Revalidating Saving-Investment Comovement in Nigeria: Surprises, Stylized Facts and Explanations

Numerous studies have attempted to examine the relationship between savings and investment without a consensus conclusion. Interestingly, there have been profound findings, arguments and scholarly contributions on the sub-ject by different authors, researchers and scholars from most first class insti-tutions around the world. To further heighten the argument around the sub-ject, Feldstein-Horioka in his hypothesis, after running many regression, suggests that saving-investment co-movement under perfect capital mobility remains a puzzle. This paper therefore proposes a reconciliation model to re-validate the co-movement between savings and investment using the dataset sourced from the Central Bank of Nigeria (CBN) Statistical Bulletin between 1981 and 2017. The approach employed followed the Autoregressive Distributed Lag (ARDL) and Granger Causality that presumed economic variables reactions are not instantaneous and effects require a feedback mechanism de-lay for some period. The results suggest the existence of strong positive correlation between national savings and business investment, proposing that policies/initiatives to increasing the domestic resource mobilization through national saving are crucial for stimulating rate of investment in Nigeria.

explanation to justifies the equality of these variables at equilibrium. Importantly, the equality of savings and investment has been the cause of debate and controversy and, perhaps created puzzle since the ancient time. Several theoretical propositions have been made and laurel credited to various scholars who have made contributions to the development of concepts aimed at resolving the puzzle around the two subjects. Despite efforts being made, reconciling the equality of the two concepts at equilibrium has led to more divergence in view rather than convergence [1]- [12]. The main source of confusion arose from the failure of critics to recognize that while savings and investment are always equal, they are not necessarily so in equilibrium. At the early stage, the proponents of classical economics are of the opinion that the existence of fully employed economy can only occur where savings and investment are equal. The classical economists also argued that investors would always invest all savings. This group of economists further blamed inequality between savings and investment on the interest rate transmission mechanism and argued that the only way to reconcile this inequality would be by using monetary toolkits to stimulate the economy, if full employment must be realized [13]- [23].
In contrast, Keynes [24] disagrees with the classical view that equality between savings and investment is brought about through the mechanism of interest rate. According to Keynes, it is change in income, which brings the two to equality, rather than the rate of interest. Keynes further refutes the classical view that savings and investment are equal at the full employment level arguing that full employment is a rare phenomenon. As such, savings and investment equality can only occur at less than employment [24] [25] [26]. Beyond this controversy, the potential of savings and investment as drivers of economic growth are well established in existing literature. A common pointer among the existing literature confirmed the possibility of capital accumulation and saving mobilization to expand production frontier which is never in doubt [1]- [6].
In Nigeria, the performance of savings, investment and economic growth has not been impressive in recent times. Possible factors responsible for this weak relationship can be attributed to policy inconsistencies, high lending rates, low income capacity and disparity between the bank and unbanked population combine with limited bank branches [27] [28]. There have been efforts by the monetary authority to reconcile the gap between savings and investment through credit policies such as enhancement of credit availability, reduction of cost and improvement of access to credit to influence private investment as well as stimulate the growth of the real sector [27].
Interestingly, the CBN has continued to persuade banks to pay greater attention to the unbanked population with a view to extending financial services and mobilize savings on one hand, while prescribing aggregate and sectorial allocation of their loans and advances to enhance attainment of long term sustainable growth. While this approach gives priority to sector-lending target and encourage flow of credit to underdeveloped sectors, it has failed to attract savings to the banking sectors; this undermines the flow of credits to financially underserved The rest of the paper is organized as follows: Section 2 focuses on review of related literature, while Section 3 presents the theoretical framework and methodology. Section 4 presents statistical inference and econometrics analysis.
The paper concludes with relevant policy strategies in Section 5.

Theoretical Groundwork
The theoretical foundation is based on the Keynesian theory that advocates for equality of investment and savings at equilibrium level of national income complimented with the financial liberation hypothesis put forth by Mckinnon [25] and Shaw [26], which postulated that financial liberation has potential of inducing high savings that can help to channel surplus fund to the need of the deficit unit, which in turn has potential of stimulating investment [24] [25] [26] [43].
The justification of this theoretical consideration is based on the fact that their studies are intuitively appealing and provide ground breaking approach to access the correlation between savings and investment in Nigeria.

Analytical Framework
Following Levy [43] and Coakley et al. [44] who earlier showed the possibility of an economy intertemporal budget constraint to be balanced, suggesting that zero frequency coherence and gain of savings and investment will equal one.
We assume that the time series of domestic investment and national saving are non-stationary at level. That is We assumed that investment and savings are cointegrated which means that the process have a common stochastic trend.
Where t T is common stochastic trend with property ( ) Applying a difference operator to yield a bivariate stationary process, we have, With spectral matrix where the element on the diagonal are spectral density functions of ( ) , while the off diagonal elements are the cross spectral density function of ( ) [44].
To compute the spectral and cross spectral density function. Levy compute the autovariance and cross covariance function and then apply Fourier transformation to the resulting series.
Following Equation (4) above, ( ) ( ) Applying Fourier transform to both sides of Equation (6), we have: Using the standard definitions of spectral and cross spectral density functions presented by Levy [43], we have Realizing that the ( ) f ω is a complex function, apply Cartesian form, written as: where c denotes the cospectral density function and q denotes the quadrature spectral function. Following the derivation results presented by Priestley [45], where bar denote complex conjugate. Thus, using Equation (9), we have: Therefore, Equation (8) can be rewritten as: Similarly, deviation of ( ) Since t z is an error term/white noise process, it sis theoretical band is flat equals ( ) 2 2π z f ω σ = for all frequencies π π ω − ≤ ≤ . In addition, i ∆ and, s ∆ are, ( )  (12) and (14), the spectral matrix in Equation (5) evaluated at zero frequency becomes: From the polar representation of ( ) and where ( )

Model Building Block
This study draws inspiration from the Keynesian theory of savings and investment as used by Feldtein and Horioka [38]. In particular, Felstein and Horioka combined the absolute income hypothesis and the life cycle hypothesis in developing their theoretical framework. The model is specified as: where I denote domestic investment, S denote national savings, Y denote income and t µ denote error term. The coefficient α referred to as saving retention coefficient measured as the proportion of the incremental saving that is invest in the domestic economy.
Two major hypotheses are in support of this framework. First, the absolute income hypothesis postulated by Keynes [24] established the link between savings and income. Keynes suggested that savings is a function of income but the relationship is not linear as represented above.
Thus our model becomes:

1) Unit Root Test
The Dickey Fuller (DF)-GLS unit root test was adopted in this study to test the stationarity of each of the variables [49]. The null hypothesis was that the variable was non stationary. If the values of the DF-GLS statistic was less than or equal to the critical value, then the null hypothesis was rejected and it can be inferred that the variable was stationary at conventional level. The expression for the unit root is given as follows.
It is important to include the lags of the dependent variable in Equation (1) to eliminate autocorrelation. The hypothesis for stationarity and non-stationarity are expressed in terms of p. When 0 ρ = , it implies that series is not stationary, hence it has unit root.

2) ARDL Bounds Cointegration Test
The study employs the Autoregressive Distributed Lag (ARDL) bounds test by Pesaran, Shin and Smith [50] to examine the effects of monetary policy on output growth in the long and the short run periods in Nigeria. With this approach,  The existence of co-integrating relationship among the variables is determined by testing the significance of the lag levels of the variables using the F-test. The calculated F-statistic is compared with the two critical values for the upper and lower bounds tabulated by Narayan [51].

3) Causality Test
Granger [52] proposed a time series procedure in order to determine causality among time series variables. In Granger sense, there are three possible situations in which a Granger-causality test can be applied. First, in a simple Granger Causality there are two variables and lag considered; second is a multivariate Granger Causality test were more than two variables are considered, while the third considered testing a VAR framework. In this present study the multivariate Granger Causality is used.
Owing to the fact that the direction of co-integration is not a priori established, then each variable is normalized as dependent variable while the existence of level relationship is tested. We study also conducted diagnostic tests such as serial correlation, normality, functional form and heteroscedasticity tests.

Unit Roots Test
Prior to our cointegration tests, it is conventionally plausible to first carry out unit root test to probe the order of cointegration of the series data.

ARDL Cointegration Results
In order to empirically examine the long-run nexus and short-run dynamic relationships among our research variables, we explore the ARDL bounds test co-integration method developed by Pesaran and Shin [50]. Our choice of method was necessitated by the fact that the method is more explicit and reliable in probing the extent of the relationship among variables in comparison with other previous and traditional co-integration methods. Specifically, the ARDL is not preconditioned to the uniformity of co-integration order for all variables. In essence, the need for all the variables to be integrated in the same order and it can equally be applied when variables are either integrated at level or first difference. More importantly, Harris and Sollis [53], noted that applying the ARDL technique enhance unbiased estimates of the long-run model. Going by the underlining assumptions of the ARDL Model, one set assumes that all variables in the model are I(0) and the other set assumes they are all I(1).
If the calculated F-statistic exceeds the upper critical bounds value, then the H 0 is rejected. If the F-statistic falls within the bounds, then the test is inconclusive. Lastly, if the F-statistic falls below the lower critical bounds value, it implies that there is no co-integration. Hence, from the ARDL Bound Test co-integration results, the value of the F-static (12.51) exceeds the critical values at the upper bound (44.68 at 1%, 4.18 at 2.5%, 3.79 at 5% and 3.35 at 10%). Therefore, the empirical findings lead to the conclusion that a long run relationship exists among business investment (

Long Run Coefficients Estimates Using ARDL Approach
Having established the existence of co-integration from Table 3, the conditional ARDL for the long run relationship can be estimated given the model as thus; where, all variables are as previously defined. The order of the ARDL ( ) , , , , , p q q q q q model in five variables are selected by using AIC Equation (21) is estimated using the ARDL (1, 0, 0, 0, 0) specification (Table 4).
From the long run estimates results in Table 4

Short Run Estimates Using ARDL Approach
Taking inferences from the studies conducted by Odhiambo [54] and Narayan, Smyth [55] and Mounir (n.d.) [56], we further estimate the short-run parameters through the error correction model in relation to the long-run parameters estimates. The stated hypothesis of no co-integration which is associated with the vector error correction model is stated thus:  with negative sign as expected. Explicitly, the coefficient of the lagged error correction term (ECT) is (0.34) and negatively significant at 1%. The magnitude of the coefficient implies that 34% of the disequilibrium caused by previous shocks converges back to the long run equilibrium in the current period.

Granger Causality Tests
Causality is a critical issue when testing co-integration and in general macroe-

Post Test: Residual Diagnostic Tests Results
The estimated ARDL was tested for heteroscedasticity, serial correlation, function form misspecification, parameter stability and normality. The results from the test are shown in Table 6.
The model for the underlying ARDL fulfills the stated criteria examined by all the diagnostic tests observable from the serial correlation (Durbin Watson test and Breusch-Godfrey test) which suggests that the model is free from serial correlation. This indicates that the model is reliable in explaining the dynamics of

Concluding Remarks
Despite the significant level of resource endowments, savings mobilization remains a puzzle to business investment in Nigeria. This paper therefore revalidates the potential of domestic resource mobilization as it affects business investment in Nigeria between 1981 and 2017. The ARDL Bound test approach was employed to check the interaction and feedback mechanism between savings and investment fundamentals. The empirical results have confirmed the strong positive correlation between national savings and investment suggesting that policies/initiatives to increasing the domestic resource mobilization through national savings are crucial for stimulating rate of investment in Nigeria. This therefore suggests that policy priority should be centered on awareness of financial inclusion by banking the unbanked as well as encouraging existing banking population. Also, the need to curtail savings export to encourage investment opportunities should be given serious policy attention as this is likely to have serious implication on future growth of the country.
Further analysis indicated that financing constraints are major determinants of investment decision in Nigeria. The negative relationship between investment and financial development shows that such financial constraints may arise from scarce domestic financial resource or financial market imperfection. Therefore, the study suggests that eliminating this constraint through restructuring of the financial markets to spur investment is crucial for future growth of the country. Beyond obvious the result has clearly shown a warning sign that the present state of the Nigerian Financial Market cannot stimulate investment. Therefore, the efficiency of the financial system emerges as the key factor to act as a channel of moving resources from the surplus unit to the deficit sector giving priority to the real drivers of the economy.