The Stability of Money Demand Function: Evidence from South Africa

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.


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;. 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 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 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. 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 andTobin, 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).

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: 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.
Where LRM3 2 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 index 3 (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 Ω 1 >0; Ω 2 <0. However, the expected sign of Ω 3 and Ω 4 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 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)

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 Y t is (n×1), A 0 is (n×1) constant matrix term, A i is (n×n) matrices coefficient and ε 1t is vector of error term.
The vector variable ΔY t and Y t-i have a unit root. Therefore, the rank Π (r) matrix determines the long-run relationship. If rank = 0, the VAR with k th 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 Where α is a strength parameter that measures the quality of co-integration and β' vector of co-integration. Hence, β' Y t is stationary at I(0). Equation (5) implies that there is a long run linear combination among variables where r < n.

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: Where φ 11 …φ 51 is a constant term, τ 12i … τ 56i represent long-run elasticity, ∆ is designed to shows the operator of the first difference, ψ 11 …ψ 51 reveals the parameter of the error correction model (ECM) which is specified as ρ 0 is constant of long term, ρ 1 …, ρ 4 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).
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).

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.

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.

Unit Root Test
Our aim in this paper is to investigate broader money demand function (M3)

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.

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.

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 x 2 is reported in Table 6 Panel B. The P-value of the χ 2 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. ( 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

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 cointegration 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.