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The stability of the demand for money and M1 velocity: Evidence from the sectoral data
The Quarterly Review of F.conomics and Wnance, Vol. 35, No. 3, Fall, 1995, pages 233-243 Cop-t 0 1995 Trustees of the Universityof Illinois AU lights of reproduction in any form reserved.
ISSN 0033-5797
The Stability of the Demand for Money and Ml Velocity: Evidence from the Sectoral Data JAMES L. BUTKIEWICZ University
of Delaware
MARGARET MARY MCCONNELL Ohio State University
Sectoral monqr demandfunctions relationships
are found
fw
are estimated usingflw
household
and
offunds
(nonfinancial)
data. Cointegrating
business sectors. Estimated
error-correction moak!s for both sectors, however, exhibit parameter nonconstancy for time @riook which roughly correspond with importantfinancial Thus, sectoral estimates of monq innovations
innovations and deregulations.
demand relationships are consistent with the view that
and deregulation contribute to the nonstationatity of Ml velocity.
The apparent nonconstancy of the parameters of the aggregate Ml demand function for the U.S., and the corresponding deterioration of the relationship between money and aggregate output is one of the most extensively examined macroeconomic phenomena of recent years. Studies examining the demand for money and/or stationarity of velocity include those by Brocato and Smith (1989)) Carlson (1989)) Dickey, Jensen and Thornton (1991)) Friedman (1984), Goldfeld (1976)) Hall and Noble
(1987),
Hendry and Ericsson
(1991),
Mascar and Meltzer
(1983),
Mehra
(1989), Melnick (1990), Miller (1991), and Rasche (1987), while Friedman and Kuttner (1992) have examined the decline in the relationship between money and income. The majority of studies conclude that there is no stable Ml demand function, but the existence of a stable M2 demand function is supported by the data.’ Typical explanations for the breakdown of Ml demand include changes resulting from disinflation, deregulation and financial innovations, and uncertainty due to increased volatility of monetary policy. This paper presents the results of another look at the demand for Ml. The approach used is unique in that the data set is the Federal Reserve’s flow of funds data disaggregated by sectors. The methodology used is the Engle-Granger (1987) approach of estimating error correction models for cointegrated relationships.
234
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
Hendry and Ericsson (1991) use this approach to estimate money demand functions (M2) for the UKand Miller (1991) uses the same approach for U.S. money demand. While Dickey, Jensen and Thornton
(1991) note that the Engle/Granger
is sensitive to the order of normalization, approach finds evidence of cointegration obtained
from the maximum
Juselius (1990).
, the cointegrating
likelihood
approach
of nonfinancial
vector is similar to that
developed
In fact, we find that the Engle/Granger
gration for all three normalizations normalizations
approach
they also find that when the Engle/Granger by Johansen
and
approach supports cointe-
of household Ml demand, and for two of three
business demand for Ml. We also find that the scale
and interest rate variables in the cointegrating regressions differ between the house hold and business sectors as do estimated elasticities. This suggests that aggregation across sectors which respond in different magnitudes to different measures of transactions
and opportunity costs may obscure long-run relationships.
Finally, the
sectoral models indicate that instability of Ml demand in the 1960s and 1970s emanated primarily from the business sector, while in the late 1970s and 1980s the source of instability was the household sector. One explanation
consistent with this
pattern of instability is that it is the result of financial innovation and deregulation. Alternatives to holding checking deposits developed first for businesses in the form of repurchase agreements and Eurodollar
deposits. Money market mutual funds and
other alternatives to checking balances became available to households in the 1970s and the 1980s.’ Part I of this paper reviews the flow of funds ownership data, the Goldfeld study of sectoral Ml demand, and discusses briefly updated results of this approach. The methodology of the Engle/Granger error correction model and the necessary pretests are discussed in Section II. Estimated results for the household and nonfinancial business sectors are presented
in Section III. The implications
of the esti-
mates for parameter constancy, including the widespread use of dummy variables in money demand models, are discussed in Section IV Concluding comments are made in Section V.
I.
FLOW OF FUNDS DATA AND THE GOLDFELD STUDY
This study examines the demand for Ml using the flow of funds estimates of sector-al ownership of Ml. The flow of funds ownership data differs in several ways from aggregate monetary data (Federal Reserve Board, 1971). Ml data are averages of daily data, while flow of funds data are end-of-month point estimates. The flow of funds data include balances held by Edge Act corporations and agencies of foreign banks in the U.S. in financial sector balances. Mail float is not included in any sector, but the Fed (1971, p. 464) suggests that mail float is largely comprised of deposits of the business sector, and Goldfeld (1973) includes mail float in the business sector estimates3
DEMAND FOR MONEY AND Ml VELOCITY
235
Goldfeld ‘s (1973) classic study of money demand includes estimation of models for the household, financial, (nonfinancial)
business (including mail float), and state
and local government sectors. Holdings by the “rest of the world” are not examined. The estimates
are obtained
using the partial-adjustment
specification,
which is
frequently called the Goldfeld model of money demand: In($),
= clo + clrln Y,, - a&r,
+ a&($-r
+ El,
S=1,...,4.
(1)
In = the natural logarithm of a variable, where: (M, /p) = the real Ml balances for each of the sectors except finance where nominal levels are used,4 Y, = a measure of transactions for each sector, r = an opportunity cost measure, and E = a random error. All of his estimated equations used a correction for first-order serial correlation. Goldfeld reported that the household and financial sectors were well explained by the model, while the results were not satisfactory for the other two sectors. As a preliminary to estimating cointegrating regressions and error correction models, we reestimated Goldfeld ‘s equations using data from the third quarter of 1952 through the first quarter of 1990.5P6 Also, we experimented with various scale and interest rate variables. The estimates are tested for coefficient constancy for various subsamples. Using Chow tests, the hypothesis of coefficient constancy is rejected for all sectors when the sample is divided at the fourth quarter of 1979. This evidence of nonconstant parameters is the same problem that plagues the aggregate money demand estimates using the partial adjustment model. As is true for aggregate money demand modeling, alternative approaches may provide greater insight into sectoral money demand.
II.
COINTEGRATION
Recent
AND ERROR CORRFXXION MODELS
advances in econometric
techniques
have established
the importance
of
testing for cointegrated relationships. If economic series must be differenced one or more times to obtain stationarity, they are said to be integrated of order d, where d is the number of differences required to obtain stationarity of the series. If one or more series are integrated of the same order, they may follow a common trend. If the residual from a regression of one of these series on the others is integrated of order d- b, where b > 1, the series are said to be cointegrated, and they follow a common trend. Before testing for cointegration, it must be established that all series are integrated of the same order. Augmented Dickey-Fuller tests are reported in Table 1 for
236
QUARTERLY
REVIEW
Table 1.
AUGMENTED
(Sample
1952.4-1990.1)
OF ECONOMICS
AND FINANCE
DICKEY-FULLER TESTS FOR UNIT ROOT
Variable
1st Difference
2nd Difference
In Household Real Ml (LRH)
-2.11
-7.77**
In Business Real Ml (LRB)
-1.03
-8.95**
In State and Local Government Real Ml (LRSL)
-1.76
-9.79**
0.95
-7.82**
In Real Disposable Personal Income (LRDPI)
-1.84
-6.14*+
In Real GNP (LRGNP)
-2.69
-6.67**
In Real State and Local Government Expenditures (LRSLX)
-1.34
+.68**
0.91
-9.36**
In Smonth Treasury Bill Rate (LTBJ)
-2.84
-6.34**
Smonth Treasury Bill Rate (TB3)
-2.73
+.45**
Financial Ml (FIN)
Deposits (DEP)
first and second differences
of all variables used in the models. In all cases, the tests
fail to reject the null hypothesis of a unit root for first differences, hypothesis of a unit root for second differences. As all variables are integrated of order one, cointegrating
but reject the null
regressions are run to
determine if long-run relationships exist among sets of variables that would be included in a money demand model. Engle and Granger (1987) recommend using the augmented Dickey/Fuller test to test for cointegration. The tests indicate cointegration of real household Ml (LRH), real disposable personal income, and the Treasury bill rate, all in logarithms, for all three normalizations.’ These results are reported in Table 2. Table 2 also reports the results of cointegrating regressions for the logarithm of real business money holding (LRB), the logarithm of real GNP, and the level of the three-month cointegration
Treasury Bill rate. ADF tests support the hypothesis of
for two of the three normalizations.
Tubb 2.
COINTEGRATING
(Sample
1952.1-1990.1) Household
No evidence of cointegration
REGRESSIONS Business Sector
Sector
Cointegrating Vector
Cointegrating Vector 1 LRH LRDPI LTB3
2
3
1
-1.27
2.3
-0.6
1
-2.57
0.103
ADF
-3.5*
NOMS: *Rejects **R+crs Augmented
-0.243
1
-4.8**
A.8**
1 LRB
1
LRGNP TB3
0.044 -3.9*
null hypothesis
of unit root in residual
at 5 percrnt
level ofconfidence.
null hypothesis
of unn root in residual
at 1 prrcen~
level ~Cconfidcnce.
tc~ts for coinleg?arion
use four lagged
Dickq-Fuller
-0.072
difTcrence
w”ns.
2
3
-0.477
12.03
1 -0.103
-4.26
-2.5
-5.o**
1
is
237
DEMAND FOR MONEY AND Ml VELOCITY found for various specifications business sectors account
for other sectors.
for 83 percent
estimation of error correction
However, the household
of all sectoral
holdings
and
in 1990. Thus,
models for these two sectors will provide insight into
the aggregate behavior of Ml.
III.
ERROR CORRECTION
MODELS OF SECTORAL HOLDINGS
Error correction models allow for flexible specification of short-run dynamics while obeying the long-run constraints implied by the existence of cointegration. Specifically, error correction models are vector autoregressions which include the lagged levels of the variables in the model or the lagged residual from the cointegrating regression. Both Engle and Granger (1987) and Hendry and Ericsson (1991) use a general to specific approach for estimation of error correction models. In the first phase, unrestricted VARs are estimated for differences of the variables for an arbitrary number of lags. These VARs include lagged levels of the cointegrated variables. The significance, signs, and magnitude of the lagged levels indicate the appropriateness of the error correction specification.* The model is then reestimated, deleting the VAR terms which are least significant and have the smallest magnitude. The lagged levels of the variables from the cointegrating regression are replaced with the lagged residual from that regression. This is the final error correction specification. The error correction columns
estimates are reported
are the unrestricted
estimates
in Table 3. The first and third
for the household
and business sectors
respectively, while columns 2 and 4 are the final error-correction In both Equations 1 and 3 (as expressed in corresponding
specifications.
columns), the relative
size of the lagged level variables is approximately the same as the cointegrating regressions with real sectoral money balances as the dependent variables. The signs indicate that excess supplies in the previous period lead to reduced real balances in the current period, which is appropriate estimated
coefficients
for an error correction
of the lagged levels are significant
specification.
in the household
The sector
equation, and the lagged level of real balances is significant in the business equation. Elimination of the least significant terms and replacing the lagged level terms with the lagged error from the cointegrating correction
regression9
obtains the final error
model. The lagged residual terms are significant in Equations 2 and 4 (in
columns of same numbers), supporting the use of an error correction specification. For both models 2 and 4, the standard error of the regression is reduced compared to the unrestricted regressions 1 and 3 respectively. This is evidence that the final error correction equation is an improved specification. A further test of the error correction specification is the convergence restriction. This is the restriction that the implied long-run income elasticity in the error correction model equals the coeffkient on the income term in the cointegrating
238
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
Tab/k 3.
ERROR
CORRECTION
MODEL
ESTIMATES
(Sample 1952.3-1990.1) Household
Sector
Dependent 1 Constant ALRH (-1) ALRH (-2) ALRH (-3) ALRH (4) ALRDPI ALRDPI (-1) ALRDPI (-2) ALLRDPI(-3) ALRDPI (-4) aTB3 hLTB3 (-1) MTB3 (-2) ALTBJ (-3) L\LTBS(4) LRH (-1) LRDPI (-1) LTB3 (-1)
0.059 (.652) -0.244 (-2.93) 0.106 (1.25) 0.039 (0.45) 0.355 (4.33) 0.407 (1.89) 0.313 (1.38) 0.076 (0.34) -0.159 (-0.721) -0.244 (-1.14) -0.015 (-0.979) -0.018 (0.992) 0.007 (0.34) a.018 (-1.04) 0.02 (1.24) -0.119 (-3.25) 0.086 (3.03) -0.017 (-1.86)
e(-1) R* 3 S.E. SSR F Log Likelihood
0.39 0.31 0.023 0.066 4.95 360.5
Business Sector
Variable ALBH
Dependent
2 -0.002 (-0.47) -0.215 (-2.75) 0.115 (1.51)
3 Constant ALRB (-1) ALRB (-2) ALRB (-3)
0.347 (4.61) 0.410 (2.01) 0.293 (1.38)
ALRB (-4) ALGNP ALGNP (-1) ALGNP (-2) ALGNP (-3)
-0.232 (-1.16) -0.015 (-1.04) a.015 (-1.06)
ALGNP (-4) ATB3 ATB3 (-1) ATB3 (-2) ATB3 (-3)
0.01 (0.71)
ATB3 (4) LRB (-1) LRGNP (-1) TB3 (-1)
-0.12 (-3.55) 0.37 0.32 0.022 0.069 7.999 357.6
0.415 (2.2) a.153 (-1.88) 0.10 (1.24) -0.06 (-0.79) 0.56 (7.57) 0.40 (1.62) 0.24 (0.92) -0.29 (1.12) -0.07 (-0.27) -0.14 (-0.54) -0.00 (4.10) -0.01 (-3.4) 0.01 (1.36) -0.01 (-2.35) 0.01 (2.55) a.10 (-2.38) 0.014 (0.93) -0.01 (-1.67)
e(-1) R* ii2 SE. SSR F Log Likelihood
0.57 0.51 0.0259 0.087 10.09 340.2
Variable &RB 4 a.002 (-0.54) -0.22 (-3.36)
0.58 (9.0) 0.414 (1.89)
a.15 (-0.69)
-0.013 (4.14)
-0.01 (3.59) 0.01 (2.65)
-0.08 (-2.57) 0.55 0.52 0.0257 0.09 20.86 336.2
DEMAND FOR MONEY AND Ml VELOCITY
regression.
The probability that this restriction
obtains for the household
239
sector is
96 percent, but it is only 44 percent for the business sector.” An F test that the sum of the income coefficients in the business money- demand equation is different from zero is significant at only the 19 percent level of confidence, while the same test for the interest rate variables is significant at the 1 percent level. The existence of strong interest rate effects and weak or no income effects in business holdings is consistent with the hypothesis that the introduction of alternatives to demand deposits had a significant effect on the business sector’s demand for money. To further test the error-correction specification, one-step static forecasts of the sectoral models are compared to a naive random walk forecast of sectoral money holdings of the form:
(2)
yt’ Cl
The Theil coefficient for the household sector is .844 and for the business sector is .674.” These test results provide further support of the error-correction specification. Tests for autocorrelation, heteroskedasticity, and normality of the residualsI fail to reject the null hypotheses of no autocorrelation or heteroskedasticity for both models. However, both models exhibit nonnormality of residuals, skewness, and excess kurtosis. These problems are discussed below.
IV.
STABILITY AND THE USE OF DUMMY VARIABLES
Inclusion
of dummy variables in money demand estimates to account for certain
“shifts” in the demand function is frequently dummy variables are used include:
observed.
Common
periods when
1. 2.
1973.4-1976.1 - the period of the “missing money.” Certain quarters in 1980 through 1983 to adjust for the introduction
3.
and OCD accounts.13 Dummies for 1986 to allow for a shift in demand.
of NOW
When these dummy variables are included in Equation 2, the problems of nonnormality, skewness, and excess kurtosis are eliminated. Similar improvements are obtained when dummies for certain quarters of the 1970s are used in the estimation of the business sector in Equation 4.14 While use of dummy variables in certain cases, such as strikes or natural disasters, is acceptable, inclusion of dummies to eliminate large residuals often fails to provide insight into the economic forces which possibly account for these shifts. As an alternative to the use of dummy variables, the parameter constancy of sectoral money demand is examined using recursive least-squares estimates of Equations 2 and 4 from Table 3. Results of the CUSUM of squares tests for the household
240
QUARTERLY
REVIEW OF ECONOMICS AND FINANCE
1.25 -
CUSUM of squares 5% significance
-----
1.00
*- ._
-I
c*
*-*
.’
.’
(/
0.75
0.50 0.25 0.00 -0.25 Figure 1.
I
I
1960 CUSUM
I
1965
I
I
I
I
1970
1975
1980
1985
1’ 30
of Squares Statistic and Confidence Interval Household
Sector.
and business sectors are displayed in Figures 1 and 2 respectively. Movement of the test statistic outside the 5 percent confidence bands is an indication of parameter nonconstancy. The household
sector begins to display parameter
evidence of nonconstancy
nonconstancy
in 1974, but
is greatest during the years immediately preceding
and
1.25
1.00
0.25 0.00 -0.25
Figure 2.
I
CUSUM
I
1960
I
1965
I
1970
1
1975
I
1980
r
1985
1 90
of Squares Statistic and Confidence Interval Business Sector.
DEMAND FOR MONEY AND Ml VELOCITY following passage of the Monetary Control Act of 1980. Parameter nonconstancy household
241 of
money demand is greatest during the period of financial deregulation
and the development of innovative alternatives to demand deposits for the household sector. The business sector displays initial parameter but evidence of nonconstancy demand parameters
nonconstancy
in the mid-1960s,
is greatest in the late 1960s and 1970s. Business money
appear constant during the 1980s. Financial innovations such
as REPOs and overnight Eurodollar
deposits were developed in the late 1960s as an
alternative to business demand deposits. The timing of parameter nonconstancy
in
business money demand coincides with these innovations.
V.
CONCLUSION
The evidence presented are cointegrated account
here indicates that household
with measures
for 83 percent
of income
and business real balances
and interest
of total money balances.
rates. These
No evidence
two sectors
of cointegrated
relationships
are found for the remaining sectors, although a number of alternative
specifications
were tested. For the household and business sectors, the scale variables
in the cointegrating
regression differ, and one uses the log of the Treasury bill rate
while the other uses the level. All of these results indicate that tests for cointegration of aggregate Ml may be plagued by problems of aggregation bias.15 Estimated error correction obtain acceptable nonconstant
models for household and business money demand
results. However, both estimated equations
display evidence of
parameters during certain periods. The periods of parameter noncon-
stancy generally coincide with the development
of innovations such as negotiable
CDS, REPOs , and money market mutual funds and deregulations
such as interest-
bearing checking accounts. Thus, the results presented here are consistent with the hypothesis that observed money demand instability may be due to financial innovations and deregulations.16 Acknowledgment:
This paper was written when McConnell was a graduate student
at the University of Delaware. The authors acknowledge helpful comments from Phil Rothman and two anonymous referees. Responsibility for any errors is the authors.
NOTES *Direct all correspondence to: James L. Butkiewicz, University of Delaware, Department of Economics, Purnell Hall, Newark, DE 197162701. 1. The above-mentioned studies by Friedman, Hall and Noble, and Dickey,Jensen and Thornton do provide results supportive of a stable Ml demand function.
242
QUARTERLY REVIEW OF ECONOMICS AND FINANCE 2.
The first significant household utilization of money market mutual funds occurred
in the mid-1970s due to a sharp increase in short-term interest rates. As rates fell, household deposits in money mutual funds stopped growing until interest rates again rose rapidly, beginning in 1978. Money market mutual fund balances included in M2 increased from $9.5 billion in 1978 to $235.6 billion in 1982. 3.
The Fed includes all currency in the household
sector, but acknowledges
that a
substantial portion of currency is actually held by the foreign sector (Federal Reserve Board, 1971, p. 464n). 4.
The price index is the GNP deflator in all cases, although alternative indices could
be used. As all sectors are active throughout the economy, use of a general price index seems justified. The model presented coefficient
above accepts the theoretical
on the price index is unity. Goldfeld
(1973)
assumption that the implied
found that this assumption was
supported by the data. 5.
First-order autocorrelation
corrections are used for every sector-al regression except
the financial sector, where there is no evidence of first-order autocorrelation. 6.
Estimates of sectoral holdings ofM1 were discontinued at this time, so no additional
data is available. 7.
A number of potential cointegrating
vectors were examined, including the use of
opportunity cost measures for Ml. These measures are the difference between the Treasury bill rate and the rate on demand deposits and the difference between the return on M2 and on demand deposits. The results of these estimates fail to support the hypothesis of cointegration. 8.
Engle and Granger
(1987, p. 271) indicate that the signs and magnitudes of the
variables should reflect those of the cointegrating
vector, and that these variables should be
statistically significant. 9.
The error from the cointegrating
regression with real balances as the dependent
variable is used in each case. 10.
Respecifications
of the household
error correction
interest rate as the dependent variables result in insignificance
model with the income
and
of the error correction
term
in the income equation but not the interest rate equation. This suggests that income is weakly exogenous. 11.
The sectoral models used in these comparisons exclude dummy variables. Inclusion
of dummy variables reduces the Theil coefficients
to .75 and .658 for the household
and
business sectors respectively. 12.
The tests are the Breush/Godfrey
LM test, the Box/Pierce
statistics, the Arch, White and Ramsey reset tests, and the Jarque/Bera 13.
and Ljung/Box
Q
normality statistic.
Dummies used are for the interval from 1773.1 through 1976.4, the first quarter of
1981 and separate dummies for the first and second quarters of 1983. 14.
The dummies are for years 1970 and 1979.
15.
However, Dickey, Jensen
and Thornton
(1991) find evidence of cointegration
aggregate Ml demand using both the Engle/Granger
and Johansen/Juselius
for
tests for cointe-
gration. 16.
Mehra (1992) draws similar conclusions
from examination
using the same methodology as is used in this paper.
of aggregate Ml data
DEMAND FOR MONEY AND Ml VELOClTY
243
REFERENCES Board of Governors of the Federal Reserve System. 1971. “Survey of Demand Deposit Ownership.” Federal Reserve Bulletin, 57tJune) : 456467. Brocato, Joe and Kenneth L. Smith. 1989. “Velocity and the Variability of Money Growth: Evidence from Granger-Causality Tests-A Comment.” Journal of Monqr, Credit and Banking, 21: 258-261. Carlson, John B. 1989. “The Stability of Money Demand, Its Interest Sensitivity, and Some Implications for Money as a Policy Guide.” Federal Reserve Bank of Cleveland Economic Review, 3: 2-13. Dickey, David A., Dennis W.Jansen and Daniel L. Thornton. 1991. “A Primer on Cointegration with an Application to Money and Income. ” Federal Reserve Bank of St. Louis Ret&w, (March/April): 58-78. Engle, Robert E and C.W.J. Granger. 1987. “Cointegration and Error Correction: Representation, Estimation, and Testing.” Econometrica, 55: 251-276. Federal Reserve Board. 1971. “Survey of Demand Deposit Ownership.” Federal Reserve Bulletin, 57: 456-467. Friedman, Benjamin M. and Kenneth N. Kuttner. 1992. “Money, Income, Prices, and Interest Rates.” American Economic Review, 82: 472492. Friedman, Milton. 1984. “Lessons from the 1979-82 Monetary Policy Experiment.” American Economic Review, 74: 397400. Goldfeld, Stephen M. 1973. “The Demand for Money Revisited.” Brookings Papers on Economic Activity, 3: 577-638. -. 1976. “The Case of the Missing Money.” BmokingsPaperson EconomicActivity, 3: 683-730. Hall, Thomas E. and Nicholas R. Noble. 1987. “Velocity and the Variability of Money Growth: Evidence from Granger-Causality Tests.” Journal of Monqr, Credit and Banking, 21: 258-261. Hendry, David F. and Neil R. Ericsson. 1991. “An Econometric Analysis of U.K. Money Demand” in Monetary Trends in the United States and United Kingdom by Milton Friedman and Anna J. Schwartz. American Economic Review, 81: 8-38. Johansen, Soren and KatarinaJuselius. 1990. “Maximum Likelihood Estimation and Inference on Cointegration-with Application to the Demand for Money.” Oxford Bulletin of Economics and Statistics, 52( 2) : 169-2 10. Mascara, Angelo and Allen H. Meltzer. 1983. “Long- and Short-Term Interest Rates in a Risky World.” Journal of Monetary Economics, 12: 485-518. Mehra,Yash P. 1989. “Some Further Results on the Source of Shift in MlDemand in the 1980s.” Federal Reserve Bank of Richmond Economic Review, 75: 3-13. -. 1992. “In Search of a Stable, Short-Run Ml Demand Function.” Federal Reserve Bank of Richmond Economic Review, 78: 9-23. Melnick, Rat?. 1990. “The Demand for Money in Argentina 1978-1987: Before and After the Austral Program.” Journal of Business and Economic Statistics, 8: 427-434. Miller, Stephen M. 1991. “Monetary Dynamics: An Application of Cointegration and ErrorCorrection Modeling.” Journal of Morq Credit and Banking, 23: 139-154. Rasche, Robert H. 1987. “Ml-Velocity and Money-Demand Functions: Dc; Stable Relationships Exist?” Pp. 9-88 in Empirical Studies of Velocity, Real Exchange Rates, Unemployment and Productivity, edited by Karl Brunner and Allen H. Meltzer. Carnegie-Rochester ConferPnce Series on Public Policy, Vol. 27.
ISSN 0033-5797
The Stability of the Demand for Money and Ml Velocity: Evidence from the Sectoral Data JAMES L. BUTKIEWICZ University
of Delaware
MARGARET MARY MCCONNELL Ohio State University
Sectoral monqr demandfunctions relationships
are found
fw
are estimated usingflw
household
and
offunds
(nonfinancial)
data. Cointegrating
business sectors. Estimated
error-correction moak!s for both sectors, however, exhibit parameter nonconstancy for time @riook which roughly correspond with importantfinancial Thus, sectoral estimates of monq innovations
innovations and deregulations.
demand relationships are consistent with the view that
and deregulation contribute to the nonstationatity of Ml velocity.
The apparent nonconstancy of the parameters of the aggregate Ml demand function for the U.S., and the corresponding deterioration of the relationship between money and aggregate output is one of the most extensively examined macroeconomic phenomena of recent years. Studies examining the demand for money and/or stationarity of velocity include those by Brocato and Smith (1989)) Carlson (1989)) Dickey, Jensen and Thornton (1991)) Friedman (1984), Goldfeld (1976)) Hall and Noble
(1987),
Hendry and Ericsson
(1991),
Mascar and Meltzer
(1983),
Mehra
(1989), Melnick (1990), Miller (1991), and Rasche (1987), while Friedman and Kuttner (1992) have examined the decline in the relationship between money and income. The majority of studies conclude that there is no stable Ml demand function, but the existence of a stable M2 demand function is supported by the data.’ Typical explanations for the breakdown of Ml demand include changes resulting from disinflation, deregulation and financial innovations, and uncertainty due to increased volatility of monetary policy. This paper presents the results of another look at the demand for Ml. The approach used is unique in that the data set is the Federal Reserve’s flow of funds data disaggregated by sectors. The methodology used is the Engle-Granger (1987) approach of estimating error correction models for cointegrated relationships.
234
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
Hendry and Ericsson (1991) use this approach to estimate money demand functions (M2) for the UKand Miller (1991) uses the same approach for U.S. money demand. While Dickey, Jensen and Thornton
(1991) note that the Engle/Granger
is sensitive to the order of normalization, approach finds evidence of cointegration obtained
from the maximum
Juselius (1990).
, the cointegrating
likelihood
approach
of nonfinancial
vector is similar to that
developed
In fact, we find that the Engle/Granger
gration for all three normalizations normalizations
approach
they also find that when the Engle/Granger by Johansen
and
approach supports cointe-
of household Ml demand, and for two of three
business demand for Ml. We also find that the scale
and interest rate variables in the cointegrating regressions differ between the house hold and business sectors as do estimated elasticities. This suggests that aggregation across sectors which respond in different magnitudes to different measures of transactions
and opportunity costs may obscure long-run relationships.
Finally, the
sectoral models indicate that instability of Ml demand in the 1960s and 1970s emanated primarily from the business sector, while in the late 1970s and 1980s the source of instability was the household sector. One explanation
consistent with this
pattern of instability is that it is the result of financial innovation and deregulation. Alternatives to holding checking deposits developed first for businesses in the form of repurchase agreements and Eurodollar
deposits. Money market mutual funds and
other alternatives to checking balances became available to households in the 1970s and the 1980s.’ Part I of this paper reviews the flow of funds ownership data, the Goldfeld study of sectoral Ml demand, and discusses briefly updated results of this approach. The methodology of the Engle/Granger error correction model and the necessary pretests are discussed in Section II. Estimated results for the household and nonfinancial business sectors are presented
in Section III. The implications
of the esti-
mates for parameter constancy, including the widespread use of dummy variables in money demand models, are discussed in Section IV Concluding comments are made in Section V.
I.
FLOW OF FUNDS DATA AND THE GOLDFELD STUDY
This study examines the demand for Ml using the flow of funds estimates of sector-al ownership of Ml. The flow of funds ownership data differs in several ways from aggregate monetary data (Federal Reserve Board, 1971). Ml data are averages of daily data, while flow of funds data are end-of-month point estimates. The flow of funds data include balances held by Edge Act corporations and agencies of foreign banks in the U.S. in financial sector balances. Mail float is not included in any sector, but the Fed (1971, p. 464) suggests that mail float is largely comprised of deposits of the business sector, and Goldfeld (1973) includes mail float in the business sector estimates3
DEMAND FOR MONEY AND Ml VELOCITY
235
Goldfeld ‘s (1973) classic study of money demand includes estimation of models for the household, financial, (nonfinancial)
business (including mail float), and state
and local government sectors. Holdings by the “rest of the world” are not examined. The estimates
are obtained
using the partial-adjustment
specification,
which is
frequently called the Goldfeld model of money demand: In($),
= clo + clrln Y,, - a&r,
+ a&($-r
+ El,
S=1,...,4.
(1)
In = the natural logarithm of a variable, where: (M, /p) = the real Ml balances for each of the sectors except finance where nominal levels are used,4 Y, = a measure of transactions for each sector, r = an opportunity cost measure, and E = a random error. All of his estimated equations used a correction for first-order serial correlation. Goldfeld reported that the household and financial sectors were well explained by the model, while the results were not satisfactory for the other two sectors. As a preliminary to estimating cointegrating regressions and error correction models, we reestimated Goldfeld ‘s equations using data from the third quarter of 1952 through the first quarter of 1990.5P6 Also, we experimented with various scale and interest rate variables. The estimates are tested for coefficient constancy for various subsamples. Using Chow tests, the hypothesis of coefficient constancy is rejected for all sectors when the sample is divided at the fourth quarter of 1979. This evidence of nonconstant parameters is the same problem that plagues the aggregate money demand estimates using the partial adjustment model. As is true for aggregate money demand modeling, alternative approaches may provide greater insight into sectoral money demand.
II.
COINTEGRATION
Recent
AND ERROR CORRFXXION MODELS
advances in econometric
techniques
have established
the importance
of
testing for cointegrated relationships. If economic series must be differenced one or more times to obtain stationarity, they are said to be integrated of order d, where d is the number of differences required to obtain stationarity of the series. If one or more series are integrated of the same order, they may follow a common trend. If the residual from a regression of one of these series on the others is integrated of order d- b, where b > 1, the series are said to be cointegrated, and they follow a common trend. Before testing for cointegration, it must be established that all series are integrated of the same order. Augmented Dickey-Fuller tests are reported in Table 1 for
236
QUARTERLY
REVIEW
Table 1.
AUGMENTED
(Sample
1952.4-1990.1)
OF ECONOMICS
AND FINANCE
DICKEY-FULLER TESTS FOR UNIT ROOT
Variable
1st Difference
2nd Difference
In Household Real Ml (LRH)
-2.11
-7.77**
In Business Real Ml (LRB)
-1.03
-8.95**
In State and Local Government Real Ml (LRSL)
-1.76
-9.79**
0.95
-7.82**
In Real Disposable Personal Income (LRDPI)
-1.84
-6.14*+
In Real GNP (LRGNP)
-2.69
-6.67**
In Real State and Local Government Expenditures (LRSLX)
-1.34
+.68**
0.91
-9.36**
In Smonth Treasury Bill Rate (LTBJ)
-2.84
-6.34**
Smonth Treasury Bill Rate (TB3)
-2.73
+.45**
Financial Ml (FIN)
Deposits (DEP)
first and second differences
of all variables used in the models. In all cases, the tests
fail to reject the null hypothesis of a unit root for first differences, hypothesis of a unit root for second differences. As all variables are integrated of order one, cointegrating
but reject the null
regressions are run to
determine if long-run relationships exist among sets of variables that would be included in a money demand model. Engle and Granger (1987) recommend using the augmented Dickey/Fuller test to test for cointegration. The tests indicate cointegration of real household Ml (LRH), real disposable personal income, and the Treasury bill rate, all in logarithms, for all three normalizations.’ These results are reported in Table 2. Table 2 also reports the results of cointegrating regressions for the logarithm of real business money holding (LRB), the logarithm of real GNP, and the level of the three-month cointegration
Treasury Bill rate. ADF tests support the hypothesis of
for two of the three normalizations.
Tubb 2.
COINTEGRATING
(Sample
1952.1-1990.1) Household
No evidence of cointegration
REGRESSIONS Business Sector
Sector
Cointegrating Vector
Cointegrating Vector 1 LRH LRDPI LTB3
2
3
1
-1.27
2.3
-0.6
1
-2.57
0.103
ADF
-3.5*
NOMS: *Rejects **R+crs Augmented
-0.243
1
-4.8**
A.8**
1 LRB
1
LRGNP TB3
0.044 -3.9*
null hypothesis
of unit root in residual
at 5 percrnt
level ofconfidence.
null hypothesis
of unn root in residual
at 1 prrcen~
level ~Cconfidcnce.
tc~ts for coinleg?arion
use four lagged
Dickq-Fuller
-0.072
difTcrence
w”ns.
2
3
-0.477
12.03
1 -0.103
-4.26
-2.5
-5.o**
1
is
237
DEMAND FOR MONEY AND Ml VELOCITY found for various specifications business sectors account
for other sectors.
for 83 percent
estimation of error correction
However, the household
of all sectoral
holdings
and
in 1990. Thus,
models for these two sectors will provide insight into
the aggregate behavior of Ml.
III.
ERROR CORRECTION
MODELS OF SECTORAL HOLDINGS
Error correction models allow for flexible specification of short-run dynamics while obeying the long-run constraints implied by the existence of cointegration. Specifically, error correction models are vector autoregressions which include the lagged levels of the variables in the model or the lagged residual from the cointegrating regression. Both Engle and Granger (1987) and Hendry and Ericsson (1991) use a general to specific approach for estimation of error correction models. In the first phase, unrestricted VARs are estimated for differences of the variables for an arbitrary number of lags. These VARs include lagged levels of the cointegrated variables. The significance, signs, and magnitude of the lagged levels indicate the appropriateness of the error correction specification.* The model is then reestimated, deleting the VAR terms which are least significant and have the smallest magnitude. The lagged levels of the variables from the cointegrating regression are replaced with the lagged residual from that regression. This is the final error correction specification. The error correction columns
estimates are reported
are the unrestricted
estimates
in Table 3. The first and third
for the household
and business sectors
respectively, while columns 2 and 4 are the final error-correction In both Equations 1 and 3 (as expressed in corresponding
specifications.
columns), the relative
size of the lagged level variables is approximately the same as the cointegrating regressions with real sectoral money balances as the dependent variables. The signs indicate that excess supplies in the previous period lead to reduced real balances in the current period, which is appropriate estimated
coefficients
for an error correction
of the lagged levels are significant
specification.
in the household
The sector
equation, and the lagged level of real balances is significant in the business equation. Elimination of the least significant terms and replacing the lagged level terms with the lagged error from the cointegrating correction
regression9
obtains the final error
model. The lagged residual terms are significant in Equations 2 and 4 (in
columns of same numbers), supporting the use of an error correction specification. For both models 2 and 4, the standard error of the regression is reduced compared to the unrestricted regressions 1 and 3 respectively. This is evidence that the final error correction equation is an improved specification. A further test of the error correction specification is the convergence restriction. This is the restriction that the implied long-run income elasticity in the error correction model equals the coeffkient on the income term in the cointegrating
238
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
Tab/k 3.
ERROR
CORRECTION
MODEL
ESTIMATES
(Sample 1952.3-1990.1) Household
Sector
Dependent 1 Constant ALRH (-1) ALRH (-2) ALRH (-3) ALRH (4) ALRDPI ALRDPI (-1) ALRDPI (-2) ALLRDPI(-3) ALRDPI (-4) aTB3 hLTB3 (-1) MTB3 (-2) ALTBJ (-3) L\LTBS(4) LRH (-1) LRDPI (-1) LTB3 (-1)
0.059 (.652) -0.244 (-2.93) 0.106 (1.25) 0.039 (0.45) 0.355 (4.33) 0.407 (1.89) 0.313 (1.38) 0.076 (0.34) -0.159 (-0.721) -0.244 (-1.14) -0.015 (-0.979) -0.018 (0.992) 0.007 (0.34) a.018 (-1.04) 0.02 (1.24) -0.119 (-3.25) 0.086 (3.03) -0.017 (-1.86)
e(-1) R* 3 S.E. SSR F Log Likelihood
0.39 0.31 0.023 0.066 4.95 360.5
Business Sector
Variable ALBH
Dependent
2 -0.002 (-0.47) -0.215 (-2.75) 0.115 (1.51)
3 Constant ALRB (-1) ALRB (-2) ALRB (-3)
0.347 (4.61) 0.410 (2.01) 0.293 (1.38)
ALRB (-4) ALGNP ALGNP (-1) ALGNP (-2) ALGNP (-3)
-0.232 (-1.16) -0.015 (-1.04) a.015 (-1.06)
ALGNP (-4) ATB3 ATB3 (-1) ATB3 (-2) ATB3 (-3)
0.01 (0.71)
ATB3 (4) LRB (-1) LRGNP (-1) TB3 (-1)
-0.12 (-3.55) 0.37 0.32 0.022 0.069 7.999 357.6
0.415 (2.2) a.153 (-1.88) 0.10 (1.24) -0.06 (-0.79) 0.56 (7.57) 0.40 (1.62) 0.24 (0.92) -0.29 (1.12) -0.07 (-0.27) -0.14 (-0.54) -0.00 (4.10) -0.01 (-3.4) 0.01 (1.36) -0.01 (-2.35) 0.01 (2.55) a.10 (-2.38) 0.014 (0.93) -0.01 (-1.67)
e(-1) R* ii2 SE. SSR F Log Likelihood
0.57 0.51 0.0259 0.087 10.09 340.2
Variable &RB 4 a.002 (-0.54) -0.22 (-3.36)
0.58 (9.0) 0.414 (1.89)
a.15 (-0.69)
-0.013 (4.14)
-0.01 (3.59) 0.01 (2.65)
-0.08 (-2.57) 0.55 0.52 0.0257 0.09 20.86 336.2
DEMAND FOR MONEY AND Ml VELOCITY
regression.
The probability that this restriction
obtains for the household
239
sector is
96 percent, but it is only 44 percent for the business sector.” An F test that the sum of the income coefficients in the business money- demand equation is different from zero is significant at only the 19 percent level of confidence, while the same test for the interest rate variables is significant at the 1 percent level. The existence of strong interest rate effects and weak or no income effects in business holdings is consistent with the hypothesis that the introduction of alternatives to demand deposits had a significant effect on the business sector’s demand for money. To further test the error-correction specification, one-step static forecasts of the sectoral models are compared to a naive random walk forecast of sectoral money holdings of the form:
(2)
yt’ Cl
The Theil coefficient for the household sector is .844 and for the business sector is .674.” These test results provide further support of the error-correction specification. Tests for autocorrelation, heteroskedasticity, and normality of the residualsI fail to reject the null hypotheses of no autocorrelation or heteroskedasticity for both models. However, both models exhibit nonnormality of residuals, skewness, and excess kurtosis. These problems are discussed below.
IV.
STABILITY AND THE USE OF DUMMY VARIABLES
Inclusion
of dummy variables in money demand estimates to account for certain
“shifts” in the demand function is frequently dummy variables are used include:
observed.
Common
periods when
1. 2.
1973.4-1976.1 - the period of the “missing money.” Certain quarters in 1980 through 1983 to adjust for the introduction
3.
and OCD accounts.13 Dummies for 1986 to allow for a shift in demand.
of NOW
When these dummy variables are included in Equation 2, the problems of nonnormality, skewness, and excess kurtosis are eliminated. Similar improvements are obtained when dummies for certain quarters of the 1970s are used in the estimation of the business sector in Equation 4.14 While use of dummy variables in certain cases, such as strikes or natural disasters, is acceptable, inclusion of dummies to eliminate large residuals often fails to provide insight into the economic forces which possibly account for these shifts. As an alternative to the use of dummy variables, the parameter constancy of sectoral money demand is examined using recursive least-squares estimates of Equations 2 and 4 from Table 3. Results of the CUSUM of squares tests for the household
240
QUARTERLY
REVIEW OF ECONOMICS AND FINANCE
1.25 -
CUSUM of squares 5% significance
-----
1.00
*- ._
-I
c*
*-*
.’
.’
(/
0.75
0.50 0.25 0.00 -0.25 Figure 1.
I
I
1960 CUSUM
I
1965
I
I
I
I
1970
1975
1980
1985
1’ 30
of Squares Statistic and Confidence Interval Household
Sector.
and business sectors are displayed in Figures 1 and 2 respectively. Movement of the test statistic outside the 5 percent confidence bands is an indication of parameter nonconstancy. The household
sector begins to display parameter
evidence of nonconstancy
nonconstancy
in 1974, but
is greatest during the years immediately preceding
and
1.25
1.00
0.25 0.00 -0.25
Figure 2.
I
CUSUM
I
1960
I
1965
I
1970
1
1975
I
1980
r
1985
1 90
of Squares Statistic and Confidence Interval Business Sector.
DEMAND FOR MONEY AND Ml VELOCITY following passage of the Monetary Control Act of 1980. Parameter nonconstancy household
241 of
money demand is greatest during the period of financial deregulation
and the development of innovative alternatives to demand deposits for the household sector. The business sector displays initial parameter but evidence of nonconstancy demand parameters
nonconstancy
in the mid-1960s,
is greatest in the late 1960s and 1970s. Business money
appear constant during the 1980s. Financial innovations such
as REPOs and overnight Eurodollar
deposits were developed in the late 1960s as an
alternative to business demand deposits. The timing of parameter nonconstancy
in
business money demand coincides with these innovations.
V.
CONCLUSION
The evidence presented are cointegrated account
here indicates that household
with measures
for 83 percent
of income
and business real balances
and interest
of total money balances.
rates. These
No evidence
two sectors
of cointegrated
relationships
are found for the remaining sectors, although a number of alternative
specifications
were tested. For the household and business sectors, the scale variables
in the cointegrating
regression differ, and one uses the log of the Treasury bill rate
while the other uses the level. All of these results indicate that tests for cointegration of aggregate Ml may be plagued by problems of aggregation bias.15 Estimated error correction obtain acceptable nonconstant
models for household and business money demand
results. However, both estimated equations
display evidence of
parameters during certain periods. The periods of parameter noncon-
stancy generally coincide with the development
of innovations such as negotiable
CDS, REPOs , and money market mutual funds and deregulations
such as interest-
bearing checking accounts. Thus, the results presented here are consistent with the hypothesis that observed money demand instability may be due to financial innovations and deregulations.16 Acknowledgment:
This paper was written when McConnell was a graduate student
at the University of Delaware. The authors acknowledge helpful comments from Phil Rothman and two anonymous referees. Responsibility for any errors is the authors.
NOTES *Direct all correspondence to: James L. Butkiewicz, University of Delaware, Department of Economics, Purnell Hall, Newark, DE 197162701. 1. The above-mentioned studies by Friedman, Hall and Noble, and Dickey,Jensen and Thornton do provide results supportive of a stable Ml demand function.
242
QUARTERLY REVIEW OF ECONOMICS AND FINANCE 2.
The first significant household utilization of money market mutual funds occurred
in the mid-1970s due to a sharp increase in short-term interest rates. As rates fell, household deposits in money mutual funds stopped growing until interest rates again rose rapidly, beginning in 1978. Money market mutual fund balances included in M2 increased from $9.5 billion in 1978 to $235.6 billion in 1982. 3.
The Fed includes all currency in the household
sector, but acknowledges
that a
substantial portion of currency is actually held by the foreign sector (Federal Reserve Board, 1971, p. 464n). 4.
The price index is the GNP deflator in all cases, although alternative indices could
be used. As all sectors are active throughout the economy, use of a general price index seems justified. The model presented coefficient
above accepts the theoretical
on the price index is unity. Goldfeld
(1973)
assumption that the implied
found that this assumption was
supported by the data. 5.
First-order autocorrelation
corrections are used for every sector-al regression except
the financial sector, where there is no evidence of first-order autocorrelation. 6.
Estimates of sectoral holdings ofM1 were discontinued at this time, so no additional
data is available. 7.
A number of potential cointegrating
vectors were examined, including the use of
opportunity cost measures for Ml. These measures are the difference between the Treasury bill rate and the rate on demand deposits and the difference between the return on M2 and on demand deposits. The results of these estimates fail to support the hypothesis of cointegration. 8.
Engle and Granger
(1987, p. 271) indicate that the signs and magnitudes of the
variables should reflect those of the cointegrating
vector, and that these variables should be
statistically significant. 9.
The error from the cointegrating
regression with real balances as the dependent
variable is used in each case. 10.
Respecifications
of the household
error correction
interest rate as the dependent variables result in insignificance
model with the income
and
of the error correction
term
in the income equation but not the interest rate equation. This suggests that income is weakly exogenous. 11.
The sectoral models used in these comparisons exclude dummy variables. Inclusion
of dummy variables reduces the Theil coefficients
to .75 and .658 for the household
and
business sectors respectively. 12.
The tests are the Breush/Godfrey
LM test, the Box/Pierce
statistics, the Arch, White and Ramsey reset tests, and the Jarque/Bera 13.
and Ljung/Box
Q
normality statistic.
Dummies used are for the interval from 1773.1 through 1976.4, the first quarter of
1981 and separate dummies for the first and second quarters of 1983. 14.
The dummies are for years 1970 and 1979.
15.
However, Dickey, Jensen
and Thornton
(1991) find evidence of cointegration
aggregate Ml demand using both the Engle/Granger
and Johansen/Juselius
for
tests for cointe-
gration. 16.
Mehra (1992) draws similar conclusions
from examination
using the same methodology as is used in this paper.
of aggregate Ml data
DEMAND FOR MONEY AND Ml VELOClTY
243
REFERENCES Board of Governors of the Federal Reserve System. 1971. “Survey of Demand Deposit Ownership.” Federal Reserve Bulletin, 57tJune) : 456467. Brocato, Joe and Kenneth L. Smith. 1989. “Velocity and the Variability of Money Growth: Evidence from Granger-Causality Tests-A Comment.” Journal of Monqr, Credit and Banking, 21: 258-261. Carlson, John B. 1989. “The Stability of Money Demand, Its Interest Sensitivity, and Some Implications for Money as a Policy Guide.” Federal Reserve Bank of Cleveland Economic Review, 3: 2-13. Dickey, David A., Dennis W.Jansen and Daniel L. Thornton. 1991. “A Primer on Cointegration with an Application to Money and Income. ” Federal Reserve Bank of St. Louis Ret&w, (March/April): 58-78. Engle, Robert E and C.W.J. Granger. 1987. “Cointegration and Error Correction: Representation, Estimation, and Testing.” Econometrica, 55: 251-276. Federal Reserve Board. 1971. “Survey of Demand Deposit Ownership.” Federal Reserve Bulletin, 57: 456-467. Friedman, Benjamin M. and Kenneth N. Kuttner. 1992. “Money, Income, Prices, and Interest Rates.” American Economic Review, 82: 472492. Friedman, Milton. 1984. “Lessons from the 1979-82 Monetary Policy Experiment.” American Economic Review, 74: 397400. Goldfeld, Stephen M. 1973. “The Demand for Money Revisited.” Brookings Papers on Economic Activity, 3: 577-638. -. 1976. “The Case of the Missing Money.” BmokingsPaperson EconomicActivity, 3: 683-730. Hall, Thomas E. and Nicholas R. Noble. 1987. “Velocity and the Variability of Money Growth: Evidence from Granger-Causality Tests.” Journal of Monqr, Credit and Banking, 21: 258-261. Hendry, David F. and Neil R. Ericsson. 1991. “An Econometric Analysis of U.K. Money Demand” in Monetary Trends in the United States and United Kingdom by Milton Friedman and Anna J. Schwartz. American Economic Review, 81: 8-38. Johansen, Soren and KatarinaJuselius. 1990. “Maximum Likelihood Estimation and Inference on Cointegration-with Application to the Demand for Money.” Oxford Bulletin of Economics and Statistics, 52( 2) : 169-2 10. Mascara, Angelo and Allen H. Meltzer. 1983. “Long- and Short-Term Interest Rates in a Risky World.” Journal of Monetary Economics, 12: 485-518. Mehra,Yash P. 1989. “Some Further Results on the Source of Shift in MlDemand in the 1980s.” Federal Reserve Bank of Richmond Economic Review, 75: 3-13. -. 1992. “In Search of a Stable, Short-Run Ml Demand Function.” Federal Reserve Bank of Richmond Economic Review, 78: 9-23. Melnick, Rat?. 1990. “The Demand for Money in Argentina 1978-1987: Before and After the Austral Program.” Journal of Business and Economic Statistics, 8: 427-434. Miller, Stephen M. 1991. “Monetary Dynamics: An Application of Cointegration and ErrorCorrection Modeling.” Journal of Morq Credit and Banking, 23: 139-154. Rasche, Robert H. 1987. “Ml-Velocity and Money-Demand Functions: Dc; Stable Relationships Exist?” Pp. 9-88 in Empirical Studies of Velocity, Real Exchange Rates, Unemployment and Productivity, edited by Karl Brunner and Allen H. Meltzer. Carnegie-Rochester ConferPnce Series on Public Policy, Vol. 27.