all my variables are integrated at 1st difference. both bond test and Johansen prove cointegration however ardl shows no long-run relationship among variables whereas VECM shows a long-run relationship. which one should I accept?
You need to check the nature of your data again. Once your variables are all of order 1 or I(1): you are require to conduct cointegrated test. If you have long run relationship, you are to proceed to run VECM but if short run you are to proceed to run VAR
There are many things that could have caused problems. The ARDL procedure is only valid if there is at most one cointegrating relationship. Any right-hand side I(1) variables are weakly exogenous, It sounds as if you have also estimated a VECM. If in any of the equations the ecm term is significant then the right-hand variable corresponding to that equation is not weakly exogenous. If this occurs in two or more of your equations then ARDL methodology is not valid. If, in particular your equilibrium equation corresponds to some economic theory I would be tempted to use the VECM methodology.
VECM model use data should co integrated I(1) different condition from ARDL method does not matter the variables
contained in the model is I (0) or I (1). Tests conducted by Pesaran (2001)
shows that the ARDL approach will produce consistent estimates
with long-term coefficients that are asymptotically normal, despite the explanation variables or regressor is I (0) or I (1), so that the result were different. Meanwhile, the model specification is also derived from different component of lag variables and method.
If your variables are all of order 1 or integrated at first difference then you should go for VECM.
When the order of integration of the variables is a mix of I(0) and I(1), ARDL is appropriate. Weak exogeneity and single cointegrating relationship is needed to validate ARDL analysis
Go for Johansen Co-integration since all the variables are significant at first difference I(1), indicating presence of long-run relationship. Since long-run relationship is confirmed, then estimate the Vector Error Correction Model(VECM)
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