Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) Results

Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) Results While analyzing time series data, it is important to check the order of integration of the variables. Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root test are used at level form and first difference of each series. The results of the unit root test are reported in Table 5.9 taking into consideration of the constant-trend variables and without the constant-trend variables. In the ADF test, the lag length is included to solve the problem of autocorrelation and to enhance the robustness of the result. The ADF t-statistics for the series without the constant and the trend term are all statistically insignificant to reject the null hypothesis of unit root. This shows that the series are non-stationary in their original form and they contain a unit root process. For the series with the trend and constant term, all the variables are non-stationary except the capital expenditure whose ADF t-statistics is significant and it is I(0). When the ADF test is carried out at the fi rst difference of each variable, the null hypothesis is rejected for both the series with the constant and rend term and without the constant and trend term. This is presented in fourth and fifth column of Table 5.9 and it shows that the variables are integrated of order 1. The results are consistent with theory as most of the macroeconomic time series data are expected to contain unit root and thus are integrated of order one I(1). ADF critical values without constant and trend:1%: -3.750; 5%: -3.000; 10%: -2.630 ADF critical values with constant and trend:1%: -4.380; 5%: -3.600; 10%: -3.240 Long run Equation The long run equation can now be estimated with the assumption that no variable contains more than one unit root and the first difference of each variable is stationary. With the aim of analyzing the effect of aid on current, capital and loan repayment, this study employ annual time series data from 1985 to 2008. Table 5.10 presents the result of the long run equation. The reg ression result reported in Table 5.9 shows that the relationship between aid and current and capital expenditures is negative and statistically insignificant. An interesting result in Table 5.9 is the positive coefficient of aid in principal repayment. This shows that aid is being employed to finance loan repayment. Urban population has elasticity coefficient of 7.58, 4.28 and 1.44 in current, capital and loan repayment respectively. This shows that urban population has a positive effect on government expenditure while population has negative effect on government expenditure with negative coefficients. R2 value is greater than 0.5 in all the three cases indicating that Aid, population , urban population and lagged GDP accounts to 71% ,50 % and 52% variation in current, capital and loan repayment expenditure respectively. Another desirable property of econometric result is the value of the Durbin Watson statistics which is close to 2 and represent the absence of serial correlation in the error term. Testing for co-integration An important property of I (1) variables is that they can be linear combinations of I (0) variables. If this is so, then these variables are said to be co-integrated (Maddala et al 1999). To test the presence of co-integration, the null hypothesis of unit root in the residuals is tested against the alternative hypothesis that there is co-integration between the variables.