How to deal with violation of common support with not-normally distributed data in PSM model?

[Ahmad zaky Ismail]

During my research analysis with internet access as the independent variable and household net worth as the dependent variable, there are several problems that I encounter: 1. There was a significant mean difference between the treated and untreated groups in my PSM model 2. The average bias reduction after matching using NN, Kernell, and Radius is both high (eg before 50 match and after 7 match 3. When I did a kdensity plot using pscore, it was found that there was a general support assumption violation With all these caveats added with the following notes: 1. I'm using Stata 17 with PSMATCH2 package to do PSM regression 2. There is an imbalance in the distribution of the sample in the independent variables (70% are not exposed to the internet and 30% are exposed to the internet 3. I used the Indonesian Family-Life Survey (IFLS) wave 5 which makes my research cross-sectional in nature 4. I have used many countermeasures to force the data distribution to be normally distributed (using the log function, omit variables that have extreme values) 5. I have included many control variables (10 variables): household demographics, characteristics, household characteristics, and community or region characteristics With all that said, how should I solve the problem and make my PSM model more robust?