The article is based on quarterly time series data obtained from Turkish Statistical Institute (TURKSTAT) and the Central Bank of the Republic of Turkey (CBRT) that covers the period from 2004:Q1 to 2015:Q4. The GDP of health and social services (HGDP) is used as a proxy variable for economic growth of the health sector, which is reported in TRY constant prices. The second variable, inbound tourism flow (HTOUR), shows the tourism demand of international visitors to Turkey for the purpose of health or for medical reasons for a period of less than a year. The third variable is real exchange rate (RER) and it is used a proxy variable in order to test the effects of relative price changes. All variables are expressed in logarithm forms and seasonally adjusted. The following model was used to investigate the relationship between inbound tourism demand and health sector growth.
$$\ln htour_{t} = \alpha_{0} + \alpha_{1} \ln hgdp_{t} + \alpha_{2} \ln rer_{t} + \alpha_{3} u_{t}$$
(1)
In this study, the Granger causality test is employed to investigate causal relationships between health GDP, inbound health tourist flow, and real exchange rate. Granger introduced the concept of Granger causality in 1969 and it has been widely used in econometric studies to test availability and the direction of the causality (Granger 1969). Furthermore, Johansen’s cointegration analysis is employed to determine any long-term relationship between the variables before the causality test.
The first step in time series analysis is to investigate the stationarity of variables, also called the unit root test. Accordingly, the existence of a unit root at frequency zero would imply that the stochastic trend is non-stationary (Torraleja et al. 2009). Gujarati and Porter (2009) point out that it is so often to meet non-stationary time series and the estimates of non-stationary variables will lead to spurious regression. Thus, their economic interpretation will not be meaningful. Furthermore, unrelated time series may appear to be related using conventional testing applications such as ordinary least squares regression. To this end, we utilise the Augmented Dickey–Fuller test (ADF), and the Phillips–Perron test (PP) to examine whether the data are non-stationary (Dickey and Fuller 1981; Phillips and Perron 1988).
The augmented Dickey–Fuller (ADF) unit root test is one of the most accepted and widely used tests to investigate the stationarity of series (Park et al. 2016). The following equations are estimated for each of the time series (Gujarati and Porter 2009):
$$\Delta Y_{t} = \beta_{1} + \beta_{2} t + \delta_{0} Y_{t - 1} + \alpha_{i} \mathop \sum \limits_{i = 1}^{m} \Delta Y_{t - i} + \varepsilon_{t}$$
(2)
where \(\Delta\) is the first difference operator, t is the time trend, k denotes the number of lags used, and ɛ is the error term. β, δ and α are parameters. The null hypothesis that series Y
t
is non-stationary can be rejected if δ
0 is statistically significant with negative sign (Huarng et al. 2006). In addition, m shows the optimal lag order, which is chosen carefully using the Schwarz criterion (AIC) in empirical method.
Another stationarity test, the Phillips–Perron (PP) unit root test, is a complementary feature of the ADF unit root test. The ADF test on the distribution of the error term is assumed to be statistically independent and constant variance. In the PP test, autocorrelation is considering changing the condition of the conditional variance of the error term that also means a more flexible assumption (Phillips and Perron 1988).
Regression analysis based on time series data implicitly assumes that the underlying data is stationary (Gujarati and Porter 2009) and it is usually the case that time series variables of macro economy are non-stationary. Alternatively, cointegration analysis allows for spurious results to be avoided by using non-stationary data, but all those series have to be integrated into the same order. Despite the range of different cointegration tests in the literature, the Engle–Granger (Engle and Granger 1987) and Johansen (1988, 1991) tests are widely used. In this study, the Johansen cointegration test is employed to test the existence of a long-run equilibrium relationship among the variables.
Following the suggestion of Granger (1988), the Granger causality test is implemented in the equations below:
$$\Delta \ln htour_{t} = \alpha_{1} + \sum\limits_{i = 1}^{p} {\beta_{1i} } \Delta \ln htour_{{t{ - }i}} + \sum\limits_{j = 1}^{q} {\beta_{2i} } \Delta \ln hgdp_{t - j} + \sum\limits_{l = 1}^{r} {\beta_{3i} } \Delta \ln rer_{t - i} + \varepsilon_{1t}$$
(3)
$$\Delta \ln hgdp_{t} = \alpha_{2} + \sum\limits_{i = 1}^{p} {\gamma_{1i} } \Delta \ln hgdp_{{t{ - }i}} + \sum\limits_{j = 1}^{q} {\gamma_{2i} } \Delta \ln htour_{t - i} + \sum\limits_{l = 1}^{r} {\gamma_{3i} } \Delta \ln rer_{t - i} + \varepsilon_{2t}$$
(4)
$$\Delta \ln rer_{t} = \alpha_{3} + \sum\limits_{i = 1}^{p} {\delta_{1i} } \Delta \ln rer_{{t{ - }i}} + \sum\limits_{j = 1}^{q} {\delta_{2i} } \Delta \ln htour_{t - i} + \sum\limits_{l = 1}^{r} {\delta_{3i} } \Delta \ln hgdp_{t - i} + \varepsilon_{3t}$$
(5)
where ln is the natural logarithm, \(\Delta\) is the first difference operator, p, q, r denote the number of lagged variables, ɛ
it
are error terms that are assumed to be normally distributed and white noise.