Increasing Returns and the Growth of Industries in the EU Regions: Paradoxes and Conundrums

Abstract

Verdoorn's law is estimated in a spatial econometric framework for individual manufacturing industries using EU regional data. Estimates of encompassing returns to scale are large, but other explanatory variables, including measures of industrial specialization and diversity, tend to be insignificant. The method of normalization with either output or input growth as the regressor matters, and the use of an instrumental variable approach does not resolve this problem. As in other studies, the static-dynamic Verdoorn law paradox exists. A theoretical argument is made, however, that the dynamic Verdoorn law is the correct specification and this is confirmed empirically.

Rendements croissants et croissance des industries dans les régions de l'UE: paradoxes et énigmes

Résumé La loi de Verdoorn est estimée dans un cadre conceptuel économétrique spatial pour les industries de fabrication individuelles en utilisant des données régionales de l'UE. Les estimations des rendements croissants à l’échelle, englobant, sont importantes, mais d'autres variables explicatives, comprenant des mesures de spécialisation et de diversité industrielles, ont tendance à être insignifiantes. La méthode de normalisation utilisant comme variable indépendante soit la croissance d'entrée soit celle de sortie importe, et l'utilisation d'une approche IV ne résout pas ce problème. Comme dans d'autres études, le paradoxe statique-dynamique de la loi de Verdoorn est présent. Cependant, dans un argument théorique, nous avançons que la loi de Verdoorn dynamique est la spécification correcte, ce qui est confirmé empiriquement.

Aumento de las ganancias y crecimiento de la industria en las regiones de la UE: paradojas y acertijos

Résumén Se estima la Ley de Verdoorn en un marco econométrico espacial para empresas manufactureras individuales usando los datos regionales de la UE. Las estimaciones para las ganancias englobadas a escala son grandes, pero otras variables explicativas, incluyendo las medidas de especialización y diversidad industrial, tienden a ser insignificantes. Importa el método de normalización ya sea usando crecimiento de ganancias o entradas como regressor, y el uso de un enfoque IV no resuelve este problema. Al igual que en otros estudios existe la paradoja estática-dinámica de la ley de Verdoorn. Sin embargo, se argumenta teóricamente que la dinámica ley de Verdoorn es la especificación correcta y esto se confirma empíricamente.

Keywords:

• Increasing returns
• Verdoorn's law
• manufacturing
• productivity growth
• spatial econometrics

JEL CLASSIFICATION:

• O18
• O33
• R11

View correction statement:

Erratum

Acknowledgements

This paper was originally prepared for a special session on spatial economics at the 5th Annual Conference on ‘Economic Theory and Policy’ at the University of the Basque Country, Bilbao, Spain, July 2008. The authors are grateful for the comments of both the participants of this special session and for those of an anonymous referee. Any remaining errors in this paper are the sole responsibility of the authors.

Notes

1. With respect to the latter see, for example, the World Bank (2008).

2. We do not analyse the service industries because of the difficulties faced by statistical agencies in providing constant price estimates of service output independent of the value of the inputs.

3. More precisely, the textbook Solow model assumes a neoclassical production function, which is one that satisfies the assumptions of: (i) constant returns to scale to the reproducible inputs, (ii) diminishing marginal returns, and (iii) the Inada conditions, which state that as the stock of capital (labour) tends to zero, the marginal product of capital (labour) tends to infinity and that as the stock of capital (labour) tends to infinity, the marginal product of capital (labour) tends to zero. See McCombie (2000) and Felipe & McCombie (2005) for a sceptical view of the neoclassical production function.

4. This does not mean that there will necessarily be divergence. If the assumption of a common technology is relaxed, it is possible that the diffusion of innovations could lead to the less developed regions growing faster than the more technologically advanced regions, notwithstanding the presence of substantial increasing returns to scale.

5. See Angeriz et al. (2008).

6. It should be noted that this discussion refers to the disequilibrium growth of a region as it converges to its steady-state value. Whether or not there is a steady-state growth rate depends upon the values of the model's parameters, notably the import and export price elasticities and the degree of returns to scale. See Dixon & Thirlwall (1975) for a discussion. (They consider that the necessary values are plausible, whereas they mention that Kaldor did not.) Moreover, the steady-state rate of growth will depend upon the values of the income elasticities of imports and exports.

7. Samuelson originally applied his argument to firms.

8. Verdoorn's law has a long history, dating back to the work of Clark (1940) and Verdoorn (1949). However, it was Kaldor (1966) who brought the law to general prominence.

9. For a more detailed derivation of the empirical form, see Angeriz et al. (2008).

10. In the data, the factor shares vary by both region and industry. However, for notational convenience, we suppress the i and j subscripts from the factor shares in the main text.

11. Ordinarily, when estimating the dynamic Verdoorn law, the restriction is applied to equation (3).

12. Arrow (1962), Romer (1986), and Marshall (1890). Also, Porter (1996) argues in the same vein.

13. The level of output is taken to be that of the initial level to avoid the possibility of reverse causation from TFP growth to lnD _j . Using the average density of production over the period made little difference to the results obtained.

14. The lower the index, the more diverse the industry. Note, for instance, that if we have five industries, excluding the industry under consideration, it will take on a value of 0.2 if activity is evenly distributed across those industries. On the other hand, it will take on a value of unity if the remaining activity is completely concentrated in just one of those industries.

15. NUTS is an acronym for Nomenclature of Units of Territorial Statistics and represents a classification of regions established by Eurostat. In this classification, NUTS1 regions represent the intermediate level of spatial disaggregation, being territorial units populated by 3–7 million people. These regions are smaller than individual European countries (classified as NUTS0 regions), and larger than NUTS2 regions, which are roughly equivalent to counties in the UK.

16. Despite not being an EU country, both Eurostat and Cambridge Econometrics provide data for Switzerland on an equivalent basis to the EU countries, and therefore it is included for completeness.

17. We estimated models composed of all combinations of definitions for specialization and diversity, as defined in equations (5)–(8). In this paper, though, we only report the combination which produced generally the most significant effects. Even in these selected results, however, the variables were generally statistically insignificant for most industries.

18. Adjusting the level of lnTFP for increasing returns to scale to be equal to that implied by the Verdoorn coefficient did not make a marked difference to the estimated degree of returns to scale. The only exception to this is there is a large increase in the value in the case of food. The estimates are given by in Table 1.

19. Thirlwall (1980, p. 420) sums up the distinction as follows: in neoclassical theory, growth is resource based. Regional growth performance is determined by, or constrained by, the rate of growth of indigenous factor supplies and productivity, exogenously given independent of demand. In the model to be presented, by contrast, regional growth is demand determined for the obvious reason that no region's growth rate can be constrained by supply when factors of production are freely mobile. If the demand for a region's output is strong, labour and capital will migrate to the region to the benefit of that region and to the detriment of others.

20. The estimated values reported throughout this paper have been adjusted to remove spurious correlation.

21. The numbers in parentheses underneath the parameter estimates are t-ratios.

22. It should be noted that this does not necessarily mean that the underlying relationship of Verdoorn's law is a Cobb–Douglas. Integrating Verdoorn's law does not necessarily give a conventional Cobb–Douglas production function—it all depends upon the constant of integration (McCombie, 1982).

23. The same argument would apply if we were to consider NUTS2 rather than NUTS1 regions.

24. In this example, we are considering only a single industry, for simplicity. As such, in equation (17) we drop the industry subscript i.

25. Of course, for meaningful estimation in practice we would require data for more than three regions. The restriction here to three regions is purely for expositional purposes. For a full and formal statement of the spatial aggregation bias argument, which allows for many regions, see McCombie & Roberts (2007).

26. For notational convenience, we omit time subscripts from this equation.