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