Social Status and the Growth Effect of Money
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HungJu Cheny
JangTing Guoz
National Taiwan University
University of California, Riverside
November 7, 2007
Abstract
It has been shown that in a standard onesector AK model of endogenous growth with
wealthinduced preferences for social status, the economy’s growth rates of real output
and nominal money supply are positively related when the cashinadvance constraint is
applied solely to the household’s consumption purchases. However, a positive output
growth e¤ect of money/in‡ation is not consistent with the existing empirical evidence. We
show that when gross investment must be …nanced by real money balances as well, this
result is overturned, i.e. higher in‡ation is detrimental to economic growth, because of a
dominating portfolio substitution e¤ect.
Keywords: Social Status, Endogenous Growth, CashinAdvance Constraint.
JEL Classi…cation: E52, O42.
We would like to thank ChingChong Lai and Richard Suen for helpful discussions and comments. Part of
this research was conducted while Guo was a visiting professor of economics at the National Taiwan University,
whose hospitality is greatly appreciated. The …nancial support provided by the Program for Globalization
Studies at the Institute for Advanced Studies in Humanities at the National Taiwan University (grant number:
95R0064AH0303) is gratefully acknowledged.
yDepartment of Economics, National Taiwan University, 21 HsuChow Road, Taipei 100, Taiwan, 8862
23519641, ext. 457, Fax: 886223511826, Email: hjc@ntu.edu.tw.
zCorresponding Author: Department of Economics, 4128 Sproul Hall, University of California, Riverside,
CA, 92521, USA, 19518271588, Fax: 19518275685, Email: guojt@ucr.edu.
1
Introduction
Recently, there has been a growing literature that examines the macroeconomic e¤ects of
wealthinduced preferences for social status within dynamic general equilibrium models.1 This
is a valuable research subject not only for its theoretical signi…cance, but also for its wide
ranging policy implications on promoting economic growth or improving social welfare. In the
existing literature, Chang, Hsieh and Lai (CHL, 2000) show that in a prototypical onesector
AK model of endogenous growth where the representative household derives utilities from
consumption as well as from its ownership of physical capital in the loglog speci…cation, the
economy’s growth rates of real output and nominal money supply are positively related when
the cashinadvance (CIA) or liquidity constraint is applied solely to consumption purchases.2
However, the result of a positive outputgrowth e¤ect of money (or in‡ation) is not consistent
with numerous empirical studies. For example, using randome¤ect regressions on two panel
data sets of 170 countries from 1960 to 1992, Gylfason and Herbertsson (2001) present strong
and robust evidence that higher in‡ation is detrimental to economic growth at all income
levels, both across countries and over time. Moreover, the same empirical …nding has been
obtained by other researchers such as Levine and Renelt (1992), Roubini and SalaiMartin
(1992), De Gregorio (1993), Barro (1995), Bruno and Easterly (1998), and Rousseau and
Wachtel (2001), among many others.
Motivated by this inconsistency with international data, the CHL model is modi…ed along
two dimensions in our analysis. First, we consider a generalized CRRA utility function where
the inverse of the intertemporal elasticity of substitution in both consumption and capital
can be less than one. Second, in addition to consumption goods, the entire expenditures of
gross investment are also subject to the CIA constraint (Stockman, 1981). We show that un
der Stockman’s liquidity formulation, CHL’s …nding of a positive relationship between output
growth and money/in‡ation is overturned, regardless of the coe¢ cient of relative risk aver
sion in the household utility. Intuitively, the growth e¤ect of money depends crucially on the
relative strength of two opposing forces dubbed as the portfolio substitution e¤ ect (from real
balances to capital) and the intertemporal substitution e¤ ect (from consumption to invest
ment). When money holdings are required for all the consumption and investment purchases,
1 See, for example, Zou (1994, 1998), Bakshi and Chen (1996), Corneo and Jeanne (1997, 2001), Gong and
Zou (2001), Chang and Tsai (2003), Clemens (2004), and Fisher and Hof (2005), among many others.
2 Under the consumptiononly liquidity constraint, it is well known that money is “superneutral” in the
growthrate sense when households have no desire for social status.
1
an increase in the monetary growth rate leads to a dominating portfolio substitution e¤ect,
which in turn raises the relative shadow price of capital and reduces its net rate of return. As
a consequence, the economy’s output growth rate will fall, thus producing a negative growth
e¤ect of money/in‡ation that exhibits strong empirical support.
2
The Economy
We incorporate a generalized CRRA preference formulation and Stockman’s (1981) cashin
advance constraint into the onesector AK model of endogenous growth with wealthenhanced
social status developed by Chang, Hsieh and Lai (CHL, 2000, section 4). Moreover, partial
capital depreciation is considered for completeness of the analysis. To facilitate comparison, we
maintain all other features as in CHL, including the assumption that the household’s wealth
does not consist of real money balances, and follow their notation as much as possible.
The economy is populated by a unit measure of identical, in…nitelylived households. Each
household provides …xed labor supply and maximizes its discounted lifetime utility
c1
k1
U = Z 1 t
1 + t
1 e tdt; > 0;
1;
(1)
0
1
1
where ct and kt are the individual household’s consumption and capital stock, respectively, and
2 (0;1) denotes the time discount rate. In addition to consumption goods, the household
derives utilities from its social status represented by the level of capital ownership, and the
parameter
measures the degree for “the spirit of capitalism”.3
On the other hand, to
guarantee the existence of a balancedgrowth equilibrium, we require that consumption and
capital possess the same inverse of the intertemporal elasticity of substitution . Based on the
empirical evidence for this preference parameter in the mainstream macroeconomics literature,
the restriction of
1 is imposed. Notice that CHL restrict their analysis to the speci…cation
with
= 1, thus the household utility is logarithmic in ct and kt.
The budget constraint faced by the representative household is given by
ct + it + _
mt = yt
tmt +
t;
(2)
where it is gross investment, t is the in‡ation rate, mt denotes the real money balances that
are equal to the nominal money supply Mt divided by the price level Pt, and t represents
3 All the results in this paper are qualitatively robust to the modi…cation that introduces the relative (not
the individual) wealth kt , where K
K
t the economywide level of capital stock, to the household’s utility function
t
(1).
2
the real lumpsum transfers that households receive from the monetary authority. Moreover,
output yt is produced by the technology
yt = Akt; A > 0;
(3)
and the law of motion for the capital stock is
_kt = it
kt; k0 > 0 given,
(4)
where
2 [0;1] is the capital depreciation rate.
As in Stockman (1981), the representative household also faces the following cashin
advance (CIA) or liquidity constraint:
ct + it
mt;
(5)
that is, all consumption and investment purchases must be …nanced by the household’s real
balances mt. Notice that when
= 1, together with
= 0 and the consumptiononly liquidity
constraint ct
mt, we recover the model that CHL have analyzed.
The …rstorder conditions for the representative household with respect to the indicated
variables and the associated transversality conditions (TVC) are
ct :
ct = mt + t;
(6)
it :
kt =
mt +
t;
(7)
kt :
_ kt = ( + ) kt
kt
A mt;
(8)
mt :
_ mt = ( + t) mt
t;
(9)
TVC1 :
lim e
t ktkt = 0;
(10)
t!1
TVC2 :
lim e
t mtmt = 0;
(11)
t!1
where mt and kt are the shadow prices (or utility values) of real money balances and physical
capital, respectively;
t denotes the Lagrange multiplier associated with the CIA constraint
(5) that is postulated to be strictly binding in equilibrium. Equation (6) equates the marginal
bene…t and marginal cost of consumption, which is the marginal utility of having an additional
unit of real dollar. In addition, equations (7) and (8) together govern the evolution of physical
capital over time, where the term
kt
represents the marginal utility bene…t of capital
accumulation. Finally, equation (9) states that the marginal values of real money holdings are
equal to their marginal costs.
3
We postulate that the nominal money supply is growing at a constant rate
> 0, hence the
resulting seigniorage returned to households as lumpsum transfers are t = mt. Furthermore,
clearing in the goods and money markets imply that
ct + it = yt;
(12)
and
_
mt = (
t) mt:
(13)
3
Balanced Growth Path
As in CHL, we focus on the economy’s balanced growth path (BGP) along which output,
consumption, physical capital and real money balances all grow at a common positive rate
denoted as g. To facilitate the subsequent dynamic analyses, we adopt the following variable
transformations: p
kt
ct
t
and zt
. With these transformations, the model’s equilibrium
mt
kt
conditions can be rewritten as the following autonomous dynamical system:
_
pt
A
= pt
z
p
t
zt + A
1;
(14)
t
pt
_zt
1
A
=
+ z
z
t
A +
+ zt:
(15)
t
pt
Therefore, a balancedgrowth equilibrium is characterized by a pair of positive real numbers
(p ; z ) such that _
pt = _zt = 0. It is straightforward to derive from (14) and (15) that p is the
solution to the quadratic equation
A
p =
+
(z ) + z +
+ 1
A
f (p ) ;
(16)
p
and that
dz
A
=
dp
(p )2 h1+ (z ) 1i > 0:
(17)
To examine the existence and number of the economy’s balanced growth path(s), we …rst
note that equilibrium p can be found from the intersection(s) of f (p ) in (16) and the 45
degree line. Moreover, using dz from (17), we obtain that
dp
A (1
)
f 0(p ) =
(p )2 h1+ (z ) 1i 5 0 when = 1;
(18)
4
and
82 f0(p )h(z ) 2i9
f 00(p ) =
f 0(p ) <
= 0 when
= 1:
(19)
:
=
p
1 +
(z )
1
positive
;
As a result, f (p ) is either a dow 
nward
{z
sloping and concave}curve (when
> 1) or a horizontal
line (when
= 1) that intersects the 45degree line once in the positive quadrant. It follows
that there exists a unique balanced growth path in our model economy.
In terms of the BGP’s local dynamics, we compute the Jacobian matrix J of the dynamical
system (14) and (15) evaluated at (p ; z ). The trace and determinant of the Jacobian are
given by
A
T r
= p +
+
(z ) + z > 0;
(20)
p
A (1
)
9
Det = p z h1+ (z ) 1i8<1
> 0:
(21)
:
=
(p )2 h1+ (z ) 1i
[1 f0(p )] > 0
;

{z
}
The local stability properties of the BGP equilibrium is determined by comparing the eigen
values of J that have negative real parts to the number of initial conditions in the dynamical
system (14)(15), which is zero because pt and zt are both jump variables. It turns out that
our model’s Jacobian matrix possesses a positive trace and a positive determinant (see equa
tions 20 and 21), indicating the presence of two eigenvalues with positive real parts, hence the
economy’s balanced growth path exhibits saddlepath stability and equilibrium uniqueness.
4
Growth E¤ect of Money
In this section, we derive and examine the analytical expression that governs the output
growth e¤ect of money or in‡ation.4 Combining (3), (4) and (12) yields the common rate of
economic growth g as follows:
g = A
z ;
(22)
4 On the balanced growth path, its in‡ation rate
is ceteris paribus positively related to the monetary
growth rate
because equation (13) implies that
=
+ g.
5
thus the BGP’s growth rate is negatively related to the transformed state variable z
dg < 0 .
dz
We then take total di¤erentiation on (22), and use the chain rule together with (16), (17) and
(18) to …nd that the growth e¤ect of money/in‡ation is given by
dg
dg dz
dp
=
;
(23)
d
dz
where
{z}dp d
( ) {z}
(+)
dp
(p )2 h1+ (z ) 1i
1
=
=
> 0:
(24)
d
(p )2 h1+ (z ) 1i+( 1)A 1 f0(p )
It follows that in contrast to CHL, our model economy displays a negative relationship between
the BGP’s output growth and money/in‡ation
dg < 0 . This result turns to be consistent
d
with the international evidence reported in Gylfason and Herbertsson (2001), and many other
empirical studies mentioned in the Introduction.
Generally speaking, within dynamic general equilibrium macroeconomic models, the sign
for the growth e¤ect of money depends crucially on the relative strength of two opposing forces.
On the one hand, a rise in the monetary growth rate
leads to a higher in‡ation, which in
turn raises the cost of money holdings. As a result, the representative household substitutes
out of real balances and into physical capital (the portfolio substitution e¤ect). This will
cause an increase in the relative shadow price of capital p because of a higher demand,
thereby reducing its net rate of return and thus the BGP’s growth rate. On the other hand, a
higher monetary growth rate
ceteris paribus induces the representative household to consume
less and invest more today in exchange for higher future consumption (the intertemporal
substitution e¤ect).5 This expands the supply of physical capital, hence reducing its relative
shadow price p . In addition, agents’ statusseeking motive further strengthens this supply
e¤ect through additional capital accumulation (see the term
kt
in equation 8). It follows
that the economy’s output growth rate will rise. Our preceding analysis shows that when
consumption and gross investment are both liquidityconstrained, the BGP’s output growth
and money/in‡ation are inversely related
dg < 0 in that the portfolio substitution e¤ect
d
outweighs the intertemporal substitution e¤ect.
5 Using (3), (4), (12) and (13), it is straightforward to show that t =
A + zt + . Therefore, holding
the in‡ation rate constant, an increase in
leads to a lower consumptioncapital ratio zt. This requires an
intertemporal substitution from current to future consumption, thus raising today’s investment.
6
By contrast, CHL show that when
= 1 and the CIA constraint is applicable only to
the purchases of consumption goods, status preference generates a dominating intertemporal
substitution e¤ect (from consumption to investment) in response to an increase in . Therefore,
the net rate of return on capital will rise because of a decline in its relative shadow price. This
in turn leads to a positive relationship between the growth rates of real output and nominal
money supply
dg > 0 , a result that is not consistent with the existing econometric evidence.6
d
5
Conclusion
We have examined the interrelations between wealthinduced preferences for social status, the
formulation of the cashinadvance constraint, and the outputgrowth e¤ect of money/in‡ation
within the context of a standard AK model of endogenous growth. It turns out that in
contrast to CHL, when real balances are required for all the purchases of consumption as well
as investment goods, the economy’s growth rates of real output and nominal money supply are
inversely related due to a dominating portfolio substitution e¤ect, regardless of the coe¢ cient
of relative risk aversion in the household utility. This result of a negative growth e¤ect of
money/in‡ation is strongly supported by the empirical evidence.
6 It can be easily shown that this “positive relationship” result continues to hold when
> 1.
7
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8