Measuring Productive Efficiency in Input–Output Models by Means of Data Envelopment Analysis

Abstract

The goal of the present research is to evaluate productive efficiency in an input–output framework by means of data envelopment analysis (DEA). This mathematical programming technique allows researchers to assess potential efficiency improvements in the form of input requirements reduction. By constructing envelopment unitary isoquants corresponding to comparable sectors across different local, regional or national economies, e.g. agriculture and manufacturing, DEA identifies as productive benchmarks those economies that exhibit the lowest technical coefficients, i.e. lowest input amount to produce one unit of output. Once these reference frontiers have been defined, it is possible to assess what would be the potential efficiency improvements available to the inefficient economies if they were to produce according to the best practice technologies of their benchmark peers. From an equivalent perspective, these simulations identify the necessary changes that each productive sector needs to undertake in order to reach the efficiency levels of the most successful economies. Finally, within Leontief’s analytical construction, these calculations allow us to assess what would have been the economy‐wid,e benefits for the inefficient economies—in terms of intermediate consumption reductions and final demand increases—of producing with best practice technologies. The model is empirically illustrated using the input–output tables for a set of OECD countries.

Key Words:

• Productive efficiency
• input–output tables
• data envelopment analysis

Jel Classifications:

• C61
• C67
• O14
• O57

Acknowledgements

We are grateful to Guido Cella and Giovanni Pica for providing us with the results of their elaborations of the OECD data on input–output tables and gross capital stocks.

Notes

1. Ten Raa & Mohnen (2001) illustrate their model using Canadian input–output tables. In a multilateral extension Shestalova (2001) applies the same methodology, including the adoption of ten Raa and Mohnen’s domestic model based on an exogenous net exports vector, to study productivity change in the USA, Japan and Europe.

2. See Førsund & Sarafoglou (2005) for a summary of DEA parallel development within the economics and OR/MS fields.

3. For a complete discussion on the alternative choices for output, e.g. gross output vs value added, as well as labor and capital inputs, and their effects when measuring aggregate and industry level productivity, see OECD (2001) and Triplett (2001).

4. We assume the standard axioms found in Färe et al. (1985).

5. Also, Dorfman et al. (1958) extensively deal with issues related to what is known as the linear programming approach to production with fixed coefficient technologies, a stream of research to which this note can be ascribed.

6. t′ _j ≤ t_j if and only if t′ _js ≤ t_js but t′ _j ≠ t_j , i.e. at least one of the s=1, …, S inputs in t′ _j is smaller than in t_j .

7. It would be possible to depart from the production possibility set given by the output correspondence L(X_j ) in (1), and approximate it empirically by means of the activity analysis model in an analogous way to (5), to finally come up with an optimizing DEA program equivalent to (6), but defined in terms of the actually observed values of intermediate inputs, labor, capital and imports, instead of its associated technical coefficients. Nevertheless, as the DEA solutions are units’ invariant—as it is the case when dividing intermediate inputs, labor, capital and imports by the gross output amount, both approaches yield the same efficiency scores and slacks.

8. Additionally, this complies with the fixed coefficients technology given by the Leontief production function in (2) as these radial projections equiproportionally reduce the amounts of the technical coefficients without altering their relative proportions, .

9. Note that the formulation of the optimizing program in terms of technical coefficients (unitary isoquant) instead of the observed amounts of gross output, intermediate inputs, labor, capital and imports—as proposed in footnote 6, renders the gross output slack equal to zero, since all economies produce one unit of sectoral output.

10. Ahmad (2002) discusses on‐going work to harmonize, improve and update the input–output database.

11. The sectors are aggregated in the following way: (1) AGR, agriculture; (2) MAN, manufacturing (FOD, food, beverages and tobacco + TEX, textile, wearing and leather + CHE, industrial chemicals rubber and plastic products + MID, mining and extractive industries + MNM, non metal products (excluding oil and coal products + BMI, metallurgic products + MEQ, metal products, machinery and equipment + WOD, wood products + PAP, paper products + MOT, other manufacturing + EGW, electricity, gas and water); (3) CST, construction; (4) SER, services (RWH, retail and wholesale trade + HOT, restaurants and hotels + TAS, transport + COM, communications + FNS, financial and insurance + RES: real state + SOC, public goods + PGS, public administration + OTR, other producers).

12. These have been modified in Cella & Pica’s (2001, p. 410) database as their intermediate inputs definition includes both domestic and/or imported inputs.