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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 subject by different authors, researchers and scholars from most first class institutions around the world. To further heighten the argument around the subject, 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 revalidate 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 delay 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.

Researchers, financial analyst and policy makers have been able to empirically establish the fact that savings and investment are inevitable ingredients for economic growth. They have however, not been able to empirically provide the 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 [

In contrast, Keynes [

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 [

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 segment within the economy [

Evidently, knowing the degree of capital mobility as well as how savings mobilization can enhance the level of investment is crucial for growth recovery potential, which is the preoccupation of this study. Consequently, this paper makes three important contributions. First, it appreciates the dynamic relationship between domestic savings and investment in Nigeria using the Autoregressive Distributed Lag (ARDL) to check the feedback mechanism among the fundamentals and re-examined their long run relationships. Second, it examines the cyclical and short run relationship among the variables considered. Third, it beams light on major obstacles to domestic investment potential vis-à-vis macroeconomic indicators. The outcome of this study is expected to serve as policy ingredient to number of audiences ranging from policy makers to investors, and the academia alike who may find the study useful and strategic for boosting private investment in Nigeria.

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.

This section is not intended to conduct a full scale review of previous empirical studies on the relationship between savings, investment and economic growth; it selectively undertook the review of selected works considered central to the study.

To start with, several studies have attempted to reconcile the question of whether or not savings hinges on the level of investment using cross country evidence. For instance, in the United State, Levy [

In Botswana, Jagadesh [

In Turkey, Kaya [

In Tunisia, Adebole and Dahalan [

A cursory look at the works/studies reviewed points at three key messages: First, existence of divergent empirical outcomes, suggesting the level of inconclusiveness on the link between savings and investment debate. Second, the methodology deficiency and measurement challenges are observed in the reviewed studies. Third, majority of the studies do not provide the theoretical basis of their analysis. This study is therefore timely as it provides forum for resolving the aforementioned issues.

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 [

Following Levy [

We assume that the time series of domestic investment and national saving are non-stationary at level. That is I t ~ I ( I ) , and S t ~ I ( I ) .

Thus,

I t = I t − 1 + μ t (1)

S t = S t − 1 + ϑ t (2)

where

u t ~ I ( 0 ) and ϑ t ~ I (0)

We assumed that investment and savings are cointegrated which means that the process have a common stochastic trend.

Let

[ I t S t ] = [ 1 1 ] T + [ i t s t ] (3)

Where T t is common stochastic trend with property ( 1 − L ) T t = z t , z t ~ i i d ( 0 , σ 2 ) , i t ~ I ( 0 ) , s t ~ I ( 0 ) .

Applying a difference operator to yield a bivariate stationary process, we have,

[ ( 1 − L ) I t ( 1 − L ) S t ] = [ 1 1 ] z t + [ ( 1 − L ) i t ( 1 − L ) s t ] , (4)

With spectral matrix

f ( ω ) = [ f Δ I f Δ I , Δ s f Δ s , Δ I f Δ s ] (5)

where the element on the diagonal are spectral density functions of ( 1 − L ) I t and ( 1 − L ) S t , while the off diagonal elements are the cross spectral density function of ( 1 − L ) I t and ( 1 − L ) S t respectively [

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, ( 1 − L ) I t = z t + ( 1 − L ) I t , with the autocovariance function

γ Δ I ( τ ) = E [ ( z t + τ + Δ i t + τ ) ( z t + Δ i t ) ] = E ( z t + τ z t ) + E ( Δ i t + τ Δ i t ) + E ( z t + τ + Δ i t ) + E ( Δ i t + τ z t ) = γ z ( τ ) + γ Δ i ( τ ) + γ Δ i , z ( τ ) (6)

Applying Fourier transform to both sides of Equation (6), we have:

1 2π ∫ − ∞ ∞ γ Δ I ( τ ) e − i τ ω d τ = 1 2π ∫ − ∞ ∞ γ z ( τ ) e − i τ ω d τ + 1 2π ∫ − ∞ ∞ γ Δ i ( τ ) e − i τ ω d τ + 1 2π ∫ − ∞ ∞ γ z , Δ i ( τ ) e − i τ ω d τ + 1 2π ∫ − ∞ ∞ γ Δ i , z ( τ ) e − i τ ω d τ (7)

Using the standard definitions of spectral and cross spectral density functions presented by Levy [

f Δ I ( ω ) = f z ( ω ) + f Δ i ( ω ) + f z , Δ i ( ω ) + f Δ i , z ( ω ) . (8)

Realizing that the f ( ω ) is a complex function, apply Cartesian form, written as:

f z , Δ i ( ω ) = C z , Δ ι ( ω ) − i q z , Δ i ( ω ) . (9)

f Δ i , z ( ω ) = C Δ ι , z ( ω ) − i q Δ i , z ( ω ) . (10)

where c denotes the cospectral density function and q denotes the quadrature spectral function. Following the derivation results presented by Priestley [

f z , Δ i ( ω ) = f Δ i , z ( ω ) ¯

where bar denote complex conjugate. Thus, using Equation (9), we have:

f z , Δ i ( ω ) + f Δ i , z ( ω ) = f z , Δ i ( ω ) + f z , Δ i ( ω ) ¯ = 2 c z , Δ i ( ω ) . (11)

Therefore, Equation (8) can be rewritten as:

f Δ I ( ω ) = f z ( ω ) + f Δ i ( ω ) + 2 c z , Δ i ( ω ) . (12)

Similarly, deviation of f Δ s ( ω ) and f Δ I , Δ S ( ω ) is express as:

f Δ s ( ω ) = f z ( ω ) + f Δ s ( ω ) + 2 c z , Δ s ( ω ) (13)

f Δ I , Δ S ( ω ) = f z ( ω ) + f Δ i , Δ s ( ω ) + f z , Δ s ( ω ) + f Δ i , z ( ω ) (14)

Since z t is an error term/white noise process, it sis theoretical band is flat equals f z ( ω ) = σ 2 / 2π for all frequencies − π ≤ ω ≤ π . In addition, Δ i and, Δ s are, I ( − 1 ) and therefore their frequency cospectral density, Cospectral density function equal zero.

Thus, combining Equations (12) and (14), the spectral matrix in Equation (5) evaluated at zero frequency becomes:

f ( ω ) | ω = 0 = [ σ z 2 2 π σ z 2 2 π σ z 2 2 π σ z 2 2 π ] . (15)

From the polar representation of f ( ω ) we have

R y , x 2 ( ω ) = | f x , y ( ω ) | 2 f y ( ω ) f x ( ω ) = c y , x 2 ( ω ) + q y , x 2 ( ω ) f y ( ω ) f x ( ω ) (16)

and

Γ y , x ( ω ) = | f y , x ( ω ) | f y ( ω ) = | c y , x 2 + ( ω ) + q y , x 2 ( ω ) | 1 / 2 f y ( ω ) (17)

where R y , x 2 ( ω ) and Γ y , x ( ω ) denote the squared coherence and the gain of investment and saving, respectively (see Jenkin & Watts, 1968). Thus, using matrix in Equation (15) along with definition of squared coherence and gain provided in Equations (16) and (17), we show the zero frequency as

R y , x 2 ( ω ) | ω = 0 = | σ z 2 2π | 2 σ z 2 2π σ z 2 2π = 1 (18)

This study draws inspiration from the Keynesian theory of savings and investment as used by Feldtein and Horioka [

| I Y | t = α + β | S Y | t + μ t (19)

where I denote domestic investment, S denote national savings, Y denote income and μ t 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 [

Thus our model becomes:

I N V t = α + β 1 S A V t + β 2 C F t + β 3 L M t + β 4 F E D t + μ t (20)

where, I N V t is the ratio of non-government gross investment to GDP (the true rate aggregate business investment) in year t; S A V t ratio of national savings to GDP (domestic savings) in year t; C F t is proxy as the net capital flow as a percentage of GDP in year t (external finance); LM is share of broad money in GDP (level of monetization in the economy) in year t; Financial development and efficiency proxy as the credit to the private sector as a ratio of banks overhead cost to total asset in year t; α is constant; β 1 - 4 are slopes, μ t error term and t is time (

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 [

Δ Y t = β + ρ Y t − 1 + ∑ j = 1 n b j Δ Y t − s + v t (21)

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 ρ = 0 , 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 [

Variable | Theoretical Basis | Expected signs | Symbols | Data Source |
---|---|---|---|---|

Aggregate Business Investment | Dobrinsky [ | no sign | (INV_{t}) | World Development Indicator, 2017; CBN Statistical Bulletin, 2017 [ |

Nation savings | Dobrinsky [ | + | (SAV_{t}) | World Development Indicator, 2017; CBN Statistical Bulletin, 2017 [ |

Capital flow | Dobrinsky [ | ± | (CF_{t}) | World Development Indicator (WDI), 2017; CBN Statistical Bulletin, 2017 [ |

Level of monetization | Feldstein and Horioka [ | ± | (LM_{t}) | World Development Indicator, 2017; CBN Statistical Bulletin, 2017 [ |

Financial Development Efficiency | Feldstein and Horioka [ | + | (FED_{t}) | World Development Indicator, 2017; CBN Statistical Bulletin, 2017 [ |

Source: Authors computation.

output growth is expressed as a function of the lagged value of itself and the current and the lagged values of the explanatory variables.

Δ I N V t = a + ∑ p = 1 n b p Δ I N V t − p + ∑ p = 1 n c p S A V t − p + ∑ p = 1 n d p C F t − p + ∑ p = 1 n e p L M t − p + ∑ p = 1 n f p F E D t − p + ρ 1 S A V t + ρ 2 C F t + ρ 3 L M t + ρ 4 F E D t + e t (20)

where Δ is the first difference operator. The parameters ρ i , where i = 1, 2, 3, 4, 5, 6, 7 are the respective long run multipliers while the parameters b, c, d, e, f, g, h are the short run dynamic coefficients of the underlying ARDL model in the equation. ε t denotes the white noise error term. The Bounds cointegration test will involve estimating Equation (19) and restricting the parameters of the lag level variables to zero. Based on this equation, we tested the following null and alternative hypotheses:

H 0 = ρ 1 = ρ 2 = ρ 3 = ρ 4 = ρ 5 = 0 (i.e. no cointegration or level relationship) as against H 1 = ρ 1 = ρ 2 = ρ 3 = ρ 4 = ρ 5 ≠ 0 .

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 [

3) Causality Test

Granger [

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.

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. The rationale behind the unit root test lies in the fact that the tests help to determine the nature of the series to avoid spurious regression results.

The unit roots estimates were based on Dickey Fuller-GLS test with the result presented in

Variables | Levels | First Difference | Order of Integration | ||||
---|---|---|---|---|---|---|---|

ADF Test Stat. | 1% | 5% | ADF Test Stat. | 1% | 5% | ||

(INV_{t}) | −4.58* | −3.62 | −2.94 | −7.80* | −3.63 | −2.94 | I(1) |

(SAV_{t}) | −1.34 | −3.62 | −2.94 | −4.37* | −3.63 | −2.94 | I(1) |

(CF_{t}) | −1.88 | −3.62 | −2.94 | −6.98* | −3.62 | −2.94 | I(1) |

(LM_{t}) | −1.18 | −3.62 | −2.94 | −12.01* | −3.63 | −2.94 | I(1) |

(FED_{t}) | −2.08 | −3.62 | −2.94 | −3.78 | −3.62 | −2.94 | I(1) |

*indicate 1%, **indicate 5%, level of significance. Source: Authors’ computation.

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 [

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 ( I N V t ), national saving ( S A V t ), Capital flow ( C F t ), Level of monetization ( L M t ) and Financial development efficiency ( F E D t ).

Having established the existence of co-integration from

ln I N V t = a + ∑ p = 1 n b p ln ( I N V t − p ) + ∑ p = 1 n c p ln ( S A V t − p ) + ∑ p = 1 n d p ln ( C F t − p ) + ∑ p = 1 n e p ln ( L M t − p ) + ∑ p = 1 n f p ln ( F E D t − p ) + e t (21)

Test Statistic | Value | K | Critical Value Bounds | ||
---|---|---|---|---|---|

Significance | I(0) | I(1) | |||

F-Statistic | 12.51 | 5 | 10% | 2.26 | 3.35 |

5% | 2.62 | 3.79 | |||

2.5% | 2.96 | 4.18 | |||

1% | 3.41 | 4.68 |

Source: Authors’ computation.

where, all variables are as previously defined. The order of the ARDL ( p , q 1 , q 2 , q 3 , q 4 , q 5 ) model in five variables are selected by using AIC Equation (21) is estimated using the ARDL (1, 0, 0, 0, 0) specification (

From the long run estimates results in

Taking inferences from the studies conducted by Odhiambo [

ln ( Δ I N V t ) = a + ∑ p = 1 n b p ln ( Δ I N V t − p ) + ∑ p = 1 n c p ln ( Δ S A V t − p ) + ∑ p = 1 n d p ln ( Δ C F t − p ) + ∑ p = 1 n e p ln ( Δ L M t − p ) + ∑ p = 1 n f p ln ( Δ F E D t − p ) + α E C T t − 1 + e t (22)

where, all variables are as previously defined. The order of the ARDL ( p , q 1 , q 2 , q 3 , q 4 , q 5 ) model in five variables are selected by using AIC Equation (22) is estimated using the ARDL (3, 2, 1, 2, 3) specification.

The short run dynamic relationship between saving and investment fundamentals in Nigeria is indicated in the second part of the estimated ARDL in

Variable | Coefficient | Std Error | t-statistic | Prob | |
---|---|---|---|---|---|

S A V t ( − 1 ) | 0.04 | 0.01 | 2.33 | 0.06 | |

C F t ( − 1 ) | −0.12 | 0.05 | −2.39 | 0.06 | |

L M t ( − 1 ) | 0.23 | 0.04 | 4.81 | 0.00 | |

F E D t ( − 1 ) | 0.49 | 0.06 | 7.52 | 0.01 | |

Short-run Equation | C | 2.86 | 4.75 | −0.60 | 0.57 |

D ( I N V t ( − 1 ) ) | 0.60* | 0.13 | −4.36 | 0.01 | |

D ( I N V t ( − 2 ) ) | 0.72* | 0.12 | −7.46 | 0.02 | |

D ( I N V t ( − 3 ) ) | −0.86* | 0.09 | −3.71 | 0.01 | |

D ( S A V t ) | −0.01 | 0.04 | −0.30 | 0.77 | |

D ( S A V t ( − 1 ) ) | 0.09* | 0.04 | 2.23 | 0.07 | |

D ( S A V t ( − 2 ) ) | 0.07* | 0.04 | 4.79 | 0.03 | |

D ( C F t ) | −0.06* | 0.01 | −3.45 | 0.01 | |

D ( C F t ( − 1 ) ) | 0.13* | 0.05 | 2.42 | 0.06 | |

D ( L M t ) | −0.01 | 0.05 | −0.25 | 0.81 | |

D ( L M t ( − 1 ) ) | 0.26 | 0.22 | 1.19 | 0.28 | |

D ( L M t ( − 2 ) ) | −0.06 | 0.10 | −0.64 | 0.54 | |

F E D t | 0.08 | 0.07 | 1.10 | 0.31 | |

D ( F E D t ( − 1 ) ) | −0.42* | 0.04 | −8.86 | 0.00 | |

D ( F E D t ( − 2 ) ) | 0.08 | 0.10 | 0.83 | 0.44 | |

D ( F E D t ( − 3 ) ) | 0.03* | 0.01 | 1.95 | 0.10 | |

F E D t E C M ( − 1 ) | −0.34* | −0.09 | −1.14 | −0.02 |

(*) (**) (***) indicate 1%, 5%, 10% level of significant. Source: Authors’ computation.

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.

Causality is a critical issue when testing co-integration and in general macroeconomic model building. Below is the Pairwise Granger causality test that determines the cause effects of the Savings-Investment fundamentals. The results are analysed based on their causal direction. In econometric analysis, unidirectional Granger Causality is usually used to predict the possibility of a variable to influence another without possibility of reversed case. Bidirectional or feedback causality of the growth rate of variables has the possibility of predicting each other, while no direction or independence between two or more variables show no Granger causality [

The pairwise Granger causality test presented aims to determine whether causality exist between savings and investment fundamentals. Precisely,

The estimated ARDL was tested for heteroscedasticity, serial correlation, function form misspecification, parameter stability and normality. The results from the test are shown in

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

Bidirectional | Unidirectional | No Causality |
---|---|---|

S A V ↔ I N V | F E D → I N V | L M − S A V |

C F ↔ I N V | L M → I N V | F E D − S A V |

Source: Authors computation.

F-Statistic | Probability | |
---|---|---|

Breusch-Godfrey Serial Correlation test | 2.35 | 0.10 |

Jarque-Bera test | 0.93 | 0.56 |

Wald Test | 31.51*** | 0.00 |

Breusch-Pagan-Godfrey Heteroskedasticity Test | 0.88 | 0.72 |

Ramsey RESET Test | 0.03 | 0.97 |

Chow Forecast Test (Likelihood ratio) | 65.66*** | 0.00 |

Note: *, ** and ***signify significant level at 1%, 5% and 10% respectively. Source: Authors’ computation.

inflation in Nigeria for the study period. Similarly, the Breusch-Pagan-Godfrey Heteroskedasticity test reveals that the disturbance term in the equation is equally homoscedastic. Going by the result of the Jarque-Bera (JB) test, the null hypothesis of normally distributed residuals cannot be rejected. While the Ramsey RESET test result shows that there is no specification error, the Wald test reinforces our standpoint about the validity and correctness of our obtained results. Finally, the Chow predictive failure test suggests that the model may possibly be useful for forecasting with 2009 as the breakpoint year.

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.

The authors declare no conflicts of interest regarding the publication of this paper.

Joseph, E. and Shobande, O.A. (2018) Revalidating Saving-Investment Comovement in Nigeria: Surprises, Stylized Facts and Explanations. Theoretical Economics Letters, 8, 3594-3610. https://doi.org/10.4236/tel.2018.815221