4.3.1 Fully modified ordinary least square (FMOLS)

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 in FMOLS estimator can be expressed as follows:

$$\hat{\boldsymbol{\beta}} = \boldsymbol{N}^{-1} \sum\_{i=1}^{N} \left[ \sum\_{t=1}^{T} \left( \mathbf{X}\_{it} - \overline{\mathbf{X}}\_{1} \right)^{2} \right]^{-1} \left[ \sum\_{t=1}^{T} \left( \mathbf{X}\_{it} - \overline{\mathbf{X}}\_{1} \right) \mathbf{Y}\_{it}^{\*} - T \hat{\boldsymbol{\pi}}\_{i} \right] \tag{7}$$

where, Y <sup>∗</sup> it <sup>¼</sup> Yit � <sup>Y</sup> � <sup>L</sup>^21<sup>i</sup> L^22<sup>i</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> <sup>21</sup><sup>i</sup> � <sup>L</sup>^21<sup>i</sup> L^22<sup>i</sup> <sup>Γ</sup>^22<sup>i</sup> <sup>þ</sup> <sup>Ω</sup>^ <sup>0</sup> 22i and L^<sup>i</sup> is a lower triangular decomposition of Ω^ <sup>i</sup>. The associated t-statistic is assumed to be normally distributed and given by:

$$t\_{\hat{\boldsymbol{\beta}}^{\*}} = \boldsymbol{N}^{-1/2} \sum\_{i=1}^{N} t\_{\hat{\boldsymbol{\beta}}^{\*}}, \text{i; where } t\_{\hat{\boldsymbol{\beta}}^{\*}}, \boldsymbol{i} = \left(\hat{\boldsymbol{\beta}}\_{i}^{\*} - \boldsymbol{\beta}\_{0}\right) \left[\hat{\boldsymbol{\Omega}}\_{11i}^{-1} \sum\_{t=1}^{T} \left(\mathbf{X}\_{it} - \overline{\mathbf{X}}\right)^{2}\right]^{1/2} \tag{8}$$

The long-run relationship between financial development and FDI inflows is measured by the coefficient (β^) from FMOLS estimator.

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

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 dependency existed for all variables (refer to Table 1), which might be due to 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]. The baseline model for generic ARDL (p,q) can be expressed as follows:

$$
\overline{\mathcal{Y}}\_{i,t} = \sum\_{k=1}^{p} \varphi\_{i,k} \overline{\mathcal{Y}}\_{i,t-k} + \sum\_{l=0}^{q} \beta'\_{i,l} \overline{\mathcal{X}}\_{i,t-1} + u\_{i,t} \tag{9}
$$

while its cointegrating form would be:

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

$$\mathcal{Y}\_{i,t} = \theta\_i \mathfrak{x}\_{i,t} + \alpha\_i'(L)\Delta \mathfrak{x}\_{it} + \tilde{u}\_{i,t} \tag{10}$$

In CS-ARDL, Eq. (9), the errors (u) is postulated a common unobserved factor structure for the errors. It can be written as:

$$
\mu\_{i,t} = \gamma'\_i F\_t + \varepsilon\_{i,t} \tag{11}
$$

Since all variables are integrated of order one, the panel cointegration test is employed to measure the existence of long-run relationship in Eq. (1). The results of

cointegration test shows that P<sup>α</sup> and P<sup>τ</sup> test statistics reject the null hypothesis of no cointegration at 1, 5 and 10% significance level for both models using DCPS and PCDM, for the specification without trend. The P<sup>α</sup> and P<sup>τ</sup> test statistics have the highest power and are the most robust to cross-sectional correlation [21]. Thus, the evidence from the second-generation panel cointegration test supports the presence of a cointegrating relationship among FDI, financial development, price and

Due to the existence of cointegration among variables in the region, the FMOLS estimator is used to estimate the long-run equilibrium. Table 9 reports that Model 1–3 estimates the linear and nonlinear relationship between financial development and FDI in the long-run, by using DCPS, LL and PCDM as a proxy for financial development, respectively. Long-run covariance estimates pre-whitening with lag 1, where the automatic bandwidth selection is based on Newey-West fixed bandwidth and Bartlett kernel. In the linear specification, the relationship between financial development and FDI are not significant in all models. However, in contrast, there is significant of nonlinear relationship between financial development and FDI. The nonlinear relationship between these variables is anti-Kuznets or U-shape curve, where α<sup>1</sup> the coefficient of financial development and α<sup>2</sup> the financial development square coefficient (Eq. (2)) is negative and positive,

second-generation of panel cointegration presented in Table 8. The panel

Variable Level First difference

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

FDI 4.0\* 1.5 4.3\* 1.4 10.0\* 8.3\* 9.7\* 7.5\* DCPS 1.0 1.0 0.6 0.5 8.5\* 5.0\* 8.0\* 4.4\* LL 0.8 0.8 0.9 1.5 4.6\* 5.1\* 3.6\* 4.3\* PCDM 0.2 2.0 1.9 0.3 3.7\* 4.0\* 3.7\* 3.4\* RGDPPC 2.2 1.0 4.4 3.1 3.5\* 3.1\* 3.8\* 4.2\* CPI 1.0 0.8 1.0 0.0 5.5\* 3.7\* 4.7\* 3.2\*

Model 1: FinDev = DCPS Model 2: FinDev = LL Model 3: FinDev = PCDM Statistics p-value Statistics p-value Statistics p-value

<sup>G</sup><sup>τ</sup> 2.975\*\*\* 0.003 3.054\*\*\* 0.002 3.398\*\*\* 0.000 G<sup>α</sup> 8.162 0.450 9.576 0.264 8.249 0.438 <sup>P</sup><sup>τ</sup> 5.701\*\* 0.018 5.240\*\* 0.040 6.038\*\*\* 0.009 P<sup>α</sup> 6.939 0.172 7.178 0.152 7.051 0.162

Z<sup>α</sup> Z<sup>τ</sup> Z<sup>α</sup> Z<sup>τ</sup> q = 0 q = 1 q = 0 q = 1 q = 0 q = 1 q = 0 q = 1

economic development in ASEAN-5 countries.

\*

Table 7.

Significant at 1% level.

\*\*\*Significant at 1% level. \*\*Significant at 5% level.

Table 8.

51

Second-generation panel unit root test of CIPS.

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

Second-generation panel cointegration results.

CS-ARDL is an augmented model from generic ARDL (p,q) by averaging crosssectional of the dependent and explanatory variables, as well as their lags, which are supposed to proxy for the unobserved common factors.

### 4.4 Panel vector error-correction model

The panel Granger causality in the framework of the panel VECM is employed to analyze the direction of the causal effect among FDI, financial development and the control variables, CPI and GDP per capita. The long-run model specified in Eq. (1) is estimated by using FMOLS to obtain the estimated residual, followed by Granger causality model estimation based on the error-correction model as follows:

$$\begin{split} \Delta \ln FDI\_{it} &= \alpha\_{1i} + \sum\_{k=1}^{m} \lambda\_{11ik} \Delta \ln FDI\_{i,t-k} + \sum\_{k=1}^{m} \lambda\_{12ik} \Delta \ln FinDev\_{i,t-k} \\ &+ \sum\_{k=1}^{m} \lambda\_{13ik} \Delta \ln RGDPCP\_{i,t-k} + \sum\_{k=1}^{m} \lambda\_{14ik} \Delta \ln CPI\_{i,t-k} + \phi\_{1i} EC\_{i,t-1} + \mu\_{1it} \end{split} \tag{12}$$

$$\begin{split} \Delta \ln \text{FinDev}\_{it} &= \alpha\_{2i} + \sum\_{k=1}^{m} \lambda\_{2iik} \Delta \ln \text{FinDev}\_{i, t-k} + \sum\_{k=1}^{m} \lambda\_{22ik} \Delta \ln \text{FDI}\_{i, t-k} \\ &+ \sum\_{k=1}^{m} \lambda\_{23ik} \Delta \ln \text{RGDPPC}\_{i, t-k} + \sum\_{k=1}^{m} \lambda\_{24ik} \Delta \ln \text{CPI}\_{i, t-k} + \oint\_{2} \text{EC}\_{i, t-1} + \mu\_{2i} \end{split} \tag{13}$$

$$\begin{split} \Delta \ln RGDDPPC\_{it} &= \alpha\_{3i} + \sum\_{k=1}^{m} \lambda\_{31ik} \Delta \ln RGDPCC\_{i,t-k} + \sum\_{k=1}^{m} \lambda\_{32ik} \Delta \ln FinDev\_{i,t-k} \\ &+ \sum\_{k=1}^{m} \lambda\_{33ik} \Delta \ln FDI\_{i,t-k} + \sum\_{k=1}^{m} \lambda\_{34ik} \Delta \ln CPI\_{i,t-k} + \phi\_{3i} EC\_{i,t-1} + \mu\_{3d} \\ \Delta \ln CPI\_{it} &= \alpha\_{4i} + \sum\_{k=1}^{m} \lambda\_{41ik} \Delta \ln CPI\_{i,t-k} + \sum\_{k=1}^{m} \lambda\_{42ik} \Delta \ln FinDev\_{i,t-k} \\ &+ \sum\_{k=1}^{m} \lambda\_{43ik} \Delta \ln RGDPCC\_{i,t-k} + \sum\_{k=1}^{m} \lambda\_{44ik} \Delta \ln FDI\_{i,t-k} + \phi\_{4i} EC\_{i,t-1} + \mu\_{4i} \end{split} \tag{15}$$

where, EC is error-correction term comes from the FMOLS estimation, and m is the lag length. The short-run causality is determined by the statistical significance of the F-statistic associated with the corresponding right hand side variables. The presence or absence of long-run causality can be established by examining the significance of the t-statistic on the coefficient ϕ, in Eqs. (12)–(15).

k¼1
