Lean-Agile offers two productivity measures: Velocity and Throughput. It is possible to improve both over time but there is little point in management demanding that a development team improve either because both metrics are very simple to fudge.
There is also little point in using either of these productivity measures in product development. The focus is discovery not churning stuff out.
Where a productivity measure is useful is in a project or programme. Where somebody is wanting to know when the team will be finished. Or, conversely, how much functionality will be delivered before the time and/or money has run out.