Overview
Data envelopment analysis (DEA) builds a frontier from the best-performing units using linear programming, with no assumption about the functional form of production. Stochastic frontier analysis (SFA) estimates a parametric frontier and separates inefficiency from random noise. DEA is flexible and handles multiple outputs easily; SFA handles measurement error and allows statistical inference. Many studies use both.
We start with your research question and the production process you are studying, because the input–output specification drives everything. We then agree the model — CCR or BCC, input or output orientation, a Malmquist index for panels, or an SFA specification with a suitable inefficiency distribution — and run it with checks for outliers, sensitivity to specification and, where relevant, bootstrapped confidence intervals.
Deliverables include efficiency scores, slacks and peer (benchmark) units, productivity decompositions, second-stage analyses of what explains efficiency, and code in R, Stata, Python, MATLAB or dedicated DEA software.
Who it’s for and the problems it solves
This is for you if you are…
- Doctoral researchers in banking, health economics, education, energy and agriculture
- Master's students measuring efficiency of firms or public services
- Public-sector and institutional analysts benchmarking units such as hospitals or campuses
- Authors responding to reviewers about DEA specification, bootstrapping or SFA distribution choices
Common problems we help with
- You do not know whether to use DEA or SFA
- Too many of your units receive a perfect efficiency score of 1
- You are unsure whether to choose input or output orientation, or constant or variable returns to scale
- Your Malmquist index results need decomposing into efficiency change and technical change
- A reviewer criticized regressing DEA scores on explanatory variables with OLS or Tobit
What’s included — and what isn’t
Included
- Specification of inputs, outputs and undesirable outputs, grounded in theory and prior studies
- Checks on sample size relative to the number of inputs and outputs, and on outliers or super-efficient units
- CCR (constant returns) and BCC (variable returns) DEA models, and scale efficiency
- Input- and output-oriented models, with slacks and target values for each unit
- Peer identification and benchmarking reports
- Super-efficiency and slacks-based measure (SBM) models where they suit the question
- Malmquist productivity index with decomposition into efficiency change and technical change
- Bootstrapped DEA (Simar–Wilson) for bias-corrected scores and confidence intervals
- Stochastic frontier models: Cobb–Douglas or translog frontiers, half-normal, truncated-normal or exponential inefficiency, and panel SFA
- Second-stage analysis of efficiency determinants, including one-step SFA inefficiency models
- Code and tables in R (Benchmarking, deaR, frontier), Stata (sfcross, sfpanel, frontier), Python or MATLAB
Not included
- Choosing inputs and outputs purely to make particular units look efficient
- Ranking named organizations for publicity or commercial claims
- Writing your thesis chapters or reports for you
- Management consulting recommendations beyond what the analysis supports
What you receive
- Model specification note
- Inputs, outputs, orientation, returns-to-scale assumption and data period, with justification and references to comparable studies.
- Efficiency results
- Technical, pure technical and scale efficiency scores with summary statistics, slacks and targets per unit.
- Productivity analysis
- Malmquist index and its components by unit and period, with charts of change over time.
- Inference and determinants
- Bootstrapped confidence intervals, SFA estimates and second-stage results explaining efficiency differences.
- Code and data log
- Reproducible scripts, with every data transformation and exclusion recorded.
How it works
Understand the production process
We discuss what the units do, what they use and produce, and what efficiency means in your context.
Specify the model
We agree variables, orientation, returns to scale and whether DEA, SFA or both are needed.
Screen the data
We check scale, zeros, outliers and the ratio of units to variables.
Estimate and test
We compute scores and productivity indices, run bootstraps or SFA and sensitivity checks.
Explain results
Tables, figures and code, with a walkthrough of what the scores mean and their limitations.
Frontier methods and decisions
- CCR model
- Assumes constant returns to scale; overall technical efficiency is appropriate when units can operate at optimal scale.
- BCC model
- Allows variable returns to scale, separating pure technical efficiency from scale efficiency (CCR score divided by BCC score).
- Orientation
- Input orientation asks how much inputs could shrink for the same outputs; output orientation asks how much outputs could grow with the same inputs. Choose based on what managers actually control.
- Malmquist index
- Measures productivity change between periods and splits it into catch-up (efficiency change) and frontier shift (technical change).
- Stochastic frontier analysis
- Composite error with symmetric noise and one-sided inefficiency; distribution assumptions and functional form (Cobb–Douglas vs translog) are tested.
- Second-stage analysis
- Simar–Wilson truncated regression with bootstrapping, or SFA with inefficiency determinants estimated in one step, rather than naive OLS on DEA scores.
DEA or SFA?
DEA suits multiple-output settings, public services without clear prices, and small to medium samples where you do not want to impose a production function. Its weakness is that all deviation from the frontier counts as inefficiency, so measurement error and outliers can shape the frontier. SFA suits settings with one output or cost data, larger samples and a need for statistical testing, but requires assumptions about functional form and the distribution of inefficiency.
Where results matter for policy or a thesis argument, running both and comparing rankings is a useful robustness check.
Specification pitfalls
DEA discriminates poorly when there are many inputs and outputs relative to units: many units then score as fully efficient. A common rule of thumb is to have at least three times as many units as the combined number of inputs and outputs, and we check this before estimation. We also look for units that define the frontier alone and test sensitivity to removing them.
Variables need consistent units and definitions across the sample and over time. Where outputs include undesirable ones, such as emissions or loan losses, we use models designed for them rather than treating them as inputs by convenience.
- Too few units per variable → inflated efficiency and weak discrimination
- Outliers on the frontier → super-efficiency and sensitivity checks
- Zeros and negative values → model choices or transformations stated explicitly
Reading efficiency scores with care
An efficiency score is relative to the best units in your sample, not to an absolute standard. Adding or removing units changes the frontier. Scores also reflect only the inputs and outputs included, so a 'less efficient' hospital may be delivering quality or complexity your variables do not capture. We help you frame findings accordingly and discuss environmental factors outside managers' control.
Explaining efficiency with regression needs care because DEA scores are serially correlated and bounded. We use approaches designed for this and describe associations with determinants rather than causal effects.
What the work can look like
Illustrative example — fictional data
Sample excerpt: efficiency of regional hospitals
A doctoral researcher assessed 64 public hospitals over 2019–2023 using beds, doctors and nurses as inputs and inpatient days and outpatient visits as outputs (input-oriented). All figures are invented.
Static efficiency
Mean BCC efficiency in 2023 was 0.82 and mean CCR efficiency 0.74, implying average scale efficiency of 0.90. Eleven hospitals were fully efficient under BCC; bias-corrected scores from 2,000 bootstrap replications were on average 0.05 lower.
Productivity change
The Malmquist index averaged 1.018 per year, driven by technical change (1.026) rather than efficiency change (0.992), meaning the frontier moved outward while the average hospital fell slightly behind it.
Cross-check with SFA
A translog input distance frontier with truncated-normal inefficiency gave a rank correlation of 0.71 with DEA scores, supporting the main conclusions.
Illustrative example with invented numbers, not a real client case.
What you’ll need to provide
- Research questions and a description of the units being compared
- Data on inputs, outputs and any environmental or contextual variables
- Reference studies that define inputs and outputs in your sector
- Time period and whether the data form a panel
- Software preference and reporting requirements
You don’t need everything ready to ask for a quote — tell us what you have and we’ll say what’s missing.
What affects price and turnaround
Price depends on
- Number of units, periods and variables
- Whether DEA, SFA or both are required
- Bootstrapping, Malmquist decomposition and second-stage analysis
- Data assembly and cleaning across years or sources
- Delivered analysis or guided learning sessions
Turnaround depends on
- Agreement on inputs and outputs, which often takes discussion
- Consistency of the data across units and years
- Number of alternative specifications to test
Every project is quoted individually. How we price our work.
Questions people ask before starting
How many units do I need for DEA?
There is no fixed minimum, but a common guideline is at least three times the total number of inputs and outputs. With fewer, many units appear efficient. We check this and suggest simplifying the specification if needed.
Which software do you use for DEA?
Often R (Benchmarking, deaR) or Stata, and MATLAB or Python where preferred. Menu-based DEA programs exist and we can work with their output if your department uses one.
Can I use a Tobit regression on DEA scores?
It is common but criticized, because DEA scores are not censored in the usual sense and are serially correlated. We explain the alternatives, such as the Simar–Wilson bootstrap approach, and help you choose.
Can SFA handle multiple outputs?
Yes, through distance function or cost frontier specifications, though these add assumptions. We discuss whether that is preferable to DEA for your question.
Is the thesis chapter written for me?
No. You receive analysis, tables, code and explanations, and we can review your draft. The chapter remains yours.