Data Envelopment Analysis MSc in Regulation and Competition Quantitative techniques in Practice John Cubbin, City University©

DEA What it is - recap Farrell measures of Efficiency –technical –allocative –scale Dangers of DEA Later today: 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 E k =  v j k Y j k /  u i k X i k X i k = input i Y j k = output j for kth unit u i k,v j k are weights chosen to maximise score of unit k, u i k,v j k are constrained. Must not cause E m > 1 for any other unit m

An Economic Interpretation Due to Michael Farrell (1957) Technical efficiency = OB/OA Capital Labour Min combinations required (isoquant) A B O Other things equal = output

An Economic Interpretation (Output maximisation orientation ) Technical efficiency = OB/OA Output 1 (e.g. calls) Output 2 (e.g. lines) Max combinations achieveable (production frontier) D C O Other things equal = inputs

Economic Interpretation (3) The isoquant and production frontier are not known directly, but might be estimated from known data, using piecewise interpolation Capital Labour Min combinations required (isoquant) A B O E F G H J K L B is an artificial observation - a combination of F and G

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

Scale efficiency Output Input O M A P Q R T.E. = PR/PA S.E. = PQ/PR T.& S.E = PQ/PA This is input orientation. What about output orientation?

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 Labour Min combinations required (isoquant) A B O E F G H J K L B is an artificial observation - a combination of F and G

Dangers of DEA(2) Technical efficiency is not economic efficiency Output 2 (e.g. meter reading) Max combinations achieveable (production frontier) D C O B is technically efficient but economically inefficient Output 1 (e.g. energy) B Iso value lines

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