Download Significance of Keynesian Legacy

Significance
of
Keynesian
Legacy
from
a
Theoretical
Viewpoint : A High-dimensional Macrodynamic Approach
Toichiro Asada
Faculty of Economics, Chuo University
742-1 Higashinakano, Hachioji, Tokyo 192-0393, Japan
E-mail : [email protected]
January 2006
Summary.
In this paper, we consider the significance of the ‘Keynesian legacy’ in modern
macroeconomics from a theoretical point of view. We present the outline of a variant of
the ‘high-dimensional dynamic Keynesian model’ with debt accumulation without
committing to the mathematical details, and investigate the economic implication of the
model. Our model is designed to shed some light on the understanding of the Japanese
economy in the 1990s and the 2000s and provide some hints on the policy prescriptions.
Keywords : Keynesian legacy, high-dimensional dynamic Keynesian model, debt
accumulation, expectation formation, stabilization policy
1
“The principal view, which drives me most, is that the working of the real world
capitalist economy can be better be elucidated along the lines suggested by
Keynes(1936) in his criticism of the Classical school rather than along the lines
currently pursued by the rational expectationists and new Classicals as descendants of
the old Classicals. It is especially his grand vision that the economy is unstable and can
be ill-behaved that seems most important.” (Hukukane Nikaido)1
1. Alternative legacies of modern macroeconomics
It is well known that there are two alternative legacies in modern macroeconomics.
One of them is the legacy of the ‘classical school’ in a broad sense, which is now
considered to be mainstream in the so-called standard textbooks of ‘advanced’
macroeconomics.2 Another legacy is the ‘Keynesian’ legacy in a broad sense, which is
often considered to be out of fashion. In the ‘classical’ legacy, it is taken for granted that
the full employment equilibrium will be automatically attained if wage and price are
flexible. According to this view, the cause of the persistent unemployment must be the
wage or price rigidities, and the sufficient reduction of nominal wages and prices will
contribute to increase the employment (cf. Asada 2004). In the ‘classical’ tradition of
thinking, the investment is automatically adjusted to the full employment saving so
that the ‘effective demand’ does not become the constraint on production and
employment as far as wages and prices are flexible, which is nothing but a version of the
‘Say’s law’. Needless to say, this vision on the working of the market economy is shared
by the ‘old classical’ economists such as M. Friedman, the ‘new classical’ economists
such as Lucas, Sargent, and Barro, and the ‘real business cycle’ theorists such as
Kydland and Prescott.3 Ironically enough, however, the same vision is shared by the
textbook version of the ‘Keynesian’ IS-LM model and the ‘new Keynesian’ economists
such as Mankiw and D. Romer who concentrate on the microeconomic interpretation of
the wage and price rigidities.4
On the other hand, there is less fashionable ‘Keynesian’ legacy in modern economic
thinking. Without doubt, the origin of such a tradition is Keynes(1936). Some of the
important works in this tradition will be Harrod(1948), Steindl(1952), Robinson(1956),
Kaldor(1960),
Kalecki(1971),
Tobin(1980),
Minsky(1986),
Okishio(1993),
and
Nikaido(1996) Introduction, p. xiv.
See Romer(1996) as a typical example of such textbooks.
3 See Blanchard and Fischer(1989) and Romer(1996) for the detailed exposition of such
theories.
4 For the ‘new Keynesian’ theories, see Mankiw and Romer(ed)(1991), Blanchard and
Fischer(1989), and Romer(1996).
1
2
2
Nikaido(1996).5 According to this tradition of thinking, the modern capitalist economy
will be characterized as follows.
(1) Production and employment are determined by the level of ‘effective demand’, and
the most important determinant of effective demand is the investment expenditure
of the firms.
(2) Firms’ investment activities are independent of households’ saving activities.
(3) Fluctuations of investment cause the fluctuations of the effective demand, which
feed back to the investment fluctuations through the investment function and
money market. These interaction between investment and effective demand causes
the endogenous business cycle.
(4) At almost every phase of the business cycle, labor is under-employed ( there exists
the involuntary unemployment ).
(5) Flexibility of wages and prices may destabilize rather than stabilize the economy, so
that wage and price flexibilities are not sufficient conditions for the attainment of
full employment equilibrium.6
(6) Monetary factors such as money supply, finance, and debt are very important factors
which affect the characteristics of the economic performance in the long run as well
as in the short run. This means that money is not neutral even in the long run.
(7) Subjective factors such as the expectation formation by the publics and the
credibility of the monetary/fiscal policies are often crucial for the effectiveness of the
economic policy.
Here we included the important contributions to the Keynesian macrodynamics by
two distinguished Japanese mathematical economists, Nobuo Okishio and Hukukane
Nikaido. Okishio, a pioneering mathematical Marxian economist, reformulated
Harrodian instability principle rigorously in the 1960s( for the collection of his papers,
see Okishio 1993). On the other hand, after publishing pioneering mathematical works
on Walrasian general equilibrium theory in the 1950s, Nikaido shifted his attention to
the general equilibrium models of imperfect competition and the Keynesian, Harrodian,
and Marxian disequilibrium macrodynamics in the 1970s and the 1980s. His original
contributions in this area of research are collected in Nikaido(1996).
6 Keynes(1936) wrote as follows. “The depressing influence on entrepreneurs of their
greater burden of debt may partly offset any cheerful reactions from the reduction of
wages. Indeed if the fall of wages and prices goes far, the embarrassment of those
entrepreneurs who are heavily indebted may soon reach the point of insolvency, – with
severely adverse effect on investment.” (Keynes 1936 p. 264 ) “It would be much better
that wages should be rigidly fixed and deemed incapable of material changes, than that
depressions should be accompanied by a gradual downward tendency of money wages.”
(Keynes 1936 p. 265) “There is, therefore, no ground for the belief that a flexible wage
policy is capable of maintaining a state of continuous full employment ; … The
economic system cannot be made self-adjusting along these lines.” (Keynes 1936 p. 267)
5
3
We assert that this ‘Keynesian’ tradition of thinking is important even if ‘it is not the
fashion of the day’(Flaschel, Krüger, and Asada 2003 ), because it still provides us some
important insight for the realistic modeling on the working of the modern capitalist
economy such as the Japanese economy in the 1990s and the 2000s, and it also provides
us some important hints on the policy prescription.
In this paper, we present the outline of a theoretical model in this ‘Keynesian’ legacy,
and consider the significance of such an approach to macroeconomic theorizing. The
model presented in this paper is based on the model in Asada(2005), which is a variant
of the ‘high-dimensional dynamic Keynesian model’ developed by Chiarella and
Flaschel(2000), Chiarella, Flaschel, and Semmler(2001), Asada, Chiarella, Flaschel,
and Franke(2003), Asada(2006) etc. This approach is based on the mathematical
modeling by means of a system of nonlinear differential equations with many variables
to capture the several important destabilizing positive feedback mechanisms as well as
the stabilizing negative feedback mechanisms which are embedded in the economy.7 In
particular, our formulation stresses the influence of the financial factors such as debt
accumulation and the expectation formation on the performance of the macroeconomic
system and the effectiveness of the monetary/fiscal stabilization policies by the
government and the central bank. We hope that the model in this paper can shed some
light on the understanding of the recent Japanese and other economies.
2. A high-dimensional dynamic Keynesian model with debt accumulation
The model formulated by Asada(2005) consists of the following system of equations,
which consists of seven subsystems.8
(A) Subsystem of capital and debt accumulation dynamics
d   ( g )  s f (r  id )  ( g   )d
(1)
i     (d ) ;  ≧ 0,  (d )＞0 for d＞0,  (d )＜0 for d＜0
(2)
g  g (r ,    e , d ) ; g r  g / r＞0, g    g / (    e )＜0, g d  g / d＜0 (3)
(B) Subsystem of effective demand and goods market dynamics
Importance of the destabilizing positive feedback mechanism is well noticed in the
recent literatures which treat complex economic dynamics. See, for example,
Agliardi(1998).
8 This model is called ‘Keynes-Goodwin model’ because it can be considered to be an
extension of Goodwin(1967)’s growth cycle model which introduces Keynesian elements
such as money and finance. See also Franke and Asada(1994), Flaschel, Krüger and
Asada(2003), and Asada, Chiarella, Flaschel and Franke(2003).
7
4
y   (c   ( g )  v  y ) ; ＞0, c  C / K  (C w  Cr ) / K ,  ( g )  I / K ,
v  G/ K
(4)
C w  W  Tw  Y  P  Tw
(5)
C r  (1  s r ) { 1(  s f ) P   ( B / p)  i ( D / p)  Tr } ; 0＜sr ≦1, 0＜s f ≦ 1
(6)
(C) Subsystem of labor market dynamics
e / e  y / y  g  (n1  n2 )  y / y  g  n
w / w   (e  e )  n2   e ; ＞0, 0＜e ＜1
(7)
(8)
(D) Subsystem of pricing and income distribution
p  z ( wN / Y )  zw / a ; z＞1
(9)
r  P / K  Y / K  y ; 0＜  1  (1 / z )＜1
(10)
(E) Subsystem of monetary sector dynamics
 0  (h1 y  m) / h2
if
h1 y  m ≧ 0
0
if
h1 y  m＜0
   ( y, m)  

(11)
m / m      g
(12)
(F) Subsystem of monetary and fiscal policies
b  B / pK  constant
(13)
t r  Tr / K  constant
v  t w  t r  m  ( g     )b
   0   ( 0  n   ) ;  0＞0,  ≧ 0
(14)
(15)
(16)
(G) Subsystem of price expectation formation dynamics
 e   { (  0  n   e )  (1   )(   e )} ; ＞0, 0 ≦ ≦1
(17)
Meanings of the symbols are as follows. Y  real output (real national income).
K  real private capital stock. y  Y / K  output-capital ratio, which is supposed to be
proportional to ‘rate of capacity utilization’. D  nominal stock of firms’ private debt.
B  nominal stock of public debt (public bond). p  price level. w  nominal wage rate.
 e  expected
d  D / pK  private debt-capital ratio. b  B / pK 
M  nominal money supply.   M / M  growth rate
m  M / pK  money-capital ratio. g  K / K  rate
  p / p  rate of price inflation.
I   (g )K 
real
investment
expenditure
rate
of
price
inflation.
public debt-capital ratio.
of nominal money supply.
of
including
capital
accumulation.
adjustment
cost.
 (g )  adjustment cost function of investment introduced by Uzawa(1969) with the
properties  ( g ) ≧ 1,  ( g ) ≧ 0. C w  workrts’ real consumption expenditure.
Cr  capitalists’ real consumption expenditure.   nominal rate of interest of public
5
bond. i  nominal rate of interest that is applied to firms’ private debt. W  pre tax
real wage income. P  pre tax real profit. r  P / K  pre tax rate of profit. Tw  real
income tax on workers. Tr  real income tax on capitalists(we neglect corporate tax for
simplicity). t w  Tw / K .
t r  Tr / K.
N  labor employment. N s  labor supply.
n1  growth rate of labor supply = constant ＞ 0. a  average labor productivity.
n2  a / a  growth rate of average labor productivity (rate of technical progress) =
constant＞0.9 n  n1  n2  natural rate of growth or ‘potential’ rate of growth, which
is assumed to be a positive constant.10
Next, we shall interpret how to derive the above equations briefly.
We assume that there is no issues of new shares, and we neglect the repayment of the
principal of the private debt for simplicity. In this case, the budget constraint of the
private firms becomes as follows.
D   ( g ) pK  s f (rpK  iD)
(18)
where s f  (0,1] is the rate of internal retention of firms, which is assumed to be a
constant parameter for simplicity. Next, differentiating the definitional equation
d  D / pK with respect to time, we have
d / d  D / D  p / p  K / K  D / D    g
(19)
Substituting Eq. 18 into Eq. 19, we obtain Eq. 1. Eq. 2 captures the fact that the
private debt and the public debt are the imperfect substitutes, and the interest rate
differentials of these assets reflect the difference of the degrees of the risk between them.
Eq. 3 is the investment function with ‘Fisher debt effect’. We can derive this type of
investment function from the optimizing behavior of firms by assuming both of
Uzawa(1968)’s hypothesis of increasing cost(Penrose effect) and Kalecki(1937)’s
hypothesis of increasing risk of investment(cf. Asada 2001).
This means that we are assuming ‘Harrodian neutral’ exogenous technical progress.
It is likely that the natural rate of growth is an increasing function of the rate of
employment as the experience of the Japanese and other economies suggests. In this
case, we have a Keynesian endogenous growth model with variable rate of employment
in contrast to the neoclassical full employment endogenous growth models represented
by Barro and Sala-i-Martin(1995). We can easily see, however, that the qualitative
conclusion is not much affected as long as the sensitivity of the natural rate of growth
with respect to the changes of the rate of employment is not extremely large, so that we
do not introduce this kind of complication in this paper. For another formulation of the
Keynesian endogenous growth theory, see Pally(1996).
9
10
6
Eq. 4 is the Keynesian/Kaldorian quantity adjustment process of the goods market
disequilibrium. In this formulation, we neglect the international trade for simplicity.
Eqs. 5-6 are Kaleckian consumption functions of workers and capitalists respectively(cf.
Kalecki 1971). In these formulations, it is assumed that workers spend all of their
income, and capitalists save a part of their income, where sr  (0,1] is the capitalists’
average propensity to save, which is assumed to be a constant. Capitalists buy public
and private bonds out of their saving.
By definition, we have
e  N / N s  yK / aN s .
(20)
Differentiating this equation with respect to time, we obtain Eq. 7. Eq. 8 is nothing
but a standard expectation-augmented wage Phillips curve.
Eq. 9 is the Kaleckian postulate of the mark up pricing rule of the imperfectly
competitive economy, where z is the mark up that reflects the ‘degree of monopoly’ of
the economy(cf. Kalecki 1971). In this case, we can derive Eq. 10, which implies that the
rate of profit is proportional to the rate of capacity utilization. By the way, we can derive
the following expectation-augmented price Phillips curve from Eqs. 8-9.
   (e  e )   e
(21)
Eq. 11 is the standard ‘LM equation’ describing the equilibrium condition for the
money market, which can be derived as follows. Following Asada, Chiarella, Flaschel,
and Franke(2003), we specify the equilibrium condition for the money market as
M  h1 pY  (  0   )h2 pK ; h1＞0, h2＞0,  0 ≧ 0.
(22)
The left hand side of this equation is nominal money supply, and the right hand side
is a type of Keynesian nominal money demand function, where  0 is the lower bound
of the nominal interest rate of the government bond. Solving this equation with respect
to  , we obtain Eq. 11. Formally, the case of    0 corresponds the case of
h2  , which is nothing but the case of the so-called ‘liquidity trap’. By
differentiating the definitional equation m  M / pK with respect to time, we obtain
Eq. 12.
Eqs. 13-14 are simplifying assumptions about the government’s attitude on the fiscal
policy.11 We can derive Eq. 15 as follows. The budget constraint of the ‘consolidated
government’ including the central bank can be written as
More complicated but realistic assumption on the taxation will be
t r   r {(1  sr )y  b  id }, where 0＜ r＜1, which implies that t r becomes to be
an increasing function of the capitalists’ income per capital stock. We can show that this
reformulation has a destabilizing rather than the stabilizing effect on the system(cf.
Asada 2005).
11
7
M  B  pG  B  pT  pG  B  p(Tw  Tr ),
(23)
which means that the government deficit must be financed through the issue of new
money or new bond. From this equation we have
m   B b  v  b  (t w  t r ),
where  B  B / B. From Eq. 13 we have
(24)
b / b  B / B  p / p  K / K   B    g  0.
(25)
Substituting Eq. 25 into Eq. 24, we obtain Eq. 15. Eq. 16 formalizes the monetary
policy rule of the central bank. If ＞0, we can consider this monetary policy rule as a
type of ‘inflation targeting rule’ (cf. Krugman 1998 and Asada 2006). The parameter  0
is the long run target growth rate of nominal money supply, and
 0  n is the long run
target rate of price inflation. It is supposed that the central bank announces this target
rate to the publics, and adjusts the growth rate of nominal money supply towards the
realization of this target.
It is worth noting that in our formulation monetary policy of the central bank and
fiscal policy of the government are closely related each other through Eq. 15, which is
derived from the budget constraint of the ‘consolidated government’, so that it is
impossible to separate monetary and fiscal policies clearly. In this case, it is
meaningless to argue which policy is more effective to stabilize the economy.
Eq. 17 formalizes the price expectation formation hypothesis, which is a mixture of a
sort of the ‘forward looking’ and ‘backward looking’(adaptive) expectation formations ( cf.
Asada, Chiarella, Flaschel, and Franke 2003, and Asada 2006 ). The case
 0
corresponds to the case of purely adaptive or backward-looking expectation. In case of
  1, the expected rate of inflation is adjusted towards the target rate of inflation that
is announced by the central bank. This means that the publics believe that the
monetary policy commitment by the central bank is highly credible. It may be said that
in this case the price expectation formation by the publics is forward-looking in a
sense.12 The specification of price expectation formation closes our model.
We can reduce the system of equations 1-17 to the following five-dimensional system
of nonlinear differential equations, which we call the ‘fundamental dynamical
equations’ of our system.
However, the use of the term ‘forward-looking’ in this context may be somewhat
misleading, because in our model the perfect foresight is not necessarily postulated even
if   1, while the term ‘forward-looking’ is usually used in the context of perfect
foresight or rational expectation models. Reiner Franke pointed out this fact to the
author.
12
8
(i)
d   ( y,  ( y, m)   e , d )  s f {y  i(  ( y( y, m), d )d}
 {g (y,  ( y, m)   e , d )   (e  e )   e }d  F1 (d , y, e,  e , m)
( ii )
y   [ ( y,  ( y, m)   e , d )  { 0   (  0  n   (e  e )   e )}m
 {g (y,  ( y, m)   e , d )   (e  e )   e   ( y, m)}b
 (1  s r ){ ( y, m)b  i (  ( y, m), d )d  {s f  (1  s f ) s r }y  s r t r ]
 F2 (d , y, e,  e , m;  0 ,  )
( iii )
e  e[ F2 (d , y, e,  e , m;  0 ,  ) / y  g ( y,  ( y, m)   e , d )  n]
 F3 (d , y, e,  e , m;  0 ,  )
( iv )
 e   { (  0  n   e )  (1   ) (e  e )}  F4 (e,  e ;  0 , ,  )
(v)
m  m[  0   { 0  n   (e  e )   e }   (e  e )   e  g ( y,  ( y, m)   e , d )]
 F5 (d , y, e,  e , m;  0 ,  )
(26)
3. Summary of the analysis
In this section, we summarize the results of mathematical analysis by Asada(2005)
without committing to the mathematical details. The ‘long run equilibrium’ solution
(d *, y*, e*,  e *, m*) of the Eq. 26 that satisfies the relationship
d  y  e   e  m  0
(27)
is determined by the following system of equations corresponding to the given
parameter values of monetary policy  0 .
(i)
( ii )
 (n)  s f [ y  { ( y, m)   (d )}d ]   0 d  0
 (n)   0 m  { 0   ( y, m)}b  (1  sr )[  ( y, m)b  { ( y, m)   (d )}d ]
 {s f  (1  s f ) s r }y  s r t r  0
( iii )
g ( y,  ( y, m)   0  n, d )  n
( iv )
ee
9
(v)
   e  0  n
(28)
It follows from Eq. 28 iii-iv that at the long run equilibrium point, the rate of capital
accumulation is equal to the ‘natural rate of growth’ (n), and the rate of employment is
equal to the ‘natural rate of employment’ (e ), both of which are assumed to be
exogenously given. Eq. 28 v means that the equilibrium rate of price inflation is equal to
the difference between the target growth rate of nominal money supply and the natural
rate of growth. Therefore, it seems that the classical postulate of the ‘neutrality of
money’ applies to the long run equilibrium of our model at first glance. But, we can
argue that this first impression is wrong because of the following reasons.
First, the equilibrium values (d *, y*, m*) depend on the value of the monetary
policy parameter  0 . Second, the choice of  0 is not irrelevant to the existence of the
long run equilibrium solution. The equilibrium real rate of interest (    ) * must
e
satisfy the following inequality, since  cannot be lower than its lower bound  0 .
(    e )*   ( y*, m*)  n   0 ≧  0  n   0
(29)
It is quite likely that in the long run equilibrium the relatively low real rate of
interest is required to support the realization of the natural rate of growth, because the
economically feasible range of the variables y and d are restricted. This means that
the long run equilibrium will not exist if the target growth rate of nominal money
supply  0 is too small to support the natural rate of growth. Therefore, money is not
neutral even in the long run in our model.
In our model, the parameter values  ,  ,  ,  , and
 do not affect the long run
equilibrium values of the main endogenous variables. These parameter values affect,
however, the dynamic stability/instability of the long run equilibrium point. In fact,
Asada(2005) proved the following proposition mathematically under some reasonable
assumptions in case of the ‘liquidity trap’
 ( y, m)   0 (h2  ). 13
Proposition.
( i ) Suppose that the parameter value
 is relatively small, which means that the
monetary/fiscal policy is relatively inactive. Then, the high speed of the quantity
adjustment in the goods market ( quantity flexibility reflected by large value of
)
and the high speed of the wage adjustment in the labor market ( wage/price
flexibility reflected by large value of
 ) tend to destabilize the equilibrium point of
Eq. 26.
13
We shall try to present the economic interpretation of this proposition in section 5.
10
( ii ) Suppose that the monetary/fiscal policy is relatively inactive ( the parameter value
 is relatively small ) and the price expectation formation by the publics are
considerably backward-looking ( the parameter value  is sufficiently close to
zero ). Then, the high speed of expectation adjustment ( expectation adjustment
flexibility reflected by large value of  ) tends to destabilize the equilibrium point
of Eq. 26.
( iii ) Suppose that the monetary policy commitment by the central bank is considerably
credible ( the parameter value
 is sufficiently close to 1 ). Then, the equilibrium
point of Eq. 26 is unstable for all sufficiently small values of the monetary policy
parameter  ≧ 0, and it is locally stable for all sufficiently large values of
＞0.
 is sufficiently close to 1. Then, at the
intermediate range of the monetary policy parameter ＞0, the endogenous
( iv ) Suppose that the parameter value
cyclical fluctuations occur.
Proposition ( iii ) means that the central bank can stabilize the intrinsically unstable
economy by adopting the sufficiently active monetary policy rule if the inflation
targeting by the central bank is highly ‘credible’. Proposition ( iv ) means that at some
range of the parameter values the endogenous business cycle occurs.
4. A numerical example
Next, we shall present a numerical example to illustrate the analytical results of the
previous section. We assume the following parameter values and the functional forms.14
s f  s r  1,       b  t r  0.2,   0.1, i    d 2 ,    0  0.01,
 ( g )  g , e  0.97, n1  0.03, n2  0.02, n  n1  n2  0.05,  0  0.09,
 0  n  0.04
(30)
g  0.1{1.8 y  (    )  0.9d  0.19}  n  0.18 y  0.1  0.09d  0.03
(31)
5
We interpret 100  ,
e
5
100 e ,
100n,
e
100 0 , and 100(  0  n) as the annual
percentages of nominal interest rate of government bond, expected rate of price inflation,
target growth rate of nominal money supply, and target rate ( equilibrium rate ) of price
inflation respectively. We also assume the following initial conditions of the main
variables.
This numerical example is based on Asada(2005). The purpose of our numerical
simulation is not to calibrate the model but to illustrate the qualitative conclusion
which can be obtained analytically.
14
11
d (0)  0.21, y (0)  0.18, e(0)  0.92,  e (0)  0.01, m(0)  0.23
(32)
In addition, we modify the model introducing the following natural nonlinearities,
which means that the capacity utilization and the rate of employment cannot exceed
their exogenously given upper bounds y max  0.32 and emax  1.
 F2 (d , y, e,  e , m;  0 ,  )
if
y  
e
min[ F2 (d , y, e,  , m;  0 ,  ),0] if
0＜y＜y max  0.32
 F3 (d , y, e,  e , m;  0 ,  )
if
e  
e
min[ F3 (d , y, e,  , m;  0 ,  ),0] if
0＜e＜emax  1
y  y max  0.32
e  emax  1
(33)
(34)
Then, we obtain figures 1 and 2, which illustrate some alternative time paths of the
variables e, d , and
.
Insert Fig. 1 and Fig. 2 here.
In these figures, we consider the following three alternative cases, where t denotes
the ‘time period’, and a unit of time is supposed to be a year.15
    0 for all t ≧ 0
Case B :   0.8,   0 for all t ≧ 0
Case C :   0.8,   0 for 0 ≦ t＜5, and   0.8,   0.3 for t ≧5
Case A :
In Case A, the price expectation formation is purely backward-looking and the
monetary/fiscal policy is inactive. In this case, the initial high debt-capital ratio causes
the serious debt deflation. Even in this case, the economy begins to recover
endogenously as the real burden of debt decreases because of the sharp decline of
debt-financed investment expenditure. But, the lower turning point comes too late
because the serious deflation prevents the real debt burden from reducing sufficiently to
induce the sufficient increase of investment expenditure. In addition, the capacity
utilization reaches its upper bound y max  0.32 at the time period t  19, and the
economic recovery fails at that time.
In Case B, the price expectation formation is considerably forward-looking in a sense,
We adopted the Euler’s algorithm with the time interval t  0.1 (years) for
computer simulations.
15
12
but the monetary/fiscal policy is inactive. Even if the monetary/fiscal stabilization policy
is inactive, in this case the speed of economic recovery is much higher than that in Case
A because of the movement of the price inflation towards the target rate, which helps to
sufficiently reduce the real debt burden to induce the sufficient increase of investment
expenditure. In this case, at the time period t  21 the capacity utilization reaches at
its upper bound and then the economic recession is triggered off.
In Case C, the price expectation formation is the same as Case B, and the
monetary/fiscal policy becomes considerably active since the time period t  5. In this
case, the economic recovery is further accelerated through the active monetary/fiscal
stabilization policy that is combined with the considerable credibility of the inflation
targeting by the central bank. At the time period t  19 the full employment of labor is
attained, and at t  19.5 the capacity utilization reaches its upper bound. Contrary to
the previous two cases, the full employment of labor and excess demand in the goods
market continue in this case.
In these examples, it is assumed that the nominal rate of interest is fixed at its lower
bound
 0  0.01 all the time. In the real economy, however, the nominal rate of
interest will begin to rise at the later stage of economic recovery. This will have the
effect to somewhat slows down the speed of economic recovery, but the qualitative
nature of the economic recovery will not seriously change even if we consider the effect
of the rising nominal rate of interest at the late stage of economic recovery.
By the way, it is worth noting that in the above three cases the structure of the
 representing the credibility of the policy
commitment of the central bank and the monetary/fiscal policy parameter  .
economy is the same except the parameter
5. Economic implication of the analysis
Finally, we shall try to interpret the economic implication of our analysis. Under the
lack of the active counter-cyclical monetary/fiscal policy, the following destabilizing
positive feedback mechanism, which is called ‘Fisher debt effect’, may dominate the
economy (cf. Fisher 1933 ).
(e )    d  ( D / pK )  g  y  (e )
(FDE)
The increase of the adjustment speed in the goods market ( quantity flexibility ) and
the increase of the adjustment speed in the labor market ( wage/price flexibility ) will
reinforce this destabilizing mechanism.
If the monetary/fiscal policy is inactive and the price expectation formation by the
13
publics is highly backward-looking ( adaptive ), the following another destabilizing
positive feedback mechanism, which is called ‘Mundell effect’, will also work through
the effect on the expected real interest rate.
(e )     e  (    e )  g  y  (e )
(ME)
The increase of the speed of expectation adaptation will reinforce this destabilizing
effect reinforcing the part     . The increase of the quantity flexibility and the
e
wage/price flexibility will also reinforce Mundell effect as well as Fisher debt effect.
On the other hand, the following stabilizing negative feedback mechanism through
the changes of the nominal rate of interest, which is called ‘Keynes effect’, will work if
the counteracting Mundell effect is relatively weak.
(e )    m  (M / pK )    (    e )  g  y  (e )
(KE)
But, this stabilizing ‘Keynes effect’ is almost negligible in the case where the nominal
rate of interest is already fallen to nearly its lower bound, like the Japanese economy in
the late 1990s and the early 2000s. Needless to say, this case corresponds to the case of
‘liquidity trap’.
Even in case of the ‘liquidity trap’, however, the sufficiently active counter-cyclical
monetary/fiscal policy, which is combined with the sufficient credibility of the monetary
policy commitment by the central bank, can stabilize the intrinsically unstable economy.
The large value of the monetary/fiscal policy parameter
 has the following direct
stabilizing effect, which may be called ‘money-financed fiscal policy effect’.
(e )    v  y  (e )
(MFE)
Even if monetary/fiscal policy is not strongly active, the sufficiently high credibility of
the inflation targeting commitment by the central bank will have a stabilizing effect
through the following mechanism, which may be called ‘inflation targeting effect’.
 0  n＞ e   e  (    e )  g  y  (e )

  d  ( D / pK )  (e )
(ITE)
14
This result is consistent with the Keynesian view which stresses the importance of
the subtle subjective factors such as expectation of the publics and the credibility of the
attitude of the policy maker.
Acknowledgment
This is a revised version of the paper which was presented at Chuo METS 05 (Chuo
Meeting on Economics of Time and Space 2005, Chuo University, Tokyo, 30 August,
2005) and Sophia Symposium on Keynesian Legacy and Modern Economics (Sophia
University, Tokyo, 24 September, 2005). Thanks are due to the helpful comments by the
participants of the conferences. Needless to say, however, only the author is responsible
for possible remaining errors. This research was financially supported by the Japan
Ministry of Education, Culture, Sports, Science and Technology (Grant-in-Aid for
Scientific Research (B) 15330037) and Chuo University Joint Research Grant 0382.
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