Firm efficiency, industry performance and the economy: three-way decomposition with an application to Andalusia

Abstract

An economy may perform better because the firms become more efficient, the industries are better organized, or the allocation between industries is improved. In this paper we extend the literature on the measurement of industry efficiency (a decomposition in firm contributions and an organizational effect) to a third level, namely that of the economy. The huge task of interrelating the performance of an economy to industrial firm data is accomplished for Andalusia.

Appendices

Appendix 1: Proof

We demonstrate that the feasible set of Eq. (3) is larger or equal than the feasible set of the industry model presented in ten Raa (2011). The latter is characterized by the pair of constraints $\sum\nolimits_{{j \in I_{k} }} {\lambda_{jk} x_{jk} } \le \sum\nolimits_{{i \in I_{k} }} {x_{ik} } ,\sum\nolimits_{{j \in I_{k} }} {\lambda_{jk} y_{jk} } \ge \sum\nolimits_{{i \in I_{k} }} {y_{ik} /\varepsilon_{k} }$. In Eq. (3) the first constraint is copied, as is the k-th component of the second constraint. The other components, ${{\sum\nolimits_{{j \in I_{k} }} {\lambda_{jk} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{y}_{jk} } \ge \sum\nolimits_{{i \in I_{k} }} {\lambda_{ik} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{y}_{ik} } } \mathord{\left/ {\vphantom {{\sum\nolimits_{{j \in I_{k} }} {\lambda_{jk} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{y}_{jk} } \ge \sum\nolimits_{{i \in I_{k} }} {\lambda_{ik} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{y}_{ik} } } {\varepsilon_{k} }}} \right. \kern-0pt} {\varepsilon_{k} }}$ are replaced by $\sum\nolimits_{{j \in I_{k} }} {\lambda_{jk} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{y}_{jk} } \ge \sum\nolimits_{{i \in I_{k} }} {\lambda_{ik} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{y}_{ik} }$. Because ε _k is an efficiency score between zero and one, this replacement is a relaxation.

Appendix 2: Data and computation details

The IEA (Instituto de Estadística de Andalucía—Regional Statistical Office of Andalusia) provided the cross-section inputs and outputs establishment data. These data were used for the elaboration of the Input–Output Andalusian Framework 2000—MIOAN00 (IEA 2006), which is the input–output table for Andalusia, based on the European System of Accounts (ESA-95) published by EUROSTAT (1996). IEA publishes two use tables, which differ by valuation. One is valued at purchasers’ prices and the other at basic prices, which is the same as the former but excluding trade and transport margins and net commodity taxes (see Viet 1994, p. 28). Trade and transport margins needs simply be reallocated from the commodities where they are included, at purchasers’ values, to the use matrix rows of trade and transport services. The make table is published exclusively at basic prices. The United Nations System of National Accounts (SNA) recommends basic values; production costs of good and services are measured before they are conveyed to the market for consumption so that the effects of tax and subsidy policies as well as of differences in types of economic transactions are isolated. Valuations are in basic prices. ten Raa and Rueda-Cantuche (2007) detail the procedure, including the assumed equality of margins and net commodity taxes between establishments in a given industry, consuming a given commodity.

There is a single capital type and a single labour type. Data for each establishment is obtained from capital consumption and total equivalent employees figures in the IO dataset. The capital endowment and the total labour force are the sum across establishments of their capital consumption and total equivalent employees figures.

Sales and purchases were classified into 86 commodities, then 88 inputs (86 commodities and 2 factor inputs: capital and labour) and 86 outputs were considered for 39,272 observations: 39,258 obtained by IEA from specific surveys done to build MIOAN00 while the other 14 observations represent data of sectors which data are obtained by IEA from different statistical sources when building MIOAN00, instead of by specifically surveying establishments: The list of this latter group of sectors is presented in Table 5.

Table 5 Industries not surveyed for MIOAN00

We do not claim that the data were measured without error. Particularly, basic prices building follow some usual assumptions. For a sensitivity analysis we refer to ten Raa (2005).

The results have been computed using a specifically designed and optimized GAMS v21.6 code that uses Cplex Solver. It has taken 10 h to run it on a laptop with a processor Pentium Centrino Duo 1.66 Ghz with 32-bits architecture and 2 Gb RAM.

Appendix 3: Industry/commodity classification

See Table 6.

Table 6 Industry classification in MIOAN00