Malmquist productivity index
Separate catching up from movement of the frontier
The Malmquist index measures productivity change between periods through distance functions relative to production frontiers. A common DEA implementation decomposes change into efficiency change, or catching up, and technical change, or frontier movement. Orientation, returns-to-scale assumptions and reference technology affect interpretation; the index is a productivity measure, not simply a change in a single-period efficiency score.
Use when repeated input-output observations allow investigation of whether productivity changes reflect catching up or a shifting frontier. Units, variable definitions and technology comparisons must remain meaningful across periods.
Strengths
- Separates efficiency change from movement of the benchmark frontier
- Can be computed from quantities without observed input or output prices
Limitations
- Sensitive to measurement consistency and frontier outliers
- Cross-period distance problems may be infeasible under some specifications
Know the boundary
Productivity growth can occur without improved relative efficiency if the frontier itself moves.