As is often the case, we're assessing the methodology by looking at our own data, which we know best. We see that only 25% of our (still operational) projects have a budget in 2018. It's somewhat better in 2017, but still much lower than we'd expect.
One fairly obvious issue is that most projects involving multilateral organisations would be front-loaded: we'll pay most if not all the money at the beginning of the project. So it's normal that these projects would not have budgets in outer years. I think this is fairly standard when dealing with multis. In our case, filtering projects by the type of partner or type of collaboration would probably exclude most of these instances. Have you tried this kind of approach?
We also wondered if comparing the total commitment with the amounts already paid (disbursements and expenditures) might help exclude the front-loaded projects. Let's say, if the total disbursments are within 10% of the total budget (allowing for some hold-back amount to be paid at closure - again, fairly standard procedure), then we'd consider that the full budget has been paid and would exclude this project from calculations.
This would not deal with all the problematic cases, but some.
The other question is: have you tried using planned disbursements instead of budgets? After all, planned disbursements are more dynamic and better reflect the actual state of the project.
We're still looking into our data, will let you know if other ideas emerge.