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A Steindlian Model of Income Distribution, Economic Growth, and Stagnation

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Secular Stagnation Theories

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Abstract

In line with the classical and post-Keynesian/Kaleckian tradition, in his original demand-side stagnation theory Josef Steindl focused on the functional distribution of income. In this chapter, Steindl’s twentieth-century theoretical model is adjusted to also include the personal distribution of income. The extended model includes both the profit share and a measure of the personal distribution of income. Based on a comparative static analysis, it is shown that economic shocks which lead to an increase in the unequal distribution of personal income and/or a rise in the profit share can be accompanied by a slowdown in long-term economic growth. Moreover, it is pointed out that changes in the long-term rate of economic growth feed back on both the personal and functional distribution of income.

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Notes

  1. 1.

    On the difficulty of solving delay differential equations, see also Andrews (2005, pp. 79–80, 92).

  2. 2.

    Dutt (2006), for instance, presents a Steindlian growth model which considers both demand- and supply-side effects. Hein (2014, pp. 375–440), on the other hand, refers to Kaleckian growth models which explicitly take account of financial markets and finance-dominated capitalism (see also Hein 2016, pp. 35–38).

  3. 3.

    On the importance of firms’ internal accumulation, the degree of capacity utilization, and technological progress for firms’ investment decisions, see also Guger et al. (2006, pp. 435–437).

  4. 4.

    Kaleckian and Steindlian growth models treat the degree of capacity utilization \((u)\) as an endogenous variable which, both in the short and the long run, is not necessarily equal to the planned degree of capacity utilization \((u_0)\). This characteristic has been criticized by several authors throughout the years, such as Committeri (1986), Auerbach and Skott (1988), and Skott (2012), who argue that long-run stable equilibria cannot be attained if \(u\) is not equal to \(u_0\) in the long run. Yet, as pointed out by Hein et al. (2011, 2012), for instance, deviations of \(u\) from \(u_0\) can be justified. In fact, the planned degree of capacity utilization \((u_0)\) must not be a definite, particular value, but may rather be understood as a range of values. Moreover, firms are likely to have multiple objectives, so they may accept deviations of \(u\) from \(u_0\) to reach other targets. Along similar lines, Dutt (2005, p. 68) concludes that “[...] there is no necessary inconsistency in the Steindlian framework.” See also Hein (2014, pp. 441–471) and Lavoie (2014, pp. 387–410).

  5. 5.

    Harrod (1948, pp. 22–23), when first defining his neutral technological progress, additionally assumed a constant interest rate. Given both a constant capital coefficient and a constant interest rate, Harrod-neutral technological progress is, in fact, characterized by a constant functional distribution of income. As will be shown further below, in the Steindlian model developed here, a change in the rate of technological progress alters the functional distribution of income. Hence, while technological progress as assumed in this Steindlian model involves key characteristics of Harrod neutrality, it does not completely conform to all of Harrod’s (1948, pp. 22–23) original assumptions. On the nexus between (Harrod-neutral) technological progress and the distribution of income, see also Krämer (1996, pp. 170–178, 193–196).

  6. 6.

    While the partial derivatives of \(u\), \(\pi \), and \(\psi \) with respect to \(z\) (see Eqs. D.8, D.16, and D.24 in Appendix D.1.1.1) seem to be uncertain, they are unambiguously defined if it is assumed that total profits \((R)\) are positive (see Eq. 8.12). With a positive \(R\), private households’ capital income \((Z)\) is also positive. The signs of the partial derivatives of \(u\), \(\pi \), and \(\psi \) with respect to \(z\) are given in Table 8.1.

  7. 7.

    In the opposite case of a cumulative upward spiral, the process comes to a halt when full capacity utilization is reached.

  8. 8.

    See Appendix D.1.2.1 for further details. From Eq. (8.49) and given the assumption that both \(\alpha _3\) and \(h_1\) are greater than zero (see Eqs. 8.8 and 8.10), it also follows that \(0 \,< \alpha _3h_1\, < 1\).

  9. 9.

    In the case of an unstable equilibrium, if the partial derivative of \(\mathrm {d}g/\mathrm {d} t\) with respect to an exogenous variable or parameter is negative (positive), the function in Fig. 8.1b shifts downward (upward) as well. A new equilibrium is not reached, however, as the actual growth rate \((g)\) keeps on falling (rising).

  10. 10.

    The terms profit-led growth and wage-led growth are used here following the discussion on profit-led and wage-led economic regimes in the existing literature, such as outlined in Bhaduri and Marglin (1990), Lavoie and Stockhammer (2013, p. 17), and Lavoie (2014, pp. 374–377). According to Lavoie (2014, p. 374), for instance, one can “[...] speak of a wage-led regime when an increase in real wages or the share of wages leads to a positive effect on the variable being considered [...].” Similarly, a profit-led regime exists “[...] when an increase in real wages or in the share of wages, that is, a decrease in the share of profits, leads to a negative effect on the variables under consideration [...].”

  11. 11.

    The terms equality-led and inequality-led are also used by Dutt (2017). He writes, “[...] [A]lthough wage and profit shares are indicators of inequality in many circumstances [...], the wage share it not an adequate measure of income equality. We should be more interested in the possibility of equality-led growth than wage-led growth [...]” (Dutt 2017, p. 193).

  12. 12.

    See also Skott (2017) on this issue.

  13. 13.

    As can be seen in Appendix D.1.2.2, the results in Tables 8.2 and 8.3 have been calculated by partially deriving Eq. (8.46) with respect to the model’s exogenous variables and parameters.

  14. 14.

    While the partial derivative of \(\mathrm {d}g/\mathrm {d} t\) with respect to \(z\) (see Eq. D.40 in Appendix D.1.2.2) seems to be ambiguous, it is definitely positive if it is assumed that \(R\), and hence \(Z\), is always positive (see Eq. 8.12). See also footnote 6 in Sect. 8.3.1.2.

  15. 15.

    The profit share \(\pi \, = \, m_1\, - \, m_2/u\) can be included in both Eqs. (8.51) and (8.52). While Eq. (8.51) can be written as \(W/K\, = \, (1 \, - \, \pi ) \, u\), Eq. (8.52) can be changed to \(Z/K\, = \,(1 \, - \, a_2) \, i\, + \, a_2\pi u\).

  16. 16.

    If there were no overhead labor costs, i.e., if \(m_2K\) in Eq. (8.12) were zero, \(\pi ^s\) would be a constant function with a value of \(m_1\). The \(\pi ^s\) schedule in Fig. 8.3 would thus be a horizontal line at \(\pi ^s\, = \, m_1\).

  17. 17.

    Additionally, Appendix D.2 provides a graphical analysis of a rise in the dividend payout parameter \((a_2)\), a rise in the saving rate of the rich private households \((s_h^r)\), and a decline in the parameter \(\alpha _2\).

  18. 18.

    The following graphical analysis is based on computer simulations of the functional relationships that have been outlined in the previous Sect. 8.4.1.

  19. 19.

    It should be noted that \(\alpha _3\, (h_0\, + \, h_1g)\), the term representing the impact of technological change in the \(g^d\) schedule, does not vary in the short run, as \(g\) is constant in the short run.

  20. 20.

    With a rise in \(m_1\), the \(g^d\) schedule shifts upward due to, first, the impact of \(m_1\) on \(S_f/K\) and, secondly, the impact of \(m_1\) on \(g\) in the term \(\alpha _3\, (h_0\, + \, h_1g)\). Yet, the impact of \(m_1\) on technological change, i.e., on the term \(\alpha _3\, (h_0\, + \, h_1g)\) in the \(g^d\) schedule, cannot alone shift the \(g^d\) schedule to such an extent that the \(g^s_1\) and \(g^d_1\) functions intersect at a growth rate \(g^*_1\) which lies above the original growth rate \(g^*_0\). The reason is that, according to the Keynesian stability condition, \(0 \,< \, \alpha _3h_1\, < \, 1\). Hence, considering only the impact of \(m_1\) on \(\alpha _3\, (h_0\, + \, h_1g)\), changes in \(m_1\) cannot shift the \(g^d\) function to the same extent as the \(g^s\) function. Only a strong impact of \(m_1\) on \(S_f/K\) can potentially raise the long-run equilibrium rate of real capital accumulation.

  21. 21.

    While in Fig. 8.6 \(\pi ^*_1\) is higher than \(\pi ^*_0\), it is also possible that \(\pi ^*_1\) falls below \(\pi ^*_0\).

  22. 22.

    While in Fig. 8.6 \(\psi ^*_1\) is higher than \(\psi ^*_0\), it is also possible that \(\psi ^*_1\) falls below \(\psi ^*_0\).

  23. 23.

    While in Fig. 8.8 \(\psi ^*_1\) is higher than \(\psi ^*_0\), it is also possible that \(\psi ^*_1\) falls below \(\psi ^*_0\).

  24. 24.

    In a similar context, Dutt (2017, p. 180) writes, “Examining the effects of changes in distribution (or some determinants of it) on growth does not, of course, imply that distribution is actually exogenous, but that this relation needs to be examined prior to embedding it into an enlarged model in which distribution (or its determinants) is made endogenous in the sense that growth and other related variables are allowed to affect it.”

  25. 25.

    The respective condition determining whether a rise (fall) in \(g^*\) raises or lowers \(\psi \) from the short to the long run has been outlined in Sect. 8.3.2.3 and Appendix D.1.2.2.

  26. 26.

    Graphically, in a typical \(u\)-\(\pi \)-diagram, ceteris paribus the \(\pi ^s\) schedule is steeper the lower \(g\) and \(u\). Hence, at low levels of economic activity, each rise in \(w\) and/or \(z\), which shifts the \(\pi ^d\) schedule upward, is accompanied by a relatively strong increase in the profit share \((\pi )\). Ceteris paribus, a rise in the profit share \((\pi )\) is more beneficial for the rich private households than for the poor private households.

  27. 27.

    For a systematic overview of the different economic regimes, see, for instance, Blecker (2002, p. 134). It should be noted that Bhaduri and Marglin (1990, p. 384) are solely concerned with the short run. Hence, although many growth models have originated from their seminal paper, their original model cannot be characterized as a growth model. In fact, Bhaduri and Marglin (1990) do not focus on the impact of changes in the profit and wage share on economic growth, but on output and capacity utilization (see also Dutt 2017, p. 172). Marglin and Bhaduri (1990), on the other hand, also refer to the rate of real capital accumulation. They write, “One advantage of the present model is that it is normalized in terms that permit it to be applied to the determination of equilibrium over a longer period [...]” (Marglin and Bhaduri 1990, p. 155).

  28. 28.

    For instance, if the degree of capacity utilization rises, but the profit rate remains constant, the profit share is necessarily lower than its initial value. Despite a higher degree of capacity utilization and a constant profit rate, real capital accumulation may decline if the impact of the profit share on real capital accumulation is relatively large. See also Lavoie (2014, pp. 370–371) and Blecker (2002, pp. 135–138).

  29. 29.

    As it has been defined that the measure of personal income inequality \((\psi )\) is always larger than one, \(Y_h^p\) must be lower than \(Y_h^r\), though.

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    Christina Anselmann

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Anselmann, C. (2020). A Steindlian Model of Income Distribution, Economic Growth, and Stagnation. In: Secular Stagnation Theories. Springer Studies in the History of Economic Thought. Springer, Cham. https://doi.org/10.1007/978-3-030-41087-2_8

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