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Scale, congestion, and technical efficiency of European countries: a sector-based nonparametric approach

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Abstract

In this paper, we investigate three aspects of economic growth of European countries: scale, congestion, and technical efficiency. The distinguishing features of the methodology used are, one, countries are exclusively defined in terms of their sectors, and, two, no specific assumptions on any aspect of the growth process (in particular the production function) are required. As such, we can better understand the performances of the countries for each of the three aspects studied, and avoid the drawbacks of specifying the production function. Our results reveal some important patterns useful for policy-makers. Firstly, we highlight the key sectors for each of the three aspects in every country. Next, our analysis reveals that, for each of the three aspects, higher progresses occur more often when more inefficient or non-optimal behaviour is present. Finally, we demonstrate that there is a relationship between these three aspects. All in all, we argue for the need of sector-specific multi-level policies. That is, policies that target the three aspects simultaneously for each sector individually.

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Notes

  1. See Färe et al. (1994), Cooper et al. (2004), Cooper et al. (2007), Fried et al. (2008) and Cook and Seiford (2009) for extensive reviews of DEA.

  2. In practice, technology axioms (such as monotonicity, convexity, returns-to-scale) are also imposed to avoid trivial reconstructions. See Sect. 2 for more details.

  3. For empirical macroeconomic works using DEA-based methods, refer, for example, to Wu (2001), Kumar and Russell (2002), Henderson and Russell (2005), Enflo and Hjertstrand (2009), Cherchye (2011), Zelenyuk (2011), Zhang et al. (2011), Bampatsou et al. (2013), Badunenko et al. (2013), Song et al. (2013), Wang et al. (2013), Wu and An (2013), Apergis et al. (2015), Wang and Feng (2015), Cantore et al. (2016), Dai et al. (2016), Chen et al. (2016), and Zhou et al. (2017).

  4. Note that the importance of sectors for growth and convergence empirical works is not new and dates to Bernard and Jones (1996), Rajan and Zingales (1998), Claessens and Laeven (2003), and Fisman and Love (2003).

  5. This also explains why most of the sector-level empirical studies are focused on a particular or a group of sectors.

  6. Let \(T_{vrs,sdo}\) and \(T_{crs,sdo}\) be the technology under variable and constant returns-to-scale, respectively. By construction, we have that \(T_{crs,sdo}=\{\lambda (\mathbf {X}, \mathbf {Y}): (\mathbf {X}, \mathbf {Y}) \in T_{vrs,sdo}, \forall \lambda >0\}\). This reflects that \(T_{vrs,sdo}\) is included in \(T_{crs,sdo}\), implying that \(Y_{crs,sdo}(\mathbf {X}) \ge Y_{vrs,sdo}(\mathbf {X})\). Intuitively, this reflects that only more technically inefficient behaviour can be found when assuming constant returns-to-scale.

  7. In practice, it is enough to evaluate \(Y_{nirs,sdo}(\mathbf {X}_{ijt})\) (i.e. when assuming non-increasing returns-to-scale) and compare to \(Y_{vrs,sdo}(\mathbf {X}_{ijt})\). If they are equal, decreasing returns-to-scale is present. Otherwise, increasing returns-to-scale is present. Note that \(Y_{vrs,sdo}(\mathbf {X}_{ijt})\) can also be estimated by a linear programme.

  8. Note that it is also possible to construct confidence intervals for the sector-level indicators. This case is not considered in the paper as country-level indicators are the most important indicators, and for the sake of compactness.

  9. The Spearman correlations are 0.9928 (p value of 0) between the weights of the scale and congestion ratios, 0.9859 (p value of 0) between the weights of technical efficiency and congestion ratios, and 0.9850 (p value of 0) between the weights of technical efficiency and scale ratios.

  10. For recent studies about the Europe 2020 strategy refer, for example, to Pasimeni and Pasimeni (2016), Rappai (2016), and Walheer (2017).

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Authors and Affiliations

  1. International Business School Suzhou, Xi’An Jiaotong-Liverpool University, Suzhou, China

    Barnabé Walheer

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  1. Barnabé Walheer
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Corresponding author

Correspondence to Barnabé Walheer.

Additional information

We thank the Editor Subal Kumbhakar and the referee for their comments that have improved the paper substantially.

This work was supported by the National Natural Science Foundation of China under Grant No. 71750110539.

Appendices

Appendix A

We make use of the following abbreviations in Appendix A: Agriculture (A), Mining (Mi), Manufacturing (Ma), Electricity, Gas and Water (EG), Construction (C), Wholesale (W), Transport (T), Public Administration (PA), Education (E), and Health (H); in 19 European countries: Austria (A), Belgium (B), Czech Republic (CZ), Denmark (DK), Estonia (EE), Finland (FIN), France (F), Germany (D), Hungary (H), Ireland (IRL), Italy (I), Luxembourg (L), Netherlands (NL), Norway (N), Poland (PL), Slovakia (SK), Slovenia (SI), Spain (E), and Sweden (S). (Av) corresponds to the average.

See Tables 1, 2.

Table 1 Added value per labour growth
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Table 2 Capital per labour growth
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Appendix B

We make use of the following abbreviations in Appendix B: Agriculture (A), Mining (Mi), Manufacturing (Ma), Electricity, Gas and Water (EGW), Construction (C), Wholesale (W), Transport (T), Public Administration (PA), Education (E), and Health (H).

See Tables 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.

Table 3 Weights for the technical efficiency ratios
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Table 4 Weights for the scale ratios
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Table 5 Weights for the congestion ratios
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Table 6 Changes for the technical ratio weights
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Table 7 Changes for the scale ratio weights
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Table 8 Changes for the congestion ratio weights
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Table 9 Country-level technical efficiency ratios
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Table 10 Technical efficiency ratios
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Table 11 Technical efficiency ratio changes per year (%)
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Table 12 Spearman correlation coefficients for technical efficiency ratios
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Table 13 Country-level scale ratios
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Table 14 Scale ratios
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Table 15 Scale ratio changes per year (%)
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Table 16 Spearman correlation coefficients for scale ratio
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Table 17 Country-level congestion ratios
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Table 18 Congestion ratios
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Table 19 Congestion ratio changes per year (%)
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Table 20 Spearman correlation coefficients for congestion ratio
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Table 21 Spearman correlation coefficients
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Appendix C

We make use of the following abbreviations in Appendix C: Agriculture (A), Mining (Mi), Manufacturing (Ma), Electricity, Gas and Water (EGW), Construction (C), Wholesale (W), Transport (T), Public Administration (PA), Education (E), and Health (H).

See Tables 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 3233, 34, 35, 36, 37, 38, 39, 40.

Table 22 Weights for the technical efficiency ratios
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Table 23 Weights for the scale ratios
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Table 24 Weights for the congestion ratios
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Table 25 Changes for the technical ratio weights
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Table 26 Changes for the scale ratio weights
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Table 27 Changes for the congestion ratio weights
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Table 28 Country-level technical efficiency ratios
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Table 29 Technical efficiency ratios
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Table 30 Technical efficiency ratio changes per year (%)
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Table 31 Spearman correlation coefficients for technical efficiency ratios
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Table 32 Country-level scale ratios
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Table 33 Scale ratios
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Table 34 Scale ratio changes per year (%)
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Table 35 Spearman correlation coefficients for scale ratio
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Table 36 Country-level congestion ratios
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Table 37 Congestion ratios
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Table 38 Congestion ratio changes per year (%)
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Table 39 Spearman correlation coefficients for congestion ratio
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Table 40 Spearman correlation coefficients
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Walheer, B. Scale, congestion, and technical efficiency of European countries: a sector-based nonparametric approach. Empir Econ 56, 2025–2078 (2019). https://doi.org/10.1007/s00181-018-1426-7

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