As the initial step for the VECM estimation, the existence of unit root in each underlying variable is assessed by both the Augmented Dickey-Fuller (ADF) test and the Phillips and Perron (PP) test. After confirming that all underlying are I, we perform the Johansen cointegration test to check whether there is a cointegrating relationship among underlying variables so that the number of cointegrating vectors (r) is determined. For avoiding autocorrelation in estimation, we properly allocate: SGD (the shock in economic growth dummy) which takes the value of one for negative EG growth periods otherwise zero; SFD (the shock in financial development dummy) which is one for negative FD growth periods, otherwise zero; and SFCD (the shock in financial crisis dummy) which takes the value of one for positive FC growth periods otherwise zero. Moreover, PCD is the pre-crisis dummy that takes the value of one for 1990Q1 to 1990Q4 and zero for other periods in India’s analysis. For the other four countries, PCD is not included. Finally, the allocation of SBGD (the structural break in economic growth dummy) is discussed below in Bai and Perron test. Stock Market
For giving interference, two types of the causality test are conducted. The first test is the weak exogeneity test in which the null of H0: aj = 0. Indeed, the weak exogeneity test calculates the significance of the ECT coefficient and thus presents the evidence of long-run causality. The second test is the strong exogeneity test that imposes the strongest restriction of H0: all Oij’s = aj = 0 in each VECM. Although not distinguishing between the short-run- and long-run causalities, the strong exogeneity test indicates the overall causality in the system. More weight is put on the strong exogeneity test results, and the two tests are based on chi-square statistics from the Wald test. The cointegration test of Johansen is based on a restrictive assumption that all the underlying variables are integrated of order one or I. This assumption is crucial since a mixture of I and I regressors makes standard statistical inference invalid. On the other hand, the ARDL estimation suggested by Pesaran et al. can be applied even if underlying variables have different orders of integration.
The ECT in Equation 9, for example, takes the form of: ECT = p41EGt + p42FDt + p43FCt + P44FR + P45SGDt + p46PCDt + p47SBGDt + inpt. The ARDL estimation provides (p +1) number of regressions where p is the maximum number of lags to be used and k is the number of variables in the ARDL equation. At the first stage, we need to conduct the bounds test — the counterpart of the Johansen cointegration test — that computes F-statistics to confirm the existence of long-run cointegrating relationships between the underlying variables irrespective of whether those variables are I or I (Pesaran and Pesaran, 2009). At the second stage, the optimal lag order for each variable is set. We look for the optimal lags by referring either to the Akaike information criteria (AIC) or to the Schwartz-Bayesian criteria (SBC). Finally, both the weak- and strong exogeneity tests, which are suggested in the VECM analysis, are carried out for each ARDL model.