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Investment, autonomous demand and long-run capacity utilization: an empirical test for the Euro Area

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Abstract

This paper reviews and empirically tests the validity of the Sraffian Supermultiplier model (SSM) and the modified Neo-Kaleckian model after the inclusion of autonomous components of aggregate demand. First, we theoretically assess whether the SSM may constitute a complex variant of the Neo-Kaleckian model. In this sense, it is shown that results compatible with the SSM can be obtained by implementing a set of mechanisms in a modified Neo-Kaleckian model. Second, the paper empirically tests the main implications of the models in the Euro Area, based on Eurostat data. In particular, the discussion outlines the short and long-run relation between autonomous demand and output, by testing cointegration and causality with a VECM model. Moreover, the role accounted by both theories to the rate of capacity utilization is empirically assessed, through a time-series estimation of the Sraffian and Neo-Kaleckian investment functions. While confirming the theoretical relation between autonomous demand and output in the long run, the results also show that capacity utilization still plays a key role in the short-run adjustment mechanism.

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Fig. 1

Source: author’s representation

Fig. 2

Source: authors’ representation, based on Eurostat (See Appendix 1)

Fig. 3

Source: authors’ representation, based on Eurostat (See Appendix 1)

Fig. 4

Source: authors’ representation, based on Eurostat (See Appendix 1)

Fig. 5

Source: authors’ representation, based on Eurostat (See Appendix 1)

Fig. 6

Source: authors’ representation, based on Eurostat (See Appendix 1)

Fig. 7

Source: authors’ representation, based on Eurostat (See Appendix 1)

Fig. 8

Source: authors’ representation, based on Eurostat (See Appendix 1)

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Notes

  1. We use the notation \(RD\) to denote autonomous business expenditures since they are considered to be equal to expenditures in research and development of the business sector, as it will be shown in Sect. 3.1. It is worth noting that the empirical literature on the SSM has often neglected the role of private R&D as a component of autonomous demand, with the notable exception of Deleidi and Mazzucato (2021). Since this expenditure category is neither financed by contractual incomes nor able to affect productive capacities, it should be treated as autonomous. This empirical analysis contributes to the literature by explicitly including private R&D.

  2. It is worth noting that the assumption of fully-induced investment does not require the absence of autonomous or innovative investment, but involves the consideration of the long-run capacity effects produced by the latter. The argument is extensively developed in Cesaratto et al., (2003, Sect. 4.2); the authors argues that “‘Unjustified’ investment […] occurs all the time […]. However, the best way to analyse these expenditures in a long-period context is to represent a wave of innovative investment […] as an exogenous increase in the aggregate estimate of […] the expected trend of the growth rate of demand, while still considering all gross investment to be induced so that we do not forget that capital stock is always adjusting” (ibid., p. 45). While the consideration of the capacity-creating effects of autonomous investment appears reasonable in the long run, it may be more problematic in a short-run framework, in which the capital stock is either fixed or adjusts sluggishly. The issue is empirically discussed and assessed in Sect. 5.

  3. In other words, this means that the definition of the actual and normal rates of capacity utilization is, respectively \(u=Y/{Y}_{fc}\) and \({u}^{n}={Y}_{n}/{Y}_{fc}\) (Hein 2014; Lavoie 2014). Subsequently, also the capital-output ratio is defined with full capacity output at the denominator \(v=K/{Y}_{fc}\). In this sense, this work differs from the long-lasting Sraffian tradition of defining variables weighted on the basis of normal positions (Kurz 1986), but it also reflects in the notation an increasing awareness within the Sraffian strand that discrepancies between normal positions and full capacity exist both in the short and in the long run.

  4. For the sake of brevity, we avoid the derivation from levels to growth rates, which can be found in Girardi and Pariboni (2016). Moreover, the interested reader can find the conditions for the dynamic stability of the equilibrium in Freitas and Serrano (2015).

  5. A formal presentation of the model, compatible with the notation used here for its amended version, can be found in Hein et al. (2012).

  6. The model presented here is similar to the medium-run version of the one by Lavoie (2016, Sect. 2.3). More specifically, we include autonomous demand components into an otherwise standard Neo-Kaleckian model. This allows, on one hand, to account for the role of autonomous demand in shaping long-run growth, in line with empirical evidence (Girardi and Pariboni 2016), without altering the nature of the baseline not fully-adjusted Neo-Kaleckian model, on the other. In this respect, the model is different from the contributions of Allain (2015) and Lavoie (2016, Sect. 3), both presenting long-run Neo-Kaleckian models encompassing a mechanism that drives the economy towards an equilibrium with normal utilization.

  7. More precisely, \(r=\frac{\Pi }{K}=\frac{\Pi }{Y}\frac{Y}{{Y}_{fc}}\frac{{Y}_{fc}}{K}=\frac{\pi u}{v}.\)

  8. In turn, the Cambridge equation is derived as the “dynamic version of […] the principle of effective demand” (Lavoie 2014, p. 348), i.e. \(S\equiv I\equiv {s}_{p}P-Z\) (ex-post). Dividing by the capital stock and rearranging, it follows that\(r={g}^{s}/{s}_{\pi }+z\), or, that is the same, \({g}^{s}={s}_{\pi }r-z\).

  9. We preserved the notation commonly used by Kaleckian authors. Therefore, it is important to note that now \({g}^{i}\) is expressed in terms of the determinants of the desired rate of capital accumulation, whereas in the previous Section it was meant to indicate the growth rate of investment. In other terms, \({g}^{i}\) is used here with the same theoretical meaning of \({g}^{K}\) in Sect. (2.1). However, as noted by Serrano and Freitas (2017), this does not cause significant alterations. Given the capital-capacity ratio, indeed, the goods market equilibrium yields the equality between the two rates.

  10. For the formal derivation, see Lavoie (2016).

  11. More specifically, while the key engine of the Neo-Kaleckian system is the long-run endogeneity of the rate of capacity utilization, the Sraffian Supermultiplier model reaches the equilibrium through the endogeneity of the marginal propensity to invest h, i.e. the sensitivity of investment to effective demand growth. In the Neo-Kaleckian model, an increase of autonomous demand growth reduces the z ratio, leading to an increase in the rate of capital accumulation via a permanently higher rate of capacity utilization (Fig. 1). Conversely, in the Supermultiplier model a change in \({g}^{z}\) implies a modification of the same sign of h and, in turn, of the supermultiplier. In the long run, the propensity to invest h will reach a constant level that is necessarily different from the initial one.

  12. See Appendix 1. Annual data on government gross fixed capital formation and R&D expenditures were cubically interpolated to convert them into quarterly frequency.

  13. More specifically, gross fixed capital formation of the public sector is added to final consumption expenditure of general government and subtracted from gross fixed capital formation as reported by the Eurozone national account systems (see Appendix 1 for data sources).

  14. Since quarterly national accounts are not consolidated for intra-area trade, balance of payment data are used to calculate exports and imports extra-Euro area. The quarterly data in millions of Euro (goods and services) of the current account are divided by nominal GDP in each period to obtain the export and import share extra-EA19.

  15. Therefore, intra-Euro exports and imports are treated as induced consumption, since they depend on the level of internal demand.

  16. The measurement of the actual rate of capacity utilization is a debated issue in the empirical literature. On the ‘utilization controversy’, see Nikiforos (2020) and Gahn and González (2020).

  17. In Sect. 4.3, we test the stationarity of the actual rate of capacity utilization. However, it is important to stress that stationarity alone is not a sufficient condition to deny the consistency of the Neo-Kaleckian model. That would require testing the persistence of changes in capacity utilization followed by increases in aggregate demand.

  18. The UR test has been carried out with the software JMulTi.

  19. A possible explanation could be that the analysis for member countries of the European Union and even more of the Euro Area fails to properly take into account the process of European integration. In particular, in the considered time frame the strong trend in the import share may undermine the cointegrating relation.

  20. In particular, this test is extensively criticized in the literature due to the fact that it finds predictive causality, which might reflect mere correlations in the case of non-stationary series that are cointegrated, as in our case.

  21. The discussion here focuses on the external sector only. As showed in Sect. 3.2, exports are the most important component of autonomous demand in the Euro Area, as well as the main driver of its growth. This does not exclude that there may be other potential sources of endogeneity, but it is meant to restrict the analysis to the component which endogeneity is more likely to influence the empirical results.

  22. For the sake of precision, the consensus on this assumption is not unanimous within Sraffian economists. In particular, the authors belonging to what Cesaratto (2015) calls the first Sraffian position will tend to refuse the strict exogeneity of \(u\). See, for example, Ciccone (1986) and Kurz (1990).

  23. For a discussion of the issue, see Hein (2014, Subsection 11.4) and Setterfield (2019).

  24. It is important to note that both the assumption of a long-run historical average and the adoption of Botte’s (2020) solution are compatible with the idea—put forward by Serrano (1995a, 1995b) – that while the normal utilization rate is a persistent variable, it could well vary in the short to medium run.

  25. Investment is defined as non-residential private gross fixed capital formation, as discussed in Sect. 3.1.

  26. It ought to be noted that this result does not affect particularly the stability of the Neo-Kaleckian model presented in Sect. 2.2, which does not require any assumption on the sign of the constant term in the investment function. For further discussion, see Lavoie (2016).

  27. Different from Girardi and Pariboni (2015, 2016) and Pérez-Montiel and Erbina (2020), in this empirical analysis we include R&D expenditures within autonomous demand. In addition, even if we do investigate the European case, since we do not use panel data for different member countries as Pérez-Montiel and Erbina (2020) do, our results ought to be interpreted as if member countries of the Eurozone were a single block. In this sense, we are excluding the effects of cross-country imbalances within the EU. This is particularly important if we consider imports and exports between member countries, which, should be interpreted as domestic demand.

  28. The point is made clear and formalized in several Kaldorian export-led models, e.g. Setterfield and Cornwall (2002).

  29. This would also be consistent with recent empirical evidence by Barbieri Góes and Deleidi (2022) on the persistence of the multipliers associated with autonomous demand components, which is a necessary condition to trigger the adjustment of supply to demand. Furthermore, as argued by Serrano et al. (2022) recent estimations of investment functions (see, among others, Fazzari et al. 2020; Haluska et al., 2021) provide support to the idea that supply accommodates to demand in line with the Supermultiplier framework.

  30. The analysis of developing economies would require the further difficulty of copying with the issue of obtaining foreign reserves, as stressed by Moraes et al. (2019).

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Acknowledgements

We would like to thank Eckhard Hein, Marc Lavoie, Franklin Serrano, Fabio Freitas, Attilio Trezzini, Riccardo Pariboni, Guilherme Haluska, and the editor for helpful comments and suggestions on earlier drafts of this article. We are also grateful to the participants in the 16th STOREP Conference at the University of Siena, the 2nd School of Advanced Studies in the Reappraisal of the Surplus Approach at Roma Tre University and the 2nd Workshop on Demand-led Growth at the Federal University of Rio de Janeiro. All remaining errors are, of course, our own.

Funding

The authors acknowledge the support of the Italian National Research Project—PRIN 2017 ‘Regional Policies, Institutions and Cohesion in the South of Italy’ (Project code 2017-4BE543; website www.prin2017-mezzogiorno.unirc.it), financed by the Italian Ministry of Education, University and Scientific Research from 2020 to 2023.

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  1. Economics Department, The New School for Social Research, 6 East 16th Street, New York, NY, 10003, USA

    Ettore Gallo

  2. Department of Political Sciences, University of Bari ‘Aldo Moro’, Bari, Italy

    Ettore Gallo & Maria Cristina Barbieri Góes

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Appendix 1

Appendix 1

  • Actual rate of capacity utilization—Eurostat, Industry: Current level of capacity utilization [ei_bsin_q_r2/BS-ICU-PC], retrieved from Eurostat: https://bit.ly/2S2erG6

  • Change in Inventories—Eurostat, GDP and main components (output, expenditure and income): Changes in inventories and acquisitions less disposals of valuables, [namq_10_gdp/P52_P53], retrieved from Eurostat https://bit.ly/3aH0FzC

  • Consumption—Eurostat, GDP and main components (output, expenditure and income): Final consumption expenditure [namq_10_gdp/P3], retrieved from Eurostat: https://bit.ly/3aH0FzC

  • Exports (intra-EA19)—Eurostat, European Union and euro area balance of payments—quarterly data (BPM6_CRE), retrieved from Eurostat: https://bit.ly/2JDVvZ8

  • Exports (total)—Eurostat, GDP and main components (output, expenditure and income): Exports of goods and services [namq_10_gdp/P6], retrieved from Eurostat: https://bit.ly/3aH0FzC

  • GDP—Eurostat, GDP and main components (output, expenditure and income): Gross domestic product at market prices [namq_10_gdp/B1GQ], retrieved from Eurostat: https://bit.ly/3aH0FzC

  • Government Investment—GFS: Government Finance Statistics, Government gross fixed capital formation [GFS.A.N.I8.W0.S13.S1.N.D.P51G._Z._Z._T.XDC_R_B1GQ._Z.S.V.N._T], retrieved from European Central Bank—Statistical Data Warehouse: https://bit.ly/373O9Yc

  • Government spending—Eurostat, GDP and main components (output, expenditure and income): Final consumption expenditure of general government [namq_10_gdp/P3_S13], retrieved from Eurostat: https://bit.ly/3aH0FzC

  • Import (extra EA-19)—Eurostat. European Union and euro area balance of payments—[BPM6_DEB], retrieved from Eurostat: https://bit.ly/2JDVvZ8

  • Imports (total)—Eurostat, GDP and main components (output, expenditure and income): Imports of goods and services [namq_10_gdp/P7], retrieved from Eurostat: https://bit.ly/3aH0FzC

  • Investment (total)—Eurostat, GDP and main components (output, expenditure and income): Gross Fixed Capital Formation [namq_10_gdp/P51G], retrieved from Eurostat: https://bit.ly/3aH0FzC

  • R&D: Eurostat, Intramural R&D expenditure (GERD) by sectors of performance and type of costs: Total R&D expenditure, business enterprise sector [rd_e_gerdcost/TOTAL/BES], retrieved from Eurostat: https://bit.ly/2OAQoff

  • Residential expenditure—Eurostat, Gross fixed capital formation with AN_F6 asset breakdowns [nama_10_an6, N111G], quarterly, retrieved from Eurostat: bit.ly/2UCzf8i

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Gallo, E., Barbieri Góes, M.C. Investment, autonomous demand and long-run capacity utilization: an empirical test for the Euro Area. Econ Polit 40, 225–255 (2023). https://doi.org/10.1007/s40888-022-00291-7

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