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Finance, Accounting and Business Analysis 
Volume 6 Issue 1, 2024 

http://faba.bg/       
ISSN  2603-5324 

 

The Asymmetric Effect of Stokvel on Banking Sector Liquidity: 

Evidence From A Nonlinear ARDL Approaches 

 

Lindiwe Ngcobo1* , Joseph Chisasa2 , Mantepu Tshepo MaseTshaba3  
Department of Finance, Risk Management and Banking, University of South Africa, Pretoria, South 

Africa1 

University of South Africa, College of Economic and Management Science, Pretoria, South Africa2 

University of South Africa, College of Economic and Management Science, Pretoria, South Africa3 

* Corresponding author 

 

 

Info Articles   Abstract 
 

History Article: 

Submitted 19 February 2024 

Revised  18 May 2024 

Accepted 19 Мау 2024 

 

 The objective of this study was to empirically investigate the possible 

nonlinear relationship between stokvel saving and banking sector 

liquidity, that is to determine whether there exists a turning point or 
a threshold level above which the effect of stokvel saving on banking 

sector liquidity switches from positive to negative in South Africa; 

to assess the long-run as well as the short-run relationship between 
the two variables, controlling for other stokvel saving determinants. 

The estimation of this relationship has been carried out using a novel 

methodology combining the autoregressive distributed lag (ARDL) 

bounds testing approach to cointegration developed by Pesaran, 

Shin and Smith (2001) and nonlinear autoregressive distributed lag 

(NARDL) applied to quarterly time series secondary data for the 

period from 2009Q4-2020Q2.  The study results found that all the 

explanatory variables were statistically insignificant in explaining 

banking sector development implying that the NARDL is not an 

appropriate model for predicting banking sector development 

proxied by banking sector liquidity. Similar results obtained when 
using stokvel savings and money supply as the dependent variables 

suggesting an insignificant influence of baking sector liquidity on 
stokvel savings and money supply. With gross domestic product 

growth (GDPG) as the dependent variable, only a negative shock on 

money supply (M3) resulted in a significant increase in GDPG at 
5%. STOKVSAV can provide the opportunity for the South African 

government and formal financial/banking sector to develop 

mutually beneficial relationships or linkages to make such 

STOKVSAV more effective and efficient in mobilising savings and 

advancing credit to the low- and middle-income households.  

 

Keywords:  

stokvel savings, banking 

sector liquidity, ARDL, 

Asymmetric effect, South 

Africa. 

 

JEL: C01, D14, G23  

Address Correspondence:  

 Email: lngcobo@unisa.ac.za1 

 chisaj@unisa.ac.za2 

 emasetmt@unisa.ac.za3 

 

 

 

  

https://orcid.org/0000-0002-3232-5956
https://orcid.org/0000-0002-8923-1424
https://orcid.org/0000-0001-7683-2661


L. Ngcobo, J. Chisasa, M. T. MaseTshaba / Finance, Accounting and Business Analysis, Volume 6, Issue 1, 2024 

 

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INTRODUCTION 

 
A stokvel saving (STOKVSAV) is a South African term for an investment group where members 

contribute a certain amount to a central fund weekly, fortnightly or monthly; they typically constitute 

themselves as clubs or societies and are also known to be financially mutual (Bozzoli 1991; Lukhele 1990; 

Verhoef 2001a; Mashigo and Schoeman 2010; Kaseke and Matuku 2014; Karlan, Ratan and Zinman 2014; 
James 2015). Worldwide, STOKVSAV are commonly known as ‘rotating savings and credit associations’ 

(ROSCAs) (Kaseke and Matuku 2014; Karlan, Ratan and Zinman 2014; Mphahlele 2011; Yusuf, Gafar, 

and Ijaiya 2009). STOKVSAV play a pivotal role in increasing access to finance for the so‐called ‘unbanked’ 

in South Africa (Dupas, Karlan, Robinson and Ubfal 2018). Instead of using banks, low- and middle-income 

households tend to save in more informal ways, such as keeping cash at home or buying illiquid assets, 

which may be costly, risky or inconvenient (Dupas, Karlan, Robinson and Ubfal 2018).  

The rate of access to savings and credit by low- and middle-income South African households in the 

banking sector remains a challenge (Mishra and Bhardwaj 2022, Omar and Inaba 2020; Biyase and Fisher 

2017; Goncharuk 2016). For instance, the banking sector in South Africa does not cater for the credit needs 

of low- and middle-income households due to information asymmetry and lack of collateral, among other 

borrower shortcomings (Atamja and Yoo 2021; Biyase and Fisher 2017; James 2014; Mashigo 2009; 

Mashigo and Schoeman 2012). This suggests that the banking sector is still not sufficiently developed to fully 

serve its diverse clientele (Duvendack and Mader 2019; Mashigo and Kabir 2016). Figure 1 below illustrates 
trends in growth of stokvel savings compared to formal bank deposits proxied by liquid liabilities. What is 

evident is that the share of stokvel savings is growing in sympathy with formal bank deposits. This trend is 

cause for concern as it is a recipe for allocational inefficiency of funds in informal financial markets due to 

financial disintermediation. In addition, the problem of information asymmetry derives from a lack of trust 

between the lender and the borrower, which results in a perceived challenge of the probability of low returns 

(Bime and Mbanasor 2019; Sackey 2018; Sukmaningsih 2018).  

 

 
Source: Author construction. 

Figure 1. Trends in stokvel savings and bank liquid liabilities 

 

The ever-deteriorating economic situation, poverty and unemployment in South Africa are significant 

reasons for households to participate in stokvel savings (Chineka and Mtetwa 2021). According to Sambo 

(2019:1), unemployment is the number one cause of poverty and inequality in the country. In 2006, more 

than two out of every five (42.2%) households in South Africa lived below the upper-bound poverty line. 

While the poverty level was similar in 2009 at 42.7%, there was a decline in households living in poverty in 

2011, with approximately a third (32.9%) of all households below this level. This shows a significant 

reduction in the proportion of poor households in the country from 2006 to 2011. However, given the results 

of the 2011 Census, this still translates into approximately 4.75 million households in South Africa living 

below the poverty line (Stats SA 2014). 

Access to and the use of financial institutions by low- and middle-income households is complicated 

4252

19724

27251

54238

78458

400 641 2460

14050

26774

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

1980 1990 2000 2010 2020

Liquid liabilities (ZAR000) Stokvel savings (ZAR000)



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88 

 

because the majority of stokvel savings members cannot provide valid Identity documents (Landman and 

Mthombeni 2021). Additionally, a lack of education influences member preference to communicate in their 

mother language when being served in financial institutions (Verhoef 2001b; Beck Kibuuka and Tiongson 

2010; Moliea 2007; Mashigo 2012; Damodaram 2013). These are also the main reasons low- and middle-

income households do not use formal financial institutions (Burkett and Sheehan, 2009; De Cock, Fitchett 

and Volkmann, 2005). Many South Africans are not part of the formal financial system; hence, they save, 

invest and use CR from stokvel savings (Kumarasinghe and Munasinghe 2016; Kaseke and Olivier 2008). 

This situation is not likely to improve in the short-term considering that unemployment has escalated by to 

32.9% in the first quarter of 2024, up 0.8 percent of a percentage point from 32.1% in the fourth quarter of 

2023 (StatsSA 2024:Q1). Additionally, in its expanded form, unemployment rose by 0.8 of a percentage 

point to 41.9% in 2024:Q1 relative to 2023:Q4. Implicitly, this is likely to cause a decrease in household 

capacity to save with formal banks and raise an appetite stokvel savings. 

Despite playing second fiddle to formal banking institutions, stokvels are community-based savings 

schemes aimed at improving the lives of low- and middle-income earners (Van Wyk 2017; Floro and Seguino 

2002). Members prefer saving with stokvels because of the transparency of transactions and the control it 

brings to their money (Bophela and Khumalo 2019; Storchi 2018). Money in this pool is then paid in full or 

partially to every member participating in the stokvel savings, either on a rotational basis or in times of 

financial need (Verhoef 2008; Matuku and Kaseke 2014; Nyandoro 2018). Low- and middle-income 

households often use precautionary savings for stokvel savings, which are meant to safeguard against any 

possible future unexpected income shocks, often referred to as “rainy days” or “emergency savings” (Simleit, 

Keeton and Botha 2011; Floro and Seguino 2002:1). Stokvel savings provide an alternative for low- and 

middle-income households which cannot meet the requirements of the banking sector (Nyandoro 2018; 

Mboweni 1990). This view is supported by Oji (2015), who observed that African countries have a 

proportion of financially excluded people, which reflects a lack of access to financial resources. 

This research is different from prior similar empirical studies because using the multiple regression 

model, it attempts to show the nonlinear relationship of banking sector liquidity affected by stokvel savings 

in South Africa. Another advantage of the multiple regression model is that its results are more likely to be 

accurate because of its completeness. This is because it includes all the important variables in a single study, 

for example, the dependent variable banking sector liquidity (BSL), independent variable stokvel savings 

(STOKVSAV) and the control variables gross domestic product growth (GDPG) and money supply (M3).  

The objective of this study was to empirically investigate the possible nonlinear relationship between 

stokvel savings (STOKVSAV) and banking sector liquidity (BSL). Thus, the paper sought to determine 

whether there exists a turning point or a threshold level above which the effect of STOKVSAV on banking 

sector liquidity switches from positive to negative in South Africa; to assess the long-run as well as the short-

run relationship between the two variables, controlling for other STOKVSAV determinants. To this end, the 

paper hypothesises that there is a nonlinear relationship between stokvel saving and banking sector liquidity 

in South Africa. The estimation of this relationship was carried out using a novel methodology combining 

the autoregressive distributed lag (ARDL) bounds testing approach to cointegration developed by Pesaran, 

Shin and Smith (2001) and nonlinear autoregressive distributed lag (NARDL). 

The remainder of the paper is organized as follows. A selected review of the theoretical and empirical 

literature, the methodology used, the empirical results, the summary, conclusions and the policy 

implications of the study are presented sequentially. 

 

EMPIRICAL LITERATURE 

 
The financial system pools together the savings generated in the household sector. (Levine, 1997). In 

the banking sector, this task is primarily performed by banks’ local branches, which, being close to savers, 

can create stable relationships with savers based on trust and on the repeated provision of financial services 

(Giovannini, Lacopettaand Minetti 2013). Banks create a relationship with household savers, and the 

financial systems pool together savings by households which are referred to as liquid liabilities due to their 

short-term nature. An increase in savings leads to output growth by allowing an increase in investments. 

The banking sector induces the mobilisation of low- and middle-income households’ savings, resulting in an 

increase in output growth (Gurley and Shaw 1960).  

In this study, banking sector liquidity (BSL) is denoted by banking sector liquid liabilities as a 

percentage of GDP (Singh and Sharma 2016; Laštůvková 2016; Marozva 2013; Marozva 2015). Banking 

sector liquidity is expected to have a direct relationship with stokvel savings.  The higher the liquidity the 

higher the households’ incomes which then promotes stokvel savings. On the other hand, stokvel savings 

are expected to positively influence banking sector liquidity. The higher the stokvel savings the higher the 

liquid liabilities of the bank.  

 



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89 

 

In South Africa, there are 11 official languages with different names for a ‘stokvel’. For example, it is 

known as ‘mohodisano’ in Sotho-speaking regions, ‘kuholisana’ in isiZulu-speaking regions, ‘umgalelo’ in 

Xhosa-speaking regions and ‘gooi-goois’ in Afrikaans-speaking regions (Van Wyk 2017). Stokvels offer 

financial services outside of the domain of the banking sector of South Africa and are not governed by 

banking regulations (Tengeh and Nkem 2017). Terminology varies among countries; however, the names 

invariably signify some sort of community activity or derive from the name of the money fund, e.g., box-

money, boxi. The participants are often referred to as ‘players’, sometimes as ‘throwers’ (Besson 1996), and 

the contributions may be termed the ‘hand’ or ‘shares’ (Handa and Kirton 1999). Sometimes the association 

may be known by the purpose for which the share-outs are to be used, e.g., kitchen ROSCAs (Niger-Thomas 

1995) or named after the day on which members meet (Geert 1962; Ardener 1964; Low 1995). Figure 2 

below presents the schematic conceptual framework of stokvels. 

Informal savings organisations are known as stokvels and are substitutes for formal banks. Stokvels 

are formed by groups of friends to encourage social inclusion and poverty alleviation (Mashigo and Kabir 

2016). They provide savings, credit and insurance services to households. They are easy to start up and banks 

have special accounts for group schemes (Mashigo 2012). A schematic framework of stokvels is presented 

in Figure 2 below. 

 
Source: Author construction  

Figure 2. Stokvel-conceptual framework 

 

Snow and Buss (2001) view microcredit as a method for linking the formal and informal sectors of 

African economies to increase the reach of the formal sector. However, according to Nawai and Shariff 

(2010), loans given to the poor are minimal and are for a short-term period. Collateral is not needed, and 

borrowers are required to make weekly repayments. Similarly, Ngcobo and Chisasa (2018) study the 

characteristics of credit instruments issued by stokvels savings to households in South Africa. The study 

showed that stokvels savings issue short-term loans from less than three to six months. Thus, participating 

in a stokvel enhances the probability of accessing credit compared to the alternative of accessing credit from 

banks and similar formal lenders. 

James (2017) examined how group lending can be used to improve access to credit by households. 

The study revealed that group lending mechanisms improve social capital and reduce the barriers that deter 

access to credit. Similarly, Karlan, Savonitto, Thuysbaert and Udry (2017) examined savings-led 

microfinance programmes in poor rural communities in developing countries to establish groups that save 

and then lend out the accumulated savings to each other. Their study’s results found that promoting 

community-based microfinance groups leads to an improvement in household business outcomes and 

women’s empowerment.  

The majority of the world’s poor live in rural areas of developing countries with little access to 

financial services. Setting up Village Savings and Loan Associations (VSLAs) has become an increasingly 

widespread intervention aimed at improving local financial intermediation (Ksoll, Lilleor, Lonborg and 

Rasmussen 2016). Habumuremyi, Habamenshi and Mvunabo (2019) assessed the role of VSLAs in 

improving the social economic development of poor households in Murundi Sector in Karongi District of 

Rwanda. The findings revealed that VSLA promotes financial inclusion where the loan is proportional to 

savings. Ksoll, Lilleor, Lonborg and Rasmussen (2016) used a cluster randomised trial to investigate the 

impact of VSLAs in Northern Malawi over a two-year period. Their study found evidence of positive and 

significant intention to increase savings and credit obtained through the VSLAs, which has increased 

agricultural investments and income from small businesses.   

Ngcobo, Chisasa and MaseTshaba (2023) established the presence of a long-run relationship and 

causality between stokvel savings, money supply, gross domestic product growth rate and banking sector 

liquidity in South Africa. Applying the Autoregressive Distributed Lag (ARDL) and Error Correction Model 

(ECM) techniques on quarterly time series data for the period from 1987Q3 to 2020Q1, the study reveals 

that in the long run, stokvel savings and money supply were found to have a negative relationship with 

Stokvel members Savings

Insurance

Credit



L. Ngcobo, J. Chisasa, M. T. MaseTshaba / Finance, Accounting and Business Analysis, Volume 6, Issue 1, 2024 

 

90 

 

banking sector liquidity albeit insignificant, however, gross domestic product growth rate exhibited a 

negative and statistically significant relationship at 1%. The coefficient of the error correction model (ECM(-

1)) was, as expected, negative and statistically significant thus providing evidence of a short-run relationship.  

 

METHODS 

 
This study used quarterly time series secondary data ranging from 2009Q4 to 2020Q2 collected from 

the South African Reserve Bank and Old Mutual South Africa. The literature extensively demonstrated, 
from both empirical and theoretical angles, that stokvels play a significant role in the development of the BSL. 

Equation 1 below is illustrative. 

BSL = 𝑓(𝑆𝑇𝑂𝐾𝑆𝐴𝑉, 𝐺𝐷𝑃𝐺, 𝑀3)  (1) 

The following general econometric model represents the impact of STOKVSAV on BSL in South 

Africa (see equation 2). 

ΔBSLt = β0 + β1 ΔLnSTOKVSAVt  + ∑ Xjt
n
j=1 + 𝗎t      (2) 

Where:  

STOKVSAV - stokvel savings 

Xjt - vector of control variables  

 

If  𝛽1 ≠0 and have significance, meaning there exists a break-point and the impact of STOKVSAV on 

BSL is the difference between the two periods. The minimum stokvel savings is 𝛽0 in the period before the 

break-point is (𝛽0 + 𝛽1 ) in the period after the break-point. If 𝛽3>0 and have significance, this implies the 

impact of stokvel savings on BSD in the period after the break-point is bigger than the effect in the period 

before the break-point. 

 
Autoregressive Distributed Lag (ARDL) approach 

The study employed the ARDL approach proposed by Pesaran, Shin and Smith (2001) and long- and 

short-run estimations econometric approaches postulated by Engle and Granger (1987), Johansen and 

Juselius (1990), and Johansen (1996). The ARDL models are presented in equation [3] as follows: 

𝛥𝐿𝑛𝐵𝑆𝐿𝑡 = 𝛼0 + 𝛽1 𝐼𝑛𝐵𝑆𝐿𝑡−1 + 𝛽2 𝑆𝑇𝑂𝐾𝑉𝑆𝐴𝑉𝑡−1  + 𝛽3 𝐺𝐷𝑃𝐺𝑡−1  + 𝛽4 𝑀3𝑡−1 + ∑ 𝛼1𝑘  𝛥𝐼𝑛𝐵𝑆𝐿𝑡−𝑘   

𝑚1

𝑘=0

+ ∑ 𝛼2𝑘  𝛥𝑆𝑇𝑂𝐾𝑉𝑆𝐴𝑉𝑡−𝑘   

𝑚2

𝑘=0

+ ∑ 𝛼3𝑘  𝛥𝐺𝐷𝑃𝐺𝑡−𝑘   

𝑚3

𝑘=0

+ ∑ 𝛼4𝑘  𝛥𝑀3𝑡−𝑘  

𝑚4

𝑘=0

+ 𝜔𝑡      

(3) 

   
Where:  

Δ - first difference 

β1, β2, β3 and β4 -coefficients of the long-run impacts 

𝝰1, 𝝰2, 𝝰3 and 𝝰4 - coefficients of the short-run impacts 

𝝎 - error 

 

The cointegration relationship is estimated as follows:  

The long-run and short-run parameters of the equations are estimated once the cointegrating 

relationship has been detected. The cointegration relationship is estimated as follows:  

ΔBSLt = β0+   β1   BSLt−1   +β2  STOKVSAVt−1  +β3   GDPGt−1   + β4  M3t−1 + μt  (4) 

STOKVSAVt = STOKVSAV + STOKVSAVt

+

 
+  STOKVSAVt

−

 
 (5) 

GDPGt = GDPG + GDPGt

+

 
+ GDPGt

−

 
 (6) 

M3t = M3 + M3t

+

 
+ M3t

−

 
 (7) 

 
Where stokvel savings control variances are partial sum processes of positive and negative changes in 

independent variables obtained as follows: 

NEG(STOKVSAVt) = ∑ STOKVSAV −
s 

= ∑ MIN(ΔSTOKVSAVs
t

S=0
, 0)                        

t

s=0
  (8) 



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91 

 

POS(STOKVSAVt) = ∑ STOKVSAV +
s 

= ∑ MAX(ΔSTOKVSAVs
t

S=0
, 0)                          

t

s=0
  (9) 

NEG(GDPGt) = ∑ GDPG −
s 

= ∑ MIN(ΔGDPGs
t

S=0
, 0)

t

s=0
  (10) 

POS(GDPGt) = ∑ GDPG t
s 

= ∑ MAX(ΔGDPGs
t

S=0
, 0)                        

t

s=0
  (11) 

NEG(M3t) = ∑ M3 −
s 

= ∑ MIN(ΔM3s
T

S=0
, 0)                         

t

s=0
  (12) 

POS(M3t) = ∑ M3 +
s 

= ∑ MAN(ΔM3s
t

S=0
, 0)                          

t

s=0
  (13) 

 

Therefore, the non-linear asymmetric long-run equilibrium relationship can be expressed as: 

BSLt = POS
+

 
STOKVSAV

+

s 
+  NEG

−

 
STOKVSAV

−

s  
+ 𝚞t (14) 

BSLt = POS +
 

GDPG +
s 

+  NEG −
 

GDPG −
s  

+ 𝚞t      (15) 

BSLt = POS +
 

M3 +
s 

+  NEG −
 

M3 −
s  

+ 𝚞t      (16) 

          

NARDL model, and non-linearity is introduced through partial sum or cumulative sum concept 
included in generating the new variables POS (+) and NEG (-), where all variables (STOKVSAV, GDPG 

and M3) are lag orders. 

ΔBSLt = α0 + + ∑ α  1i
ΔBSLt−i   

p

i=0
+ ∑ α  2i

ΔNEG(STOKVSAV)t−i   

p

i=0
+

 ∑ α  3i
ΔPOS(STOKVSAV)t−i   

p

i=0
+ ∑ α  4i

ΔNEG(GDPG)t−i   

p

i=0
+ ∑ α  5i

ΔPOS(GDPG)t−i   

p

i=0
+

∑ α  6i
ΔNEG(M3)t−i   

p

i=0
+ ∑ α  7i

ΔPOS(M3)t−i   

p

i=0
+ α  8i

BSLt−i   
 + α  9i

NEG(STOKVSAV)t−1   +

α  10i
POS(STOKVSAV)t−1   + α  11i

NEG(GDPG)t−1   + α  12i
POS(GDPG)t−1   + α  13i

NEG(M3)t−1   +

α  14i
POS(M3)t−1   + ωt      

(17) 

 

RESULTS AND DISCUSSION 

 

Unit root test with breakpoints  

The study applies the structural break method for determining the time series properties of the 

variables investigated by the ADF test. The results of unit root tests in levels and at intercept are presented 

in Table 1. The variable tests were employed for this study to see whether the data was stationary. The test 

is more robust to heterogeneity and unit roots when under a non-standard distribution. The variables were 

found to be I(0) and I(1), thus confirming that variables that are I(2) were not present. The presence of I(2) 

variables in the model would result in spurious F-statistics since the F-statistics computed by Pesaran, Shin 

and Smith (2001) and Nayaran (2005) have their root in the presumption that the variables are I(0) or I(1). 

The results of the study suggest that the variables are mutually integrated in the order of either zero or one, 

or both, which supports the conditions for the use of the ADF unit root test. 

 

Table 1. Stationarity tests of variables using Augmented Dickey-Fuller (ADF) unit root 

Variable Trend Intercept Trend and Intercept  Diagnosis 

Stationary tests of variables using Augmented Dickey-Fuller (ADF) test: 

Trend Specification: Intercept only 

BSL - -5.282460*** - I(0) 

STOKVSAV - -4.600730*** - I(0) 

GDPG - -6.394021*** - I(0) 

M3 - -7.126778*** - I(1) 

Stationary tests of variables using Augmented Dickey-Fuller (ADF) test:  

Trend Specification: Trend and Intercept 

BSL -6.810936*** -6.753963*** -6.680936*** I(0) 

STOKVSAV -7.763481*** -6.578931*** -5.978431*** I(0) 

GDPG -17.42696*** -6.441841*** -8.182452*** I(0) 

M3 -4.210961** -5.328696*** -4.307545** I(0) 

Source: Author’s own compilation from E-Views ***; **; * indicates that we reject the null hypothesis of 

unit root tests at 1%, 5% and 10%, respectively 



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92 

 

ARDL and Non-linear ARDL Long-run Results: Bounds F-test for cointegration 

ARDL Long-run Results: Bounds F-test for cointegration 

Table 2 show that the value of the F-statistic for all three models is greater than the upper-bound 

critical values suggesting that the null hypothesis can be rejected. The F-statistics were all significant at the 

1% level. Thus, it can be concluded that there is a long-run relationship between STOKVSAV and BSL. 

These results align with the findings of Khan and Qayyum (2006). Additionally, a long-run relationship 

exists between GDPG, M3 and BSL. 

 

Table 2. Bounds F-test for ARDL cointegration 

Dependent 

variable 
Independent variable F-test statistic Lower and upper- bounds 

BSL STKOVSAV GDPG M3 16.03214*** 4.45– 6.36 

STOKVSAV GDPG M3 BSL 6.070329*** 4.45-6.36 

GDPG STKVSA M3 BSL 9.043872*** 4.45-6.36 

M3 STKVSA GDPG BSL 4.281633*** 4.66-3.2 

Source: Author’s own compilations, ARDL F-statistic values are calculated by bounds testing approach 

Source: Author’s own compilations, data from SARB & Old Mutual South Africa (2022) 

 

Non-linear ARDL Long-run Results: Bounds F-test for cointegration 

Results revealed an F-statistic lower than the lower bound and were statistically significant. This 

implies that the null hypothesis of no cointegration was accepted as the F-statistic lay below the lower bound 

of the F-statistic. Thus, it was concluded that there is no long-run relationship between BSL and its 
explanatory variables. When STOKVSAV and GDPG were used as dependent variables, the F-statistics of 

67.82906 and 7.074817, respectively, were found to be greater than the upper bounds, suggesting the 

presence of a long-run relationship between the dependent variables and their predictors. Thus, the null 

hypothesis of no cointegration was rejected. However, the same could not be said about the relationship 

between STOVSAV, GDPG and M3. The F-statistic of 3.613920 was found to be between the upper and 

lower bounds, implying that the relationship is inconclusive. The F-statistics were statistically significant at 

1% in all four cases.  

 

Table 3. Banking sector liquidity 

BSL 

BSL STOKVSAV GDPG M3 1.398563*** 2.53-3.59 

STOKVSAV BSL GDPG3 M3 67.89206*** 3.59-4.9 

GDPG BSL STKVSA M3 7.074817*** 3.59-4.38 

M3 BSL STKVSA GDPG 3.613920*** 3.2-4.66 

Note: F-statistic values are calculated by bounds testing approach by Pesaran, Shin and Smith (2001) and 

Shin, Yu and Greenwood-Nimmo (2014). The null hypothesis of asymmetric cointegration is p = Ɵ+ = Ɵ− =
0 

 

Asymmetric non-linear ARDL long-run results 
The presence of asymmetry in the long-run equilibrium due to negative and positive shocks in stokvel 

savings was examined.  Using banking sector liquidity as the dependent variable, all the explanatory 

variables were found to be statistically insignificant in explaining banking sector development implying that 

the N-ARDL is not an appropriate model for predicting banking sector development proxied by banking 

sector liquidity. Similar results obtained when using stokvel savings and money supply as the dependent 

variables suggesting an insignificant influence of baking sector liquidity on stokvel savings and money 

supply. With GDPG as the dependent variable, only a negative shock on money supply resulted in a 

significant increase in GDPG at 5%. 
  



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Table 4. N-ARDL Long Run Form and Bounds Test (3.4.4.4.4.4.4) on BSL 

N-ARDL Long-Run Coefficients Result 

BSL 

Variable Coefficient St.Error t.Statistic Prob 

STOKVSAV_POS -0.148380 0.053603 -2.768109 0.0697 

STOKVSAV_NEG -0.168193 0.068647 -2.450116 0.0917 

GDPG_POS -1.432016 0.836693 -1.711519 0.1855 

GDPG_NEG -1.335738 0.771733 -1.730830 0.1819 

M3_POS -0.000454 0.001863 -0.243590 0.8233 

M3_NEG -0.000323 0.000875 -0.368924 0.7367 

STOKVSAV 

BSL_POS 99.12984 38.07290 2.603685 0.0801 

BSL_NEG 150.7024 54.76167 2.751968 0.0706 

GDPG_POS -44.22538 20.48404 -2.159017 0.1197 

GDPG_NEG -49.40970 22.31685 -2.214008 0.1137 

M3_POS -0.411536 0.160589 -2.562666 0.0830 

M3_NEG 0.283400 0.113765 2.491108 0.0884 

GDPG 

BSL_POS -1.407221 0.809725 -1.737900 0.1258 

BSL_NEG -0.911961 0.551559 -1.653425 0.1422 

STOKVSAV_POS -0.074372 0.036830 -2.019350 0.0832 

STOKVSAV_NEG -0.072385 0.039913 -1.813560 0.1126 

M3_POS -0.001263 0.001185 -1.066353 0.3217 

M3_NEG -0.002837 0.001051 -2.698173 0.0307 

M3 

STOKVSAV_POS -43.55979 23.53003 -1.851242 0.1013 

STOKVSAV_NEG -43.19048 26.22274 -1.647062 0.1382 

BSL_POS -468.8431 271.1939 -1.728811 0.1221 

BSL_NEG -303.9212 206.5404 1.471486 0.1794 

GDPG_POS -231.4554 109.5958 -2.111901 0.0677 

GDPG_POS -291.8407 127.8901 -2.2811965 0.0519 

 

Short- and long-run multipliers 

The adjustment of asymmetry in the long-run equilibrium due to negative and positive shocks in 
stokvel savings have been explored with the use of a dynamic multiplier graph. The multipliers for the variables 

are plotted in Figure 3, which portrays adjustments to a new equilibrium after positive and negative shocks. 

The black dotted line indicates the non-linear adjustment of BSL to adverse shocks, whereas the solid black 

line portrays the adjustment of BSL to a positive shock. The asymmetric pattern indicated by the red dotted 

line is the difference between both negative and positive shocks (Andriamahery and Qamruzzaman 2022). 

In the long-run, when BSL is the dependent variable, any positive or negative changes in stokvel savings 
(STOKVSAV+ or STOKVSAV-) do not significantly impact BSL. The same is observed for gross domestic 

product growth and money supply (GDPG+ or GDPG-; M3+ or M3). Therefore, N-ARDL is not the best 

model to detect the presence of a long-run relationship between BSL and stokvel savings, GDPG and M3, 

which are used as the independent variables. 
  



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BSL (STOKVSAV GDPG M3) 

STOKVSAV 

-60,000,000

-40,000,000

-20,000,000

0

20,000,000

40,000,000

60,000,000

1 3 5 7 9 11 13 15

Multiplier for STKVSA(+)

Multiplier for STKVSA(-)

Asymmetry Plot (with C.I.)

 

GDPG 

-30,000,000

-20,000,000

-10,000,000

0

10,000,000

20,000,000

1 3 5 7 9 11 13 15

Multiplier for GDPG(+)

Multiplier for GDPG(-)

Asymmetry Plot (with C.I.)

 

M3 

-300,000

-200,000

-100,000

0

100,000

200,000

300,000

1 3 5 7 9 11 13 15

Multiplier for M3(+)

Multiplier for M3(-)

Asymmetry Plot (with C.I.)

 

STOKVSAV (BSL GDPG M3) 

BSL 

-400

-200

0

200

400

600

800

1 3 5 7 9 11 13 15

Multiplier for BSL(+)

Multiplier for BSL(-)

Asymmetry Plot (with C.I.)  

GDPG 

-200

-100

0

100

200

300

400

1 3 5 7 9 11 13 15

Multiplier for GDPG(+)

Multiplier for GDPG(-)

Asymmetry Plot (with C.I.)  

 

M3 

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

1 3 5 7 9 11 13 15

Multiplier for M3(+)

Multiplier for M3(-)

Asymmetry Plot (with C.I.)

 

GDPG (BSL STOKVSAV M3) 

STOKVSAV 

-30

-20

-10

0

10

20

30

1 3 5 7 9 11 13 15

Multiplier for STKVSA(+)

Multiplier for STKVSA(-)

Asymmetry Plot (with C.I.)

 

 

GDPG 

-30

-20

-10

0

10

20

30

1 3 5 7 9 11 13 15

Multiplier for STKVSA(+)

Multiplier for STKVSA(-)

Asymmetry Plot (with C.I.)

 

M3 

-300,000

-200,000

-100,000

0

100,000

200,000

300,000

400,000

1 3 5 7 9 11 13 15

Multiplier for STKVSA(+)

Multiplier for STKVSA(-)

Asymmetry Plot (with C.I.)

 

M3(BSL STOKVSAV GDPG) 

BSL 

-600

-400

-200

0

200

400

1 3 5 7 9 11 13 15

Multiplier for BSL(+)

Multiplier for BSL(-)

Asymmetry Plot (with C.I.)  

STOKVSAV 

-300

-200

-100

0

100

200

300

400

1 3 5 7 9 11 13 15

Multiplier for GDPG(+)

Multiplier for GDPG(-)

Asymmetry Plot (with C.I.)

 

GDPG 

-100

-80

-60

-40

-20

0

20

40

60

1 3 5 7 9 11 13 15

Multiplier for STKVSA(+)

Multiplier for STKVSA(-)

Asymmetry Plot (with C.I.)

 

Figure 3. Short- and long-run multipliers 

 

CONCLUSION 

 
The study empirically investigates the possible nonlinear relationship between stokvel saving and 

banking sector liquidity using quarterly time series secondary data ranging from 2009Q4-2020Q2. The 

results of the break-even unit root tests reveal that variables were found to be I(0) and I(1), thus confirming 



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95 

 

that variables that are I(2) were not present. The findings of ARDL show that the value of the F-statistic for 
all three models (STOKVSAV, GDP and M3) are greater than the upper-bound critical values suggesting 

that the null hypothesis can be rejected. The asymmetry results revealed that in the long-run equilibrium due 
to negative and positive shocks in STOKVSAV was examined using BSL as the dependent variable, all the 

explanatory variables were found to be statistically insignificant in explaining banking sector development 

implying that the N-ARDL is not an appropriate model for predicting banking sector development proxied 

by BSL. Similar results obtained when using multipliers that in the long-run, when BSL is the dependent 
variable, any positive or negative changes in stokvel savings (STOKVSAV+ or STOKVSAV-) do not 

significantly impact BSL. The same is observed for gross domestic product growth and money supply 

(GDPG+ or GDPG-; M3+ or M3). N-ARDL is not the best model to detect the presence of a long-run 
relationship between BSL and STOKVSAV, GDPG and M3, which are used as the independent variables. 

The study suggests that STOKVSAV can provide the opportunity for the South African government and 

formal financial/banking sector to develop mutually beneficial relationships or linkages to make such 
STOKVSAV more effective and efficient in mobilising savings and advancing credit to the low- and middle-

income households.  

 
ACKNOWLEDGMENTS 

 
This research paper is a product of my unpublished Doctor of Philosophy’s degree 2023 thesis 

entitled: “The role of stokvels in banking sector development in South Africa”. This thesis may be found in 

the UNISA repository but is unpublished material.  

 

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