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 tale it must be interpreted as rejecting 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 capital has not led to any major revision of the interpretation of the law.

The technical progress function was developed by Kaldor in 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 (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 cross-industry 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 at 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