Malmquist-Luenberger Productivity Indicator
Malmquist-Luenberger Productivity Index · Also known as: ML index, Malmquist-Luenberger index, ML productivity
The Malmquist-Luenberger (ML) Productivity Index combines concepts from the Malmquist index and Luenberger's directional distance functions to measure total factor productivity (TFP) change over time. It decomposes productivity growth into technical efficiency change and technological progress, enabling comprehensive productivity assessment without requiring specific functional form assumptions.
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When to use it
Apply the Malmquist-Luenberger index when assessing productivity changes over time in organizations or industries, particularly when undesirable outputs (emissions, waste) must be incorporated. It is especially useful in environmental economics, energy efficiency assessment, and sustainable performance measurement. Use it when you need to understand whether improvements stem from efficiency gains or technological advances, and when production functions are unknown or complex.
Strengths & limitations
- Incorporates undesirable outputs naturally (e.g., emissions, pollution), crucial for environmental productivity analysis
- Decomposes productivity into interpretable components (efficiency and technological change)
- Does not require knowledge of specific production function forms or prices
- Flexible directional vector allows focus on specific improvement dimensions
- Handles multiple inputs and outputs simultaneously
- Longitudinal comparisons provide clear productivity trajectories
- Computationally intensive, especially for large datasets or many periods
- Requires high-quality data; sensitive to measurement errors and outliers
- Can be difficult to interpret directional distance functions intuitively
- Assumes constant returns to scale unless variants are used
- Choice of directional vector can influence results significantly
Frequently asked
What is a directional distance function and why is it better than standard distance functions?
A directional distance function measures distance in a specified direction rather than radially. This allows simultaneous improvement in outputs and reduction in inputs in the direction most relevant to management goals, more realistic than radial projections.
How is the ML index different from the standard Malmquist index?
The standard Malmquist index uses radial projections and does not naturally handle undesirable outputs. The ML index uses directional distance functions, enabling incorporation of undesirable outputs like emissions, waste, or pollution directly in the productivity measurement.
What does an ML index value of 1.05 mean?
An ML index of 1.05 indicates 5% productivity growth between periods. If the efficiency change component is 1.02 and technical change is 1.03, then 2% comes from efficiency gains and 3% from technological progress.
How sensitive is the ML index to the choice of directional vector?
The directional vector choice can significantly affect results. Use vectors aligned with management objectives and industry norms. Sensitivity analysis should be conducted to ensure robustness of conclusions across plausible directional choices.
Sources
- Malmquist, S. (1953). Index numbers and indifference surfaces. Trabajos de Estadistica y de Investigacion Operativa, 4(2), 209-242. DOI: 10.1007/BF03006863 ↗
- Luenberger, D. G. (1992). New optimality conditions for stochastic control problems. Mathematics of Operations Research, 17(3), 657-663. link ↗
- Chambers, R. G., Chung, Y., & Färe, R. (1996). Benefit and distance functions. Journal of Economic Theory, 70(2), 407-419. DOI: 10.1006/jeth.1996.0096 ↗
How to cite this page
ScholarGate. (2026, June 3). Malmquist-Luenberger Productivity Index. ScholarGate. https://scholargate.app/en/operations-research/malmquist-luenberger-productivity-indicator