It's best to give up the idea of measuring software productivity entirely. Almost no one would seriously wonder how to measure artistic productivity and software engineering is a lot more like art than most people realize because it is fundamentally a creative activity.

Software is also too abstract to be measured the same way assembly line productivity is measured so there is no point in trying to impose a metric based productivity framework on top of software engineering. It's unlikely any such effort will be successful or will lead to any positive outcomes.