I've helped half a dozen organisations implement a PM competency framework, although there are some good public examples (here179 and here107) Product Management is very contextual and in my experience you are far better off investing the time to define what it means to be a PM in your organisation.
Here's an overview of the process I typically take clients through to construct a competency framework within their organisation.
Step 1: Define the career ladder for a PM in your org
This step is usually the easiest. Begin by simply mapping out the PM levels that you currently have - do you have APMs? Senior PMs? Group PMs? etc. Begin by simply mapping out what exists today, don't worry about whether you should or shouldn't have certain roles just yet.
Once you've got those now start to consider what levels you may want to add either now or in the not too distant future. Best to start to forward plan with these things.
In the end you should have something like this.
Notice that there is a split between what I've called 'Team Contributor' (thanks John Cutler for that naming73) often referred to as an 'Individual Contributor' and people-management. This is because of the 'Peter Principle65' and the fact that people management is a different skill and not suited for everyone.
The idea behind splitting the two tracks is to allow people to remain as a 'Team Contributor' (akak doing what they're good at) and still have a career path as opposed to hitting a glass ceiling because they are not suited to or don't want to become a people manager.
Step 2: Brainstorm competency themes/areas
The second step is to brainstorm the competency areas you want your framework to have. You can do this by simply brainstorming themes or by doing some synthesis/groupings from a skills brainstorm.
This is a great activity to start to involve your peers, or if you're a Product Leader to do with your team.
You might end up with something that looks like this:
Step 3: Decide on you competency themes and plot your matrix
Next is to distill those themes down into a concise set that you will use across your competency framework.
It's up to you how many themes you have but remember that each theme will break down into specific skills so there is an element of "less is more" - you don't want to have a 20 page competency framework but equally you don't want to have a list of only 5 skills.
Once you've decided on the themes that you wanted now is the time to build out your matrix. Plot the themes down one axis and your roles across the other.
Might look something like this:
Step 4: Fill out your matrix
The final step is to then break down each competency theme/area into skills across the spectrum of different levels of PM in your company.
Now is the time to start to decide if you want there to be a 1:1 mapping of roles = levels or whether you want to have a many to one. There's no right or wrong on this - I've done both - it will be more dependent on how nuanced you want/need the levels and skill break down to be.
If you haven't involved a wider group until now, this is the time. Building out the details of what is expected for each level in each competency area is important that everyone has a say in this. That you generate buy-in and allow for disagreements and discussion to happen. This is where you will iterate and really strengthen your competency framework.
Finally don't try to make it perfect as you will add, modify and remove things over time as your company and team grows.
In the end you'll have something that looks similar to this.
Note: You'll notice that in that example above the VP of Product and I decided to add two levels for both PM and Senior PM. This was because they have the most PMs and Senior PMs having a bit more nuance between those who recently got promoted to Senior vs those who have been there for a while and those who are getting close to being promoted to PM vs more junior people was something we thought made sense for there context.
Compare that to the 'People leader' track and since the company is still growing there are actually only currently 3 Product Leaders in the org thus a 1:1 mapping felt more appropriate for now, doesn't mean it wont change in the future. In fact, going back to thinking forward we had added in the Director of PM level in there as they're growing rapidly and believe we'll be needing to introduce that role soon.
Step 5: Formalise it
Your end result will typically end up in a more formal format, typically as tables in a doc or as a spreadsheet. However for the previous steps, the crafting, I prefer the flexibility of post-it notes - easier to move things around, add levels, remove levels, etc.
And that's it.
It can be a long process, especially as you dive into the details of what each skill-level looks like and discussing it as a team but in my experience the clarity and ability to facilitate career conversations and goal setting is well worth the effort.
I've talk with too many PMs who have little-to-no clarity on the career paths within their company and what they need to do to get to the next level (and have experienced this myself). Solving that problem makes these frameworks worth their weight in gold.