Embed Size (px)
Citation preview
CONSUMER AND CORPORATE DEBT IN A BASIC POST-KEYNESIAN MODEL
OF GROWTH AND INCOME DISTRIBUTION
Emilia Marsellou1
Labor Institute of the General Confederation of Greek workers (INE/ GSEE) and UADPhilEcon
Economics Department, University of Athens.
Abstract: In this paper a basic Post-Keynesian model of growth and income distribution is developed incorporating consumer and corporate borrowing. Consumer borrowing is incorporated in the short-run and corporate borrowing is introduced in the long-run. Assuming a neoliberal regime, workers borrow to fill the consumption gap, and set targets for both living standard and interest payments. Capitalists borrow to finance investment. In the long-run model two cases are examined: the consumer debt-rate of accumulation relation and the consumer debt-corporate debt-rate of accumulation relation. In both cases the stable point corresponds to high growth and low workers’ debt-capital ratio and the saddle to low growth and high workers’ debt-capital ratio. Changes on parameters affect the volume of the stability of the system.
INTRODUCTION
Consumer debt and its role in business cycles and growth is much less investigated in
formal models than corporate debt is. Palley (1996a, 1996b) and Dutt (2006) are
exceptions. In particular, Palley (1996a) in a Kaleckian model of aggregate demand
introduces inside debt and a generational structure and finds that workers’ borrowing and
population growth serve to increase aggregate demand. However, increased borrowing by
young workers has a negative impact on both the profit rate and share in order to preserve
equilibrium between savings and investment. Palley (1996b) within a Minskyan framework
developed three simple linear multiplier-accelerator models that incorporate the effects of
debt on the business cycle and found that borrowing initially serves aggregate demand and
output yet subsequently debt service payments tend to reduce them. Dutt (2006) extended a
Steindlian model of growth and income distribution to incorporate consumer credit and
showed that it has a favorable effect on aggregate demand in the short-run while in the
long-run the effects are ambiguous. This is because, workers’ interest payments are
equivalent to a redistribution of income towards the rich, who have a lower propensity to
consume and this might contract growth.
1 I would like to thank A. Maniatis for the provision of data for the Hourly real wage index and Dr. Kotsios and Dr. Athanasiou for their
helpful comments. Address for correspondence: 71A, Em. Benaki st., GR-10681, Athens tel: 0030 210 3327722 e-mail: [email protected]
Recently, Bhaduri (2010) examined three interrelated facets of a financial crisis: the
evolution of a debt financed consumption boom supported by rising asset prices, a process
where consumer-borrowing driven by capital gains can lead to a ponzi borrowing and the
lack of short-term liquidity of the system as financial firms try to sell assets to cover the
defaulted loans. Charpe et al. (2009) in a Keynes-Goodwin model that incorporates
consumer debt investigate the stability conditions under different hypothesis about income
distribution, credit rationing and Central Bank’s policy against debt default. Charpe and
Flaschel (2011) investigate the conditions under which financial instability arises in the
event of household debt taking into account the functional income distribution and the
credit supply and they extend the analysis for the possibility of debt default and the role of
the adequacy ratio.
There is also a steadily growing empirical literature on households’ debt. Pollin (1988)
examined econometrically a series of demand-side explanations of the rise in net borrowing
to income and found that the latter had the major effect. Pollin (1990) and Blecker (1990)
provide further arguments that support these findings. Dabelle (2004) found that household
debt in a series of developed countries presents some common features such as the share of
the stock of debt increases with households’ income and wealth, the debt-income (wealth)
ratio is higher at the low and low-middle income (wealth) households, and the debt-service
ratio is higher for lower income households. The author concludes that rising household
debt makes households more sensitive to shocks to interest rates, income and asset prices.
Barba and Pivetti (2009) analyze household’s indebtedness in the US economy for the
period 1980-2005 and find the same features of household debt with Dabelle (2004). They
also find that it is stagnant wages combined with increasing inequality that caused the rise
in household debt and by that providing a solution to the problem of low demand within a
system which is based on unequal income distribution. By contrast, Maki (2000), based on
the standard life-cycle model, finds a positive correlation between consumer credit and
durable expenditures suggesting that consumer credit “is not primarily a bridge to get
household through tough times”. Maki and Palumbo (2001) argue that capital gains during
the 1990s contributed in large part to the rise in borrowing, since those upper-income
households that benefited the most from the rising prices of assets are those whose net
savings flows fell the most. These findings however are questioned by Barba and Pivetti
(2009) on the ground that even if wealth effects have led rich people to consume over their
rising incomes, which is quite implausible, this argument “is associated with the idea that
low and middle-income households would have nearly doubled their saving rate despite the
decline in the income share allotted to them”. Finally, Cynamon and Fazzari (2008),
explain the rise in household debt and in particular the tendency for higher consumption
expenditures, through the connection of the evolving social norms on which consumer
preferences are based with the changes in financial institutions that took place in the 1980s.
The authors argue that financial innovation in consumer finance along with consumerism
has shifted the locus of financial instability to the consumer sector. Contrary to the standard
life cycle model, the reason that the burst haven’t occurred until 2008 is the favorable
macroeconomic environment that sustained household debt obligations at reasonable levels
and not the rational smoothing of consumption during the last 25 years.
In this paper, we examine the short and long-run implications of consumer debt on income
distribution and growth. This model is an extension of Dutt’s (2006) model in several
ways. First, we capture the demand side explanation of households’ debt according to
which households borrow to sustain their standard of living in a period of growing
inequality and stagnant wages. Also, workers are assumed to set a ceiling of the debt
service burden they can afford and whenever their actual debt service burden exceeds it
they reduce borrowing. Second, we follow Marx’s analysis in Volume III of Capital (part
IV) and assume three classes: workers and industrial and financial capitalists. The latter
own commercial banks and their role is rather passive since their task is to collect interest
payments by workers and capitalists in order to provide new loans. Commercial banks are
the sole providers of credit. Third, we introduce corporate borrowing for investment
purposes.
Our economy is a mature monetary economy. Consumption and investment are partly
financed by borrowing and as a result borrowers accumulate debt. Credit is generated
endogenously. We deal only with consumer loans. Loans provided to industrial capitalists
are for investment purposes and assume away any other source of investment finance
(corporate bonds, share issuance). The only source of income for the working class is
wages, neglecting any dividends from ownership of shares of stock and interest income
accruing from deposits. Workers and industrial capitalists in every period repay some part
of their outstanding debt. Financial capitalists do not borrow.
In this basic model, we assume a closed economy without state intervention. The only
institution that intervenes is the Central Bank in the “passive” sense implied by the post-
Keynesian horizontalist2 monetary view. The CB sets the interest rate and provides the
necessary reserves for the financial sector when needed in pursuing its ultimate
responsibility of ensuring the liquidity of the system, implying that industrial capitalists and
workers always have access to credit. We assume away inflation and for simplicity a
common interest rate is applied for both consumption and corporate credit.
The rest of the paper proceeds as follows. Section 2 provides a brief review of the empirical
findings concerning the patterns of consumer debt in several counties and compares them
with the Greek case. Sections 3 and 4 outline the short-run and the long-run model,
respectively. In Section 5 we consider the implications of changes in the basic variables
and parameters. Section 6 concludes by considering the main results.
1. HOUSEHOLD BORROWING AND DEBT ACROSS COUNTRIES
Household indebtedness rose substantially in most developed countries over the past two or
three decades with a different timing and extent. For instance, Debelle (2004) finds that in
France, Japan, Italy and the United Kingdom household indebtedness grew more rapidly
during the 1980s, in Australia, the Netherlands and Denmark during the 1990s while in the
US it kept increasing steadily during the two decades. Several semi-industrialized
countries, such as India, have also experienced increases in consumer indebtedness (Dutt,
2006). Debelle (2004) for a number of developed countries and Barba and Pivetti (2009)
for the US find the following patterns of household debt: a) the share of the stock of debt
increases with households’ income and wealth, b) the debt-income (wealth) ratio is higher
at the low and low-middle income (wealth) households and c) the debt-service ratio is
higher for lower income households.
These patterns also characterize the household debt in Greece since 2000. Household
borrowing, consumer credit in particular which is our main interest, increased rapidly. It
took less than a decade to reach debt to income ratios that for other developed countries it
took several decades. As shown in Figure 1, in 1995 consumer debt was 1.5% of
households’ disposable income and 1.1% of GDP, in 2000 it was 4.9% and 3.4%,
respectively, while in 2009 the ratio more than quadrupled reaching 21.7% and 15.5%,
respectively.
2 The reader can trace the post-Keynesian ‘horizontalist’ monetary theory in Kaldor (1982, 1985), Lavoie (1992, 1996), Moore (1988, 1989) and Rousseas (1986).
Figure 1: Consumer Debt-Income Ratio, Greece. Source: CBG and AMECO (Net disposable income: households and NPISH).
These developments rely on both supply and demand side explanations. Financial
liberalization and the low interest rates that occurred with the adoption of Euro is definitely
the most prominent supply3 side explanation. The inability of Greece to raise its
competitiveness compared to the core European countries forced the Greek economy to
rely heavily on internal consumption and hence to consumer indebtedness.
Housing debt accounts for the most part of total household debt. The proportion of housing
to consumer debt was 3.5 in 1995. In the following decade this proportion fell and
stabilized around 2 implying that consumer credit was growing faster than housing. In
2011, during the Greek public debt crisis, the proportion increased slightly to 2.3 more
likely because it is easier to constrain consumer credit than to reduce the housing debt.
Table 1: Household debt as percentage of disposable income, GREECE
Total Outstanding
loans Housing Loans
Consumer Credit
Other Housing/Consumer
Loans
1995 6,6 5,1 1,5 3.5
2000 15,5 10,6 4,9 0,1 2.2
2005 47,0 30,6 15,2 1,2 2.0
2009 70,6 47,2 21,7 1,8 2.2 Source: CBG - AMECO (Net disposable income: h/h and NPISH). Authors’ Calculations.
Data from three surveys conducted by the Central Bank of Greece (CBG) in 2002, 2005
and 2007 show the aforementioned patterns of household’s indebtedness. In these surveys
the term “other loans” includes all non-housing bank loans, i.e. credit card borrowing and
3 The supply side explanations mostly concern the competition between financial institutions that induced banks to lower interest rates, relax credit rationing processes, remove debt burden ceilings, proliferate securitization etc.
0,02,55,07,5
10,012,515,017,520,022,525,0
Consumer Debt to Net Disposable Income (current prices)Consumer Debt to/Gross domestic product (current prices)
loans from private individuals with the latter being insignificant. In Figure 2, we observe
that the average consumer debt increases with income, while the median of consumer debt
as a percentage of household disposable income is negatively related to income-groups.
Figure 2: a) Average consumer debt by Income Group, b) Median of consumer debt as a % of disposable income by Income Group. Source: CBG, Sample Survey on household’s indebtedness 2002, 2005 and 2007.
Figure 3 below, shows for the years 2005 and 2007 (the only available data for this ratio)
the median of debt service to disposable income ratio by income group. The ratio increased
in all income groups and it is higher for lower income households. Note that it increased by
52.3% for the lower income group and only by 6.5% for the richer.
Figure 3: Median of debt service to disposable income ratio. Source: CBG, Sample Survey on household’s indebtedness 2005 and 2007.
It has been well documented that during the last 15-20 years many industrialized countries
have experienced increasing inequality as well as stagnant or anemically increasing wages.
These developments are seen as the demand-side causes for the rising household
indebtedness (Barba and Pivetty, 2009; Pollin 1988, 1990). In Figure 4 below we observe
the course of the hourly real wage index in Greece during the last 50 years. The index
0
2000
4000
6000
8000
10000
12000
7.500,00 7.501-15.000 15.001-25.00025.001-35.000 35.001+
2002 2005 2007
25,220,2
10,2 8,55,1
41,3
21,8
15,312,4 10,3
45,8
30,825,8
19,414,9
0,0
10,0
20,0
30,0
40,0
50,0
2002 2005 2007
28,3
21,6
15,8 14,210,7
43,1
24,1
18,2 17,8
11,4
0,0
10,0
20,0
30,0
40,0
50,0
<7500 7501-15000 15001-2500025001-35000 >35000
2005 2007
indicates that from 1985 to 1993 it fell by approximately 26.0% whereas it increased from
1994 until 2009, by 32.2%, only to reach the levels of 1985 in 2008. Meanwhile, the real
GDP grew almost twice this rate, by approximately 63.0%, during the period 1994-2008.
Thus, the picture that emerges is one in which workers even if they experienced increases
in real wages since 1995, they were in a worse financial position than they were more than
10 years before (1978-1985). This contradicts those suggesting that increasing household
indebtedness is the result of a rapidly rising income that led to a “consumption binge”, by
implying that for the period 1995-2008, during which the debt/income ratio rose (Figure 1),
real wages were not only below their historical high values but also below their trend-line
for a course that lasted almost 20 years.
Figure 4: Hourly Real Wage Index. Source: Hellenic Statistical Authority. National Accounts.
2. STRUCTURE OF THE MODEL
The economy produces a single good with two factors of production, homogeneous labour
(L) and capital (K). A fixed proportions production function is assumed and the production
coefficients are considered constant. The supply of labour grows at an exogenously given
rate. Firms function with excess capacity. Hence, since there is excess supply of labour,
output is constrained by the amount of the capital stock of the economy. The capital stock
is assumed fixed in the short-run and for simplicity there is no depreciation of capital.
Net National product, Y , is equal to the sum of consumption and investment and it is
distributed between wages, w L , and gross profits, .
( ) Pr n w IY wL wL iD Ind iD (1)
100103107110122
129137
146157
166174177
190190179
197
216
232
253250239
232
247240243
256
232
215223
224217
202195
189193198199
197208
201203
198
215219224224
233243
255263
75
100
125
150
175
200
225
250
275
19601962 196419661968 197019721974 197619781980 198219841986 198819901992 199419961998 200020022004 20062008
Hourly real wage index
with ( )nwL the net wage-income, wiD and IiD workers’ and industrial capitalists interest
payments, respectively, i the interest rate and PrInd the profits of enterprise. Financial
capitalists’ income at any point in time equals the sum of wiD and IiD . For simplicity, we
assume that financial capitalists save all their income in order to lend workers and
enterprises.
WORKERS
Workers borrow to finance part of their consumption. Thus, wage-income splits into net
wage-income and workers’ interest payments. Workers consume their entire net wage, so
workers’ consumption equals the sum of their net wage and the amount of new borrowing.
It follows that the propensity of workers’ consumption is larger than one. We denote with
wC workers borrowing-induced consumption.
(1 )w
w wdD
C Y iDdt
(2)
with Y
the share of gross profits. Another way of seeing (2) is by considering workers’
net borrowing, (1 ) ww wY
dDC iD
dt , as the difference between workers’ new
borrowing minus the interest payments which is equal to the level of consumption minus
the wage-income. A positive difference between consumption and wage-income must be
financed by an injection of credit, a negative difference implies that workers save in excess
of their interest payments while an equality implies that new borrowing equals interest
payments.
We assume that workers’ debt adjusts to new borrowing according to the following:
wW
dDB
dt (3)
Workers’ desired borrowing ( dWB ), is determined by the following partial adjustment
mechanism:
1 2(1 ) (1 )dW WB w L Y Y iD (4)
in which, 1 and 2 are two constant adjustment coefficients where 1 20 , 1 . These
coefficients are determined by workers’ behavior and reflect how quickly they set their
spending plans. If these coefficients are equal to unity, the adjustment of borrowing to
changes in current wages or in interest payments is instant. If they are less than unity,
borrowers adjust their borrowing demand gradually.
w is the wage target that workers set according to the socially determined standard of
living or in a similar way the “conventional wage”4. The wage target w is determined by
social conditions and in periods of intense income inequality together with conspicuous
consumption from the upper income class it tends to be higher than the real wage. This
induces workers to borrow in order to sustain their living standard5.
is the debt service to workers’ income ratio which is assumed constant and 0 1 .
determines workers’ maximum affordable interest payments as a percentage of their
income capturing workers’ prudency: a large represents a careless borrower while a low
a prudent one, given they do not face any borrowing constraints. In effect, it is workers
who set the ceilings on borrowing and initially they are all considered as creditworthy.
Equation (4) says that whenever the “conventional wage” exceeds current wage desired
borrowing by workers will increase as a result of workers struggle to sustain their living
standard, and vice versa. Similarly, whenever the “ceiling” of interest payments exceeds
the actual interest payments, workers will increase borrowing6. This ceiling however
depends on the level of current wage too and therefore changes in current wage affect both
terms of (4) towards the opposite direction (i.e. a potential fall in current wage will have a
positive effect on borrowing due to the increase of the difference between “conventional
wage” and current wage and a negative effect due to the fall in the “ceiling” of interest
payments). Rearranging (4) we take the following relation:
1 2 2 1( )(1 )dW W
wL
B Y iD w L (5)
4 We find this term in Marglin (1984) and it is similar to the subsistence wage used by classical economists such as Marx, Smith and Ricardo. This term takes into account the biological as well as the historical and cultural conditions of any period of time. 5 Pollin (1988, 1990) uses the term “necessitous demand for credit” to describe this phenomenon. Household’s tendency to sustain their living standard can also be traced back in the writings of Duesenberry (1949) as well as in Veblen (1899). 6 This formulation draws from empirical and experimental research on microfinance suggesting that the amount of borrowing demanded is affected differently by changes in income, interest rates and interest payments. In particular, interest payments (proxied by the loan maturity) have a much more significant effect on the borrowing demand than the cost of borrowing especially for the low and middle income borrowers (Karlan and Zinman, 2007; Attanasio et al., 2007).
where 1 2( ) is the sensitivity of workers’ borrowing to changes in current wages
where it is assumed 1 2 , and 1 2( )(1 ) expresses the additional amount of
workers’ borrowing due to a change in output. 2 now reflects the sensitivity of workers’
borrowing to changes in interest payments, while 1 shows the effect of any change in the
“conventional wage” on borrowing where the positive sign reflects their positive relation.
INDUSTRIAL CAPITALISTS
As noted before, gross profits are distributed to the owners of the capitalist firm as profits
of enterprise and to its lenders as interest payments. Industrial capitalists pay dividends to
the stakeholders of the company and they save the rest of the profits of the enterprise i.e.
the retained profits. The retention rate (or the business propensity to save), s, is assumed
constant. Retained profits are saved in order to finance future investment plans. In contrast,
dividends are used by their owners (members of the industrial capitalist class) for
consumption. For simplicity, we assume away any other source of income of financial
capitalists except from interest payments.
Pr
Pr (1 ) PrI I
Ind
R Div iD sInd s Ind iD , where Pr IInd iD (6)
where R denotes the retained profits, s the retention rate and Div are the dividends.
Industrial capitalists’ consumption function cC is given by:
(1 )( )IcC s id Y (7)
where Iid is the interest payments of industrial capitalists as a share of national income.
Investment demand in the short-run is assumed fixed. We denote the investment rate, that
is the growth rate of K , as:
Ig
K (8)
where I is gross and net investment since we ignore depreciation. However, in the long-run
we assume that industrial capitalists adjust their actual investment rate to their desired rate
of investment using the formula7 below:
7 This formulation is common in the Post-Keynesian literature (see for instance Jarsulic (1990), Dutt (2006, 1995), Charles (2008)).
ddgg g
dt (9)
where dg is the desired accumulation rate and is the adjustment speed where0 1 .
Formulation (9) implies that whenever the desired rate of accumulation is above the current
rate, the actual rate will rise.
The desired level of industrial capitalists’ borrowing is given by the following:
I IB b id Y , 0b (10)
where π is the gross profit share. Industrial capitalists’ level of borrowing is a fraction of
the profits of enterprise. For simplicity we abstract from any other financing costs except
from interest. Coefficient b can be taken as a proxy of the leverage ratio. This ratio can be
determined either by bank lending practices or by industrial capitalists’ decisions. The
latter allows for a consideration of b as capitalists’ propensity to borrow. Equation (10)
says that there is a positive relationship between firm’s borrowing and gross profits and a
negative to interest payments. This relation captures Kalecki’s (1937) principle of
increasing risk’ according to which diminished internal means of finance for real
investment purposes reduce access to external means of finance in imperfectly competitive
capital markets.
Note that industrial capitalists do not borrow in the short-run and hence their stock of debt
is fixed, i.e. 0 II
dDB
dt and thus b=0. However, following Hein (2006) and Lavoie
(1995) their debt-to-income ratio is taken into account because of past borrowing.
New borrowing IdD
dt has a positive impact on desired investment dI .
( ) ( )Id r I r I
dDI id Y b id
dt (11)
Where r , captures the sensitivity of desired investment to the profits of enterprise and
0 1r . Equation (11) reflects classical economists’ view of the centrality of the profits
of enterprise on investment decisions.
3. THE SHORT-RUN MODEL
In the short-run we assume that firms function with excess capacity so that the level of
output adjusts in response to aggregate demand. It is also assumed that the levels of debt,
capital stock and investment are given. So, short-run equilibrium is given by:
w cY C C I (12)
Assuming dW WB B and inserting 4 into 2 and then the resulting into 12, inserting 8 into 12
and then normalizing by K we get:
1 2 2 1(1 )(1 ) (1 ) (1 )( )W Iu u i w l s u i g (13)
with Yu =
K the rate of capacity utilization, 1 2(1 ) the sensitivity of workers’
consumption to changes in the wage-income and 1 20 1 1 for reasonable values
of * and 1w l reflecting the impact of conventional wage on workers’ consumption
which can also be seen as a proxy of workers’ autonomous consumption. Also, Ww
D
K is
the stock of worker’s debt-to-capital ratio and L
lK the fixed technological coefficient of
labor-capital ratio. If we solve for u we take the short-run equilibrium value of capacity
utilization u :
1 2
1 2
(1 ) (1 )
(1 )( )wg w l i s i
us
(14)
The stability of the short-run equilibrium requires that the denominator in (14) is positive8.
To ensure that we always have a positive u we also require that the numerator in (14) is
positive. Moreover, the standard macroeconomic stability condition requires the savings
rate to respond more elastically to changes in capacity utilization than the investment rate
does. This implies that the denominator in (14) (which is the sensitivity of the saving rate to
changes in capacity utilization) must exceed the r term (which is the sensitivity of the
investment rate to changes in capacity utilization) derived by (11) after the normalization
by K and the differentiation with respect to u.
8 Obviously, all terms are positive.
Thus the stability condition in the goods market requires thatS Idg dg
du du is satisfied, i.e.:
1 2(1 )( ) rs (15)
We now examine the effects of changes in the variables and parameters of the model on the
short-run equilibrium level of the rate of capacity utilization. Through partial derivation of
(14) with respect to W , Id , g , 1 , 2 , w , , , s and i we have: 0gu , 0w
u ,
0u , 0du
, 0
wu , 0iu , 0su , 0u depending on 1 2( )s ,
10u
depending on * (1 )w l u and 2
0u depending on (1 ) Wi .
As expected for a demand-driven model the investment rate, g , the conventional wage w
and the interest burden on income have a positive effect on capacity utilization. In
contrast, workers’ debt-capital ratio, W , industrial capitalists’ debt-income ratio,
Id , the
interest rate, i , and the retention rate s have a negative impact on capacity utilization.
However, the two parameters 1 and
2 and the gross profit share may have either
positive or negative impact on capacity utilization.
First we consider an increase in worker’s debt-capital ratio. It has a contractionary effect on
u because it redistributes income from workers who consume to financial capitalists, who
neither consume nor invest. There are two channels through which a higher W affects
aggregate demand: it reduces the net wage and therefore consumption and curtails worker’s
borrowing that finance consumption. A similar effect on u has a rise in the interest rate.
The profits of enterprise are also negatively affected by an increase in the rate of interest
yet there is no impact on investment in the short-run but only a distributional outcome
toward financial capitalists’ income.
A higher industrial capitalist’s debt-output ratio Id also impacts negatively u because the
profits of enterprise (as well as the share of profits of enterprise) and thus the dividends
will decrease resulting to a fall in capitalists’ consumption. Again there is no investment
side effect but only a distributional one.
A fall (increase) in the retention rate has a positive (negative) impact on u reflecting the
Paradox of the thrift. This happens because part of retained profits that are saved to finance
future investment plans are directed to current consumption resulting to an increase in
aggregate demand.
As in Dutt (2006), in the short-run although changes in the capacity utilization have no
effect in the rate of accumulation and hence the growth of the economy, they do affect
income distribution. Thus, increases in u are not translated into investment yet the
accumulated profits that derive by increasing demand increase the share of profits (of
enterprise). This happens because with the stock of capital constant, industrial profits
increase and temporarily the profit share increases. Yet, in the long-run as K starts to
expand the profit share will return to its initial level.
For 1 depends on whether current wages are greater or lower than the conventional wages
while for 2 it depends on whether the maximum affordable part of wages that goes to
interest payments is greater or lower than the actual interest payments.
Finally, for it depends on whether the propensity to save out of profits, s, is greater than
workers’ propensity to borrow, 1 2 . If the former exceeds the later the effect of the
share of profits of enterprises on capacity utilization will be negative and vice versa. Note
that the term 1 2s expresses also the derivative of (Sdg
du) with respect to the share
of gross profits. This implies that if s is higher than the propensity of workers to borrow
then the increase in the saving rate with respect to capacity utilization will be increasing
while on the contrary, if s is lower than the propensity of workers to borrow the increase in
the saving rate will be decreasing. On the other hand, concerning the rate of investment, the
derivative of (Idg
du) with respect to the share of gross profits is equal to 0r . It follows
that other things being equal, the 1 2 s case will eventually lead to the failure of the
standard macroeconomic stability condition and therefore we assume 1 2 s .
4. THE LONG-RUN MODEL
The two dimensional case
In order to study the dynamics of the model we have to reduce the above equations into a
three-dimensional system of differential equations. We are interested on the dynamics of
the state variables g , w and I . However, the analysis first starts with the two dimension
case, in which we assume that industrial capitalists do not borrow so that b=0, and
concentrate on the g and w dynamics. For simplicity henceforth we use this notation:
*1 21 , *
1 2 1 A and 1 2(1 )( )s .
The differential equation describing the path of w (overhats denote growth rates) is
specified as follows,
w WD K
(16)
Inserting (3), (5) and (8) into (16) and assuming dW WB B we obtain:
*
1 2(1 )(1- )(1- ) ] (1- )(1- ) - - (1- )(1- )- [
Iw w wsg s i sd w
dt
A l A i A
(17)
The term (1- )(1- )A w is positive. Second, the term 2 - (1- )(1- )As is also positive and
reflects the relation between capitalists’ and workers’ contribution to savings due to
changes in capacity utilization. It’s plausible to assume that the capitalist class, as a whole,
has a higher tendency to save than workers’ do and this is assumed to hold even if β2 is
lower than one, provided that the term in question remains positive.
The dynamic path of the rate of accumulation is specified by (9), in which (11) normalized
by K and (14) are inserted. Then we get:
1 2(1 ) (1 )wr
dg
g
dt
g w l i s ii
(18)
where we have already assumed that the denominator r is positive as well as the
numerators of the intercept and the slope are.
The vertical asymptote of the 0wd
dt
isocline rests in the second quadrant and its
expression is given by (1 )(1 )
W
A
while the horizontal is 2- (1- )
0(1- )
gs A
which is below the horizontal axis but pretty close to it. Since our intention is to focus on
consumer credit and its effect on growth we concentrate only to the first quadrant and
specifically the area above the LIM line which represents the
1 2(1 ) (1 )wg w l i s i condition (see 14).
Given the above conditions, the paths of g and w are shown in the Figure 5 below. As we
can observe there are two equilibrium points A and B, the former corresponding to a
positive but low rate of accumulation combined with high workers’ debt-to-capital ratio
while the later corresponds to a combination of a positive and high rate of accumulation
with low levels of workers’ debt-to-capital ratio.
Figure 5: Dynamics of workers’ debt-to-capital ratio and the rate of accumulation
In what follows we deduce the stability properties of the dynamical system, consisting of
(17) and (18), algebraically. The stability requires that the Jacobian Matrix gives [ ] 0Det J
and [ ] 0tr J .
The Jacobian Matrix is the following:
2(1 )(1 ) (1 )(1
[
)
]
ww
w
g
r r g
g i A u A uJ
u u
(19)
Evaluating the determinant of the Jacobian at equilibrium point A9 we obtain
[ , ] 0
w
Det g , which means that it is a saddle point, since , and are
always positive.
Evaluating the Determinant at equilibrium point B we obtain:
[ , ] 0
w
Det g (20)
while the trace is given by the following expression which is always negative since all the
terms are positive10:
2 2[ ( , )][ (1 )(1 )(1 )]
w
rtr J gi
g
(21)
9 See Appendix 1. 10 See Appendix 1.
Hence the equilibrium point B is asymptotically stable.
Consequently, the economy will converge at B while if it reach A the economy will be
driven to negative values of growth and capacity utilization. Actually, this two-dimensional
case of the model suggests that structural instability is inherent to the model without the
need to rely in any special assumption about over-indebtedness. In essence, it shows that
the engagement of workers to borrowing as a result of their struggle to sustain their living
standards introduces instability into the system by itself. In other words, even if the real
side of the economy is stable, which is given by the standard macroeconomic stability
condition, financial variables may be sources of instability that destabilize the economy
(Dutt, 1995). Moreover, instability mostly appears there where the rate of growth is low11.
Note, also, that changes in the parameters of the system only change the volume of
structural stability12. Otherwise stated, whether equilibrium points tend to come closer,
instability increases because a sudden shock might produce oscillations able to move the
system from the stable to the unstable path, while when they become more distant
instability falls (Jarsulic, 1990). In Figure 6 below, the vector field of the system is
illustrated.
Figure 6: Phase Diagram
We first examine the area close to equilibrium point A. It is clear that no matter in which of
the sectors in the neighborhood of A the system begins, all the forces push the system away
from A and towards B. This happens even if a trajectory crosses from one sector into
another. Let us consider equilibrium point B. Starting from a point close to B, for instance
at the south-east of B. There the actual investment rate is less than the desired rate implying
11 Jarsulic (1990), Dutt (1995) and Charles (2008) also find the high-growth eq. point as the stable one. 12 This is also found in Jarsulic (1990).
B
A
-0.5 0.5 1.0 1.5 2.0 2.5 3.0δω
-0.4
-0.2
0.2
0.4
0.6
0.8
1.0g
that enterprises will tend to raise their actual investment rate. Aggregate demand, output
and capacity utilization will increase in consequence and this will make workers to reduce
the desired level of borrowing which will decelerate their stock of debt. Eventually, the
workers’ debt-to-capital ratio ( w ) will fall. However, this fall in workers’ debt, will
increase consumption, aggregate demand and capacity utilization which will increase the
desired rate of investment making the actual rate to rise even more. At the same time, the
abovementioned fall in workers’ debt will induce workers to increase the desired level of
borrowing and accelerate the accumulation of debt. Given that the slope of the 0dg
dt
isocline is lower than that of 0wd
dt
, the combined outcome will be that w
will increase.
The previous increase in workers’ debt will reduce the desired level of borrowing
decelerating the stock of debt. In the meanwhile, the actual rate of investment surpasses the
desired rate and thus the former will start to fall. As a consequence, w will rise.
Eventually, the increase in workers’ debt reduces workers’ consumption, aggregate
demand, capacity utilization and hence the desired rate of accumulation making the actual
rate to fall. As workers’ debt has already fallen (due to the fall of desired borrowing
resulting from the increased interest payments), w will start to fall again because the slope
of the 0wd
dt
isocline is higher than that of 0
dg
dt .
On the other hand, if we start from a point in the proximity of A, the economy will be
trapped in a downward spiral of increasing indebtedness, w , and falling rate of
accumulation that will eventually lead to zero levels of growth.
Sources of instability and macrodynamics
We can now examine the impact of changes in the parameters of the two dimensional
model on the long-run equilibrium points. We will examine changes in r , the interest rate
i , the adjustment coefficients 1 and 2 , the retention rate s, the profit share σ and the
debt service burden λ*.
Figure 7: Increase in γr Figure 8: Increase in the Interest Rate
Figure 9: Increase in β1 Figure 10: Increase in β2
Figure 11: Increase in the gross profit share π Figure 11: Increase in the retention rate s
Figure 12: Increase in λ*
Let us first consider an increase in r (the coefficient that shows the responsiveness of
investment to changes in the profit of enterprise). It will affect only the desired investment
function shifting upwards the 0dg
dt isocline, leaving the 0w
d
dt
isocline unaffected
(Figure 7). This implies that the long-run equilibrium point A moves slightly to the right
(Α’) while point B has a clear movement towards left (B’). This change implies that other
things equal if industrial capitalists invest a larger proportion of their profits of enterprise
they can achieve higher levels of growth ( g ) for any given level of workers’ debt-to-
capital ratio ( w ). Hence, in the region of low workers’ indebtedness, growth and income
distribution for workers (in relation to financial capitalists) improve. Note, however, that,
concerning the saddle point A, there is a slight deterioration of both growth and income
distribution. This is quite plausible since in the region of highly indebted workers capacity
utilization will be below some acceptable level and thus any increase in investment would
only expand excess capacity. This implies that if the economy reached the region of A an
increase in animal spirits would not be sufficient to move the economy towards the stable
path, on the contrary it will move the economy to an even worse position. Therefore, only a
strong state intervention might create an effective shock that will make the system jump
away from the unstable trajectory. The increase in r reduces the instability of the system
since it makes the two points more distant. However, note that if the economy is already at
the saddle point, the more distant it is from the stable path an increasingly stronger shock
will be needed for the economy to escape from its trajectory.
An increase in the interest rate shifts the 0wd
dt
isocline (not visible in Figure 8)
downward while it makes the 0dg
dt isocline steeper (Figure 8). B’ remains almost at the
same position ( g falls slightly and w increases slightly) but A’ corresponds to a lower w
and a higher g . Note, that by increasing i income distribution improves for workers at the
expense of financial capitalists because they reduce borrowing (although in the short-run
the opposite happens)13. The critical points move closer and therefore the instability of the
system increases.
13 This is also found in Dutt (2006).
An increase in 1 (workers’ borrowing responds less gradually to changes in wages) shifts
the 0wd
dt
isocline in a counter-clockwise direction and 0
dg
dt isocline becomes flatter
(Figure 9). A’ reflects a higher w and an ambiguous whereas negligible change in g , while
B’ a lower g while w changes slightly in an ambiguous direction depending on the
volume of the change in the 0wd
dt
isocline. At A’, the increase in w implies a definite
deterioration of income distribution for workers in relation to financial capitalists and a fall
in capacity utilization as a result of the relatively constant g and the increase in w . As far
as B’ is concerned, the affect on capacity utilization is negative because it is affected
negatively by g while w remains almost constant. The new equilibrium points become
more distant so the system reduces its instability.
An increase in 2 (workers’ borrowing responds less gradually to changes in interest
payments) shifts the 0wd
dt
isocline slightly in a clockwise direction and the 0
dg
dt
isocline becomes steeper (Figure 10). A’ reflects a lower w and a slightly higher g , and B’
reflects a higher g while the effect on w is ambiguous. At both A’ and B’ capacity
utilization and income distribution improve. The instability of the system increases because
A’B’ move towards a steeper region in the Figure and hence come closer.
An increase in (gross profit share) swifts upwards both the 0dg
dt
and the 0w
d
dt
isoclines (Figure 11). The new equilibrium point A’ reflects a higher w and a lower g ,
while B’ a higher g but an ambiguous change in w . So, the growth of the economy is
profit led at the area of B while it is wage led around the point A. At point A’, the increase
in w implies that income distribution and capacity utilization fall while at B’ the opposite
happens. The two new points become more distant so instability decreases14.
An increase in s (retention rate), swifts downwards the 0dg
dt isocline and upwards the
0wd
dt
(Figure 12). B’ corresponds to a lower g and a slightly higher w , while A’ to a
14 This is also found in Jarsulic (1990).
lower w and a slightly higher g . At B’ both income distribution and capacity utilization
deteriorate while the opposite happens at A. The two points move closer increasing the
instability of the system.
An increase in λ* (workers’ debt service burden ceiling) swifts upwards both the 0dg
dt
and the 0wd
dt
isoclines (Figure 13). B’ corresponds to a higher g while the effect on w
is ambiguous and small, and A’ to a higher w while the effect on g is ambiguous and
small. At B’ capacity utilization improves because g increases significantly while w
changes slightly whereas the status of income distribution is ambiguous. On the contrary, in
A’ capacity utilization deteriorates because w improves substantially while g roughly
changes, whereas income distribution exacerbates. Furthermore, note that the two points
become more distant decreasing the instability of the system, implying that higher
borrowing expands the stable region of B’. This is because it enhances growth and capacity
utilization which in turn creates higher profits of enterprise and retained earnings. In other
words the capital stock will grow at a sufficiently high rate to keep the w rate low.
The three dimensional case
In this section the three-dimensional case is considered, where the dynamics of workers’
and industrial capitalists’ debt and the rate of accumulation interact. Note that the dynamics
of workers’ debt and the rate of accumulation are the same as before with the only
difference that in (25) below 0b . The dynamics of corporate debt are given by:
I ID K
(22)
Inserting (8), (10) and (14) into (22) we obtain:
1 2(1 ) (1 )w II
db
dt
g wl i s ii g
(23)
The rest as said before are:
*
1 2(1 )(1- )(1- ) ] (1- )(1- ) - - (1- )(1- )- [
Iw w wsg s i sd w
dt
A l A i A
(24)
1 2(1 ) (1 )( ) w I
r
d
dg
g
t
g w l i s ib i
(25)
By solving this system we get three equilibrium points: one that corresponds to a
combination of a positive and high rate of accumulation with low levels of workers’ debt-
to-capital ratio and positive corporate-debt-to-capital ratio (A), one that corresponds to a
positive but low rate of accumulation combined with high workers’ debt-to-capital ratio
and positive corporate-debt-to-capital ratio (B) and one with zero capital accumulation
positive, positive workers’ debt-to-capital ratio and negative corporate-debt-to-capital ratio
(C). The stability of these critical points is examined by using the Routh—Hurwitz
Theorem. The Routh—Hurwitz conditions for the stability of the three-dimensional
dynamical system require that the Trace (J) < 0, det(J1) + det(J2) + det(J3) > 0, det(J) < 0
and -Trace(J)(detJ1+detJ2+detJ3)+ det(J)>0.
Plugging the critical points into the Routh-Hurwitz conditions we find that A is
asymptotically stable, and B and C are unstable15. These results show that the stability
characteristics of the two-dimensional system are sustained with the introduction of
industrial capitalists’ borrowing. As in the two dimensional case it is the high rates of
accumulation and the low level of consumer debt that ensures stability.
CONCLUSIONS
In this paper we introduced consumer credit in a basic post-Keynesian model of growth and
income distribution and examined its short-run and long-run effects. Workers set two
targets: one for their standard of living and borrow to fill the gap between their wage and
consumption and one for the level of interest payments which they consider they can
afford. In the short-run our findings are common with the other papers that deal with
household borrowing: it boosts consumer demand and capacity utilization yet the interest
payments decelerate this tendency. In the long run, however, consumer credit creates
endogenous instability by resulting to two equilibrium points: a stable and a saddle. We
then examined the effects of changes in the parameters of the system and found that r , 1 ,
and * reduce the instability of the system while i , 2 and s increase it. None of the
15 See Appendix 2.
parameters is sufficient to reverse the downward course of the economy or to jump to the
stable path once the system reaches the unstable path. Any policy that would push the
system from the unstable to the stable path is exogenous to the system. The only possible
effective intervention might be either a strong shock by public investments that would
create income without altering income distribution between workers and industrial
capitalists but would certainly reduce borrowing and thus the debt-income ratio while at the
same time the growth rate would increase rapidly or a massive “hair-cut” on workers’ debt
partially backed by the Central Bank so that there will be no lack of liquidity in the system
and the rate of accumulation will remain unaffected. Finally, the introduction of capitalists’
borrowing in the three dimensional system produces one stable equilibrium point which
corresponds to a high level of rate of accumulation and a low level of workers’ debt to
capital stock and two unstable points: one with a low level of rate of accumulation and a
high level of workers’ debt to capital stock and one with a zero level of rate of
accumulation, a positive level of workers’ debt to capital stock and a negative level of
capitalists’ debt to capital stock.
Appendix 1.
Equilibrium point A is of the following form:
*1 2 2
2
( ) [ (1 )(1 )] [ (1 ) ]
2 (1 )r r
w Ar
w l i i s i s
i
*1 2 2( ) [ (1 )(1 )] [ (1 ) ]
2[ ]r r
Ar
w l i i s i sg
and B:
*1 2 2
2
( ) [ (1 )(1 )] [ (1 ) ]
2 (1 )r r
wr
w l i i s i s
i
*1 2 2( ) [ (1 )(1 )] [ (1 ) ]
2[ ]r r
r
w l i i s i sg
Where Δ:
* *2 1 1
2*1 2 2 2
4 (1 ) (1 )(1 )[ (1 )] ( ) (1 )(1 )
( ) [ (1 )(1 )(1 )] [ (1 ) ]
r r I r
r r
i A w l i s w l A i
w l i i i s
We have assumed that Δ>0 so that the system (17)-(18) has two roots.
Numerical simulations give a positive sign for Δ (we set the following parameter values
γr=0,7, π=0,55, i=0,05, w*=0.50, β1=0.9, β2=1, Γ=0,720, Α=0,5, s=0.9 and dI=0.35) and we
obtain Δ=0.017, { w A Aδ =3.74, g =0.06 }, { w B Bδ =0.37, g =0.45 }.
Appendix 2.
The 3x3 dynamical system (23)-(25) has three equilibrium points.
The Jacobian of the dynamical system (23)-(25) is:
2 2
2
2
(1 )(1 )(1 ) (1 )(1 ) (1 )(1 )(1 )
( ) (1 ) ( ) (1 )( )
(1 ) (1 )
w
r rr
i i A A i A sg
i b b sJ b i
bi b sg bi
The Routh – Hurwitz necessary and sufficient conditions for the local asymptotic stability
are: Det(J)<0, Tr(J)<0, Det(J1)+Det(J2)+Det(J3)>0, –Tr(J)(DetJ1+DetJ2+DetJ3)+ Det(J)>0.
Equilibrium point A satisfies the Routh – Hurwitz necessary and sufficient conditions for the local asymptotic stability.
Proof:
2 * 2 2* * 1 2 2
2
2 1 2
( ) ( ) [ (1 )(1 )] [ (1 )]( )( , , ) ( ,
2 ( ) (1 )2
, )( ) (1 )(1 )(1 ) ( ) (1 ) [ ( )]
2( )[ ( ) ]
r
r r r
rr r
b w l i i s A i s brA g Aw I i b r
b
b
b i A w l b ib s i b
b b
The determinant of J at eq. point A is the following:
2 1 2
2
( ) (1 )(1 )(1 ) ( ) (1 ) [ ( )][ ]
2( ) [ ( ) ]
r r r
A
r
b i A w l b ib s i bDet J
b br
[ ]ADet J is negative if we want the eq. point A to reflect a positive g (along with a positive
w and I ). Obviously, 2 1 2(1 )(1 )(1 ) ( ) (1 ) [ ( )]r ri A w l b ib s i b .
The trace of the Jacobian at point A is equal to the following:
2(2 ) [ (1 )(1 )] [ (1 )] ( )
[ ] 0A r
A
g i s A ib s bTr J
We assume that 2
(2 ) [ (1 )(1 )] [ (1 )] ( )A r
g i s A ib s b so that the trace is negative. We now take the determinants of the three principal minors at point A which they come out to be positive and thus their sum is positive:
1
( ) (1 )( )
(1 )
r
r
A
A
A
b sb i
Jb s
g bi
2 1 2
1
( ) (1 )(1 )(1 ) ( ) (1 ) [ ( )][ ]
2( )
r r r
A
r
b i A w l b ib s i bDet J
b
which is positive since we have already assumed
2 1 2(1 )(1 )(1 ) ( ) (1 ) [ ( )]
r ri A w l b ib s i b .
2 2
2
2
(1 )(1 )(1 ) (1 )(1 )(1 )
(1 ) (1 )
A
A
i i A i A sg
Jbi s
g bi
Since a11<0, a33<0, a31<0 and a13>0 it comes out that 2[ ] 0ADet J .
3[ ] 0
( )A
r
Det Jb
The above imply that 1 2 3[ ] [ ] [ ] 0A A ADet J Det J Det J
Assuming a strong trace we obtain a positive sign for the last stability condition
1 2 3[ ] [ ] [ ] [ ] [ ] 0B B B B BTr J Det J Det J Det J Det J
This implies that according to the following relation Γ and s have to be large implying that the sensitivity of savings with respect to changes in capacity utilization is large and the propensity to save out of profits is also large
2(2 ) [ (1 )(1 )] [ (1 )] ( )A rg i s A ib s b . These assumptions
imply that industrial capitalists have a weak reliance on external finance.
Equilibrium point B fails to satisfy all the Routh – Hurwitz criteria so it is unstable.
Proof:
The equilibrium point B is the following:
2 * 2 2* * 1 2 2
2
*
2 2 1
( ) ( ) [ (1 )(1 )] [ (1 )]( )( , , ) ( ,
2 ( ) (1 )2
( ) [ ( )] [ (1 )] (1 )(1 )(1 ) ( ), )
2( )[ ( ) ]
r
w I
r r r
rr r
rb w l i i s A i s bB g B
i b r
b i b ib s i A w l b b
b b b
Equilibrium point B has to reflect a positive g, which implies
*2 2 1[ ( )] [ (1 )] (1 )(1 )(1 ) ( )r ri b ib s i A w l b .
From this it follows that:
*
2 2 1
2
( ) [ ( )] [ (1 )] (1 )(1 )(1 ) ( )[ ] 0
2( ) [ ( ) ]
r r r
Br r
b i b ib s i A wl bDet J
b b
This means that the Det(JB) < 0 requirement for stability fails.
Equilibrium point C fails to satisfy all the Routh – Hurwitz criteria so it is unstable.
Proof:
The equilibrium point C is the following:
* *
2 2
* *1 1
[(1 )(1 ) [ (1 ) ]] [(1 )(1 ) [ (1 ) ]]( , , ) ,0,w I
w l w l
i A i s s i A i s sC g C
The determinant and the trace of the Jacobian Matrix at equilibrium point C is negative since all the terms of the numerators are positive.
2 2 2 1
*[ (1 )(1 )(1 )] (1 ) ( )
[ ] 0r
c
i ib A ib s w l bDet J
2 2[ (1 )(1 )(1 )] [ (1 ) ] [ ( ) ]
[ ] 0rc
i A ib s bTr J
We now examine the determinants of the three principal minors at C:
1
( ) (1 )( )
(1 )
r
r
C
C
b sb i
Jb s
g bi
J21>0 is positive because C is negative: 2
*1 0
[(1 )(1 ) [ (1 ) ]]Cw l
i A i s s
, so we have that
J11<0, J22<0, J12<0 and J21>0 and thus 1 0J .
We have that the second principal minor of the Jacobian at C is positive and very low
(because of the very low term 2bi
and the fact that gc=0).
2
2 2[ ] (1 )(1 ) 0
c
biDet J A
From the third minor principal we have:
2 2
3
2
(1 )(1 )(1 ) (1 )(1 )
( ) (1 ) ( )
wC
C
r r
i i A Ag
Ji b b
where J11<0, J22<0, J12<0 and J21<0 which implies that the determinant is either positive or
negative. However, we now that at point C 2
*1 0
[(1 )(1 ) [ (1 ) ]]wCw l
i A i s s
is very high
while gc=0, so it is safe to consider this determinant as negative and high. Given the above considerations we can reach the conclusion that the sum of the determinants of the principal minors is negative:
3
1 2
1 2 2 2
2
[ ] [ ] [ ]
1 *( ) [ ] [ (1 )(1 )] [ (1 )(1 ) [ (1 ) ]] 0
r
Det J Det J Det J
b w l i bi A i s A b s
This means that the 3
1 2[ ] [ ] [ ] 0Det J Det J Det J condition fails which makes the
[ ] [ ] [ ] [ ] [ ] 01 2 3Tr J Det J Det J Det J Det JB BB B B condition to fail as well.
Simulations result to the same conclusions.
Table: Simulation Results
Parameter set
i=0.05, λ*=0.3, b=0.1, β1=0.9, β2=Λ=1, Α=0.5, γr=0.7, π=0.55, Γ=0.720, w*l=0.5
Results:
Equilibrium Point A {δw=0.145, g=0.7, δΙ=0.125}
Det[J]= -0.161, Tr[J]= -1.754, Det[J1]+ Det[J2]+ Det[J3]= 0.966
-Tr[J]*(Det[J1]+ Det[J2]+ Det[J3])+ Det[J]= 1.54
Equilibrium Point B {δw=4.074, g=0.053, δΙ=0.125}
Det[J] = 0.0127, Tr[J]= -0.52, Det[J1]+ Det[J2]+ Det[J3]= -0.215
-Tr[J]*(Det[J1]+Det[J2]+Det[J3])+Det[J]= -0.098
Equilibrium Point C {δw=15.2308, g=0, δΙ=-15.2308}
Det[J] = -0.014 , Tr[J]= -0.413 , Det[J1]+ Det[J2]+ Det[J3]= -0.281
-Tr[J]*(Det[J1] + Det[J2] + Det[J3]) + Det[J]= -0.130
References
Attanasio O. P., Goldberg P. K., Kyriazidou E. (2007): ‘Credit Constraints in the Market for Consumer Durables: Evidence from Micro Data on Car Loans’, International Economic Review, 49(2), pp. 401–36.
Barba A., Pivetti M., (2009): ‘Rising household debt: Its causes and macroeconomic implications—a long-period analysis’, Cambridge Journal of Economics, No 33, pp. 113–137.
Blecker R. (1990): Are Americans on a consumption binge? The evidence reconsidered, Economic Policy Institute.
Bhaduri A. (2010): ‘A Contribution to the Theory of Financial Fragility and Crisis’, Working Paper No 593, The Levy Economics Institute.
Charles S. (2008): ‘A Post-Keynesian Model of Accumulation with a Minskyan Financial Structure’, Review of Political Economy, 20:3, 319-331.
Charpe M., Flaschel P., (2011): ‘Worker Debt, default and diversity of financial fragility’, Macroeconomic Policy Institute, Working Paper
Charpe M., Flaschel P., Proaňo Chr., Semmler W., (2009): ‘Overconsumption, Credit Rationing and Bailout Monetary Policy: A Miskyan Perspective’, Macroeconomic Policy Institute, Working Paper
Cynamon B. Z., Fazzari S. M., (2008): ‘Household Debt in the Consumer Age: Source of Growth—Risk of Collapse’, Capitalism and Society, 3, 2, Article 3
Debelle G. (2004): ‘Macroeconomic Implications of Rising Household Debt’, BIS Working Paper, No. 153
Duesenberry J. S. (1949): Income, Saving and the Theory of Consumer Behavior, Cambridge MA, Harvard University Press
Dutt A. K. (2006): ‘Maturity, stagnation and consumer debt: a Steindlian approach’, Metroeconomica 57:3, pp. 339–364
Dutt A.K. (1995): ‘Internal finance and monopoly power in capitalist economies: A reformulation of Steindl’s growth model’, Metroeconomica, 46, pp. 16-34.
Domovitz I., Sartain R.L., (1999): ‘Determinants of the Consumer Bankruptcy Decision’, Journal of Finance, 54: 403-420.
Foley D. (2003): ‘Financial fragility in developing economies’, in A. K. Dutt and Jamie Ros (ed.): Development Economics and Structuralist Macroeconomics, Northampton, MA: Edward Elgar
Hein E. (2006): ‘Interest, debt and capital accumulation-a Kaleckian approach’, International Review of Applied Economics, 20(3), 337-352.
Jacoby M.B., Sullivan T.A., Warren E. (2000): ‘Medical Problems and Bankruptcy Filings’ Norton Bankruptcy Law Adviser, 5: 1-12.
Jarsulic M. (1990): ‘Debt and macro stability’, Eastern Economic Journal, 15, pp. 91–100.
Kaldor N. (1982): The Scourge of Monetarism, Oxford University Press, Oxford.
Kaldor N. (1985): ‘How monetarism failed’, Challenge, May/June, pp. 4-13.
Kalecki M. (1937): ‘The Principle of Increasing’, Economica, 4(16), pp. 440-447.
Karlan D.S., Zinman, J. (2007): ‘Credit Elasticities in Less-Developed Economies: Implications for Microfinance’, Working Paper, Economic Growth Center, Yale University.
Lavoie M. (1992): Foundations of Post-Keynesian Economic Analysis, Edward Elgar, Aldershot.
Lavoie M. (1995): ‘Interest rates in post-Keynesian models of growth and distribution’, Metroeconomica, 46, 146-177.
Lima G.T., Meirelles A.J.A. (2006): ‘Debt, financial fragility and economic growth: a post-Keynesian macromodel’, Journal of Post Keynesian Economics 29(1), 93-115.
Maki D.M. (2000): ‘The growth of consumer credit and the household debt service burden’, Board of Governors of the Federal Reserve System, Working Paper No. 2000/12.
Maki D.M., Palumbo M.G. (2001): ‘Disentangling the Wealth Effect: A Cohort Analysis of Household Saving in the 1990s’, Board of Governors of the Federal Reserve System, Finance and Economics, Discussion Series no. 2001-21.
Marglin S.A. (1984): ‘Growth, Distribution and Inflation: A centennial synthesis’, Cambridge Journal of Economics, (8)2, 115-44.
Moore B.J. (1988): Horizontalists and Verticalists: The macroeconomics of credit money, Cambridge University Press, Cambridge.
Moore B.J. (1989): ‘The endogeneity of credit money’, Review of Political Economy, 1, pp. 65-93.
Palley T. (1996a): ‘Inside Debt, Aggregate Demand, and the Cambridge Theory of Distribution’, Cambridge Journal of Economics, 20, 465-74.
Palley T. (1996b): Post Keynesian Economics: Debt, Distribution, and the Macro Economy, Macmillan Press
Pollin R. (1988): ‘The Growth of U.S. Household Debt Demand Side Influences’, Journal of Macroeconomics, 10(2), pp. 231-248.
Pollin R. (1990): Deeper in Debt. The Changing Financial conditions of U.S. Households, Economic Policy Institute.
Rousseas S. (1986): Post Keynesian monetary economics, Houndmills: MacMillan
Sullivan T.A., Warren E., Westbrook J.L. (2000): The Fragile Middle Class: Americans in Debt, Yale University Press.
Veblen T. (1899): The Theory of the Leisure Class, Fairfield NJ, August M. Kelley 1991.
