Monthly data regarding the variable inflows of foreign direct investment (FDI) (Million USD), exports (EXP), exchange rate (EXR) and industrial production (IND) are taken from the Central Bank of Turkey (CBT). All the variables including dependent and independent variables used in this study are in real form; EXP is constant at 2010 USD prices, EXR is constant at 2003 USD prices and IND is constant at 2015 USD prices. The variable FDI is measured by real FDI adjusted by CPI and then was converted into log form. The Data description and source, descriptive statistics of the variables, Graphs, correlation table, which are included in the empirical model, are presented in the table below.
This study intends to analyze the influence of exchange rate (EXR) and exports (EXP) on the economic growth (IND) in Turkish economy over the period of 2010 to 2018 by employing the ARDL Bound testing and also intends to find out the causal links between these variables by using Granger causality test. The foreign direct investment (FDI) has been taken as control variable. Industrial production has been used as a proxy for real economic growth in Turkey.
Here, we lay our discussion about the relevant methods utilized for conducting of this paper. Which include the unit root tests and bounds test for cointegration and causality within the ARDL modelling approach. This model has been developed by Pesaran et al. (2001); and can be applied without considering the order of integration of the variables (whether regresses are purely I (0), purely I (1) or mutually co-integrated). This is particularly linked with the ECM models that are called VECMs.
In ARDL model normally first step is determining the order of integration of each variable because it uses the variables at the level which they are stationary Shabbir and Muhammad (2019). For testing the stationary of the series, the paper uses the Augmented Dickey Fuller (ADF) unit root testing procedure (Dickey and Fuller, 1979). In the ADF test, we want to determine the size of the coefficient δ2 in the following equation:

The ADF regression tests for the existence of unit root of Zt, in all model variables at time t. The variable ΔZt−1 shows the first differences with n lags and final εt is the variable that modifies the errors of autocorrelation. The coefficients, δ0, δ1, δ2, and βi are estimated ones. The null and alternative hypothesis for the presence of unit root in variable Zt is as follow:
H0: δ2 = 0, H1: δ2 < 0
3.1 Testing for Granger causality in the Bounds test approach
In this study we carry out the Bounds test to evaluate the existence of causality between exports, exchange rate, and economic growth in Turkey. The model for the relationship between export, exchange rate, and economic growth carried out in this paper is defined as: INDt = f (EXPt, EXRt, FDIt) in which INDt, EXRt, and FDIt represent net export, exchange rate, and foreign direct investment. The following equations are the error correction models estimated under the ARDL Bounds testing methodology:
INDt = α11 + δ12 INDt−1 + δ13EXPt−1 + δ14EXRt−1 + δ15LFDIt−1 + Σ φ1iINDt−i + Σ β1iEXPt−i + Σ ψ1iEXRt−I + Σϒ1iLFDIt−i + εt (2)
EXPt = α21 + δ22 INDt−1 + δ23EXPt−1 + δ24EXRt−1 + δ25LFDIt−1 + Σ φ2iINDt−i + Σ β2iEXPt−i + Σ ψ2iEXRt−i + Σϒ2iLFDIt−i+εt (3)
EXRt = α31 + δ32 INDt−1 + δ33EXPt−1 + δ34EXRt−1 + δ35LFDIt−1 + Σ φ3iINDt−i + Σ β3iEXPt−i + Σ ψ3iEXRt−i + Σϒ3iLFDIt−i + εt (4)
LFDIt = α41 + δ42 INDt−1 + δ43EXPt−1 + δ44EXRt−1 + δ45LFDIt−1 + Σ φ4iINDt−i + Σ β4iEXPt−i + Σ ψ4iEXRt−i + Σϒ4iLFDIt−i + εt (5)
Where α11, α21, α31, and α41 are constants for the four equations. We can test for cointegration among INDt, EXPt, EXRt, and LFDIt using the Bounds test approach. For Eq. (2), (3), (4), and (5) the F-test (normal Wald test) is used for analyzing one or more long run relationships. Where for one or more long run relationships, the F-test specifies which variable should be normalized Saleem et al, (2019) and (Koop, 2005).
In Eq. (2) in which INDt is the dependent variable the null hypothesis of no cointegration is H0: δ12 = δ13 = δ14 = δ15 = 0 and the alternative hypothesis of cointegration is H1: δ12 ≠ δ13 ≠ δ14 ≠ δ15 ≠ 0. In Eq. (3) the null hypothesis of no cointegration is H0: δ22 = δ23 = δ24 = δ25 = 0 and the alternative hypothesis of cointegration is H1: δ22 ≠ δ23 ≠ δ24 ≠ δ25 ≠ 0. In Eq. (4) the null hypothesis of no cointegration is H0: δ32 = δ33 = δ34 = δ35 = 0 and the alternative hypothesis of cointegration is H1: δ32 ≠ δ33 ≠ δ34 ≠ δ35 ≠ 0. Lastly, in Eq. (5) the null hypothesis of no cointegration is H0: δ42 = δ43 = δ44 = δ45 = 0 and the alternative hypothesis of cointegration is H1: δ42 ≠ δ43 ≠ δ44 ≠ δ45 ≠ 0. If the calculated F-statistic is less than the lower critical bound, then hypothesis of no cointegration might be accepted. However, if the calculated F-statistic outreaches the upper critical bound then there might be Cointegration. In addition, the long run relation would be unresolved if the calculated F-statistic lies between the lower and the upper critical values.
After demonstration of cointegration then there has to be at least a uni-directional causality. Granger causality existence implies the presence of cointegration between variables which provides information regarding long run and short run Granger causality. For empirical aims, the error correction representation can be derived from the VECM Granger method provided as follow:
│ INDt │ │α11│ n │φ1i β1i ψ1i ϒ1i │ │ ϴ │ │η1t │
│ EXPt │= │α21│ + Σ (1-L) │ φ1i β1i ψ1i ϒ1i │ + │ ϖ │ (ECMt−1) + │ η1t │
(1-L) │ EXRt │ │α31│ n=1 │ φ1i β1i ψ1i ϒ1i │ │ ϛ │ │ η1t │
│ LFDIt │ │α41│ │ φ1i β1i ψ1i ϒ1i │ │ ϣ│ │ η1t │
In which (1 − L) is the difference operator, ECMt−1 is the lagged error correction term which is developed from long run co-integrating relationship while η1t, η2t and η3t are white noise serially independent random error terms.
INDt = α0 + Σ α1iINDt−i + Σ α2iEXPt−i + Σ α3iEXRt−i + Σ α4iLFDIt−i + Σ βECTt−1 + εt (6)
If the first difference of variables shows a significant relation it is an evidence for the direction of short run causality; whereas, long run causality is represented through a significant t-statistic concerning to the error correction term (ECMt−1). Error Correction model specification is a combination of short run equations and long run representation: