Modern Economy, 2011, 2, 416-420
doi:10.4236/me.2011.23046 Published Online July 2011 (http://www.SciRP.org/journal/me)
A Longitudinal Analysis of the Stability of Household
Money Demand
Jan Tin
U.S. Department of Commerce, Washington DC, USA
Received March 15, 2011; revised May 5, 2011; accepted May 20, 2011
Abstract
Past aggregate time-series studies, conducted under the assumption of a representative economic agent, fre-
quently show that the demand for narrowly defined M1, especially non-interest-yielding demand deposit, is
unstable during periods of financial innovations. Whether this is longitudinally the case among life-cycle
savers is unclear. This study utilizes longitudinal data to take another look and find that volatility in the de-
mand for non-interest-earning checking accounts in the mid and late 1990s is attributable solely to the por-
tion held for the transactions motive. When the conventional Baumol-Tobin model is extended to include
human capital and family formation variables representing the life-cycle motive, equilibrium money demand
is a stable function of both economic and demographic variables.
Keywords: Life-Cycle Motive, Money Demand Stability, Longitudinal Data
1. Introduction
A stable money demand or velocity of money in circula-
tion is theoretically a matter of fundamental importance
in order for monetary policies to have predictable im-
pacts on general economic activities, as suggested in the
Keynesian IS-LM framework [20] and the classical
quantity theory of money [16]. Empirical studies on
money demand were mostly conducted within the
frameworks of the inventory-theoretic transactions ap-
proach [12,21] and the asset approach [3]. Before the
1970s, the focus of most time-series studies was on the
relative importance of the scale variables and interest
rate [13]. The focus of cross-sections studies was also on
the relative importance of the scale variables determining
long-run money demand, but the rate of interest was of-
ten omitted from the analysis because of the lack of mi-
cro data [2,5,22,23]. During the 1970s and 1980s, the
discovery of a stable partial dynamic adjustment model
of aggregate money demand [14] and its collapse during
the 1974-1976 and 1979-1982 periods greatly diverted
the attention from both long-run aggregate money de-
mand and cross-sectional studies [1,11,17,18]. In the
post-1990 literature, the attention has shifted to the
search for a stable long-run aggregate money demand
based on the cointegration approach. However, findings
in the early 1990s were inconclusive [6,7,15,25], while
the banking reform and retail sweep programs of the
1994-1999 period have further challenged the existence
of a stable long-run aggregate money demand in the
United States [8-10,19].
Nevertheless, a moment of reflection suggests that
time-series studies are mostly conducted under the as-
sumption of a representative economic agent whose pa-
rametric behavior is presumed to be identical to those of
the underlying individuals with different propensities to
save. At the microeconomic level, equilibrium demand
for money is not only a function of the transactions mo-
tive but also a function of the life-cycle and other mo-
tives, as postulated by Keynes [26]. Volatility in the
quantity demanded for the transactions motive alone may
not necessarily destabilize the overall equilibrium level if
a stable relationship exists between the life-cycle motive
and money demand. In fact, empirical findings in recent
cross-section studies indicate that the life-cycle motive
has an important role to play and that money demand
functions are not homogeneous among money-holders
with divergent socio-economic backgrounds [4,27].
The purpose of this study is to examine the micro-
foundations of aggregate money demand and its stability
during periods of financial innovations by utilizing lon-
gitudinal data within the frameworks of the inven-
tory-theoretic transaction approach and the life-cycle
hypothesis [2]. When data on money demand are free

J. TIN417
from the identification problem and the assumption of a
representative economic agent, findings reveal that the
demand for transactions money balances is longitudi-
nally stable during the 1996-1999 period of banking re-
form and financial innovation. The evidence also sug-
gests that instability in money demand function is largely
related to the omission of a life-cycle motive from the
conventional Baumol-Tobin model.
This paper is organized in the following manner. Sec-
tion 2 discusses the restricted and unrestricted economet-
ric models employed in this study. Section 3 explains
data sources and definitions. Section 4 presents empirical
findings, and a brief conclusion is given in the final sec-
tion.
2. Econometric Model s
Following the literature, the inventory-theoretical trans-
actions model [3,4] widely adopted in past studies [11,
15] can be stated in log-linear form as
lnln ln
ititit it
m = + y + r +

 (1)
where lnmit is the log of real money demand at time t for
individual i, lnyit is the log of real income as a proxy for
total transactions, lnrit is the log of interest rate on an
alternative asset, and εit is an error term representing
omitted variables. The restrictions, β > 0 and θ < 0, are
assumed to hold.
At the macroeconomic level, since money demand,
real income, and interest rate are simultaneously deter-
mined, ordinary least squares (OLS) estimates of income
and interest elasticities are likely biased and may even be
spurious. In past studies, the difficulty is usually over-
come by employing cointegration techniques such as the
stationarity and cointegration tests. At the microeco-
nomic level, since income and prices are predetermined
cointegration techniques cannot be easily applied. Ne-
vertheless, OLS estimates of income and interest elastic-
ities in the standard Baumol-Tobin model may still be
biased, because, according to the life-cycle hypothesis
[9], human capital and family formation variables not
only have direct impacts on the quantity of saving held in
the form of monetary assets but also interact with real
income and time preference. In order to obtain unbiased
estimates, human capital and family formation variables
representing the life-cycle motive must be separated
from the error term [27]. Rewriting equation (1) gives
lnln ln
itititit it
m = + y + r +D+

 (2)
where Dit is a vector of demographic variables with the
corresponding set of parameters, γ/, and it

is an error
term with zero mean and constant variance. If γ = 0,
Equation (2) reduces to Equation (1) or its aggregate
economic agent. In order to facilitate the analysis, Equa-
tions (1) and (2) will be referred to as the simple model
and the life-cycle model, respectively, whenever appro-
priate.
Econ
counterpart under the assumption of a representative
ometrically the simple or life-cycle model per se
ca
i
i
nnot be used to test the stability of money demand
unless it is disaggregated into individual components for
each of the underlying cross-sectional time periods. Un-
restricting Equation (2) gives
111 11
lnln ln m = + y + 111 1
222 22222 2
ln ln ln
lnln ln
iiii
iiii
iTTTiTTiTTiTiT
r +D+
m = + y+ r+D+
m = + y + r+D+










(3)
Subscripts 1, 2, and T stand for the first, second, and
the final survey periods, respectively. If 12






0
T



, equation (3) reduces to its unrestr
r the simple model. Based on the restricted and
unrestricted models, the hypothesis of a stable money
demand can be tested by Chow statistics derived from
the sum of squared residuals and the associated degrees
of freedom.
icted coun-
terpart fo
3. Data Sources and Definitions
The 1996 panel of the Survey of Income and Program
cy are not available in SIPP,
m
Participation (SIPP) conducted by the United States Bu-
reau of the Census from 1996 through 1999 is the pri-
mary source of data for this study. The 1996 SIPP panel
is selected mainly because it contains time-series
cross-sections data on financial assets, household income,
and demographic variables and enables this study to
examine the stability of money demand during the
1996-1999 period of financial innovations. Longitudinal
data for the entire 1996-1999 period are constructed by
merging data in the core and topical modules of waves 3,
6, 9, and 12 for those who are 15 years of age or over.
Structural breaks of the 1974-1976 and 1978-1982 peri-
ods cannot be examined in this study because of the lack
of SIPP data. Likewise, data for 1995 are not available in
SIPP and must be excluded from regression analysis.
Although the 1993 SIPP panel contains data on financial
assets in 1994, the samples are not the same as those in
the 1996 SIPP panel. Consequently the two panels can-
not be combined together for regression analysis. In
general SIPP is a short panel with different samples and
sample sizes in different panels which cannot simply be
combined together to obtain a workable longitudinal file
with more time-periods and observations. Real quanti-
ties are obtained by deflating nominal quantities by the
Consumer Price Index (CPI) compiled by the U. S. Bu-
reau of Labor Statistics.
Since data on curren
oney demand is narrowly defined as non-interest-

J. TIN 418
4. Regression Results
Restricted and unrestricted OLS regression results for the
stimates of interest elas-
tic
ddition to the indirect impacts of the life-cycle
m
5. Conclusions
Intuition suggests that human capital and family forma-
earning checking accounts possessed by householders in
their own names or jointly with spouses. The rate of in-
terest is measured by the ratio of gross return on inter-
est-earning checking accounts, regular or passbook sav-
ings, money market deposits, and certificates of deposit
to the gross amount of these assets. Household income is
measured by the sum of labor and nonlabor incomes.
Labor income consists of wages, salaries, and self-em-
ployment income, while nonlabor income is the sum of
interests and dividends from financial assets, retirement
incomes, Social Security income, government transfers,
and other types of income. A householder is defined as a
reference person in whose name the home is bought or
rented. In this study, the life-cycle motive is measured
by age, age squared, education, marital status (Married =
1; 0 otherwise), number of children (with children = 1; 0
otherwise), gender (female = 1; 0 otherwise), and race
(African American = 1; 0 otherwise).
simple and life-cycle models are reported in Table 1.
Income elasticity is positive and significant at the 1%
level in each regression of the simple and life-cycle
models. In the simple model, the longitudinal estimate of
income elasticity for the entire 1996-1999 period is ap-
proximately 0.21, about eight-percentage points smaller
than the 0.29 in the life-cycle model. This means that a
rise real income by 100% would raise money demand by
about 29% in the life-cycle model and only 21% in the
simple model. Similarly cross-sectional estimates of in-
come elasticity in 1996, 1997, 1998, and 1999 in the
simple model are considerably smaller than their coun-
terparts in the life-cycle model. More specifically,
cross-sectional estimates in the simple model range from
0.19 in 1998 to 0.22 in 1996 or 1997, whereas
cross-sectional estimates in the life-cycle model range
from 0.28 in 1998 to 0.31 in 1999. Within the simple
model, the longitudinal estimate is somewhat smaller
than the cross-sectional estimates in 1996 and 1997. It is,
however, about two-percentage points greater than the
estimate in 1997 and is quite similar to the estimate in
1999. For the life-cycle model, the longitudinal estimate
is smaller than the 1996 or 1999 estimate but greater than
the estimates in 1997 and 1998.
As predicted by the theory, e
ity are negative in all regressions and significant at the
5% level in nearly all regressions. Longitudinal estimates
in the simple and life-cycle models are –0.05 and –0.04,
respectively. A rise in the rate of interest on near monies
by 100% would therefore raise money demand by about
5% in the simple model and 4% in the life-cycle model.
Cross-sectional estimates for 1996, 1998, and 1999 in the
simple model are greater than their counterparts in the
life-cycle model in absolute terms. However, the esti-
mates in 1997 are not significantly different from zero at
the 5% level in both models. For the simple model, the
longitudinal estimate is smaller than the cross-sectional
estimate in 1996 or 1998 but greater than the cross-sec-
tional estimates in 1997 and 1999. For the life-cycle
model, the longitudinal estimate is somewhat smaller
than the cross-sectional estimates in 1996 and 1998 but
greater than the cross-sectional estimates in 1997 and
1999.
In a
otive on money demand via its interaction with income
and interest rate, human capital and family formation
variables also exert direct impacts on money demand.
Qualitatively the coefficients of age and age squared are
opposite in sign, indicating that the demand for narrow
money initially declines with age, reaches a minimum,
and then rises. Money demand increases with education.
Married people hold less and spend more than those who
are separated, divorced, widowed, or never married.
Households with the presence of children spend more
than those without any children. Women hold less than
men. African Americans tend to spend more than Whites.
Quantitatively the coefficient of marital status is largest
in magnitude, followed by the coefficients of race, chil-
dren, gender, education, age, and age squared in absolute
terms. Judging from the relatively large magnitudes of
most demographic variables, the strength of the relation-
ship between money demand and the life-cycle motive is
quite strong. More importantly, the value of Chow statis-
tic for the simple model is substantially greater than the
critical value at the 1% level. The hypothesis of a stable
money demand is evidently rejected. In contrast, the hy-
pothesis cannot be rejected for the life-cycle model, be-
cause the value of Chow statistic falls far short of the
critical value at the 1% level. Values of R squared also
indicate that the life-cycle model outperforms the simple
model.
tion variables change gradually over time, whereas eco-
nomic variables, especially income and interest rate, may
be quite volatile during periods of financial innovations
and economic shocks. Indeed, findings in this study re-
veal that estimates of income and interest elasticities in
the United States are not only volatile but also biased in
the simple model during the mid and late 1990s. How-
ever, when the life-cycle motive is explicitly captured by
the simple model, the demand for non-interest-earning

J. TIN 419
stricted mode ls with and without the life-cycle motive.
Simple model Life-cycle model
Explanatory
Table 1. OLS regression results for restricted and unre
Variables 1996-1999 1996 1997 1998 1999 1996-9991996 1997 1998 1999
Constant 0.0125 -0.0850 0.0971 –0.06810.0971 –2.9809***–0.3289***–2.7520*** –3.1188***–2.7789***
1
(0.26) (0.73) (0.96) (0.77) (1.12) (18.23) (9.77) (8.74) (9.53) (8.11)
Real income 0.0.0.0.0.21010.0.0.0.0.
Rate of –0.0523*** –0.0649*** –0.0275* –0.0742***–0.0420***–0.0350*** –0.0428***–0.0097 –0.0613***–0.0239***
7.70) (3.72) (1.81) (6.02) (3.51) (5.33) (2.54) (0.66) (5.13) (2.06)
Age –0.*–0.–0.–0.*–0.
Age squared 0.0.0.0.0.
(8.01) (3.31) (3.64) (4.79) (3.93)
Education 0.0.0.0.0.
(24.18) (11.74) (12.01) (12.99) (11.71)
Married –0.*–0.*–0.* –0.*–0.*
Children –0.*–0.*–0.* –0.*–0.*
Female –0.*–0.*–0.* –0.*–0.*
Afr–0.*–0.*–0.* –0.*–0.
Am
4.88*** 0.97
R0.0184 0.0193 0.0189 0.0186 0.0181 0.0836 0.0861 0.0809 0.0842 0.0861
Number of 28,375 6,059 7,419 7,472 7,425 28,375 6,059 7,419 7,472 7,425
2113*** 2177*** 2247*** 1947******2949***2951***2916*** 2835*** 3067***
(21.43) (10.27) (11.80) (9.91) (10.93) (27.08) (12.58) (13.91) (12.98) (14.52)
return
(
0145**0096 0117* 0209**0156*
(3.86) (1.30) (1.67) (2.72) (1.86)
0003***0002***0002*** 0003*** 0003***
0793***0826***0766*** 0831*** 0761***
4443**4299**4393**4292**4747**
(19.49) (9.03) (10.02) (9.55) (10.35)
1861**2058**1709**1789**2024**
(8.20) (4.41) (3.96) (3.96) (4.28)
1751**1922**2159**1309**1663**
(8.75) (4.58) (5.60) (3.33) (4.14)
ican 2017**2726**2659**1857**1349*
erican (5.48) (3.21) (3.64) (2.62) (1.94)
Chow
statistic
squared
observations
Notes are in parentheses, * denotes statistical significance at 10% level, ** denotes statistical significance at 5% level, and *** denotes statistical
hecking deposits becomes a stable function of economic
ation is that past aggregate
tim
ties. If these findings can serve as a useful guide during
: t-statistic
significance at 1% level.
c
and demographic forces.
One important implic
e-series studies might have erred for neglecting the
stabilizing effects of human capital and family formation
variables on the demand for narrow money which is
mainly held by households as normal goods or necessi-
periods of financial innovations, the impact of monetary
policy on the economic activities of households may not
be as unpredictable as those suggested in past time-series
studies. In formulating monetary policies, however, de-
cision-makers ought to consider not only the volatile
relationship between money demand and the transactions

J. TIN 420
those of the author and do
not reflect those of the Commerce Department or the
Mr. Keynes and the Classics―A Suggested
Interpretation,” Econometrica, Vol. 5, No. 2, 1937, pp
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motive on money demand both directly and indirectly via
real income and interest rate.
6. Acknowledgements
The views expressed here are
Census Bureau.
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