Impact of Sub-Economic on Money Supply in Nigeria: An Autoregressive Distribution Lag (ARDL) Approach

The escalation in dollar rates and the price instability in the Nigerian econo-my went through some significant structural and institutional changes such as the liberalization of the external trade, the elimination of price and interest rate controls, and the adoption of a managed float exchange rate system as well as the changes in monetary policy including innovations in the banking sector. Hence, the study examines the impact of financial development on money demand in Nigeria by means of ARDL approach. It examined the quarterly returns of M2, exchange rate (EXR), inflation rate (IFR), currency in credits to private sector (CPS) and circulation (CIC). The data span from 1991 to 2018. The study utilizes regression model techniques where the regression model’s residual is tested for Cointegration using Engle-Granger residual approach, the significances of the variable’s co-movement are checked by pairwise Granger Causality tests and ARDL and VECM are estimated in order to account for the short run and long run relationship among the variables. From the empirical results, Engle-Granger residuals and pairwise Granger Causality tests confirm cointegration among variables. The ARDL and VECM confirm the long run relation between money demand (M2) and financial development variables: CPS and CIC. ARDL models (short run relationship) are estimated for exchange rate and inflation rate. Long run (VECM) analysis has confirmed significance of financial development variables (CPS and CIC) with positive sign; implies that money demand function is stable in long run. The VECM granger causality


Introduction
The demand for money refers to the total amount of riches held by the households and companies; this is affected by several factors such as income levels, interest rates, price levels (inflation) and uncertainty. The impact of these factors on demand for money can be attributed to these three reasons: transaction, precautionary and speculative. The demand for money function creates a contextual to review the efficacy of monetary policies, as an imperative issue in terms of the overall macroeconomic stability. Money demand is an important indicator or pointer of growth for a particular economy. [1] affirmed that increment in money demand mostly indicates a country's improved economic situation, as against the falling demand which is normally a sign of abating economic climate.
Monetarists accentuate the role of governments in controlling for the amount of money in circulation. Their assessment on monetary economics is that the variation on money supply has a major influence on national product in the short run and on price level in the long run. As well, they claim that the objectives of monetary policy are paramountly met by steering the increment rate of money supply.
Today's monetarism is allied with the work of Friedman, who was one among the generation of economists to agree to take Keynesian economics and then disparage it on its own terms. Friedman debated that inflation is at all times and universally a monetary phenomenon. Similarly, he backed that central bank policy aimed at keeping the supply and demand for money in equilibrium, as measured by growth in productivity and demand [2]. For instance, the European Central Bank formally bases its monetary policy on money supply goals. Adversaries of monetarism, including neo-Keynesians, debated that demand for money is central to supply of money and the money supply is controlled by its Central Bank, for example, Central Bank of Nigeria (CBN) while some conservative economists disputed that demand for money cannot be predicted. production relates to the long-term aspect of money demand or the need for money (transaction demand). This means that the increased issue of money which is consistent with price stability may solely be achieved in the long run if it follows the growth of output. [1] stated that the increased issue of money which is consistent with price stability may solely be achieved in the long run if it follows the growth of output. In the short term, a decreasing rate of money circulation may cause the money demand to rise irrespective of the movements in real production. However, the ongoing increase in money supply, regardless of the trends in production, leads to the stronger inflator pressures. Hence, this study set out to examine the relationship between money supply and other macroeconomic time series.
[8] studied the money demand functions for long run and short run for Nepal using the annual data set of 1975 to 2009. The ARDL modeling to cointegration had used to analysis cointegration. The bounds test shows the exists of long run cointegration relationship among demand for real money balances, real GDP and interest rate in case of both narrow and broad monetary aggregates. Furthermore, the CUSUM and CUSUM SQ test reveals that both the long run narrow and broad money demand functions are unchanging (stable). [9] queried velocity of money demand function and its relationship with interest rate fluctuations of Pakistan data. The results established stable money demand function via velocity of money, real permanent income per capita, real interest rate, transitory income, and expected inflation. It revealed that money velocity is independent from interest rate. [10] revisited money demand function for Japanese economy. The results showed that instability in money demand due to many changes in monetary policy of Japan. [11] tested the stability of money demand function for Tonga using approaches of LSE Hendry's General to Specific (GETS) and Johansen's Maximum Likelihood (JML). The results projected that there is a stable long run cointegrated relationship that exists between real narrow money, real income and rate of interest.
[12] examined whether financial innovation makes money demands is stable or not in Kenya. They used quarterly data (1998Q4 to 2013Q3) and utilized ARDL bounds test. They found out that in the face of financial innovation, money demand in Kenya is stable. Similarly, an earlier study by [13] examined the effect of financial liberalization on money demand in Uganda based on data (1982Q4 to 1998Q4). He employed Johansen cointegration test and found that M2 and its determinants are cointegrated. Thereafter, he used Chow test to assess the stability of the money demand during the period when a financial reform was implemented in the study. The author found out that the introduction of financial liberalization does not make M2 unstable in Uganda. [14]

Aim and Objectives
This study aims at providing a comprehensive analysis of money demand while the specific objectives are: 1) To estimate the effect of financial development on money demand.
2) To analyze the relationship between money demand and other macroeconomic variables in Nigeria.
3) To brings to light the short and long run impacts of money demand on inflation and other macroeconomic variables in Nigeria.

Source of Data
The nature of this study required the usage of secondary data. Data utilized are quarterly time series and covers a period of 1991 to 2018; they are sourced from Central Bank of Nigeria database. The analyses are carried out using the EViews 9.0 package.

Regression Model (Ordinary Least Square Method)
A priori Expectation: The ordinary Least Square (OLS) technique will be employed in obtaining the numerical estimates of the coefficients of the equation. The OLS method is chosen because it possesses some optimal properties; its computational procedure is fairly simple and it is also an essential component of most other estimation techniques. The regression model is given as where i Y and i X are the dependent and independent in the ith observations respectively. 0 β and 1 β are unknown and are usually obtained by method of Least Square, and i ε is the error term. The least square estimates in this case are given by simple formulas.

Auto-Regressive Distributed Lagged (ARDL) Model
The autoregressive distributed lag (ARDL) models are the standard ordinary least squares regressions, which include the lags of both the dependent variable and independent variables as regressors (Erdoğdu H. and Çiçek H., 2017). The basic form of an ARDL (p, q) regression model is given as: where t ε is a disturbance term, the dependent variable is a function of its lagged values, the current and lagged values of other exogenous variables in the model; p lags are used for dependent variable while q lags are for exogenous variables. The bounds testing procedure, developed by [16], requires the estimation of the following equation, which derives the relationship between money supply (M2) and its determinants, exchange rates (EXR), inflation rate (IFR), credit to private sector (CPS) and currency in circulation (CIC) as a conditional autoregressive distributed lag (ARDL): where LM2 is the natural log of money supply, ∆ is the first difference operator , , , p q q q and 4 q are the lag lengths. The null hypothesis in the long-run is λ is the coefficient of the error (or equilibrium) correction term (ECT).
A negative and statistically significant error correction term ensures convergence of the dynamics to the long-run equilibrium. The significance of the error correction model provides further confirmation to the co-integration evidence, giving the impression of a long run movement between economic growth and the explanatory variables. Implying that in the incidence of the presence of external shock resulting to disequilibrium of the system, the model can still converge with time to its normal state with a relatively average speed of adjustment of 6 % λ percent per time.
Conversely, for the short-run relationship model;

Presentation of Data
The data are quarter and generally covers the period from 1991 to 2018. E-Views 9.0 analysis package is utilized to carry out all the analysis in this study. Table 1 presents the variables descriptions of the time series data considered in this study.  Its standard deviation and Jarque-Bera statistic value are 0.8839 and 15.73 respectively with p-value of 0.0004. However, M2, CPS and CIC data are converted into natural logarithm in order to stabilize the variance.
From the descriptive statistics results and considering the p-values of the variables, this can be deduced; the p-values confirm abnormality for all the variables at 1% level of significance. Figure 1 and Figure 2 present the time series plots of the series.
In Figure 1, it shows that LM2 has been gradually increasing over the years.  The results from the ADF test with a linear time trend are reported in Table 3.
Using the ADF test, the unit root cannot be rejected for all the four variables at 5% level of significance which conforms to the time series plots earlier presented. The ADF test with trend is further used at the 1st difference, the unit root can be rejected for all the five (5)    el's residual is tested for Cointegration using Engle-Granger residual approach (see Table 5).   Moreover, as results of the presence of Cointegration among the variables (see Table 5), it is crucial to know the nature or significance of the variables' comovement. The pairwise Granger Causality tests were carried out; Table 6 presents the tests' results.     The results of VECM granger causality has reported in Table 9. The path of causality can be divided into short run and long run causality. The results show that LM2 causes LCIC (a financial development variable) in short-run only but LCIC causes LM2 both in short-and long-run. Thus, we can approximately say that bidirectional causality exists between "currency in circulation" and money demand (LM2). Also, LM2 causes LCPS (a financial development variable) both in short and long run while LCPS does not cause LM2 both in short and long run. So, unidirectional causality exists between money demand and "credits to private sectors". Lastly, LCIC cause itself only in both short.

4) Autoregressive Distribution Lags Estimation
The VECM residual diagnostic test was also applied to the empirical model to measure the adequacy of the specification of the model. As displayed in Table  10, the computed Residual Serial Lagrange multiplier (LM) test for AR [4] = 31.41 is statistically insignificant at conventional significance levels, which suggests that the disturbances are serially uncorrelated.

6) Variance Decomposition Approach
Variance Decomposition Approach is an improved approach to Granger causality. It signposts the magnitude of projected error variance for a series accounted      (1) signifies the short run while down to period (10) it signifies long-run.

Summary
This research work examined the impact of financial development on money demand in Nigeria by means of ARDL approach. It examined the quarterly returns of M2, exchange rate (EXR), inflation rate (IFR), currency in credits to private sector (CPS) and circulation (CIC). The data span from 1991 to 2018.
In the preliminary analysis, the descriptive statistics and distribution of all the series revealed conventional facts. Also, the time series plots and augmented dickey-fuller tests of the original series indicate non-stationarity thus necessitating appropriate transformation to achieve stationarity.
In successive analysis, the study further employed regression model. The regression model's residual is tested for Cointegration using Engle-Granger residual approach, the significances of the variable's co-movement are checked by pairwise Granger Causality tests and ARDL and VECM are estimated in order to account for the short run and long run relationship among the variables.

Conclusions
The VECM Granger causality was applied to check causality in short-and long-run.
Results revealed that bidirectional causality exists between currency in circulation and money demand in both short and long run. Unidirectional causal relationship exists between credits to private sector and money demand in both short-and long-run.