I don't wear a tie and neither does anyone else where I teach. I used to work somewhere where everyone wore ties but most of the instructors there were only interested in moving into airlines not in being instructors. Where I am now, everyone wants to instruct, there's no gold braid and the students get excellent service from a very professional team who are committed to teaching PPLs.
I asked all the students that I met this week what they thought and several said that they had visited other airfields and chose us because we seemed to have a passion about flying and a practical approach - not one thought that we would be better instructors if we wore ties. I then asked a colleague who works somewhere where they had to wear ties - and all his students said that they didn't care whether their instructors wore ties as long as they cared about their students and were professional in their approach to flying and teaching.
Not scientific research, I know - but maybe all the people who are adamant that ties make them look better should seek their students' opinions.