Economics & Sociology

ISSN: 2071-789X eISSN: 2306-3459 DOI: 10.14254/2071-789X
Index PUBMS: f5512f57-a601-11e7-8f0e-080027f4daa0
Article information
Title: (Non-)Convex production metafrontier for the Baltic states
Issue: Vol. 13, No 2, 2020
Published date: 06-2020 (print) / 06-2020 (online)
Journal: Economics & Sociology
ISSN: 2071-789X, eISSN: 2306-3459
Authors: Linas Rudminas
Vilnius University

Tomas Baležentis
Vilnius University
Keywords: efficiency, productivity, metafrontier, data envelopment analysis, Baltic states
DOI: 10.14254/2071-789X.2020/13-2/15
Index PUBMS: b57888a2-bef8-11ea-9cc3-fa163e0fa1a0
Language: English
Pages: 228-244 (17)
JEL classification: C44, O47

The productive technology can be defined for different levels of aggregation (e.g., enterprises, economic sectors, economies). The groups of relatively homogenous observations can be established in order to model their performance with respect to the corresponding frontiers. The grand technology comprising all the frontiers is termed as the metafrontier. In this paper, we look into the dynamics of productivity of the three Baltic States, namely, Estonia, Latvia and Lithuania over the period of 2000-2016. We establish country-specific frontiers and a metafrontier in order to identify technological superiority of the countries against each other. What is more, we apply both convex and non-convex metafrontier in order to ascertain whether the underlying axioms impact the technological gaps. The results confirm the technological superiority of Estonia with regards to the other two Baltic states. Capital productivity requires improvement in Lithuania, whereas both capital and labour productivity gains are necessary in Latvia in order to approach the metafrontier.


1. Afsharian, M., & Podinovski, V. V. (2018). A linear programming approach to efficiency evaluation in nonconvex metatechnologies. European Journal of Operational Research, 268(1), 268-280.

2. Assaf, A., Barros, C. P., & Josiassen, A. (2010). Hotel efficiency: A bootstrapped metafrontier approach. International Journal of Hospitality Management, 29(3), 468-475.

3. Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078–1092.

4. Beltrán-Esteve, M., Giménez, V., & Picazo-Tadeo, A. J. (2019). Environmental productivity in the European Union: A global Luenberger-metafrontier approach. Science of The Total Environment, 692, 136-146.

5. Bilan Y., Mishchuk, H., Roshchyk, I. & Kmecova I. (2020). Analysis of Intellectual Potential and its Impact on the Social and Economic Development of European Countries. Journal of Competitiveness, 12, 22-38.

6. Bjurek, H., Hjalmarsson, L., & Forsund, F.R. (1990). Deterministic Parametric and Nonparametric Estimation of Efficiency in Service Production: A Comparison. Journal of Econometrics, 46, 213-228.

7. Bogetoft, P., & Otto, L. (2011). Benchmarking with DEA, SFA, and R. International Series in Operations Research and Management Science, Vol. 157. Springer.

8. Bogetoft, P., & Otto, L. (2018). Benchmarking with DEA and SFA, R package version 0.27.

9. Çalik, A., Yapici Pehlivan, N., & Kahraman, C. (2018). An integrated fuzzy AHP/DEA approach for performance evaluation of territorial units in Turkey. Technological and Economic Development of Economy, 24(4), 1280-1302.

10. Carrillo, M. (2019). Measuring and ranking R&D performance at the country level. Economics and Sociology, 12(1), 100-114.

11. Chang, M. C. (2019). Studying the room for improvement in energy intensity by data envelopment analysis under the metafrontier framework. Energy Strategy Reviews, 26, 100398.

12. Chang, M. C., & Hu, J. L. (2019). A long-term metafrontier analysis of energy and emission efficiencies between G7 and BRICS. Energy Efficiency, 12(4), 879-893.

13. Charnes, A., Cooper, W., & Rhodes, E. (1978). Measuring the efficiency of decision making

14. units. European Journal of Operational Research, 2, 429-444.

15. Charnes, A., Cooper, W. W., & Rhodes, E. (1981). Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through. Management science, 27(6), 668-697.

16. Chen, L., Huang, Y., Li, M. J., & Wang, Y. M. (2020). Metafrontier analysis using cross-efficiency method for performance evaluation. European Journal of Operational Research, 280(1), 219-229.

17. Chiu, C. Y., Lin, C. C., & Yang, C. H. (2019). Technological catching-up between two ASEAN members and China: A metafrontier approach. China Economic Review, 54, 12-25.

18. Cooper, W. W., Seiford, L. M., & Tone, K. (2007). Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA–Solver Software. Second Edition. Springer.

19. Daraio, C., & Simar, L. (2007). Advanced Robust and Nonparametric Methods in Efficiency

20. Analysis: Methodology and Applications (Vol. 4). Springer.

21. Debreu, G. (1951). The coefficient of resource utilization. Econometrica 19(3): p. 273–292.

22. Deprins, D., Simar, L., & Tulkens, H. (1984). Measuring labor inefficiency in post offices. The Performance of Public Enterprises: Concepts and measurements. M. Marchand, P. Pestieau and H. Tulkens (eds.), Amsterdam, North-Holland, 243-267.

23. Ding, T., Wu, H., Dai, Q., Zhou, Z., & Tan, C. (2019). Environmental efficiency analysis of urban agglomerations in China: A non-parametric metafrontier approach. Emerging Markets Finance and Trade, 1-16.

24. Färe, R., & Primont, D. (1995). Multi-Output Production and Duality: Theory and Applications. Kluwer Academic Publishers, Boston.

25. Farrell, M. J. (1957). The measurement of technical efficiency. Journal of the Royal Statistical Society, Series A, Vol. 120(3), p. 253–281.

26. Giraleas, D., Emrouznejad, A., & Thanassoulis, E. (2012). Selecting between different productivity measurement approaches: An application using EU KLEMS data.

27. Huguenin J. M. (2012). Data Envelopment Analysis (DEA): A pedagogical guide for decision makers in the public sector. Institut de hautes études en administration publique.

28. Jäger, K. (2017). EU KLEMS Growth and Productivity Accounts 2017 release Description of Methodology and General Notes September 2017, Revised July 2018.

29. Joro, T., & Korhonen, P. J. (2015). Extension of data envelopment analysis with preference information: Value efficiency. New York: Springer Science + Business Media.

30. Karnitis, G., & Karnitis, E. (2017). Sustainable growth of EU economies and Baltic context: Characteristics and modelling. Journal of International Studies Vol, 10(1).

31. Kattel, R., & Raudla, R. (2013). The Baltic Republics and the Crisis of 2008–2011, Europe-Asia Studies, Vol. 65, No. 3, p. 426-449.

32. Kerstens, K., O’Donnell, C., & Van de Woestyne, I. (2019). Metatechnology frontier and convexity: A restatement. European Journal of Operational Research, Vol. 275, Issue 2, p. 780-792

33. Koopmans, T. C. (1951). An analysis of production as an efficient combination of activities. In: Koopmans, T. C. (Ed.) Activity Analysis of Production and Allocation. Cowles Commission for Research in Economics. Monograph No. 13. New York: Wiley, p. 33–37

34. Kounetas, K., & Zervopoulos, P. D. (2019). A cross-country evaluation of environmental performance: Is there a convergence-divergence pattern in technology gaps?. European Journal of Operational Research, 273(3), 1136-1148.

35. Latruffe, L. (2010). Competitiveness, productivity and efficiency in the agricultural and agrifood sectors. OECD Food, Agriculture and Fisheries Working Papers, No. 30, OECD Publishing.

36. Lin, Y. H., & Hong, C. F. (2020). Efficiency and effectiveness of airline companies in Taiwan and Mainland China. Asia Pacific Management Review, 25, 13-22.

37. Liu, J. S., Lu, L. Y. Y., Lu, W. M., & Lin, B. J. Y. (2013). Data envelopment analysis 1978–2010: a citation-based literature survey. Omega, 41, 3–15.

38. Liu, L., Kang, C.H., Yin, Z.Y., & Liu, Z.Y. (2019). The effects of fiscal and taxation policies on the innovation efficiency of manufacturing enterprises: A comparative study from the perspective of economic regions. Transformations in Business & Economic

39. Lovell, C. (1993). "Production frontiers and productive efficiency", in Fried, H., Lovell, C.,

40. Schmidt, S. (eds). The Measurement of Productive Efficiency: Techniques and Applications, Oxford University Press, New York, p. 3-67.

41. Ma, G., Li, X., & Zheng, J. (2019). Efficient allocation of coal de-capacity quota among Chinese provinces: a zero-sum gains data envelopment model. Chinese Journal of Population Resources and Environment, 17(3), 229-240.

42. O’Donnell, C.J., Rao, D.S.P., & Battese, G.E. (2008). Metafrontier frameworks for the study of firm-level efficiencies and technology ratios. Empirical Economics, 34, 231-255.

43. Pastor, J. T., & Lovell, C. K. (2005). A global Malmquist productivity index. Economics Letters, 88(2), 266-271.

44. Podinovski, V.V. (2016). Optimal weights in DEA models with weight restrictions. European Journal of Operational Research, 254(3), 916-924.

45. Ramanathan, R. (2003). An Introduction to Data Envelopment Analysis: A Tool for Performance Measurement. Sage Publications.

46. Saulaja, I., Zvaigzne, A., & Mietule, I. (2016). Labour costs and Productivity in Latvia. Economic Science for Rural Development, 42, 150-156.

47. Shephard, R.W. (1970). Theory of cost and production functions. Princeton, NJ: Princeton University Press.

48. Stehrer, R., Bykova, A., Jäger, K., Reiter, O., & Schwarzhappel, M. (2019). Industry level growth and productivity data with special focus on intangible assets, WIIW Statistical Report No. 8.

49. Thompson, R. G., Langemeier, L. N., Lee, C. T., Lee, E., & Thrall, R. M. (1990). The role of multiplier bounds in efficiency analysis with application to Kansas farming. Journal of Econometrics, 46(1–2), 93–108.

50. Timmer, M. P., Dietzenbacher, E., Los, B., Stehrer, R., & de Vries, G. J. (2015). An Illustrated User Guide to the World Input–Output Database: the Case of Global Automotive Production. Review of International Economics, 23, 575–605.

51. Wang, H., Zhou, P., Xie, B. C., & Zhang, N. (2019). Assessing drivers of CO2 emissions in China's electricity sector: A metafrontier production-theoretical decomposition analysis. European Journal of Operational Research, 275(3), 1096-1107.

52. Wilson, P. W. (2008). FEAR 1.0: A Software Package for Frontier Efficiency Analysis with R. Socio-Economic Planning Sciences, 42, 247–254.

53. Zha, J., Yuan, W., Dai, J., Tan, T., & He, L. (2020). Eco-efficiency, eco-productivity and tourism growth in china: a non-convex metafrontier DEA-based decomposition model. Journal of Sustainable Tourism, 28(5), 663-685.

54. Zhang, D., Li, M., Ji, X., Wu, J., & Dong, Y. (2019). Revealing potential of energy-saving behind emission reduction: A DEA-based empirical study. Management of Environmental Quality, 30(4), 714-730.