4. Methodology

The flow of methodology started with the panel unit root test with crosssectional dependency to ensure the variables are integrated at first difference before proceed with cointegration test of panel cointegration second-generation. Since the existence of cross-sectional dependency among ASEAN-5 countries, hence, this study considers the using Westerlund's cointegration test as the second-generation of panel cointegration. In addition, the fully modifies ordinary least square

(FMOLS) and cross-sectional dependency autoregressive distributed lag (CS-ARDL) are used to estimate the long run coefficient in the specification. FMOLS estimator is used to overcome the endogeneity and heterogeneity problem. Meanwhile, the cross-sectional dependency needs to take into account in the estimation by using CS-ARDL. The causality test by using panel vector error correction model (VECM) is used to investigate the direction of causality among the variables.

## 4.1 Panel unit root test

The panel unit root test of second-generation in used in order to incorporating the cross-sectional dependency. For the case of ASEAN-5 countries, the common stochastic trends may occur due to global developments and strong relationships between economies. The heterogenous panel unit root test with cross-sectional dependence is employed for clarity [20]. The standard Dickey-Fuller (DF) or augmented Dickey-Fuller (ADF) regressions are augmented with the cross-section averages of lagged levels (xit�1) and first-differences (Δxit�1) of the individual series to eliminate cross-sectional dependence. Hence, the cross-sectional dependence ADF (CADF) test [20] expressed as follows:

$$
\Delta \mathbf{x}\_{it} = a\_i + \rho \mathbf{x}\_{it-1} + v\_{it} \tag{3}
$$

versus H1: θ<sup>i</sup> < 0 for at least one i for the G<sup>α</sup> and G<sup>τ</sup> statistic tests. If H0 is rejected, it means that cointegration exists for at least one of the cross-sectional units. Meanwhile, the P<sup>α</sup> and P<sup>τ</sup> test statistics pooled the information over all the cross-sectional units to test H<sup>0</sup> : θ<sup>i</sup> ¼ 0 for all i versus H<sup>1</sup> : θ<sup>i</sup> < 0 for all i. The rejection of H0

Nonlinear Effect of Financial Development and Foreign Direct Investment in Integration…

The long-run coefficient estimation is proceeded if the evidence of cointegration

The FMOLS estimator allows for cross-sectional heterogeneity in the alternative hypothesis. The endogeneity and serial correlation problems are allowing in the FMOLS long-run coefficients estimation in order to obtain consistent and asymptotically unbiased estimates of the cointegrating vectors [22, 23]. The definition of

> ∑ T t¼1

<sup>i</sup> � β<sup>0</sup> <sup>Ω</sup>^ �<sup>1</sup>

<sup>Δ</sup>Xit, ^τ<sup>i</sup> � <sup>Γ</sup>^21<sup>i</sup> <sup>þ</sup> <sup>Ω</sup>^ <sup>0</sup>

The long-run relationship between financial development and FDI inflows is

Cross-sectional dependency autoregressive distributed lag (CS-ARDL) estimator is used for robustness that allows for cross-sectional dependency among ASEAN-5 countries in the alternative hypothesis. The dataset shows cross-sectional depen-

integrational economies among neighbor countries in ASEAN-5. This element needs to consider in estimating the long-run coefficient by using CS-ARDL estimator [24].

q

l¼0 β0

lower triangular decomposition of Ω^ <sup>i</sup>. The associated t-statistic is assumed to be

Xit � X<sup>1</sup> Y <sup>∗</sup>

> <sup>21</sup><sup>i</sup> � <sup>L</sup>^21<sup>i</sup> L^22<sup>i</sup>

> > <sup>11</sup><sup>i</sup> ∑ T t¼1

it � T^τ<sup>i</sup> (7)

<sup>Γ</sup>^22<sup>i</sup> <sup>þ</sup> <sup>Ω</sup>^ <sup>0</sup>

Xit � <sup>X</sup> <sup>2</sup> <sup>1</sup>=<sup>2</sup>

i,lxi,t�<sup>1</sup> þ ui,t (9)

22i and L^<sup>i</sup> is a

(8)

among the variables is proven. Fully modified ordinary least square (FMOLS) estimator is used to estimate the long-run coefficient for financial development and FDI inflows relationship. The long-run coefficients are further estimates by using cross-sectional dependency autoregressive distributed lag (CS-ARDL) in order to considering the element of cross-sectional dependency among ASEAN-5 countries

indicating the evidence of cointegration for the panel as a whole.

4.3.1 Fully modified ordinary least square (FMOLS)

in FMOLS estimator can be expressed as follows:

N i¼1 ∑ T t¼1

L^22<sup>i</sup>

<sup>t</sup>^<sup>β</sup> <sup>∗</sup> , i; where <sup>t</sup>^<sup>β</sup> <sup>∗</sup> , i <sup>¼</sup> <sup>β</sup>^ <sup>∗</sup>

4.3.2 Cross-sectional dependency autoregressive distributed lag (CS-ARDL)

dency existed for all variables (refer to Table 1), which might be due to

The baseline model for generic ARDL (p,q) can be expressed as follows:

<sup>φ</sup>i,kyi,t�<sup>k</sup> <sup>þ</sup> <sup>∑</sup>

measured by the coefficient (β^) from FMOLS estimator.

yi,t ¼ ∑ p

while its cointegrating form would be:

k¼1

Xit � X<sup>1</sup> <sup>2</sup> �<sup>1</sup>

<sup>β</sup>^ <sup>¼</sup> <sup>N</sup>�<sup>1</sup> <sup>∑</sup>

normally distributed and given by:

N i¼1

it <sup>¼</sup> Yit � <sup>Y</sup> � <sup>L</sup>^21<sup>i</sup>

4.3 Long-run estimation

DOI: http://dx.doi.org/10.5772/intechopen.86104

for robustness.

where, Y <sup>∗</sup>

49

<sup>t</sup>^<sup>β</sup> <sup>∗</sup> <sup>¼</sup> <sup>N</sup>�1=<sup>2</sup> <sup>∑</sup>

where, vit ¼ gi θ<sup>t</sup> þ μit:θ<sup>t</sup> is a common factor and is white noise.

The CADF model is given by, without the autocorrelation of μit can be written as follows:

$$
\Delta \mathbf{x}\_{it} = a\_i + \rho \mathbf{x}\_{it} + c\_i \overline{\mathbf{x}}\_{t-1} + d\_i \Delta \overline{\mathbf{x}}\_{t-1} + \varepsilon\_{it} \tag{4}
$$

The cross-sectionally augmented Im, Pesaran and Shin (IPS) or CIPS [20] is given by:

$$\text{CIPS } (N, T) = \frac{1}{N} \sum\_{i=1}^{q} t\_i(N, T) \tag{5}$$

where ti indicates the statistics from each CADF model for each individual i of the panel and significance level based on the critical value (see [20]). If the p-value of CIPS statistics is lower than 0.05 indicating the null hypothesis of non-stationary of the variables is rejected.

## 4.2 Panel cointegration test

The second-generation panel cointegration test with cross-sectional dependence has four error-correction-based tests, which allows for large degree of heterogeneity in both long-run cointegration and short-run dynamics [21]. The presence of cointegration is tested by determining whether or not the existence of errorcorrection for individual panel of also the panel as a whole. Transforming Eq. (1) to the error-correction model can be expressed as follows:

$$\begin{split} \Delta \ln FDI\_{it} &= \mathbf{c}\_{\text{li}} + \varrho\_{\text{i1}} \sum\_{j=1}^{p} \Delta \ln FDI\_{it-j} + \varrho\_{i2} \sum\_{j=0}^{p} \Delta \ln FinDev\_{it-j} + \varrho'\_{i} \sum\_{j=0}^{p} \Delta \mathbf{X}\_{it-j} \\ &+ \theta\_{i} [\beta\_{\text{li}}(\ln FDI\_{it-1}) - \beta\_{\text{2i}}(\ln FinDev\_{it-1}) - \beta'\_{i}(\mathbf{X}\_{it-1}) + \mathbf{e}\_{\text{it}} \end{split} \tag{6}$$

where θ<sup>i</sup> measures the speed of error-correction towards the long-run equilibrium, FDIit ¼ �ð Þ� φi=θ<sup>i</sup> xit for the series i. The null hypothesis, H<sup>0</sup> : θ<sup>i</sup> ¼ 0 for all i Nonlinear Effect of Financial Development and Foreign Direct Investment in Integration… DOI: http://dx.doi.org/10.5772/intechopen.86104

versus H1: θ<sup>i</sup> < 0 for at least one i for the G<sup>α</sup> and G<sup>τ</sup> statistic tests. If H0 is rejected, it means that cointegration exists for at least one of the cross-sectional units. Meanwhile, the P<sup>α</sup> and P<sup>τ</sup> test statistics pooled the information over all the cross-sectional units to test H<sup>0</sup> : θ<sup>i</sup> ¼ 0 for all i versus H<sup>1</sup> : θ<sup>i</sup> < 0 for all i. The rejection of H0 indicating the evidence of cointegration for the panel as a whole.

#### 4.3 Long-run estimation

(FMOLS) and cross-sectional dependency autoregressive distributed lag (CS-ARDL) are used to estimate the long run coefficient in the specification. FMOLS estimator is used to overcome the endogeneity and heterogeneity problem. Meanwhile, the cross-sectional dependency needs to take into account in the estimation by using CS-ARDL. The causality test by using panel vector error correction model (VECM) is used to investigate the direction of causality among the variables.

Accounting and Finance - New Perspectives on Banking, Financial Statements and Reporting

The panel unit root test of second-generation in used in order to incorporating the cross-sectional dependency. For the case of ASEAN-5 countries, the common stochastic trends may occur due to global developments and strong relationships between economies. The heterogenous panel unit root test with cross-sectional dependence is employed for clarity [20]. The standard Dickey-Fuller (DF) or augmented Dickey-Fuller (ADF) regressions are augmented with the cross-section averages of lagged levels (xit�1) and first-differences (Δxit�1) of the individual series to eliminate cross-sectional dependence. Hence, the cross-sectional

θ<sup>t</sup> þ μit:θ<sup>t</sup> is a common factor and is white noise. The CADF model is given by, without the autocorrelation of μit can be written as

The cross-sectionally augmented Im, Pesaran and Shin (IPS) or CIPS [20] is

<sup>N</sup> <sup>∑</sup> q

where ti indicates the statistics from each CADF model for each individual i of the panel and significance level based on the critical value (see [20]). If the p-value of CIPS statistics is lower than 0.05 indicating the null hypothesis of non-stationary

The second-generation panel cointegration test with cross-sectional dependence has four error-correction-based tests, which allows for large degree of heterogeneity in both long-run cointegration and short-run dynamics [21]. The presence of cointegration is tested by determining whether or not the existence of errorcorrection for individual panel of also the panel as a whole. Transforming Eq. (1) to

p

j¼0

<sup>i</sup>ð Þþ Xit�<sup>1</sup> εit ½

where θ<sup>i</sup> measures the speed of error-correction towards the long-run equilibrium, FDIit ¼ �ð Þ� φi=θ<sup>i</sup> xit for the series i. The null hypothesis, H<sup>0</sup> : θ<sup>i</sup> ¼ 0 for all i

Δln FinDevit�<sup>j</sup> þ φ<sup>0</sup>

<sup>i</sup> ∑ p

j¼0

ΔXit�<sup>j</sup>

(6)

i¼1

CIPS Nð Þ¼ ; <sup>T</sup> <sup>1</sup>

Δxit ¼ α<sup>i</sup> þ ρxit�<sup>1</sup> þ vit (3)

tið Þ N; T (5)

Δxit ¼ α<sup>i</sup> þ ρxit þ cixt�<sup>1</sup> þ diΔxt�<sup>1</sup> þ εit (4)

dependence ADF (CADF) test [20] expressed as follows:

the error-correction model can be expressed as follows:

Δln FDIit�<sup>j</sup> þ φ<sup>i</sup><sup>2</sup> ∑

þ θ<sup>i</sup> β1<sup>i</sup>ð Þ� ln FDIit�<sup>1</sup> β2<sup>i</sup>ðln FinDevit�<sup>1</sup>Þ � β<sup>0</sup>

p

j¼1

4.1 Panel unit root test

where, vit ¼ gi

of the variables is rejected.

4.2 Panel cointegration test

Δ ln FDIit ¼ c1j þ φ<sup>i</sup><sup>1</sup> ∑

48

follows:

given by:

The long-run coefficient estimation is proceeded if the evidence of cointegration among the variables is proven. Fully modified ordinary least square (FMOLS) estimator is used to estimate the long-run coefficient for financial development and FDI inflows relationship. The long-run coefficients are further estimates by using cross-sectional dependency autoregressive distributed lag (CS-ARDL) in order to considering the element of cross-sectional dependency among ASEAN-5 countries for robustness.
