# Data Envelopment Analysis - City University London

Data Envelopment Analysis MSc in Regulation and Competition Quantitative techniques in Practice John Cubbin, City University DEA What it is Farrell measures of Efficiency technical allocative scale Running DEA Dangers of DEA Productivity over time

What it is Mathematical programming approach to measuring distance from a frontier. Uses Inputs , outputs, (and noncontrollables) Can be expressed as a ratio of weighted outputs to weighted inputs Ek = vjk Yj k /ui k Xi k Xi k = input i Yj k = output j for kth unit uik ,vjk are weights chosen to maximise score of unit k, uik ,vjk are constrained. Must not cause Em > 1 for any other unit m An Economic Interpretation Due to Michael Farrell (1957) Technical efficiency = OB/OA Capital A Other things

equal = output B Min combinations required (isoquant) O Labour An Economic Interpretation (Output maximisation orientation) Technical efficiency = OB/OA Output 2 (e.g. lines) D Other things

equal = inputs C Max combinations achieveable (production frontier) O Output 1 (e.g. calls) Economic Interpretation (3) The isoquant and production frontier are not known directly, but might be estimated from known data, using piecewise interpolation Capital K

E B is an artificial observation - a combination of F and G O F A L B G H

Min combinations J required (isoquant) Labour Allocative efficiency Depends on knowing prices AE = min cost/actual cost = OD/ OB Capital A B Efficient Isocost line

D O C Min combinations required (isoquant) Labour Scale efficiency Output M T.E. = PR/PA S.E. = PQ/PR T.& S.E = PQ/PA

P Q R A O This is input orientation. What about output orientation? Input Running DEA

Purpose - built software Excel/Solver macros Organise data for input Identify inputs, outputs and noncontrollables Run Interpret How reliable is DEA? Depends on whether frontier can be populated by efficient firms: number of observations number of dimensions closeness to frontier of enough firms distribution of variables Dangers of DEA(1) Outliers appear efficient

Capital K F B is an artificial observation - a combination of F and G O L B G A

H E J Min combinations required (isoquant) Labour Dangers of DEA(2) Technical efficiency is not economic efficiency Output 2 (e.g. meter reading) B is technically efficient but economically

inefficient Iso value lines B C O D Max combinations achieveable (production frontier) Output 1 (e.g. energy) Dangers of DEA (3)

Dilemma: to include or not to include variables Include => spuriously efficient Exclude => spuriously inefficient No well-established statistical test for inclusion/ exclusion

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