Why don't you try the VAR model? The Granger Test might be of some assistant too.

You may use instrumental variables, panel data methods or experiments

Granger causality test - if you google that you will come up with plenty of information.

To all,

Thank you very much for valuable suggestions

Yes, Granger Causality Test is the appropriate.

You should run the Granger Causality test. It can be run on both time series and panel data sets.

Granger causality test is appropriate to test bidirectional relationships but you have to study the stationarity of your series first.

Please be also aware of the integration status of the variables when using the Granger causality test, in fact a VECM framework may be more appropriate both in time series and panel approaches