Hello, I have 6231 household data as a total number of observations of which 351 of them are classified as the treatment groups and I utilize PSM to estimate the impact of the social assistance program. The PS graph shows the propensity score histogram on treated individuals has a very diverse score between 0 to almost 1. On the contrary, most of the untreated individuals have a very low probability close to 0. I have the following questions:
1. Does it mean I still have sufficient common-support to estimate the ATE or ATT?
2. Could I still use the nearest neighbor matching, kernel, or radius matching to estimate ATE or ATT?
3. Shall I drop some observations to find a good match (balanced ps score histogram for both groups treated on and untreated) before proceed to check to balance and estimate ATE, ATT? If so, kindly let me know how can I choose the relevant unit of observation?
Thank you.

Regards,

Gede Heprin