Policy, Research, and Exlernal Atfairs
WORKING PAPERS
Public Economics
Country Economics Department
The World Bank
March 1991
WPS 630
The Spirit of Capitalism
and Long-run Growth
Heng-fu Zou
In thie long rUIn cltUtral attribltes and thle spirit ot capitalismll hlellp
explain why Japan. the foLur- Asianii "iimirclces." and manly colill-
tries wk itil Protestant reliuion have succeeded econlonmiicallv.
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Policy, Research, and External Affairs
I [ _
Public Economics
WPS 630
'Illis lpaper a p)lo)ilnCt o lt'h PU)hliC ICeononi ics Di ision, Country ELonom ics Decpartment is part ol
a largoC! Cilltl III 1l'R l to stlu) 10u-rii) -i.o\\ %ll and eCoonCiiic policies. (Copies are amailable lI'ct'e loli thle
\World Banrrk, I 8 11 8 S IreI S NrVt \NW, aslliinLron DC' 2(033. P'lease c(ntact Anni Blhal Ia, room; N 10-1)55.
extenIsion 37699 (28 paes).
W\h (lo di lIvcnlCi countlirSies have dil;l'er-CInt lolg- Zou provides a lor111roa IllO(im l Ihllat is sup-
term savings and growth[1 rates? Whk is thie ported by m;any cinpil-ical and historical studies
prodUCtiVit\ AIC 1iot tIle sanc around(i thC world? on cultural atitibutes and ecololilmic devcelopment.
Recenit new thcories o lendogcnous gro% lil have lis model help,s cxplaii:
tric(l to answer thlsC (lucstionis by) replacing IltC
usual assump[)tion of'i (iiiiilisIlilln retulins ill * Wiy) Japan and tlic four Asiani "n-miracics''
production. Zou ol[er's an11 altelllativc: lie have succecded.
initroduces -thc spirit of'capitalisni" (as Max
Weher use(d Ilc teteII) iito the model. * Wlhy nations that had an11 cstablished Protes-
ta1n religion in 1I 870 had a peri capita in;com11e in
Inl the long I-uIn, Countries wjiltI (I ICI Cent 1979 that was i morc than zia third hieicr than in
degtees of capitalist spiriit wvill have difflerenit Catholic nat ions.
Consumption, capital stock, and endogenous
gron tih ratecs. In Zou's Imlodel (unlike traditional * Whv Britishi indlusIt) has (Iccli med since
milodels), inflation is nio longer supeincutral in 1 850.
relation to long1-un g')rowthl.
Th I'RI \PF 'rkiit P,iqp,r I,ix ii1icl liihti , iiiL vol %ork uindt- in it ln thBank' Pitkh\ . R%car th. :Indt E\tmcnla
;1!. I.(\ll \l(1; s ^ i;tr> t ; l>}lllllg l IitW 1 : w * ll.:s;r tR l r ,1 X>l
"The Spirit of Capitalism" and Long-Run Growth
By
Heng-fu Zou
Table of Contents
I. Introduction 1
II. "The Spirit of Capitalism" and Its Mathematical
Representation 3
III. "The Svirit of Capitalism" and Endogenous Growth 10
IV. Two Examples 13
V. Inflation and Endogenous Growth 15
VI. Empirical Relevance of the Capitalist Spirit Model 20
VII. Concluding Remarks 23
References 25
Appendix 27
"The Spirit of Capitalism" and Long-Run Growth
I. Introduction
Traditional optimal growth models such as Phelps (1961), Cass (1965) and
Koopmans (1965) have demonstrated that, with typical neoclassical production
function and exogenously given time dlscount factor, the maximization of an
additive utility function defined on per capita consumption by a
representative agent or family leads to a unique steady state where the net
marginal productivity of capital equals the time discount rate. If two
countries have the same technology and the same discount rate, It is expected
that per capita consumption, per capita capital stock, saving rate and returns
on capital are all equalized in steady state.
This well-known convergence theorem of economic growth has been faced
with a growing number of challenges In recent years. Empirically, the
convergence theorem cannot explain several puzzling economic facts: (i) why
the growth rates In some developing countries with Confucian culture, like
four East Asian 'miracles' of South Korea, Taiwan, Hong Kong and Singapore are
so high and the rates In some developing countries so low; (ii) why the
relative income gap between developed countries and developing countries is
getting wider rather than narrowing; (MIl) why productivity levels have not
converged; and (iv) why the nations with Protestant religious establishment In
1870 had 1979 per caplta income more than one-third higher than the nations
with Catholic religion (DeLong, 1987). To try to answer these problems, some
This paper Is based In part on the flrst two chapters of my Ph.D thesis
subwltted to Harvard University In May 1989. I am grateful to Jeffrey Sachs,
Richard Caves, Dwight Perkins, Bela Balassa, Andrew Newman, Lawrence Summers,
Philippe Well, Danyang Xie, Xlnsheng Zeng for helpful discussions ana
comments.
1
new theories have emerged. A typical starting point for these new theories is
to depart from the usual assumption of diminishing returns (Romer, 1986,
and Lucas, 1988). Romer (1986) has snown that, under increasing returns to
scale, the level of per capita Income In different countries need not
converge.
We believe that culture differences among countries, In addition to
technology, play an important role In the determination of economic growth,
Here our alternative growth model is based on Max Weber's theory of "the
spirit of capitalism" and a mathematical model of Mordecal Kurz (1968). In an
unduly neglected paper of tne economics profession, Kurz (1968) deviates from
the conventional wisdom of economics and defines utility function on both
consumption and capital which he calls wealth effects. As we will see In
Section II, this novel definition of preference function reflects the essence
of the spirit of capitalism: the continual accumulation of wealth for Its own
sake, rather than for the materlal rewards that It can serve to brlng. (We
hasten to add that Kurz's original model Is a purely technical one and he does
not offer any explanation or Justification for his Inclusion of capital Into
the preference. We hope that our reasoning will not distort Kurz's original
Ideas.)
As a result of the presence of so-called wealth effects in the
preference function, the steady state capital stock Is larger than the
modified golden rule level, and the forms of utility functions play a crucial
role in determining equilibrium consumption and capital. Therefore, countries
with the same technology and the same time discount rate may have different
steady state depending on the difference In their wealth effects or their
capitalist spirit.
In recent contributions to endogenous growth theory, the technology Is
often assumed to be constant or Increasing returns In capital Input. To
2
generate growth, for all levels of capital stock, the net marginal product of
capital is further assumed to be hounded below by the time liscount rate. In
Sections III and IV, we will demonstrate how the capitalist spirit can cause
endogenous growth even though the net marginal product of capital can be
smaller than the time discount rate or can go to zero as capital increases
without bound. Through a specific example, It is shown that the stronger the
capltalist spirit, the higner the endogenous growth rate and the saving rate.
In Section V, we extend the model to a monetary economy. In a hybrid
Sidrauski-Kurz model, we find that there exist multiple balanced growth paths
and Inflation can increase the balanced growth rates.
Section VI discusses the empirical relevance of the capitalist spirit
lel. By citing work of sociologists, historians and economists, we will
see that the capitalist spirit approach to economic growth and development has
been widely used in many historical and empirical studies.
We conclude this paper In Section VII with a few remarks.
II. "The Spirit of Capitalism" and Its Mathematical Representation
Here we first present a model essentially the same as in Kurz 8'. A
representative agent maximizes a discounted utility over an infinite time
horizon subject to a dynamic constraint of capital accumulation:
Max f [ u(c) + v(k) le Ptdt (1)
0
s.t.
k = f(k) - c (2)
where c Is consumption, k Is capital stock, and p is the time discount rate
and 0 < p < 1. f(k) Is the r.et cutput function (= gross output - capital
depreciation). A dot over a variable denotes time derivative. The utility
function has the following standard properties:
3
u (c) > 0, u' ' (c) < 0, u' (0) - > and u' () -> 0;
v' (k) > 0, v' ' (k) < 0, v' (m) > 0;
The net output function f(k) is typically neoclassical:
f(G) = 0, f'(k) > 0, f''(k) < 0, f'(0)--> x, f'(w) ->O, f(W)->.
so f(k) is strictly concave; and when capital stock Increases without bound,
the net marginal product of capital goes to zero and the net output increases
to infinity.
The optimal path of capital accumulation is described by the following
two dynamic equations:
-u '(cjc = v'(k) + u'(c)( f'k) - p ) (3)
k = f(k) - c (2)
_ 0
Let the steady state values be denoted is k and c , then
v'(k ) + u'(c )( f'(k ) -p ) 0 (4)
f(k ' - c = 0 (5)
Two facts Immediately follow from these two equations. First, the steady
state capital sLock Is higher than modified golden rule level. To see this, we
compare the steady state condition (4) to the modified golden rule In Cass
(1965),
* ~~v'Ck)
f'(k ) =p - , < p = f'(kmg)
u' (c )
where kmg denotes the modified golden rule capital. Since f''(k) < 0, v'(k)
and u'(c! are positive for all k and c, k > kmg. Second, the steady state
capital Is no longer independent of the preference functions as In the -ss
model. Tn fact, even if different countries have the same time discount rate
and technology, the difference In the utility functions can give rise to
diferent per capita capltal stock and per capita consumption across countries
In the long run.
4
It the rest of this section, we are going to argue why the Inclusion of
capital or wealth Into the preference reflects "thke spirit of capitalism" in
Max Weber's sense and how some great economists In history have developed the
same idea in their growth theories.
In "The Pro!estant Ethic and th, 'pirit of Capitalism", Max Weber (1958)
defines capitalism as the rational org&ilzatlon of formally free labour
(p.21). The essence of the spirit of capitalism Is the continual accumulation
of wealth for Its own sake, rather than only for the material rewards that It
can serve to bring (p.4).
"At all periods of history, wherever It was possible, there has been
ruthless acquisition, bound to no ethical norms whatever". But only
in a capitalist economy, "man Is dominated by the making of money, by
acquisition as the ultimate purpose of his life. Economic acquisition
is no longer subordinated to man as the means for the satisfdction of
his material needs. This reversal of what we should call the natural
relationship, so irrational from a naive point of view, Is evidently a
leading principle of capitalism as it Is foreign to all people not
under capitalist Influence" (p.53, Italic added.).
Weber's idea Is cl-r: capital act lation In a capitalist economy is
motivated not only by the maximization of the long-run consumption, but also
by the enjoyment (utility) from enhancing wealth itself. This capitalist
spirit approach to long-run growth has been also taken by Adam Smith (1937),
Karl Marx (1977) and John Maynard Keynes (1971), among many others.
In the "Wealth of Nations", Adam Smith (1937) makes the following
description of a capitalist society's saving behavior:
"The principle which prompts to save, Is the desire of bettering our
condition, a desire which though generally calm and dispassionate,
comes with us from the womb, and nceer leaves us tlll we go into the
5
grave. ... An augmentation of fortune Is the means by which the
greater part of men propose and wish to better their condition. It Is
the means of the most vulgar and the most obvious; and the most likely
way of augmenting their fortune, Is to save and accumulate some part
of what they acquire, either regularly and annually, or upon some
extraordinary occasions. Though the principle of expence, thereforr,
prevails In almost all men upon some occaslons, and In some men upon
almost all occasions, yet In the greater part of men, taking the whole
course of their life at an average, the principle of frugality seems
not only to predominate, but to predominate very greatly." (The Wealth
of Nations, pp.324-25)
Adam Smith is so occupied by the moral of savings, he declares that
"every prodigal appears to be a public enemy, and every frugal man a public
benefactor." (P.324)
Karl Marx (1977) also shares this view with many so-called classlcal
economist:. He regards the Instinctive nature of accumulation by capitalists
as an essential part of capitalism:
"Accumulate, accumulate! That is Moses and the prophets! 'Industry
furnishes the material which saving accumulatesl' Therefore save,
save, I.e., reconvert the greatest possible portion of surplus-value
into capital! Accumulation for the sake of accumulation, production
for the sake of production: this is the formula In which classical
economists expressed the historical mission of the bourgeoisie in the
period of its domination." (Capital, Vol.1, p.742)
John Maynard Keynes (1971) develops the same idea In his statement of
1
the "psychology" of capitalist society . He sa_s that
1
I thank Jeffrey Sachs for directing my attention to Keynes' work "The
Economic consequences of the Peace".
6
"Europe was se organlsed socially and *-^onomically as to secure the
maximun accumulation of capital. While there was some continuous
improvement in the daily conditions of life of the mass of the
population, society was so framed as to throw a great part of the
Increased lncoi.ie Into the control of the class least likely to consume
it. The new rich of the nineteenth century were not brought up to
large expenditureb, and preferred the power which investment gave them
to the pleasures of immediate consumption.... Herein lay, in fact, the
main justification of the capitalist system. If the rich had spent
their new wealth on their own enjoyments, the world would long ago
have found such a regime Intolerable. But like bees they saved and
accumulated, not less to the advantage of the whole community because
they themselves held narrow ends in prospect." (The Economic
Consequences of the Peace, p.11, Italic added)
Keynes continues to describe the saving behavior of the capitalist
class:
They "were allowed to call the best part of the cake theirs and were
theoretically free to consume It, on the tacit underlying condition
that they consumed very little of it In practice. The duty of 'saving'
became nine-tenths of virtue and the growth of the cake the object of
true religion. ... And so the cake increased; but to what end was not
clearly contemplated. Individuals would be exhorted not so much to
abstain as to defer, and to cultivate the pleasures of security and
anticipation. Saving was for old age or for your children; but this
was only In theory --- the virtue of the cake was that It was never to
be consumed, neither by you nor by your children after you" (P.12,
italic added).
7
Therefore, defining utility on both cornsumption and capital Is a way to
model the nature of capitalism mathematically. In this respect, for spzace
limitation, we add only one more excellent quotation from Gustav Cassel(1924):
"There Is a formation of capital for which it Is hardly possible to
assign any concern about the future as motive. It cannot be said of
the leading capitalists who satisfy all their wants of any
consequence, and have a capital the returns on which guarantees this
satisfaction of wants for all time to them and their families, yet
constantly set aside large sum to In-_rease their wealth, that they
save out of the concern about the future. in these cases there must be
some other motive. It Is the economic Interest of the capitalist to
increase his wealth, and this in time becomes an end In Itself. The
motives that are at work are numerous. Ihe senseless cupidity that in
times finds its sole pleasure In contemplating the growth of its
wealth, and may very well be described as an abnormal sluggishness of
spirit and a pathological impoverishment of the emotional life, is
certainly not the sole explanation. The desire of splendor and ci the
higher position In the society which the possession of great wealth
assures, the stimulation of jealousy of other men, the healthy joy of
the strong man in successful work as such, in ruling large masses, in
influence especially --- these are all factors that have to be taken
into account." ( The theory of Social Economy, pp.228-29.)
To define utility function on both consumption and capital or wealth Is
also a way to model man no only as an economic animal, but also a political
animal. Ever since Aristotle, we are taught that "man Is by nature an animal
of Intended to live In a polls". (see Aristotle, 1958). Wealth or property
provides man not only consumptlon means but also political power and social
8
prestige. Possession of wealth Is, to a considerable degree, a measure and
standard of a person's success In a society. Thus capital and wealth directly
enter to the utility function of the representative agent of the capitalist
economy. ,n a recent book on power, Galbraith (1984), following the long
traciltion of sociology and political science, classifies wealth as one of
three resources of political power. "In past 'ime, so great was the prestige
of property that ... it accorded power to Its possessor. What the mar r
wealth said or believed attracted the belief of others as a matter of course."
(p49) To this day, "wealth per se no longer gives automatic access to
conditional power. The rich man who now seeks such influence hires a public
relations firm to win others to his beliefs. Or he contributes to a politician
or a political action committee that reflects his views. Or he goes Into
polUtics himself and uses his property not to purchase votes but to persuade
voters."(p.50)
This analysis agrees with what Lord Acton's (1988) contention that:"
Power goes wlth property" (P.572). In a laisser-faire capitalist et .iomy,
"fLeedom of accumulation not only carries with It the possibility of
cumulative Increase In the inequallty of economlc power,... In additlon,
economic power confers power In other forms, including the political." (Frank
Knight, 1942, P.82). Seeking high social position and power has been long
recognized as one of the most Important motivation In capital accumulation. In
the discussion related to the spirit of capitalism, Max Weber (1958)
explicitly states that "the desire for the power and recognition whilch the
mere fact of wealth brings plays Its part" (P.70) In capital accumulation.
So much is the Justifications why we should define a representative
agent's utility function on both consumptlon and capital (or wealth). We turn
next to the relation between the capltalist spirit and endogenous growth.
9
III. "The Spirit of Capitalism" and Endogenous Growth
Recent contributions to endogenous growth theory have shown that
long-run growth rate can be endogenously determined by preference and
technology. A common starting point of many models Is to assume that the
prod ction technology 's Increasin_ or constant returns to scale instead of
diminishing returns: e.g., Romer (1986), Lucas (1988), Barro (1990) and Rebelo
(1991!. In a convex model of endogenous growth, while allowing decreasing
returns to scale, Jones and Manuelli (1990) assume that the net marginal
product of capital does not go to zero as the stock of capital Increases
without bound. In fact, In all these models, in order to generate endogenous
growth, it Is required that the net marginal product of capital Is always
greater than the time discount rate. This Is the so-called lower boundary
condition on technology.
We are going to show that the Inclusion of the capitalist spirit into
the model can generate endogenous growth without this l^war boundary
condition. In this section we will retain all the assumptions regarding the
utility functions in the last section. In the following, unless otherwise
noted, the net production function Is strictly concave and, when capital stock
Increases to Infinity, the net output also Increases to Infinity, but the net
margir-al product of capital can be less than the time discount rate, p:
f''(k) < 0, and f(w)-> w, and f'(w) < p.
From the last section, the optimal conditions regarding the time
path of consumption and capital accumulation can also be written as:
c = {v'(k)/u'(c) + ( f'(k) - p Dam(c) (6)
k = i(k) - c (2)
where mr(c) Is the coefficient of the absolute risk aversion:
o(c) = - u" (c)/u' (c).
10
It Is Immediate from (6) that, if there is no capitalist spirit and v(k)
and v'(k) are zero, we go back to the standard Cass model: in the long run, as
the net marginal product of capital is less than the time discount rate, p,
consumption growth will stop when the net marginal product equals the time
discount rate, i.e., f'(k) = p. All the new endogenous growth models have
tried to "escape" from this rule by modifying the technology such that the net
marginal product of capital is always larger than the time discount rate (the
lower boundary condition). With this lower boundary condition, capital and
consumption will grow for ever.
Due to the existence of capitalist spirit In our model, the lower
boundary condition Is not necessary for unbounded growth of capital and
consumption:
ProposItlon 1: Suppose that f'(k) + v'(k)/u'(f(k)) is larger than the
time discount rate p and k is any value satisfying the inequality:
f'(k) < p. Then consumption and capital will rise for ever.
Proof: In equation (6), if f'(k) a p, the right hand side will be positive and
consumption will rise: c > 0. If ' (k) < p, and suppose that there exists a
steady state, then, from k = 0, f(k) = c, and from c = 0,
v'(k)/u'(f(k)) + [f'(k) - p] = 0 (7)
But equation (7) cannot hold because by assumption, f'(k) + v'(k)/u'(f(k)) > p
for any k satisfying f' (K) < p. So c cannot be zero. The case that c is
negative can be ruled out. This Is because a negative c can happen only If c <
f(k) for any value of k that Is higher than modified golden rule level. In
this case, [v'(k)/u'(c)] is less than [v'(k)/u'(f(k))I for u'(c) > u'(f(k)).
But then, k in (2) will be positive for f(k) > c and capital will increase to
infinity at the same time when consumption keep decreasing. Sooner or later,
the marginal utility of consumption will be significantly higher than the
11
marginal utility of capital (for v'(O) -> 0) and the representative agent's
utility can be raised by reversing this process. Therefore, the only optimal
path Is to have consumption Increase for ever: c > 0. But without an ever
Increasing capital stock, this ever growing consumption Is not sustainable, so
k > 0 always. QED.
Proposition 1 Implies that, to have unbounded growth, It Is essential
to require that, as both consumption and capital Increase to Infinity, the sum
of the net marginal productivity of capital and the marginal rate of
substitution between capital and consumptlon Is larger than the time discount
factor. In particular, if the marginal rate of substitution between capital
and consumption, v'(k)/u'(f(k)), is larger than the time discount rate for all
k such that f'(k) < p, consumption and capital will keep growing even though
the net marginal product of capital can go to zero when capital increases
without bound.
The optimal dynamic path is depicted in the following phase diagram:
c
k =p0
P~~~~~~
c = 0
k
Figure 1: P is the optimal path
In figure 1, both curves are upward slopping because the slope for k = 0 and c
= 0 are positive and are given by [v"(k') + u'(c')f"(k')]/u"(c')[p - f'(k')l
and f'(k''), respectively. Here c' and k' denote the values of consumption and
capital satisfying the equation c = 0, and c" and k" denote the value for k -
0. Given the condition in Proposition 1, there Is no Intersection (i.e., no
steady state) for these two curves. Since both consumption and capital are
12
Increasing, the optimal path, P, is bounded in the region between k = 0 and c
0. Below the curve k = 0, c Is smaller than f(k) and k Is positive; above
the curve c = 0, for given k', c Is larger than the value of consumption, c',
which satisfies that c = 0, so c will be positive as u'(c) is deceasing In c,
c > c', and v'(k')/u'(c) is larger than v'(k')/u'(c').
IV. Two Examples
We first present an example by assuming that the net output is constant
returns to capital as in Barro (1990) and Rebelo (1991):
f(k) = Ak (7)
Just for simplicity, we let the utility functions be:
u(c) logc, v(k) = jllogk
here the parameter l is positive and it measures the capitalist spirit.
To generate endogenous growth In the Barro-Rebelo model, it is essential
to have the net marginal product of capital be greater than the time discount
rate: A > p. This condition can be easily relaxed in our capitalist spirit
model. In fact, let A < p and so f'(k) (= A) < p. Furthermore, for u(c) = logc
and v(k) = Slogk, v'(k)/u'(f(k)) = 1lA. If RA > p though A < p, by Proposition
1, there will be endogenous growth. But since f'(k) equals to A (A > 0) for
all k, we have:
Proposition 2: Let f(k) = Ak and A < p. there will be endogenous growth
if (1 + J)A is larger than the time discount rate p; and the balanced
growth rate, denoted as y, is given by:
I = A - p/(l + 13).
Proof: The current value Hamiltonian is:
H = logc + 1llogk + A (Ak - c)
13
here A Is the costate variable. The optimal conditions are:
=1 (8)
(g/kA) + A - p = - A/A (9)
(A - I/kA) = k/k (10)
Differentiate condition (8) with respect to time and denote the constant
growth rate of consumption as 1,
- A/A = c/c
Substitute I into (9):
kA = V(z + p - A) (11)
Differentiate (11) with respect to time on both sides,
k/k = - A/A =
That is to say, the growth rate of capital on the balanced growth path Is the
same as the growth rate of consumptlon. Substitute k/k = i into (10):
kA = (A - 7) -I (12)
Then use (11) and (12) to solve for the balanced growth rate 7,
,3/(T + p - A) = (A - 7) 1
and
e = A - p/(1 + 0) (13)
To have positive growth rate In (13), A - p/(l + g) needs to be positive,
namely, (1 + J)A > p. From equation (13), the growth rate Is higher if the
spirit of capitalism Is stronger:
dT/djl = p/(l + 1)2 > 0.
Even If technology and the time discount rate are the same across countries,
the growth rates will be different If the capitalist spirit is different.
On the balanced growth path, the saving rate, s, Is
s = k/f(k) = (k/k)(k/Ak) = 7/A = 1 - p/(l+i)A (14)
So the saving rate is an Increasing function of the capitalist spirit:
ds/dir = p/A(1+1)2 > O.
14
As a second example, we let:
f(k) = k and 0 < a < 1 (15)
so f'(k) -> 0 as k -> m. Let u(c) = logc and v(k) = 1lk , then, If Oa > p,
c and k will be positive all the time. To see this, we only need to check that
the condition in Proposition 1 Is satisfied:
v'(k)/u'(f(k)) = Oak k Oa
Thus there exists no steady state if ga > p, and consumption and capital stock
will keep rising.
V. Inflation and Endogenous Growth
The capitalist splrit model provides a convenlent framework to study
money and growth. While the general analysis of a hybrid Kurz-Sidrauski model
can be done, for tractability and simplicity, we will mainly rely on some
specific functions to see how inflation affects the endogenous growth rate.
Again let the technology be the same as in Barro-Rebelo model:
f(k) = Ak.
With money, the wealth accumulation equation becomes:
a = f(k) + x - c - nm = Ak + x - c - rm
a = k + m.
where m stands for the real balances, a for wea.th, x for the government
transfer, and n is the expected inflation rate.
We assume that the representative agent maximizes the following
discounted utility with "the spirit of capitalism" separable from the typical
utility function In the Sidrauski model:
max J[u(c,m) + Rloga]e t dt
0
is
To explicitly calculate the endogenous rate of growth, we let:
u(c,m) = logc + logm.
The optimal conditions are (A Is the costate variable):
A = c1 (16)
A(A + n) = m1 (17)
$(k+m) + A(A - p) = - A (18)
Ak + x - c - lm = k + m (19)
By definition,
m = (E - p/p)m (20)
here 9 is the money growth rate and p is the price level. On the perfect
foresight path, the expected inflation rate equals the actual one:
f = p/p (21)
In addition, the government transfer, x, is just the revenue from Inflation:
x = em (22)
Substituting (20), (21) and (22) into (17), (18) and (19), we obtain:
A =c (16)
m/c = (A + O - m/m)1 (23)
(m + k)/c = (p - A -A/A) (24)
k = Ak - c (25)
In the rest of this section, we focus on a particular solution to the
dynamic system: the balanced growth path. Along this path, all real variables
grow at a constant rate. Let y be the growth rate of consumption, 7 = c/c =
A/A. Differentiate (23) on both sides with respect to time and note that m/m
Is a constant:
mn/m = c/c =
Similarly from (25),
k/k = c/c =
Therefore, on the balanced growth path, consumption, real balances and capital
16
all growth at the same rate, 1.
Next we want to solve the balanced growth rate, 1, In terms of
technology, preference parameters and money growth rate. In (23), (24) and
(25), substitute all the growth rates with the common variable A:
m./c = (A + 0 - )1 (26)
k/c = (A - 7)1 (27)
(m + k)/c = [(p - (A - 7)l (28)
As (26) plus (27) equals (28):
(A + 6 - 7) + (A - ') = 3p - (A - 7)]
Simple algebra leads to
- [(3+1)0 -2p] _ 4[(0+1)e _ 2p]2 + 4(2+g)0p
A v 2(2 + R)
Therefore we have two possible balanced growth rates:
[(fr+1)e -2p] - 4[(1+1)e - 2p]2 + 4(2+0)Op
. = A + 2(2+ 29)
2 (2 +~~~~
ECP+I)e -2p] + 4f1C+1)e - 2p]2 + 4(2+g)Op
2_ = A + 2(2+ ) (30)
In passiag we note that, If the capitalist spirit is not present In the
model, In other words, if 13 = 0, the utility function Is (logc + logm) and
the unique balanced growth rate Is directly given by equations (16) and (18):
7 = A - p
which is exactly the same as the case of the real economy and Is Independent
of Inflation. In this case, to guarantee positive growth, the net marginal
product of capltal has to be larger than the time discount rate (the lower
boundary condition). By the way, we cannot set 1 = 0 In (29) and (30) to get
the balanced growth rate because (29) and (30) are derived with the assumption
17
that 0 > 0.
In (29) and (30), we can show:
Proposition 3: The higher the inflation rate, the higher the balanced
growth rates.
Proof: Differentiate w and 72 with respec. to 9 In (29) and (30):
d - 1 ((+1)0-2p](a+1) + 2(2+13)p
= {(fr.) - (31)
dO 2(2+3) 2
V [((+1)0-2pJ + 4(2+1l)Op
d72 1 [(1+1)0-2pJ(13+1) + 2(2+3)p
_= {(+1) + , (32)
dO 2(2+3) 2
V t($+1)6-2p] + 4(2+i)Op
In the appendix, it is shown that the right hand side of (31) Is positive
and 8a /aO > 0. As the right hand side of (32) Is larger than the one in (31),
072/8e > 0 as well. The possible reason for this result might be the
following: with higher rate of money supply and higher Inflation, the
representative agent tends to substitute real balance holdings with capital.
That will stimulate the rate of Investment and capital accumulation, which In
turn raises the balanced growth rate in the economy. In the end, as the
balanced growth rate goes up, the rise in the rate of money growth does not
bring about a full proportional rise In Inflation rate. To see this, Just look
at the following Identity:
m/m = -n
On the balanced growth paths,
7 = e - n, i = I and 2.
Differentiate this equation with respect to the rate of money growth:
die d7
- = 1 - - <1
dO dO
Therefore, Inflation falls short of the money growth rate.
18
Proposition 3 Is a very strong result. In the Sidrauski model, It Is
well known that lnflation does not affect long-run capital accumulation
(superneutrality of money). When the purchase of both consumption and
Investment goods are subject to the cash-in-advance constraint, Stockman
(1982) has shown a negatlve association between inflation and capital
accumulation. Our capitalist spirit model supports the result derived from the
ad hoc Tobin (1965) model.
Proposition 4: The stronger the capitalist spirit, the higher the
balanced growth rates.
Proof: In equations (29) and (30), differentiate 7 and y2 with respect to
5, and rearrange terms,
1 2
- = - - {(0+2p) + V E(C+1)0-2p] +4(2+8)op -
da3 2 (2+i3)2
(2+0)(1l+1)2
(33)
V [(9+1)0-2p]2+4(2+f3)op
_ 2 = . {(e+2p) - V [(1+1)0-2p]2+4(2+0)op +
do 2(2+g)2
(2+3) ($+1)2
+ (34)
V [(9+1)0-2p]2 4(2+1l)Op
Again (33) and (34) are shown to be positive In the appendix. Thus the
positive association between the spirit of capitalism and economic growth
holds in both real economy and monetary economy.
19
VI. The Empirical Relevance of the Capitalist Spirit Model
It Is interesting to observe tha' we economists tend to explain growth
and development by dealing with capital, labor and technology, while
historians, political scientists and sociologists pay much more attention to
the cultural and other institutional background of growth and development.
That might be the division of labor among intellectuals. Our model is an
attempt to reconcile in part both stories told by economists and other social
scientists.
Since Max Weber published his famous study, "The Protestant Ethic and
the Spirit of Capitalism", there has been tremendous accumulation of
literature on capitalist spirit and Its relation to religions and wealth
creation. Though sociologists and historian (M. Weber, W. Sombart, 1915, R. H.
Tawney, 1926) often argue more about which religious belief leads to
capitalist spirit, the positive link between capitalist spirit and wealth
accumulation has been taken for granted. Recently there are even studies to
provide theological Justifications for the capitalist spirit. For Interested
readers, a good collection is Peter Berger's (1990) "The Capitalist Spirit:
Toward a Religious Ethic of Wealth Creation".
Empirically, recent examples of capitalist spirit approach to growth and
development are numerous. To cite a few, there are Harilson's (1985) study:
Underdevelopment is a State of Mind, Wiener's (1981) work on the decline of
British Industries: English Culture and the Decline of the Industrial Spirit:
1850 - 1980, and MacFarquhar's (1985) study on the four Asian 'miracles' of
South Korea, Taiwan, Hong Kong and Singapore: The Post-Confucian Challenge.
Our economics profession Is not immune from this capitalist spirit
approach. I quote two studies here. The first one Is DeLong (1988). Contrary
to the clalm by William Baumol (1986), DeLong finds that the productivity
levels among once-rich twenty-two countries In 1870 did not converged In 1979.
20
In fact, "holding constant 1870 per capita Income, nation that had Protestant
religious establishments In 1870 had 1979 per capita Income more than
one-third higher than do nations thiat had Catholic estaAiishments". And he
shows that "there Is one striking ex-ante association between growth over
1870-1979 and an exogenous variable: a nation's dominant religious
establishment. ... A religious establishment variable that Is one for
Protestant, one-half for mnixed, and zero for Catholic nations is significantly
correlated with growth as long as measurement error variance is not too high".
Indeed, "it does Eerve as an example of how culture may be associated with
substantial divergence In growth performance". DeLong is not the first
economist to put forward such an argument. Kenrneth Boulding (1973) entitles
one of his Interesting papers as "religious foundations of economic progress",
In which he argues that Protestant ethic has not only Influenced the
development of capitalism, but "the Protestant ethic has contributed to the
success of capltalist Institutions, particularly In regard to their fostering
a high rate of economic progress."(p.45)
The second colorful example is Morishima (1982): Why Has Japan
'Succeeded'?. Under this sensational title, Michio Morishima attributes the
economic success of Japan Into Western technology and Japanese Confucianism.
His approach Is typical Weberian and his comparison between protestant ethic
and Japanese etheos is Illuminating. For modern capitalism to be established,
a religious revolution had to come first. In the Western, "Puritanism's
worldly frugality meant opposition to enjoyment and consumption, and luxury
consumption especially was completely squeezed out, In this way the formation
of capital was carried out through frugality; new capital was then used
productively and became a new source of profit. Thus the religious revolution
resulting from Protestantism created the modern entrepreneur and capitalism -
a new type of person who was the possessor of an earnest faith, and who
21
controlled huge wealth, but nevertheless contended himself with a life of
extreme simplicity, striving to accumulate capital" (pp 83 - 84).
"If the Japanese had not adopted the belief of frugality, which was
another of the prerequisites of capitalJsm, then modern capitalism could
certainly not have been achieved In Japan. In Japan in those days Buddhism and
Shinto, the traditional religions, did not have that great Influence on the
everyday life of the Japanese people. However, ... as a result of the Tokugawa
Bakufu's cultural policy, Confucianism had spread widely and deeply among the
Japanese people. Confucianism was understood In Japan as an ethical system
rather than a religion, and it directly taught the Japanese people that frugal
behavior was noble behavior. Therefore Japan, at the end of the Meiji
Revolution, had already fulfilled the second prerequisite for capitalism"
(p.86).
Japan's story Is not exceptional. Now South Korea, Taiwan, Singapore
and Hong Kong are following the Japanese example. As observed by Roderlck
MacFarquhar (1985), for all these countries, "the significant coincidence Is
culture, the shared heritage of centuries of Inculcation with Confucianism.
That Ideology Is as Important to the rise of the east Asian hyper-growth
economies as the conjunction of Protestantism and the rise of capitalism in
the west." "Post-Confucian economic man works hard and plays hard, buys much,
but saves more".
As another example to Illustrate how change In the capitalist spirit may
affect Industrial growth, we quote from Martin Wiener (1982): English
Culture and the Decline of the industrial Spirit, 1850 - 1980:
For Britain, Wiener argues that, after the Great Exhibition of 1851,
"social and psychological currents began to flow In a different directlon'
(plS7). "The emerging culture of industrialism ... was itself transformed. The
thrust of new values borne along by the revolution In Industry was contained
22
in the later nineteenth century; the social and Intellectual revolution
implicit In industrialism was muted, perhaps even aborted" (p157). "For a
century and a half the Industrialist was an essential part of English society,
yet he was never quite sure of his place. The educated public's suspicions of
business and industry inevitably colored the self-image and goals of the
business community. Industrialists responded to their mental environment,
sometimes by seeking to leave the world of production for more acceptable
realms of gentility, and sometimes by striving to adapt their way of life to
the can-ns of gentility. ... As a rule, leaders of commerce and Industry in
England over the past century have accommodated themselves to an elite
culture blended of preindustrial aristocratic and religious values and more
recent bureaucratic values that Inhibited their quest for expansion,
productivity, and profit" (p.127). The gentrification of the industrialists
discouraged "commitment to a wholehearted pursuit of economic growth" (P.127)
and led to "the waning of the industrial spirit" (P.159) or the capitalist
spirit.
VII. Concluding Remarks
This paper has shown that a strong capitalist splrlt can lead to
unbounded growth of consumption and capital even though the net marginal
product of capital Is less than the tlme discount rate or goes to zero when
capital stock Increases to infinity. In doing this we have relaxed the
technology condition required In many endogenous growth models and at the same
time integrated two approaches to economic growth and development --- the
production technology approach and the cultural approach --- Into a single
model.
While we have mainly focused on the role of capitalist spirit In
23
generating long-run growth, we want to emphasize that our model Is strictly
complementary to many existlag models which have more or less concentrated on
the technology and productivity progress. In fact, as the capitalist spirit
model Just adds a cultural element to the existing models, It can embody all
the contributions by both the traditional growth theory and the new growth
theory. It Is a mistake to totally ignore the cultural elements in economic
growth and development, but it is a blunder to just talk about culture without
putting technology in its right place. This Is why Morishima (1982) explains
the successful story of Japan by two factors: Western technology and Japanese
Confucianism. The balance between culture ind technology should be always
maintained.
24
References
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Barro, R.:"Government Spending in a Simple Model of Endogenous Growth", J. P.
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Berger, P. (ed.):"The Capitalist Spirit: Toward a religious Ethic of Wealth
Creation." Institue for Conyemporary Studies, San Francisco, CA, 1990.
Boulding, K.:"Religious Foundations of Economic Progress", In "Collected
Papers of Kenneth Boulding". Vol. 3, pp.43-51, Colorado Associated
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25
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MacFarquhar, R.:"The Post-Confucian Challenge", In Korea: Past, Present and
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Morishima, M.:"Why Has Japan 'Succeeded'?", Cambridge University Press, 1982.
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1928, pp.543-59.
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26
Appendix
Here we prove Propositions three and four.
For proposition three, we only need to show that the terms In the
parentheses of equation (31) is positive. Suppose not, then:
[C(9+1)0 - 2p](g+1) + 2(2+g)p
+ 1) < (Al)
V [(0+1)O-2p]2 + 4(2+9)6p
For 8 > 0, the numerator on the right hand side of (Al) ls positive, so both
sides are positive. Take square on both sides, and cross multiply:
(9+1) 2{ [(3+1)e-2p 2+4(2+0)op I < { [(($+l)-2p](l+l)+2(2+1)p 2 ()
Expand the expression:
($+1) [(R+l)O-2pI2+(+1)2 (2+9)40p < (+1)2 [((+l)Q-2p] 2+(+l) 2(2+13)40p -
Sp 2(j+0(2+1) + 4p2(2+1) (A3)
Namely,
O < - 8p2(1+1)(2+1l) + 4p2(2+3)2 (A4)
or
O < 4p 2(2+9)(2+1-243-2) (AS)
O < - 4p 2(2+g) (A6)
Inequality (A6) Is a contradiction for both 1 and p are positive, and the
right hand side Is negative. Hence the right hand side of equation (31) is
positive.
Next we show that the terms In the parentheses of equation (33) Is
positive, which Is the same as:
(2+) (3+1)i 2
(0+2p) + V [(Cl+1)0-2p] 2+4(2+9)Op > (A7)
V[((+1)e-2p) 2+4(2+i3)ep
27
Multiply both sides by the positive number V/[(+1)9-2p 2+4(2+1)ep, and
simplify:
(6+2p)V1((+1)0-2p] 2+4(2+1)ep + 4p2 + 46p > (g + 1)02 (AS)
But the left hand side of Inequality (AS) is the same as:
2 2 22 2
(C+2p)v/ (0+1)2 2+4p2+40p + 4p + 40p > (0+2p)(1.+1)9 + 4p + 46p >
> (i + 1)o2 (A9)
which Is Just what we need to prove.
To show that (34) Is positive, we need:
2 - (2+1) (4+)02
V [((l+1)-2pJ +4(2+l)ep < + (0+2p) (AIO)
V[(0+1)09-2p 2+4(2+i)Gp
or:
[((+1)e-2p]2+4(2+ )9p < (2+9)(Sl)92 + (2+2p),/(3+l)G-2p]2+4(2+1l)ep
Cancel terms on both sides:
48p2 + 4p2 < 22 + l2 + (0+2p)-/Ujl+l)9-2pl2+4(2+18)P (All)
This Is definitely true because:
(4p2 + 2 )2 < (0 + 2p) 2 2+ 4p 2 (2+ 40p2 + 4p2)4p 2 42
92 + J32 + (O+2p)V1((l+l)G-2p12+4(2+il)Op )2. (A12)
28
PHIL Wouikinu Paper S
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A,r-e"" "a