I don't think the concept of productivity can span multiple fields. Does a C programmer have the same productivity as a Ruby programmer? On the other hand, maybe some part of a Ruby project needs optimizing, so a routine is written in C. Maybe there can be a definition of productivity that crosses languages... but we don't have one yet.
So I would choose to politely disagree. You can measure productivity.
Am I negatively productive under your measures?
1. Familiarity with the library set / language
2. Familiarity with the problem space
3. Familiarity and speed with tools/programming environment
4. Research speed (and research tools/materials)
5. Mental Program structural planning speed
6. Previous Experience with the specific problem
7. Knowledge with time saving programming structures
8. Skill with mathematics and algorithms
9. Computer Hardware & Internet Connections
10. Ability to choose the best tools for the job
11. Learning speed
12. Motivation, energy, ability to concentrate for long periods of time
And that's listing mostly external factors that are somewhat obvious, not some less obvious speed of mental thinking or something similar.
You can define developer productivity as speed to complete an identical project compared to another and the quality/maintainability/readability of the software they produce to match the project requirements.
Now back to Terminal and vi so I can be productive again...
Part of my point was, though, that nobody should need to do an objective study. :) Because it's pretty frickin obvious to anybody with a brain who works in the field, in my judgment. And it's not limited to our field. It's a human-wide phenomenon.