Savings, Investment and Economic Growth Nexus in Nigeria

The economists disagree about the order of causality among savings, investment and economic growth. Moreover, the order of causality among savings, investment and economic growth has not been adequately or fully established in economic literature. As a result of these problems, we decided to establish the order of causality among gross domestic savings, gross domestic investment and economic growth in Nigeria from 1986 to 2017 using Vector Autoregression (VAR) model. The annual time series data of gross domestic savings, gross domestic investment and gross domestic product, a proxy of economic growth that are obtained from World Bank World Development Indicators are used in the estimation of the model. The results of the impulse response functions and variance decomposition reveal that the order of causality among gross domestic savings, gross domestic investment and gross domestic product in Nigeria, runs from gross domestic savings to gross domestic investment, gross domestic investment to gross domestic product and gross domestic product to gross domestic savings. There would be steady growth of output if adequate savings are mobilized for investment expenditures in Nigeria.


Introduction
The major task of the economists is to establish the order of causality among economic variables so that appropriate economic policies that enable us to achieve the main macroeconomic objectives can be put in place. The order of causality among savings, investment and economic growth is not adequately or fully established in economic literature. Moreover, there is disagreement among economists about the order of causality among savings, investment and economic growth at both theoretical and empirical literature. The following discussions illuminate the above statements.
In classical view, savings Granger causes investment but savings and investment do not Granger cause economic growth because it is assumed that the capitalist economic system always tend towards the full employment level of output. As a result of this believe, the classical economists do not explain how a change in economic growth would affect savings and investment. According to them, savings and investment do not depend on income but they are functions of interest rate.
In Keynesian economic theory, economic growth positively Granger causes savings and investment and investment positively Granger causes economic growth but savings negatively Granger causes economic growth when savings exceeds investment and this they called the paradox of thrift or savings positively Granger causes economic growth when savings is equal to investment. The Keynesians do not explain the cause and effect relationship between savings and investment. According to them, savings is a positive function of income but investment depends on income and non-income factors: profit expectation, risk associated with investment, final demand, existing stock of capital and availability of new technology.
In Harrod-Domar model, savings Granger causes investment and investment Granger causes economic growth but Harrod (1939) and Domar (1946) do not explain the effect of a change in economic growth on savings and investment. In view of the above discussions, each of the three schools of economic thought mentioned above could not fully explain the order of causality among savings, investment and economic growth. Moreover, the order of causality among savings, investment and economic growth as explained by each of these three schools of economic thought are not in tandem with each other.
The classical theory suggests that savings has no effect on economic growth. The Keynesian economic theory indicates that savings has negative or positive effect on economic growth. The Harrod-Domar model shows that savings has positive effect on economic growth. Due to these divergent views among economists about the effect of savings on economic growth, one is not certain of the appropriate savings policy to put in place in order to achieve the desired level of output. There are several empirical studies on savings, investment and economic growth nexus in Nigeria. For example, Akinola and Omolade (2013), Nwanne (2014) and Odey et al. (2017) conducted a research on savings, investment and economic growth nexus in Nigeria but they could not establish the order of causality among these three economic variables. The Ordinary Least Square method used by Nwanne (2014) and Error Correction Model employed by Odey et al. (2017) are not appropriate for their studies because they are not useful in dealing with multivariable causality. They could have used the Vector Autoregression (VAR) technique because it is very useful in dealing with multivariable causality. actual savings and investment are always equal at any period of time and at all levels of income. Symbolically, St = Yt -Ct ---(1) It = Yt -Ct ---(2) Where Y is income, C is consumption, S is savings and t is time in the current period. Since Yt -Ct is common in equations (1) and (2), we can say that savings is equal to investment. Symbolically, St = It ---(3) The expressions in equations (1) and (2) can be re-arranged and written as follows: Yt = Ct + St ---(4) Yt = Ct + It ---(5) Since Yt is common in equations (4) and (5), we can say that: Ct + St = Ct + It ---(6) Since Ct is common in equation (6), we can say that: St = It ---(7) Based on the accounting or definitional equality between savings and investment, Keynes states that savings and investment are always equal. He disagrees with the classical view that savings-investment equality takes place only at full employment level of output. He believes that since full employment level of output is a rare phenomenon, savings-investment equality can take place at less than full employment level of output.
The second is the functional equality between savings and investment. The savings-investment equality in the functional or schedule case is brought about by the adjustment mechanism of income rather than the classical view of the adjustment mechanism of interest rate. In this scenario, savings and investment are equal only at the equilibrium level of income. Both savings and investment are increasing functions of income. When savings is greater than investment, income falls, and when investment is greater than savings, income rises. This dynamic adjustment mechanism in income, savings and investment will continue until savings and investment are not only equal but are also in equilibrium. Keynes believes that economic growth will increase only if the savings by households is equal to investment expenditures by businesses.
According to Harrod (1939) and Domar (1946), savings increases economic growth through an increase in investment. They believe that the main purpose of savings is for investment and so when savings increases, investment increases and an increase in investment will lead to an increase in economic growth. The Harrod-Domar model is specified as follows: G = (ΔY/Y) = (s/k) ---(8) Where G is growth rate of output, Y is output or income, s is the savings rate and k is capital output ratio. The model shows that growth is directly related to savings. Increasing the savings rate will increase the growth rate of output because savings generates investment which in turn stimulates economic growth.
There are several studies on savings, investment and economic growth nexus in many countries of the world. Attanasio et al. (2000) examine the short run and long run relationship among savings, investment and economic growth for 123 countries from 1961 to 1994 using ordinary least square method, Granger causality test and impulse response functions. The results of the investigation show that lags of saving rates are positively related to investment rates, investment rates negatively Granger causes economic growth rates and economic growth rates positively Granger causes investment rates. Verma and Wilson (2005) investigate the relationship among savings, investment, foreign inflows and economic growth in India from 1950 to 2001 using ordinary least square regression model. The results indicate that savings and investment have an influence on economic growth while economic growth has insignificant impact on savings and investment. Verma (2007) determines the relationship among gross domestic savings, gross domestic investment and economic growth in India from 1951 to 2004 using Autoregressive Distributed Lag (ARDL) bounds test. The results of the investigation reveal that economic growth, gross domestic savings and gross domestic investment have a long run relationship except when economic growth is the dependent variable. The results show that gross domestic savings does not determine economic growth, but economic growth determines gross domestic savings. It is found that gross domestic savings generates investment both in the short run and in the long run and gross domestic investment stimulates economic growth in India during the period.
Ramesh (2011) examines the direction of causality among savings, investment and economic growth in India from 1951 to 2008 at both aggregate and sectoral levels using Granger causality test, Johansen co-integration test and vector error correction model. The results of the co-integration tests indicate that there is a long run relationship among all the variables except private corporate savings. It is found that the direction of causality runs from savings and investment to economic growth collectively as well as individually and there is no causality from economic growth to savings and/or investment. Budha (2012) examines the relationship among savings, investment and economic growth in Nepal from 1975 to 2010 using Autoregressive Distributed Lag (ARDL) approach to test for co-integration and Granger causality test. The results of the investigation reveal that there is evidence of co-integration among savings, investment and economic growth when each of them is taken as dependent variable. The results of the Granger causality test indicate that there is bi-directional causality between investment and economic growth as well as between savings and investment. There is no evidence of causal relationship between savings and economic growth in Nepal within the period under investigation. Mohamed (2014) determines the causal relationship among savings, investment and economic growth in Ethiopia from 1970-2011 using Autoregressive Distributed lag (ARDL) bounds test. The result of the investigation shows that there is long run relationship among savings, investment and economic growth when GDP is taken as dependent variable. The result also show that investment has significant positive effect on economic growth in Ethiopia both in the short run and in the long run while the effect of savings on economic growth is statistically insignificant.
Hundie (2014) analyzes the causal relationship among savings, investment and economic growth in Ethiopia from 1969 to 2011 using ARDL approach to co-integration and Toda-Yamamoto and Dolado-Lutkepohl Grangercausality tests. The results of the ARDL bounds test indicates that there is evidence of co-integration among gross domestic savings, gross domestic investment, gross domestic product, labor force and human capital when GDP is taken as dependent variable. Labor and investment have significant positive effect on economic growth in both the short run and long run while gross domestic savings and human capital are statistically insignificant. The results of Toda-Yamamoto and Dolado-Lutkepohl as well as Innovative Accounting Technique to Granger causality analysis shows that there is a bi-directional causality between gross domestic investment and economic growth as well as between gross domestic savings and gross domestic investment. Granger causality running from investment to savings and from investment to economic growth is confirmed and it is statistically significant as shown in the results of impulse responses and variance decompositions. A unidirectional Granger causality running from economic growth to gross domestic savings is observed although it is statistically insignificant. Ruranga et al. (2014) analyze the relationship among real gross domestic product, domestic investment, foreign direct investment, domestic savings and trade in Rwanda from 1970 to 2011 using VAR and Granger causality test. Granger causality test shows that there is bi-directional causality between gross domestic product and trade and trade and domestic investment and unidirectional causality from gross domestic product to domestic investment, from domestic savings to gross domestic product, from domestic savings to domestic investment and from domestic savings to trade. Domestic savings has significant impact on gross domestic product, domestic investment and trade. There is no evidence that domestic investment Granger causes gross domestic product. The estimated VAR results reveal that forecasted values of gross domestic product, domestic investment and foreign direct investment are 3,843.6233 million, 22.67% and 0.95% respectively in 2011 while their actual values are 3891.9 million, 22.7% and 1.66% respectively in the same period of time. These results show that there is underprediction for gross domestic product, domestic investment and foreign direct investment. The differences are explained by the efforts of the Government of Rwanda to promote gross domestic product, domestic investment and foreign direct investment. Akinola and Omolade (2013) determine the relationship among gross national savings, gross capital formation and economic growth in Nigeria from 1975 to 2008 using co-integration test and vector error correction model. The results of the co-integration test show that there is evidence of a long run relationship among the three variables. The results of the vector error correction model indicate that economic growth has stronger influence on both gross national savings and gross capital formation than the influence of gross national savings and gross capital formation on economic growth. The results reveal that there is a bi-directional causality between economic growth and gross capital formation, economic growth and gross national savings, and gross national savings and gross capital formation in Nigeria. Nwanne (2014) analyzes the implications of savings and investment on economic growth in Nigeria from 1981 to 2014 using ordinary least square method. The results of the unit root tests show that all the variables are integrated at order one. The results of the Johansen co-integration test show that there is a long run relationship among savings, investment and economic growth. The regression results show that gross domestic savings has significant negative effect on economic growth and gross domestic investment has significant positive effect on economic growth in Nigeria. Odey et al. (2017) evaluate the impact of savings and investment on economic growth in Nigeria from 1970 to 2015 using co-integration test and error correction model. The results of their investigation show that gross domestic savings, gross fixed capital formation, labour force and savings facility stimulate economic growth. The results of investment model show that economic growth and gross domestic savings propel investment expenditures in Nigeria.
From empirical studies on savings, investment and economic growth nexus in Nigeria, we observe that there are gaps in the literature that need to be filled. The findings by Akinola and Omolade (2013) indicates that there is a bi-directional causality between economic growth and gross capital formation, economic growth and gross national savings, and gross national savings and gross capital formation but they could not establish the order of causality among these three economic variables. The ordinary least square method used by Nwanne (2014) and error correction model employed by Odey et al. (2017) are not appropriate for their studies because they are not useful in dealing with multivariable causality. To establish the order of causality among savings, investment and economic growth in Nigeria, we have to apply the classical theory, Keynesian economic theory and Harrod-Domar model to Nigerian economy. In other words, the classical theory, Keynesian economic theory and Harrod-Domar model are the theoretical framework for this study. In classical theory and Harrod-Domar model, savings Granger causes investment. In Keynesian economic theory and Harrod-Domar model, investment Granger causes economic growth. In Keynesian economic theory, economic growth Granger causes savings. Therefore, we expect that the order of causality among savings, investment and economic growth in Nigeria, run from savings to investment, investment to economic growth and economic growth to savings. The order of causality among these three economic variables is established in this paper using Vector Autoregression (VAR) model.

Model Specification
This paper uses a three variable VAR approach following Attanasio et al. (2000) to establish the order of causality among savings, investment and economic growth in Nigeria. The model is summarized in the reduced-form VAR: Where Yt is a 3*1 vector of variables (GDS, GDI, GDP); βi are coefficient matrices of size 3×3 and ui is the one-step ahead prediction error with variance-covariance matrix Σ , αo is the intercept, t is time, i is the lag length, GDS is Gross Domestic Savings, GDI is Gross Domestic Investment and GDP is Gross Domestic Product-a proxy of economic growth. All variables are in normal form.
The VAR methodology deals with several endogenous variables together. Each endogenous variable is explained by its lagged, or past, values and the lagged values of all other endogenous variables in the model; usually, there are no exogenous variables in the model. Since there are three variables, the VAR technique is employed because it is very useful in dealing with multivariable causality. Forecasting is an important part of economic analysis, for some people probably the most important. Vector autoregression has become quite popular method of forecasting economic variables.
As in any standard VAR model analysis, the way the variables enter the model is extremely important for the interpretation of the results. The most appropriate ordering is: GDS -GDI -GDP. The gross domestic savings has great influence on gross domestic investment. The gross domestic investment has great influence on economic growth. The economic growth has great influence on gross domestic savings. So, GDS should come first in the VAR model.

Estimation Method
The VAR model is estimated using e-view 9. The time series properties of the data are analyzed using Augmented Dickey-Fuller (ADF) unit root test of Dickey and Fuller (1979). Test of co-integration is carried out using the Johansen (1988) maximum likelihood procedure. The lag length is determined by the likelihood ratio (LR), final prediction error (FPE), Akaike information criteria (AIC), Schwarz information criteria (SC), and Hannan-Quinn information criteria (HQ). The VAR residual portmanteau tests for autocorrelations are used to verify the assumption of no autocorrelation. The cusum test and VAR residual normality tests are used to verify whether the VAR model satisfy the stability and normality assumptions respectively.

Data
The empirical analysis is conducted using annual data. The time span covered is 1986 to 2017. The choice of 1986 as the base year is due to the fact that the policy of deregulation of Nigerian economy started that year. The choice of 2017 as the terminal year is premise on the fact that the time series data of the variables required for the study are available only up to that year. This study is confined within the period of deregulation in other to take into cognizance the classical view of a capitalist economic system. The data of gross domestic savings, gross domestic investment and gross domestic product are obtained from World Bank World Development Indicators.

Pre-Estimation Tests
The unit root test was conducted using Augmented Dickey-Fuller (ADF) test (Table 1). All the variables are nonstationary at levels because ADF-statistic is less than test critical value in absolute term at 5 percent level and p-value of each variable is greater than 5 percent. All the variables are stationary at first differences because ADFstatistic is greater than test critical value in absolute term at 5 percent level and p-value of each variable is less than 5 percent. The ADF test indicates that the variables are integrated at order one at 5 percent level. The co-integration test was conducted using Johansen test for co-integration vectors ( Table 2). The trace statistic is greater than 0.05 critical value and p-value is less than 5 percent for none hypothesized number of cointegrating equations. The max-eigen statistic is greater than 0.05 critical value and p-value is less than 5 percent for none hypothesized number of co-integrating equations. Both trace and maximum eigenvalue tests indicate 1 co-integrating equations at 5 percent level. Both trace and maximum eigenvalue tests denote rejection of no cointegration at 5 percent level. The lag length selection was done using the VAR lag order selection criteria (Table 3). The sequential modified LR test statistic (LR), Final prediction error (FPE), Akaike information criterion (AIC) and Hannan-Quinn information criterion indicate maximum lag length 2 while Schwarz information criterion indicates maximum lag length 1 at 5 percent level. Since the value of LR (23.3447) at lag 2 is the smallest out of the values indicated by these five criteria, the VAR model is estimated at a maximum lag length 2 based on sequential modified LR test statistic.

Post-Estimation Tests
The results of the VAR residual portmanteau tests for autocorrelations are presented in table 4. The computed Qstatistic at lag 3 and 9 degrees of freedom is 44.5616. The critical value of Q at 5 percent level of significance and at 9 degrees of freedom is 4.756. The computed Q-statistic is greater than the critical Q-statistic at 5 percent level of significance and at 9 degrees of freedom. Therefore, we accept the null hypothesis that there is no residual autocorrelations up to the specified number of lags.  Figure 1 presents the cusum for stability test. The cusum is used to verify whether the VAR model is stable. The VAR model is stable if the cusum lies within 5 percent critical bound dotted lines. As we can see in Figure 1, the cusum lies within 5 percent critical bound dotted lines. The cusum indicates that the VAR model is stable at 5 percent level of significance. The results of the VAR residual normality tests are shown in table 5. Instead of going for any rule of thumb for the acceptable ranges of skewness and kurtosis for normal distribution of data, we check Jarque-Bera test. This is because Jarque-Bera test is based on skewness and Kurtosis and so the acceptance of the null hypothesis in this test means that skewness and kurtosis are within the acceptable ranges for normality, and the rejection of the null hypothesis in this test means that skewness and kurtosis are not in acceptable ranges for normality of the data. The Jarque-Bera (JB) statistic is 92.3266 and the computed p-value is zero percent. The computed p-value of JB statistic is too low which indicates that the value of the JB statistic is very different from zero. Therefore, we reject the null hypothesis that the residuals are multivariate normal.  Figure 2 (a) presents the response of Gross Domestic Investment (GDI) to Gross Domestic Savings (GDS). The response of GDI to GDS ranges from 1.16E+12 to 9.21E+11 during the period under investigation. The response of GDI to GDS is positive. The GDS has significant positive impact on GDI. Sims (1987) suggests that for impulse responses, significance can be crudely gauged by the degree to which the functions are bounded away from zero. The finding that GDS has significant positive impact on GDI is in line with the classical theory and Harrod-Domar model that savings has a strong positive influence on investment. Figure 2 (b) shows the response of Gross Domestic Product (GDP) to GDI. The response of GDP to GDI ranges from 1.04E+12 to 9.92E+11 during the period under review. This result indicates that GDI has significant positive impact on GDP. This finding conforms to the Keynesian economic theory and Harrod-Domar model that investment has a strong positive impact on economic growth. Figure 2 (c) reveals the response of GDS to GDP. The response of GDS to GDP ranges from 1.18E+11 to 5.16E+11 during the period under study. This result shows that GDP has insignificant positive impact on GDS. This finding tally with the Keynesian economic theory because even though Keynes believe that savings is an increasing function of income, he identifies the non-interest rate motives for savings and these non-interest rate motives for savings generate savings regardless of the level of income. The results of the impulse response functions reveal that the order of causality among GDS, GDI and GDP in Nigeria, runs from GDS to GDI, GDI to GDP and GDP to GDS.  Figure 3 (a) presents the variance decomposition of GDI to GDS. The variance decomposition of GDI to GDS ranges from 30.4257 percent to 80.9637 percent during the period under investigation. On average, the variance decomposition of GDI to GDS is 60.15 percent. This result indicates that GDS has a significant positive impact on GDI. Runkle (1987) suggests a probability range above 10 percent for significance in variance decomposition. This finding shows that GDS contributes 60.15 percent to variation of GDI during the period under review. Figure 3 (b) shows the variance decomposition of GDP to GDI. The variance decomposition of GDP to GDI ranges from 5.3413 percent to 42.4257 percent during the period under study. On average, the variance decomposition of GDP to GDI is 20.09 percent. This result shows that GDI has a significant positive impact on GDP. This finding implies that GDI contributes 20.09 percent to variation of GDP during the period under review. Figure 3 (c) reveals the variance decomposition of GDS to GDP. The variance decomposition of GDS to GDP ranges from zero percent to 1.8899 percent during the period under review. On average, the variance decomposition of GDS to GDP is 1.34 percent. This result shows that GDP has insignificant positive impact on GDS. This finding indicates that GDP contributes 1.34 percent to variation of GDS during the period under investigation. The results of the variance decomposition also reveal that the order of causality among GDS, GDI and GDP in Nigeria, runs from GDS to GDI, GDI to GDP and GDP to GDS.

Conclusions
Based on the results of the investigation, the following conclusions are drawn. The gross domestic savings has significant positive impact on gross domestic investment. The gross domestic investment has significant positive impact on gross domestic product. The gross domestic product has insignificant positive impact on gross domestic savings. The order of causality among gross domestic savings, gross domestic investment and gross domestic product in Nigeria, runs from gross domestic savings to gross domestic investment, gross domestic investment to gross domestic product and gross domestic product to gross domestic savings. There would be steady growth of output if adequate savings are mobilized for investment expenditures in Nigeria. To mobilize adequate savings for investment, there must be an increase in interest rate because interest rate is an incentive for people to save. However, the order of causality among savings, interest rate and investment has not been established in this paper. Further studies should establish the order of causality among savings, interest rate and investment in Nigeria.  Vol.10, No.14, 2019