My research question examines whether firms adopting fair value accounting for their 

pensions change their pension plan  assets. I was wondering if you could help me with the following 

quick questions about Coarsened Exact Matching.

1. What is the best practice for selecting the cut points? (I have read that Scott and Freedman-Diaconnis are the preferred methods.) 

2. My treatment sample is very small and using Scott or Freedman-Diaconnis leads  me to lose many treated firms. So I use deciles for certain matching variables instead of the Scott or FD.  Would this still be a concern if the imbalance is low? 

3. Is there a reasonable value for L1? I know that the lower value means less imbalance but is there a rule of thumb?

4. After creating a matched sample, are there any practical guides on how to run the regression? Some treated firms are matched with multiple control firms, and I believe that it is not a problem to run the regression even if some firms are matched with more control firms. Is there an issue if we don't have exact number of paired  treated and controlled firms?

Thank you so much for your time and consideration.

Kind Regards,

Pureum Kim