The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Verdoorn’s Law

  • J. S. L. McCombie
Reference work entry


One of the most notable features of the postwar economic performance of the advanced countries has been the substantial and persistent differences between the various economies in their rates of growth of productivity and output. Yet these disparities are merely one aspect of the more general picture of economic development. Since the beginning of the Industrial Revolution, at which time there appears to have been little variation between areas in terms of per capita income, some countries have achieved a sustained growth in productivity whilst others have shown little or no improvement. The reasons for this, of course, remain a source of controversy.

One of the most notable features of the postwar economic performance of the advanced countries has been the substantial and persistent differences between the various economies in their rates of growth of productivity and output. Yet these disparities are merely one aspect of the more general picture of economic development. Since the beginning of the Industrial Revolution, at which time there appears to have been little variation between areas in terms of per capita income, some countries have achieved a sustained growth in productivity whilst others have shown little or no improvement. The reasons for this, of course, remain a source of controversy.

Verdoorn’s Law is an empirical generalization that provides the basis for one such explanation. Although originally discussed in terms of the differences in productivity growth of the advanced countries, the law is now recognized as having a wider significance for the more general process of economic growth and development.

In its simplest form, the law states that there is a close relationship between the long run growth of manufacturing productivity and that of output. (The law has also been found to hold for public utilities and the construction industries but not for any other sector of the economy.) The importance of the law is that it suggests that a substantial part of productivity growth is endogenous to the growth process, being determined by the rate of expansion of output through the effect of economies of scale.

The development of this approach to the theory of economic growth owes much to the writings of Lord Kaldor (see, in particular, Kaldor 1978a, b, and the symposium on Kaldor’s growth laws published in the 1983 edition of the Journal of Post Keynesian Economics). Indeed, interest in the law primarily dates from Kaldor’s (1966) inaugural lecture which examined why the United Kingdom had grown so much more slowly over the postwar period than most other industrial countries. (It was P.J. Verdoorn, however, who had first discussed the relationship between productivity and output growth in an article published in 1949. The paper was written in Italian which may explain why it had largely escaped notice, with the notable exception of Colin Clark (1957), until Kaldor drew attention to it. Kaldor was also the first to discuss the broader implications of the law for economic growth.)

In the inaugural lecture, Kaldor observed that there was a close relationship for the advanced countries between the growth of manufacturing output per worker (p) and that of output (q). When the Verdoorn Law was estimated in the form p = a + bq using cross-country data for twelve advanced countries over the early postwar period, it was found that the estimate of b, the ‘Verdoorn coefficient’, took a value of about one half. (Other studies have discovered similar results using cross-industry, time-series and regional data for both the advanced and the less developed countries.) Since the exponential growth of productivity is definitionally equal to the difference between output and employment growth (e), the law is sometimes expressed as e = −a + (1 − b) q. But the implications are the same. An increase in the growth of output will cause an increase in the growth of employment of about half a percentage point and an increase in productivity growth of a similar magnitude. Kaldor argued that this implies that manufacturing is subject to substantial increasing returns to scale.

The emphasis on the role of economies of scale as an important factor in determining the rate of economic progress has a long history. It is the basis of Adam Smith’s (1776) principle enunciated in the opening sentence of Book I of The Wealth of Nations that ‘[the] greatest improvement in the productive powers of labour, and the greater part of the skill, dexterity, and judgement with which it is anywhere directed, or applied, seem to have been the effect of the division of labour’. The latter in turn is limited by the extent of the market. This is nothing more than the phenomenon of economies of scale, in the broad sense of the term. The theme was subsequently elaborated in Allyn Young’s (1928) classic paper. In particular, Young argued that an important implication is that the capital–labour ratio is not to be understood as a response to relative factor prices but is primarily determined by the scale of production. He further stressed that economies of scale are primarily a macroeconomic phenomenon, the result of increased inter-industry specialization. (But it should be emphasized that the law has been found to apply to individual manufacturing industries.)

Another major tenet of the argument is that the law reflects both static and dynamic economies of scale. The former is a function of the volume of output and the gains in productivity from this source are reversible – if output contracts so the benefits of scale will be lost. Dynamic returns to scale, on the other hand, reflect such factors as ‘learning by doing’ and are usually ascribed to the rate of growth of output. These gains in productivity represent the acquisition of knowledge concerning more efficient methods of production and as such are irreversible. Substantial gains in productivity have been found to arise from this source even in the absence of any gross investment. A more rapid expansion of production will also lead to (as well as be the result of) a greater rate of innovation and a climate more favourable to risk taking. Investment will also be more efficiently used if it is introduced as part of a planned modernization scheme under conditions of rapidly expanding output rather than added, in an ad hoc manner, to existing capacity in stagnating industries. (Lamfalussy 1963, has termed these ‘enterprise’ and ‘defensive’ investment, respectively.)

For the law to provide evidence of the degree of returns to scale, it must be interpreted as reflecting a production relationship such as a form of the technical progress function. This being the case, the law is now usually specified as including the growth of the capital stock. This allows a separation to be made between the growth of productivity due to the greater use of machinery and that resulting from increasing returns to scale, per se. The inclusion of the growth of capital has not led to any major revision of the interpretation of the law.

The technical progress function was developed by Kaldor in an attempt to avoid the misleading dichotomy of growth into shifts of the production function and movements along the function. It is therefore all the more ironic that Verdoorn (1949, 1980) himself regards the law as being derived from the neoclassical Cobb–Douglas production function, although with the latter expressed in terms of growth rates. (The linear technical progress function may also be integrated to yield a conventional production function, although this is not necessarily true of the non-linear specifications.) Nevertheless, a paradox arises in that the estimation of the law using the levels of the various variables (the ‘static Verdoorn Law’) suggests either constant or small increasing returns to scale, whereas large estimates are obtained by estimating the ‘dynamic law’ using the same data sets. One explanation is that while the Verdoorn Law may be derived by differentiating a Cobb–Douglas production function with respect to time, it does not follow that the latter is the correct underlying structure. Integrating the law will lead to innumerable structures, depending upon the constant of integration.

The implications of Verdoorn’s Law are far-reaching. It suggests that there is an inherent tendency for growth to proceed in a self-reinforcing manner and provides an economic rationale for Myrdal’s (1957) notion of ‘cumulative causation’. An increase in output causes a faster growth of productivity for the reasons already noted. Provided all the gains are not absorbed by increased real wages, countries (or firms) will experience an increasing cost advantage over their competitors. Improvements in the non-price aspects of competition, such as quality, are also positively related to productivity growth. Of course, growth is not observed to be explosive and formalizations of the cumulative causation model show how the growth of various countries may converge to (differing) equilibrium rates.

(However, it has been suggested that the Verdoorn Law may simply result from this reverse causation from productivity to output growth. Large differences in exogenous productivity growth could lead to variations in output growth through the price mechanism – the ‘Salter effect’. This could generate a Verdoorn-type relationship even though constant returns to scale prevail. However, the evidence suggests that this is unlikely to be significant for total manufacturing or for an individual industry, although it may be an important factor in crossindustry studies.)

Since the Verdoorn Law shows that differences in productivity growth are caused by variations in the growth of output, the problem is to explain why disparities in the latter arise. In the inaugural lecture, Kaldor argued that the United Kingdom’s economic problems stemmed from the limited supply of labour available to the manufacturing sector and it was this that prevented a faster rate of growth. If this is the case, the Verdoorn Law may be mis-specified since employment and not output growth should be the regressor (Rowthorn 1975). When this specification (sometimes confusingly known as Kaldor’s Law) is estimated, most studies find that constant returns to scale prevail. However, Kaldor later retracted his earlier position. The long run growth of the advanced countries (and, equally, the less developed countries) is not determined by the exogenously given growth of factor inputs but rather by the growth of ‘effective demand’. Under these circumstances, the original specification of the law is to be preferred, although the very nature of the cumulative causation mechanism suggests that both output and employment growth may be jointly determined.

The importance of the rate of growth of demand as the driving force behind the pace of economic growth extends beyond the issues concerning the correct specification of the law. Long-run growth is best understood in a Keynesian (or, more appropriately, ‘Kaldorian’) framework. The rate of capital accumulation cannot be seen as an independent determinant of development since it is as much a result as a cause of the growth of output. The evidence further suggests that labour supplies were not a serious factor in limiting the growth of the advanced countries even during their most rapid expansionary phase which lasted from the end of World War II until 1973 (Cornwall 1977). There was either disguised unemployment in the primary and tertiary sectors or sufficient immigration to satisfy the demand for labour emanating from the manufacturing sector. The question naturally arises as to what is it that determines the growth of exogenous demand. In the early stages of development it is the growth of the agricultural surplus and the rate of land-saving innovations. With industrialization and the decline of the importance of agriculture, the key determinant becomes the growth of exports. This provides a source of the growth of autonomous demand both directly through the Harrod foreign trade multiplier and indirectly by relaxing the balance of payments constraint. Growth can thus be regarded as being ‘export-led’.

An important result of this approach is that, given the cumulative nature of economic growth, there is no inherent tendency for free trade to be to the benefit of all countries. Trade liberalization may well lead to a further deterioration in the growth of those countries which are already lagging as they find they become increasingly less competitive internationally. This is, of course, the converse of the inference that is sometimes drawn from the neoclassical theory of trade.

See Also


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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • J. S. L. McCombie
    • 1
  1. 1.