INTRODUCTION
There is an ongoing argument among scholars concerning the direction of causality between bankrelated and stock exchangebased financial development and savings, investment and economic growth. As far as economic growth causality studies are concerned, a considerable number of empirical works have been conducted on a number of countries though with conflicting results (see Nyasha and Odhiambo, 2015; Rehman et al., 2015; Acaravci et al., 2009). There are four views that have been empirically proven to exist in literature, that is, the supplyleading hypothesis, demandfollowing hypothesis, bidirectionalcausality view and the fourth view stipulating that financial development and economic growth have no causal relationship (Nyasha and Odhiambo, 2015). The supply leading hypothesis claims that financial development stimulates economic growth (see Bayar et al. 2014; Masoud, 2013; Nazir et al., 2010; Tachiwou, 2010; Nowbusting and Odit, 2009; Caporale et al., 2004; Boubakari and Jin, 2010), and the demand following hypothesis claims that growth instigates the demand for financial commodities (see Odo et al., 2016; Isu and Okpara, 2013; Carby et al., 2012; Paramati and Gupta, 2011; BaliamouneLutz, 2003; Onwumere et al., 2012). The bidirectional causality hypothesis stipulates that financial progression and economic growth are bidirectionally causal while the fourth view states that financial progression has no relationship with economic growth (see Nyasha and Odhiambo, 2015; Acaravci et al., 2009).
However, causality studies that focused on the additional variables used in this study have not been as numerous and as widely researched on as the financegrowth nexus. The relationship between financial development and investment is articulated as having four main conclusions by Muyambiri and Odhiambo (2017), that is:

Financial development Grangercauses investment (Xu, 2000; Caporale et al., 2005, Rousseau and Vuthipadadorn 2005; Chaudry, 2007; Carp, 2012; Hamdi et al., 2013; Asongu, 2014);

Investment Grangercauses financial development (Odhiambo, 2010);

There is a bidirectional causality between financial development and investment (Shan et al., 2001; Shan and Jianhong, 2006; Lu et al., 2007; Nazlioglu et al., 2009; Huang, 2011); and

No causal relationship exists between the two variables (Majid, 2008; Shan and Morris, 2002; Marques et al., 2013).
Conversely, most of the studies conducted to evaluate the causal relationship between either of the variables employed in this study, made use of mostly bankrelated financial development indicators while ignoring the stock exchangebased side of the financial sector. In addition to the contradictory results that came from such studies, there has been no study to be best of our current knowledge that has sought to investigate the multivariate causal relationship between bankrelated financial development, stock exchangebased financial development, savings and investment in one study especially for a country like Botswana. Given these existing gaps, this study takes advantage of the multivariate causality analysis framework using the autoregressive distributed lag bounds testing approach to assess such a relationship.
METHODOLOGY
Shadowing Nyasha and Odhiambo (2015), the estimated ARDL model is given as follows.
\[\mathrm{\Delta}\text{INV}_{t} = \propto_{0} + \sum_{i = 1}^{n}{\propto_{1i}{\mathrm{\Delta}INV}_{t  i}} + \sum_{i = 0}^{n}{\propto_{2i}{\mathrm{\Delta}BFA}_{t  i}} + \sum_{i = 0}^{n}{\propto_{3i}{\mathrm{\Delta}MFA}_{t  i}} + \sum_{i = 0}^{n}{\propto_{4i}{\mathrm{\Delta}GDP}_{t  i}} + \sum_{i = 0}^{n}{\propto_{5i}{\mathrm{\Delta}GDS}_{t  i}} + \alpha_{6}\text{INV}_{t  1} + \alpha_{7}\text{BFA}_{t  1} + \alpha_{8}\text{MFA}_{t  1} + \alpha_{9}\text{GDP}_{t  1} + \alpha_{10}\text{GDS}_{t  1} + \varepsilon_{1t}\] 
(1) 
\[\mathrm{\Delta}\text{BFA}_{t} = \beta_{0} + \sum_{i = 1}^{n}{\beta_{1i}{\mathrm{\Delta}BFA}_{t  i}} + \sum_{i = 0}^{n}{\beta_{2i}{\mathrm{\Delta}INV}_{t  i}} + \sum_{i = 0}^{n}{\beta_{3i}{\mathrm{\Delta}MFA}_{t  i}} + \sum_{i = 0}^{n}{\beta_{4i}{\mathrm{\Delta}GDP}_{t  i}} + \sum_{i = 0}^{n}{\beta_{5i}{\mathrm{\Delta}GDS}_{t  i}} + \beta_{6}\text{BFA}_{t  1} + \beta_{7}\text{INV}_{t  1} + \beta_{8}\text{MFA}_{t  1} + \beta_{9}\text{GDP}_{t  1} + \beta_{10}\text{GDS}_{t  1} + \varepsilon_{2t}\] 
(2) 
\[\mathrm{\Delta}\text{GDS}_{t} = \rho_{0} + \sum_{i = 1}^{n}{\rho_{1i}{\mathrm{\Delta}GDS}_{t  i}} + \sum_{i = 0}^{n}{\rho_{2i}{\mathrm{\Delta}INV}_{t  i}} + \sum_{i = 0}^{n}{\rho_{3i}{\mathrm{\Delta}BFA}_{t  i}} + \sum_{i = 0}^{n}{\rho_{4i}{\mathrm{\Delta}MFA}_{t  i}} + \sum_{i = 0}^{n}{\rho_{5i}{\mathrm{\Delta}GDP}_{t  i}} + \rho_{6}\text{GDS}_{t  1} + \rho_{7}\text{BFA}_{t  1} + \rho_{8}\text{MFA}_{t  1} + \rho_{9}\text{INV}_{t  1} + \rho_{10}\text{GDP}_{t  1} + \varepsilon_{3t}\] 
(3) 
\[\mathrm{\Delta}\text{GDP}_{t} = \gamma_{0} + \sum_{i = 1}^{n}{\gamma_{1i}{\mathrm{\Delta}GDP}_{t  i}} + \sum_{i = 0}^{n}{\gamma_{2i}{\mathrm{\Delta}INV}_{t  i}} + \sum_{i = 0}^{n}{\gamma_{3i}{\mathrm{\Delta}BFA}_{t  i}} + \sum_{i = 0}^{n}{\gamma_{4i}{\mathrm{\Delta}MFA}_{t  i}} + \sum_{i = 0}^{n}{\gamma_{5i}{\mathrm{\Delta}GDS}_{t  i}} + \gamma_{6}\text{GDP}_{t  1} + \gamma_{7}\text{BFA}_{t  1} + \gamma_{8}\text{MFA}_{t  1} + \gamma_{9}\text{INV}_{t  1} + \gamma_{10}\text{GDP}_{t  1} + \varepsilon_{4t}\] 
(4) 
\[\mathrm{\Delta}\text{MFA}_{t} = \delta_{0} + \sum_{i = 1}^{n}{\delta_{1i}{\mathrm{\Delta}MFA}_{t  i}} + \sum_{i = 0}^{n}{\delta_{2i}{\mathrm{\Delta}INV}_{t  i}} + \sum_{i = 0}^{n}{\delta_{3i}{\mathrm{\Delta}BFA}_{t  i}} + \sum_{i = 0}^{n}{\delta_{4i}{\mathrm{\Delta}GDP}_{t  i}} + \sum_{i = 0}^{n}{\delta_{5i}{\mathrm{\Delta}GDS}_{t  i}} + \delta_{6}\text{BFA}_{t  1} + \delta_{7}\text{INV}_{t  1} + \delta_{8}\text{MFA}_{t  1} + \delta_{9}\text{GDP}_{t  1} + \delta_{10}\text{GDS}_{t  1} + \varepsilon_{5t}\] 
(5) 
The multivariate causality model is then presented as follows:
\[\mathrm{\Delta}\text{INV}_{t} = \alpha_{0} + \sum_{i = 1}^{n}{\alpha_{1i}{\mathrm{\Delta}INV}_{t  i}\ } + \sum_{i = 1}^{n}{\alpha_{2i}\mathrm{\Delta}\text{BFA}_{t  i}\ } + \sum_{i = 1}^{n}{\alpha_{3i}\mathrm{\Delta}\text{MFA}_{t  i}\ } + \sum_{i = 1}^{n}{\alpha_{4i}{\mathrm{\Delta}GDP}_{t  i}\ } + \sum_{i = 1}^{n}{\alpha_{5i}{\mathrm{\Delta}GDS}_{t  i}\ } + \alpha_{6}\text{ECT}_{t  1} + \mu_{1t}\] 
(6) 
\[\mathrm{\Delta}\text{BFA}_{t} = \ \beta_{0} + \sum_{i = 1}^{n}{\beta_{1i}{\mathrm{\Delta}INV}_{t  i}\ } + \sum_{i = 1}^{n}{\beta_{2i}{\mathrm{\Delta}BFA}_{t  i}\ } + \sum_{i = 1}^{n}{\beta_{3i}{\mathrm{\Delta}MFA}_{t  i}\ } + \sum_{i = 1}^{n}{\beta_{4i}{\mathrm{\Delta}GDP}_{t  i}\ } + \sum_{i = 1}^{n}{\beta_{5i}{\mathrm{\Delta}GDS}_{t  i}\ } + \beta_{6}\text{ECT}_{t  1} + \mu_{2t}\] 
(7) 
\[\mathrm{\Delta}\text{GDS}_{t} = \ \rho_{0} + \sum_{i = 1}^{n}{\rho_{1i}\mathrm{\Delta}\text{INV}_{t  i}\ } + \sum_{i = 1}^{n}{\rho_{2i}\mathrm{\Delta}\text{BFA}_{t  i}\ } + \sum_{i = 1}^{n}{\rho_{3i}\mathrm{\Delta}\text{MFA}_{t  i}\ } + \sum_{i = 1}^{n}{\rho_{4i}\mathrm{\Delta}\text{GDP}_{t  i}\ } + \sum_{i = 1}^{n}{\rho_{5i}\mathrm{\Delta}\text{GDS}_{t  i}\ } + \rho_{6}\text{ECT}_{t  1} + \mu_{3t}\] 
(8) 
\[\mathrm{\Delta}\text{GDP}_{t} = \gamma_{0} + \sum_{i = 1}^{n}{\gamma_{1i}{\mathrm{\Delta}GDP}_{t  i}} + \sum_{i = 1}^{n}{\gamma_{2i}{\mathrm{\Delta}INV}_{t  i}} + \sum_{i = 1}^{n}{\gamma_{3i}{\mathrm{\Delta}BFA}_{t  i}} + \sum_{i = 1}^{n}{\gamma_{4i}{\mathrm{\Delta}MFA}_{t  i}} + \sum_{i = 1}^{n}{\gamma_{5i}{\mathrm{\Delta}GDS}_{t  i}} + \gamma_{6}\text{ECT}_{t  1} + \mu_{4t}\] 
(9) 
\[\mathrm{\Delta}\text{MFA}_{t} = \delta_{0} + \sum_{i = 1}^{n}{\delta_{1i}{\mathrm{\Delta}MFA}_{t  i}} + \sum_{i = 1}^{n}{\delta_{2i}{\mathrm{\Delta}INV}_{t  i}} + \sum_{i = 1}^{n}{\delta_{3i}{\mathrm{\Delta}BFA}_{t  i}} + \sum_{i = 1}^{n}{\delta_{4i}{\mathrm{\Delta}GDP}_{t  i}} + \sum_{i = 1}^{n}{\delta_{5i}{\mathrm{\Delta}GDS}_{t  i}} + \delta_{6}\text{ECT}_{t  1} + \mu_{5t}\] 
(10) 
where
\(\text{INV}\)= investment to GDP ratio.
\(\text{BFA}\) = acceleratoraugmented index of bankrelated financial development index, calculated as the meansremoved average (of M3 to GDP, domestic credit to private sector to GDP ratio, and total domestic credit to GDP ratio) multiplied by the growth rate of GDP per capita.
\(\text{MFA}\) = acceleratoraugmented index of stock exchangebased financial development index, calculated as the meansremoved average (of stocks traded, total value to GDP ratio, market capitalisation to GDP ratio, and the turnover ratio) multiplied by the growth rate of GDP per capita.
\(\text{GDP}\)= real GDP growth rate.
\(\text{GDS}\)= gross domestic savings.
ECT = errorcorrection term,
\(\propto_{0}\), \(\beta_{0}\), \(\rho_{0}\), \(\gamma_{0}\) and\(\ \delta_{0}\)= respective constants,
\(\propto_{1},\ldots, \propto_{10}\),\(\ \beta_{1},\ldots,\beta_{10}\), \(\rho_{1},\ldots,\rho_{10}\), \(\gamma_{1},\ldots,\gamma_{10}\) and \(\delta_{1},\ldots,\delta_{10}\)=respective coefficients,
\(\mathrm{\Delta}\) = difference operator,
\(n\) = lag length,
\(\varepsilon\) = error term and \(\mu\) = whitenoise errorterm.
EMPRICAL RESULTS
Stationarity tests are employed to ensure that all variables are integrated of maximum order 1. Otherwise, the ARDL bounds test methodology will break down if there are variables integrated of an order greater than 1. The Perron (1997) PPURoot unit root and the Augmented DickeyFuller Generalised Least Square tests unit root tests were employed to check the order of integration. The results for the test of stationarity of the variables are presented in Table 1.
Table 1. Stationarity Test Results
DickeyFuller Generalised Least Square (DFGLS)

Variable

Stationarity in levels

Stationarity in differences


With intercept, no trend

With intercept and trend

With intercept, no trend

With intercept and trend

INV

2.7471*

2.7773

6.2222***

6.2291***

GDP

4.5213 ***

5.4507 ***





BFA

1.7833*

2.0434

9.9352***

11.0932***

MFA

4.0963**

4.9413*





GDS

2.1037**

2.5491

5.5152***

5.5653***

Perron (1997) PPURoot

Variable

Stationarity in levels

Stationarity in differences

INV

6.3488***

6.6408***





GDP

6.3130***

6.2841***





BFA

6.4923***

7.0091**





MFA

5.6991*

5.1882

6.7414***

6.4492***

GDS

4.0141

4.3253

6.3954***

6.2451***

Note: *, ** and *** denote stationarity at the 10%, 5% and 1% significance levels respectively

Table 1 confirms that the ARDL bounds testing procedure is appropriate for the data and it is therefore employed. Table 2 reports the results of the bounds Ftest for cointegration.
Table 2. Bounds FTest for Cointegration Results
Dependent Variable

Function

Fstatistic

Cointegration Status

INV

F(INV GDP, BFA, MFA, GDS)

5.1612***

Cointegrated

BFA

F(BFA GDP, INV, MFA, GDS)

6.5637***

Cointegrated

MFA

F(MFA GDP, BFA, INV, GDS)

1.0799

Not cointegrated

GDP

F(GDP INV, BFA, MFA, GDS)

3.3418

Not cointegrated

GDS

F(GDS GDP, BFA, MFA, INV)

3.8044*

Cointegrated

Asymptotic Critical


1%

5%

10%

Pesaran et al. (2001:301) Table CI(iii) Case III

I(0)

I(1)

I(0)

I(1)

I(0)

I(1)

3.74

5.06

2.86

4.01

2.45

3.52

Note: *, ** and *** denotes significance at the 10%, 5% and 1% significance levels respectively

The results from the bounds cointegration test indicate that three out of the five equations have a long run relationship. Consequently, the multivariate Granger causality test is run and the results are reported in Table 3. The equations with a cointegrated relationship are estimated, as expected, with the inclusion of an error correction term. Otherwise, no error correction term is included.
The empirical results of the multivariate Granger causality test are reported in Table 3.
Table 3. GrangerCausality Test Results
Investment (I), Bankrelated Financial Development (BG), and Savings (S)

Dependent Variable

Fstatistics (probability)



ECT_{t}
[tstatistics]

∆INV_{t}

∆BFA_{t}

∆MFA_{t}

∆GDP_{t}

∆GDS_{t}

∆INV_{t}



1.0580
(0.387)

1.7160
(0.234)

4.6903**
(0.040)

4.1479*
(0.053)

0.83473**
[3.1077]

∆BFA_{t}

4.1163**
(0.044)



9.4632**
(0.010)

0.61525
(0.557)

0.0060698
(0.939)

0.19494*
[1.7746]

∆MFA_{t}

7.2592**
(0.011)

0.15822
(0.856)


0.96271
(0.415)

0.55967
(0.588)


∆GDP_{t}

2.0094
(0.190)

3.4138*
(0.066)

1.2810
(0.324)


2.4408
(0.131)


∆GDS_{t}

0.75629
(0.407)

1.6111
(0.251)

3.8186*
(0.082)

6.3678**
(0.019)



0.88920***
[4.2538]

Note: *, ** and *** denotes significance at the 10%, 5% and 1% significance levels, respectively

The results in Table 3 reveal that they are only unidirectional causal relationships amongst a number of the variables under discussion. Economic growth is found to Grangercause investment and savings both in the shortrun and long run. Only bankrelated financial development is found to Grangercause economic growth in Botswana in the short run.
Inherently, investment, according to the results, precedes financial development. However, there is only a shortrun unidirectional causal relationship from investment to stock exchangebased financial development. The same unidirectional relationship in both the short run and the long run is found from investment to bankrelated financial development. Therefore, consistent with Odhiambo (2010), the results show that it is chiefly investment that drives the bankrelated and stock exchangebased financial sectors. To induce financial sector development, there is need to put in place policies that encourage increased investment. Nevertheless, investment is found to be Grangercaused by economic growth and savings in both the long run and the short run in Botswana.
Notwithstanding that stock exchangebased financial development is Grangercaused by only investment, it precedes both bankrelated financial development and savings in both the short run and the long run.
As already noted, investment and stock exchangebased financial development Grangercause bankrelated financial development in the short run and long run. The only variable that is Grangercaused by bankrelated financial development is economic growth and this is only in the short run. This finding tends to confirm the findings of Bayar et al., 2014; Masoud, 2013; Nazir et al., 2010; Tachiwou, 2010; Nowbusting and Odit, 2009; Caporale et al., 2004; and Boubakari and Jin, 2010.
Savings Grangercause investment in both the long run and the short run. Stock exchangebased financial development and economic growth Grangercause savings in both the short run and the long run.
Table 4 summarises the results of the Grangercausality tests.
Table 4. Summary of Grangercausality test results
Dependent Variable

Direction of Causality AND SIGNIFICANT VARIABLES

PERIOD of Causality

Short Run

Long Run

GDP

⇒INV, GDS

✔

✔

INV

⇒BFA

✔

✔


⇒MFA

✔



MFA

⇒BFA

✔

✔


⇒GDS

✔

✔

BFA

⇒GDP

✔



GDS

⇒INV

✔

✔

NB: GDP=Economic growth, GDS=Savings, INV=investment; BFA=bankrelated financial development; MFA=stock exchangebased financial development, ⇒indicates direction of causality, ✔indicates presence of causality in respective period.

CONCLUSION
In this paper, the causal relationship between financial development, split into bankrelated and stock exchangebased financial development, savings, and investment and economic growth has been empirically examined for the period of 1976 to 2014 for Botswana with the aid of a multivariate Grangercausality model. The study results show that it is chiefly investment that drives the bankrelated and stock exchangebased financial sectors in the short run. However, the same deduction is true for bankrelated financial development in the long run. Inherently, results also show that stock exchangebased financial development drives bankrelated financial development and savings in both the short run and the long run. While, savings are found to Grangercause investment. Economic growth is found to Grangercause investment and savings both in the shortrun and long run. Only bankrelated financial development is found to Grangercause economic growth in Botswana.
Therefore, to induce financial sector development in the short run, there is need to put in place policies that encourage increased investment. These must focus on the economic growth and savings that have been found to precede investment as per the results of this study.

See Muyambiri and Odhiambo (2015) for a fuller examination of the sequential development of the finance sector in Botswana