What are typical insurance premium reductions for renters and owners as they earn instrument and commercial tickets?
(This is a US-based answer.) 

There's no statistical information that I could find out there about this, but aircraft type, total hours, hours in type, age, previous claims etc. are all factored into the premium as well, so it's hard to make a simple comparison based on one variable. And as AOPA says:


  Not all carriers have the same guidelines for when they will offer a
  premium reduction.


But having said all that, it looks like an instrument rating is the key qualification to get. AOPA's insurance FAQ recommends it:


  Typical actions you can take to reduce your rates include:
  
  [...] Obtain an instrument rating.


I guess you could go through AOPA's quote process multiple times with different data to see what premiums come out, but just calling them is probably easier.

Avemco is a well-known aviation insurer and they're more specific. The wording is bit awkward but it looks like an instrument rating reduces your premium with them by 10%:


  Q: Is there any type of additional training that would lower my premiums?
  A: [...] obtain an upgraded certificate or Instrument
  Rating and you become eligible for the full 10% savings.


They don't say what an "upgraded certificate" means, but if you're one of the few people who have a commercial certificate but no instrument rating then perhaps that would count. Other insurance companies also say that advanced ratings can reduce your rates (here, here).

Finally, I can add a couple of comments from personal experience. I have AOPA renter's insurance and it's flat rate: your certification and experience don't matter at all. Second, when I was looking for life insurance, having an instrument rating cut my premiums a lot but it was a while ago and I can't remember the exact numbers. I do remember that they were reluctant to even consider me without it.