Window Data Envelopment Analysis
Also known as: Sliding-Window DEA, Temporal DEA, Rolling-Period DEA, Pencere VZA
Window Data Envelopment Analysis (Window DEA) is a non-parametric panel efficiency method that evaluates decision-making units (DMUs) over time by embedding each DMU's observations across a rolling temporal window into a single cross-sectional DEA problem. Introduced by Charnes, Clark, Cooper, and Golany in 1984, it enables longitudinal efficiency tracking without requiring a full panel, increasing discriminatory power by pooling observations across consecutive periods.
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When to use it
Use Window DEA when you have panel data with relatively few time periods or DMUs, and you need to track efficiency change over time without imposing parametric assumptions. It is appropriate when a Malmquist index cannot be computed due to infeasible inter-period projections. Key assumptions: constant or variable returns to scale, isotonicity of inputs and outputs, and that the production technology is stable within each window. Limitations include sensitivity to window width choice, inability to decompose efficiency change into technical change and catch-up (unlike Malmquist), and inflated effective sample sizes that may mask real frontier shifts.
Strengths & limitations
- Increases discriminatory power by pooling DMU-period observations without requiring large cross-sections.
- Enables longitudinal efficiency tracking under the familiar non-parametric DEA framework.
- Provides multiple scores per DMU-period, allowing robustness checks across overlapping windows.
- Applicable even when inter-period linear programming problems are infeasible, unlike Malmquist-based approaches.
- Window width w must be chosen subjectively; results can be sensitive to this choice.
- Cannot decompose efficiency change into technical change and pure efficiency change without additional structure.
- Pooling periods assumes stable technology within the window, which may be violated during structural breaks.
- Computational burden grows with the number of DMUs, periods, and window widths, though it remains tractable for moderate panel sizes.
Frequently asked
How do I choose the window width?
There is no universally optimal rule. Common practice sets w between 3 and 5 periods, balancing reference-set richness against the assumption of technological stability. Sensitivity analysis by running models with several window widths and comparing score distributions is recommended before reporting final results.
How does Window DEA differ from the Malmquist Productivity Index?
Both handle panel data, but the Malmquist index decomposes productivity change into technical efficiency change and frontier shift using inter-period LP problems, which can be infeasible. Window DEA avoids inter-period projections entirely by pooling observations, making it more robust when the data are sparse, but it cannot provide the same decomposition.
Can Window DEA handle variable returns to scale?
Yes. Adding the convexity constraint (sum of λ equals one) to the linear program in each window converts the CRS model to the VRS model of Banker, Charnes, and Cooper (1984). The choice between CRS and VRS should be guided by economic reasoning about scale efficiency in the application domain.
Sources
- Charnes, A., Clark, C. T., Cooper, W. W., & Golany, B. (1984). A developmental study of data envelopment analysis in measuring the efficiency of maintenance units in the U.S. Air Forces. Annals of Operations Research, 2(1), 95–112. DOI: 10.1007/BF01874734 ↗
How to cite this page
ScholarGate. (2026, June 2). Window Data Envelopment Analysis. ScholarGate. https://scholargate.app/en/efficiency-analysis/window-dea
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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