# Augmented Dickey Fuller And Phillips Perron Tests Economics Essay

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.

Referring to Table 5.9, 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 first 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).

Table 5.9: Unit root test (ADF and PP test)

Augmented Dickey Fuller Test

Level form

Phillips-Perron

Without constant

and trend

With constant and trend

Without constant

and trend

With constant and trend

Current

-0.871

-2.643

-3.980*

-3.991**

Capital

-1.742

-3.708**

-3.530**

-3.231***

Repayment

-2.288

-2.544

-3.992*

-3.866**

Aid

-1.526

-1.172

-3.485**

-3.621**

Population

-2.150

-1.115

-2.829***

-3.252***

Urban population

-1.801

-1.984

-2.924***

-3.063***

Lagged GDP

-1.581

-2.459

-3.314**

-3.219***

Source: Computed

Note:

* stationary at 1%,**stationary at 5%, *** stationary at 10%

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.

Table 5.10: Impact of Foreign aid on government expenditure in Mauritius, 1985 to 2008

Equation:

Log(Current Expenditure)

Log(Capital Expenditure)

Log(Principal

Repayment)

Constant

5.005**

-5.299**

15.150**

-0.028^

-0.041^

0.094^

-2.256**

-4.615*

-3.593**

7.579***

4.727^

1.444^

0.573*

.309**

1.564**

0.71

0.50

0.52

Number of observations

24

24

24

Degrees of freedom

19

19

19

Durbin Watson Statistics

1.91

2.06

1.88

Source: Computed

Note:

*significant at 1% level, **significant at 5% level,***significant at 25% level,

^ insignificant

The regression 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.

Table 5.11: Result of unit root test in the residuals

Residual

ADF

PP

Levels

Levels

Current

-3.575**

-3.136**

Capital

-4.359*

-3.885*

Repayment

-3.102**

-5.639*

Source: Computed

Note:

* stationary at 1%,**stationary at 5%, *** stationary at 10%

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

The t-statistics values presented in Table 5.11 are significant and the null hypothesis is rejected. These indicate that there is a stationary combination of non-stationary variables and the variables are co-integrated.

## Error Correction Model

As co-integrating relationship was observed among the variables, the short run equation can be estimated. This shows whether long run system adjusts toward equilibrium by using alpha α coefficient.

ECM model in 1st difference

Current

Capital

Repayment

Constant

-0.070^

0.164^

0.117^

Aid

-0.023^

-0.069^

-0.228^

Population

-5.894^

-3.361***

-6.767^

Urban population

2.774

6.707^

0.445^

Lagged GDP

0. 531*

1.177**

6.493*

α-coefficient

-0.685*

-0.502**

-0.648*

R2

0.59

0.48

0.46

Durbin Watson Statistics

1.84

1.79

2.10

Number of observations

22

22

22

Degrees of freedom

16

16

16

Source: Computed

Note:

*significant at 1% level, **significant at 5% level,***significant at 25% level,

^ insignificant

Table 5.9 presents the short run effects of changes in aid flow on current, capital and loan repayment. The result of the ECM models compare well with the long run model. Once again, aid does not have a significant impact on government expenditure in Mauritius. In the short run, aid has a negative impact on loan repayment. An important revelation of the ECM model, is the α coefficient which measures the rate of feedback effect of the disequilibrium in co-integrating relation to the variable. The speed of adjustment is negative and significant in all the three cases as theoretically expected. It indicates that 69%, 50% and 65% of disturbances are adjusted toward long run steady state to current, capital and loan repayment respectively.

Both the short run and the long run model shows that external funds do not have a significant impact on government expenditure and foreign aid is fungible in Mauritius. These results contradict the findings of Nath and Sobhee (2002), who found that there is no substitution of external development funds in the country. One reason why the findings of this study might be different from that of Nath and Sobhee (2002) is the variation in the time period and model used to analyze foreign aid fungibility. Their study covered the period 1973 to 1995 and they use a trade off model of development from both external and internal sources to capture foreign aid in fungibility of external assistance. However, in a panel data analysis in which Mauritius was included in the sample of countries, Devarajan and et al. (1999) found that foreign aid is partially fungible in Africa.

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