Kaldor 3.0: An Empirical Investigation of the Verdoorn-augmented Technical Progress Function

ABSTRACT

Consistent with neoclassical theory, the recent slowdown in labour productivity is generally regarded as one of the main causes of the current phase of economic stagnation. By contrast, post-Keynesian economics looks at productivity growth as positively affected by the rate of growth of output in the long run as well. By focusing on this alternative perspective, in our exploration we deal with an extended version of the Kaldorian technical progress function in which the trend growth rate of productivity is endogenously shaped by the dynamics of both output and capital−labour ratio. We empirically verify such a relationship for the total economy and the manufacturing sector through a structural vector autoregressive (SVAR) model for G7 countries (1970–2017). Our findings support the validity of a technical progress function, which admits increasing returns to scale, thus indicating that both the rate of growth of output and the process of capital intensification exert positive effects on productivity growth, even beyond the business cycle.

KEYWORDS:

• Labour productivity
• technical progress function
• increasing returns to scale
• investment
• SVAR

JEL CODES:

• O47
• D24
• E22

Acknowledgements

This research was conducted as part of the works of the Jean Monnet Centre of Excellence on ‘Labour, Welfare and Social Rights in Europe’ hosted by Roma Tre (Department of Economics). A preliminary draft of this paper has been presented at the 16th STOREP Conference (Siena, 27–29 June 2019) and the 21st FMM Conference (Berlin, 24–26 October 2019). We acknowledge all participants for fruitful comments. We also thank two anonymous referees for their precious advice and suggestions. Finally, we have benefited from stimulating discussion with Hubert Gabrisch, Santiago Gahn, Gian-Luca Merlini and Riccardo Pariboni. The usual disclaimer applies.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 The causal relationship between productivity and output growth rates is usually based on a theoretical approach that has a canonical representation in the Solow’s neoclassical growth model, where output growth is exclusively determined by supply-side factors.

2 Markedly, McCombie and Spreafico (2015) underlined that the original Kaldor technical progress function (Kaldor 1957) was featured by decreasing returns to scale, ‘because new ideas are exploited first and there are limits to the capacity to absorb these’, and hence ‘the increase in induced productivity growth will be at a diminishing rate’ (p. 1120).

3 According to this view, labour market deregulation is supposed to increase productivity by also reducing labour misallocation (Papageorgious 2014). Nevertheless, empirical works demonstrated that increasing labour market flexibility could have encouraged the adoption of labour-intensive techniques to the point that possible positive effects on employment (where obtained) could have occurred at the expense of lower productivity growth (Gordon and Dew-Becker 2008; Daveri and Parisi 2010; Enflo 2010).

4 Although the R&D has to be considered as a determinant of innovation processes and then a supply-side factor, R&D spending can also be considered as a part of aggregate demand. As stated by Cesaratto, Serrano, and Stirati (2003) and Deleidi and Mazzucato (2019a), R&D is considered as an expenditure of firms, different from investments, and it does not create productive capacity.

5 This mainly depends on the fact that canonical growth models assume full employment equilibrium and a production function where capital and labour are regarded as endowments, and that in turn they are the only variables determining the level of economic activity.

6 Recently, a re-emerging line of research based on the so-called ‘Baumol effect’ considers the shift towards the tertiary sector as an additional causes of slow productivity growth. According to Szirmai and Verspagen (2015), ‘a transfer of resources from manufacturing to services may provide a structural change burden if many service activities indeed have little potential for productivity increase’ (p. 47).

7 It should be underlined, however, that Verdoorn ([1949] 2002, 1956) did not regard the output as determined by aggregate demand, as instead advocated by supporters of the Keynesian tradition as Kaldor (see Palumbo 2015).

8 This cumulative process is also present in the notion of path dependency of most evolutionary models, for which the pioneer was Veblen (1919) in his theory of cumulative change and then Myrdal (1957) with a peculiar focus on institutional aspects.

9 For a wider discussion, the reader can refer to McCombie and Thirlwall (1994), Skott and Auerbach (1995) and Setterfield (1997).

10 A similar view can also be found in Verdoorn (1956) through the idea of ‘internal’ and ‘external’ economies, with the former related to specialisation processes, whereas the latter is explained by the development of skilled labour force and technological discoveries.

11 Notably, the first attempt by Kaldor to identify increasing returns to scale have been harshly called into question for methodological reasons by Rowthorn (1975).

12 Moreover, Kaldor (1966) found ‘a positive correlation between the overall rate of economic growth and the excess of the rate of growth of manufacturing output over the rate of growth of the non-manufacturing sectors. […] Since the differences in growth rates are largely accounted for by differences in rates of growth of productivity (and not of changes in the working population), the primary explanation must lie in the technological field’ (p. 104).

13 The work of Young (1928) was clearly inspired by Smith. On the relationships between Kaldor, Smith and Young contributions, see Chandra (2019).

14 As Kaldor’s stylised facts provided for a constant relationship between output and capital stock, a proxy for capital accumulation has been traced by Kaldor himself in the investment-output ratio.

15 As we will discuss below, econometric methodologies based on a single equation incorrectly deal with the portion of technical progress embodied in the investment−output ratio as a full exogenous variable, while post-Keynesian economics, which is the perspective endorsed in this work, suggests the plausible endogeneity of investment.

16 For the sake of completeness, it is worth noting at this stage that the original Kaldor technical progress function, which we refer to in this paper, is traceable in Kaldor (1957, 1961), while in Kaldor and Mirrlees (1962) there is a different specification. However, McCombie and Spreafico (2015) argued that ‘the latter was not markedly different from the former’ (p. 1119).

17 The fact that in Kaldor (1966, p. 128) the investment to output ratio is used instead of the growth rate of the capital per worker (as in Kaldor 1957) does not pollute, however, the overall reasoning on the determinants of technical progress: as suggested by Lavoie (2014), ‘although Kaldor himself nowhere links this version of Verdoorn’s law to his own previous work, it is clear that […] is close to Kaldor’s technical progress function’ (p. 428, emphasis added).

18 Similarly, an increase in the capital−labour ratio may also represent a shift of the economy (that is, a structural change) towards high-tech branches, or symmetrically a change in the output composition. As these sectors are supposed to exhibit higher levels of value added per person employed, this would not undermine the whole reasoning behind Kaldor’s technical progress function.

19 Notably, the neoclassical growth accounting typically decomposes labour productivity growth into the contributions of three components: capital deepening, labour quality and multifactor productivity. Then, labour productivity growth depends on i) the increase in capital per worker, ii) the substitution toward workers with higher marginal products, and iii) the impact of technical change and other factors that raise output growth beyond the measured contribution of inputs (Stiroh 2001). An interesting comparison of the two approaches – namely, the total factor productivity and the Kaldorian technical progress function – which is focused on the empirical analysis of productivity growth, has been provided by Paniccià, Piacentini, and Prezioso (2013).

20 More recently, several authors extended the concepts of investment and capital beyond private investment in tangible assets, including human capital (Becker, Murphy, and Tamura 1990), R&D expenditures (Romer 1990), and investment in public infrastructures (Aschauer 1989). What may to some extent differ from this view can be the so-called ‘new growth theory’, which attributes greater significance to certain types of investment that create externalities and additional productivity increase through spillovers and/or technology diffusion (see, among others, Arrow 1962; Grossman and Helpman 1993).

21 Notably, while Verdoon’s coefficient is usually estimated by using macroeconomic data, McCombie and De Ridder (1984), McCombie (1985), McCombie and Roberts (2007) and Deleidi et al. (2020) also discussed and validated this law at regional level.

22 Importantly, a lower magnitude of the Verdoorn coefficient is due to the introduction of a variable capturing the effect of investment.

23 Arguably, in the post-Keynesian framework the process of capital accumulation is supposed to be endogenously determined – consistent with the accelerator principle (Kaldor 1972) – and dependent on current and expected demand.

24 To capture the intensity of use of the factors of production, Basu (1996), in the context of a neoclassical production function, suggests the use of an index of the ratio of materials to the weighted capital stock and employment, and finds constant returns to scale (namely, a null Verdoorn effect). Other works using capacity utilisation to correct for cyclical conditions are Harris and Lau (1998) and Harris and Liu (1999).

25 Even if a cross-section analysis could give different results (cf. Felipe and McCombie 2014), in our framework time series are necessary to isolate the role of capital intensification from increasing returns to scale.

26 The use of productivity per hours worked instead of per person employed would avoid potential biases caused by part-time contracts. Unfortunately, due to lack data for all countries throughout the time span our analyses cannot refer to productivity in hours worked. However, for the available data we tested the pairwise correlation between productivity growth rates (expressed in persons employed and hours worked), whose values are 0.824 for total economy (well above the rule of thumb of 90 per cent in all countries, except for 0.792 for the United States) and 0.934 for the manufacturing sector (well above 90 per cent in all countries, except for 0.776 for France). Moreover, by including capacity utilisation in our reference model we are able to take into account the intensity of use of labour, thus overcoming the possible limitations of the use of productivity per person employed.

27 This choice is also consistent with the theoretical cornerstone of demand-led growth models based on the Sraffian Supermultiplier (Cesaratto, Serrano, and Stirati 2003), where the rates of growth of output and capital accumulation converge to the rate of growth of autonomous demand. In the most recent versions of these models, autonomous demand is also considered among the drivers of productivity (Deleidi and Mazzucato 2019a; Nah and Lavoie 2019).

28 This does not mean that our model is not able to preserve the cumulative causation nested in the Kaldorian framework: as we will discuss below, SVAR modelling considers all variables as exogenous, thus considering also all the possible feedback loop effects (for example, the effects of productivity growth on output growth).

29 For an in-depth discussion, see, among others, Kaldor (1968), Basu (1996) and Jeon and Vernengo (2008).

30 Concerning the United States, this finding may be related to the profound changes of the US production structure due to the increase of offshoring practices (for example, Mexican Maquiladoras, South-East Asian countries) and imports of intermediate goods (Borjas, Freeman, and Katz 1992; Feenstra and Hanson 1999; Antenucci 2018). In this regard, in several branches of the US manufacturing sector, the increase of the output−labour ratio was not due to a greater capital−labour ratio, and then labour productivity growth was not the result of growing investment. Indeed, the output−labour ratio has increased because employment fell more than the output did (Acemoglu et al. 2014; Antenucci 2018).

31 Notably, for Italy the average Verdoorn coefficient falls from 0.419 in the manufacturing sector to 0.122 in the total economy. Deleidi, Paternesi Meloni, and Stirati (2019) indicated that this should be not associated with the process of tertiarisation, but rather to the presence of relevant returns to scale in the Italian manufacturing sector.

32 With respect to France, the findings of a work by Cette, Corde S, and Lecat (2017) belied the idea that the decline in productivity was related to a faltering of the technological frontier. On the contrary, the slowdown in productivity may be ascribed to sustained misallocation phenomena.

33 Chirinko (1993), Khotari, Lewellen, and Warner (2014), Schoder (2014), Girardi and Pariboni (2018) and Girardi, Paternesi Meloni, and Stirati (2020) assessed the positive role of aggregate demand, and particularly its autonomous components, in shaping the process of capital formation. While Deleidi (2018) finds no significant relationship between loans granted to enterprises and the corresponding interest rates.

34 Certainly, a positive Verdoorn coefficient implies that demand-side policies would stimulate productivity growth, but being lower than one, such measures would also have positive effects on employment dynamics and then contribute to the breaking out of the current and prolonged phase of economic stagnation.