1. There is no objective measure of productivity that can be applied to software development.
2. Accurate estimation of development times is impossible (not difficult, actually theoretically impossible). All estimates of development times are wrong, some by more than an order of magnitude.
The second one is especially hard to grok for non-techies. I have to explain that if you insist on accurate estimates, you will get grossly padded estimates [0]. And the work will expand to fit the time available (sometimes resulting in the task exceeding even the massively padded estimates because the work expanded with the estimate). I've had many entertaining conversations attempting to explain this.
[0] Because every developer knows that an estimate will magically become a deadline.