Bootstrap DEA: Bias Correction and Confidence Intervals for Efficiency Scores
Bootstrap Data Envelopment Analysis · Also known as: Bootstrapped DEA, DEA Bootstrap Inference, Simar-Wilson Bootstrap, Bootstrap Sınır Analizi
Bootstrap Data Envelopment Analysis (Bootstrap DEA) is a resampling-based extension of standard DEA that provides statistically valid inference for efficiency scores. Introduced by Simar and Wilson in 1998, it addresses the core weakness of classical DEA — its inability to quantify uncertainty in estimated scores — by constructing bootstrap confidence intervals and bias-corrected efficiency estimates from repeatedly resampled pseudo-frontiers.
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When to use it
Use Bootstrap DEA when efficiency scores obtained from standard DEA need to be accompanied by measures of statistical uncertainty, such as confidence intervals or formal hypothesis tests. It is appropriate for any production or service context with cross-sectional data where the true frontier is unobservable and sampling variability matters. Limitations include computational cost (B resamples × n LP problems), sensitivity to bandwidth choice in the kernel smoother, and the maintained assumption that observed DMUs are drawn i.i.d. from an underlying population. When panel data are available, Malmquist productivity index bootstrapping may be preferred.
Strengths & limitations
- Provides bias-corrected efficiency scores, reducing the systematic overestimation inherent in classical DEA.
- Produces valid bootstrap confidence intervals, enabling statistical comparison of DMUs.
- Nonparametric: makes no distributional assumption on the error or inefficiency term.
- Compatible with both input-oriented and output-oriented DEA under CRS and VRS assumptions.
- Computationally intensive: requires solving B × n linear programs, which may be prohibitive for large samples.
- Requires specification of a kernel bandwidth; results can be sensitive to this choice.
- Assumes i.i.d. sampling of DMUs from a fixed population, which may not hold in convenience samples or census data.
- Bias correction can make scores exceed 1 under VRS, requiring truncation and careful interpretation.
Frequently asked
How many bootstrap replications (B) are sufficient?
Simar and Wilson recommend at least B = 2000 replications for stable confidence intervals. For exploratory analysis B = 1000 may suffice, but for publication-quality inference B = 2000 to 5000 is standard. Increasing B beyond 5000 yields diminishing returns relative to the additional computation time.
Can Bootstrap DEA handle variable returns to scale (VRS)?
Yes. The bootstrap procedure is applicable under both constant returns to scale (CRS) and variable returns to scale (VRS). Under VRS the bias correction may push some scores above one, and practitioners typically truncate these to one or interpret them as indicating DMUs very close to the frontier with high sampling variability.
What is the difference between Bootstrap DEA and a standard DEA followed by a second-stage regression?
Standard two-stage DEA ignores the statistical noise in first-stage scores, producing biased and inconsistent second-stage estimates. Simar and Wilson (2007) showed that a double-bootstrap procedure — first bootstrapping DEA scores, then using truncated regression in stage two — is required for valid inference when explaining efficiency with environmental variables.
Sources
- Simar, L., & Wilson, P. W. (1998). Sensitivity analysis of efficiency scores: How to bootstrap in nonparametric frontier models. Management Science, 44(1), 49–61. DOI: 10.1287/mnsc.44.1.49 ↗
How to cite this page
ScholarGate. (2026, June 2). Bootstrap Data Envelopment Analysis. ScholarGate. https://scholargate.app/en/efficiency-analysis/bootstrap-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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- Network DEAEfficiency Analysis↔ compare