Do you encourage your subordinates or employees to do self-appraisal periodically?

If deptt set goals quarterly basis then review is ok for quarterly basis bcoz It reflects the things staff did well and didn't do so well.

NO.

Half yearly.

In many public sector undertakings self appraisal is a must and I used to be part of it every year.  But in private, it is optional...Such compulsions/encouragements  were not formed a part of my career.  Any way we used to appraise them every quarter/half year basis and reward them with additional benefits.

That's right. Every subordinates should be display his performance to his superior. Finally the superior can be to meausure what the strong / weaknes his subordinates. I think better can do every 6 months. 

it is important to estabish "self-awareness" actually regardless if you consider or not. 

I used to let them do self-appraisal and found that all rated themselves as "Excellent" ! 

Yes it helps a person improve themself.

Yes, it is always beneficial to introspect, prioritise and keep at it.

Its inportant because nothing is contant except change, is what I believe in and for any goal you set for yourself requires this to make course correction as you set sail to achiev it!