Basu can you elaborate!

I think I just have to take log, Subrata Chakraborty. If you know the answer to my new question, it will be helpful. The new problem is this: I have same percentile distribution for my dependent variable until 90 percentile for both years for the treatment group. Is it ok to continue with difference-in-differences model?

I would also like to know more about the application.  What exactly is the response variable, and what are the main goals in your study?  Which statistical modeling and analysis have you chosen, and why?

If you are doing regression using continuous data, then scatterplots might be helpful in determining if what you are doing is correct. I do not understand your question(s), but perhaps you are saying there may be nonlinearity?  If so, then scatterplots could help you to investigate.  You could also investigate the estimated variances of the prediction errors.