www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 Dynamic Relationship between Gross Domestic Product and Domestic Investment in Rwanda Bruno Ocaya1,*, Charles Ruranga1,2, & William Kaberuka1 1 School of Statistics and Planning, Makerere University, Kampala, Uganda 2 Department of Applied statistics, National University of Rwanda, Butare, Rwanda *Corresponding author: School of Statistics and Planning, Makerere University, P.O.Box 7062, Kampala, Uganda E-mail: [email protected] Received: October 28, 2012 Accepted: November 19, 2012 Online Published: December 13, 2012 doi:10.5430/wje.v2n6p79 URL: http://dx.doi.org/10.5430/wje.v2n6p79 Abstract This study uses a VAR model to analyse the dynamic relationship between gross domestic product (GDP) and domestic investment (DI) in Rwanda for the period 1970 to 2011. Several selection lag criteria chose a maximum lag of one, and a bivariate VAR(1) model specification in levels was adopted. Unit root tests show that both GDP and DI series are nonstationary in levels but stationary in first differences, implying that both are integrated of order one I(1). Tests of cointegration established that GDP and DI are CI(1,1), suggesting there is a long-run equilibrium relationship between the two series. The error correction model indicates that DI adjusts to GDP with a lag whereby 0.2 percent of the discrepancy between long-term and short-term DI is corrected within the year. Granger causality tests show that there is unidirectional causality where GDP causes DI. The bivariate VAR (1) was unstable when estimated at levels, but was stable in first differences. Finally it was found out that GDP almost perfectly predicts DI in the estimated VAR (1) model. The forecasted value of DI in 2011 was 22.6%of GDP while the actual value was 22.7% of GDP. The small discrepancy may be attributed to the appropriate policy measures the Rwandan government and the private sector federation have thus far taken to facilitate investors in their businesses. Keywords: Gross Domestic Product (GDP); Domestic Investment (DI); Granger Causality; Cointegration; Vector Autoregression (VAR) and Vector Error Correction Model (VECM) 1. Introduction Investment is a powerful channel for innovation, economic growth and therefore poverty reduction. Recent empirical studies have established linkages between investment and economic growth (e.g., Barro, 1991; Barro & Lee, 1993; Ben-David, 1998; Collier & Gunning, 1999; Ghura & Hadjimichael, 1996; Hernandez, 2000; Khan & Reinhart, 1990; Ndikumana, 2000). Analysis of causality between economic growth and domestic investment conducted in different countries are marred with ambiguities and inconclusive results. For example, several researchers have found bi-directional relationship (Tang, Selvanathan & Foreign, 2008; Tan & Lean, 2010). Others found the direction of causality to be from economic growth to domestic investment (Choe, 2003; Quin, Cagas, Quising & He, 2006) while some found the direction of causality to be from domestic investment to economic growth (Villa, 2008). Also in other studies, private investment was shown to be super-exogenous, meaning investment was the primary determinant of economic growth (Montek, 2002). Rwanda has made significant progress in poverty reduction and has improved the conditions of doing business (World Bank, 2011). Different policies have been adopted in order to increase gross domestic product and promote domestic investment but there has been no empirical study which has attempted to establish the relationship between the growth of GDP and investment. In other words, the question about the forecasting power of investment growth and economic growth remains a moot point. The few and sketchy studies that exist are mainly descriptive in nature and offer limited understanding of the relationship for policy prescription in Rwanda. Rwanda is a land-locked country located in east and central Africa. It borders Uganda to the north, Tanzania to the east, the Democratic Republic of Congo to the west, and Burundi to the south. Rwanda covers 26,338 square Published by Sciedu Press 79 ISSN 1925-0746 E-ISSN 1925-0754 www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 kilometres of land. The current population is about 10.7 million, exhibiting a very high population density of 407 inhabitants per square kilometre. Agriculture and Services are the principal sectors contributing to more than 80% of GDP. Coffee and tea are the main primary products exported and they constitute 40% of export earnings. Due to limited diversification of its economy, Rwanda’s balance of payments has continued to be unfavourable with current account balance always in the negative. After the 1994 genocide, Rwanda Government embarked on a new development path. The new government ushered in peace, political stability, good governance and minimal corruption among others. As a result, Rwanda’s economy has since 2002 been experiencing robust, resilient and sustained GDP growth in the East African region averaging over eight percent annually. The Rwanda government has also made significant efforts to promote private sector led growth to spur domestic investment currently at 22% of GDP (World Bank, 2012). Extreme poverty has fallen from 40% in 2000 to 24% in 2011. Though still high, the percentage of the population living below poverty line has significantly reduced from 77.8% to 44.9% between 1994 and 2011 respectively (NISR, 2011). The objective of this paper is to analyse and establish the unknown feedback mechanism between GDP and DI for shaping the development policy in Rwanda. A bivariate VAR model was used to analyse the dynamic relationship between gross domestic product and domestic investment in Rwanda for the period 1970 to 2011. 2. Data and Methodology 2.1 Data The data used for our analysis consists of 42 observations, collected from World Bank publications for the period 1970-2011 (World Bank, 2012). The variables analysed are GDP (at 2000 US$ prices) and gross fixed capital formation as percent of GDP, proxies of economic growth and domestic investment respectively. Economic growth represents the increase in the amount of the goods and services produced by an economy over time. It is conventionally measured as percentage rate of increase in real gross domestic product. Domestic investment represents gross fixed capital formation or gross domestic fixed investment. It includes land improvements, plant, machinery, equipment purchases, commercial and industrial buildings; and construction of roads, railways, schools, offices, hospitals and private residential dwellings. In order to have a feel of the data used, we first plotted the time series for GDP and DI as shown in Figure 1 and Figure 2 GDP (constant 2000 US$ in million) Domestic investment(current US$ in million) 4,000 1,600 1,400 3,500 1,200 3,000 1,000 2,500 800 2,000 600 1,500 400 1,000 200 500 0 1970 1975 1980 1985 1990 1995 2000 2005 2010 1970 1975 1980 1985 1990 1995 2000 2005 2010 Figure 1: GDP and DI, Rwanda, 1970-2011 (annually) Source: World Bank, World development indicators, 2012. Published by Sciedu Press 80 ISSN 1925-0746 E-ISSN 1925-0754 www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 Domestic investment (% of GDP) GDP annual growth 24 40 22 20 20 18 0 16 14 -20 12 10 -40 8 6 -60 1970 1975 1980 1985 1990 1995 2000 2005 2010 1970 1975 1980 1985 1990 1995 2000 2005 2010 Figure 2: DI as a share of GDP and GDP growth, Rwanda, 1970-2011 (annually) Source: World Bank, World development indicators, 2012. Except for the brief period of conflict and genocide in Rwanda in 1994, Figure 1 shows there has been an upward trend in the time series for both GDP and DI. Between 1970 and 2011, Rwanda’s DI increased more than seventy times, from US$15.8 million to US$1.4 billion. Figure 2 shows that the annual growth rate of GDP plummeted to -50% (genicide period) and theafter fluctuating around 8%. However, DI as a share of GDP exhibited an upward trend increasing from 7% in 1970 to 22.7% in 2011. Both graphical representations in Figure 1 and Figure 2 indicate general trending and fluctuation of GDP and DI series, implying their nonstationarity. 2.2 Model Specification The general form of bivariate vector autoregressive (VAR model used to analyse the dynamic relationship between GDP and DI is expressed as p p GDP GDP  DI u (1) t 1i ti 1j tj 1t i1 j1 p p DI  GDP  DI u (2) t 2i ti 2j tj 2t i1 j1  , , , where and  are intercepts, 1i 2i 1i 2i represent coefficients, GDPis gross domestic product (constant 2000 in US$), DIis domestic investment as percent of GDP, t(t 1,2,...,42) is time period and p represents equal lags for GDP and DI. The u ,u are the stochastic error terms, also known as shocks, 1t 2t innovations or impulses with the assumptions: (i) E(u )E(u )0 1t 2t  var(u ) cov(u u ) (ii) E(u u )  1t 1t 2t  1t 2t cov(u u ) var(u )  1t 2t 2t with E(u u )2 for i1,2 it it i E(u u )0 for t . it i 3. Results and Discussions The following sections present empirical time series analysis on the relationship between GDP and DI(Note 1): Published by Sciedu Press 81 ISSN 1925-0746 E-ISSN 1925-0754 www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 3.1 Lag Order Selection Determination of maximum lag p was carried out using Akaike information criteria (AIC) and Schwarz information criteria. The lower the values of Akaike and Schwarz statistics, the better is the model. Incidentally, all the lag criteria reported by EViews chose lag one, suggesting a bivariate VAR (1) model as the appropriate for analysing the dynamic relationship between GDP and DI. These results are shown in Table 1. Table 1: VAR Lag Order selection VAR Lag Order Selection Criteria Endogenous variables: GDP DI Exogenous variables: C Sample: 1970 2011 Included observations: 39 Lag LogL LR a FPE b AIC c SC d HQ e 0 -385.7850 NA 1484637. 19.88641 19.97172 19.91702 1 -318.9473 123.3928* 59208.31* 16.66396* 16.91989* 16.75579* 2 -317.6407 2.278132 68129.82 16.80209 17.22864 16.95513 3 -317.4289 0.347633 83154.82 16.99635 17.59353 17.21061 Note. * indicates lag order selected by the criterion a LR: sequential modified LR test statistic (each test at 5% level) b FPE: Final prediction error c AIC: Akaike information criterion d SC: Schwarz information criterion e HQ: Hannan-Quinn information criterion The VAR model after lag determination becomes GDP   GDP  DI u (3) t 10 11 t1 12 t1 1t DI   GDP  DI u (4) t 20 21 t1 22 t1 2t or GDP     GDP  u   t  10 11 12 t1 1t  DI      DI  u  t 20 21 22 t1 2t 3.2 Unit Root Tests Tests for unit roots were undertaken in order to determine the stationarity of the series for GDP and DI. The Augmented Dickey-Fuller (ADF) tests provided in Table 2 show that GDP and DI are not stationary at levels. Instead, their first differences were found to be stationary, in Table 3, implying that both GDP and DI are integrated of order one [I(1)]. Published by Sciedu Press 82 ISSN 1925-0746 E-ISSN 1925-0754 www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 Table 2: The results of unit root test in levels Included GDP a DI b in test ADF Test Critical Value at different levels ADF Test Critical Value at different equation Statistic of significance Statistic levels of significance 1% 5% 1% 5% Constant & 0.254149 -4.198503 -3.523623 -3.188530 -4.198503 -3.523623 trend Constant 1.929356 -3.600987 -2.935001 -1.777599 -3.600987 -2.935001 a GDP represents Gross Domestic Product b DI represents Domestic Investment The null hypothesis of existence of unit root is not rejected since the Augmented Dickey-Fuller (ADF) test statistics are lower than the absolute critical values at 1% and 5% significant levels. These results establish that GDP and DI are non stationary in levels. However Table 3 rejects the null hypothesis of unit roots for both GDP and DI in their first differences because the absolute values of the ADF are less than the stipulated absolute critical values at 1% and 5% significant levels. Results obtained using Phillips-Perron tests for unit roots arrive at similar conclusions. Table 3: The results of unit root tests in first differences Included ΔGDPa ΔDIb in test ADF Test Statistic Critical Value at different ADF Test Statistic Critical Value at different equation levels of significance levels of significance 1% 5% 1% 5% Constant & -5.587328*** -4.205004 -3.526609 -7.481835*** -4.205004 -3.526609 trend Constant -5.103964*** -3.605593 -2.936942 -7.579278*** -3.605593 -2.936942 Note. *** denote the significance at 1 percent a GDPrepresents a change in GDP Δ bΔDI represents change in Domestic Investment 3.3 Tests of Cointegration Cointegration tests were used to determine the existence of long-run equilibrium relationship between GDP and DI. The Augmented Engle-Granger test for cointegration was adopted for this purpose. This test involves unit root tests on residuals obtained from the estimation of the following models: GDP  DI e t 0 1 t 1t (5) DI  GDP e t 0 1 t 2t (6) The ADF was applied on eˆ1tand eˆ2tto test for unit roots. The tests were based on testing the significance of  and  for the following residual models: eˆ e  1t 1t1 1t (7) eˆ e  . 2t 2t1 2t (8) The results of the estimation of equations (7) and (8) are presented in Table 4(a) and 4(b) respectively: Published by Sciedu Press 83 ISSN 1925-0746 E-ISSN 1925-0754 www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 Table 4(a) Augmented Dickey-Fuller Test Equation Dependent Variable: eˆ 1t Method: Least Squares Sample (adjusted): 1971 2011 Included observations: 41 after adjustments Variable Coefficient Std. Error t-Statistic Prob. eˆ 1t1 -0.300829 0.115390 -2.607060 0.0128 R-squared 0.145191 Mean dependent var 2.205344 Adjusted R-squared 0.145191 S.D. dependent var 293.3920 S.E. of regression 271.2583 Akaike info criterion 14.06811 Sum squared resid 2943242. Schwarz criterion 14.10990 Log likelihood -287.3962 Hannan-Quinn criter. 14.08333 Durbin-Watson stat 1.847711 Table 4(b) Augmented Dickey-Fuller Test Equation Dependent Variable eˆ 2t Method: Least Squares Sample (adjusted): 1971 2011 Included observations: 41 after adjustments Variable Coefficient Std. Error t-Statistic Prob. eˆ -0.467489 0.119829 -3.901300 0.0004 2t1 R-squared 0.273575 Mean dependent var 0.081744 Adjusted R-squared 0.273575 S.D. dependent var 1.554870 S.E. of regression 1.325225 Akaike info criterion 3.425129 Sum squared resid 70.24885 Schwarz criterion 3.466924 Log likelihood -69.21515 Hannan-Quinn criter. 3.440349 Durbin-Watson stat 1.929877 The null hypotheses of no-cointegration or unit root are rejected in both models, implying that GDP and DI are cointegrated of order 1, 1 [i.e., GDP, DI(cid:0)CI(1,1)]. This verifies that there is a long-run equilibrium relationship between GDP and DI in Rwanda. Similar conclusions were also obtained using the Johansen cointegration test. 3.4 Vector Error Correction Model (VECM) We have found that GDP and DI are each I(1) and co-integrated of order 1,1. With cointegration present, there exists a dynamic interrelationship between the two variables with a disequilibrium correction error term given by the Published by Sciedu Press 84 ISSN 1925-0746 E-ISSN 1925-0754 www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 following VECM GDP  EC  GDP  DI  (9) t 10 t1 11 t1 12 t1 1t DI  EC  GDP  DI  (10) t 20 2 t1 21 t1 22 t1 2t where EC represents the error correction component of the model. The estimates of the vector t1 error-correction model are as follows: (cid:0)GDP 63.462190.001022EC  0.352458GDP - 29.93540 DI t t1 t1 t1 t  [2.13337] [0.01842] [1.78619] [-1.57162] F(3,36) 1.264, Prob(F-statistic)=0.301 (cid:0)DI  0.2964640.001528EC 0.001044GDP - 0.074123DI t t1 t1 t1 t  [1.01524] [2.80681] [0.53921] [-0.39643] F(3,36) 3.259, Prob(F-statistic)=0.0324 The t-ratios on the coefficients of EC , GDP and DI in the (cid:0)GDP equation are all t1 t1 t1 t individually insignificant. They are also collectively insignificant as indicated by the F-statistic. This implies that GDP does not respond to disequilibrium between itself and DI. The coefficient of EC in the (cid:0)DI equation is t1 t positive and statistically significant, suggesting that DI adjusts to GDP with a lag. Approximately 0.1528 percent of the discrepancy between long-term and short-term DI is corrected within the year. These results underscore the irrelevance of the GDP equation and the appropriateness of DI equation as was established by Granger causality tests in the next section. 3.5 Granger Causality The Granger-causality tests investigate if a scalar "y"can help forecast another scalar"x". If it doesn’t, then we say thatydoes not Granger cause "x" (Hamilton, 1994). In other words, "y"does not help in predicting"x". Granger Causality test is generally sensitive to the number of lags adopted for the VAR model. Given that the assumptions in equations (1) and (2) hold, we investigated the following four possible cases of bilateral causality between GDP and DI (Gujarati & Porter, 2009) 1) Unidirectional causality from DI to GDP which is indicated if the estimated coefficients on the lagged DI in (1) are statistically different from zero as a group (i.e.,  0) and the set of estimated coefficients on 1j the lagged GDP in (2) is not statistically different from zero (i.e.,  0). 2i 2) Conversely, unidirectional causality from GDP to DI exists if the set of lagged DI coefficients in (1) is not statistically different from zero (i.e.,  0)and the set of lagged GDP coefficients in (2) is statistically 1j different from zero (i.e.,  0). 2i 3) Feedback, or bilateral causality, suggested when the sets of DI and GDP coefficients are statistically significantly different from zero in both regressions. Published by Sciedu Press 85 ISSN 1925-0746 E-ISSN 1925-0754 www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 4) Finally, independence suggested when the set of DI and GDP coefficients are not statistically significant in both the regressions. Using OLS, the following steps were taken to test whether DI “Granger” causes GDP ︵DI→GDP︶: (i) Regress current GDP on lagged GDP excluding lagged DI. This gives the restricted regression which is used to obtain the restricted residual sum of squaresRSS . R (ii) Run regression (i) including lagged DI. This gives the unrestricted regression where we obtain the unrestricted residual sum of squares, RSS . UR (iii) The null hypothesis isH : 0, that is, lagged DI terms do not belong in the regression. The null 0 1j hypothesis in each case is that the variable under consideration does not “Granger cause” the other variable. In this case, DI does not “Granger cause” GDP”. (RSS RSS )/m (iv) The general test statistic is given by F  R UR F[m,(n-(2m1))] (cid:0) RSS /(n-(2m1)) UR where m is the number of lagged terms and n is the number of observations used to estimate the model(Note 2). If the p-value is less than 5%, we reject the null hypothesis that GDP does not Granger-cause DI. By rejecting the null hypothesis, we accept that lagged DI belongs in the regression, another way of saying that DI causes GDP. (v) Steps (i) to (iv) can be repeated to test the model in equation (2), that is, whether GDP causes DI. From these steps, the results of the bivariate Granger Causality test are summarized in Table 5 Table 5: Results of Granger causality tests Null Hypothesis Number of lags F-value Prob. Decision DI does not Granger Cause GDP 1 0.54720 0.4640 Do not reject GDP does not Granger Cause DI 1 7.95147 0.0076 Reject at 5% DI does not Granger Cause GDP 2 1.01294 0.3735 Do not reject GDP does not Granger Cause DI 2 3.38214 0.0454 Reject at 5% DI does not Granger Cause GDP 3 0.65607 0.5851 Do not reject GDP does not Granger Cause DI 3 2.08297 0.1220 Do not reject These results indicate a unidirectional causality from GDP to DI for the first two lags. Likewise, there is also no causality from DI to GDP for the two lags. However from lag three onwards, it was found out that there was no statistically significant causality from GDP to DI and vice versa. Since our lag selection is one, Rwanda like many other countries have been found to have one way causality from GDP growth to DI growth (Choe, 2003). Hence, policies towards GDP provide useful information for forecasting DI likely to be realized in Rwanda. 3.6 VAR Estimation There is an issue of whether the variables in a VAR need to be stationary for estimation (Hamilton, 1994). Some researchers (Sims, Stock & Watson, 1990) recommend against differencing even if the variables contain a unit root. They argue that the goal of a VAR analysis is to determine the interrelationships among the variables, not the determination of the parameter estimates. The main argument against differencing is that it “throws away” information concerning the comovements in the data (such as the possibility of cointegrating relationships). Similarly, it is argued that the data need not be detrended. In a VAR, a trending variable will be well approximated by a unit root plus drift. However, the majority view is that the form of the variables in the VAR should mimic the true data generating process (Sims et al., 1990). Taking into account these concerns our bivariate VAR (1) model was estimated in levels using equations (3) and (4) and the results are presented in table 6. Published by Sciedu Press 86 ISSN 1925-0746 E-ISSN 1925-0754 www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 Table 6: Vector Autoregression Estimates of GDP and DI Sample (adjusted): 1971 2011 Included observations: 41 after adjustments Standard errors in ( ) & t-statistics in [ ] GDP a DI b GDP(-1) 1.117271 (0.07207) [15.5018] 0.001986 (0.00070) [2.81983] DI(-1) -11.26149 (15.2237) [-0.73973] 0.492495 (0.14876) [3.31073] C 48.36127 (140.480) [0.34426] 4.608133 (1.37268) [3.35704] Adj. R-squared 0.953536 0.761513 Sum sq. Resids 1075141. 102.6545 S.E. equation 168.2058 1.643604 F-statistic 411.4423 64.86199 Log likelihood -266.7515 -76.99131 a GDP represents Gross Domestic Product, b DI represents Domestic Investment From the t-values the results show that lagged GDP and DI excluding the constant term in the GDP regression is insignificant (i.e., not different from zero). But all coefficients in the DI regression are individually significant at the 5% level. These results conform with those for the Granger causality tests which suggest the adoption of DI regression for forecasting. 3.7 VAR Stability The regression equations of our estimated VAR (1) in levels are expressed as G(cid:0)DP  48.36127 1.117271 - 11.26149GDP   t   t1  D(cid:0)It  4.608133 0.001986 0.492495  DIt1  from where we define 1.117271 - 11.26149 A  . * 0.001986 0.492495  The estimated equations for the same model (output not shown) in first differences were found to be G(cid:0)DP  63.51862 0.352210 - 30.04025 GDP   t   t1  D(cid:0)It  0.380861 0.000674 - 0.230943  DIt1  from where we define 0.352210 - 30.04025  A  . ** 0.000674 - 0.230943  The stability of our VAR (1) model estimated in levels and first differences are then determined using eigenvalue stability condition of matrices A and A . By this condition, the eigen values of matrix A are * ** * 1.0792 and 0.53059, implying that GDP and DI estimated at levels are not stationary since at least one eigenvalue is approximately unity. However fist difference estimation of the model shows that GDP and DI are stationary since all the eigenvalues of matrix A which are 0.315 and -0194 lie inside the unit circle. ** Published by Sciedu Press 87 ISSN 1925-0746 E-ISSN 1925-0754 www.sciedu.ca/wje World Journal of Education Vol. 2, No. 6; 2012 4. Forecasting For forecasting, the bivariate VAR (1) was re-estimated in levels for data covering the period 1970-2010. The data for 2011 was excluded for comparison of forecasted and actual values. Table 7 gives the results of the re-estimation of our model. Table 7: Vector Auto-regression of GDP and DI Sample (adjusted): 1971 2010 Included observations: 40 after adjustments Standard errors in ( ) & t-statistics in [ ] GDP DI GDP(-1) 1.106071 (0.07596) [ 14.5616] 0.001978 (0.00074) [ 2.65553] DI(-1) -10.83555 (15.3952) [-0.70382] 0.492795 (0.15097) [ 3.26422] C 58.11948 (143.116) [ 0.40610] 4.615025 (1.40342) [ 3.28841] R-squared 0.945363 0.740036 Adj. R-squared 0.942409 0.725984 Sum sq. resids 1067482. 102.6506 S.E. equation 169.8554 1.665635 F-statistic 320.0969 52.66379 Log likelihood -260.5962 -75.60658 a GDP represents Gross Domestic Product b DI represents Domestic Investment The DI regression equation for forecasting now becomes D(cid:0)I 4.6150250.001978GDP 0.492795DI 2011 2010 2010 D(cid:0)I 4.6150250.0019783593.7420.49279522.132722.6303%. 2011 The forecasted value of DI in 2011 is 22.6303%of GDP while the actual value in 2011 was 22.7% of GDP. The difference between actual and forecasted is 22.7%-22.6303%=0.0697% which represents a small under-prediction. This implies that GDP almost perfectly predicts DI in our bivariate VAR (1) model. The small difference between the actual and forecasted values in DI may be explained by the appropriate policy measures the Rwandan government and the private sector federation have so far taken to facilitate investors in their businesses. The World Bank reports on doing business have shown great improvement in the ranking of Rwanda since 2008 (World Bank, 2012). 5. Conclusion Dynamic relationship between gross domestic product and domestic investment was analysed using time series data of Rwanda for period 1970 to 2011. A bivariate model with lag one selected and considered appropriate for the analysis. The Augmented Dickey-Fuller (ADF) tests and Phillips-Perron tests indicate that GDP and DI are not stationary at levels but their first differences were stationary, meaning that they are integrated of order one. The Augmented Engle-Granger and Johansen tests of co-integration show that GDP and DI series are co-integrated. While GDP does not appear to respond to disequilibrium between itself and DI, the error correction model establishes that DI adjusts to GDP with a lag. Approximately 0.1528 percent of the discrepancy between long-term and short-term DI is corrected within the year. Our analysis indicates a unidirectional causality from GDP to DI for the first two lags with no evidence of causality from DI to GDP. The unidirectional causality suggests that policies initiated towards GDP provide important information for predicting DI in Rwanda. The results of the estimation of the bivariate VAR together with Published by Sciedu Press 88 ISSN 1925-0746 E-ISSN 1925-0754