Data Envelopment Analysis MSc in Regulation and Competition

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 = 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