Impact of input substitution and output transformation on data envelopment analysis decisions

ABSTRACT

Data envelopment analysis (DEA) can aid managerial decision-making because it offers an opportunity to measure organizational performance in a holistic manner, aggregating data from partial indicators into a single comprehensive measure. However, there are some methodological hazards associated with the use of DEA that are especially relevant to managerial decisions, but which have been largely ignored in the literature. Herein, we identify and show the impact of a ubiquitous methodological hazard in DEA modelling – the economic assumptions regarding input substitutions and output transformations.

KEYWORDS:

• Data envelopment analysis
• DEA
• efficiency
• product transformation
• factor substitution
• decision-making

JEL CLASSIFICATION:

• D24
• L25

Acknowledgements

We appreciate the financial support for summer research provided by the Dean, College of Business Administration, University of Illinois at Chicago. We thank Stanley Sclove and Georgios Karras for statistical and econometric advice, and are especially grateful for the valuable comments of Finn Førsund over a number of drafts. We also thank the anonymous referees whose suggestions and corrections significantly improved the article. Of course, we are fully responsible for any misinterpretations and remaining deficiencies.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental material

Supplemental data for this article can be accessed here.

Notes

¹ When a DEA problem is solved using linear programming, a specific algorithm is used (often the simplex method or a variant thereof). But all of the approaches result in solutions in which the weights of the coordinates of any two points on the same facet of the frontier will be such that the ratio of those weights will equal to the absolute value of that facet’s slope – that is, its MRTS or MRTT. And, of course, linear programming itself assumes variable substitution in optimizing its objective function.

² We thank Finn Førsund for identifying this situation.

³ For example, instead of using the equality constraints on weights in the linear programme, which we illustrate in this article for pedagogical reasons, in practice we make use of the following fact: if multiple variables are restricted to the same weight, then they can be aggregated without weights:$\sum _{i=1}^{N}w{x}_i=w\sum _{i=1}^N{x}_i$. Whether the variable values are aggregated or not, the DEA programme assigns the appropriate value to w. Although, the math does not require it, for valid use in DEA all of the variables must be measured using a common physical unit. This shortcut sometimes can avoid inserting weight constraints in the DEA programme.

⁴ We conducted standard statistical tests for normality and IID, adapted for cross-sectional data where necessary, using Barnum et al. (2012).

⁵ In generating our DEAs for comparison with the DEAs reported in the three articles we analyse, we include or exclude truncation of DEA efficiency scores at 1 to match the model in the article.

Additional information

Funding

This work was supported by the Dean, College of Business Administration, Univ of Illinois at Chicago [Summer Salary Support].