TX_1~AT/TX_2~AT


International Journal of Economics and Financial 
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ISSN: 2146-4138

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International Journal of Economics and Financial Issues, 2020, 10(5), 16-22.

International Journal of Economics and Financial Issues | Vol 10 • Issue 5 • 202016

The Stability of Money Demand Function: Evidence from 
South Africa

Farhan Abdi Omar1*, Abdishakur Mohamed Hussein2

1Department of Research and Development, Egalle Minds, Hargeisa, Somaliland, 2Faculty of Business and Economics, Beder 
International University, Hargeisa, Somaliland. *Email: farhan.omar@egalleminds.com

Received: 18 April 2020 Accepted: 23 July 2020 DOI: https://doi.org/10.32479/ijefi.9799

ABSTRACT

The main purpose of this paper is to assess whether the Money Demand Function is stable in South Africa by employing the Johansen co-integration 
and the Vector Error Correction Model. The results indicate unstable money demand function among its determinant including real income, interest 
rate, stock price, and real exchange rate. More importantly, the M3 has a significant long-run relationship among its determinant except the interest 
rate. Furthermore, the short term dynamics show that unidirectional causality runs from determinants to the broader money except interest rate and 
exchange rate. This paper provides crucial evidence for policy-makers to consider the importance of the stock market activity to avoid misspecification 
of the money demand function.

Keywords: Money Demand, Johansen, Vector Error Correction Model, Stock Price 
JEL Classifications: E5, E41

1. INTRODUCTION

Many macroeconomists acknowledged the importance of behavior 
of money demand function when formulating an efficient monetary 
policy. The stability of the money demand function among 
its determinant including income and interest rate is a crucial 
component for the success of monetary intermediate targeting 
or direct approaches. This paper shows new evidence about the 
stability and relationship of the money demand function among 
its determinants in South Africa by including stock market activity 
in the function using the Johansen co-integration and Vector Error 
Correction Model (VECM). 

The literature over the past two decades indicates that financial 
reforms and switching between monetary policies have increased 
uncertainty about the stability of the money demand function 
(Kumar et al., 2013; Maki and Kitasaka, 2006; Nchor and 
Adamec, 2016). South Africa has experienced several different 
financial reforms and monetary regimes since the 1960s. A 

liquid asset ratio, cash reserve-based system, monetary targets 
regime, and inflation targeting were the main systems that the 
South Africa Reserve Bank (SARB) adopted (Table 1) (Aron 
and Muellbauer, 2002; 2007).

In 2000, SARB implemented an inflation targeting system. The 
inflation targeting policy is that the central bank (SARB) forecasts 
the future rate of inflation and compares it with a predetermined 
inflation rate (3-6% in the case of SA). The approach proposed 
that the monetary policy is being directly forward-looked that 
employing inflation forecasting for guidance. The inflation 
rate is directly affected by policy instruments (interest rate, for 
example). Hence, it is argued that monetary aggregates have no 
role under this approach (Baltensperger et al., 2001). However, 
Baltensperger et al. (2001) investigated the nexus between broader 
money (M3) and inflation where they proposed that monetary 
aggregates are still effective in the process of forecasting and 
targeting inflation. The fact is that M3 provides useful information 
about the movements of the price. Besides, stable monetary 

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Omar and Hussein: The Stability of Money Demand Function: Evidence from South Africa

International Journal of Economics and Financial Issues | Vol 10 • Issue 5 • 2020 17

aggregates is a useful instrument to stabilize the inflation rate 
(Kumar et al., 2013; Nell, 2003).

The above argument emphasizes that stable money demand 
function is powerful under inflation targeting regime but the 
question is whether the money demand function is stable in 
South Africa?. In the South African context, a few papers 
examined the relationship between money demand and its 
determinant. The results show stable money demand before 
implementing the inflation targeting regime (Tavlas, 1989) 
(Hurn and Muscatelli, 1992) (Jonsson, 2001)(Bahmani-Oskooee 
and Gelan, 2009)1. However, most of the empirical literature 
conducted after the regime indicates that stable money demand 
function (M3) does not exist (Nell, 2003) (Tlelima and Turner, 
2004) (Kapingura, 2014). The core variables were income and 
interest rate, but stock price and other financial variables are 
omitted.

Earlier studies such as Friedman (1988) carried out empirical 
literature analyzing the nexus between stock market activity 
and money demand function in the US using data from 1961 to 
1986. Friedman proposed stock market affects money demand 
in different channels: (1) Through income effect (positive): An 
increase of stock price reveals a rise of wealth that can result 
in higher money demand. (2) Substitution effect (negative) 
an increase in the price of assets reveals that the investment 
market is more attractive than holding money where the 
people tend to invest and as a result, it reduces the demand 
for money. Finally, Friedman concluded that the impact of 
the stock market on money demand function is ambiguous 
(Baharumshah et al., 2009).

Following the seminal work of Friedman (1988), empirical 
literature highlighted inserting stock price in the money 
demand function improves the functional form. Kia (2006), 
Baharumshah et al., (2009) and others showed that the stock 
price is an important determinant in both developed and 
developing countries. Furthermore, the omission of such an 
important variable could result in instability in the money 
demand function. In this regard, whereas the previous literature 
on South Africa neglected (to our knowledge) the impact of 
the stock price on monetary aggregate, our study includes this 
crucial variable in the model.

This study aims to address the stability and determinant of 
the money demand function by including the stock market 

1 Bahmani-Oskooee used M2 instead of M3 and they found that M2 demand 
function is stable using a data between 1971Q1 and 2001Q3. 

activity. Our objective is to shed light on the co-integration 
analysis of broader money, real income, stock price index and 
real exchange rate by using the most recent data. We examine 
broader money rather than M0, M1 or M2 because M3 is an 
important indicator of inflation targeting which South Africa 
is adopting currently.

In brief, we find that real income has a positive and significant 
relationship on M3. In contrast, both interest rates and exchange 
rates are negatively related to broader money. Additionally, the 
stock price has a significant positive influence on the money 
demand function. For the period of investigation, the short term 
dynamics show all determinant have unidirectional causality 
except interest rate and exchange rate. The rest of the paper 
is planned as follows: Section 2 provides a review of existing 
literature. The methodology is discussed in section 3. Section 4 
provides results and discussions. Finally, policy recommendation 
is found in Section 5.

2. LITERATURE REVIEW

Keynes (1936) developed the liquidity preference theory in order 
to analyze the money demand function. Keynes started with the 
question of why money is held by people. Three motives are 
underlined (1) transaction motive (2) precautionary motive (3) 
speculative motive. Keynes asserted the reason that people hold 
cash balance is to fill up the gap between receipts and payment 
as same as for precautionary propose. Keynes determined that 
both of the first two motives are a function of income (Nchor 
and Adamec, 2016). Subsequently, some other researchers 
followed Keynes’s proposal whereby the income is determinant 
of money demand, this researches including Adekunle (1968) 
and Sowa (1993).

Baumol, 1952 and Tobin, 1956 latter argued the interest rate is 
one of the crucial explanatory variables that affect all money 
demand motives. Besides, interest estimates the opportunity cost 
of holding money. For instance, if the interest rate increases, the 
opportunity cost of holding money will rise. Hence, people desire 
to decrease their holding quantities of money (Mishkin, 2007; 
Nchor and Adamec, 2016).

After these different theories are carried out, the literature 
turns to investigate money demand function empirically. 
Baharumshah et al., 2009; Bahmani-Oskooee and Bohl, 2000; 
Bahmani-Oskooee and Shabsigh, 1996; Bahmani-Oskooee* 
and Rehman, 2005; Bhaskara and Singh, 2006; Cheong, 2007; 
Dreger and Wolters, 2010; Hamdi et al., 2015; Hamori and 
Hamori, 2008; Kjosevski, 2013; Knell and Stix, 2005; Mall, 
2013; Samreth, 2008 are consider both determinant of demand 
function and its stability. In the African continent, a sufficient 
number of empirical evidence ware published in particular 
(Darrat, 1986; Kapingura, 2014; Kumar et al., 2013; Nchor and 
Adamec, 2016; Tlelima and Turner, 2004). Table 2 indicates 
how the elasticity of income and interest rate differ across 
countries in Africa.

Table 1: Summary of monetary policy regimes in South 
Africa
Duration Monetary policy adopted 
1960-1980 Liquid asset ratio based system
1980-1985 Cost of the cash reserve
Mid 1985-1999 Monetary targeting
2000-current Inflation targeting
Source: (Aron and Muellbauer, 2007)



Omar and Hussein: The Stability of Money Demand Function: Evidence from South Africa

International Journal of Economics and Financial Issues | Vol 10 • Issue 5 • 202018

3. METHODOLOGY

3.1. Data and Model Specification
The study considers quarterly time series data from 2000Q1 
through 2017Q2 (70 observations) where all data was collected 
from IMF International Financial Statistics (IFS) database except 
broader money (M3) and stock price index. The former is obtained 
from South Africa Reserve Bank (SARB) whereas the latter is 
collected from Fred economic data. All variables are in natural 
log form excluding interest rate.

Following (Sriram, 2000) and base on the Friedman (1988) 
seminal, the broader money demand function is specified as:

   
( ),3   = f ScaleM

P
OC

 
(1)

Where the demand for real broader money (M3/P) is a function 
of scale variable represent economic activity and opportunity cost 
which stands for the cost of holding money. We extend equation 
(1) into the econometric equation.

      0 1 2 3 43    ε= Ω +Ω + Ω + Ω + Ω +t t t t ttLRM LY R LSP LEX  (2)

Where LRM32 is a log of real demand for broader money. LY 
is the proxy of the scale variable. In fact, the appropriate scale 
variable has been strongly debated in the existing literature 
(Kjosevski, 2013). Some authors emphasize that using GDP as 
a proxy of scale variable could cause an overload of the level 
of the transaction in the economy. Consequently, following 
Kjosevski (2013), Payne (2003), Pelipas (2006) and others, 
the industrial production index (IPI, 2010=100) is used as a 
scale variable in this paper. Following Nell (2003), the (R) 
in the equation represents government bonds rate to estimate 
opportunity cost for holding money. LSP is the log of the stock 
price index3 (2015=100). Finally, LEX is the real exchange 
rate (domestic/foreign) which is used to capture the cost of 
holding domestic money against foreign currency. Besides, 
the expectation of parameters is Ω1>0; Ω2<0. However, the 
expected sign of Ω3 and Ω4 are ambiguous. The former is 
discussed in the introduction section and the latter is due 
to different possible effects of the real exchange rate. For 

2 South Africa reserve bank (SARB) defines M3 as “M2 plus all long term 
deposit with monetary banking institutions”.

3 Johannesburg stock exchange (JSE) provides the index and it contains all 
share prices of 150 companies listed in the market. 

instance, if the real exchange rate depreciates, the domestic 
residents benefiting from increasing the value of the foreign 
asset, therefore, if the wealth follows and goes up the demand 
for money increases. On the other hand, if further depreciation 
expected, it leads to a decline in money demand (Bahmani-
Oskooee and Malixi, 1991) (Kia, 2006) (Tang, 2007)

3.2. Johansen Co-integration Specification
It has been reported in the literature that most macroeconomic 
data have unit root and conventional thinking was to convert data 
into stationary before testing (Johansen, 1991; Ramachandran, 
2004). However, Engle and Granger (1987) first proposed that if 
such a linear combination between two or more non-stationary 
variables is stationary, the variables are co-integrated. Afterward, 
(Johansen, 1991) and (Johansen and Juselius, 1990) developed 
a useful model to test long-run co-integration to analyze 
multivariate time series. In order to investigate the existence 
of co-integration among variables, first, we consider Vector 
Autoregressive model (VAR) with a vector variable Yt is (n×1), 
A0 is (n×1) constant matrix term, Ai is (n×n) matrices coefficient 
and ε1t is vector of error term.

  0 1 1 2 2 1   ε− −= + + +t t t tY A A Y A Y  (3)

  

1

0
1

  ε
−

− −
=

∆ = + Π + +∑
k

t t k i t i t
i

Y A Y AY
 

(4)

The vector variable ΔYt and Yt–i have a unit root. Therefore, the 
rank Π (r) matrix determines the long-run relationship. If rank = 0, 
the VAR with kth lags will proceed and there is no cointegration 
among variables in the long run. Despite that, if 0 <r<n, express 
into r×n matrix in such that rank with cointegration determined by

   
' Π = αβ  (5)

Where α is a strength parameter that measures the quality of 
co-integration and β’ vector of co-integration. Hence, β’ Yt is 
stationary at I(0). Equation (5) implies that there is a long run 
linear combination among variables where r < n.

3.3. Vector Error Correction (VECM) Specification
Subsequently, the second step after confirming the existence of 
linear combination among variables is to employ Vector Error 
Correction (VECM) to conduct the long-run coefficients, Error 
correction model that indicates the speed of adjustments towards 
long-run equilibrium and granger causality test. The VECM model 
is specified as the following:

Table 2: Summary of income and interest rate elasticity in Africa
Author Country Monetary aggregates: Period Methodology Income Interest rate Stability
Nchor and Adamec (2016) Ghana M1; 1990-2014 ECM 2.43 (0.574)*** ‒0.81 (0.66)*** Stable 
Kapingura (2014) South Africa M3; 1995Q1-2012Q4 JML &VECM 5.013(1.090) 0.073(0.024) Not stable 
Kumar et al. (2013) Nigeria M1; 1960-2008 ECM 0.90 (4.52)*** ‒0.19 ((3.16) *** Stable
Herve and Shen, (2011) Côte d’ivoire M1; 1980-2007 JML 5.31 (6.16)** ‒0.19 (0.24)** Not stable 
Akinlo, (2006) Nigeria M2; 1970Q1-2004Q4 JML 1.09 (43.8)*** ‒0.09(1.91)* Stable 
Nell (2003) South Africa M3; 1965-1997 JML 1.27 (6.5)*** ‒0.006 (-2.6)*** Not stable 
Darrat (1986) Kenya M1; 1969Q1-1978Q4 OLS 1.843 (8.91)* −0.169(3.40)* Stable 
***, ** and * represents 1%, 5% and 10% significant of level respectively. (…) The number in parenthesis shows t-value. OLS, ECM, ARDL, JML are ordinary least square, 
autoregressive distribute lag, Johansen maximum likelihood respectively



Omar and Hussein: The Stability of Money Demand Function: Evidence from South Africa

International Journal of Economics and Financial Issues | Vol 10 • Issue 5 • 2020 19

     

11 12 13 14
1 1 1

15 16 11 1, 1 1
1 1

3   3      

      

ϕ τ τ τ

τ τ ψ ε

− − −
= = =

− − −
= =

= + ∆ + ∆ + ∆

+ ∆ + ∆ − +

∑ ∑ ∑

∑ ∑

k k k

t t i t i i t i i t i
i i i

k k

i t i i t i t t
i i

LRM LM LY R

LSP LEX ECM

 

 
(6)

       

21 22 23 24
1 1 1

25 26 21 2, 1 2
1 1

  3      

      

ϕ τ τ τ

τ τ ψ ε

− − −
= = =

− − −
= =

= + ∆ + ∆ + ∆

+ ∆ + ∆ − +

∑ ∑ ∑

∑ ∑

k k k

t t i t i i t i i t i
i i i

k k

i t i i t i t t
i i

LY LM LY R

LSP LEX ECM

 

 
(7)

        

31 32 33 34
1 1 1

35 36 31 3, 1 3
1 1

  3      

      

ϕ τ τ τ

τ τ ψ ε

− − −
= = =

− − −
= =

= + ∆ + ∆ + ∆

+ ∆ + ∆ − +

∑ ∑ ∑

∑ ∑

k k k

t t i t i i t i i t i
i i i

k k

i t i i t i t t
i i

LR LM LY R

LSP LEX ECM

 

 
(8)

       

41 42 43 44
1 1 1

45 46 41 4, 1 1
1 1

  3      

      

ϕ τ τ τ

τ τ ψ ε

− − −
= = =

− − −
= =

= + ∆ + ∆ + ∆

+ ∆ + ∆ − +

∑ ∑ ∑

∑ ∑

k k k

t t i t i i t i i t i
i i i

k k

i t i i t i t t
i i

LSP LM LY R

LSP LEX ECM

 

 
(9)

       

51 52 53 54
1 1 1

55 56 51 5, 1 5
1 1

  3      

      

ϕ τ τ τ

τ τ ψ ε

− − −
= = =

− − −
= =

= + ∆ + ∆ + ∆

+ ∆ + ∆ − +

∑ ∑ ∑

∑ ∑

k k k

t t i t i i t i i t i
i i i

k k

i t i i t i t t
i i

LEX LM LY R

LSP LEX ECM

 

 
(10)

Where φ11…φ51 is a constant term, τ12i… τ56i represent long-run 
elasticity, ∆ is designed to shows the operator of the first difference, 
ψ11…ψ51 reveals the parameter of the error correction model (ECM) 
which is specified as

    1, 1 1 0 1 2 3 4 3  ρ ρ ρ ρ ρ− −= − − − − −t tECM LRM LY R LSP LEX  (11)

ρ0 is constant of long term, ρ1…, ρ4 is long term elasticity and 
finally k is the optimal lag length chosen by using Akaike 
Information Criterion (AIC) conducted from VAR lag selection 
(Wang and Wang 2017).

The third step is to calculate the Granger causality test in order 
to investigate the direction of the relationship among variables. 
The VECM Granger causality is estimated. The granger causality 
hypothesis should be detailed as:
H0: ρ11k=0, ρ12k=0, ρ13k=0, ρ14k=ρ15k=0 (the lagged variable does not 

cause to LRM3).
HA: ρ11k≠0, ρ12k≠0, ρ13k≠0, ρ14k≠ρ15k≠0 (the lagged variable does 

cause to LRM).

By computing the Wald test, if the P < 0.10 we reject the null 
hypothesis and conclude that the lagged value does granger cause to 
the dependent variable and vice-versa (Bah and Azam, 2017, p. 8).

3.4. Test Stability of the Model and Robustness Check
In this study, we performed cumulative sum of recursive residuals 
(CUSUM) and cumulative sum of recursive residuals square 

(CUSUMSQ) developed by Brown et al. (1975) to test the stability 
of parameters in the long run. Subsequently, it is used to test the 
robustness of the model is to obtain the co-integration among 
variables. The study applied several diagnostic tests including 
the Breusch–Godfrey LM test and ARCH heteroskedasticity test 
to test the existence of autocorrelation and heteroskedasticity 
respectively.

4. RESULTS AND DISCUSSIONS

This section reports our empirical findings, including the results 
of the unit root test, co-integration test, long-run elasticity, granger 
causality, robustness, and stability check.

4.1. Unit Root Test
Our aim in this paper is to investigate broader money demand 
function (M3) in South Africa using Johansen Maximum 
Likelihood (JML) co-integration test and Vector Error Correction 
Model (VECM). Conducting the unit root test is necessary to check 
the validity of the JML assumption which assumes all variables 
are stationary at first deference I(1). An augmented Dickey-Fuller 
test (ADF) is employed. The null hypothesis of ADF shows the 
existence of a unit root. A maximum of 4 lags was chosen using 
the Schwartz information criterion (SIC).

Table 3 presents the results of the test. The result reveals that all 
variables are non-stationary at the level and therefore, they are 
stationary at the first difference I(1).

4.2. Lag Order Selection
Since all variables are stationary at the first difference I(1), it 
is reasonable to proceed and obtain the number of appropriate 
lags for the JML test by formulating the VAR lag order selection 
method. Consider that we have quarterly short term observation 
data (only 70), we selected a maximum of 6 lags. Base on the 

Table 3: ADF unit root test
Level First difference Conclusion

Constant Constant 
with trend

Constant Constant 
with trend

LM3 ‒2.00 ‒1.75 ‒9.03*** 9.26*** I(1)
LY ‒2.32 ‒2.60 ‒4.06*** ‒3.62*** I(1)
R ‒2.18 ‒2.95 ‒4.08*** ‒7.36*** I(1)
LSP ‒0.91 ‒2.43 ‒6.01*** ‒5.97*** I(1)
LEX ‒0.94 ‒1.56 ‒7.37*** ‒7.34*** I(1)
***, ** and * denotes significant at 1%, 5% and 10% significance level, respectively. The 
optimum lag length selected based on Schwarz Info Criterion

Table 4: VAR Lag order selection
Lag LR FPE AIC SC HQ
1 NA 2.04e-10 ‒8.13 ‒7.28* ‒7.80
2 58.31 1.53e-10 ‒8.42 ‒6.74 ‒7.76
3 39.40 1.54e-10 ‒8.45 ‒5.92 ‒7.45
4 65.97 8.02e-11 ‒9.17 ‒5.80 ‒7.84
5 47.24* 5.83e-11* ‒9.60* ‒5.38 ‒7.93*
6 16.18 9.46e-11 ‒9.29 ‒4.23 ‒7.30
 *Indicates lag order selected by the criterion (each test at 5% level). LR: Sequential 
modified LR test statistic. FPE: Final prediction error. AIC: Akaike information 
criterion. SC: Schwarz information criterion. HQ: Hannan-Quinn information criteria



Omar and Hussein: The Stability of Money Demand Function: Evidence from South Africa

International Journal of Economics and Financial Issues | Vol 10 • Issue 5 • 202020

results presented in Table 4, LR, FPE, AIC and HQ suggested 5 
lags. Hence, 5 lags are included in the model. Another important 
diagnostic before investigating co-integration is to ensure that no 
significant lag was left. Correlogram of residuals is taken into the 
account where no significant lag left.

4.3. Johansen Co-integration Test
Subsequently, equation (3) - (5) is employed to test the number of 
co-integration equations in the model. As Panel A in Table 5 reveals 
the results of the JML test where both trace and maximum eigen 
value statistics confirm that at least two co-integration equations 
exist in the model. However, we tasted only one co-integration 
equation since our interest is only to assess the relationship of 
broader money (M3) among its determinants. Panel B in Table 5 
shows Normalised long-run elasticity. The result indicates that signs 
of income and interest rate are consistent with the prediction of 
theoretical signs. Moreover, the result shows that the stock market 
price has positively and significantly related to M3. The positive 
relationship reflects income effect is large than the substitution 
effect of stock market activity. The positive elasticity of stock price 
consistent with (Baharumshah et al., 2009). On the other hand, the 
depreciation of the exchange rate causes a decrease of M3 which 
possibly comes from the expectation of the people that the domestic 
money depreciation can be deeper in the future and thereby holding 
it causes loss of its value. Kapingura (2014) found that elasticity 
of exchange rate is - 0.945 in South Africa, which is greater than 
our elasticity.

4.4. Short-run Dynamics
Afterwards, the short term relationship was tested. The VECM 
is required in order to check the validity and convergence of 
the long term relationship. To determine the existence of a short 
term relationship at least one of the ECM coefficients should 
be significant. The results presented Panel A in Table 6 indicate 
that The error correct model (ECM) is negative as expected and 
significant. Therefore, the ECM emphasized the existence of 
the long-run co-integration among variables. Additionally, the 
ECM shows the departure of the dependent variable from the 
independent variable is corrected 94% each period. In other words, 

the disequilibrium of long-run relationship is corrected 94% each 
period where the convergence to the long-run equilibrium takes 
approximately a quarter and 2 months.

The short term dynamics also explained the causality between 
variable which is when a variable past behaviour predicts 
the future value of another variable. The granger causality is 
tested to detect this dynamic behaviour within VECM. The 
results as illustrated in Table 6 indicate the presence of this 
dynamic behaviour and it is directions are are ∆LY→∆LRM3, 
∆LSP→∆LRM3, ∆LSP→∆LY, ∆LSP→∆LR, ∆LSP→∆LEX. 
In other words, results in Table 6 Panel A show significant 
unidirectional causality runs from real income and stock price 
to the broad money. The result reveals interest rate and the 
real exchange rate does not granger causes broader money. In 
contrast, the results highlight that there is no causality running 
from RM3 to determinant variables.

4.5. Robustness Check and Stability Test
In Panel B of Table 6, we turn to check several diagnostic checks 
including model stability, autocorrelation, and heteroskedasticity 
test. First, the Breusch–Godfrey LM test is calculated to capture 
the existence of serial correlation in the residuals. The x2 is 
reported in Table 6 Panel B. The P-value of the χ2 is 0.07 which 
is >0.05 level of conventional significance. This implies that the 
model is fit and free from serial correlation problems. Next, we 
turn to estimate ARCH Heteroskedasticity. The same procedure 
has been followed where it is concluded that heteroscedasticity 
is not present.

Finally, the cumulative sum of recursive residuals (CUSUM) and 
cumulative sum of recursive residuals square (CUSUMSQ) are 
estimated to test the model stability. The results are presented 
in Figure 1. The results show that the two tests lead to different 
conclusions. The former indicates a stable long-run relationship, 
whereas the latter shows a deviation of the money demand 
function. Therefore, to ensure the existence of a structural break, 
the Chow test is calculated. The results of the Chow test indicate 
that there is structural break 2010q2 through 2011Q1 where 
F-statistics rejected. The result of the Chow test is not reported 
in order to save some space.Table 5: Johansen Maximum Likelihood result of the RM3 

demand function
Panel A: JML trace statistics and maximum Eigen value results
Null Alternative Trace 

statistics
95% 

Critical 
value

λmax
Statistics

95% 
Critical 
value

r=0a r=1 97.42* 69.82 34.29* 33.88
r≤3 r=2 63.14* 47.86 28.08* 27.58
r≤2 r=3 35.06* 29.80 18.14 21.13
r≤2 r=4 16.92* 15.49 8.67 14.26
r≤1 r=5 8.25* 3.84 8.25* 3.84
Panel B: Normalized co-integration coefficients
LRM3=0.95LY–0.012R+0.45 LSP–0.40LEX
(0.48) (0.02) (0.07) (1.33)
[–1.96] [–0.49] [-6.50] [-5.65]
(a) Indicate the rank of the co-integration equation. (*) Shows the significance of 
t-statistics at 5%. Trace and maximum Eigen-value statistics are obtained including 
intercept with no trend. P-values is base on (Mackinnon et al., 1999). (…) The number in 
parentheses represents standard error and […] the number in brackets indicates t-statistics

Table 6: Panel A: Granger causality test results
Dependent variable

ΔLRM3 ΔLY ΔR ΔLSP ΔLEX ECM
ΔLRM3 - 1.89 0.60 1.13 2.17 –0.95***
ΔLY 19.75*** - 0.62 4.21 4.86 0.054
ΔR 2.83 3.91 - 3.33 3.22 –0.11
ΔLSP 15.15*** 20.60*** 10.57* - 10.81* -0.07
ΔLEX 10.08* 2.61 3.10 5.32 - –0.29
*** and ** denotes significant at 1% and 5% significance level, respectively

Panel B: Robustness check
Test Value 
R-square 0.71
Autocorrelation LM test 5.27a
ARCH heteroskedasticity test 0.64a

***and *indicates the level of significance 1% and 5% respectively. (a) Represents χ2 
value



Omar and Hussein: The Stability of Money Demand Function: Evidence from South Africa

International Journal of Economics and Financial Issues | Vol 10 • Issue 5 • 2020 21

5. CONCLUSION

The importance of money demand stability has been underlined 
to attain long term objectives of monetary policy. The previous 
research has shown that financial reforms and changing monetary 
policies could affect the stability of money demand function. 
Furthermore, the current literature in South Africa indicates that 
money demand is unstable since SARB adopted the inflation 
target policy in 2000.

The purpose of this paper was to investigate the stability of 
money demand function in South Africa. The paper included 
a new variable (our best knowledge) in the money demand 
function in South Africa. The stock market activity is included 
following by Friedman’s (1988) seminal work. The long-run co-
integration of real broader money (RM3), income, interest rate, 
stock price, and real exchange rate is confirmed by the Johansen 
co-integration model test. The VECM supported the existence of a 
long-run relationship. CUSUM and CUSUMSQ are also tested to 
investigate the stability of the money demand function. The money 
demand function is found unstable according to CUSUMSQ. And, 
Chow test confirmed the existence of a structural break in 2010Q2. 

For the policy-makers, the results suggest the importance of 
stock price and foreign activity to generate long term effective 
money demand function. Although the money demand function 
still unstable when the two variables are included, however, 
the exclusion of them could delay the recovery of the stability. 
Furthermore, both variables showed their influence in the long run. 
Another important point is that income elasticity is approximately 
unitary which suggests to the policy-makers should allow the 
money supply to grow the same rate with income growth to avoid 
mismatching between money demand and money supply. Finally, 
the study suggests further research on money demand stability by 
taking a structural break into the account.

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Figure 1: Cumulative sum of recursive residuals and cumulative sum of recursive residuals square for stability test



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