Hello,

I am a PhD student and I am planning to apply natural experiment methods (I have a proper shock date and also cut-off point) and I have several questions.

I am going to evaluate the impact of shocks on some types of firms (three groups) and although two of them have the same feature (X and Z), the third firm (Y) has a different feature (in the same sector but does not have all the variables like the other firms such as although other firms collect deposits from customers this firm does not so does not have a total deposits and also I cannot employ cut-off points for this firm due to not having one variable (total deposits etc.) which is necessary to employ cut-off).

This firm and one of the other firms are in the control group which are not affected by the shock. So in the control group, there will be two firms (X, Y) and in the treatment group just one firm (Z). Due to not being competent about the natural experiment methods, I am worried about whether or not I may employ both difference-in-differences (DID) and also regression discontinuity (RD) methods for these firms under this conditions. So my questions are;

* Is it possible to employ DID method for these three firms? If it is possible could you please tell me how (Is propensity matching score applicable or any method suggestion)?

* Is the number of the firm in the three groups of firms is important for pre-treatment balance and application of DID and RD methods? In the X group, there are 500 firms, in the Z group there are only 10 firms or less and in the Y group, there are over 8000 firms.

* Is pre-treatment balance main assumption of DID and RD?

* Should all the variables need to be available for all firms? If it is not possible having the same variables for all type of firms is there any way to solve this issue?

* If DID and RD is not proper method under these conditions any method suggestion?

I very much appreciate if you can answer my questions.