Kyoto University,
Graduate School of Economics
Research Project Center Discussion Paper Series

Financialization and its Long-run Macroeconomic Effects
in a Kalecki-Minsky Model

Shinya Fujita and Hiroaki Sasaki

Discussion Paper No. E-11-001

Research Project Center
Graduate School of Economics
Kyoto University
Yoshida-Hommachi, Sakyo-ku
Kyoto City, 606-8501, Japan

April 2011

Financialization and its long-run macroeconomic effects in a
Kalecki-Minsky model∗

Shinya FUJITA
Graduate School of Economics, Nagoya University
Hiroaki SASAKI
Graduate School of Economics, Kyoto University

Abstract
One of the main characteristics of “financialization” is the redistribution of income infavor of shareholders, at the expense of workers. In this paper, we interpret
pro-shareholder redistribution as a decrease in both retention ratio and wage share.
Using both the Kaleckian macroeconomic model and the Minskyan taxonomy offinance regime, we investigate the long-run effects of such parametric changes on therate of capital accumulation and the debt-capital ratio, on the one hand, and on thefinancial structures of firms, on the other. A decrease in the retention ratio leads tohigher capital accumulation, but makes financial structures fragile. Moreover, a rise inprofit share improves the financial position in the long run if the short-run equilibrium
is profit-led growth regime; this is not necessarily so with wage-led growth.

The authors acknowledge the financial support provided by a grant-in-aid from the
Zengin Foundation for Studies on Economics and Finance.
∗

1 Introduction
An extensive body of literature describes examinations of “financialization,” which has
been in progress over the last two decades in advanced capitalist countries.
Financialization, in fact, has broad and various senses: the appearance of new financial
commodities, along with deregulation of the financial market; an increase in financialtransactions, including financial investment by firms and credit-financed consumption
by households; and the restructuring of corporate governance so as to favorshareholder value. This paper focuses on the redistribution of income in favor ofshareholders and at the expense of workers; it also investigates the long-run effect ofsuch redistribution on the rate of capital accumulation and the debt-capital ratio, on the
one hand, and on the financial structures of firms, on the other.
Many empirical studies have investigated the short-run effect of pro-rentier (i.e.,shareholder) income redistribution on effective demand. Stockhammer (2004) showsthat the negative effect of a rise in rentier income (dividends and interest) per GDP on
capital accumulation is statistically significant in the United States, the United
Kingdom, and France, but not in Germany.1 Onaran, Stockhammer, and Grafl (2011),
in surveying how the U.S. rentier income share started to increase in the 1980s at theexpense of both non-rentier income share and wage share, indicates that the overall
effect of such redistribution on aggregate demand was neutral: the positive effect of arise in rentier income with the higher wealth effects on consumption is canceled out by
its negative effect on investment and declining consumption, caused by a fall in thewage share.
It is worth noting that with financialization, a decrease in the wage share—causedby firms looking to compensate for a loss of retained earnings—has been observed not
only in the United States, but also in other advanced countries. Epstein and Power(2003) shows that some OECD countries after 1980s experienced a modest increase innon-financial corporate profit share with a drastic increase in the rentier income share,both of which worked to reduce the wage share.
Some studies have presented theoretical analyses concerning pro-rentier
redistribution and its influences.2 Skott and Ryoo (2008) investigate how a fall in the1retention ratio—which the current study regards as one of the features offinancialization in the United States—affects macroeconomic variables; they do so byusing Harrodian and Kaleckian models. They show that a decrease in the retention
ratio raises the long-run rates of capacity utilization and of economic growth in a
Kaleckian model. Hein and van Treeck (2010a) consider the case where the rentiers’
rate of profit, which is the sum of dividends and interest per capital, and the mark-up
rate on pricing are increasing functions of shareholder power. They demonstrate that
there exist diverse growth regimes, because shareholder power influences short-run
aggregate demand through many channels.
Following Skott and Ryoo (2008), this paper expresses income redistribution infavor of shareholders as decreases in both retention ratio and wage share. It isappropriate to consider that shareholder value orientation is proxied not by the sum of
dividends and interest, but by dividends alone (or the retention ratio, which determines
the share of the dividend) (van Treeck 2008, p. 380). Using the Kaleckian
model—which takes into account monetary factors (Lavoie 1995; Taylor 2004; Hein
2006, 2007)—this paper pays special attention to the effects of a decrease in theretention ratio and a increase in the profit share on both the rate of capital
accumulation and the debt-capital ratio in the long-run period when capital and debt
are accumulated.
Another contribution of this paper is that it considers the effect of changes in theretention ratio and the profit share on the financial structure of firms, based on thetaxonomy of the financial regime (i.e., hedge, speculative, and Ponzi), as defined by
Minsky (1975, 1982). We expect that there might exist a situation theoretically andactually where firms confront a more fragile financial structure in spite of higher
capital accumulation.
A pioneering study by Foley (2003)—which specifies Minskyan financial
taxonomy in line with the Kaleckian model—indicates that, in an open economy
framework, the long-run dynamics of the macro economy could temporarily enter thePonzi finance regime throughout the convergence to the equilibrium.3 Meirelles andLima (2006) study the relationship between parameters in both saving and investment
2and the areas of each finance regime under a constant interest rate and debt-capitalratio. They derive an interesting proposition: the financial structure of firms worsens,
despite a higher capital accumulation, if investment does not responds sensitively
enough to the rate of interest. However, Meirelles and Lima (2006) adopt two strong
assumptions—namely, that the saving propensities of productive and financial
capitalists are equal, and there do not exist in the dividend. In contrast, in relaxing
those assumptions, the current study shows that a decrease in the retention ratio will
promote capital accumulation, even as it creates a more risky financial position in thelong run.
The remainder of this paper is organized as follows. Section 2 presents a
Kaleckian model with debt accumulation; section 3 constructs the Minskyan taxonomy
of financial structure in line with that Kaleckian model, and examines the properties ofa boundary between speculative and Ponzi finance regimes. Section 4 investigates thelong-run effect of changes in retention ratio, profit share, and rate of interest on thedebt-capital ratio, rate of capital accumulation, and financial structures of firms.
Section 5 concludes the paper.
2. Kaleckian model
2.1 Basic settings
A closed economy without a government is assumed. There exists a single good with aconstant price level, which can be used for both production and consumption.
Technological progress is not explicitly considered: both the potential output-capitalratio and the output-labor ratio are assumed to be constant.
This closed economy contains three agents: firms, households, and banks. Firms
with excess capacity produce goods by means of capital stock and labor services.
According to the post-Keynesian “horizontalist” view (Moore 1988 ; Rochon 1999), it
is assumed that firms invest by using a part of the profits and external funds that are
financed by households via banks; this in turn sets the constant nominal loan rate (i.e.,interest rate). Although firms do not issues new shares—but they issue shares only
once, when they start to operate—these shares are now owned by households. Thus,3households acquire wage income, interest, and dividends (Taylor 2004; Kurose 2004;
Skott and Ryoo 2008). The current study, additionally, assumes that banks merelytransfer deposits from households to firms and interest payments from firms tohouseholds.
Based on the aforementioned assumptions, firms’ real retained earnings ( Π f ) andhouseholds’ real income ( Π h ) are given asΠ f = s f (πY − iL ) , s f ∈ (0,1) , π ∈ (0,1) , i (> 0) ,

Π h = (1 − π )Y + iL + (1 − s f )(πY − iL ) ,

(1)
(2)

where Y denotes aggregate income in real terms, L denotes the real stock of debt
held by firms, s f denotes the retention ratio, π denotes the profit share, and idenotes the interest rate. The last three variables are assumed to be constant.
There is also the assumption that households save a constant fraction, s h , of theirincome. Total savings, S , in real terms, comprises retained profits and savings fromhouseholds’ incomes. Using equations (1) and (2), the aggregate saving function is
obtained.
S= s f (πu − iλ ) + sh (1 − s f π )u + s f iλ , s h ∈ (0,1) ,
K

[

]

(3)

where K denotes real capital stocks, u (≡ Y / K ) denotes the rate of capacity
utilization, and λ (≡ L / K ) denotes the debt-capital ratio.
Kaleckian models feature many variants of the desired investment function.
Charles (2008a, 2008b, 2008c) assumes that investment is an increasing function ofretained profits. Meirelles and Lima (2006) and Lima and Meirelles (2007) assume thatinvestment is related positively to profits and negatively to the interest rate. Dutt(1992) uses a similar equation, but adds the rate of capital utilization to the explanatory
variable. The current study’s model assumes that real investment, I , per capital is anincreasing function of the profit rate and the rate of capacity utilization (Marglin andBhaduri 1990) and a decreasing function of the interest payment per capital (Hein2007; Taylor and Arnim 2008; Hein and van Treeck 2010b).4
I= α + βπ + γu − θiλ , α > 0 , β > 0 , γ > 0 , θ > 0 .
K
4

(4)

The estimated result of the investment function by each of Stockhammer (2004),
Orhangazi (2008), and van Treeck (2008) supports our behavioral equation.
2.2 Short-run equilibrium
In the short run, disequilibrium between investment and savings is adjusted throughchanges in capacity utilization, under given capital and debt stocks.
The short-run equilibrium rate of capacity utilization is obtained from equations(3) and (4).
u=α + βπ + [s f (1 − s h ) − θ ]iλ.
s f π (1 − s h ) + s h − γ(5)This equilibrium will be stable if investment is sufficiently insensitive to variations incapacity utilization—that is, if s f π (1 − s h ) + s h − γ > 0 , which we assume in thefollowing discussion.
The short-run equilibrium rate of capacity utilization is called debt-led (DLCU,
hereafter) if s f (1 − s h ) − θ > 0 (Hein 2007; Taylor 2004; Lavoie and Godley 2001–2).
This is because increases in the debt-capital ratio and the interest rate raise
consumption demand by raising interest payments to households. In contrast, if
s f (1 − s h ) − θ < 0 , the short-run equilibrium rate of capacity utilization is called thedebt-burdened (DBCU, hereafter), because increases in the debt-capital ratio and theinterest rate restrain investment demand.
Substituting equation (5) in equation (4) obtains the rate of capital accumulation,g (≡ I / K ) , in the short-run equilibrium.
g = A + Bλ ,A=

{γs f (1 − sh ) − θ [s f π (1 − sh ) + sh ]}i .
(α + βπ )[s f π (1 − sh ) + sh ], B=
s f π (1 − s h ) + s h − γ
s f π (1 − s h ) + s h − γ

[

]

(6)

If γs f (1 − s h ) − θ s f π (1 − s h ) + s h > 0 , then the short-run equilibrium is debt-led growth[](DLG, hereafter). If, on the other hand, γs f (1 − s h ) − θ s f π (1 − s h ) + s h < 0 , then the
short-run equilibrium is debt-burdened growth (DBG, hereafter).5
Next examined, as in the standard Kaleckian models, is the effect of a change inthe profit share on the demand level and the growth rate. Differentiating u and g5with respect to π yields[]

du − s f (1 − s h ){α + s f (1 − s h ) − θ iλ }+ β (s h − γ ),=2dπ
s f π (1 − s h ) + s h − γ

(7)

[
]
dg − [s (1 − s )α − β (s − γ )][s π (1 − s ) + s ] − s γ (1 − s )[s (1 − s ) − θ ]iλ
. (8)
=
dπ
[s π (1 − s ) + s − γ ]
f

h

h

f

h

f

h

h

h

f

h

f

h

2

Here, the terms concerning the distributive regimes in Blecker (2002) are accepted. An
exhilarationist and profit-led growth regime (PLG, hereafter) will be established if thefollowing conditions are met: α is sufficiently small, θ is sufficiently large, and β
is sufficiently large under s h − γ > 0 . If these conditions are not satisfied, then astagnationist and wage-led growth regime (WLG, hereafter) will appear. Moreover,since there exists the term s f (1 − s h ) − θ in the numerators of the right-hand side ofequations (7) and (8), a stagnationist and WLG (exhilarationist and PLG) will tend to
appear if the short-run equilibrium is DLCU (DBCU).
2.3 Long-run equilibrium
In the long run, the debt-capital ratio becomes an endogenous variable, while the goods
market always clears. The growth rate of the debt-capital ratio is given by


 L
L
− g λ = − gλ ,KL

λ = 

(9)where the dot over the variable denotes its time derivative.
In the firms’ cash flow identity, an operating fund comprising new borrowing andprofit is equal to total expenditure, including investment, interest, and dividends.
L+ πu ≡ g + iλ + (1 − s f )(πu − iλ )K

(10)Equation (10) implies that an increment of the debt is the difference between
investment and retained earnings.
L= g − s f (πu − iλ )K

(11)Substituting equation (11) into equation (9) yields the dynamical equation of thedebt-capital ratio.
6

sfπ




s f shiλg +s f π (1 − s h ) + s h
s f π (1 − s h ) + s h .
s h (1 − s f π ) A  s h (1 − s f π ) B + s f s h i− A λ − Bλ2+=s f π (1 − s h ) + s h  s f π (1 − s h ) + s hλ ≡ F (λ ) = 1 − λ −(12)The long-run equilibrium is defined by λ = 0 . Then, the equilibrium value of thedebt-capital ratio, λ* , is obtained by solving F λ* = 0 . Using the λ , λ plane, the

( )

( )

existence of the positive equilibrium value and its local stability in the long run can beeasily verified.
Now, assume that the short-run equilibrium is DLG—that is, B > 0 . Then, F (λ )( )shows a parabola with its vertex oriented upwards in the λ , λ plane. The inflexion
axis of the curve is given by

λ=

[

] .

s h (1 − s f π ) B + s f s h i − s f π (1 − s h ) + s h A[

2 B s f π (1 − s h ) + s h

]

(13)

Figure 1 shows that F (λ ) always intersects the horizontal axis once within λ > 0 ,regardless of the sign of the inflexion axis. It is obvious that this intersection is thelong-run equilibrium.
The long-run equilibrium is always locally stable in the DLG case. Even if anexternal shock moves the debt-capital ratio to the point λ0 on the horizontal axis, thisratio continues to decrease in the range of λ < 0 until it converges to the equilibrium.
In contrast, even if the debt-capital ratio happens to be below its equilibrium, this ratio
continues to increase because of λ > 0 , and it finally converges to the equilibrium.
(Figures 1 and 2 around here)
Next considered is the case where B < 0 , which means that the short-run
equilibrium is DBG. In this case, F (λ ) depicts a parabola with its vertex oriented( )downwards in the λ , λ plane, as shown in Figure 2. The necessary and sufficientconditions for the existence of the positive equilibrium value are that the discriminantofF (λ ) = 0

is positive and[λ > 0 . The latter condition, which implies]s h (1 − s f π ) B + s f s h i − s f π (1 − s h ) + s h A < 0 under B < 0 , is satisfied if the parameters

α and β are sufficiently large. However, it is difficult to specify the former
condition, given the complexity of the calculations. Here, we assume that the7discriminant is positive.

()

Figure 2 shows that the DBG case has multiple equilibria λ1* , λ*2 . The smaller
equilibrium, λ1* , is locally stable, while the larger one, λ*2 , is locally instable.
Additionally, note that the following condition is always satisfied, regardless of
the DLG or DGB, in the aforementioned long-run positive equilibrium.

( ) s h (1 − s f π ) B + s f s h i∂F (λ )− A − 2 Bλ* < 0 .
=
∂λ λ =λ*  s f π (1 − s h ) + s h


(14)

From F λ* = 0 , we obtain the relation between the equilibrium value of thedebt-capital ratio and that of the capital accumulation rate, g ∗ , in the long run.

g* =

[

s f s h iλ*](s f π − s f π (1 − s h ) + s h 1 − λ*

(15)

)

Here, only the case where 0 ≤ λ∗ ≤ 1 is considered because, in reality, the debt-capitalratio remains between 0 and 1 (Taylor and Arnim 2008; Hein and Schoder 2009).
Moreover, it is appropriate to expect that the capital accumulation rate would have apositive value. Then, the positive value of g ∗ under λ∗ > 0 requires that there be apositive denominator on the right-hand side of equation (15). Therefore, there is a[]lower limit of λ∗ —that is, λ* > s h (1 − s f π )/ s f π (1 − s h ) + s h , for g ∗ > 0 .6 It is

assumed that this condition is always satisfied; the long-run equilibrium value of thecapital accumulation rate has a positive value.
3 Minskyan taxonomy of the financial structure
3.1 Financial regime and position of the long-run equilibrium
Minsky classifies the financial structures of firms into three categories, according tocash-flow accounting: hedge finance, speculative finance, and Ponzi finance (Minsky,
1975, 1982). Earlier examples that specify the taxonomy of the financial structure offirms by using Kaleckian models include Foley (2003), Meirelles and Lima (2006),
Lima and Meirelles (2007), and Charles (2008a, 2008b).7
Table 1 shows the condition for each financial regime, based on the present
notation. Hedge finance is a situation where the financial structure is the most sound,and it is defined as a situation where the profits of firms are larger than or equal to the8sum of investment, interest payments, and dividends. Rearranging the condition forhedge finance obtains the following relation:()

g * − s f πu * − iλ* ≤ 0 ,(16)

where u * denotes the long-run equilibrium value of the rate of capacity utilization.
Next, speculative finance is defined as a situation where the profits of firms areless than the sum of investment, interest payments, and dividends, but larger than thesum of interest payments and dividends. Rearranging the condition for speculative
finance obtains the following relation:()

g * − s f πu * − iλ* > 0 and πu * > iλ* .

(17)Finally, Ponzi finance is a situation where the finance structure is the most fragile,and it is defined as a situation where the profits of firms are less than the sum ofinterest payments and dividends. Rearranging the condition for Ponzi finance obtains
the following relation:πu * ≤ iλ* .

(18)(Table 1 around here)
In which financial regime is the long-run equilibrium located? First, from equation(11), it is known that L / K < 0 under hedge finance. Because the goods market clears
in the long-run equilibrium, from equations (3) and (11), the borrowing of firms isconsequently equal to the savings of households.
L= s h (1 − s f π )u * + s f iλ* .
K

[

]

(19)

The right-hand side of equation (19) is clearly positive, which contradicts L / K < 0 .
Therefore, the long-run equilibrium is not hedge finance.8 In addition, this fact meansthat the former condition of equation (17) necessarily holds.
Moreover, when the goods market clears, equation (3) can be rearranged asfollows:g * − sh u *= πu * − iλ* .
s f (1 − sh )(20)

The condition for speculative finance is identical to g * − sh u * > 0 . By using equation(15), we can rewrite the left-hand side of this inequality as follows:
9

*

*

g − sh u =

[

](

)

sh s f π (1 − sh ) + sh 1 − λ* iλ*[](s f π − s f π (1 − s h ) + s h 1 − λ*

).

(21)

The assumption in the previous section was that the denominator of the right-hand sideof equation (21) is positive; consequently, g * − s h u * > 0 is obtained. Therefore, thelong-run equilibrium is located in the speculative finance regime. In other words, thelong-run equilibrium is never located in the Ponzi finance regime.
3.2 A comparative static analysis of financial regime
As the previous subsection showed, the long-run equilibrium is located in the
speculative finance regime. However, depending on whether the equilibrium is near thehedge finance regime or the Ponzi finance regime, the sustainability of firms can differ
greatly. If the equilibrium is near the Ponzi finance regime, a negative shock to an
economy temporally drives firms into the Ponzi finance regime—for example, as
shown as λ0 in Figure 3. Firms eventually converge to the equilibrium λ* , but it is
not certain whether firms can precisely predict the convergence. Unless firms canpredict the convergence toward the equilibrium, they will stop production; if the worst
happens, they must go bankrupt due to default.
(Figure 3 around here)
Based on the above observation, the next task is to investigate under what
condition the long-run equilibrium approaches the Ponzi finance regime. As apreliminary step, the boundary between the speculative finance and Ponzi financeregimes are derived.
At the boundary between speculative finance and Ponzi finance is a situation
where the profits of firms are equal to the sum of interest payments and dividends.
From this, by using equation (5), the boundary value, λS − P , is derived, as follows:

λS − P =(α + βπ )π(sh + θπ − γ )i

.

(22)

Here, the assumption is that the coefficient of the investment function γ is smallenough for the denominator of the right-hand side of equation (22) to be positive: theboundary λS − P is positive. Note that because the long-run equilibrium λ∗ is located10

in the speculative finance regime, λ* < λS − P always occurs.
To judge whether, after financialization, the long-run equilibrium is near the hedge
finance regime or the Ponzi finance regime, the following two things need to beinvestigated: whether or not a rise in a parameter increases the long-run equilibrium
value of the debt-capital ratio (i.e., a change in λ* ), and how the rise in the parameter
shifts the boundary (i.e., a change in λS − P ). In this section, the latter issue wasconsidered; the former issue will be considered in the next section.
The effects of increases in the retention ratio, profit share, and interest rate are as
follows:dλS − P
= 0,
ds f

(23)

dλ S − P (α + 2 βπ )(s h − γ ) + βθπ 2,=dπ(s h + θπ − γ )2 i(24)

dλS − P
(α + βπ )π < 0 .
=−(sh + θπ − γ )i 2
di

(25)

First, as equation (23) shows, the boundary is independent of the retention ratio offirms. Accordingly, to know the effect of a fall in the retention ratio on the financial
structure of firms, one need only know the effect of the fall in the retention ratio on thelong-run equilibrium value of the debt-capital ratio. Second, as equation (24) shows,the effect of a rise in the profit share on the boundary is ambiguous; however, if thecoefficient γ is small enough, dλS − P / dπ > 0 is obtained—that is, the rise in the
profit share shifts the boundary in the positive direction. Third, a rise in the interest
rate shifts the boundary in the negative direction.
4 Long-run effect of the retention ratio, profit share, and interest rate
4.1 Retention ratio
This subsection investigates the effect of a rise in a parameter on the long-run
equilibrium values of the debt-capital ratio and the rate of capital accumulation.
As stated in the Introduction, one of the important features of financialization is a()

fall in the retention ratio. Totally differentiating F λ* ; s f = 0 obtains
11 ∂F   ∂F 
dλ*
/
.
= −
 ∂s   ∂λ* 
ds f
f



(26)

∂F / ∂λ* < 0Because the long-run equilibrium is stable,

is obtained fromequation (14). The term ∂F / ∂s f can be calculated as follows:9

(
]{

)
[

s h 1 − λ* ∆iλ*
∂F
.
=
∂s f
s f π (1 − s h ) + s h − γ s f π − s f π (1 − s h ) + s h 1 − λ*

[

[

](

)}

(27)

]

Here, ∆ = − s h + γ s h + (1 − s h )λ* and the sign of the right-hand side of equation (27)depends on the sign of ∆ . If one were to consider a realistic case where the debt offirms does not exceed the total capital—that is, λ* ≤ 1 —then s h + (1 − s h )λ* is lessthan or equal to unity. Accordingly, unless the coefficient γ takes an extremely large
value, then ∆ < 0 , which yields ∂F / ∂s f < 0 , and hence dλ* / ds f < 0 . Moreover, as
shown in the preceding section, a fall in the retention ratio never affects the boundary.
In summary, unless γ takes an extremely large value, a fall in the retention ratio will
move the financial structure of firms closer to the Ponzi finance regime.
Next investigated is the effect of a fall in the retention ratio on the long-run
equilibrium value of the rate of capital accumulation. Considering that the long-run
equilibrium value of the debt-capital ratio is a function of the retention ratio, one candifferentiate equation (15) with respect to s f , which yields
dg *
=
ds f

dλ*
− s 1 − λ iλ + s f s i (1 − s f π )
ds f
2
h

(

*

)

*

2
h

{s π − [s π (1 − s ) + s ](1 − λ )}
f

f

h

h

*

2

.

(28)

Because dλ* / ds f < 0 , the right-hand side of equation (28) is negative. Hence, a fall in
the retention ratio increases the long-run equilibrium value of the rate of capital
accumulation. This means that a kind of paradox of thrift—where an increase in thepropensity to save (i.e., the retention ratio of firms) lowers the economic
growth—holds in the long run.
In summarizing the above analysis, the following proposition is obtained.
Proposition 1. In the long-run equilibrium, a fall in the retention ratio increases therate of capital accumulation but worsens the financial structure of firms.
12

4.2 Profit share
Firms facing a decrease in retained earnings as a result of financialization tend to offset
the loss by increasing profit share. Therefore, we must investigate the effect of anincrease in profit share on the long-run equilibrium.
Proposition 2. Suppose that the short-run equilibrium is PLG. Then, an increase in the
profit share decreases the long-run equilibrium value of the debt-capital ratio.
Proof. See Appendix 2, which is available on request.
Recall that as long as the coefficient γ is sufficiently small, an increase in the
profit share shifts the boundary λS − P in the positive direction. Accordingly, if theshort-run equilibrium is PLG and if γ takes a small value, then an increase in the
profit share improves the financial structure of firms. On the other hand, if these two
conditions are not satisfied—if, for example, the short-run equilibrium is WLG—thenthe effect of an increase in the profit share on the long-run equilibrium value of thedebt-capital ratio is ambiguous. In other words, an increase in the profit share does notalways improve the financial structure of firms. In addition, the effect of an increase in
the profit share on the long-run equilibrium value of the rate of capital accumulation is
also ambiguous.
4.3 Interest rate
Next, let us investigate under what condition the monetary policy of the central bankthat controls the interest rate improves the financial structure of firms.
In the current model, the interest rate is a nominal lending rate, which is usuallyspecified as a base rate multiplied by a mark-up. Because the base rate depends on themonetary policy of the central bank, the lending rate moves with the base rate, as longas the mark-up remains constant. In summary, the central bank can decisively affect thefinancial structure of firms by controlling the base rate.

13

Proposition 3. Suppose that the short-run equilibrium is DBG; then, a decrease in theinterest rate lowers the long-run equilibrium value of the debt-capital ratio.
Proof. See Appendix 3, which is available on request.
Recall that a decrease in the interest rate shifts the boundary λS − P in the positive
direction. Therefore, when the short-run equilibrium is DBG, a decrease in the interest
rate by the central bank will improve the financial structure of firms.
Note that when an investment largely reacts to the interest payments iλ —that is,when θ is sufficiently large—the short-run equilibrium tends to be both DBG and
PLG, as shown in subsection 2.2. When these two regimes are attained, a decrease in
the base rate by the central bank and an increase in the profit share by firms arecomplementary. However, if θ is sufficiently small and, consequently, the short-run
equilibrium is both WLG and DLG, then it is possible that neither an increase in the
profit share nor the monetary policy (i.e., the decrease in interest rate) can improve thefinancial structure of firms.
(Table 2 around here)
Table 2 shows the results of sections 3 and 4, and adds the results with regard to
the effects of changes in the parameters of the investment function on the debt-capitalratio, the rate of capital accumulation, and the financial structure of firms.10
5 Conclusion
Many studies have investigated both the advantages and disadvantages of“financialization,” a situation that has been taking place over the last two decades inadvanced capitalist economies. This paper confines itself to a redistribution of incomethat favors shareholders, at the expense of workers; this is a main characteristic offinancialization.

This

paper

also

soughttoidentify

certainredistribution

patterns—including decreases in the retention ratio and wage share—and analyze thelong-run effect of a decrease in the retention ratio and an increase in the profit share on
the rate of capital accumulation rate, the debt-capital ratio, and firms’ financial position.
It did so through the use of the Kaleckian model with debt accumulation and a
14

Minskyan taxonomy vis-à-vis the financial structures of firms.
The main results of the present study are summarized as follows. First, a fall in theretention ratio has an important role in the occurrence of the ambivalent situation
where the financial structure becomes more fragile, in spite of higher economic growth.
Because of the paradox of thrift, a decrease in the retention ratio raises the equilibrium
rate of capital accumulation in the long run, irrespective of the debt-led or
debt-burdened growth regime. However, since it increases the long-run equilibrium
debt-capital ratio and has no effect on the boundary value between speculative andPonzi finance regimes, a pro-shareholders dividend policy will cause financial
fragility; this implies that a negative shock easily moves the financial positions offirms into a Ponzi finance regime. Second, firms facing a decrease in the retention ratio
will increase the profit share by lowering wage income. This action improves thefinancial structure if the short-run equilibrium is in a profit-led growth regime, largely
by reducing the long-run equilibrium debt-capital ratio and raising the boundary value.
However, the effect of increasing profit share is ambiguous (or, in some cases, may
worsen the financial structure) when the short-run equilibrium is in a wage-led growth
regime. Thus, a pro-shareholder redistribution of income in the financialization era
appears to bear higher risk, in the sense that it brings about financial fragility. Finally,
the monetary policy—such as when the central bank reduces the base rate—will beeffective if the equilibrium is debt-burdened growth regime in the short run, but this is
not necessarily so with debt-led growth.
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Charles, S. “Corporate Debt, Variable Retention Ratio and the Appearance of Financial
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Endnotes1

See also similar studies by Orhangazi (2008) and van Treeck (2008). Using firm-level

data, Orhangazi (2008) demonstrates that financial payments (i.e., dividends and stockbuybacks) depress real investment, especially large-sized manufacturing industry in the
United States. van Treeck (2008) explicitly distinguishes dividends and interest, andshows that both terms negatively affect investment in the United States, the United
Kingdom, France, and Germany.
2

The following is the literature that considers financialization. Dutt (2006) and Palley(2010) each investigate the relationship between the debt accumulation of households
and economic growth. Hein (2010) presents a model in which the outside
finance-capital ratio is an endogenous variable in the long run.
3

Other literatures that take into account the Minskyan taxonomy of financial structure

are as follows. Charles (2008a) explains the instable process of the macro economy byconstructing a model in which the interest-profit ratio, which implies the state of thefinancial structure, evolves over time. Lima and Meirelles (2007) show that macro
18

economic instability always appears when the long-run equilibrium of the debt-capitalratio is located in the Ponzi finance area, regardless of adjustments to the rate ofinterest.
4

We can add dividends to the explanatory variables of the investment function.

Because a rise in the dividend is identified as a signal of firms’ good performance, it
might reduce the capital cost and raise investment. In contrast, an increase in thedividend—which would imply a decrease in retained earnings—might have a negative
impact on investment. van Treeck (2008) shows that the latter effect is statisticallysignificant.
5

As previously seen, the condition for DLCU (DBCU) differs from the condition for

DLG (DBG). Note that DBCU is not compatible with DLG. The condition for theformer is given byx ≡ s f (1 − s h ) − θ < 0 .

The condition for the latter is given by[]y ≡ γs f (1 − s h ) − θ s f π (1 − s h ) + s h > 0 .

Using these two equations obtains

[

]

[

]

y ≡ γ ( x + θ ) − θ s f π (1 − s h ) + s h = γx − θ s f π (1 − s h ) + s h − γ .

Here, x < 0 and s f π (1 − s h ) + s h − γ > 0 imply y < 0 . The DBCU necessarily leads
to DBG. Therefore, there exist the following three cases: Case (a): DLCU and DLG;(b) DLCU and DBG; and (c) DBCU and DBG.
6

This lower limit is positive and smaller than 1. Thus, assuming that λ∗ is larger thanthe lower limit does not contradict the case 0 ≤ λ∗ ≤ 1 .
7

These earlier studies consider only investment and interest payments; they do notconsider dividends.
8

The long-run equilibrium value of the debt-capital ratio under the hedge financeregime is negative. When the goods market clears, from equation (3), we obtain

[

][

]

u * = g * + s f (1 − s h )iλ* / s f π (1 − s h ) + s h . Substituting this equation in equation (16)and rearranging the resultant expression obtains(1 − s π )g.
λ ≤−s (1 + s π )i
*

f

*

h

19

f

This means that λ* is negative, as long as g ∗ is positive.
9

For the derivation, see Appendix 1, which is available on request.

10

For proofs, see Appendix 4, which is available on request.

20

Figure 1: DLG caseλ
F (λ )λλ0

λ*Figure 2: DBG caseλ

F (λ )

λ1*

λ

λ*2

Figure 3: Convergence process from the Ponzi to the speculative areaλ

λS − PF (λ )
Speculative area

Ponzi area

Negative shockλ*λConvergence path021

λTable 1: Taxonomy of the financial structures of firms
Finance regime

Definition of each financial regime

Existence of thelong-runπu * ≥ g * + iλ* + (1 − s f )(πu * − iλ* )Hedgeequilibrium
eq. (16)No

πu * < g * + iλ* + (1 − s f )(πu * − iλ* ) andSpeculative

πu * > iλ* + (1 − s f )(πu * − iλ* )eq. (17)πu * ≤ iλ* + (1 − s f )(πu * − iλ* )

Ponzi

Yes

eq. (18)

No

Table 2: Results of comparative static analysis in the long-run equilibrium
sf

π

i

α, β, γθλ*－－ under PLG＋ under DBG

－

＋

g*

－

Ambiguous－ under DBG＋－

λS − P

0

＋

－

＋

－

Financial＋＋ under PLG＋under DBG＋－

structure
Note: Several results assume that γ is sufficiently small. DBG: debt-burdened
growth; PLG: profit-led growth.

22Appendix (not for publication)
A-1 Derivation of equation (27)First, ∂F / ∂s f is derived.

(

[
[

)
]

](
]

)

s f π − s f π (1 − s h ) + s h 1 − λ ∂g *s πg * − s h iλ*
∂F
.
=− h
−
2
∂s f
s f π (1 − s h ) + s h∂s f
s f π (1 − s h ) + s h

[

*

(A1)

Using equation (6), ∂g * / ∂s f is obtained as follows:(α + βπ )π − (s h + θπ − γ )iλ*∂g *= −γ (1 − s h ).
2∂s f
s f π (1 − s h ) + s h − γ

[

(A2)

]

Using equation (5), equation (A2) can be rewritten as follows:

[

] [
]

]

(α + βπ )π − { s f π (1 − s h ) + s h − γ − π s f (1 − s h ) − θ }iλ∂g *= −γ (1 − s h )2∂s f
s f π (1 − s h ) + s h − γ=−[

γ (1 − s h )(πu * − iλ* )s f π (1 − s h ) + s h − γ

*

.

(A3)

γ (1 − s h )(πg * − s h iλ* )=−[s f π (1 − sh ) + sh − γ ][s f π (1 − sh ) + sh ]Substituting equation (A3) in equation (A1) obtains:()∆ πg * − s h iλ*∂F.
=s f π (1 − s h ) + s h s f π (1 − s h ) + s h − γ
∂s f

[

][

(A4)

]

Using equation (15), πg * − s h iλ* can be transformed into

πg * − s h iλ* =

[

](

)

s h s f π (1 − s h ) + s h 1 − λ* iλ*[](s f π − s f π (1 − s h ) + s h 1 − λ*

).

(A5)

Substituting equation (A5) in equation (A4), equation (27) of the text is obtained.
A-2 Proof of Proposition 2
This study investigated the effect of a change in the profit share on the long-run
equilibrium value of the debt-capital ratio. Totally differentiating F λ* ; π = 0 obtains(

the following relation:)

dλ* ∂F   ∂F = −
 / *  .
dπ
 ∂π   ∂λ 
The term ∂F / ∂π leads to

(A6)

[

](

)

s f shs f π − s f π (1 − s h ) + s h 1 − λ* ∂g *∂F
= − 2 g * + s f (1 − s h )iλ* −.
∂π
s f π (1 − s h ) + s h
∂π
σ

[

]

(A7)

The first term on the right-hand side of equation (A7) is negative. The sign of thesecond term on the right-hand side depends on the sign of ∂g * / ∂π . Because theshort-run equilibrium is also attained in the long run, equation (8) holds even in the longrun. From this, if the short-run equilibrium is PLG, then ∂g * / ∂π > 0 , which implies
that the second term on the right-hand side of equation (A7) is negative. Hence, both

∂F / ∂π < 0 and ∂F / ∂λ* < 0 , and consequently, dλ* / dπ < 0 —that is, an increase in
the profit share decreases the long-run equilibrium value of the debt-capital ratio if theshort-run equilibrium is PLG.
By considering that the long-run equilibrium value of the debt-capital ratio can be afunction of the profit share, one can differentiate the long-run equilibrium value of therate of capital accumulation with respect to π as follows:dλ*sh (1 − s f π )+ s f λ* λ* + sh (1 − λ* )
*
dg
d
π
.
(A8)
= − s f sh idπ
{s f π − s f π (1 − sh ) + sh (1 − λ* )}2

[

[

]

]

When the short-run equilibrium is PLG, then dλ* / dπ < 0 . However, the sign ofequation (A8) is ambiguous.
A-3 Proof of Proposition 3
Totally differentiating F λ* ; i = 0 obtains the following relation:

( )

dλ*
 ∂F   ∂F = −
 / *  .
di ∂i   ∂λ 

(A9)Here, ∂F / ∂i leads to

[
[

{

] }
][

[

]

*
∂F  s h (1 − s f π ) − s f π (1 − s h ) + s h λ {γs f (1 − s h ) − θ s f π (1 − s h ) + s h } *
=
λ

∂i 
s f π (1 − s h ) + s h s f π (1 − s h ) + s h − γ+s f shs f π (1 − s h ) + s h].(A10)

λ*For both the positive long-run equilibrium value of the debt-capital ratio and thepositive long-run equilibrium value of the rate of capital accumulation, one needs

[

](

)

s f π − s f π (1 − s h ) + s h 1 − λ* > 0 , which has already been assumed. This inequality can[]be rewritten as s h (1 − s f π ) − s f π (1 − s h ) + s h λ* < 0 . If the short-run equilibrium is DBG,[]

then γs f (1 − sh ) − θ s f π (1 − s h ) + s h < 0 , which yields ∂F / ∂i > 0 . Moreover, from thestability condition of the long-run equilibrium, there is ∂F / ∂λ* < 0 , which finallyyields dλ* / di > 0 . On the other hand, if the short-run equilibrium is DLG, the sign ofequation (A9) cannot be determined.
Furthermore, differentiating the long-run equilibrium rate of capital accumulation,*
g = A + Bλ* , with respect to the interest rate yields[]∂λ* {γs f (1 − s h ) − θ s f π (1 − s h ) + s h } *dλ* 
 λ + i.
=∂i
s f π (1 − s h ) + s h − γ
di 


[

(A11)

]

In the case of DBG, dg * / di < 0 is obtained because γs f (1 − sh ) − θ s f π (1 − s h ) + s h < 0and dλ* / di > 0 . However, in the case of DLG, the effect is not clear.
A-4 Comparative static analysis of other parameters
This study investigated the effect of a change in a parameter of the investment function
on the boundary from the speculative finance to the Ponzi finance regime, and on thelong-run equilibrium value of the debt-capital ratio.
To start, the effect of α on the boundary is given bydλ S − P
π
(A12)
=
> 0.
(sh + θπ − γ )idαHence, an increase in α shifts the boundary in the positive direction.
Next, this study examined the effect of α on the long-run equilibrium value of thedebt-capital ratio. Totally differentiating F λ* ;α = 0 obtains the following relation:

(

)

dλ
 ∂F   ∂F = −
 / *  .
dα
 ∂α   ∂λ 
*

(A13)

From the stability condition of the long-run equilibrium, it is known that ∂F / ∂λ* < 0 .
On the other hand, ∂F / ∂α leads to

[

](

)

s f π − s f π (1 − s h ) + s h 1 − λ ∂g *
∂F
=−
.
∂α
s f π (1 − s h ) + s h∂α*With the aid of equation (6), the term ∂g * / ∂α can be calculated as follows:(A14)

s f π (1 − s h ) + s h
∂g *
> 0.
=
∂α s f π (1 − s h ) + s h − γ

[

(A15)

](

)

With equation (A15) and the inequality s f π − s f π (1 − s h ) + s h 1 − λ* > 0 , ∂F / ∂α < 0
is obtained, which in turn yields dλ* / dα < 0 . Therefore, an increase in α shifts theboundary in the positive direction and lowers the long-run value of the debt-capital ratio,
thus improving the financial structure of firms.
Moreover, from equation (15), the relationship between the rate of capital
accumulation and the debt-capital ratio in the long-run equilibrium leads tos f s h2 iλ* (1 − s f π )
dg *
=
−
< 0.
2
dλ*
s f π − s f π (1 − s h ) + s h 1 − λ*[Hence, dg / dα = (dg / dλ )(dλ / dα ) > 0 .
{

*

*

*

](

)}

(A16)

*

A similar procedure applies to the effects of other parameters on the long-run
equilibrium.