Does Quantitative Easing directly influence M1 or M2? If so, why?

An in-depth explanation of whether QE affects either one would be greatly appreciated.

What impact evaluation method will be most suitable to serve this analytical purpose? Why?

I have the choice of Propensity Score Matching, Regression Discontinuity and Panel Data Methods. I am leaning towards panel methods, but I am unsure.

Thank you!