Dear Gianluca,

When there is a shock to X on Y, the actual effect that you will obtain is a joint effect taking into account the direct and inderect effect (through Z) on this variable. One way to look for the pure direct effect of X on Y, you can "switch off" the channel through Z affect Y, by restricting your VAR to a SVAR. This way is like a counterfactual exercise.Then the difference between the total effect (regular IRF) and the direct effect computed (Restricted IRF, counterfactual) is your indirect effect through the Z channel.

Some papers you can see are: 

Monetary Policy Transmission through the Consumption-Wealth Channel (Ludvigson, Steindel, Lettau), 

Policy transmission and the consumption-wealth channel (Siokis)

I hope it'll be useful for you.

Best regards,

Dear Sebastian,

thanks a lot for your reply. I am gonna check the references you suggested as well as the theory of IRFs more in details.

Hope to figure it out.

Best Regards,

Gianluca

Dear Gianluca,

in order to see the indirect effect of any variable on the other through anintervening variable, mediation analysis can be done. here u have to first estimate the effect of X on Z and take the estimated value of Z and then use that estimated Z as one of the independent variables to estimate Y in the second regression. in this way the coefficient of this estimated Z in second regression will give you the indirect effect of X on Y through Z .

Regards,

Iffat

Dear Iffat,

thanks a lot for your reply.

Do you have any reference about this? Any example of an application?

Thanks a lot.

g

Dear Gianluca,

I am not sure, but maybe the attached link can be useful for you.

Regards,

Ehsan

http://www.sciencedirect.com/science/article/pii/S2212567116300648

Dear Ehsan,

thanks a lot for your suggestion. Although, it does not seem applicable to the research topic I have mind.

Kind Regards,

Gianluca