In the modern capitalist economies, income distribution has a tendency to be in favor of shareholders; this has arisen from an increase in the power of shareholders. For example, Stockhammer (2004) points out the increased income share of rentiers in France, Germany, the UK, and the US. Epstein/Power (2003) reveal that, in the OECD countries after the 1980s, the income share of the rentiers has been rapidly increasing and the profit share of non-financial corporations mildly increasing. Skott/Ryoo (2008) show that, in the US economy, the retention ratio of firms declined from 1970 up to 2005.
This tendency also holds true in the Japanese economy. The corporate governance of Japanese firms has turned to shareholder value orientation since the late 1990s, and the propensity to distribute dividends has accordingly increased. In other words, the retention ratio of Japanese firms has decreased. 1 The main reason for this is that the old custom of mutual shareholding has collapsed and the number of foreign shareholders has increased rapidly. As Figure 1 shows, the retention ratio of Japanese firms consistently exceeded 60 percent from the late 1960s through the late 1980s, although has remained consistently lower than 30 percent from the late 1990s to the present day. 2
Many empirical and theoretical studies have investigated the effect of pro-shareholder income distribution on the macro economy. 3
To begin with, we turn to a few empirical studies. Stockhammer (2004), already cited above, shows that the increased income share of rentiers in France, the UK, and the US depresses the equipment investment of firms. Van Treeck (2008) shows that increases in the profit share and the income share of rentiers can lead to increased profitability by increasing the consumption demand on the one hand, but not leading to higher capital accumulation on the other. Onaran et al. (2011) analyse how financialization and the resulting changes in income distribution affect the aggregate demand in the US economy. They conclude that any change in income distribution favoring capital has a positive effect on consumption demand through a wealth effect and a negative effect on investment demand; these two effects offset each other and consequently have a neutralizing effect on the economy's aggregate demand.
However, Stockhammer (2004) estimates the investment functions only and does not consider consumption demand. Furthermore, he performs a short-run analysis and does not consider endogenous changes in the debt–capital ratio. Van Treeck (2008) and Onaran et al. (2011) consider the effects of financialization on both consumption and investment and hence are more general than Stockhammer (2004). However, these studies too are short-run analyses and do not consider debt/capital accumulation.
Next, we turn to a few theoretical studies. Hein/van Treeck (2010a) analytically investigate the effect of increased shareholder power on the macro economy by using a Kaleckian model with two investment functions, the Kalecki-type investment function and Bhaduri/Marglin's (1990) investment function. 4 They show that various demand regimes occur in accordance with the size of parameters. Hein (2012) builds a Kaleckian model that considers the effect of a rise in shareholder power on productivity growth, and theoretically investigates its effect on the short-run capital accumulation and labor productivity growth. He concludes that, even if the productivity-enhancing effect of rising shareholder power is considered, the total effect of the power of shareholders on the macro economy is likely to be negative. These studies do not assume a constant financial structure of the firm sector. However, they do not explicitly analyse endogenous change of the financial structure.
For a long-run theoretical analysis, we can refer to Skott/Ryoo (2008). First, this study shows that the US economy experiences pro-shareholder income distribution under financialization. Then, using both a Harrodian model and a Kaleckian model (without labor supply constraints), they theoretically investigate the effect of a decrease in retention ratio of firms on the macro variables. Limiting our discussion to the Kaleckian model used in their paper, we find the effect of a decrease in the firms' retention ratio on the macro economy to be expansionary.
We investigate the effect of pro-shareholder income distribution on the macro variables by using an otherwise Kaleckian model with debt accumulation. In order to investigate pro-shareholder income distribution of a capitalist economy with near-full employment, we need to build a mature economy model in which labor supply constraints bind. When we incorporate labor supply constraint into the Kaleckian model, the model turns into a Kaldorian model in that the rate capital accumulation is equal to the natural rate of growth, and firms' animal spirits do not affect the rate of capacity utilization in the steady state. Therefore, we consider our model as Kaldorian.
To our knowledge, Ryoo/Skott (2008) is the only study using an otherwise Kaleckian model with labor supply constraints to examine the effect of income distribution on the macro economy. This study is a continuation of Skott/Ryoo (2008) and theoretically shows that the effect of a decrease in the retention ratio of firms is expansionary even in a labor-constrained economy. In the present paper, we build a similar model. However, our method and objectives are largely different from those of Ryoo/Skott (2008).
First, Ryoo/Skott (2008) use numerical calculations for their comparative static analysis. This is because their model is complicated and analytical solutions are hard to obtain. By contrast, we simplify their somewhat complicated settings and obtain our main results through comparative static analysis by using an analytical method.
Second, they limit their analysis to the steady-state equilibrium and hence do not consider the stability and transitional dynamics of a long-run equilibrium. By contrast, we explicitly investigate the stability and transitional dynamics of the equilibrium. According to our analysis, the steady-state equilibrium can be stable or unstable, and, depending on conditions, there can be perpetual business cycles.
Moreover, we employ the Minskyan taxonomy of financial structure of firms. That is, we investigate whether the financial structure of firms becomes hedge finance, speculative finance, or Ponzi finance (Minsky 1975; 1982).
For existing studies investigating the financial structure of firms using Kaleckian models, we consider Charles (2008a), Foley (2003), Lima/Meirelles (2007), and Nishi (2012). In these studies, the financial structure remains as speculative or Ponzi finance after the economy reaches the steady-state equilibrium. By contrast, we show that cyclical fluctuations can occur such that the financial structure of firms changes periodically between speculative finance and Ponzi finance.
The rest of the paper is organized as follows. Section 2 derives the dynamic equations of the rate of capital accumulation, debt–capital ratio, and capital–effective labor supply ratio. Section 3 obtains the steady-state equilibrium, investigates which financial regime the firms belong to, and in addition examines the stability of the steady-state equilibrium. Section 4 presents the results of comparative static analysis. Section 5, using numerical simulations, analyses how the financial structure of firms evolves along a transitional path to the steady state. Section 6 concludes the paper.
We consider a one-sector, one-good, closed economy with no government sector. The economy has three types of agents: firms, households, and banks. Firms produce goods using capital stock and labor services supplied by households. Following the post-Keynesian horizontalist approach (Moore 1988; Rochon 1999), we assume that firms borrow their investment funds from households via the banking sector at a constant nominal lending interest rate, and engage in investments using the borrowed funds and their retained earnings. Further, they do not issue new equities for investment but issue equities at the time of starting their business. Since all these equities are held by households, households receive wage income, interest income, and dividend income (Ryoo/Skott 2008; Skott/Ryoo 2008; Taylor 2004). Households spend a constant fraction of their total income on consumption and save the rest. Banks lend the deposits they receive from the households to the firms. However, we assume that the deposit and lending interest rates are equal and hence banks incur no costs and make no profits.
2.1 Dynamics of the rate of capital accumulation
The firms in the economy produce goods with a fixed coefficient production function. We assume that the potential output–capital ratio is constant. If we denote the actual output and the capital stock as
The households receive wage income, interest income, and dividend income, and hence their total income
In a short-run adjustment process, saving adjusts to given investment
We assume that the firms' target capital accumulation rate
In addition, we introduce the effect of the employment rate on the target capital accumulation rate in order to consider the role of the employment rate in a mature economy. The usual method of endogenously determining the employment rate is to introduce the negative effect of the employment rate – that is, the reserve army effect – on the profit share (Cassetti 2003; Dutt 1992; Flaschel/Skott 2006; Sasaki 2013). However, if we adopt this method, we have to add a dynamic equation of the profit share to our dynamic model and conduct more complicated calculations. Thus, introducing the employment rate into the investment function is the simplest way to endogenize the employment rate (Ryoo/Skott 2008; Skott/Zipperer 2012). In this paper, we consider a negative effect of the employment rate on investment.
The negative effect of the employment rate on investment is justified by the following two factors. First, if the economy is near full employment, the firms' opportunity to employ more workers and expand production will be lost, just as will their incentive to accumulate capital stock. Remember that, in our model, labor supply constraints bind. Second, as the economy approaches full employment, the bargaining power of the workers would increase, which in turn raises the real wage rate via the reserve army effect. An increase in the real wage rate squeezes the profit of firms and reduces investment. These possibilities are given by Ryoo/Skott (2008) and Skott/Zipperer (2012).
However, we must note that the second justification has a shortcoming. When the employment rate increases and, accordingly, the real wage increases, the profit share necessarily decreases as long as labor productivity is constant, which contradicts the assumption of a constant profit share in our model. Therefore, in the following analysis, we proceed with the first justification.
Next, if we denote employment as
We assume that the actual capital accumulation rate is adjusted according to the difference between the target and actual capital accumulation rates (Skott/Zipperer 2012):
2.2 Dynamics of the debt–capital ratio
Log-differentiating the debt–capital ratio, we obtain:
The increment of debt is equal to the actual investment less the retained earnings. Therefore, from Equation (4), the increment of debt per capital can be shown as follows:
2.3 Dynamics of the capital–effective labor supply ratio
We assume that the productivity of labor and the supply of labor grow at constant rates
3 PROPERTIES OF THE STEADY-STATE EQUILIBRIUM
3.1 Steady-state values
From the above analysis, we have a dynamic system composed of Equations (8), (11), and (12). The steady-state equilibrium of the system is a situation in which
Assumption 1. The following inequality holds:
Under this assumption,
Furthermore, Equation (14) can be rewritten as follows:
The denominator of the right-hand side of Equation (16) is positive, whereas the numerator is ambiguous. If the trend term in the target rate of capital accumulation
Assumption 2. The following inequality holds:
3.2 The financial structure of firms
Minsky (1975; 1982) classified the financial structure of firms into three regimes based on cash-flow accounting: hedge finance, speculative finance, and Ponzi finance. Our next task is to find out which financial regime the steady-state financial structure belongs to. 10
Table 1 shows the conditions for each financial regime based on the present notation. Hedge finance is a situation with the soundest financial structure; it is defined as the situation in which the profits of firms are larger than or equal to their total expenditure – that is, the sum of their investment, interest payments, and dividends. By rearranging the conditions for hedge finance, we obtain the following relation:
Speculative finance is defined as a situation in which the profits of firms are less than the sum of their investment, interest payments, and dividends but larger than the sum of their interest payments and dividends. By rearranging the conditions for speculative finance, we obtain the following relations:
Ponzi finance is a situation with the most fragile financial structure; it is defined as a situation in which the profits of firms are less than the sum of their interest payments and dividends. By rearranging the conditions for Ponzi finance, we obtain the following relation:
To which financial regime does the steady-state equilibrium belong?
Equation (20) contradicts the fact that both the capital accumulation rate and debt–capital ratio are positive, implying that the steady-state equilibrium does not become hedge finance. In addition, this means that the former condition of Equation (18) necessarily holds.
If Equation (21) holds, the financial structure of firms becomes speculative; otherwise, the firms are in a Ponzi finance regime. By substituting Equations (13) and (14) into Equation (21), we obtain the following inequality:
Equation (22) is the same as Assumption 1. Thus, the financial position of firms in the steady-state equilibrium would necessarily become speculative when the steady-state value of the debt–capital ratio is smaller than unity. Moreover, if
We next consider the local stability of the steady-state equilibrium. To analyse the local stability of the steady-state equilibrium, we linearize Equations (8), (11), and (12) around the equilibrium and investigate the corresponding Jacobian matrix. 11
We introduce the following definition.
Definition 1. If
With this definition, we obtain the following propositions.
Proposition 1. Suppose that, in the steady-state equilibrium, the rate of capital accumulation is debt-led. Then, the steady-state equilibrium is locally stable.
Proposition 2. Suppose that, in the steady-state equilibrium, the rate of capital accumulation is debt-burdened. Then, in the case of
We will now explain why there occur limit cycles under the debt-burdened case. First, when the adjustment speed of the rate of capital accumulation is sufficiently high, the dynamics of the system could become stable because the negative self-feedback mechanism of the rate of capital accumulation becomes strong. Second, under the debt-burdened regime, a rise in the debt–capital ratio decreases the rate of capital accumulation (
4 COMPARATIVE STATIC ANALYSIS
We investigate the effects of changes in the natural rate of growth, retention ratio, profit share, and interest rate on the debt–capital ratio, rate of capacity utilization, capital–effective labor supply ratio, and employment rate. Table 2 shows the results of our comparative static analysis. 14
Summarizing the above results, we obtain the following propositions. 15
Proposition 3. A decrease in the retention ratio of firms worsens the financial structure of firms. By contrast, an increase in the profit share, a decrease in the interest rate, and an increase in the natural rate of growth improve the financial structure of firms.
Proposition 4. A decrease in the retention ratio increases the rate of capacity utilization. By contrast, an increase in the profit share and a decrease in the interest rate decrease the rate of capacity utilization.
Proposition 5. Suppose that, in the steady-state equilibrium, the rate of capital accumulation is debt-led. Then, a decrease in the retention ratio of firms increases both the capital-effective labor supply ratio and the rate of employment. Moreover, an increase in the profit share and a decrease in the interest rate decrease both the capital–effective labor supply ratio and the rate of employment.
Proposition 6. Suppose that, in the steady-state equilibrium, the rate of capital accumulation is debt-burdened. Then, a decrease in the retention ratio of firms decreases the capital–effective labor supply ratio. However, an increase in the profit share and a decrease in the interest rate increase the capital–effective labor supply ratio. Moreover, these effects on the rate of employment can be positive or negative.
5 CHANGES IN FINANCIAL STRUCTURE THROUGH TRANSITIONAL DYNAMICS
In Section 3.2, we showed analytically that the financial structure of firms exhibits a speculative finance regime in the steady-state equilibrium. However, a situation exists in which the financial structure diverges from the domain of speculative finance and enters the domain of Ponzi finance through transitional dynamics. In other words, the cash flow
It is unreasonable to expect firms to pay dividends to shareholders when the cash flow is negative. Therefore, in the following numerical simulations, we assume that when the cash flow is strictly positive (
5.1 Debt-led case
Let us now consider a case in which the rate of capital accumulation is debt-led in the steady-state equilibrium. In our numerical example, we set the parameters as follows:
Setting, additionally, the initial conditions to
Now, leaving the parameters unchanged, we raise the initial value of the capital–effective labor supply ratio from
5.2 Debt-burdened case
Next, we consider the case in which the capital accumulation rate is debt-burdened in the steady-state equilibrium. Here, we set the parameters as follows:
In this setting, if the adjustment speed of the capital accumulation rate is assumed to be
The mechanism of the financial structure of firms circulating between speculative finance and Ponzi finance is explained as follows. Suppose that a shock in an economy leads to a reduction in the capital–effective labor ratio. Now, the employment rate would decrease and the firms' incentive to expand production would become strong. Increases in the incentives for investment would raise the rate of capital accumulation and decrease the debt–capital ratio. The financial position would then become speculative finance. However, a rise in the rate of capital accumulation has a positive impact on both the capital–effective labor supply ratio and employment rate. When the employment rate approaches its peak, the rate of capital accumulation begins to pass through its downturn phase. A decrease in the rate of capital accumulation would increase the debt–capital ratio, which in turn drives the financial position to Ponzi finance. In a situation where the debt–capital ratio is sufficiently high, the rate of capital accumulation starts to decrease due to the debt-burdened property, and the economy returns to its initial position.
Note, here, that the cycles in our model are not Minskyan. According to Lavoie (1986–1987), Minskyan models have the following two characteristics: (1) the leverage ratio and the rate of capital accumulation move in the same direction, that is, the leverage ratio is pro-cyclical to capital accumulation; and (2) the rate of capital accumulation and the interest rate move in the same direction, that is, in investment booms, the interest rate increases.
With regard to the first characteristic, as Appendix A1 shows, the sign of
With regard to the second characteristic, the interest rate is fixed in our model. Our contribution is that we show the occurrence of cycles even though the interest rate is constant.
The range of fluctuations in business cycles depends on the parameters of the model. If we decrease the retention ratio from
In this paper, we have presented a post-Keynesian model in which both finance and labor supply constraints influence economic growth. With this model, we have analytically investigated the impacts of pro-shareholders' income distribution on capital/debt accumulation and firms' financial structure. Our results can be summarized as follows.
Stability analysis. If the rate of capital accumulation is debt-led, the steady-state equilibrium is locally stable. On the other hand, if the rate of capital accumulation is debt-burdened, there exist three cases: (1) the steady-state equilibrium is locally stable; (2) the steady-state equilibrium is locally unstable; and (3) limit cycles occur when the adjustment speed of the rate of accumulation lies within some range.
Comparative static analysis. A decrease in the retention ratio makes the financial structure fragile. However, there are three alternative ways to improve the financial structure: increasing profit share, decreasing interest rate, and increasing natural rate of growth. Moreover, a decrease in the retention ratio raises the employment rate in the debt-led case, whereas it does not necessarily do so in the debt-burdened case. Furthermore, an increase in the profit share and a decrease in the interest rate would lead to a decline in the employment rate in the debt-led case. By contrast, they have an ambiguous effect on the employment rate in the debt-burdened case, at least from an analytical point of view.
Transitional dynamics of financial structure. In the steady-state equilibrium, the financial structure of firms becomes speculative finance irrespective of whether the economy exhibits the debt-led or debt-burdened regime. However, a difference exists in the transitional dynamics of the financial position between the debt-led and debt-burdened cases. Our numerical simulations have shown that in the debt-led case, a relatively large shock causes the debt–capital ratio to overshoot, and the financial structure to fall temporally into a Ponzi finance regime; on the other hand, if there occur limit cycles in the debt-burdened case, the financial position circulates between the speculative finance and Ponzi finance regimes. Furthermore, we have clarified that a decrease in the retention ratio diminishes the range of cyclical fluctuations.
Finally, we sum up the total effects of pro-shareholder income distribution on the macroeconomic performance. As we have shown, a decrease in the retention ratio worsens the financial structure of firms and diminishes the range of cyclical fluctuations. By contrast, a rise in the profit share contributes to a sound financial position. Thus, we can conclude that an increase in the profit share is more effective for economic performance than a decline in the retention ratio. However, raising the profit share reduces the rate of capacity utilization, which in turn may lead to a decrease in employment. Therefore, the total assessment of income distribution in favor of shareholders largely depends on which objective – that is, a high employment rate, high growth, stable growth, or healthy financial structure – firms or policymakers would choose.
In Hein/van Treeck (2010a) and in Hein (2012), shareholder power affects the dividend rate and thus the retention ratio. See also Hein (2010), where rising shareholder power is associated with a rising dividend rate and decreasing management animal spirits. Some researchers believe that the retention ratio is not a policy variable determined by firms but a variable determined ex post. However, some studies empirically show that firms determine their dividend payout ratio – that is, their retention ratio. See Brav et al. (2005), DeAngelo et al. (1992), Denis/Osobov (2008), and Fama/French (2001).
The retention ratio is calculated by dividing the retained earnings (defined as the net profits of a term
We consider Hein/van Treeck (2010b) as a related study. They theoretically analyse whether financialization has an expansive effect or a contractive effect on the macro economy from some aspects. Using a Kaleckian model, Hein (2010) analytically investigates how increasing shareholder power affects the macro economy. He considers both the medium term, where the outside finance–capital ratio changes, and the short term.
Strictly speaking, the rate of capacity utilization in this paper is the output–capital ratio. The rate of capacity utilization is decomposed into output–capital ratio and capital–potential output ratio. If we assume that the capital–potential output ratio is constant, then the rate of capacity utilization and the output–capital ratio change in the same direction. Therefore, we can regard the output–capital ratio as the rate of capacity utilization.
It is necessary to assume Harrod-neutral technical progress and a constant potential output capital ratio – that is, a constant capital productivity for the existence of a steady-state equilibrium.
Here, we exclude a trivial solution,
The earlier studies specifying the taxonomy of the financial structure using Kaleckian models include Charles (2008a: 320–321), Foley (2003: 158–160), Lima/Meirelles (2007: 570–572), Meirelles/Lima (2006: 102–104), and Nishi (2012: 12–14). These earlier studies include only the investment and interest payments in firms' expenditure and do not consider dividends. However, we should not exclude dividends because it is one of the most important expenditure items when considering pro-shareholder income distribution. In addition, Minsky himself explicitly explains that dividend is a component of the firms' expenditure: ‘The cash payments made by a unit over a relevant time period equal the spending on current labor and purchased inputs, tax payments, the remittance due to debts that fall due, and dividends’ (Minsky 1982: 24).
For details of the stability analysis, see Appendix A1. In Appendix A1, we assume the Keynesian stability condition to hold, which ensures the stability of quantity adjustment of the goods market. However, Skott (2010; 2012) and Skott/Zipperer (2012) challenge the validity of the Keynesian stability condition in the long run.
In our model, the regime of rate of capital accumulation depends on the level of endogenous variable,
Table 2 shows the effect of an increase in animal spirits
Bhaduri A. & Marglin S. , ' Unemployment and the real wage: the economic basis for contesting political ideologies ' ( 1990 ) 14 ( 4 ) Cambridge Journal of Economics : 375 - 393 .
Cassetti M. , ' Bargaining power, effective demand and technical progress: a Kaleckian model of growth ' ( 2003 ) 27 ( 3 ) Cambridge Journal of Economics : 449 - 464 .
Charles S. , ' A post-Keynesian model of accumulation with a Minskyan financial structure ' ( 2008a ) 20 ( 3 ) Review of Political Economy : 319 - 331 .
Charles S. , ' Teaching Minsky's financial instability hypothesis: a manageable suggestion ' ( 2008b ) 31 ( 1 ) Journal of Post-Keynesian Economics : 125 - 138 .
Delli Gatti, D. & Gallegati M. , ' Financial instability, income distribution, and the stock market ' ( 1990 ) 12 ( 3 ) Journal of Post Keynesian Economics : 356 - 374 .
Denis D.J. & Osobov I. , ' Why do firms pay dividends? International evidence on the determinants of dividend policy ' ( 2008 ) 89 ( 1 ) Journal of Financial Economics : 62 - 82 .
Epstein G.A. & Power D. , ' Rentier incomes and financial crises: an empirical examination of trends and cycles in some OECD countries ', ( Institute for International Political Economy Working Paper , 2003 ) No. 57 .
- Export Citation
Epstein G.A. Power D. Rentier incomes and financial crises: an empirical examination of trends and cycles in some OECD countries 2003 Institute for International Political Economy Working Paper No. 57
Fama E.F. & French K.R. , ' Disappearing dividends: changing firm characteristics or lower propensity to pay? ' ( 2001 ) 60 ( 1 ) Journal of Financial Economics : 3 - 43 .
Fazzari S.M. , Hubbard R.G. & Peterson B.C. , ' Financing constraints and corporate investment ' ( 1988 ) 1988 ( 1 ) Brookings Papers on Economic Activity : 141 - 206 .
Foley D. , A.K. Dutt & J. Ros (eds), Development Economics and Structuralist Macroeconomics: Essays in Honor of Lance Taylor , ( Edward Elgar , Aldershot 2003 ) 157 - 168 .
Hayashi F. & Inoue T. , ' The relation between firm growth and Q with multiple capital goods: theory and evidence from panel data on Japanese firms ' ( 1991 ) 59 ( 3 ) Econometrica : 731 - 753 .
Hein E. , ' Interest rate, debt, distribution, and capital accumulation in a post-Kaleckian model ' ( 2007 ) 56 ( 2 ) Metroeconomica : 310 - 339 .
Hein E. , ' Shareholder value orientation, distribution and growth – short- and medium-run effects in a Kaleckian model ' ( 2010 ) 61 ( 2 ) Metroeconomica : 302 - 332 .
Hein E. , ' ‘Financialization,’ distribution, capital accumulation, and productivity growth in a post-Keynesian model ' ( 2012 ) 34 ( 3 ) Journal of Post-Keynesian Economics : 475 - 496 .
Hein E. & van Treeck T. , ' Financialization and rising shareholder power in Kaleckian/post-Kaleckian models of distribution and growth ' ( 2010a ) 22 ( 2 ) Review of Political Economy : 205 - 233 .
Hein E. & van Treeck T. , M. Setterfield (ed), Handbook of Alternative Theories of Economic Growth , ( Edward Elgar , Cheltenham 2010b ) 273 - 292 .
Hoshi T. , Kashyap A. & Scharfstein D. , ' Corporate structure, liquidity, and investment: evidence from Japanese industrial groups ' ( 1991 ) 106 ( 1 ) Quarterly Journal of Economics : 33 - 60 .
Kaldor N. , ' Marginal productivity and the macroeconomic theories of distribution: comment on Samuelson and Modigliani ' ( 1966 ) 33 ( 4 ) The Review of Economic Studies : 309 - 319 .
Lavoie M. & Seccareccia M. , R. Bellofiore & P. Ferri (eds), Financial Fragility and Investment in the Capitalist Economy: The Economic Legacy of Hyman Minsky , ( Edward Elgar , Cheltenham 2001 ) 76 - 96 .
Lima G.T. & Meirelles A.J.A. , ' Macrodynamics of debt regimes, financial instability and growth ' ( 2007 ) 31 ( 4 ) Cambridge Journal of Economics : 563 - 580 .
Meirelles A.J.A. & Lima G.T. , ' Debt, financial fragility, and economic growth: a post Keynesian macromodel ' ( 2006 ) 29 ( 1 ) Journal of Post Keynesian Economics : 93 - 115 .
Ndikumana L. , ' Debt service, financing constraints, and fixed investment: evidence from panel data ' ( 1999 ) 21 ( 3 ) Journal of Post Keynesian Economics : 455 - 478 .
Nishi H. , ' A dynamic analysis of debt-led and debt-burdened growth regimes with Minskian financial structure ' ( 2012 ) 63 ( 4 ) Metroeconomica : 634 - 660 .
Onaran Ö. , Stockhammer S. & Grafl L. , ' Financialisation, income distribution and aggregate demand in the USA ' ( 2011 ) 35 ( 4 ) Cambridge Journal of Economics : 637 - 661 .
Ryoo S. & Skott P. , ' Financialization in Kaleckian economies with and without labor constraints ' ( 2008 ) 5 ( 2 ) Intervention: European Journal of Economics and Economic Policies : 357 - 386 .
Sasaki H. & Fujita S. , ' The importance of the retention ratio in a Kaleckian model with debt accumulation ' ( 2012 ) 63 ( 3 ) Metroeconomica : 417 - 428 .
Skott P. , M. Setterfield (ed), Handbook of Alternative Theories of Economic Growth , ( Edward Elgar , Cheltenham 2010 ) 108 - 131 .
Skott P. & Zipperer B. , ' An empirical evaluation of three post-Keynesian models ' ( 2012 ) 9 ( 2 ) Intervention: European Journal of Economics and Economic Policies : 277 - 307 .
Van Treeck T. , ' Reconsidering the investment–profit nexus in finance-led economies: an ARDL-based approach ' ( 2008 ) 59 ( 3 ) Metroeconomica : 371 - 404 .
APPENDIX A1 STABILITY ANALYSIS
Note that all the elements are evaluated at the steady-state values.
We suppose that quantity adjustment in the goods market is stable – that is,
The characteristic equation that corresponds to the Jacobian matrix J is given as
The necessary and sufficient conditions for the local stability of the steady-state equilibrium are given by
If the rate of capital accumulation is debt-led, we have
Assumption 3. Even if the rate of capital accumulation is debt-burdened,
This assumption is satisfied in the situation where the trend term
We next examine the sign of
If the rate of capital accumulation is debt-led,
However, if the rate of capital accumulation is debt-burdened,
Summarizing these results, we obtain Propositions 1 and 2 in the text.
APPENDIX A2 COMPARATIVE STATIC ANALYSIS
A2.1 The debt–capital ratio
The effects of changes in the retention ratio, profit share, interest rate, and natural rate of growth on the steady-state value of the debt–capital ratio are given as follows:
A2.2 The rate of capacity utilization
From Assumption 1, we have
The effects of changes in the retention ratio, profit share, interest rate, and natural rate of growth on the steady-state value of the rate of capacity utilization are given as follows:
Only the sign of
A2.3 The capital–effective labor supply ratio
We examine the effects of changes in the retention ratio, profit share, interest rate, and natural rate of growth on the capital–effective labor supply ratio.
Note that we have
In the debt-led case, we obtain
In the debt-burdened case, we obtain
A2.4 The employment rate
The steady-state value of the rate of employment is given by
When the rate of capital accumulation is debt-led, we obtain both
From similar deductions, we can examine the effect of changes in other parameters on the rate of employment.
Sasaki, Hiroaki - Graduate School of Economics, Kyoto University, Japan
Fujita, Shinya - Graduate School of Economics, Nagoya University, Japan