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Theoretical Background

Finance and economics literature are awash with studies that link domestic investments with savings and interest rates. For instance, the demand and supply of capital theory of interest, otherwise called the classical theory of interest, puts forth an explanation of the possible link between investment and interest rates as that of inverse or negative function. Simply put, investment is a negative function of interest rate. Thus, when interest rate experiences a declining trend, the investor or producer gets motivated to invest more in order to take advantage of imminent reduction in production cost. This he does until his marginal productivity of capital equates the rate of interest. Invariably, investment demand makes upward movement when interest rate falls and takes the opposite direction as interest rate increases (Ezirim, 2005; Priyadarshin, S., 2018; Moyo & Le Roux, 2018 ; Meghana, 2018; Scribd Inc., 2018, and Shaikh & Saqib, 2018.

Senior's abstinence or waiting theory reasoned that "capital is the result of savings", and that savings is an integral part of capital goods, which necessarily requires sacrifice in the form of abstinence. Economic agents have the natural propensity to channel all monies received into present consumption of goods, if they so elect, but when they choose the alternative option by refraining from present consumption, they save. Savings is thus defined in terms of postponing present consumption to future consumption. Deferring present consumption for a certain period implies that the money set aside is meant to be put to productive use and not necessarily kept idle or hoarded. By that token, it is channeled to bear some 'fruits' through productive uses, and in event of time, the fruits would be realized in an increasing flow, afterwards. Thus, abstinence from present consumption is said to give impetus to making resources available for productive uses, in the form of investments, in the process of time (Ezirim, 2005; Shaikh, 2018).

By and large, supply of capital or investible funds would thus be a positive function of savings. Savings are, thus, construed as prime sources and vehicles of investments. Both the classical and abstinence theories agree that demand for capital (investment) implies demand for savings, where rational investors would venture to pay interest, on savings they borrow, simply because resultant investment activities engaged in would promise greater returns than their cost of borrowing, otherwise called Interest. Therefore, the rate of interest is not only seen as important determinant of investments, but also as a prime driver of savings, more or less. Further justification for this point is readily tenable. The economic act of waiting or abstinence, implying savings, is said to be a necessary, but not sufficient, condition for production (investment). But economic agents are averse to waiting, naturally, and thus, require some incentives to compensate for their sacrifice. The price they receive for this sacrifice is interest. (Ezirim, 2005; Shaikh, 2018).

Financial intermediation theory offer complementary explanation on how interest rates coordinate savings and investments in the economy. The mutual existence, co-habitation, cooperation, interaction or otherwise, between deficit economic units (borrowers and investors) and surplus economics units (savers) breeds financial imbalance or inequality and unpleasant conditions among the two sets of economic agents, which only the rate of interest tends to be the impartial umpire. Being unwilling to part with their current liquidity, which they have unbridled preference for going by the tenets of the liquidity preference theory, interest rate becomes the compensation mechanism for the parties to relinquish their cash holding today. The idea of interest rate satisfies the promise to receive more money in the future than they can part with currently. An alternative explanation derives from the demand and supply for loanable funds associated with what is referred to as the loanable funds theory.

Interest rate is simply seen as how much deficit agents need to pay for monies borrowed as well as what lenders receive on their accumulated funds, called savings. When loanable funds' demand by investors rises relative to their supply, interest rate increases. The converse is true when loanable funds' supply declines relative to demand, price for such funds falls. This is the angle where investments and savings also determine interest rates. Notwithstanding, appealing to the demand and supply bareheads' theory, upward-sloping supply for loanable funds curve and downward-sloping demand counterpart equilibrates to bring about the natural rate of interest that controls transaction in the financial market. It is the equilibrium rate that is theorized to allocate funds in the loanable funds market, signaling to surplus agent how valuable their savings could be, and to deficit agents how valuable their use of borrowed funds need to be in order to justify their cost of funds (Investopedia, 2018). It becomes imperative that theoretically, there are some forms of plausible connecting links between investments, savings, and interest rates. But, are these links causal? This is an empirical question, the answer to which this study seeks to unravel?

A further theoretical question that begs for an answer relates to which type of interest rate do actually affect savings and investments? Is it lending rate or is it deposit rate? Is it short-term rate or is it long-term rates? Commonsense would naturally link lending rates to investment and deposit rate to saving. It is plausible to settle with the classical, abstinence, loanable funds theories that a negative relationship exist between lending rate and investment. It is also plausible to think that saving should relate positively with deposit rate of interest. Such separation is convenient. But can saving and investment ever be a positive function of any of the defined interest rates, just like income is postulated? Of course, both the classical, Keynesian and neo-classical thinking associated income levels to determine both saving and investment. Answering the poser, the McKinnon-Shaw theorizing attempted to address that point. As in Molho (1986), the McKinnon-Shaw hypothesis states in part that savings and investments are a positive function of interest rates. Thus, when interest rates are raised, savings and investments could be promoted in developing countries "by alleviating financial repression, defined in terms of excess demand for loans and nonprice credit rationing" (Molho, 1986).

The two theorist (McKinnon and Shaw) saw the effective constraints to capital formation differently: internal financing possibilities for McKinnon and debt finance for Shaw, respectively. There different perceptions as to what constrains capital formation that leads to actual investment made other theorist to adduce to the mutual inconsistency of the two hypothesis. However, protagonists like Molho (1986) have shown that the so-called different conceptual conceivability constitute complementary rather than resulting in competing theories. Specifically, it is argued that McKinnon's complementarity hypothesis (that investment is positively related to deposit rates) may hold, not only under pure self-finance, but also under partial debt finance, especially when all rates of return on investments are certain. When the rates are uncertain, it is reasoned, the hypothesis may not hold, even for the case of pure self-finance. Molho (1986) had shown that in keeping with the McKinnon proposition, "interest rate affect aggregate saving, investment, and money holding, with a complex and possibly very long lag".

Theory further, stipulates saving as the very part of income that has not been spent for consumption purposes (i.e., income minus consumption expenditure; where the other part of the total expenditure basket is the investment expenditure). Investment represents the net additions to the stock of capital, being a flow concept, and not necessarily the stock of capital itself. Ferdousi (2009) sees investment as the economic activity "devoted to enhancing or maintaining the existing stock of capital in the economy, which provides goods and services necessary for better standard of living". In every succeeding period, say year after year, the stock of capital is expanded through the vehicle of net investments. Investment expenditures are, thus, deemed to be made out of saved income on investment. Thus, when an individual makes investment expenditure he is deemed to spend his "saved income on the nominated investment" (Ezirim, 2005; Guru, 2018).

Guru (2018) articulated an important controversy surrounding the identity (equality) or otherwise between savings and investments. Many pre-Keynesian protagonists maintained that savings and investments are largely unequal, except at equilibrium. Starting with Keynes, many post-Keynesian economists argue to the contrary, that there is identity between the two economic activities, equilibrium or no equilibrium. The pre-Keynesian contention is benchmarked on the fact that saving and investment are made by entirely two different classes of people: the general public as opposed to the entrepreneurial class, respectively. A second point advanced is that saving and investment "depend upon different factors and are made for different purposes and motives" (Guru, 2018). More so, much more investments than savings can be achieved such as when excess investments are financed the new bank credits, like in the case of possible money creation and deposit multiplication, Thus, except at natural levels, there cannot arise any chance of equality or identity between savings and investments.

Keynes and his followers maintained that in general, actual or ex-post savings do equate actual or ex-post investments. They posited that in every economy, national income is equal to the sum of consumption and investment; and also equal to the sum of consumption and saving (Consumption + Saving = Consumption + Investment). Striking out like-terms in the above equation reduces to the equality between savings and investments. Thus, from the equation, investment represents "that part of national income which is obtained from the production of goods other than those consumed", while "saving is that part of national income which is not spent on consumption" (Guru, 2018). Given these, in actual or ex-post parlance, saving and investment are equal.

Savings and investments can also be mirrored in the light of desired, intended or planned; otherwise defined as ex-ante saving and ex-ante investment. Planned or ex-ante saving are usually not equal to planned or ex-ante investment, though the mechanism of changes in the income level can give rise to the tendency for ex-ante saving and ex-ante investment to equate. Thus, in the event that in a given time period, say 1 year, planned investment exceeds planned saving, the level of income would go up. When the level of income rises, more is naturally saved and as a result, intended saving tends to equate intended investment. Conversely, when ex-ante saving exceeds ex-ante investment, income level declines. With lower income level, fewer saving would be recorded and therefore planned savings would tend to equate planned investment. Noteworthy, however is that ex-ante saving and investment can only equate income level at equilibrium. In all, ex-post or realized saving and investment are bound to be equal in all conditions, ex-ante or intended savings and investments "have only a tendency to be equal and are equal only at the equilibrium level of income" (Guru, 2018).

Empirical Background

Whereas a plethora of studies have documented the existence of significant negative effects of interest rate on investments (Greene & Villanueva, 1990; Mohsen & Rezazadeh, 2011; Geng & N'Diaye, 2012; Tokuoko, 2012; Pattanaik et al.,2013; Muhammad et al., 2013; Mushtaq, & Siddiqui, 2016; and Malawi, 2010), some others have reported the insignificance of interest rate in driving investments (Salahuddin et al., 2009; Nasir & Khalid, 2004; and Ferdousi; 2009). Yet others like Athukorala (1998) found positive relationship between investments and interest rates, as in Athukorala (2007) and Wuhan and Khurshid (2015). Christy and Clendinon (1976), Nasir and Khalid's (2004) studies submitted that the savings and lending rates are two important determinants of investment. Some studies conform with the Mckinnon-Shaw hypothesis when they found a significant positive relationship between savings and deposit rate of interest as in Salahuddin et al. (2009) and Athukorala (2007). Ogbokor and Samahiya (2014), Nasir and Khalid (2004) and Udude (2015), however, found this savings-deposit rate relationship to be statistically insignificant. Mushtaq and Siddiqui (2016) found interest rate to be important drivers of savings in non-Islamic countries, but irrelevant in Islamic economies.

Mohsen and Rezazadeh (2011) and Onwumere et al. (2012) observed dual states of effects of interest rate in an economy, when different policies are put in place. For instance, in Onwumere et al. (2012), in the years prior to liberalization in Nigeria, interest rate effect was positive and insignificant on saving and investment but in the years after liberalization the interest rate effect turned negative and insignificant on savings, and negative but significant on investment. For Mohsen and Rezazadeh (2011) interest rate effect was positive within the threshold level of 5 to 6 %, but turns negative beyond this threshold. This present study, hereunder, reviews some of these studies in greater details.

Ferdousi (2009) examined interest rates and investment spending relationship in Bangladesh from 1980-81 through 2005 period using trend and regression analysis, which modelled and estimated such factors as income, savings, interest rate, lending rate, and exchange rate. The author reported insignificant but negative influence of both deposit and lending rates of interest on investment. It was also reported that the findings conform with the few past empirical studies' results based on Bangladesh data, which also found interest rates as exerting weak impact on investments in the country. Income, savings, and exchange rates strongly and positively related with investments in Bangladesh. These caused the author to suggest reduced attention given to "providing low cast fund for increasing investment spending" in preference to greater attention accorded to "other economic and non-economic factors that significantly drive investments such as creating an investment-friendly environment.

Wuhan and Khurshid (2015) empirically tested the effect of interest rate on investment in Jiangsu Province of China using the VECM procedure. Use was made of one-year lending rate as proxy for interest rate and the price-index of the logarithmic transformed fixed assets investment to represent investment. Results indicated that in the long run, interest rate and investment were positively related, with the implication that rate reduction would promote investment in Jiangsu. However, the observed impact of interest rate on investment was relatively weak. The study documented that apart from interest rate, many other factors affect the investment in Province, namely market size, economic development level, investment environmental and preferential policies.

Athukorala (2007) examined the interest rate-saving investment nexus in the Indian economy from 1955-95. It was discovered that higher real interest rates positively ginger up both financial and total savings. Higher interest rates also moved in the same direction and actually impacted or boosted private investment. The works of Athukorala (2007), above appear to have challenged the claims of existing theory about the postulated negative relationship between investments and interest rates, while those of Wuhan and Khurshid (2015), Ferdousi (2009) casted doubt on the possibility of significant relationship between them.

Udude (2015) used the VAR technique to study the impact of interest rate on savings as well as the joint influence of savings and income on total national savings, based on the Nigerian evidence, from 1981-2013. It was found that rise in deposit rate of interest caused only marginal increase in savings, but nothing significant. To the contrary, increased income and propensity to save actually resulted in remarkably high level of savings. It does appear from the result that the prime move for economic agents in the country to save is not actually the interest income they receive but some other factors such as habit and income levels. On the bases of these findings, the author suggested CBN policy that will increase deposit rates in order to boost savings in the country; and particularly to increase interest paid on deposit made by individuals and investors, local and foreign alike. It is a wonder that Udude could make such a recommendation that does not strictly stem from the study's finding noting the observed relationship between the savings rate of interest and savings proper.

Ogbokor and Samahiya (2014) empirically investigated the determinants of savings in Mamibia using co-integration and error correction mechanisms against quarterly and annual data ranging from 1991 to 2012. The findings are that inflation and income positively impacted savings, population growth rate negatively impacted savings, whereas deposit rate and financial deepening, though positive were not significant in their effect on savings. The authors' recommendation favored improving income levels in order to achieve a higher level of savings in Namibia.

Mushtaq and Siddiqui (2016) x-rayed the effects of interest rate on economic performance, drawing evidences from both Islamic and non-Islamic economies. Specifically, they applied the random effect and system generalized method of moments (GMM) model separately to data of 17 non-Islamic and 17 Islamic countries from 2005 to 2013. Among other results, it was revealed that in non-Islamic countries, interest rates are prime movers of savings, but the contrary is true for non-Islamic countries. For Islamic and non-Islamic economies, interest rate exerted a negative effect on investment in both Islamic and non-Islamic countries.

Moyo and Le Roux (2018) examined the impact of interest rate reforms on economic growth through the channels of savings and investments in SADC countries for the period 1990-2015. The study approached the topic by modeling and estimating three levels of relationships aimed at verifying the savings-interest rate reforms relations, followed by savings-investments nexus, and finally the investment-economic growth link. Use was made of the Pooled Mean Group (PMG) and ARDL estimation techniques The findings reveal the existence of long-run relationships between the variable at all levels for all the countries. Interest rate reforms was found to have a positive impact on economic growth through savings and investments.


Modelling and Estimation Procedure

The study involves the specification of an investment model that expresses investment as a positive function of savings but a negative function of interest rate. Residual diagnostic tests were conducted on the model including serial correlation LM., heteroscedasticity, normality, multicollinearity, inverse root of characteristic polynomial, unit root stationarity tests among others. Employment was made of the pairwise Granger causality, VEC Granger Causality/Block Exogeneity Wald Tests, Johansen co-integration and Hansen co-integration procedure, error correction modelling, impulse response and variance decomposition analysis to determine the full causality implications of the variables in the model. The Least squares and the fully modified least squares regressions were applied to test the contemporaneous and long-run relationships' hypotheses. The Eviews 9.0 software was used for the purposes of estimation.

Sample and Data Collection

Data for the study were obtained from the Central Bank of Nigeria Statistical Bulletin and the World Bank Development Statistics. Investment was proxied by the gross fixed capital formation. Saving was represented by the aggregate national savings of Nigeria, while the prime lending rate was the measure for interest rate. The number of observations was 37 annual data points from 1981 through 2017.


Residual Diagnostics of the Investment Model

The analyses in this study involve the examination and or determination of the global utility of the specified investment model, Inter alia. The model is subjected to five different diagnostic tests, namely residual correlation matrix, serial correlation, heteroscedasticity, normality, and inverse roots of the autoregressive characteristic polynomial. The results of the correlation matrix, serial correlation and heteroscedasticity are set forth in Panels A, B, and C of Table 1, respectively. The correlations of the residuals of the variables are all low and insignificant, implying that the observed residuals are not correlated. Therefore, the absence of multi-collinearity among the residuals of the variables in the model. This is clearly seen in Panel A of Table 1. It is also indicative from Panel B that for lag lengths of 1 and 2, the LM statistics are 8.538 and 10.617 with probabilities of 0.481 and 0.302, respectively. Being non-significant, the study does not reject the null hypothesis of no serial correlation. This implies that there is no reason to worry about the problem of residual serial correlation. Similarly, the chi-square of 79.99 and probability of 0.604 in Panel C leads to the acceptance of the null hypothesis of hhomoscedasticity. Invariably heteroscedasticity is not a problem of the specified investment model.

Figure 1 describes the results of the Jargue-Bera normality test of the residuals along with implicated descriptive statistics. Jarque-Bera statistic of 0.389 with a probability of 0.823, indicates that a hypothesis of the existence of a normal distribution of the residuals cannot be rejected, but accepted. Thus the residuals are normally distributed. The residuals are observed to average 0.5, with the maximum score being 13.4 and the minimum score being 10.4. The variability of the residuals as measured by the standard deviation is observed to be relatively low at 4.8. the observed skewness of 0.21 portends that the distribution of the residuals is positively skewed, having long right tail. Also the observed kurtosis of 3.28 indicates that the residuals' distribution is peaked relatively to the normal; being greater than 3; and implying that very few observations are within the region where the median resides. However, these deviations from normality are not significant.

Figure 2 depicts the inverse roots of the characteristic AR polynomial. All roots fall within the unit circle. As a rule, if all roots have modulus less than one and lie inside the unit circle, then the estimated VAR model is said to be stable or stationary.

From the above diagnostic tests' results, it is obvious that the specified investment model possess satisfactory global utility and is, therefore, suitable for further relative finametric analyses to determine the extent to which savings and interest rates causally relates and or affect investments in the short- and long-runs as well as contemporaneously. The ensuing analysis starts with the contemporaneous relations.

Contemporaneous Relationship between Investment, Savings and Interest rates

Table 2 depicts the contemporaneous least square relationship between investment, savings and interest rates in Nigeria. Savings (SAV) is seen to relate positively and significantly with investments (INV), as a priori expected. The observed beta coefficient is 0.25 with tstatistic of 2.16 and probability of 0.038, which is significant at the 5% level. This result suggests that savings fuel investments in Nigeria, in support of both classical and neo-classical theory. Interest rates (INT) are observed to relate significantly to investments (INV) but in the opposite direction, as expected. The observed beta coefficient is -0.45 with t-statistic of -2.89 and probability of 0.007, which is significant at the 1% level. This result agrees with the classical theory about the behavior of interest rates in the economy as well as the Keynesian indirect influence theory of money, interest rates and investments (Ezirim, 2005).

The regression coefficient for the constant term was 16.9 with a t-statistic of 3.87 and probability of 0.0005, which is significant at the 1% level. By implication, even when savings and interest rates are excluded from the model (zero value), the other factors that are not presently modelled would significantly influence investments positively and significantly in developing countries such as Nigeria. That savings and investments relate significantly with investment in expected directions does not fully answer the question of causation between the variables. In order to address the causality concerns, the pairwise Granger causality test was conducted. The results of the Granger causality test are reported in Table 3.

Pairwise Causal Relationship between Investment, Savings and Interest rates

From the results in Table 3, under the lag length of 5, the first panel indicates that savings granger-causes and as such are causally prior to investments (F-statsav = 2.28; probsav = 0.08, which is significant at the 10% level). In panel 2, interest rates are revealed also to Granger cause investments ([] = 4.57; probint = 0.006, which is significant at the 1% level). Though both savings and interest rates are significant causal correlates of investments, interest rates are shown to be causally superior to savings, in their effects on investments in Nigeria. Thus, we cannot accept hypotheses of no significant causation flowing from savings and interest rates to investments.

However, we cannot hold the same as true when reference is made to causality flowing from investments to both savings and interest rates, based on the evidence of the results of the pairwise causality tests in Table 3. It is also noteworthy and equally insightful that interest rates are causally prior to savings ([], = 3.258, probint = 0.025 as against F-statsav = 0.993; probsav = 0.45) as seen in the third panel of Table 3. It should also be noted that the pairwise causality is a general causality analysis, which shows that causality exists, or otherwise, between any two variables. It does not show whether the identified causality, or otherwise, is in the short-run or in the long-run. To do this, the study will embark upon the determination of short-run and long-run causality among the modelled variables.

Stationarity Properties of the Variables

The study proceeded to test the stationarity imperatives of the modelled variables, in view of the peculiarities of time-series data used. This is also necessary to unravel the long-rum equilibrium links and causality between the variables. Use is made of the Augmented Dickey-Fuller unit root test depicted in Table 4. Investments variable did not attain stationarity at level data (tau = -1.97, prob = 0.299, not sig.), implying the acceptance of the null hypothesis that investment variable has a unit root at level data. It however became stationary at first difference (tau = -4.42, prob = 0.0014, sig.), which is significant at the 1% level, suggesting the rejection of the null hypothesis that investment has a unit root at first difference. Savings was not stationary at level data (tau = -1.17, prob = 0.22, not sig.); but attained stationarity at first difference (tau = -9.22; prob = 0.0000, sig.),

Similarly, interest rates were not stationary at level data (tau = 0,635, prob = 0.848, not sig.) , but were stationary at first difference (tau = -6.596; prob = 0.0000, sig.). These results confirm that all the variables under study were integrated at order one or I(1). This allows the study to proceed with the nominated co-integration tests.

Co-integration and Long-run Equilibrium Analysis

The study, inter alia, proceeded with the Johansen co-integration test to determine whether or not there exist equilibrium long-run relationships between the variables: INV, SAV, INT, i.e., if they are co-integrated- at order 1. The results of both the trace and maximum eigenvalue unrestricted co-integration rank are summarized in Panels A and B of Table 5. In Panel A, the observed number of co-integrating equations is at most 1, with trace statistics of 40.25 and 12.90 and probabilities of 0.0002 and 0.04 for the respective hypotheses of "None" and "At most 1".

These are significant at the 1% and 5% levels, respectively. By implication, the trace statistic test indicates that there are significant long-run equilibrium relationships between INV, SAV, and INT variables. The variables are co-integrated at order 1.

In Panel B, which depicts the maximum eigenvalue statistical test, the results reveal the same conclusions that are implicated in the trace statistical test. Two co-integrating equations were revealed at the hypotheses of 'None" and "at most1". For instance, in the case of the hypothesis of "at most 1 co-integrtaing equation, the observed max-eigen statistic is 12.75 with a probability of 0.0268, which is significant at the 5% level. This implies that we reject the null hypothesis that there is at least one co-integrating equation but accept the alternative that there is at most one co-integrating equation. Thus, long-run co-integrating equilibrium relationships are inferred to exist between investments, savings and interest rates in Nigeria.

The study also conducted the Hansen parameter instability co-integration procedure to confirm validity of the Johansen test. As in Table 6, the null hypothesis that the series are cointegrated cannot be rejected, since the observed Lc statistic with stochastic trends posted a probability of 0.107, which is greater than the critical probability of 0.05. Thus, the results of the Johansen test are also confirmed by the Hansen parameter instability co-integration procedure. INV, SAV, and INT are co-integrated.

Error Correction and Long-run Causality Analysis

That the variables are co-integrated implies that there are possibilities of adjustment from short-run to long-run states. Invariably, errors that are encountered in the short-run can be corrected in the long-run, such that equilibrium conditions and results obtained in the short-run can persist in the long-run, depicting considerable consistency. In order to confirm that the cointegration results can be relied upon, and necessary adjustment is tenable from short-run to long-run, the study estimated the vector error correction model. The extract from the results are summarized in Table 7. Accordingly, the VEC variable (represented as cointEq1) posted a coefficient of -0.3115 and t-statistic of -3.269, which is significant at the 1% level. Thus, the error correction parameter is negative and significant, satisfying the a priori expectation; and thus yields to the conclusion that adjustments and correction of errors and distortions that existed in the short-run are tenable in the long-run. Thus, the variables are confirmed co-integrated. The speed of adjustment is observed to be a rate of 31.15% per annum. Thus, about 31% of the error that occurred in the short-run are corrected in the long-run.

A further implication of the error term being negative and significant relates to long-run causality. The study, thus, confirms that long-run causality flows from the independent variables, namely savings and interest rates to the dependent variable, namely investments. Savings and interest rates cause investments, jointly and severally, in the long-run. But can the same inference be made of causality in the short-run.

Short-run Causality Analysis

To determine the short-run causality implications of the variables, the study estimated the vector error correction (VEC) Granger causality/block exogeneity Wald tests. The results are set forth in Table 8. As seen, the savings variable posted an observed chi-square statistic of 3.29, which is not significant at the conventional levels. Thus, though savings cause investments in the long-run, they do not in the short-run. This has a commonsense application. Savings take time to mature and aggregate to investments. The savings that are made today don't get invested today or in a relatively 'short time'. Ultimately, in the long-run when all variables are allowed to vary, they are aggregated and converted into investments.

Interest rates, on the other hand, are revealed to cause investments in the short-run as well as in the long-run. The observed chi-square statistic is 6.87 with a probability of 0.032, which is significant at the 5% level. This indicates that we cannot accept a null hypothesis of no short-run causality flowing from interest rates to investments. This agrees with Keynesian investment theorizing that interest rates determine investments and thus output/income.

Furthermore, when all the independent variables (SAV and INT) are tested jointly for short-run causality, the result is quite interesting. Savings and interest rates jointly cause investments. The observed chi-square is 12.46 with a probability of 0.014, which is significant at the 5% level. Thus, it is inferred that, in the short-run, causation jointly flows from savings and interest rates to investments, but not severally or individually, as earlier indicated.

Long-run Co-integrating Estimates and Further Hypotheses Testing

That there exist short-run and long-run causality is one thing, the direction and sign implication of observed relationships is another. Equally, it is proper to ask: are the observed magnitude, direction, and sign implications in the contemporaneous relations remain the same even in the inter-temporal long-run? In order to address these concerns, the study utilized the fully modified least squares (FMOLS) technique to determine the long-run co-integrating estimates of the variables. The results are shown in Table 9. Just like, in the contemporaneous relations depicted in Table 2, savings are found to significantly and positively associate with investments (beta = 0.32, t = 2.65, prob = 0.012). In the light of the earlier causality analysis, the study can safely infer that savings significantly affect or impact investments in developing countries such as Nigeria, in the long-run. This agrees with theory and commonsense that savings eventually flow into investment expenditures of a country. Aggregate Savings boost aggregate domestic investments positively, both in the short-run and long-run.

Interest rates are also found to negatively and significantly relate to investments, in the long-run (beta = -0.49, t = -2.84, prob = 0.0076). The study safely infers that interest rates drive investments in developing countries such as Nigeria, both in the long-run and short-run. The direction of effect is, however, inverse, such that when interest rates increase, investments shrink. This is not unconnected with the tendency of investors to reduce their productive activities due to increased cost arising from high borrowing rates. The investors demand for loanable funds decrease when the rates at which they borrow funds for operations increase. This condition is applicable both in the short- and long-runs.

Impulse Response of Investment to its Own Shock and Shocks from Savings and Interest Rates

From the analysis thus far, it is clear that both savings and interest rates do cause or significantly affect investments both contemporaneously and inter-temporally. The next question would relate to the direction and degree to which unexpected changes, otherwise known as shocks or innovations, in the variables affect investments. This would include the shocks from investments itself (own shocks). To answer this question, the study appeals to the estimations of impulse response functions and variance decomposition analysis. As theory would have it, "An impulse response function traces the effect of a one-time shock to one of the innovations on current and future values of the endogenous variables. On the other hand, variance decomposition separates the variation in an endogenous variable into the component shocks to the VAR". Variance decomposition supplies information about the relative importance of each random innovation in affecting the variables in the VAR" (IHS Global Inc., 2015).

Table 10 and Figure 3 summarize the results of the impulse response function estimation. Own shock elicited positive and significant impulse response from investments in the first, second, and third year. The effects of own shock started dying out in the fourth year, when it was no longer significant. The magnitude of effects were 1.725, 1.626, 0.856, and 0.191 for the first, second, third, and fourth years, respectively. Unanticipated positive changes from SAV and INT shocks affected investments only during the second, third and fourth period. They were, however, not significant to cause any real change in investments, being less that unity in each period. Invariably, shocks in savings do not elicit remarkable response from investments. On the other hand, shocks from savings and interest in the first period did not cause any change in investments, but caused insignificant but positive change in the second year, and thereafter shocks produced negative response in investments in the third and fourth periods. The negative changes in or responses by investments due to the interest rate and saving shocks were not significant all through the periods. Only own shocks produced significant effects on investments in years 1 through 3, but not in year four.

Relative importance of own shocks and of Shocks from Savings and Interest ratesVariance Decomposition Analysis

In keeping with the underlying point that variance decomposition separates the variation in an endogenous variable into the component shocks to the VAR, the study analyzed the relative importance of the effects of own shock and those of the other variables in causing variations in investments. Accordingly, the relative importance of a random innovation in savings (savings shock) in affecting investments, in causing real changes in investments, is computed to be 0% in period 1, 5.83% in period 2, 12.69% in period 3, and 17% in period 4. Whereas the relative importance of interest rates shock in causing variations in investment is calculated to be 0%, 3.63%, 4.48%, and 10.99% for periods 1, 2, 3, and 4, respectively.

Own shock caused 100% of the variations in investments in period 1, 90.53% of variation in period 2, 82.83% of variations in period 3, and 72% of the total variations in period 4, respectively as presented in Table 11. By and large, own shocks accounted for the greatest influence in causing variations in investments, followed by savings, and thereafter interest rates for each of the four periods. It is noteworthy that whereas the influences of own shock kept decreasing consistently, those of savings continued on an increasing trend over the selected periods. Put more succinctly, own shocks are the most important source of fluctuations in domestic investments in Nigeria. Over time, this importance continues to decrease and wane remarkably, while savings and interest rates kept gathering momentum and continued to gain importance as sources of variations in domestic investments over the chosen periods.


The investment model specified for the purposes of analysis displayed ample global utility after passing rigorous diagnostic tests such as serial correlation, multicollinearity, heteroscedasticity, normality, and inverse roots characteristic polynomial tests. It equally showed relative usefulness in terms of performance in hypotheses' tests results and a priori theoretical confirmations in respect of the variables and relations between them. This accorded the findings, inferences and conclusions of this study a high level of empirical and theoretical plausibility.

A major finding of this study is that there exist a positive and significant contemporaneous relationship between saving and investment. Savings were seen to be an important causal variable of investments in Nigeria, though causally inferior to interest rates. Another finding of the study is that interest rate, at all levels, contemporaneous or inter-temporal, static or dynamic, short-run or long-run, is a very significant causal factor of investment in the country. Being revealed as causally superior to savings, interest rates strongly influence domestic investments in Nigeria, More specifically, whereas individually, savings significantly cause investments in the long-rum more than in the short-run, interest rates individually cause investments both in the short- and long-runs. Jointly, both variables cause investments in the short- and long-runs. So, the incipient question that gave impetus to this study can be answered cursorily: Savings and investments truly cause investments in Nigeria. It is very insightful that in line with theory, savings positively affected investments, while the effects of interest rates were negative.

An extension of the analysis revealed that domestic investments respond positively to shocks in investment (own shocks) and also positively to shocks in savings but negatively to interest rates shocks, over the periods under consideration. However, own shocks represent the most important sources of fluctuations or variations in domestic investments, followed by innovations in savings and lastly by innovations in interest rates. Noteworthy is that relative importance and influences of the sudden and unexpected changes or innovations in savings and interest rates were observed to follow an increasing trend, while those of own shocks continued to decline, over time.


Since savings positively drive investments, it is only a proper economic and financial action to encourage economic agents to engage in concerted savings and accumulation of resources that will eventually flow into productive activities in the country. Financial intermediation activities geared to promote fund mobilization by financial institutions should be encouraged, since when financial savings increase over time, investments are boosted. Thus, such policy actions that encourage or provide incentives to surplus economic agents should be put in place. For instance, financial intermediaries should not engage in actions that cause savers to withdraw or reduce patronages. Such would include unnecessary, secret, and or 'back-door' charges by intermediaries, high withholding, income, and value-added taxes (taxes on interest earnings, dividends, and services rendered). The Central Bank of Nigeria's stated deposit rates should be stepped up, even when this would reduce the interest rates spread that banks enjoy.

Interest rates was revealed to significantly but negatively relate to investments. Invariably, when lending rates are reduced, investments increase, as producers would be motivated by cheaper funds that reduce their cost of production. Then, it would be a wise policy to reduce the stated lending rates of interest among the intermediaries. This again will further reduce the interest rates' spread and, perhaps, earnings by the intermediary, but the guarantee of affordable funds to investors may be more beneficial and over-ridding.


It is suggested that the analyses done in the present study be extended to data based on other developing countries of Africa and Asia in order to provide robust comparative evidence that can be advanced for possible validation of theory and for concerted policy alignments, adjustments and refinements, where applicable.


The authors wished to include evidence from other countries in Africa in the present study, but we are yet to source all the relevant data needed. The present study is based only on the Nigerian data. We hope that the relevant data would be obtained in due course so as to enlarge the study.


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Chinedu B. Ezirim

University of Port Harcourt

Chukwu A. Ejem

Abia State Polytechnics

Udochukwu Ogbonna

Board of Internal Revenue, Abia State Umuahia

Ude Oko Chukwu

Government House, Abia State Umuahia

About the Authors:

Chinedu B. Ezirim is a professor of Finance, Banking and Finametrics at the University of Port Harcourt. He has published widely both locally and internationally in reputable journals and other outlets. He has attended, participated, and facilitated in many Conferences and professional meetings locally and internationally. He is a fellow of many professional societies.

Chukwu Ejem is a lecturer at the Abia State Polytechnics Nigeria. He has attended and participated in many conferences and presented papers. He has a good number of publications to his advantage. He is a fellow of the international Academy of Business and Behavioral Sciences.

Udochukwu Ogbonna is the chief executive officer of the Abia State Board of Internal Revenue. He is a fellow of a number of professional bodies including the chartered Institute of Taxation of Nigeria, Institute of chartered accountants of Nigeria, and the international academy of business and behavioral sciences USA. He has a number of publications in reputable journals to his credit.

Ude Oko Chukwu is the Deputy Governor of Abia State Nigeria. He has a PhD in Finance. He holds the fellowship of many professional bodies like the Instutute of Chartered Accountants of Nigeria, International Academy of Business Washington DC, USA and The International Academy of Business and Behavioral Sciences Connecticut, USA. He is also a legal lumininary. He has attended and participated in several professional conferences in and outside Nigeria.
Table 1
Results of the Residual Correlation Matrix, Serial Correlation and
Heteroscedasticity Tests

Variable            INV       SAV       INT

INV                 1.00000   0.376484  0.162577
SAV                 0.37648   1.000000  0.032554
INT                 0.16257   0.032554  1.000000
Panel B: Residual
Serial Correlation
LM Tests
Null Hypothesis:
no serial
correlation at
lag order h
Lags                LM-Sat    Prob
1                    8.537514 0.4810
2                   10.61673  0.3029

Panel C:
Joint test:
Chi-Sq              DF        Prob
79.98957            84        0.6037

Table 2
Least Squares Regression Results of the Model

Dependent Variable: INV
Variable                 Co-efficient  Std. Error   t- value   Prob.

C                         16.89859     4.363436      3.872771  0.0005
SAV                       0.247828     0.114480      2.164819  0.0375
INT                      -0.447265     0.154680     -2.891561  0.0066
R-squared                 0.290724     F-statistic             6.96810
Adjusted R-squared        0.249002     Prob(F-sta              0.00291

Table 3
Pairwise Granger Causality Tests Results

Null Hypothesis:                Obs  F-Statistic  Prob.

SAV does not Granger Cause INV  32   2.27961      0.0837
INV does not Granger Cause SAV       0.95746      0.4657
INT does not Granger Cause INV  32   4.56624      0.0056
INV does not Granger Cause INT       1.22388      0.3328
INT does not Granger Cause SAV  32   3.25804      0.0248
SAV does not Granger Cause INT       0.99355      0.4454

Table 4
ADF Unit Root Test Results at Level and First Differenced Data

Variable  Level     Level   1st Diff.  1st Diff.  Order of
          ADF       Prob    ADF        Prob       Integration
INV       -                 -                     I(1)

          1.965327  0.2999  4.419087   0.0014
SAV       -                 -                     I(1)
          1.172985  0.2152  9.216747   0.0000
INT                         -                     I(1)
          0.634722  0.8486  6.596741   0.0000

Table 5
Results of Johansen Co-Integration Test of the Series: INV SAV

Panel A: Unrestricted
Rank Test (Trace)
Hypothesized                       Trace      0.05
No. of CE(s)           Eigenvalue  Statistic  Critical Value  Prob. (**)
None (*)               0.542203    40.24695   24.27596        0.0002
At most 1 (*)          0.305321    12.90039   12.32090        0.0399
At most 2              0.004268    0.149706   4.129906        0.7493
Panel B: Unrestricted
Rank Test
(Maximum Eigenvalue)
Hypothesized                       Max-Eigen  0.05
No. of CE(s)           Eigenvalue  Statistic  Critical Value  Prob. (**)
None (*)               0.542203    27.34656   17.79730        0.0014
At most 1 (*)          0.305321    12.75069   11.22480        0.0268
At most 2              0.004268    0.149706   4.129906        0.7493

Table 6
Co-integration Test - Hansen Parameter Instability

Null hypothesis: Series are co-integrated
Co-integrating equation deterministics: C
              Stochastic  Deterministic   Excluded
Lc statistic  Trends (m)  Trends (k)      Trends (p2)  Prob. (*)

0.363673      2           0               0            0.1071

(*) Hansen (1992b) Lc(m2=2, k=0) p-values, where m2=m-p2 is the number
of stochastic trends in the asymptotic distribution

Table 7
Vector Error Correction Estimates

Standard errors in ( ) & t-statistics in [ ]
Error Correction:  D(INV)      D(SAV)      D(INT)

CointEq1            -0.311501    0.891806    0.120099
                    (0.09529)   (0.51085)   (0.25439)
                   [-3.26909]  [ 1.74574]  [ 0.47211]
R-squared            0.630023    0.293233    0.262598
Adj. R-squared       0.530414    0.102950    0.064066
F-statistic          6.324942    1.541036    1.322701

(*) Sig. At 1% level.

Table 8
VEC Granger Causality/Block Exogeneity

Wald Tests
Dependent variable: D(INV)
Excluded                    Chi-sq    Df  Prob.

D(SAV)                      3.290376  2   0.1930
D(INT)                      6.874949  2   0.0321
All                         12.46071  4   0.0142

Table 9
Table Fully Modified Least Squares (FMOLS) Results

Dependent Variable: INV
Long-run covariance estimate (Bartlett kernel, Newey-West fixed
bandwidth = 4.0000)
Variable  Coefficient  Std. Error  t-Statistic  Prob.

SAV        0.326230    0.123086    2.650432     0.0122
INT       -0.493128    0.173353    -2.844652    0.0076
C         15.30733     4.715619    3.246091     0.0027

Table 10
Responses of INV to Innovations from itself and from SAV and

Period  INV             SAV        INT

1        1.725653 (**)   0.000000   0.000000
        (0.20625)       (0.00000)  (0.00000)
2        1.626734 (**)   0.601968   0.475236
        (0.33279)       (0.34676)  (0.31304)
3        0.855786 (*)    0.781758  -0.343205
        (0.35849)       (0.49263)  (0.38145)
4        0.191299        0.731880  -0.795257
        (0.32385)       (0.50214)  (0.43447)

Table 11
Results of Variance Decomposition of GFCF

Period  S.E.      INV        SAV        INT

1       1.725653  100.0000    0.000000   0.000000
2       2.492459   90.53153   5.832972   3.635493
3       2.770137   82.83543  12.68640    4.478170
4       2.979654   72.00790  16.99822   10.99388
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Author:Ezirim, Chinedu B.; Ejem, Chukwu A.; Ogbonna, Udochukwu; Chukwu, Ude Oko
Publication:International Journal of Business and Economics Perspectives (IJBEP)
Geographic Code:9CHIN
Date:Sep 22, 2019

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