An econometric modelling of the savings – investments nexus for Ghana

Results. The results indicate that a 1% increase in savings, GDP and financial development would result in a 0.069%, 0.266% and 0.125% increase respectively in investment in the short-term. It is discovered that savings do not cause investment in the long-run but rather in the short-run. The Granger causality test establishes a unidirectional causality running from savings to investment in the short-run.


INTRODUCTION
S ince Feldstein and Horioka original article [6], huge writing has developed that analyses the potential relationship between savings and investment in an economy. The subject of whether savings and investment are linked emphatically, feebly, or not in any manner has been an issue specifically compelling (Sach, 1981;Murphy, 1984;Obstfeld, 1986;Tesar, 1991;Baxter and Crucini, 1993). Feldstein and Horioka note that the savings-investment relationship is not predictable with capital versatility across fringes for the short run. This proposes that capital is fixed universally [6].
As substantiated by different analysts [3; 16] this has a suggestion for global trade and business. On the off chance that savings are associated with an investment, the legitimate ramifications are that capital is fixed globally. Be that as it may, on the off chance that savings are not related to investment, at that point capital is versatile globally. In this way, it is imperative to investigate the legitimacy of the savings-investments relationship theory as an experimental actuality in an open but small economy such as Ghana.
The present paper adds to the collection of information in writing in the zone of global capital mobility by empirically looking at the relationship between savings and investments in the context of a developing country with an underdeveloped financial sector in terms of mobilising and allocating financial resources (financial intermediation). The investigation is roused by the mixed findings which can be attributed to the choice of proxies use or the econometric techniques employed. Thus, we explicitly test the long-term and short-term link between savings and investments using the ARDL (with bounds testing) which performs better when dealing with small samples compared to the conventional cointegration techniques. The study answer questions such as, what is the nature of the link between savings and investments? and what is the direction of causality between savings and investment? The paper assumes that domestic savings are cointegrated with investment in the long-run and also saving predicts investment in the short-term.
The rest of the paper is organised into four sections. Section 2 deals with the literature survey. Section 3 considers the methodology and data, whereas section 4 looks at the results and discussions. Section 5 concludes the study and provides recommendations.

LITERATURE REVIEW
The empirical writings referred to arrive at the resolution that savings and investments are related utilizing both time-series information and cross-sectional information (Ozman & Parmaksiz [18]; Narayan [14]; Payne [19]; Kim et al. [11]; E. Telatar, F. Telatar, & Bolatoglu [22]; Fouquau, Hurlin, & Rabaud [7]; Singh [20]; Apergis & Tsoumas [2]; Onafowara, Owoye, & Huart [17]). The key element of each of these examinations is that they worked upon the crafted work of Feldstein and Horioka [6] and arrived at a conclusion that savings are connected to investments and the relationship is strong in larger nations than smaller nations. Variables that accounted for the observed relationship are the existence of a policy target for the current account, the exchange rate regime, common shocks to investments and savings, the degree of openness, and country size (large or small).
Analysts have observed that for certain nations the size of the effect between savings and investments remains high whereas in others the effect size keeps declining. For instance, Onafowara et al. [17] detailed in their investigation that the relationship between savings and investments remained generally high in the OECD countries, about 0.57 over the period 1991-2001, yet it has significantly declined in the EU countries to 0.36 and in the Eurozone to 0.14.
The experimental check of the relationship between savings and investments has created blended discoveries in the writing. For instance, while some past examinations report a relationship between savings and investments different investigations do not bolster the nexus among reserve funds and speculation. Nasiru and Usman [16] observed a noteworthy long-run link between savings and investments for Nigeria for the period 1980 to 2011. Their discoveries bolster the Feldstein-Horioka [6] theory that proposes low capital versatility globally.
Kollias et al. [12] revealed a connection between savings and investments in Austria, Germany, Greece, Italy, Luxembourg, Spain, and the Assembled Realm. Anyway, a significant association was found in Denmark, Finland, France, Ireland, the Netherlands, and Sweden; while there was an uncertain connection in the Belgium and Portugal studies. Esso and Keho [5] in their investigation showed that savings and investments are related and that household savings are significant factors in financing investments in three nations in their study. In the other four nations in their investigation, household savings rate and investment rate are not associated. Onafowara et al. [17] revealed a relationship between savings and investment in six nations. Be that as it may, the aftereffects of the course of causality delivered blended discoveries. There was proof of a long-run link between savings and investments with causality running from savings to investments in the Netherlands and a reverse causality existing in Denmark, Germany, and Luxembourg study, with bidirectional causality reported in Belgium study, and neutrality causality in France and Italy study. Chakrabarti [4]  Narayan [14] investigation of the connection between savings and investments for the period 1960-1999 for Japan reported a significant stable long-term link between the two variables in line with the Feldstein and Horioka theory. The examination by Singh [20] on the savings-investment link for the period 1950-51 to 2001-02 indicated a significant long-term association between investments and savings which supports the existence of Feldstein-Horioka theory for India. Esso and Keho [5] validated the Feldstein and Horioka assumption for member countries of UEMOA by testing for the long run and the direction of causality between savings and investment using the Toda and Yamamoto (1995) and the Pesaran et al. (2001). The findings of their study indicate significant cointegration and a stable long-run link in the model estimated. The was unidirectional causality from savings to investment in Niger, Benin, and Côte d'Ivoire. They concluded that there is capital imperfect mobility in the Benin economy and capital immobility in the economy of Niger. In other countries in their study, savings does not play a significant role in investment, which indicates capital mobility internationally.
Mishra P., Das, and Mishra S. [13] investigated the savings-investments association for the period 1950-51 to 2008-09 in India. Their findings indicated a significant and stable shortterm and long-term correlation between savings and investments. Their discoveries bolster the Feldstein-Horioka theory. Tehranchian and Behravesh [21] examined the Feldstein-Horioka assumption for Iran by testing the long run and short run nexus. Their study findings revealed a stable long-run and short-run association between the two variables and indicated that the association is stronger in the long run than in the short run. They concluded that capital is immobile in Iran for the period under discussion. Al-Afeef and Ali Al-Qudah [1] investigated the savings-investment link for Jordan economy for the period 1980 to 2013 using the Johansen cointegration method and reported a significant long-run association between savings and investment and concluded that there is perfect capital mobility international in Jordan. Irandoust [8] assessed the direction of causality between savings and investment for six transition countries using the bootstrap panel causality test to verify whether capital is fixed internationally or mobile. The study findings indicate significant causality between savings and investment in the countries reviewed, indicating capital immobility internationally.
Other similar investigations have not bolstered the Feldstein-Horioka hypothesis for different nations. For instance, P. Narayan and S. Narayan [15] study did not bolster the theory for G7 nations over the period 1971-2002. Ketenci [10] study did not bolster the theory for Estonia and Portugal between 1995-2009. In any case, the examination upheld the theory for other 23 EU nations.

Data and variables measurements
Time-series techniques unlike panel data techniques are considered to explain the specificity of individual countries and give an avenue for researchers to examine the causality and its

Model Specification
For estimation and modelling, we specify the following general model to capture the association amongst the variables.
Where INVt is Gross capital formation as a ratio of GDP at a time (t), SVt is domestic savings as a ratio of GDP at a time (t), GDPt is a gross domestic product at a time(t), and, FDt is Domestic credit by banks as a ratio of GDP at a time (t). The estimation equation is thus stated as follows in a log-linear form: The estimation employs the use of the autoregressive distributed lag model (ARDL) bound test put forward by Pesaran et al. (2001) which is based on the ordinary least square regression (OLS) modelling technique. This method is used since the ARDL test is appropriate for a smaller sample size such as the current study. It is also appropriate when the data set is differently orderly integrated. That is I(0) and I(1) but not I(2). In estimating the long-run association between investment and savings, the study employs the bounds testing approach for cointegration within the ARDL framework. The ARDL is generally specified as: Where is the first-difference operator, Y is the dependant variable and X is a vector of independent variables is the error term and is the constant term. In this current study, for analysis, we conceptualize only one model using INV as the dependent variable for reasons of parsimony.
The first part with Ϥ 1 , Ϥ 2 , Ϥ 3 , Ϥ 4 coefficients represent the long-run relationship of the model and the second part with ϗ i , β i , δ i , μ i coefficients represent the short-run dynamics of the model, α 0 represents the drift element and ε t signifies the white noise term. Concerning ARDL technique, (p +1) k regressions are estimated to obtain the optimal lag length for each series.
"p" denotes the maximum number of lags that can be used and "k" is the maximum possible number of equations in the model (4) that can be estimated. Our optimal lag selection criteria were based on the Akaike Information Criteria (AIC). Using the bound testing approach for cointegration, the null hypothesis of no cointegration H 0 : However, if there is evidence of cointegration or long-run association, we then proceed to estimation the long-run coefficients using the OLS techniques as stated in equation (6): If cointegration is present, then we estimate the error correction term using the reduced form of equation (7): In equation (8) and (9), X does not Granger cause Z if ω 1i parameters are jointly 0 and Z does not Granger X if ψ 2i parameters are jointly 0.
However, neither ARDL nor Granger Causality tests give evidence whether any series responds to shocks in another series or not. Therefore, we use the GIRF of Koop et al. (1996) and Pesaran and Shin (1998) to ensure that that VAR innovation is not contemporaneously correlated. The ability of the GIRF to trace one-off shock to one of the innovations on the current and future values of the endogenous variables made it a preferred choice over the Where σ jj is the jj th element in the covariance matrix ∑, and e j is an mx1 vector The GIRF is obtained by transforming the VAR model into an infinite moving average representation (see Pesaran and Shin, 1998).
Hence, the GIRF in equation (11) establishes the effect of a unit shock to the ith variable pm the jth cointegrating relations.

Time Series Plot
The time series plot results are accounted for in figure 1 to figure 6. The figures show that the factors (SV, INV, and GDP) are non-stationary in levels ( figure 1 to figure 4), notwithstanding, the factors achieved stationarity after they were first differenced ( figure 5 to figure 8). The stationarity properties are further experimentally explored utilizing the ADF test, and the KPSS tests. The aftereffects of the test appear in Table 3.

Unit root tests
The two-unit root tests utilized in the present investigation are the Augmented Dickey-

Fuller test (ADF), and Kwiatkowski, Phillips, Schmidt, and Shin (KPSS). The Augmented
Dickey-Fuller test was first used to test for stationarity properties of the factors. The aftereffects of the ADF test in levels and first difference (logarithm) show that a portion of the series is non-stationary in levels (investment and gross national output) however, accomplished stationarity on first differenced. The null assumption of the ADF unit root was supported in levels for the two factors. Savings are stationary at levels and on the first difference.
The null assumption of the ADF unit root was not supported for savings in levels and on first differenced. The KPSS test for analysing the stationarity properties (considering the null assumption that the data under scrutiny are stationary in levels against the alternative hypothesis that the data are not stationary in levels) was utilized notwithstanding the use of the ADF test. The outcomes (in levels and the first difference in their logarithm form) are accounted for in Table 3. Investment and income have unit roots in levels though savings do not have a unit root at a level. However, all the variables achieved stationarity on the first difference. The outcomes demonstrate that shock to investment and income is perpetual and not impermanent. Be that as it may a shock to savings is brief and not lasting. The results of the unit root tests also justify the use of the ARDL approach.  Hence, we conclude there is a cointegration relationship between investment, savings, GDP, and financial development. Since there is cointegration, the next logical step is to estimate the long-run equation and the error correction model as stated in equations (6) and (7) respectively. We estimated the long-run coefficient elasticities of the cointegrating vectors using the ARDL model and the results are reported in Table 4. The results show that none of the coefficients of the predictor variables is statistically significant at the conventional levels. However, if the predictor variables were to be significant, it would have promoted investment (i.e. positive coefficients). One intuitive expectation is a positive impact of savings on investment which is also supported by the endogenous growth models. However, the empirical data does not support this view given the insignificant impact of savings on investment. It is worthy to note that although the impact of GDP and financial development are statistically insignificant, given the size of the parameter estimates, they are economically significant.

ARDL Bound Test Results
The short-run dynamics using the ECM version of the ARDL are also displayed in Table 5.
The model contains the error correction term (ECT -1 ). The coefficient of the error correction term (i.e. speed of adjustment) captures the size of disequilibrium in investment in one period which is corrected in the next period. The higher the error correction coefficient, the shorter the period whereby the economy returns to a steady (i.e. equilibrium) rate of investment after a shock. Theoretically, the coefficient of the ECT -1 , where -1 indicates that 100% of the disequilibrium in investment is corrected in the next period. However, the error correction term should be negative and statistically significant. The coefficient of our error correction term is -0.272 which implies that approximately 27% of last year's disequilibria are corrected in the current year, indicating a poor speed of adjustment in the relationship process following a shock in the last year. The negative sign on the error correction coefficient gives evidence to support the expected convergence process in the long -run. In the short-run, savings, GDP, and financial development significantly at the 1% level promote investment. A 1% increase in savings, GDP, and financial development would result in a 0.069%, 0.266% and 0.125% increase respectively in investment.
Additionally, Table 5 presents the diagnostic test performed on the ARDL model. The results indicate that the estimated long-run and error correction model is free from serial correlation, heteroscedasticity, and non-normality as all their estimated coefficients are not significant. The adjusted R-Squared which is approximately 88% indicates a good fit for the model. The model is free from any functional misspecification as indicated by the Ramsey RESET test. The plots of the CUSUM and CUSUMSQ statistics (see Figure 1) are well fitted within the 5% critical bounds implying that the model is stable over the sample period of 1960-2016.     4 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 CUSUM of Squares 5% Significance  In the Model, the results show that a large response of investment in the system is due to its shock. This is consistent with the result of the variance decomposition (VDC) reported in Table. Investment remained positive over the horizon, though it was declining as the forecast horizon increased into the future. This suggests that the investment will return to its initial equilibrium value of zero if there are no further shocks in the system over some time. A standard innovation to domestic savings results in a decline in investment.

Note: a denotes significance level at 1%; Values in (#) denote T-values; Values in [#] denote P-values
The impact of the shock was positive up to about the middle of the 3 rd year when it crossed the zero line and became negative, persisting all through the period of the forecast.
Furthermore, the response of investment to a standard innovation in financial development is positive from the beginning of the forecast period and remained so for a greater part of the period till the effect of the shock began to fissile out and move towards the zero lines from about the beginning of 7 th year. GDP shock is quite high at the initial stage but after the 2 nd period, the effect begins to decline yet it remains positive and continues after the 10 th period.
We can conclude that there is a unidirectional Granger causality from the shock to investment in Ghana. However, the results should be analysed with caution. This is because the impact of one standard deviation innovation in any of the shock variables is associated with a gamut of economic interactions at the macro level.

Figure 10
Generalised Impulse Response of the Unrestricted VAR Model

Variance Decomposition Test Results
Results of the variance decomposition analysis for the VAR model are reported in Table 8.
The forecast horizon remains 10 years to allow us to observe how the system advances over Examining the whole forecast horizon, the share of financial development in the variability in investment increased from 0.09% in the 2 nd year to 0.136% and 0.182% in the 6 th and 10 th year respectively. The share of investment declined from 95.32% in the 2 nd year to 83.81% and 77.37% in the 6 th and 10 th year respectively, in explaining itself. Also, the share of variability in investment explained by domestic savings increased from 1.04% in the 2 nd year to 9.50% at 15.25% in the 6 th and 10 th year respectively. The variability in investment explained by domestic savings is not as large as we expected, hence we conclude that domestic savings shock has an indirect and a marginal impact on investment. The share of GDP tends to follow a similar trend as that of domestic savings. The result shows that the contribution of GDP to the variability in investment increased from 3.56% in the 2 nd year to 6.55% and 7.21% in the 6 th and 10 th year respectively.
The evidence from the VDC suggests that a contemporaneous shock in domestic savings and GDP would have a significant impact on investment over time. The implication is that the variability in investment due to own shock will decline over a longer period following a contemporaneous shock in domestic savings and GDP, unless the government, monetary or fiscal authorities intervene by putting up measures to cushion the impact of the shock.

DISCUSSIONS
The paper has inspected the savings-investments nexus utilizing the ARDL and the Granger predictability test for Ghana for the period 1960-2016. There is a marginally significant cointegration link between savings and investment, but there is a stable short-run association between savings and investments. There is also, a significant positive weak correlation between savings and investment according to the correlation matrix test results. The weak association between savings and investments is in sync with the original work of Feldstein and Horioka [6] and other previous investigations, for example, Kollias et al. [12], Esso and Keho [5], Onafowara et al. [17] that established a significant association between savings and investments. The ramifications of the discoveries are that worldwide capital fixed status does exist in Ghana for the period being talked about. The discoveries do not bolster the study of P. Narayan and S. Narayan [15] that did not support the savings -investments link for G7 nations over the period 1971-2002, and Ketenci [10] for Estonia and Portugal between 1995-2009. The findings of causality from savings to investments in the study are in line with that of Esso and Keho [5], and Irandoust [8] that reported unidirectional causality from savings to investment, indicating, savings spur domestic investment.

CONCLUSIONS AND RECOMMENDATIONS
The paper re-examined the savings-investments nexus utilizing the ARDL bound testing approach, and the Granger causality test for Ghana for the period 1960-2016. The study found evidence of a significant and weak correlation and a short-run link between savings and investment. The findings of weak association indicate that capital is fixed in Ghana which supports the hypothesis under investigation. Since capital is reported to be fixed universally, the burden of corporate annual taxes does not fall basically on work/labour; and that public deficit swarm/crowd out private investment; that increments in savings do raise residential investment; and that monetary and tax policies alter the real net rate of return on domestic capital.
Future research should take into consideration the effect of structural breaks Likewise, a similar examination utilizing different nations in a comparative study using small but open economy and large and open economy ought to be considered to determine if the current findings would be reproduced.