Add Journal to My Library
Cambridge Journal of Economics
, Volume Advance Article – Jun 7, 2018

30 pages

/lp/ou_press/a-supermultiplier-stock-flow-consistent-model-the-return-of-the-xRz304EE0b

- Publisher
- Oxford University Press
- Copyright
- © The Author(s) 2018. Published by Oxford University Press on behalf of the Cambridge Political Economy Society. All rights reserved.
- ISSN
- 0309-166X
- eISSN
- 1464-3545
- D.O.I.
- 10.1093/cje/bey008
- Publisher site
- See Article on Publisher Site

Abstract Supermultiplier models have been recently brought to the post-Keynesian debate. Yet these models still rely on quite simple economic assumptions, being mostly flow models which omit the financial determinants of autonomous expenditures. Since the output growth rate converges in the long run to the exogenously given growth rate of “non-capacity creating” autonomous expenditure and the utilization rate moves towards the normal utilization rate, the paradoxes of thrift and costs remain valid only as level effects (average growth rates). This paper investigates whether the core conclusions of supermultiplier models hold in a more complex economic framework, described by means of a supermultiplier SFC model, in which private business investment is assumed to be completely induced by income while the autonomous expenditure component—in this case consumption out of wealth—becomes endogenous. The results of the numerical simulation experiments suggest that the paradox of thrift can remain valid in terms of growth effects and that a lower profit share can also be associated with a higher accumulation rate, though with a lower profit rate. 1. Introduction Supermultiplier models, as conceived by Sraffian authors (Serrano, 1995A; Bortis, 1997), keep the “Keynesian hypothesis” (Lavoie, 2014, p. 359), emphasizing the idea that growth can be demand-led even in the long run. This is made possible through the introduction of a “non-capacity creating” autonomous expenditure which grows at an exogenously given rate and towards which capital accumulation rate will converge in the long run, as business investment is completely induced by income. One of the consequences of these assumptions is that, since both capital accumulation and utilization rates converge to given exogenous values, the paradox of thrift and the paradox of costs are no longer valid in terms of growth effects in the long run, but only in short and medium runs (Freitas and Serrano, 2015; Lavoie, 2016). That is to say, growth rates can be higher during the traverse period, but not in the fully adjusted position of the system, when utilization rates reach the normal level (Lavoie, 2016). Supermultiplier models have been recently brought to the post-Keynesian debate by Allain (2015B) and Lavoie (2016). Besides, some empirical evidence for its main results is provided by Girardi and Pariboni (2015). However, these models still do not properly account for the interactions between financial stocks and flows, which—as we sustain here—could lead to different results regarding the paradoxes in the long run. The aim of the paper is to verify whether these key results of the supermultiplier model—that is, that the paradoxes only hold for level effects in the long run—remain valid in a more financially complex economic framework with interactions between financial stocks and flows. To accomplish this, we propose to build a Stock Flow Consistent model keeping the supermultiplier approach essentials—namely, the autonomous expenditure component, induced business investment and the Harrodian investment behaviour through which firms react to the discrepancies between actual and desired utilization rates. We adopt a consumption function found in most post-Keynesian models, in which households consume a proportion of their wages and of their wealth. The consumption out of wealth is the autonomous expenditure component of this economy and since the dynamics of household wealth is endogenous to the system, we can say that at least part of the autonomous expenditure component is also endogenous to the model. We call ‘autonomous’ the expenditure decisions that cannot be directly deduced from the circular flow of income (Serrano, 1995B), following Freitas and Serrano (2015, p. 4) when they state that consumption has an autonomous component (in their case, loosely related to credit and not functionally connected to wealth, as in our model) ‘unrelated to the current level of output resulting from firms’ production decisions’. Endogenizing a specific component of autonomous expenditures1 means that its contribution to the system’s dynamics will be conditioned by the way it interacts with other variables and parameters, which may contribute to further explore the implications of supermultiplier models. Besides this introduction, the paper is organized as follows. The second section of the paper briefly reviews the heterodox growth models literature debate over the utilization rate and the consequences of each model, culminating in the proposal of these alternative (mainly supermultiplier) growth models. In Section 2.1, we further discuss the features and results of the recent supermultiplier models and highlight the lack of financial complexity, which motivates the building of the model in the third section. In Section 3, we present the framework of the model as well as short- and long-run equilibrium conditions. Following this, in the fourth section three numerical simulation experiments are carried out. The experiments are a reduction in firms’ mark-up (Section 4.1); an increase in the propensity to consume out of wages (Section 4.2); and, finally, an increase in the autonomous expenditure component (an increase in the propensity to consume out of wealth) (Section 4.3). Still, in this section, we make a general assessment of the shared results of the shocks (Section 4.4). Section 5 concludes the paper. 2. Heterodox demand-led growth models Heterodox growth theories, as well as the neoclassical model of growth,2 have emerged as an attempt to get around the instability presented by Harrod’s model (Kregel, 1980; White, 2008; Fazzari et al., 2013; Cesaratto, 2015). One of the issues raised by Harrod (1939) is that the steady growth state of the model is unstable because deviations of the growth rate of the economy from the ‘warranted growth rate’ will make the path explode or collapse (Fazzari et al., 2013). Accordingly, the models based on the Cambridge equation (Kaldor, 1961; Robinson, 1962) avoided instability assuming endogenous income distribution, what makes it possible for the system to reach the exogenously given utilization rate in the long run. However, in these models, a higher profit share was associated with higher accumulation and profit rates,3 which means that getting around instability had come at the cost of not reproducing the stylized fact that a higher capital accumulation rate can be accommodated through an increase in the utilization rate without changing income distribution between wages and profits (Cesaratto, 2015). During the 1980s, some central features of Cambridge models began to be more fiercely questioned, such as full employment, the endogenous income distribution and the contradiction between short- and long-run dynamics (Lavoie, 2014).4 These controversies originated the first neo-Kaleckian models, as put forward by Rowthorn (1981), Dutt (1984) and Amadeo (1986), which extended the effective demand principle to the long run without assuming full capacity utilization and price mechanisms to bring about the adjustment between investment and savings (Amadeo, 1987; Skott, 2010; Hein et al., 2012). These neo-Kaleckian models considered income distribution to be exogenous, so changes in the capital accumulation rate would take place through the endogenous capacity utilization rate, even in the long run. They came up with two particularly interesting features at the same time: the paradox of thrift and the paradox of costs. The paradox of thrift says that an increase in the saving rate5 would lead to lower capital accumulation, profit and utilization rates in the new equilibrium. The paradox of costs—in the version initially presented by Rowthorn (1981)—means that an increase in real wages after a fall in firms’ mark-up would boost consumption and lead to a higher utilization rate and, consequently, to higher-capacity accumulation and profit rates (Dutt, 2011; Lavoie, 2014). One could say that the paradoxes that emerge from the canonical neo-Kaleckian model are dynamic paradoxes or paradoxes in terms of ‘growth effects’. The initial paradox of thrift as presented by Keynes (1936) referred to the negative effect of a higher propensity to save on the level of output. Likewise, the paradox of costs as put forward by Kalecki (1969) considered only the static effect of a decrease in wages on firms’ level of profit (Lavoie, 2014). The neo-Kaleckian approach, despite its predominance among post-Keynesian authors, has been repeatedly criticized for not dealing with the Harrodian instability issue. The point is: since the utilization rate is endogenous in the long run, it could be permanently higher or lower than the normal or planned utilization rate. In neo-Kaleckian models, long-run accumulation is ultimately exogenous, so a higher utilization rate does not affect investment plans and, consequently, firms do not revise the trend growth of sales even with a persistently higher or lower demand. For authors from other heterodox strands, as some Sraffians, deviations between actual and normal utilization should foster changes in growth expectations and in investment decisions, giving rise to Harrodian instability (Hein et al., 2011, 2012; Lavoie, 2014).6 As an alternative to neo-Kaleckian models, Serrano (1995A) and Bortis (1997) proposed the so-called ‘Sraffian’ supermultiplier model, in which long-run growth is demand-led and capacity utilization converges towards the normal or planned levels, by means of the adjustment of the marginal propensity to invest of private firms. This is made possible by the introduction of an autonomous demand component growing at an exogenously given rate while private business investment is assumed to be induced by income without losing the Keynesian causality of investment to savings. The full inducement of private business investment addresses the criticism that firms must reevaluate their expected long-run growth rate, when the utilization rate diverges from the normal one. The approach solves a previously impossible trinity, harmonizing the Keynesian hypothesis, exogenous income distribution and the long-run balance between productive capacity and the aggregate demand (Cesaratto, 2015). The first versions of the supermultiplier model (Serrano, 1995A; Bortis, 1997) lacked a clear depiction of the endogenous mechanism by means of which the utilization rate tends towards its normal rate. However, a Harrodian mechanism through which the propensity to invest becomes endogenous and changes according to the discrepancy between the actual utilization and the normal one was included in a recent version of the supermultiplier by Freitas and Serrano (2015), which means at least a conditional solution to Harrod’s knife-edge instability problem (Allain, 2015B; Lavoie, 2016). In a similar fashion to this latest version, the supermultiplier model was brought to the post-Keynesian debate, within the neo-Kaleckian framework, by Allain (2015A, 2015B) and by Lavoie (2016). They both combine a ‘non-capacity creating’ autonomous expenditure component—which grows at an exogenously given rate towards which the rate of capital accumulation will converge in the long run—and the Harrodian adjustment mechanism. These supermultiplier models bring into the scene a whole new spectrum of demand-led models, which could enrich the post-Keynesian literature, since in most neo-Kaleckian models, private business investment is the demand component which leads growth, while there is no reason why this should always be the case.7 From the canonical version of the neo-Kaleckian model (Dutt, 2011; Hein et al., 2011) to its most popular variant, the ‘post-Kaleckian’ (Lavoie, 2014) model of Bhaduri and Marglin (1990), this remains as a predominant feature. This also applies to the more financially complex stock-flow consistent (SFC from now on) models. To be fair, we can find some models in which government expenditures assume the leading role of growth, as in chapter 11 of Godley and Lavoie’s (2007) book. However, to our best knowledge, only recently the implications of different growth-regimes—as, for instance, consumption-led ones—started to be explored.8 In the next subsection, we deal with these recent supermultiplier growth models and how they still need to add some financial complexity to the economic framework to do justice to the post-Keynesian debate about the roles of money and finance on the dynamics of capitalism. 2.1 The lack of financial determinants in supermultiplier growth models According to Lavoie (2010), one of the main reservations of post-Keynesians about the supermultiplier approach is that it does not include the financial features of the economy, differently from several neo-Kaleckian models, which in the 1990s began to link the financial and real sides of the economy (Lavoie, 2006; Dutt, 2011).9 This has not been significantly altered by recently published papers such as Freitas and Serrano (2015), Lavoie (2016) and Allain (2015A). So far these supermultiplier growth models rely on quite simple economies in order to obtain analytical solutions. Most of them have only two or three sectors, firms and households (investment and consumption) and, more recently, government or the foreign sector; they typically feature only one kind of real asset (the capital stock) and one kind of financial asset (government debt), if at all. In Tables 1 and 2, in which we present respectively the balance sheet and the transactions flow matrix of the recent models in this literature, we can notice they are mainly flow models, not paying enough attention to the interaction between stocks of financial assets and income flows. Table 1. Balance sheet of supermultiplier models Assets Households Firms Government ⋄ ∑ 1. Fixed Capital +Kf +Kf 2. Equities † +E −E 0 3. Govt. Bills ⋄ +B −B 0 4. Net worth Vh Vf −B +Kf Assets Households Firms Government ⋄ ∑ 1. Fixed Capital +Kf +Kf 2. Equities † +E −E 0 3. Govt. Bills ⋄ +B −B 0 4. Net worth Vh Vf −B +Kf Notes: The papers considered in this table are the following: Allain (2015A, 2015B); Freitas and Serrano (2015); Dutt (2016); Lavoie (2016); Hein (2016) and Nah and Lavoie (2017). The white cells are part of the models in all papers considered in this table. †Equities are included only in Hein (2016). ⋄Government bills are included only in Dutt (2016) and Hein (2016). View Large Table 1. Balance sheet of supermultiplier models Assets Households Firms Government ⋄ ∑ 1. Fixed Capital +Kf +Kf 2. Equities † +E −E 0 3. Govt. Bills ⋄ +B −B 0 4. Net worth Vh Vf −B +Kf Assets Households Firms Government ⋄ ∑ 1. Fixed Capital +Kf +Kf 2. Equities † +E −E 0 3. Govt. Bills ⋄ +B −B 0 4. Net worth Vh Vf −B +Kf Notes: The papers considered in this table are the following: Allain (2015A, 2015B); Freitas and Serrano (2015); Dutt (2016); Lavoie (2016); Hein (2016) and Nah and Lavoie (2017). The white cells are part of the models in all papers considered in this table. †Equities are included only in Hein (2016). ⋄Government bills are included only in Dutt (2016) and Hein (2016). View Large Table 2. Transactions flow matrix of supermultiplier models Households Firms Government † Foreign sector ⋆ ∑ Current Capital 1. Consumption –C +C 0 2. Investment +I –I 0 3. Govt. expenditures † +G –G 0 4. Exports ⋆ +X –X 0 5. Imports ⋆ –M +M 0 6. Wages +W –W 0 5. Taxes † –T +T 0 7. Profit +FD –F +FU 0 8. Interest ⋄ +iB –iB 0 9. Subtotal Sh 0 Sf Sg Sex 0 Households Firms Government † Foreign sector ⋆ ∑ Current Capital 1. Consumption –C +C 0 2. Investment +I –I 0 3. Govt. expenditures † +G –G 0 4. Exports ⋆ +X –X 0 5. Imports ⋆ –M +M 0 6. Wages +W –W 0 5. Taxes † –T +T 0 7. Profit +FD –F +FU 0 8. Interest ⋄ +iB –iB 0 9. Subtotal Sh 0 Sf Sg Sex 0 Notes: The models considered are the same ones of Table 1. The white cells are part of the models in all papers considered in this table. †The Government sector and government expenditures are included in Allain (2015B); Dutt (2016) but not in Hein (2016). ⋆The foreign sector and exports and imports are included only in Nah and Lavoie (2017). ⋄Interest payments on bills are included only in Dutt (2016) and Hein (2016). View Large Table 2. Transactions flow matrix of supermultiplier models Households Firms Government † Foreign sector ⋆ ∑ Current Capital 1. Consumption –C +C 0 2. Investment +I –I 0 3. Govt. expenditures † +G –G 0 4. Exports ⋆ +X –X 0 5. Imports ⋆ –M +M 0 6. Wages +W –W 0 5. Taxes † –T +T 0 7. Profit +FD –F +FU 0 8. Interest ⋄ +iB –iB 0 9. Subtotal Sh 0 Sf Sg Sex 0 Households Firms Government † Foreign sector ⋆ ∑ Current Capital 1. Consumption –C +C 0 2. Investment +I –I 0 3. Govt. expenditures † +G –G 0 4. Exports ⋆ +X –X 0 5. Imports ⋆ –M +M 0 6. Wages +W –W 0 5. Taxes † –T +T 0 7. Profit +FD –F +FU 0 8. Interest ⋄ +iB –iB 0 9. Subtotal Sh 0 Sf Sg Sex 0 Notes: The models considered are the same ones of Table 1. The white cells are part of the models in all papers considered in this table. †The Government sector and government expenditures are included in Allain (2015B); Dutt (2016) but not in Hein (2016). ⋆The foreign sector and exports and imports are included only in Nah and Lavoie (2017). ⋄Interest payments on bills are included only in Dutt (2016) and Hein (2016). View Large We are aware that increasing complexity and dealing with both the real and the financial sides of the economy might not have been the goals of these models so far. Yet the inclusion of financial determinants and the analysis of debt and deficit dynamics is starting to gain momentum (see Dutt, 2015, 2016; Hein, 2016). In Allain (2015B), government expenditures lead growth in the long run, but the government budget deficit is balanced, so there is neither government debt nor interest payments accruing from government bills. On the other hand, Dutt (2015, 2016) and Hein (2016) address the effects of debt dynamics on income inequalities in a system where government plays the leading role of growth. Dutt (2016) highlights how the supermultiplier mechanism impacts public debt:10 an increase in the growth rate of autonomous government expenditures leads to a higher accumulation rate during the transition, which means a reduction in the government deficit to capital ratio and consequently leads to a reduction in the debt to capital ratio, due to the increase in income and taxation, reducing the financial needs of the government. The lower debt to capital ratio also means a reduction in the financial income received by capitalists as a share of capital, thus reducing income inequality; in turn, Hein (2016) does not deal with taxation issues, focusing on the ambiguous effect of an increase in the debt to capital ratio on the pre-tax functional distribution of income: a higher deficit pushes activity, thus increasing production and income from real activity (reducing the financial income share). On the other hand, the consequent increase in government debt to capital ratio increases the financial income share received from interest payments. In Table 3, we exhibit the main features and results of these models. The ultimate source of growth varies: it is consumption out of credit11 in Freitas and Serrano (2015), the capitalists’ consumption in Lavoie (2016) and government expenditures in Allain (2015B). In Allain (2015A), the author proposes an interesting model in which subsistence consumption, through a redistributive mechanism between employed and unemployed workers, works as the autonomous variable growing at the exogenous population growth rate.12 Most of these models explicitly deal with the Harrodian instability problem, by means of an adjustment mechanism of the expected trend growth rate of sales or of the propensity to invest (in the case of Freitas and Serrano (2015)), which makes the utilization rate converge to the normal rate. In both adjustment mechanisms presented, Harrodian instability is needed for the utilization to converge to the normal one, as long as it is not too strong. Therefore, the adjustment of the expected trend growth rate (or propensity to invest) by firms must be slow. Despite conciliating the autonomous expenditure component with some financial complexity—through government debt dynamics—it is important to stress that neither Hein (2016) nor Dutt (2016) deeply discuss the Harrodian instability issue. Hein (2016) assumes that the normal utilization is not precisely defined in a world of uncertainty or that it adjusts endogenously to the actual utilization rate. Indeed, Hein (2016) keeps the usual neo-Kaleckian investment function, in which animal spirits are exogenous and capacity utilization adjusts endogenously to the changes in aggregate demand even in the long run. Differently, Dutt (2016) considers that firms have rational expectations and assume that the trend growth rate of sales equals the growth rate of the autonomous demand component chosen. As far as we know, a more ‘complete’ stock-flow consistent supermultiplier model, which deals with Harrodian instability issues and which is concerned with growth dynamics, is still rare. In Dos Santos and Zezza (2008), the authors already suggested that it could be interesting to study an investment function with a Harrodian mechanism, according to which firms would adjust their investment demand to stabilize the capacity utilization, within an SFC framework. More recently, we can find three papers which include an investment function of the accelerator type in an SFC framework. Both Bortz (2014) and Leite (2015) provide an investment function which makes investment endogenous and dependent on income, but they rely on the assumption that government expenditures are completely exogenous, so the dynamics of their models will be closely related to the supermultiplier models described in the present section. Pedrosa and Macedo e Silva (2014) also provide a model in which investment is endogenous and in which government expenditures are a fraction of the capital stock, thus the dynamics of their model are closely related to the one presented by the model proposed here. However, the purpose of the authors is to analyse the government debt dynamics and its relation to private sector debt, which is not our focus here. As Freitas and Serrano (2015) acknowledge, it is essential to focus on the financial determinants and on the dynamics of the different ‘non-capacity creating’ components of autonomous demand which could take on the leading role on growth. Allain (2015B) also suggests that the results of supermultiplier models may vary according to the autonomous expenditure chosen as the growth engine. Hein (2016) stresses that the insights provided by his model should be examined and assessed in ‘more complex models, which might include taxes and thus the post-tax distribution of income, more complicated investment functions, explicitly considering the issue of investment finance for example, wealth-based and debt-based consumption, or a foreign sector’ (Hein 2016, p. 20). However, in the (still too simple) supermultiplier models summarized in Table 3, the choice of the engine of growth seems to be inconsequential. The accumulation rate will converge to the exogenously given growth rate of the leading variable, whatever it is. A decrease in the propensity to save, for instance, will increase the level of output but will not permanently effect the growth rate of the economy, since the capital accumulation rate will converge towards the exogenously given growth rate of autonomous consumption or government expenditures. The same applies to the paradox of costs. In the case of (e.g.) a reduction in the profit share, the level of output and the level of profits will be higher as a consequence of the increase in household expenditures, but the rate of profits will be lower since the utilization rate converges to the normal utilization rate.13,14 Table 3. Supermultiplier models features and results Model Y Z Investment behaviour Results of a decrease in s Results of a decrease in π Y gk, gy, u Y gk, gy, u Allain (2015B) C+I+G Government expenditures Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Allain (2015A) C+I Subsistence consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Dutt (2016) C+I+G Government expenditures Rational expectations Permanent + Transient + Permanent + Transient + Hein (2016) C+I+G Government expenditures Animal spirits, endogenous u Permanent + Transient + Permanent + Transient + Freitas and Serrano (2015) C+I Consumption financed by credit Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Lavoie (2016) C+I Capitalist’s consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Nah and Lavoie (2017) C+I+XL Net exports Harrodian instability mechanism Permanent + Transient + Permanent +/- Transient +/- Model Y Z Investment behaviour Results of a decrease in s Results of a decrease in π Y gk, gy, u Y gk, gy, u Allain (2015B) C+I+G Government expenditures Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Allain (2015A) C+I Subsistence consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Dutt (2016) C+I+G Government expenditures Rational expectations Permanent + Transient + Permanent + Transient + Hein (2016) C+I+G Government expenditures Animal spirits, endogenous u Permanent + Transient + Permanent + Transient + Freitas and Serrano (2015) C+I Consumption financed by credit Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Lavoie (2016) C+I Capitalist’s consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Nah and Lavoie (2017) C+I+XL Net exports Harrodian instability mechanism Permanent + Transient + Permanent +/- Transient +/- Legend: Y is for output, Z for the autonomous expenditure component, gk for capital accumulation rate, gy for output growth, u for utilization rate, s for propensity to save and π for the profit share. View Large Table 3. Supermultiplier models features and results Model Y Z Investment behaviour Results of a decrease in s Results of a decrease in π Y gk, gy, u Y gk, gy, u Allain (2015B) C+I+G Government expenditures Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Allain (2015A) C+I Subsistence consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Dutt (2016) C+I+G Government expenditures Rational expectations Permanent + Transient + Permanent + Transient + Hein (2016) C+I+G Government expenditures Animal spirits, endogenous u Permanent + Transient + Permanent + Transient + Freitas and Serrano (2015) C+I Consumption financed by credit Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Lavoie (2016) C+I Capitalist’s consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Nah and Lavoie (2017) C+I+XL Net exports Harrodian instability mechanism Permanent + Transient + Permanent +/- Transient +/- Model Y Z Investment behaviour Results of a decrease in s Results of a decrease in π Y gk, gy, u Y gk, gy, u Allain (2015B) C+I+G Government expenditures Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Allain (2015A) C+I Subsistence consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Dutt (2016) C+I+G Government expenditures Rational expectations Permanent + Transient + Permanent + Transient + Hein (2016) C+I+G Government expenditures Animal spirits, endogenous u Permanent + Transient + Permanent + Transient + Freitas and Serrano (2015) C+I Consumption financed by credit Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Lavoie (2016) C+I Capitalist’s consumption Harrodian instability mechanism Permanent + Transient + Permanent + Transient + Nah and Lavoie (2017) C+I+XL Net exports Harrodian instability mechanism Permanent + Transient + Permanent +/- Transient +/- Legend: Y is for output, Z for the autonomous expenditure component, gk for capital accumulation rate, gy for output growth, u for utilization rate, s for propensity to save and π for the profit share. View Large As mentioned by Lavoie (2016), although the paradoxes of thrift and costs are lost as growth effects in supermultiplier models, they still hold if redefined as level effects. This also means that during the traverse from one steady state to the other, growth rates change, being higher or lower on average. However, the disappearance of the growth effects reflects the assumption that ‘non-capacity creating autonomous expenditures’ are completely exogenous. A different picture may emerge if, by means of a more complete description of the feedbacks between financial stocks and flows, one allows for a specific engine of growth to become partially endogenous to the model. This is what we propose in Sections 3 and 4. 3. A supermultiplier Stock-Flow Consistent model Based on the brief review of the previous section, we propose to build an SFC model in which the “non-capacity creating” autonomous expenditure component is the consumption out of household wealth and in which private business investment is totally induced. Since household wealth is endogenous to the model, it follows that the autonomous expenditure component is also endogenous.15 Firms follow the Harrodian investment behaviour and adjust their propensity to invest when the utilization rate seems to significantly deviate from the desired utilization rate or band. Our aim at first is to analyse whether the supermultiplier model results still hold when the autonomous expenditure component is endogenous in the long run and how the interaction between stocks and flows can influence these results. In the next subsections, we present the framework of the model, the short-run equilibrium condition, the dynamics equations and the long-run equilibrium conditions. 3.1 Framework of the model In the present subsection, we describe our SFC model that attempts to incorporate some of the supermultiplier approach features. Table 4 presents the balance sheet of the four institutional sectors featured: households, firms, government and banks. The model deals with a pure credit closed economy without inflation (price level is stable and equals the unity). This is so because introducing a Central Bank and/or inflation would make the model unnecessarily complex for the initial purpose we have in mind. Of course, we allow for the price of equity to change in order to account for household capital gains or losses. Table 4. Balance sheet matrix Assets Household Firms Banks Government ∑ 1. Deposits +M −M 0 2. Loans −L +L 0 3. Fixed capital +Kf +Kf 4. Equities +pe.E −pe.E 0 5. Government Bills +B −B 0 6. Net worth Vh Vf 0 −B +Kf Assets Household Firms Banks Government ∑ 1. Deposits +M −M 0 2. Loans −L +L 0 3. Fixed capital +Kf +Kf 4. Equities +pe.E −pe.E 0 5. Government Bills +B −B 0 6. Net worth Vh Vf 0 −B +Kf Notes: We obtain the net worth for both household and firm sectors summing up lines 1 to 5 of the respective columns: Vh=M+peE+B and Vf=Kf−L−peE. View Large Table 4. Balance sheet matrix Assets Household Firms Banks Government ∑ 1. Deposits +M −M 0 2. Loans −L +L 0 3. Fixed capital +Kf +Kf 4. Equities +pe.E −pe.E 0 5. Government Bills +B −B 0 6. Net worth Vh Vf 0 −B +Kf Assets Household Firms Banks Government ∑ 1. Deposits +M −M 0 2. Loans −L +L 0 3. Fixed capital +Kf +Kf 4. Equities +pe.E −pe.E 0 5. Government Bills +B −B 0 6. Net worth Vh Vf 0 −B +Kf Notes: We obtain the net worth for both household and firm sectors summing up lines 1 to 5 of the respective columns: Vh=M+peE+B and Vf=Kf−L−peE. View Large Banks lend to firms and receive deposits from households. As banks do not make profits, deposits earn the same interest rate of loans granted to firms. Firms sell equities to households and are not credit constrained, for banks grant all demand for loans. As prices are held constant, one can assume that a monetary authority determines the real interest rate, as in Ryoo and Skott (2013). Households in this economy hold three kinds of assets. They buy equity from productive firms and bills issued by the government and hold the rest of their wealth in the form of deposits at banks. Table 5 shows the transactions between institutional sectors in its first part and the flow of funds in the second part. At this point we can describe the transactions of each sector and the behavioural assumptions. Table 5. Transactions and flow of funds matrix Household Firms Banks Government ∑ Current Capital 1. Consumption −C +C 0 2. Investment +I −I 0 3. Government expenditures +G −G 0 4. Wages +W −W 0 5. Taxes −T +T 0 6. Profit +FD −F +FU 0 7. Deposits interest +ir.M−1 −ir.M−1 0 8. Loans interest −ir.L−1 +ir.L−1 0 9. Bills interest +ir.B−1 −ir.B−1 0 10. Subtotal Sh 0 Sf 0 Sg 0 11. ΔDeposits −ΔM +ΔM 0 12. Δ Loans +ΔL −ΔL 0 13. Δ Equity −pe.ΔE +pe.ΔE 0 14. Δ Bills −ΔB +ΔB 0 15. ∑ 0 0 0 0 0 0 Household Firms Banks Government ∑ Current Capital 1. Consumption −C +C 0 2. Investment +I −I 0 3. Government expenditures +G −G 0 4. Wages +W −W 0 5. Taxes −T +T 0 6. Profit +FD −F +FU 0 7. Deposits interest +ir.M−1 −ir.M−1 0 8. Loans interest −ir.L−1 +ir.L−1 0 9. Bills interest +ir.B−1 −ir.B−1 0 10. Subtotal Sh 0 Sf 0 Sg 0 11. ΔDeposits −ΔM +ΔM 0 12. Δ Loans +ΔL −ΔL 0 13. Δ Equity −pe.ΔE +pe.ΔE 0 14. Δ Bills −ΔB +ΔB 0 15. ∑ 0 0 0 0 0 0 View Large Table 5. Transactions and flow of funds matrix Household Firms Banks Government ∑ Current Capital 1. Consumption −C +C 0 2. Investment +I −I 0 3. Government expenditures +G −G 0 4. Wages +W −W 0 5. Taxes −T +T 0 6. Profit +FD −F +FU 0 7. Deposits interest +ir.M−1 −ir.M−1 0 8. Loans interest −ir.L−1 +ir.L−1 0 9. Bills interest +ir.B−1 −ir.B−1 0 10. Subtotal Sh 0 Sf 0 Sg 0 11. ΔDeposits −ΔM +ΔM 0 12. Δ Loans +ΔL −ΔL 0 13. Δ Equity −pe.ΔE +pe.ΔE 0 14. Δ Bills −ΔB +ΔB 0 15. ∑ 0 0 0 0 0 0 Household Firms Banks Government ∑ Current Capital 1. Consumption −C +C 0 2. Investment +I −I 0 3. Government expenditures +G −G 0 4. Wages +W −W 0 5. Taxes −T +T 0 6. Profit +FD −F +FU 0 7. Deposits interest +ir.M−1 −ir.M−1 0 8. Loans interest −ir.L−1 +ir.L−1 0 9. Bills interest +ir.B−1 −ir.B−1 0 10. Subtotal Sh 0 Sf 0 Sg 0 11. ΔDeposits −ΔM +ΔM 0 12. Δ Loans +ΔL −ΔL 0 13. Δ Equity −pe.ΔE +pe.ΔE 0 14. Δ Bills −ΔB +ΔB 0 15. ∑ 0 0 0 0 0 0 View Large Government issues bills to finance its expenditures that are not covered by taxation of household income.16 Besides, government bills, firms’ loans and household deposits yield the same interest rate. Government expenditures are a fraction of aggregate income at the beginning of the period (equation (2)).17 In equation (1), which shows how government debt evolves over time, ir is the real rate of interest, G is the government expenditure, T is the taxation of household income and B−1 is the stock of bills issued by the government and held by households at the beginning of the period. In equations (2) and (3), respectively, σ represents the ratio of government expenditures to past income18 and τ represents the ratio of taxes on household income. B=B−1+G−T+ir.B−1 (1) G=σ.Y−1 (2) T=τ.Yh (3) Household income comprehends wages and financial income (interest on deposits and bills and dividends) (equation (4)). The wage share of income is defined by equation (5), in which π is firms’ profit share. Household disposable income is defined as the after-tax household income (equation (6)). Households consume a fraction ( α1) of their after-tax wages and a fraction ( α2) of their stock of wealth at the beginning of the period (equation (7)), as in Dos Santos and Zezza (2008). Consumption out of wealth represents the autonomous expenditure component. Despite being autonomous (in relation to current income), it is endogenous to the model, since it depends on household wealth, so we can analyse its dynamics through household wealth dynamics. Household savings are defined by equation (8). In the model, financial income does not affect consumption directly, but through its effect on wealth. Yh=W+FD+ir.(B−1+M−1) (4) W=(1−π).Y (5) Yd=(1−τ).Yh (6) C=α1(1−τ).W+α2Vh−1 (7) Sh=Yd−C (8) Following Dos Santos and Zezza (2008), we suppose that the proportion of household wealth allocated in equities ( λ) depends positively on the given expectation of return ( λ0) and negatively on the real interest rate (equation (9)). The stock of equities issued is decided by firms. As households buy all equities issued by firms, the price of equities ( pe) comes into play to clear the market (equation (10)).19 To avoid indetermination, since bills and deposits have the same remuneration rate, we suppose that households buy all government bills (Ryoo and Skott, 2013; Pedrosa and Macedo e Silva, 2014).20 λ=λ0−ir (9) pe=λ.VhE (10) The stock of wealth changes due to household savings and due to capital gains (equation (11)). As households are assumed to buy all bills issued by the government, deposits share in wealth must be treated as a residual (equation (12)). Vh=Vh−1+Sh+Δpe.E−1 (11) M=M−1+Sh−pe.ΔE−ΔB (12) Firms decide the mark-up ( μ) on wage costs. The mark-up on costs defines functional income distribution (Lavoie and Godley, 2001), as in traditional neo-Kaleckian models (equation (13)). Firms must also make their investment decisions, and this is where the supermultiplier approach comes properly into the scene. Aggregate investment of firms is induced by output (equation (14)) (Serrano, 1995A; Freitas and Serrano, 2015). Firms as a whole have a marginal propensity to invest out of income ( h), which is endogenous to the model and reacts to discrepancies between the utilization rate ( u) and the normal utilization rate ( un) (equation (15)), following a Harrodian adjustment mechanism (see Lavoie, 2016; Freitas and Serrano, 2015), in which γ represents the speed of adjustment of the propensity to invest to the discrepancies between the actual utilization rate and the desired utilization rate. π=μ(1+μ) (13) I=h.Y (14) Δh=(h−1.γ.(u−un),if |u−un|>x0,otherwise (15) Since we agree with Sraffian and Classical authors when they say that the utilization rate cannot be ‘anywhere’ in the long run, but also agree with the neo-Kaleckians when they point out that there is no reason for firms to choose a specific number for the utilization rate, we believe that adopting a range, out of which the propensity to invest reacts, is a satisfying option, as suggested by Hein et al. (2012). As highlighted by Dutt (2011), in a world of uncertainty, firms may want to keep their investment strategy unchanged if the capacity utilization is within a reasonable band. This corridor is represented by the parameter x (equation (15)). The change in the stock of capital is given by equation (16) and differs from the flow of investment because we include capital depreciation in the model ( δ). The actual utilization rate is given by the ratio of output to full-capacity output (equation (18)), and full-capacity output (equation (17)) is determined by the ratio of the initial capital stock to the given capital-output ratio ( v). From these equations, we can draw the actual rate of growth of the capital stock (equation (19)). K=K−1−δK−1+I (16) Yfc=K−1v (17) u=YYfc (18) gk=huv−δ (19) Firms must still decide how they will finance their investment. We suppose firms finance their investment through retained earnings, equity issuance and bank loans, which are assumed to clear firms’ demand for funds (equation (20)).21 Equities are a fixed proportion ( a) of the capital stock at the beginning of the period (equation (21)). Firms retain a fraction of their profit ( sf) discounting the payment of interest on loans (equation (22)) and distribute the rest of net profit to households in the form of dividends (equation (23)). Total net profits are given by gross profit less interest payment on the opening stock of loans (equation (24)). Gross profit is given by equation (25). L=L−1+I−FU−pe.ΔE (20) E=a.K−1 (21) FU=sf(π.Y−irL−1) (22) FD=(1−sf)(π.Y−ir.L−1) (23) F=π.Y−ir.L−1 (24) Fg=πY (25) Normalizing equation (24) by the stock of capital at the beginning of the period, we get what we can call a net profit rate (equation (26)). Gross profit rate (equation (27)) is attained through the same procedure for equation (25). rn=πuv−irl−1(1+gk−1) (26) rg=πuv (27) After presenting the framework of the model, we can move on to the short-run goods market equilibrium and to the dynamic equations of the system. 3.2 Short-run goods market equilibrium In our closed economic system, real output is the sum of household consumption, firms’ investment and government expenditures (equation (28)). If we substitute equations (7), (14) and (2) into equation (28), normalize it by the opening stock of capital and make some algebraical rearrangements, we get the short-run equilibrium utilization rate (equation (29)). The term α2vh−1, which represents the normalized consumption out of wealth, is the truly autonomous expenditure component of this system (the z component).22 The supermultiplier appears on the RHS of equation (29) within the parentheses and shows the effect of induced consumption, induced investment and government expenditures on the level of output. The essence of the supermultiplier approach is maintained as the level of output and the utilization rate in the short run are determined by an autonomous component of demand, which is not private business investment, times the supermultiplier (see Freitas and Serrano, 2015). Y=C+I+G (28) u(1(1+gk−1)[1−h−α1(1−τ)(1−π)−σ1+gy−1])α2vh−1v (29) Assuming, as in neo-Kaleckian models, that the model presents Keynesian stability, savings should react more than investment to changes in output and capacity, which means that for the denominator of equation (29) to be positive the following condition should be satisfied: 1−α1(1−τ)(1−π)−σ(1+gy−1)>h (30) 3.3 Short- and long-run behaviour of the normalized stock ratios This section describes the main features of short- and long-run normalized23 stock ratios—government debt, firms’ debt and household wealth—as well as the long-run growth rate of the economy. In the long run, all growth rates are jointly determined (31), normalized stock ratios attain their steady growth value and the utilization rate converges to the normal utilization rate, or gets into the inertia zone, as in (32)—which implies that the propensity to invest stabilizes. Most of the equations are shown in Appendix A. g*=gk=gvh=gb=gl=gy (31) u*≃un (32) Government debt ratio to the lagged capital stock24 (see equations (A1) and (A2)) increases (in the short as in the long run) in the government propensity to spend ( σ), in the after-tax interest rate (which remunerates bills held by households) and in π, the profit share (for in our model retained profits are not taxed). It decreases in the capital accumulation rate, in the taxation of distributed profits and in firms’ normalized stock of loans at the beginning of the period, for when (cet. par.) firms increase their leverage, government debt falls. While in the short run it decreases in the utilization rate ( u), as long as the taxation of distributed profits is positive,25 the steady growth ratio increases in the normal utilization level ( un), assuming as an stylized fact that both government and firms’ debt are positive.26 Firms’ loans to capital ratio (equations (A3) and (A4)) depends positively on the interest rate they pay ( ir), as well as on their propensity to invest ( h). In the short run, it depends negatively on the profit share ( π), and the very capital accumulation rate, as well as on the equities share in wealth ( λ).27 The short- and long-run ratios depend positively on the current and on the normal utilization rate, respectively, as long as the propensity to invest is larger than the retained earnings share. What changes in the long run is that the effect of the capital accumulation rate on the firms’ loans to capital ratio is ambiguous. The normalized stock of household wealth (equations (A5) and (A6)) is positively affected by after-tax dividend income, as by interests on the stock of government bills and on firms’ loans (transferred by banks to households) and (as the case may be) by the current or the normal utilization rate. It is negatively influenced by the propensities to consume out of wealth ( α2) and out of after-tax wages ( α1). The equities’ share on wealth has an ambiguous and transient effect, since its effects vanish in the long run. The effect of the growth rate depends on the combination of the parameters of the model. Assuming that long-run conditions (31) and (32) have been reached, and consequently, Δh=0, it is easy to calculate the long run growth rate of the economy, based on equation (29): g*=α2vh*v+unσun[1−h*−α1(1−τ)(1−π)]−1 (33) In equation (33), we can observe that long-run growth is determined by the terms containing the normalized consumption out of wealth ( α2vh*) and the government propensity to spend ( unσ), as well as by the typical supermultiplier components, as the propensity to invest ( h*), the propensity to consume out of wages ( α1) and the income distribution ( π). The equation does not lend itself well to simple comparative dynamic exercises. In the steady growth configuration, g*, h*28 and vh* (as well as b* and l*, through household wealth29) are simultaneously determined, given the initial conditions and the shocks in exogenous parameters that may have been introduced. In other words, the long-run equilibrium is composed of a system of simultaneous equations. The intrinsic complexity of the model can be more easily understood by means of simulation experiments, as those presented in Section 4. 4. Experiments From the steady growth state, we run some simulation experiments to evaluate the long-run features of the model. The first shock is a decrease in the mark-up, which means an increase in the wage share, in order to assess whether the paradox of costs holds in terms of level and growth effects, considering the initial values and parameters of the model.30 The second shock is an increase in the propensity to consume out of after-tax wages ( α1) (a reduction in the propensity to save) in order to assess whether the paradox of thrift holds in terms of level and growth effects. At last, we shock the autonomous consumption component, through an increase in the propensity to consume out of wealth ( α2), to analyse how it changes the dynamics of the economy in the long run. The results of the shocks are summarized in Table 6.31 Table 6. Effects of the shocks Reduction in μ(π) Increase in α1 Increase in α2 Short run Long run Short run Long run Short run Long run g + + + + + + u + = + = + = rg − − + = + = rn − − + − + − Reduction in μ(π) Increase in α1 Increase in α2 Short run Long run Short run Long run Short run Long run g + + + + + + u + = + = + = rg − − + = + = rn − − + − + − View Large Table 6. Effects of the shocks Reduction in μ(π) Increase in α1 Increase in α2 Short run Long run Short run Long run Short run Long run g + + + + + + u + = + = + = rg − − + = + = rn − − + − + − Reduction in μ(π) Increase in α1 Increase in α2 Short run Long run Short run Long run Short run Long run g + + + + + + u + = + = + = rg − − + = + = rn − − + − + − View Large 4.1 The paradox of costs A decrease in the mark-up raises the wage share and leads to a higher consumption out of wages, which translates into a higher income and activity level. The increase in capacity utilization following the increase in consumption and income makes firms change their expectation of growth, which raises their propensity to invest, increasing the rate of capital accumulation, as we can see in Figure 1a. We also observe that as the rate of growth of household wealth during the transition is lower than the capital accumulation rate (Figure 1a), the ratio of household wealth to capital will be lower in comparison to the baseline (Figure 2a). As in the original supermultiplier model [a], as investment increases in relation to output, through a higher propensity to invest h (Figure 1c), the autonomous expenditure component (consumption out of wealth) z loses relative weight on output (Figure 1d). From Figure 1b, we note that the utilization rate converges towards the desired rate in the long run, through the adjustment of the propensity to invest. From equations (A1) and (A2), we know that the reduction in the profit share contributes directly to reduce government debt ratio. This is due to the positive effect on wage income and to the reduction in the share of retained profits (since larger retained profits mean a smaller fraction of profit income will be taxed). Besides that, a reduction in the normalized stock of bills contributes to reduce itself further since the normalized amount of interest the government pays on bills (to households) also decreases. The increase in the utilization rate following the boost in activity has on the ratio of bills to capital both a positive effect for the government spends a constant fraction of output, and a negative effect, through the increase on taxes (Figure 2a). In the short run, the primary government deficit to output falls sharply due to the increase in household income in relation to total income, which makes taxed income exceed government expenditures. However, due to the stimulus to activity, total output accelerates, turning the temporary primary surplus into a deficit in the long run (Figure 2c). It’s worth noticing that total government deficit to output—including interest payments on the outstanding stock of bills—will decrease but it will not turn into a surplus, meaning that government debt will be always increasing, but at a slower pace. Since only household income is taxed, the channel through which loans affect government debt is distributed profits of firms. An increase in firms’ loans will increase the interest paid on loans and contribute to reduce distributed profits to households (considering that firms distribute their net profit) and thus taxation of this type of financial income. On the other hand, an increase in the interest payment on loans has both a positive effect on taxation through the reduction of non-taxed profit income and through the increase in household financial income accruing from the interest payments received from deposits. As a result, both the increase in firms’ loans and the higher accumulation rate contribute to reduce the government bills to capital ratio. In the case of firms, the increase in the propensity to invest will be larger than the increase in profit income—and in net retained profits. Given the reduction in the market value of newly issued equities due to the fall in equity prices brought about by the lower household wealth to capital ratio (the supply by firms will exceed the demand of households for these assets), there will be a decrease in total equities as a source of finance in comparison to the baseline (Figure 2d). Firms will thus recur more intensively to external funding to finance investment, increasing the loans to capital ratio in the long run (Figure 2a). Household wealth to capital ratio will be negatively influenced by the initial reduction in distributed profits (as a fraction of the capital stock) following the fall in the profit share, which will also contribute to diminish the immediate need for the government to issue bills since household income increases in relation to total income in the short run. This will lead to a reduction in the share of government bills in total household wealth and to an increase in the share of deposits. Besides that, the increase in household wealth growth rate is mitigated by capital losses related to the reduction in equity prices in the short run. However, during the transition, household wealth will accelerate and stabilize at higher levels in comparison to the baseline as a result of the overall increase in income and activity, which increases the positive contributions of wages and distributed profits to its growth rate (Figure 1a). Fig. 1. View largeDownload slide Effects of an increase in real wages (reduction in μ). (a) Growth rates of capital and household wealth. (b) Capacity utilization rate. (c) Firms’ propensity to invest. (d) Autonomous expenditure component to income. Fig. 1. View largeDownload slide Effects of an increase in real wages (reduction in μ). (a) Growth rates of capital and household wealth. (b) Capacity utilization rate. (c) Firms’ propensity to invest. (d) Autonomous expenditure component to income. Regarding the gross and net profit rates of firms (Figure 2b), it is clear that since the utilization rate converges to a desired rate or range, both rates decrease in relation to the baseline. In the short run, the positive effect of an increase in income and utilization is not enough to compensate the reduction of firms’ profit share. However, gross and net profit levels increase in relation to the baseline.32 Fig. 2. View largeDownload slide Effects of an increase in real wages (reduction in μ). (a) Financial assets to capital ratios. (b) Profit rates. (c) Primary government deficit to output. (d) Equities as a source of finance for firms. Fig. 2. View largeDownload slide Effects of an increase in real wages (reduction in μ). (a) Financial assets to capital ratios. (b) Profit rates. (c) Primary government deficit to output. (d) Equities as a source of finance for firms. Based on these results, we realize that income distribution can influence growth in the long run, even if the utilization rate converges to the desired rate or range. This is made possible by the inclusion of the endogenous autonomous expenditure component in the model, which means that there are factors other than the utilization rate through which income distribution can affect output growth. Yet the profit rate cannot increase in the long run, since the profit share decreases and the utilization rate goes back to its normal range. In sum, the paradox of costs is partially held, since it remains valid in what concerns the growth rate, though not in what concerns the effects on the utilization rate and on the rate of profit. 4.2 The paradox of thrift Following an increase in the propensity to consume out of wages ( α1), consumption increases and leads to an increase on output and capacity utilization. This leads to an increase in the propensity to invest of firms and in the capital accumulation rate (Figures 3a and 4c). Consumption out of wealth loses participation in income (Figure 4d), with capital accumulation growing faster than wealth, as in the first simulation experiment. The difference here is that in the short run, the reduction in workers’ propensity to save impacts negatively households’ savings and, consequently, the rate of growth of their wealth (Figure 3a). However, as soon as consumption affects activity, the higher income will raise the financial income received by households, which contributes positively to wealth growth. Fig. 3. View largeDownload slide Effects of an increase in the propensity to consume out of after-tax wages ( α1). (a) Growth rates of capital and household wealth. (b) Capacity utilization rate]. (c) Financial assets to capital ratios. (d) Profit rates. Fig. 3. View largeDownload slide Effects of an increase in the propensity to consume out of after-tax wages ( α1). (a) Growth rates of capital and household wealth. (b) Capacity utilization rate]. (c) Financial assets to capital ratios. (d) Profit rates. Fig. 4. View largeDownload slide Effects of an increase in the propensity to consume out of after-tax wages ( α1). (a) Firms’ loans ratio. (b) Household wealth to capital ratio. (c) Propensity to invest. (d). Autonomous expenditure component to income. Fig. 4. View largeDownload slide Effects of an increase in the propensity to consume out of after-tax wages ( α1). (a) Firms’ loans ratio. (b) Household wealth to capital ratio. (c) Propensity to invest. (d). Autonomous expenditure component to income. The government debt to capital ratio also decreases as household income—due to an increase in dividend payment and wages—taxation and capital accumulation increase. In the short run, as firms’ loans ratio decreases, the debt ratio falls at a slower pace. In the long run, the reduction in the payment of interest to households, due to the lower debt ratio, and the higher accumulation rate together with a higher loans to capital ratio make the debt to capital ratio decrease even further (Figures 3a and 3c). Differently from the previous experiment, in this case, firms’ loans to capital ratio falls in the short run and stabilizes at a higher ratio in the long run in comparison to the baseline. In the short run, as retained profits increase more than investment, there will be a reduction in the loans to capital ratio even considering the decrease in market value of equities due to the lower ratio of household wealth to capital (Figures 3a, 4a and 4c). Still, in the longer run, the growth of retained profits is no longer able to avoid the increase in the loans to capital ratio, given the decrease in profit rates and the fall in the market value of equities. Household wealth to capital suffers the negative impact of the lower normalized stock of government bills, since interest payments decrease, and also the negative impact of the lower interests on deposits, as a result of lower firms’ loans ratio. However, as income and capacity utilization increase, they have a positive effect on wealth, even if wealth grows at a lower rate than capital accumulation. In addition to this, in the long run, as firms’ loans attain a higher position in comparison to the baseline, they positively influence wealth (Figures 3a and 4b). Gross and net profit rates increase in relation to their baseline values due to the temporary increase in the utilization rate. As the utilization rate converges to its desired level, and there are no changes in the profit share, the gross profit rate goes back to its baseline value. The net profit rate decreases as the ratio of loans to capital rests at a higher level, which means that a larger part of profits is destined to the payment of interest on loans (Figure 3d). In sum, we observe that the paradox of thrift in terms of growth effects is still valid in the long run in this framework, in which there is an autonomous expenditure component growing endogenously and in which the utilization rate converges to a desired range. This happens because the reduction in the propensity to save stimulates the economy, boosting consumption from wages, which entails both a higher output level in relation to the baseline, and a higher growth rate in the long run, through the supermultiplier. Differently from neo-Kaleckian models, in which the effect happens through the utilization rate, raising the level of activity and the accumulation rate, in this model the effect happens through the utilization rate in the short run; however, in the long run, as the utilization rate stabilizes at its normal range, the accumulation rate depends ultimately on the feedbacks among the autonomous expenditure component (consumption out of wealth), the propensity to invest of firms and the growth rate itself. The changes in the propensity to invest as well as the exogenous shock to the propensity to consume out of income will permanently increase the supermultiplier, raising the overall rate of growth of the economy. 4.3 A shock to the propensity to consume out of wealth An increase in the propensity to consume out of wealth increases consumption, which reduces household savings and, consequently, household wealth growth in the short run. Differently from the previous experiment, the autonomous component of demand increases relatively to income, but as soon as the effect on capacity kicks in, consumption out of wealth decreases in relation to output (Figure 5d). As in earlier experiments, the higher utilization rate (Figure 5b) leads firms to increase their propensity to invest, which increases the accumulation rate at a faster pace than that of household wealth (Figures 5a and 5c). The effects on the ratios of government bills to capital, firms’ loans to capital and household wealth to capital are very similar to the effects of a shock in the propensity to consume out of wages. Government bills and household wealth to capital ratios stabilize at lower positions in comparison to the baseline, while the firms’ loans ratio decreases in the short run but increases in the long run. The gross profit rate increases in the short run but goes back to its baseline rate while the net profit rate decreases as the amount of interest payment on loans increases in the long run. Fig. 5. View largeDownload slide Effects of an increase in the autonomous expenditure component (increase in α2 α2 α2). (a) Growth rates of capital and household wealth. (b) Capacity utilization rate. (c) Firms’ propensity to invest. (d) Autonomous expenditure component to income. Fig. 5. View largeDownload slide Effects of an increase in the autonomous expenditure component (increase in α2 α2 α2). (a) Growth rates of capital and household wealth. (b) Capacity utilization rate. (c) Firms’ propensity to invest. (d) Autonomous expenditure component to income. 4.4 An assessment of the shocks All the scenarios have in common the fact that changes in exogenous parameters alter (directly or indirectly) the supermultiplier, and thus affect the long-run growth rate as well. A shock, say, to the propensity to consume out of income will change the supermultiplier straightforwardly but also indirectly, since this shock has an effect on the propensity to invest. A shock to the propensity to consume out of wealth will change the supermultiplier indirectly through the propensity to invest. Therefore, as long as the autonomous expenditure component is endogenous to the model—otherwise, the growth rate would be exogenous—the effects of the shocks are not restricted to the transition period. The experiments then show that while the utilization converges back to its desired level or range, the adjustments of a shock to income distribution or to the propensity to save can be absorbed through an endogenous change in the growth rate. It is worth mentioning that this happens without the loss of the Keynesian causality, since the adjustment of capacity to demand occurs through changes in the autonomous component of demand, whose share in income falls when investment rises. It goes without saying that a great deal of the results of our experiments were more easily achieved by the adoption of an SFC framework. In the original supermultiplier approach, autonomous demand growth is given once and for all—or until it is exogenously changed. This exogeneity makes it impossible to establish the connections between a change in the propensity to invest and the determinants of the autonomous expenditure (household wealth, in the case of this paper). Moreover, the omission of financial variables prevents the evaluation of the effects of an increase in capital accumulation and in the autonomous expenditure growth rate on the financial stocks of the economy (loans, bills, household wealth). It also prevents understanding that a permanent (say) increase in the supermultiplier allows for a permanent increase in the growth rate of wealth despite the reduction of the household wealth to capital ratio. 5. Final remarks As we have seen, so far supermultiplier models do not deal properly with financial issues. They do not take into consideration the interactions between financial stocks and flows and how such interactions could impact growth in the long run. Since the growth rate of the autonomous expenditure component is exogenously given, these models do not allow for the emergence of the paradoxes of thrift and costs in terms of growth effects. It does not matter which ‘non-capacity creating’ autonomous expenditure is leading growth in the long run, whether consumption, government expenditures or net exports, only the level effects of changes in income distribution and in the propensity to save will last. However, when we allow for the autonomous expenditure component to be endogenous, as in the model we built here, which depends on household wealth, we also allow for feedbacks between financial income and financial stocks, as for feedbacks between the latter and the capital stock. Changes in income distribution and in the propensity to save will permanently affect the growth rate of the economy, through the supermultiplier, and through the dynamics of household wealth to capital ratio. The main results obtained through the experiments of Section 4 can be summarized as follows: An essential claim of the supermultiplier approach is that a higher growth rate of the autonomous expenditure component is associated with a higher investment to income ratio. This assumption still holds for a more complex model even if the autonomous expenditure component is endogenous to the economic system. As the autonomous expenditure component grows at a faster pace, it increases the income, which will stimulate more expenditures, say by increasing consumption out of wages, and these higher expenditures will boost investment, as the utilization of capacity rises. As investment accelerates induced by income, the investment share increases relatively to income while the reverse happens to the autonomous expenditure component share (Serrano, 1995B); The paradox of costs is still valid in terms of level effects. A reduction in the mark-up of firms (lower profit share) leads to lower profit rate, but to a higher level of profits in the long run, as a consequence of the higher capital accumulation. However, differently from other supermultiplier models, a higher wage share has a permanent growth effect, through the supermultiplier mechanism. The discrepancy between actual and desired utilization rates promotes a permanent increase in the propensity to invest. This, along with the higher wage share, compensates the effect of a lower wealth to capital ratio on the growth rate of this economy; The paradox of thrift is valid both in level and in growth terms in the long run. An increase in the propensity to consume out of after-tax wages permanently affects the growth rate of the economy in the long run through the supermultiplier; The relation between stocks and flows matters, since an increase in the propensity to invest contributes to increase the ratio of firms’ debt to capital. This implies that the propensity to invest can find a constraint in the values it can assume, coming from the amount of loans firms borrow in order to finance this same investment and which also depends on the how the propensity to invest will impact the accumulation rate, in order to compensate the higher loans to capital ratio; The behaviour of the autonomous component reveals once more the centrality of stock and flow interactions, for consumption out of wealth is influenced by the government debt ratio, by firms’ propensity to invest and by the capital accumulation rate. Needless to say, the discussion presented here could be enriched in several ways. The first concerns the generality of our conclusions, which should be evaluated by means of a stability analysis of the model and a sensitivity analysis of the parameters to verify for which range of (economically meaningful) parameters the paradoxes remain valid in the long run. Second, it would be important to move to an open economy setting; it is well known that the paradox of costs may not hold when international transactions are taken into account. Third, it would also be important to test the same hypothesis for an economy with a more complex financial system, for instance incorporating consumer credit and assuming a more ‘active’ and profit-earning banking sector, including the possibility of credit rationing. A final and possibly important front which would require further research refers to the implication of specific growth engines. There is no reason to assume that a consumption-led growth regime will be as durable as (say) a government- or an export-led one. Each growth engine will feature specific interactions between stocks and flows, will face specific financial constraints and will present different stability conditions. Acknowledgements We would like to thank Ítalo Pedrosa, Marc Lavoie, Olivier Allain, Dany Lang, Fabio Freitas and Claudio Dos Santos for quite helpful comments to earlier drafts of the paper. Previous drafts were presented at the 20-year-anniversary conference of the FMM Research network: Towards Pluralism in Macroeconomics? (Berlin, October 2016), at the URPE panel in the 43rd Eastern Economics Association Annual Conference (New York, February 2017) and at the 4th Nordic Post Keynesian Conference (Aalborg, April 2017). We are also grateful to the participants of these events for their comments. While the first author also thanks Ana Rosa Ribeiro de Mendonça Sarti for her assistance in the preliminary research, the second author wishes to thank Franklin Serrano for his generosity throughout a long-lasting dialogue. Last but not least, we thank all three anonymous referees for raising interesting questions that were essential to improving the quality of the paper. Bibliography Allain, O. 2014. Macroeconomic Effects of Consumer Debt: Three Theoretical Essays, paper presented at the 18th FMM Conference: The Inequality and the Future of Capitalism, Berlin, 30 October to 1 November 2014, available at https://halshs.archives-ouvertes.fr/halshs-01147612. Allain, O. 2015A. Demographic Growth, Harrodian (In) Stability and the Supermultiplier, paper presented at the 19th FMM Conference: The Spectre of Stagnation? Europe in the World Economy, available at https://www.boeckler.de/pdf/v_2015_10_23_allain.pdf Allain, O. 2015B. Tackling the instability of growth: a Kaleckian-Harrodian model with an autonomous expenditure component, Cambridge Journal of Economics , vol. 39, no. 5, 1351– 71 Google Scholar CrossRef Search ADS Amadeo, E. 1986. Notes on capacity utilization, distribution and accumulation, Contributions to Political Economy , vol. 5, no. 1, March, 83– 94 Google Scholar CrossRef Search ADS Amadeo, E. 1987. Expectations in a steady-state model of capacity utilization, Political Economy: Studies in the Surplus Approach , vol. 3, no. 1, 75– 89 Barba, A. and Pivetti, M. 2008. Rising household debt: its causes and macroeconomic implications—a long-period analysis, Cambridge Journal of Economics , vol. 33, noet al. 113– 37 Google Scholar CrossRef Search ADS Bhaduri, A. and Marglin, S. 1990. Unemployment and the real wage: the economic basis for contesting political ideologies, Cambridge Journal of Economics , vol. 14, 375– 93 Google Scholar CrossRef Search ADS Bibow, J. 2010. Financialization of the U.S. Household Sector: The ‘Subprime Mortgage Crisis’ in the U.S. and Global Perspective , IMK Studies No. 3/2010, Dusseldorf, available at https://www.boeckler.de/imk_6456.htm?produkt=HBS-004733. Blecker, R. 2009. Long-Run Growth in Open Economies: Export-Led Cumulative Causation or a Balance-of-Payments Constraint?, paper presented at 2nd Summer School on ‘Keynesian Macroeconomics and European Economic Policies’, Berlin, available at http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.523.8083& rep=rep1&type=pdf Bortis, H. 1997. Institutions, Behaviour and Economic Theory: A Contribution to Classical-Keynesian Political Economy , Cambridge, Cambridge University Press Bortz, P. G. 2014. Foreign debt, distribution, inflation and growth in a SFC model, European Journal of Economics and Economic Policies: Intervention , vol. 11, no. 3, 269– 99 Brown, C. 2007. Financial engineering, consumer credit, and the stability of effective demand, Journal of Post Keynesian Economics , vol. 29, no. 3, 427– 50 Google Scholar CrossRef Search ADS Cesaratto, S. 2015. Neo-Kaleckian and Sraffian controversies on the theory of accumulation, Review of Political Economy , vol. 27, no. 2, 154– 82 Google Scholar CrossRef Search ADS Cesaratto, S., Serrano, F. and Stirati, A. 2003. Technical change, effective demand and employment, Review of Political Economy , vol. 15, no. 1, 33– 52 Google Scholar CrossRef Search ADS Cynamon, B. Z. and Fazzari, S. M. 2008. Household debt in the consumer age: source of growth—risk of collapse, Capitalism and Society , vol. 3, no. 2, 1–32 Dejuán, Ó. 2014. ‘ How to Escape from the Trap of the Warranted Rate of Growth’, Working Paper 2014/1, Department of Economics and Finance, Universidad de Castilla-La Mancha, DT-DAET Dos Santos, C. H. and Zezza, G. 2008. A simplified, ‘benchmark’, stock-flow consistent post-Keynesian growth model, Metroeconomica , vol. 59, no. 3, 441– 78 Google Scholar CrossRef Search ADS Dutt, A. K. 1984. Stagnation, income distribution and monopoly power, Cambridge Journal of Economics , vol. 8, no. 1, March, 25– 40 Google Scholar CrossRef Search ADS Dutt, A. K. 2011. Growth and income distribution: a post-Keynesian perspective, pp. 61– 87 in Hein, E. and Stockhammer, E. (eds.), A Modern Guide to Keynesian Macroeconomics and Economic Policies , Cheltenham, UK, and Northampton, MA, Edward Elgar Dutt, A. K. 2015. ‘ Growth and Distribution with Exogenous Autonomous Demand Growth and Normal Capacity Utilization’, Working Paper, Department of Political Science, University of Notre Dame, Notre Dame, IN, and FLACSO, Quito, Ecuador Dutt, A. K. 2016. ‘ Autonomous Demand Growth and Government Debt in the Short Run’, Working Paper, Department of Political Science, University of Notre Dame, Notre Dame, IN, and FLACSO, Quito, Ecuador Fazzari, S. M., Ferri, P. E., Greenberg, E. G. and Variato, A. M. 2013. Aggregate demand, instability, and growth, Review of Keynesian Economics , vol. 1, no. 1, 1– 21 Google Scholar CrossRef Search ADS Fiebiger, B. 2017. Semi-autonomous household expenditures as the ‘causa causans’ of postwar US business cycles: the stability and instability of Luxemburg-type external markets, Cambridge Journal of Economics , vol. 42, no. 1, 155– 75, https://doi.org/10.1093/cje/bex019 Google Scholar CrossRef Search ADS Fiebiger, B. and Lavoie, M. 2016. ‘ Trade and Business Cycles with External Markets? Non-Capacity Generating Semi-Autonomous Expenditures and Effective Demand’, available at http://www.pkconference.aau.dk/digitalAssets/291/291512_lavoie-and-fiebiger—non-capacity- generating-semi-autonomous-expenditures.pdf [date last accessed 5 May 2017] Freitas, F. and Serrano, F. 2015. Growth rate and level effects, the stability of the adjustment of capacity to demand and the Sraffian supermultiplier, Review of Political Economy , vol. 27, no. 3, 258– 81 Google Scholar CrossRef Search ADS Girardi, D. and Pariboni, R. 2015. ‘ Autonomous Demand and Economic Growth: Some Empirical Evidence’, Working Paper No. 714, Quaderni Del Dipartiment Di Economia Politica e Statistica, Universita di Siena, available at https://www.deps.unisi.it/sites/st02/files/allegatiparagrafo/20-08-2015/714.pdf Godley, W. and Lavoie, M. 2007. Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth , New York, Palgrave Macmillan Guttmann, R. and Plihon, D. 2008. O endividamento do consumidor no cerne do capitalismo conduzido pelas finanças, Economia e Sociedade , vol. 17, no. número especial, 575– 610 Google Scholar CrossRef Search ADS Harrod, R. F. 1939. An essay in dynamic theory, Economic Journal , vol. 49, no. 193, 14– 33 Google Scholar CrossRef Search ADS Hein, E. 2011. ‘Financialisation’, distribution and growth, pp. 294– 324 in Hein, E. and Stockhammer, E. (eds.), A Modern Guide to Keynesian Macroeconomics and Economic Policies , Cheltenham, UK, and Northampton, MA, Edward Elgar Hein, E. 2016. ‘ Autonomous Government Expenditure Growth, Deficits, Debt and Distribution in a Neo-Kaleckian Growth Model’, Working Paper No. 68/2016, Institute for International Political Economy Berlin, Berlin School of Economics and Law, available at http://www. ipe-berlin.org/fileadmin/downloads/Papers_and_Presentations/IPE_WP_68.pdf Google Scholar CrossRef Search ADS Hein, E., Lavoie, M. and van Treeck, T. 2011. Some instability puzzles in Kaleckian models of growth and distribution: a critical survey, Cambridge Journal of Economics , vol. 35, no. 3, 587– 612 Google Scholar CrossRef Search ADS Hein, E., Lavoie, M. and van Treeck, T. 2012. Harrodian instability and the ‘normal rate’ of capacity utilization in Kaleckian models of distribution and growth—a survey, Metroeconomica , vol. 63, no. 1, 139– 69 Google Scholar CrossRef Search ADS Hein, E. and van Treeck, T. 2008. ‘ “Financialisation” in Post-Keynesian Models of Distribution and Growth—Systematic Review’, IMK Working Paper No. 10/2008, Dusseldorf, Germany, Macroeconomic Policy Institute (IMK), available at https://www.econstor.eu/ bitstream/10419/105896/1/imk-wp_2008-10.pdf Google Scholar CrossRef Search ADS Kaldor, N. 1961. Capital accumulation and economic growth, pp. 177– 228 in The Theory of Capital , St. Martin’s Press, New York Google Scholar CrossRef Search ADS Kalecki, M. 1969. Studies in the Theory of Business Cycles 1933–1939 , Oxford, Basil Blackwell Keynes, J. M. 1936. The General Theory of Employment, Interest and Money , London, Macmillan Kregel, J. A. 1980. Economic dynamics and the theory of steady growth: an historical essay on Harrod’s ‘knife-edge’, History of Political Economy , vol. 12, no. 1, 97– 123 Google Scholar CrossRef Search ADS Lavoie, M. 2006. Do heterodox theories have anything in common? A post-Keynesian point of view, Intervention, European Journal of Economics and Economic Policies , vol. 3, no. 1, 87– 112 Google Scholar CrossRef Search ADS Lavoie, M. 2010. Should Sraffian Economics Be Dropped Out of the Post-Keynesian School?, paper presented at Sraffa’s Production of Commodities 1960–2010, Critique and Reconstruction of Economic Theory at Roma Tre, Roma, available at http://host.uniroma3.it/eventi/sraffaconference2010/abstracts/pp_lavoie.pdf Lavoie, M. 2014. Post-Keynesian Economics: New Foundations , Cheltenham, UK, and Northampton, MA, Edward Elgar Publishing Limited Google Scholar CrossRef Search ADS Lavoie, M. 2016. Convergence towards the normal rate of capacity utilization in neo-Kaleckian models: the role of non-capacity creating autonomous expenditures, Metroeconomica , 67( 1): 172– 201 Google Scholar CrossRef Search ADS Lavoie, M. and Godley, W. 2001. Kaleckian models of growth in a coherent stock-flow monetary framework: a Kaldorian view, Journal of Post Keynesian Economics , vol. 24, no. 2, 277– 311 Google Scholar CrossRef Search ADS Le Heron, E. and Mouakil, T. 2008. A post-Keynesian stock-flow consistent model for dynamic analysis of monetary policy shock on banking behaviour, Metroeconomica , vol. 59, no. 3, 405– 40 Google Scholar CrossRef Search ADS Leite, F. P. 2015. Taking Godley’s ratios seriously, Metroeconomica , vol. 66, no. 3, 508– 33 Google Scholar CrossRef Search ADS Nah, W. J. and Lavoie, M. 2017. Long run convergence in a neo-Kaleckian open-economy model with autonomous export growth, Journal of Post Keynesian Economics , February, vol. 40, no. 2, 223–38 Pedrosa, Í. and Macedo e Silva, A. C. 2014. A Minskyan-Fisherian SFC Model for Analyzing the Linkages of Private Financial Behavior and Public Debt, paper presented at 18th FMM Conference: The Inequality and the Future of Capitalism, Berlin, available at https://www.boeckler.de/pdf/v_2014_10_30_pedrosa_macedo_e_silva.pdf Robinson, J. 1962. Essays in the Theory of Economic Growth , Joan Robinson Series, London, Macmillan Google Scholar CrossRef Search ADS Rowthorn, B. 1981. Demand, real wages and economic growth, Thames Papers in Political Economy , Autumn, 1– 39 Ryoo, S. and Skott, P. 2013. Public debt and full employment in a stock-flow consistent model of a corporate economy, Journal of Post Keynesian Economics , vol. 35, no. 4, 511– 28 Google Scholar CrossRef Search ADS Serrano, F. 1995A. Long period effective demand and the Sraffian supermultiplier, Contributions to Political Economy , vol. 14, 67– 90 Google Scholar CrossRef Search ADS Serrano, F. 1995B. The Sraffian multiplier , PhD dissertation, University of Cambridge Skott, P. 2010. Growth, instability and cycles: Harrodian and Kaleckian models of accumulation and income distribution, pp. 108– 31 in Setterfield, M. (ed.), Handbook of Alternative Theories of Economic Growth , Cheltenham, UK, and Northampton, MA, Edward Elgar Google Scholar CrossRef Search ADS White, G. 2008. Growth, autonomous demand and a joint-product treatment of fixed capital, Metroeconomica , vol. 59, no. 1, 1– 26 Zezza, G. 2008. US growth, the housing market, and the distribution of income, Journal of Post Keynesian Economics , vol. 30, no. 3, 375– 401 Google Scholar CrossRef Search ADS Footnotes 1 Fiebiger and Lavoie (2016) and Fiebiger (2017) call these expenditures ‘semi-autonomous’ since it would be unrealistic to consider that any of the effective demand components could be fully autonomous in the real world. 2 As we focus on heterodox growth theories, namely theories in which growth is led by demand and in which autonomous components of demand can also play a role in the long run, we do not deal with neoclassical growth theories. 3 While a higher propensity to save would reduce them both, in consonance with the paradox of thrift. 4 Contradiction between short-run and long-run behaviour of the economy refers to the fact that in the short run, quantities change to adjust output to demand, through the endogenous utilization rate, while in the long run, capacity is at its full level, so prices must change to equal output to demand (Lavoie, 2014, pp. 347–59). 5 Since in most neo-Kaleckian models, as a simplification, workers spend all their income and only capitalists save, they usually refer to the saving rate of capitalists. 6 ‘It seems unrealistic to assume that the growth rate of sales expected by firms, which is captured by the parameter γ in the investment function, stays at the same value forever. Overtime, it should slowly adjust to past changes in the growth rate of sales’(Nah and Lavoie, 2017, p. 14). 7 The recent US experience suggests that consumption, for instance, can autonomously grow in relation to current income to a large extent and for a considerable period of time (Guttmann and Plihon, 2008; Cynamon and Fazzari, 2008; Barba and Pivetti, 2008; Bibow, 2010; Lavoie, 2014; Allain, 2014). The ‘funding effect’ (see Brown, 2007) of some institutional arrangements put forward by financial innovation, as well as consumer credit with real estate collateral, are good examples of how consumption can grow independently of current income growth. In Fazzari et al.’s (2013) words: ‘the rising importance of finance for consumer spending strongly suggests that consumption dynamics could play a much more important role in demand growth than is the case with the passive income based consumption’ (Fazzari et al., 2013, p. 19). 8 Apart from the balance of payment constrained growth models, in which net exports lead growth. However, these models are too partial: most of them do not even include investment decisions, and were thus excluded from this paper (see Blecker, 2009). 9 For more on how neo-Kaleckians include financial issues in their models, see Dutt (2011), and on how neo-Kaleckians deal with the impacts of financialization on these models, see Hein (2011). 10 Dutt (2016) also shows how debt dynamics changes long-run stability conditions—the growth rate of government expenditure should be lower than the normalized saving rate and higher than the after-tax interest rate for stability to hold. 11 Girardi and Pariboni (2015) find some evidence that consumption out of credit bears a close correlation to the GDP and that GDP growth precedes the increase in household consumption credit. Based on this, they question whether this variable should be considered autonomous in the long run. 12 In this paper, Allain claims to have a solution also to the second of Harrod’s problem since the growth rate in the long run also matches the natural rate of growth. 13 To be fair, in Nah and Lavoie (2017) there are some different short- and medium-run effects, as the sensitivity of the real exchange rate due to changes in income distribution may give rise to wage or profit-led regimes (Table 3). 14 Dejuán (2014) also proposes a supermultiplier model in which net exports lead growth but, differently from Nah and Lavoie (2017), does not analyse the impacts of the sensitivity of real exchange rates to income distribution, which could change the short-and medium-run results of the model. 15 While the notion of exogeneity vs. endogeneity to the model can be clearly defined, the notion of autonomy vs. inducement seems to be somewhat arbitrary. In supermultiplier models, investment is not necessarily induced by current income. In Cesaratto et al., 2003, p. 42, induced investment is a function of the ‘expected average rate of growth of normal effective demand over the life of the investment that is currently being installed’. 16 As in LeHeron and Mouakil (2008), the government only taxes household (not firms’) income. 17 Since many countries pursue austerity measures and we are not focusing on fiscal policy, considering government expenditures as procyclical should not be a problem, as in LeHeron and Mouakil (2008). 18 Since we are building the model in a discrete time framework, one may wonder whether the stability of the model would depend on the lagged effect of income on government expenditures. We have tested the model for government expenditures based on current income (results can be provided upon request). If government expenditures depended on current income, the short-run effects of the supermultiplier on the model would be amplified. This means the model would present a higher growth rate, requiring a slower adjustment of the trend growth of sales or the propensity to invest to keep instability away. This is the same effect observed in the models of Allain (2015A), Lavoie (2016) and Freitas and Serrano (2015): a higher growth rate requires a lower speed of adjustment of investment. In Appendix C, we provide the short-run utilization rate and the long-run growth equations for case in which government expenditures depend on current income. 19 We use the same simplification of the Tobinesque set of asset demand equations presented in Lavoie and Godley (2001) and proposed by Dos Santos and Zezza (2008). A more detailed examination of household wealth composition would require an explicit and full Tobinesque portfolio choice framework. 20 We assume, as Ryoo and Skott (2013), that short-run government bonds and bank deposits are perfect substitutes. For the purposes of the paper, the assumption of different rates of return of deposits and bills would make the deduction of the dynamic equations more complicated without affecting substantially the results. However, it is important to highlight that this simplifying assumption would have to be lifted and a more realistic description of the financial instruments would have to be introduced, if we were to analyse firms’ or household financial fragility. 21 As in many SFC models (see Lavoie and Godley, 2001; Godley and Lavoie, 2007; Zezza, 2008, among others), we present firms’ loans as the buffer of the sector, considering, as a matter of simplification, that firms exhaust their internal funds before recurring to external funding for investment. However, this simplification is not suitable for analysing the firms’ process of increasing debt and their likelihood of becoming more fragile. 22 The normalized household wealth to capital ratio in period t is vht=VhtK−1, while the same ratio in the previous period ( t−1) is given by Vh−1=Vh−1K−2. This means that Vh−1K−1 can be rearranged as Vh−1K−2(1+gk−1)=vh−1(1+gk−1). And this goes for all the normalized stocks and flows. This normalization procedure allows for the capital accumulation rate to be explicitly accounted for in the short-run utilization rate equation. 23 All stocks are normalized by the capital stock in the beginning of the period. 24 Needless to say, the level of any of the following normalized stocks at the end of period t depends positively on its respective value at the beginning of that period. 25 The intuition is that since in the short run government expenditures depend on past income, past capacity utilization should have a positive effect on government debt to capital ratio but not the current capacity utilization, which increases government revenues. 26 The effects presented here are drawn based on reasonable and positive values for the parameters, as well as on the assumption that the model presents Keynesian stability and that the steady growth ratios converge to a stable equilibrium, which requires as a necessary condition for the denominator of the equilibrium ratios to be positive. 27 At least in normal times, when the capital accumulation rate is positive. 28 From equation (15), we can derive the long-run equilibrium equation for h*. The equation is presented in Appendix A. 29 See equation (A6) in Appendix A. 30 The parameters and long-run values of the variables are presented in Table B1 in Appendix B. 31 All numerical simulations were computed using R and Eviews 9 software. The programming codes of the simulations are available upon request. 32 One could say that, as firms have more than one goal in the long run, they may be willing to cut profit rates in order to grow and to increase their market shares (Lavoie, 2014). As pointed out by one of the anonymous referees, the results regarding the rate of profit could also be related to a fallacy of composition between the decisions of firms at the microeconomic level and the aggregate macroeconomic results. For more on this, see Hein and van Treeck (2008). Appendix A In order to shed some light in the dynamic process of the model, we obtain the dynamic equations of government debt, household wealth and firms’ loans normalized by the capital stock at the beginning of the period. After this step, we obtain the long-run equilibrium ratios, or the steady growth ratios of the stocks. Dividing equation (1) by the lagged capital stock and making some algebraic manipulation, we get the normalized stock of government debt (equation (A1)). b=b−1[1+ir(1−τ)]+σu−1−τirsfl−1(1+gk−1)−τ(1−sfπ)uv (A1) Given conditions (31) and (32), and thus considering that all stocks grow at the same rate, normalized stocks at the beginning of the period equal normalized stocks at the end of the period (thus Δbt=0) in the long run. The normalized government debt (A1) can be rewritten as: b*=[σ−τ(1−sfπ)(1+g*)]unv−τirsfl*g*−ir(1−τ) (A2) The same procedure is applied to firms’ loans. We divide equation (20) by the lagged capital stock and get equation (A3). l=(1+sfir)l−1+λvh1+gk−1+(h−sfπ)uv−λvh (A3) Applying the long-run conditions, we arrive at the long-run normalized stock of loans: l*=(1+g*)[(h*−sfπ)unv]−g*λvh*g*−sfir (A4) As for the normalized stock of household wealth, we divide equation (11) by the lagged capital stock. The algebra gets slightly more complicated: vh=(1−α2−λ)vh−1+(1−τ)[(1−α1+π(α1−sf))uv(1+gk−1)+sfirl−1+irb−1]1+gk−1−λ (A5) The equilibrium normalized stock of household wealth, obtained through equation (A5), is given by: vh*=(1−τ)[(1−α1+π(α1−sf))unv(1+g*)+irb*+sfirl*]g*+α2 (A6) The same procedure can be applied to find the equilibrium propensity to invest. Substituting the equation for the utilization rate (equation (29)) into the dynamic equation of the propensity to invest (equation (15)) and then supposing that in equilibrium, Δh=0 and u≃un, we obtain the following equation for the propensity to invest: h*=(1+g*)γun[1−α1(1−τ)(1−π)]−σγun−γα2vh*vγun(1+g*) (A7) Appendix B Table B1. Parameters and long-run value of variables Parameters/variables Baseline Scenario 1 Scenario 2 Scenario 3 τ 0.37 0.37 0.37 0.37 σ 0.34 0.34 0.34 0.34 α1 0.8 0.8 0.84 0.8 α2 0.03375 0.03375 0.03375 0.0374 a 0.1 0.1 0.1 0.1 x 0.001 0.001 0.001 0.001 λ0 0.08 0.08 0.08 0.08 pe 0.9880292 0.8493563 0.8571246 0.846402 δ 0.044 0.044 0.044 0.044 ir 0.02 0.02 0.02 0.02 v 2.5 2.5 2.5 2.5 μ 0.7 0.63 0.7 0.7 π 0.411765 0.3865031 0.411765 0.411765 sf 0.4 0.4 0.4 0.4 γ 0.014 0.014 0.014 0.014 h 0.2 0.2131375 0.2091036 0.2101661 u≃un 0.8 0.8 0.8 0.8 m*=l* 0.7953325 1.054224 0.840638 0.8442299 b* 0.7525772 0.276434 0.5021906 0.4817999 vh* 1.646715 1.415594 1.428541 1.41067 g* 0.02 0.02421 0.02291702 0.023161 Parameters/variables Baseline Scenario 1 Scenario 2 Scenario 3 τ 0.37 0.37 0.37 0.37 σ 0.34 0.34 0.34 0.34 α1 0.8 0.8 0.84 0.8 α2 0.03375 0.03375 0.03375 0.0374 a 0.1 0.1 0.1 0.1 x 0.001 0.001 0.001 0.001 λ0 0.08 0.08 0.08 0.08 pe 0.9880292 0.8493563 0.8571246 0.846402 δ 0.044 0.044 0.044 0.044 ir 0.02 0.02 0.02 0.02 v 2.5 2.5 2.5 2.5 μ 0.7 0.63 0.7 0.7 π 0.411765 0.3865031 0.411765 0.411765 sf 0.4 0.4 0.4 0.4 γ 0.014 0.014 0.014 0.014 h 0.2 0.2131375 0.2091036 0.2101661 u≃un 0.8 0.8 0.8 0.8 m*=l* 0.7953325 1.054224 0.840638 0.8442299 b* 0.7525772 0.276434 0.5021906 0.4817999 vh* 1.646715 1.415594 1.428541 1.41067 g* 0.02 0.02421 0.02291702 0.023161 Note: For the initial period, given the initial rate of growth: K0=100 and Y0=unKv(1+g*), following equations (17) and (18). View Large Table B1. Parameters and long-run value of variables Parameters/variables Baseline Scenario 1 Scenario 2 Scenario 3 τ 0.37 0.37 0.37 0.37 σ 0.34 0.34 0.34 0.34 α1 0.8 0.8 0.84 0.8 α2 0.03375 0.03375 0.03375 0.0374 a 0.1 0.1 0.1 0.1 x 0.001 0.001 0.001 0.001 λ0 0.08 0.08 0.08 0.08 pe 0.9880292 0.8493563 0.8571246 0.846402 δ 0.044 0.044 0.044 0.044 ir 0.02 0.02 0.02 0.02 v 2.5 2.5 2.5 2.5 μ 0.7 0.63 0.7 0.7 π 0.411765 0.3865031 0.411765 0.411765 sf 0.4 0.4 0.4 0.4 γ 0.014 0.014 0.014 0.014 h 0.2 0.2131375 0.2091036 0.2101661 u≃un 0.8 0.8 0.8 0.8 m*=l* 0.7953325 1.054224 0.840638 0.8442299 b* 0.7525772 0.276434 0.5021906 0.4817999 vh* 1.646715 1.415594 1.428541 1.41067 g* 0.02 0.02421 0.02291702 0.023161 Parameters/variables Baseline Scenario 1 Scenario 2 Scenario 3 τ 0.37 0.37 0.37 0.37 σ 0.34 0.34 0.34 0.34 α1 0.8 0.8 0.84 0.8 α2 0.03375 0.03375 0.03375 0.0374 a 0.1 0.1 0.1 0.1 x 0.001 0.001 0.001 0.001 λ0 0.08 0.08 0.08 0.08 pe 0.9880292 0.8493563 0.8571246 0.846402 δ 0.044 0.044 0.044 0.044 ir 0.02 0.02 0.02 0.02 v 2.5 2.5 2.5 2.5 μ 0.7 0.63 0.7 0.7 π 0.411765 0.3865031 0.411765 0.411765 sf 0.4 0.4 0.4 0.4 γ 0.014 0.014 0.014 0.014 h 0.2 0.2131375 0.2091036 0.2101661 u≃un 0.8 0.8 0.8 0.8 m*=l* 0.7953325 1.054224 0.840638 0.8442299 b* 0.7525772 0.276434 0.5021906 0.4817999 vh* 1.646715 1.415594 1.428541 1.41067 g* 0.02 0.02421 0.02291702 0.023161 Note: For the initial period, given the initial rate of growth: K0=100 and Y0=unKv(1+g*), following equations (17) and (18). View Large Appendix C Assuming that government expenditures depend on current income instead of depending on the lagged income would lead to slightly different versions for the short-run utilization rate and the long-run equilibrium growth rate equations provided in Section 3.3. The short-run utilization rate and the long-run growth rate would be rewritten as follows: u=(1(1+gk−1)[1−h−α1(1−τ)(1−π)−σ])α2vh−1v (C1) g*=α2vh*vun[1−h*−α1(1−τ)(1−π)−σ]−1 (C2) From these equations, we notice that if government expenditures depend on the current income, there will be a larger short-run impact of the multiplier. In the long run, the effect of the government’s propensity to spend will appear in the multiplier instead of appearing in the numerator (as was the case in equation (33)). © The Author(s) 2018. Published by Oxford University Press on behalf of the Cambridge Political Economy Society. All rights reserved. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

Cambridge Journal of Economics – Oxford University Press

**Published: ** Jun 7, 2018

Loading...

personal research library

It’s your single place to instantly

**discover** and **read** the research

that matters to you.

Enjoy **affordable access** to

over 18 million articles from more than

**15,000 peer-reviewed journals**.

All for just $49/month

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Read from thousands of the leading scholarly journals from *SpringerNature*, *Elsevier*, *Wiley-Blackwell*, *Oxford University Press* and more.

All the latest content is available, no embargo periods.

## “Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”

Daniel C.

## “Whoa! It’s like Spotify but for academic articles.”

@Phil_Robichaud

## “I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”

@deepthiw

## “My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”

@JoseServera

DeepDyve ## Freelancer | DeepDyve ## Pro | |
---|---|---|

Price | FREE | $49/month |

Save searches from | ||

Create lists to | ||

Export lists, citations | ||

Read DeepDyve articles | Abstract access only | Unlimited access to over |

20 pages / month | ||

PDF Discount | 20% off | |

Read and print from thousands of top scholarly journals.

System error. Please try again!

or

By signing up, you agree to DeepDyve’s Terms of Service and Privacy Policy.

Already have an account? Log in

Bookmark this article. You can see your Bookmarks on your DeepDyve Library.

To save an article, **log in** first, or **sign up** for a DeepDyve account if you don’t already have one.