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Semiparametric stochastic metafrontier efficiency of European manufacturing firms

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Abstract

In this paper a semiparametric stochastic metafrontier approach is used to obtain insight into the performance of manufacturing firms in Europe. We differ from standard TFP studies at the firm level as we simultaneously allow for inefficiency , noise and do not impose a functional form on the input–output relation. Using AMADEUS firm-level data covering ten manufacturing sectors from seven EU15 countries, (1) we document substantial and persistent differences in performance (with Belgium and Germany as benchmark countries and Spain lagging behind) and a wide technology gap, (2) we confirm the absence of convergence in TFP between the seven selected countries, (3) we highlight a more pronounced technology gap for smaller firms.

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Notes

  1. See e.g. Hulten (2000), Van Biesebroeck (2007), Del Gatto et al. (2011) and Van Beveren (2012) for an overview.

  2. The focus in parametric TFP estimation is on loosening exogeneity assumptions [on input choice, attrition, see Olley and Pakes (1996), Levinsohn and Petrin (2003) and Ackerberg et al. (2006)], the omitted price bias (see e.g. Klette and Griliches 1996; Foster et al. 2008; De Loecker 2011) and modeling multi-product firms (see e.g. Bernard et al. 2009).

  3. See Färe et al. (2008) for an overview of nonparametric TFP indices that use distance functions such as the Malmquist index (Caves et al. 1982) and the Hicks–Moorsteen index (Bjurek 1996).

  4. Although recent nonparametric frontier approaches such as the order-m approach of Cazals et al. (2002) and the order-\(\alpha\) approach of Aragon et al. (2005) deal with the problems of outliers and extreme noise, they are still deterministic.

  5. Parametric stochastic frontier approaches were introduced by Meeusen and van Den Broeck (1977) and Aigner et al. (1977).

  6. The literature on metafrontier estimation starts with Battese and Rao (2002), who proposed a stochastic parametric metafrontier approach. Battese et al. (2004) improved the analysis by ensuring that the stochastic metafrontier always envelops the group frontiers. O’Donnell et al. (2008) introduced nonparametric deterministic metafrontier estimation. Dynamic versions, based on the Malmquist index and its decompositions are proposed by Oh and Lee (2010) and Chen and Yang (2011).

  7. See e.g. Kumbhakar et al. (2007), Martins-Filho and Yao (2007), Simar and Zelenyuk (2011), Henderson et al. (2012), Kuosmanen and Kortelainen (2012), Parmeter and Racine (2013), Sun and Kumbhakar (2013), Martins-Filho and Yao (2015) and Sun (2015).

  8. See http://www.bvdinfo.com/Products/Company-Information/International/AMADEUS.aspx.

  9. Bartelsman et al. (2009) point out that any cross-country comparison of firm dynamics are hampered by definitional problems as well as measurement problems due to differences in coverage, unit of observation, classification of activity and data quality.

  10. The comparison is limited to 2002–2007, as the SBS-statistics changed since 2008 from nace rev. 1.1 classification to nace rev. 2.

  11. CompNet follows a “distributed micro-data analysis” approach to overcome confidentiality issues and has set up a research infrastructure that is able to deliver cross-country firm-based indicators. The research infrastructure involves the ECB as well as 13 national Central Banks, one National Statistical Institute (ISTAT) and the EFIGE team. CompNet Task Force (2014) presents the database and some applications of the data.

  12. For our estimation of technical efficiency, the output of firms has been deflated using national industry-level price indices from EU KLEMS. The firm-level output volumes, expressed as value added in constant prices, do not take into account possible differences in price levels between countries. This may affect the comparison of efficiency levels across countries. Purchasing power parities (PPP) could provide volumes that account for these price differences. Sondermann (2012) uses OECD-Eurostat PPPs to compute PPP-adjusted productivity levels based on EUKLEMS data for the period 1970–2007. In manufacturing, out of the 12 EU countries considered, Belgium comes second after Ireland with the highest PPP-adjusted productivity. The ranking of the other countries is rather similar to the ranking based on our estimation though Finland seems to perform better when considering PPP-adjusted productivity. Italy and Spain clearly lag behind Belgium, Finland, France and Germany in terms of PPP-adjusted productivity. Sondermann (2012) points out that the use of PPPs implies some strong assumptions. PPPs are only available on an aggregate level, e.g. only for manufacturing as a whole. When applying PPPs to individual sectors, we assume that the evolution of price levels is similar in all sectors to the evolution in manufacturing as a whole, an assumption that is clearly refuted by the data. Moreover, if differences in the prices of similar products reflect differences in quality , it is not clear whether the differences in output prices should be discarded.

  13. All in euro. For the deflators, we used industry-level price indices from EU KLEMS.

  14. To avoid effects of extreme outliers and extreme noise in the whole dataset, we limit the sample to observations of firms with at least five employees, deflated value added per employee smaller than 1,000,000 euro, deflated value added per employee at least 100 euro, deflated tangible fixed assets of at least 1,000 euro, the number of months in a book year equal to 12 and growth rates of input and output are lower (higher) than 10 (\(-\)10). As our estimation methodology is sensitive to extremely large observations, we delete for the two inputs and deflated value added, the top 1 % percentile per year per sector. Additionally, improbable labour-capital combinations are removed by deleting the top and bottom percentile of Labour use/Deflated tangible assets per year per sector. Further, we deleted the bottom percentile of Deflated Added Value over Deflated Tangible Fixed assets and Deflated Added Value over Number of employees to eliminate obvious cases of erroneous reporting.

  15. Although the outline is limited to the output-oriented case, the extension to input-orientation is straightforward.

  16. Bjurek (1996) somewhat confusingly called it the Malmquist TFP index.

  17. We do not decompose TFP change as this goes beyond the scope of this paper and we do not wish to impose convexity (and thus estimate a stochastic Free Disposal Hull instead of a stochastic DEA frontier).

  18. The value of the LMLSF approach is shown in recent applications. Kumbhakar et al. (2007) have used the LMLSF approach to analyze the cost function of a random sample of 500 U.S. commercial banks. Additionally, Kumbhakar and Tsionas (2008) have applied the approach to estimate stochastic cost frontier models for a sample of 3691 U.S. commercial banks, while Serra and Goodwin (2009) use the approach to compare efficiency ratings of organic and conventional arable crop farms in the Spanish region of Andalucía.

  19. Simar and Zelenyuk (2011) also extend the Kumbhakar et al. (2007) approach to the full multivariate model without imposing parametric assumptions on the production relationship by the use of polar coordinates as in Simar (2007).

  20. Note however that this is a rather strong assumption. Smith (2008) shows that the stochastic frontier estimates are significantly biased if the error component dependence is wrongly ignored.

  21. The procedure implies that the likelihood function needs to be optimized for each observation. As optimizing bandwidth sizes implies that the routine runs in its leave-one-out version over hundred times (in our case 300 times), this approach is computationally very cumbersome. By making use of parallel programming techniques as discussed in Knaus (2013) and running the code, making use of the ‘np’ and ‘FEAR’ package as discussed in respectively Hayfield and Racine (2008), Wilson (2008) and Wilson (2014), on the High Performance Computing network of Ghent University, we were able to estimate the localized stochastic frontier for all the 560 cases (10 sectors, 7 countries, 8 years). As numerical issues are a priori hard to exclude in observation-specific optimization, we removed outliers when estimating the Free Disposal Hull of the frontier fit. Code in R available upon request.

  22. EU KLEMS data (http://www.euklems.net) of industry-level TFP show that of the group of seven countries that we consider, the UK and Spain are clearly dominated by the other countries in manufacturing industries in the period 2003–2007, whereas Belgium and France had the highest average TFP levels. A first assessment of TFP in COMPNET indicates that the TFP level of Belgium was higher over the period 2000–2009 than in Germany and France (Angeloni and Bernatti 2012). Analysis of the EFIGE data show that over the period 2001–2009 Germany and France perform substantially better than Italy, Spain and the UK in terms of TFP (Altomonte et al. 2012). See also European Commission (2013), wherein the low productivity of the UK manufacturing sector and high productivity of the UK service sector is described.

  23. See e.g. Asplund and Nocke (2006) for an application of stochastic dominance testing with firm-level data.

  24. However, it is not possible to reject non-dominance in favor of dominance over the whole support of the distribution (i.e., not possible at the boundaries). Therefore, as in Davidson and Duclos (2012), we test whether we can reject non-dominance over restricted ranges of metafrontier efficiency. In particular, we restrict the range of metafrontier efficiency studied between the 5 and 95 percentile.

  25. We could include inventories into the output, but correct valuation of inventories can be problematic. Therefore, we focused on revenue, as in standard work in the firm-level TFP literature (e.g. Olley and Pakes 1996).

  26. Note that the sample size of micro firms and large firms may be small.

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Acknowledgments

We sincerely thank the National Bank of Belgium for supporting this project, the members of the research department of the National Bank of Belgium for their comments, the participants of the EWEPA 2013 conference in Helsinki and participants of the CompNet-ECB 2014 Workshop in Rome for their useful suggestions. In particular, we are grateful to Catherine Fuss for her support. Further, we would like to thank Sietse Bracke, Klaas Mulier, Antonio Peyrache, Valentin Zelenyuk and two anonymous referees for useful comments. Marijn Verschelde acknowledges financial support from the Fund for Scientific Research Flanders (FWO Vlaanderen). The computational resources (STEVIN Supercomputer Infrastructure) and services used in this work were kindly provided by Ghent University, the Flemish Supercomputer Center (VSC), the Hercules Foundation and the Flemish Government - department EWI

Funding

The authors received for this study financial support from the National Bank of Belgium.

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Authors and Affiliations

  1. IÉSEG School of Management, LEM (UMR-CNRS 9221), Socle de la Grande Arche - 1 Parvis de La Défense, Paris La Défense cedex, 92044, France

    Marijn Verschelde

  2. Center for Economic Studies, KU Leuven, Leuven, Belgium

    Marijn Verschelde

  3. Federal Planning Bureau, Brussels, Belgium

    Michel Dumont

  4. SHERPPA, Department of General Economics, Ghent University, Ghent, Belgium

    Glenn Rayp

  5. CERISE, Department of General Economics, Ghent University, Ghent, Belgium

    Bruno Merlevede

  6. Department of General Economics, Ghent University, Ghent, Belgium

    Michel Dumont

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  1. Marijn Verschelde
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Verschelde, M., Dumont, M., Rayp, G. et al. Semiparametric stochastic metafrontier efficiency of European manufacturing firms. J Prod Anal 45, 53–69 (2016). https://doi.org/10.1007/s11123-015-0458-7

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