Malmquist Productivity Index
Also known as: MPI, Malmquist Index, Malmquist DEA Productivity Index, Malmquist Verimlilik Endeksi
The Malmquist Productivity Index (MPI) is a non-parametric measure of total factor productivity (TFP) change over time. Formally grounded in distance functions by Caves, Christensen, and Diewert (1982) and operationalized using Data Envelopment Analysis by Färe, Grosskopf, Norris, and Zhang (1994), MPI decomposes productivity growth into two components: efficiency change (catching-up to the frontier) and technical change (shift of the frontier itself).
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When to use it
Use MPI when you have panel data on multiple DMUs (firms, hospitals, schools, countries) observed across at least two periods and wish to decompose TFP change without imposing a parametric functional form. Key assumptions: production sets are convex and freely disposable; DMUs are comparable in inputs and outputs. MPI is preferable to parametric TFP indices when functional form is uncertain. Limitations include sensitivity to outliers, inability to handle negative values, and the need for balanced panels. Alternatives include stochastic frontier analysis when a statistical noise separation is required.
Strengths & limitations
- Requires no price data or behavioral assumptions such as cost minimization or profit maximization.
- Decomposes TFP change into economically meaningful components: efficiency change and technical change.
- Non-parametric approach avoids misspecification of the production function.
- Applicable to public-sector entities (hospitals, universities) where market prices are absent or distorted.
- Sensitive to extreme observations because DEA frontiers are piecewise-linear and outlier-driven.
- Cannot separate statistical noise from genuine inefficiency — all deviations from the frontier are attributed to inefficiency.
- Requires balanced panel data; missing observations across periods complicate the analysis.
- Distance function computations may be infeasible when the observed point lies outside the reference-period frontier, yielding undefined ratios.
Frequently asked
Does MPI require price data for inputs and outputs?
No. One of MPI's principal advantages over index-number approaches such as the Törnqvist index is that it relies entirely on quantity data. Distance functions are estimated from observed input-output quantities via DEA linear programs, making MPI suitable for regulated industries and public services where market prices are unavailable or distorted.
What does an MPI value of 0.95 mean?
An MPI of 0.95 indicates a 5% productivity decline between the two periods. This can be further decomposed: for example, if EC = 1.02 and TC = 0.93, the unit improved its efficiency relative to the frontier (caught up by 2%) but the frontier itself regressed by 7%, resulting in net productivity loss.
How many DMUs and periods are needed for a reliable MPI analysis?
A common DEA rule of thumb requires the number of DMUs to be at least three times the sum of input and output counts. For MPI, you need a minimum of two time periods; more periods enable Luenberger or sequential MPI extensions. Fewer than 15–20 DMUs per period tend to produce very coarse, unstable frontiers and should be avoided.
Sources
- Färe, R., Grosskopf, S., Norris, M., & Zhang, Z. (1994). Productivity growth, technical progress, and efficiency change in industrialized countries. American Economic Review, 84(1), 66–83. link ↗
- Caves, D. W., Christensen, L. R., & Diewert, W. E. (1982). The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica, 50(6), 1393–1414. DOI: 10.2307/1913388 ↗
How to cite this page
ScholarGate. (2026, June 2). Malmquist Productivity Index. ScholarGate. https://scholargate.app/en/efficiency-analysis/malmquist-productivity-index
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