i}\left(0.05\right)=\mathrm{c}\mathrm{i}\left(0.1\right)=\dots =\mathrm{c}\mathrm{i}\left(0.95\right)$

${\mathit{H}}_0^{\mathit{s}}:\mathit{ }\cdot \mathrm{d}\mathrm{i}\left(0.05\right)=\mathrm{d}\mathrm{i}\left(0.1\right)=\dots =\mathrm{d}\mathrm{i}\left(0.95\right)$

In a similar fashion, the long-run symmetry is tested using the following null hypothesis:

${\mathit{H}}_0^{\mathit{l}}:\mathit{ }\cdot {\mathsf{\beta }}_1\mathrm{i}\left(0.05\right)={\mathsf{\beta }}_1\mathrm{i}\left(0.1\right)=\dots ={\mathsf{\beta }}_1\mathrm{i}\left(0.95\right)$

${\mathit{H}}_0^{\mathit{l}}:\mathit{ }\cdot {\mathsf{\beta }}_2\mathrm{i}\left(0.05\right)={\mathsf{\beta }}_2\mathrm{i}\left(0.1\right)=\dots ={\mathsf{\beta }}_3\mathrm{i}\left(0.95\right)$

${\mathit{H}}_0^{\mathit{l}}:\mathit{ }\cdot {\mathsf{\beta }}_3\mathrm{i}\left(0.05\right)={\mathsf{\beta }}_3\mathrm{i}\left(0.1\right)=\dots ={\mathsf{\beta }}_4\mathrm{i}\left(0.95\right)$

At the end of estimation, several stability and diagnostic tests are conducted to assess the goodness of fit of the model in equation 2. Breusch-Pagan-Godfrey Heteroscedasticity test is employed to assess the residuals are homoscedastic. Breusch-Pagan LM test is employed to assess whether there is serial correlation in the lags of residuals. A Wald test is used the assess whether there should be variables that should be omitted. The Ramsey Reset test is employed to assess the robustness of the model specification. The CUSUM together with the Recursive coefficient’s tests are employed to assess the stability of the model and the estimated parameters.