**3. Data and Methodology**

### *3.1. Sample Selection and Variables*

The dataset used in this study spans the period from 2003 to 2016, common for all selected measures and comprises 11 Central and Eastern European countries, namely Bulgaria, Croatia, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, Slovenia. World Bank and Eurostat databases have been employed to gather the statistical data. The selected variables are listed in Table 4. Throughout the sample period, there is missing data on many variables, which diminish our data set for each model differently. Following preceding studies [2,19,39,41,42,46,57,61], we consider our dependent variable as GDP per capita. In line with earlier studies [2,41,57,61,69], inflows of FDI were considered. Furthermore, we comprise measures set out in the 2030 Agenda for Sustainable Development [48], relating to poverty [13], inequality of income distribution [59,112], education [3,13,20,34,39,41–43,46,52,71,112,118], innovation [14,28,65,104], transport infrastructure [3, 13,52,114], information technology [13,28], institutional quality [2,13–15,18–20,28,39,41,42,44,46,52,107, 115,117,118]. The estimate of each Worldwide Governance Indicators provides the nation's score on the aggregate indicator, in units of a standard normal distribution, fluctuating from roughly −2.5 to 2.5, with higher values pertaining to better governance. Moreover, country-level control measures are included, namely government expenditure [12,40,42,46,64,71,72,116], urbanization [69], domestic credit to the private sector [41,46,72] and trade [2,5,13,18,19,34,40,42–44,46,52,53,55,61,64,69,72,118].

**Table 4.** Description of the variables.


*Sustainability* **2019**, *11*, 5421

**Table 4.** *Cont*.


#### *3.2. Quantitative Techniques*

The most common methods identified in the literature concerning the influence of FDI on economic growth are panel data fixed-effects and random-effects estimations [1,2,13,28,41,53,64,65,69,107,114], as well as the generalized method of moments [9,18,41–45,71,72,113,117]. Current paper employs the first approach, the econometric specifications being depicted as follows:

$$\text{GROWTH}\_{it} = \beta\_0 + \beta\_1 \times \text{FDI}\_{it} + \beta\_2 \times \text{SDGs}\_{it} + \beta\_3 \times \text{CV}\_{it} + \varepsilon\_{it} \tag{1}$$

*i* = 1, 2, ... , 11, *t* = 2003, 2004, ... , 2016.

where the dependent variable is GDP per capita in CEECs. *FDI* is a measure of inward FDI flows. *SDGs* signifies a vector of explanatory variables concerning sustainable development goals [48]. *CV* depicts the country-level control variables. β<sup>0</sup> describes the country-specific intercept, β1–β<sup>3</sup> are the coefficients to be estimated, ε is the error term, *i* is the subscript of recipient FDI CEE nation, and *t* is the subscript of time and accounts for the unobservable time-invariant individual specific effect, not included in the regression [34].

Likewise, to inspect for a potential non-linear association between FDI and growth, the squared term of FDI (hereinafter "FDI\_SQ") will be encompassed in the aforementioned equation:

$$\text{GROWTH}\_{\text{it}} = \beta\_0 + \beta\_1 \times \text{FDI}\_{\text{it}} + \beta\_2 \times \text{FDI\\_SQ}\_{\text{it}} + \beta\_3 \times \text{SDGs}\_{\text{it}} + \beta\_5 \times \text{CV}\_{\text{it}} + \varepsilon\_{\text{it}} \tag{2}$$

*i* = 1, 2, ... , 11, *t* = 2003, 2004, ... , 2016.

The next step is to determine the order of integration. To examine the stationarity of the series, several tests will be performed, such as Augmented Dickey–Fuller (hereinafter "ADF") [1,3,8,14,39,56–58,61,70, 73], Phillips–Perron (hereinafter "PP") [1,7,39,58,61,70,73], Levin–Lin–Chu (hereinafter "LLC") [1,13, 14,39,70,73,118], Im–Pesaran–Shin (hereinafter "IPS") [1,7,13,14,39,70,73,118] and Breitung [3,39,70,73]. In the ADF and PP tests, the size of the coefficient δ<sup>2</sup> from the further equation should be established [58]:

$$
\Delta Z\_t = \delta\_0 + \delta\_1 t + \delta\_2 Z\_{t-i} + \sum\_{i=1}^n \beta\_i \Delta Z\_{t-i} + \|\varepsilon\_t\| \tag{3}
$$

where the variable Δ*Zt*−<sup>1</sup> depicts the first differences with *n* lags. ε*<sup>t</sup>* signifies the variable that adjusts the errors of autocorrelation. The coefficients δ<sup>0</sup> − δ<sup>2</sup> and β<sup>i</sup> are those estimated. The ADF regression checks for the occurrence of unit root of *Zt* in all model variables at time *t*. The null and the alternative hypothesis for the presence of unit root in variable *Zt* is depicted below:

$$H\_0 \colon \delta\_2 = 0 \quad H\_1 \colon \delta\_2 < 0 \tag{4}$$

Regarding the PP test, the equations and hypotheses are analogous to those of ADF, but the lags of the variables are left out from the models, as follows:

$$
\Delta Z\_t = \delta\_0 + \delta\_1 t + \delta\_2 Z\_{t-i} + \varepsilon\_t \tag{5}
$$

The LLC test presumes homogeneity in the dynamics of the autoregressive coefficients for all panel members, whereas the IPS test allows heterogeneity in dynamic panel and intertemporal data [1]. Breitung proposes a test statistic that does not apply a biased adjustment whose power is considerably higher than LLC or the IPS tests by means of Monte Carlo trials [70].

Moreover, several panel co-integration tests will be achieved, respectively Pedroni [1,7,39,70], Kao [70] and Fisher-type Johansen [8,56,61,73]. If the variables are cointegrated, there occurs a force

that converges into a long-run equilibrium [73]. Pedroni [120] advised the calculation of the regression residuals from the hypothesized cointegrating regression, as below:

$$y\_{i,t} = a\_i + \delta\_i t + \beta\_{1i} \mathbf{x}\_{1i,t} + \beta\_{2i} \mathbf{x}\_{2i,t} + \dots + \beta\_{\text{Mi}} \mathbf{x}\_{\text{Mi},t} + \quad c\_{i,t} \tag{6}$$

for *t* = 1, ... , *T*, *i* = 1, ... , *N*, *m* = 1, ... , *M*.

where *T* denotes the number of observations over time, *N* signifies the number of individual members in the panel, and *M* depicts the number of regression variables.

Kao [121] proposed a parametric residual-based panel co-integration, whereas Maddala and Wu [122] suggested the use of Fisher-type panel co-integration test via the methodology of Johansen [123] for the reason that the maximum-likelihood procedure has significantly large and finite sample properties.

After co-integration is settled, the long-run associations will be estimated via Fully Modified Ordinary Least Squares (hereinafter "FMOLS") and Dynamic Ordinary Least Squares (hereinafter "DOLS") in line with prior studies [1,14,39]. The FMOLS estimator produces consistent estimates in small samples and controls for the endogeneity of the regressors and serial correlation, whereas the DOLS estimator removes the second order bias triggered by the fact that the independent variables are endogenous [1]. Therefore, the causal relationships will be established, similar to earlier studies [7,51,58,61,70]. Thus, six tri-variate panel vector error-correction models (hereinafter "PVECM") for investigating the connection between FDI, each institutional quality measure and economic growth will be estimated:

$$(\mathbf{1} - \mathbf{L}) \times \begin{bmatrix} \text{GROWTH}\_{l} \\ \text{FDI}\_{l} \\ \text{I}Q\_{l} \end{bmatrix} = \begin{bmatrix} a\_{11} \\ a\_{21} \\ a\_{31} \end{bmatrix} + \sum\_{i=1}^{p} (\mathbf{1} - \mathbf{L}) \times \begin{pmatrix} \phi\_{1l} & \beta\_{1l} & \psi\_{1l} \\ \phi\_{2l} & \beta\_{2l} & \psi\_{2l} \\ \phi\_{3l} & \beta\_{3l} & \psi\_{3l} \end{pmatrix} + \begin{bmatrix} \theta \\ \phi \\ \xi \end{bmatrix} \times \text{ECT}\_{l-1} + \begin{bmatrix} \eta\_{1l} \\ \eta\_{2l} \\ \eta\_{3l} \end{bmatrix} \tag{7}$$

where *IQ* denotes the institutional quality variables, (1 − L) depicts the difference operator, *ECTt*−<sup>1</sup> signifies the lagged error-correction term that ensues from the long-run cointegrating connection, η1*<sup>t</sup>* − η2*<sup>t</sup>* exhibits the white noise serially independent random error terms. The occurrence of a significant association in first differences of the variables reveals the direction of short-run causality, whereas long-run causality is exposed by a significant t-statistic relating to the error-correction term (hereinafter "ECT") [58].

#### **4. Empirical Results and Discussion**
