Here's what I have (year is production year based on serial number)
2001 - rifle - 22lr sportster - has partial serial number engraved on barrel,
--------shotgun - 12 ga pardner - no engraving
2002 - rifle - 22mag sportster - has partial serial number engraved on barrel,
--------shotgun - 20 ga ultra - no engraving
So based on mine and others experiences, rifle get enscribed, shotguns/muzzy's don't. As a rule.
later,
scruffy