**3.1 Data**

In order to achieve the objective of this study, annual Gross Domestic Product of Bahrain (GDP) at constant prices is obtained from the World Bank Data and used as a measure for economic growth. Oil & Gas Revenues (Rev), Total Expenditure (Exp), Ministry of Health Expenditure (H-Exp) and Ministry of Education Expenditure (E-Exp) are obtained from the Ministry of Finance. The time period of the study is from 1989 to 2015. All the variables have been transformed using natural logarithm transformation. **Table 1** presents the descriptive statistics of all the variables.


*The Reform in Government Expenditure and the Standard of Living in Bahrain DOI: http://dx.doi.org/10.5772/intechopen.98249*


*Notes: GDP is the Gross Domestic Product, Rev. is the Oil & Gas Revenue, Exp is the Total Expenditure, H-Exp is the Ministry of Health Expenditure and E-Exp is the Ministry of Education Expenditure. All the data are in millions of Bahraini Dinars.*

#### **Table 1.**

*Descriptive statistics.*

#### *3.1.1 Stationarity tests*

The basic procedure for testing the variables includes three steps. The first step is to test the stationarity of the variables and examine their integration level. In order to do so, the Augmented Dickey and Fuller [18] ADF test, Phillips and Perron [19] - PP and Kwiatkowski et al. [20] - KPSS are employed.

#### *3.1.2 Cointegration test*

After checking the stationarity of all the series and getting all the variables to be integrated of the same order, the second step is to investigate the presence of long run relationship between all the variables in each Model. Cointegration shows that the variables jointly move in the long run and the error term generated from the linear combination of all the variables measures the divergence of the variables from their joint long run relationship, which can be used to forecast their values in the future [21]. To determine this relationship, Johansen Cointegration Test is used [22, 23].

The procedure of cointegration is estimated using an unrestricted vector autoregressive model (VAR) with error correction specification:

$$
\Delta Y\_t = \Pi Y\_{t-1} + \sum\_{i=1}^{k-1} \Gamma\_i \Delta Y\_{t-i} + \Phi D\_t + v\_t \tag{1}
$$

where *Yt* contains all n variables of the model which are integrated of order one – I(1), Π, *Γ<sup>i</sup> and Φ* are parameter matrices to be estimated, *Dt* is a vector with deterministic elements (constant, trend) and *vt* is a vector of random errors. Eq. (1) indicates that there will be no relationship between two series of different cointegration order. Johansen cointegration test estimates the rank (r) of the matrix Π. If *r* = 0, all variables are not cointegrated. If 0 < *r* < *N*, r cointegrating vectors exist. Johansen's cointegration test uses two likelihood statistics. The first is the Trace test, which examines whether the number of cointegrating vectors (r) is less than or equal to r. The second is the maximum eigenvalue, which test the number of cointegrating vectors is *r* against the alternative of *r* + 1 cointegrating vectors.

#### **3.2 Methodology**

Finally, when getting all the variables to be integrated of order one, I(1) and cointegrated (joint movement in the long run), the short and long run relationships between Economic Growth, Revenues and Government Expenditure can be estimated. This can be done using the Vector Error Correction Model (VECM) that was developed by Engle and Yoo [24]. The VECM is used to allow for short-run adjustment dynamics and show the speed of this adjustment to the long-run equilibrium.

In a VECM it does not matter if some of the variables are endogenous, because no contemporaneous terms appear in the equation.

Model 1 is used to estimate the long and short run relationship between Bahrain economic growth, oil and gas revenues and total government expenditure.

Model 1:

$$\begin{aligned} \Delta \ln GDP\_t &= a\_1 + a\_2 \ln GDP\_{t-1} + a\_3 \ln Rev\_{t-1} + a\_4 \ln Exp\_{t-1} + \sum\_{i=1}^2 \beta\_{1i} \Delta \ln GDP\_{t-1} \\ &+ \sum\_{i=1}^2 \beta\_{2i} \Delta \ln Rev\_{t-1} + \sum\_{i=1}^2 \beta\_{3i} \Delta \ln Exp\_{t-1} + \gamma\_1 ECT\_{t-1} + \varepsilon\_t \end{aligned} \tag{2}$$

where Δ represents the first difference, ln *GDP* is the natural logarithm of gross domestic product, ln *Rev* is the natural logarithm of oil and gas revenues, ln *Exp* is the natural logarithm of total expenditure and *ECT* is the error correction term.

To examine the relationship between sectoral government expenditure and economic growth, Model 2 estimates the long and short relationships between economic growth and ministry of health expenditure.

Model 2:

$$
\Delta \ln GDP\_t = a\_1 + a\_2 \ln GDP\_{t-1} + a\_3 \ln HExp\_{t-1} + \sum\_{i=1}^2 \beta\_{i1} \Delta \ln GDP\_{t-1}
$$

$$
+ \sum\_{i=1}^2 \beta\_{3i} \Delta \ln HExp\_{t-1} + \gamma\_1 ECT\_{t-1} + \varepsilon\_t \tag{3}
$$

where ln *HExp* is the natural logarithm of ministry of health expenditure. Model 3 examines the short and long run relationship between Bahrain economic growth and ministry of education appending.

Model 3:

$$
\Delta \ln GDP\_t = a\_1 + a\_2 \ln GDP\_{t-1} + a\_3 \ln EExp\_{t-1} + \sum\_{i=1}^2 \beta\_{1i} \Delta \ln GDP\_{t-1}
$$

$$
+ \sum\_{i=1}^2 \beta\_{3i} \Delta \ln EExp\_{t-1} + \gamma\_1 ECT\_{t-1} + \varepsilon\_t \tag{4}
$$

where *lnEExp* is the natural logarithm of ministry of education expenditure and *ECT* is the error correction term. The Akaike Information Criteria (AIC) is used to select the appropriate lag length.

#### **4. Results**

#### **4.1 Unit root and Cointegration test results**

The null hypothesis of the Augmented Dickey Fuller and Phillips and Perron tests is the existence of a unit root, whereas the null hypothesis of the KPSS test is that the time series variable is stationary. The three tests are implemented for the variables at level and at first difference. **Table 2** summarizes the results of the unit root tests. The results show that all the variables are stationary at first difference, which means that all of them are I(1).

Since lnGDP, lnRev and lnExp are integrated of the same level, therefore Johansen's cointegration test is conducted to examine the long-run equilibrium *The Reform in Government Expenditure and the Standard of Living in Bahrain DOI: http://dx.doi.org/10.5772/intechopen.98249*


*Notes: ADF is the Augmented Dickey and Fuller [18] unit root test. PP is Phillips and Perron [19] unit root test. KPSS is Kwiatkowski et al. [20] Stationarity test.*

*\*, \*\*, \*\*\* present 10%, 5% and 1% level of significance, respectively. lnGDP is the natural logarithm of Gross Domestic Product, lnRev is the natural logarithm of Oil & Gas Revenue, lnExp is the natural logarithm of Total Expenditure, lnH-Exp is the natural logarithm of Ministry of Health Expenditure and lnE-Exp is the Ministry of Education Expenditure.*

#### **Table 2.**

*Unit root test results.*


*\* indicates that this is the value of rank (r) selected by Johansen's multiple-trace test procedure.*

#### **Table 3.**

*Model 1 Cointegration test results.*

relationship between the three series. **Table 3** shows the results of Model 1 Eq. (2) Cointegration Test Results. This test was estimated using 2 lags according to the AIC of a VAR model for the variables of interest. The trace statistic and maximum eigenvalue states that the null hypothesis of the presence of a maximum of one cointegrating equation (*r*≤1Þ cannot be rejected. This indicates the existence of a long-run relationship between economic growth, oil and gas revenues and government expenditure in Bahrain.

Johansen's cointegration test is applied to the variables employed in Model 2 Eq. (3) and Model 3 Eq. (4) using a maximum lag of 1 according to the AIC of a VAR model for both models. **Tables 4** and **5** indicate the presence of long-run relationships between economic growth and health expenditure and between economic growth and education expenditure, respectively.



#### **Table 5.**

*Model 3 Cointegration test results.*

#### **4.2 Vector error correction model (VECM) results**

#### *4.2.1 Model 1 estimation results*

Since the economic growth, oil and gas revenues and government expenditure variables are stationary at first difference and have a long run cointegration, the VECM can be employed to investigate this relationship. **Table 6** presents the results of estimating Eq. (2) using VECM approach. The results show that oil and gas revenues have a significant positive impact on the economic growth of Bahrain whereas the government expenditure has a significant negative impact on Bahrain economic growth. The error correction term is negative and significant.
