Velocity variability: Directly an interest-rate driven phenomenon

The Qnartedy Review of Economicp and F-, Vol. 33, No. 4, Winter, 1993, pages 423-@7 Copyright8 1993 Trusteesof the Universityof Illinois All rightsof reproductionin any form reserved. ISSN 00335797

Velocity Variability: Directly An Interest-Rate Driven Phenomenon George M. Ratsimbris and Stephen M. Miller* University of Bridgeport and University of Thessaloniki, University of Connecticut

Unexpected declines in the United States Ml income velocity of monq during the 1980s has received considerable attention. Some analysts argue that since the instability of velocity occurred in tandem with a “monetarist poliq experiment nby the Federal Reserve, thefallaq of monetarists’ policy@xriptions is now clear forall to see. Monetarists demure, arguing that the Federal Reserve never realty conducted a test of monetarist po1C.ydoctrine. Rather the Federal Reserve by creating so much variability in m~nq, growth caused the velocity’s dmmatic declines. Hall and Noble (1987) jnvvide evidence to suf@rt the monetarist position white Brocato and Smith (1989) off er evidence that su#nts the anti-monetarist view. We employ bi-variate and multi-variate tests of Granger causality to reexamine the issues. Of the variables considered-i.e., money growth variability, the money stock, the interest rate, real GNP, and the GNP implicit price deflator, the interest rate wins hands-down. That is, the interest rate Granger causes the Ml income velocity of monqr for all samples that include some 1980s data. Nonetheless, the monetarist response may still be accurate, since monq growth uncertainty helps to ea$ain the movements in the interest rate during most of the 1980s.

Macroeconomic reassess cherished

theorists,

both monetarists

beliefs and assumptions

during the 1980s. The unprecedented this period

receive considerable

and Keynesians,

declines in the income

attention

in the literature.

that since this instability of velocity occurred experiment”

that no such monetarist so much monetary

money October

policy experiment

to

markets

velocity of money over Some analysts conclude

with a “monetarist

of monetarists’

policy

policy pallia-

for all to see. Monetarists object to such conclusions,

arguing

took place. The Federal Reserve by creating

variability in money growth caused

the velocity declines;

in other

words,

policy, not velocity, was unstable.’

The dramatic triggered

in tandem

by the Federal Reserve, the dangerousness

tives has been unmasked

have been forced

given the events in the financial

reduction

in the Ml income

a search for an explanation

and too little velocity (Gordon

velocity of money during

the 1980s

of the reverse “Goldfeld puzzle” of too much 1984, p. 404).

19’79, when the Federal Reserve adopted 423

Velocity variability arose after

new operating

procedures,

placing

424

QUAIZTERLY REYIEW OF ECONOMICS

more

emphasis

funds

rate. Though

fluctuations

on controlling

AND FINANCE

the money supply and less on stabilizing

the Federal

Reserve

abandoned

its effort

in Ml growth in 1982, velocity remained

the federal

to control

short-run

highly variable throughout

most

of the 1980s. The variability income

of velocity broke

and weakened

the important

money growth rule. Such a rule is, as Benjamin now, no longer during

a going concern. (1984)

it generated,

policy experiment”

the targeting

The use of non-borrowed requirements

resulted

reserves

first provide

evidence

ability caused finding

necessarily First,

some

argue

unexpected during

the demand velocity.

income

On the other by affecting interest

hand,

interest

decrease

in the demand

changes

over time relative sharp declines

(1989)

(1987)

growth vari-

second

dispute

this

though

not

of alternative, the variability because

of the

interest rate reduces

interest

sharp

in actual or expected

inflation

rates

through

the opportunity

inflation

rate. A fall in (expected) real interest

and

cost

for money and a decline

in

affect velocity

inflation,

given the

rate and lower income;

in income

if the

will result in a less than proportionate

innovations

in velocity.

and financial

deregulation

to this view, the introduction

the basic nature of Ml as a medium

sensitivity, as the share of these saving-type

to the regular

of velocity.’

rates affect velocity directly

for money and thus, in a decrease

deposits changes

in market

that money

for money is less than unity, as most of the empirical

then the decline

its interest

occurs

in the demand

velocity variability. According

transaction

and increases

and caused

Hall and Noble

rates and actual and expected

the real interest

others argue that financial

1980s explain

a number

interest

rate, leads to a higher

suggests,

variability of

uncertainty

hypothesis

in velocity

in nominal

elasticity of the demand

Second,

of perceived

exist to explain

for money; a fall in the nominal

evidence

bearing

variability,

money and leads to an increase

indirectly

the exceptional

and Smith

the three

the “demise of monetarism.”

hypotheses

in nominal

during

since at least the end of

contributions,

and Brocato

the decline

the 1980s. Changes

of holding

nominal

that

decline

degree

growth.

with the lagged reserve

period

to Milton Friedman,

growth

exclusive,

The evidence

failed since monetarist

coupled

three-year

M. Friedman’s

supporting

to money

mutually

(p. 69).

Reserve over the

anti-monetarist.

variability which “... was higher

the public’s

to support

with evidence

and prices

of a steady rate of monetary

in velocity. In two recent

velocity variability

In addition

notes “... at least for

and practically.”

as monetarism

as an instrument

than in any earlier

growth heightened decline

of a constant

money, income

by the Federal

was rather

and maintaining

World War II.” (p. 397).* According the dramatic

(1988)

among

conducted

be interpreted

in monetary

years of the experiment money

Friedman

it both intellectually

which, in his opinion,

he argues, cannot

policy requires

and nominal

argues that the sharp decline in velocity in 1982 was the direct

result of the “monetary 1979 to 1982 period,

money

policy prescription

The interactions

the 198Os... have undermined

Milton Friedman

link between

the case for the monetarists’

checking

deposits

(Hetzel

rates after 1982 decrease

of exchange

deposits

and Mehra the spread

in the

of interest grows

1989). between

The the

THE THOERY AND PRACTICE OF FINANCE

425

return on Ml and on other non-Ml assets; this makes Ml more attractive and velocity more variable than previously Third, though the modern quantity theory assumes that the rate ofvelocity change and the rate of money growth are uncorrelated

in the long run, in the short run it is

possible that money growth may affect velocity. One, empirical evidence suggests that a change in money growth affects GNP with a lag; an acceleration

of money growth

will cause a temporary decline in velocity with income growing at a slower rate than the money supply (Friedman

1984; Fisher and Serletis 1989). Two, acceleration

of

money growth will raise expected inflation and the cost of holding money, reducing the demand for money and raising velocity. In this case, changes in velocity amplify rather than offset changes in money growth (Gould, Miller, Nelson, and Upton 1978) .4 Finally, an income elasticity of the demand for money of less than unity suggests pro-cyclical movements in velocity-rising during expansions and falling during recessions (Fisher and Serletis 1989; Tatom 1983). In addition, autonomous changes in individual components of the aggregate demand for goods and services increase the variability of velocity.

REVlEWOFTHEEMPlRICALLITERATURE Much of the discussion about the potential causes of the dramatic decline in velocity during the 1980s proceeds using standard regression analysis. Only recently have analysts begun to examine the issues, using Granger causality tests. While Granger causality has its critics (Zellner 1979; Conway, Swamy,Yanagida, and von zur Muehlen 1984; Cooley and LeRoy 1985), we offer our analysis to extend and critique those existing studies that consider what variables may Granger cause the Ml income velocity. In this regard, a finding of Granger causality (i.e., a rejection of the Granger non-causality null hypothesis) implies a rejection of strict exogeneity; a failure to reject Granger non-causality does not necessarily imply strict exogeneity (see Cooley and LeRoy 1985, p. 298).5 Thus, evidence of Granger causality provides information; evidence of Granger non-causality presents ambiguous signals. We shall emphasize this point in the rest of this article. These studies of the causes of the dramatic decline in velocity generally consider only bi-variate causality tests. Our research also provides multi-variate causality tests to examine the possibility of spurious causality due to omitted variables. That is, Granger causality (non-causality) in a bivariate system may result from omitted variables (see Lutkepohll982, p. 367). For example, if it is discovered that money growth variability Granger causes velocity in a bivariate system, then it cannot be concluded that money growth variabilitywill also Granger cause velocity in a higher order system that includes other variables, such as the interest rate. Hall and Noble (1987), using quarterly data, test the hypothesis advanced by Milton Friedman, that money growth variability causes velocity with the Granger

426

QUARTERLY REVIEW OF ECONOMICS AND FJNANCE

causality method.

They perform

and the level of money standard

deviation

causality tests between

growth

of money

variability,

growth

the rate of change

measured

rates.

Based

on Fstatistics

regressions

over the 1963:i to 1984:ii and 1963:i to 1979:iii periods,

hypothesis

that the standard

Fischer

and

significance

Serletis

deviation

(1989)

of the money

velocity with monthly aggregates

from

moving estimating

they reject the null

of money growth does not cause velocity.

conduct

Grangercausality

stock and money

growth

data and nine definitions

to divisia indices.

in velocity

by the eight-quarter

They find support

tests to investigate

variability

the

as determinants

of money, ranging

of

from simple sum

for both hypotheses

for the 1970:2

to

1985:3 period. When Fischer and Serletis omit, however, the 1979:lO to 1982:8 period, money growth variability no longer causes velocity, which suggests “. . . that the results for the entire period are largely traceable rate

to the extreme

volatility of the money growth

. . from 1979 to 1982.” (p. 328, fn. 6). Brocato

and

significant

structural

conclusion monthly

Smith

changes

may be biased data, Brocato

to 1985:9,

and the pm-1979

in financial

markets

strengthen Brocato

we find

evidence

period.”

(p.260).

structural

regressions

of Fisher (1989)

of Gordon’s The demise

(1989)

period conclude

‘demise

concludes rather

break

(1989),

Using

I;statistics

reject

where

in 1979.

Friedman’s

greater

money

that “. . . in contrast

a modified Brocato

and

hypothesis

as

growth variability to Hall and Noble,

in the post-October

1979

results, however, hinge on an observed

non-causality

finding.

As already noted,

the latter

causality finding.

that Hall and Noble’s

results

are sensitive

to model

He notes that Hall and Noble use the level of money

than its first difference is stationary.

under

Employing

the untested

the Dickey-Fuller

of a unit root in money growth variability, suggesting

enter the regressions

Moreover,

since the causal relationship

of monetarism’

of monetarism

and sample period.

growth variability

evidence

Hall and Noble’s

Their

period.

of no structural

and Serletis

in the post-1979

and Smith

growth variability

by

over a full sample from 1962:2

1979 s&periods.

carries much less weight than a Granger

Mehra

are characterized

years in their sample.

as they note, with Milton

break and on a Granger

specification

1980s

and institutions,

but not for the post-1979

the null hypothesis

occurs.

the

that money growth variability does not cause velocity for the total

results are inconsistent,

should

since

the post-1979

and Smith estimate

well as with the findings

money

that,

by including

sub-period,

Chow test rejects

finding

argue

and over pre- and post-October

the null hypothesis

Smith’s

(1989)

in first differences.

Mehra performs

assumption

that

test, Mehra finds

that this variable

must

causality tests over the 1963:i

to 1984:ii and 1963:i to 1987:iv periods based on (1) the first difference the level of money

growth variability,

(3) both regressors

in levels with a time trend. His tests based on (1) and (3) provide

support

for the hypothesis

to 1984:ii

period,

(2) the first difference

of velocity and

of both regressors,

and

that money growth variability causes velocity for the 1963:i

but not for the 1963:i

results based on b) do not support

to 1987:iv period.

the hypothesis.

On the other

hand,

the

THE THOERY AND PRACTICE OF FINANCE This

existing

variability changes

evidence

Friedman’s

hypothesis,

and inconclusive.

acting simultaneously, (1989)

general

the bi-variate-causality

framework

that controls

growth

recognizing

of a number

to reexamine

the influence

that

of factors

tests may be subject to specification

“... it is necessary

concludes,

that money

In addition,

in velocity may be the result of the causal influence

As Mehra more

on Milton

causes velocity, is limited

427

bias.

the role of volatility in a

of other

factors

on velocity...”

(p.265). McMillin

(1991)

a multi-variate

examines

the pre-and

vector-autoregressive

short- and long-term

interest

He assesses the importance decompositions

to 1981:4

decompositions

only at longer except

from

shift occurs

We investigate

the causal

growth variability,

price deflator consider

where velocity depends inflation,

and historical

employing

on real income,

and money growth variability.6 velocity through

decompositions

to mid-1983.

with respect

to

effect in the variance

Nonetheless,

to all variables,

variance

over 1982:l

lags while it does not help to explain 1982:l

variability, in the vector autoregression money

of velocity employing

of money growth variability has a significant

decomposition, that a structural

behavior

of these variables in explaining

over 1961:l

1988:4. The measure

model,

rates, expected

post-1982

the historical

McMillin

including

concludes

money

growth

after 1982:l.’

relationship

the nominal

between

interest

both bi-variate

velocity

and the money

stock,

rate, real GNP, and the GNP implicit

and multi-variate

only the Ml money stock, and not any broader

causality frameworks.

measures,

We

since the problem

of velocity variability after 1979 seems most acute for the narrow definition.

MJ3THODOLOGY In order

to investigate

determinants,

the causal

relationship

we employ the following

between

general

velocity

multi-variate

and its potential

autoregressive

n

Dvl = a() +

a:(L)D Vt + c

model:

(1)

ajk(L)Dx,, + /.tl

j=2

where

v1 is the natural

operator, operator,

Xj~

logarithm

of the income

are the factors that potentially

a;(L)

and a,k(L) are polynomials

cX;= (aI~+aIrL+cZ,2L2+.

in the lag operator

methodology

(1985).

procedures

All estimations

to identify Equation use ordinary

identify the multi-variate

for Dv, by constructing

is the first difference L is the lag

such that, for instance,

variance.

of Hsiao’s (19’79; 1981) bi-variate autoregressive Miller

D

. . . + CC&~), and n, is a white noise error term, distributed

with a zero mean and constant The empirical

velocity,

affect velocity, aa is a constant,

the following

1 relies basically on an extension

modelling least squares.

method

model. First, we determine univariate

due to Ahking and

The following

autoregressive

sequential

the optimal lag length process:

428

QUARTERLY REVIEW OF ECONOMICS AND FINANCE

Dv, = 010 + and by employing

Akaike’s

a;(L)Dvt + PI

final prediction

error

(2)

(FEE)

criterion

to select

length. That is, we allow the lag length to vary from one to a maximum FPEs at each lag; and we choose optimal

the order

with the smallest

the lag

of k; we compute

FEE. Assume

that the

order for Dvl is v.

Second,

to determine

Dvt as a controlled

the first of the DT~ factors

variable with optimal

turn as a manipulated

variable.

to enter

Equation

lag order v and include

We then estimate

the following

1, we treat

each D3ejtfactor in

bi-variate

autoregres-

sive processes: ~,=ap+aJ(L)Dv,+oljk(L)D~i,+~~~~;

j=2,3,.

For each Dz+ we allow the lag length to vary from one to a maximum the

optimal

minimum

lag order

for which

the bi-variate

FEE. Next, we use the computed

including

Dxjrto rank the regressions

smallest FEE is admitted x3 is ranked Third,

and include

We then estimate

Again, for each manipulatedvariable, the FBE at each lag; and we choose optimal

Finally, this procedure

Our estimations

employ

1989:i.

Since

causality

whole

period

1963:i

direct Mehra

comparison

models,

lags v and m, variables.

processes: + pjl; j=

234, . .

(4)

j TL.

we vary the lag length from one to k; we compute the lag order that yields the minimum

FEE. The

next to the multi-variate

model

lag order.

continues

until all Dqt variables are admitted to Equation

Citibase

Data File quarterly

tests are sensitive to 1989:i

period

data for the period

to the sample

period,

as well as the 1963:i

of our findings

to those of other

to those used by Hall and Noble

(1989).

the money income,

with optimal

1.

Specifically,

stock, by money

(1987);

we test the hypotheses growth variability,

and by the price level. Since other we also report bi-variate-causality

studies,

1963:i

our tests include

to 1979:iii,

the 1963:i to 1987:iv, and the 1970:i to 1985:i sub-periods;

correspond

that

RESULTS

EMPIRICAL

1984:ii,

+ a;(L)D,,

variable with the smallest FPE is admitted

with its predetermined

order. Suppose

DXjlfactors as manipulated

u-i-variate autoregressive

Dv, = ap + a: (L)Dv, + oT(L)Dx3,

manipulated

variables

each of the remaining

the following

the

is m.

we treat Dv, and Dx~~as controlled

respectively,

yields

the regressions

Dvl. The DXjlwith the

1 with its prespecified

lag length

k and determine

process

FPEs across

in their ability to explain

first into Equation

first and its optimal

autoregressive

minimum

(3)

..,n

to the

the 1963:i

to

this allows a more

since these subperiods

Fisher and Serletis

(1989);

and

that velocity is Grangercaused

by

by the nominal

studies employ

results to compare

interest

bi-variate

rate, by real autoregressive

our results to theirs. But,

THE THOERY AND PRACX-ICE OF FINANCE

we also use a multi-variate model that examines

429

the robustness of the bi-variate

findings. Bi-Variatc&ausality Tests

We estimate the following bi-variate autoregressive

processes for each sample

period. Dv, =

010 +

c&L)&,

+ c&L)hnl

Dvl =

CQJ+

c&L)&

+ a$L)Ds, ;

Llvt= alJ + c&L)&

+ c&L)&

; (6)

;

Dv, = oo + &L)Dv, + c&L)Dyl ; and Dvt = a0 + c&L)Dv, + &L)opt

;

(9)

where m,, yt, and pt are the natural logarithms of the Ml money stock, real GNP, and the GNP implicit price deflator, respectively; ir is the three-month Treasury bill rate; and S, is the eightquarter moving standard deviation of the Ml growth rate. A maximum lag length (k) of 12 quarters is used to search for the optimal lag lengths. Mehra (1989) notes that some disagreement exists as to whether stationary data are preferred for causality tests. Unit roots in the data cause problems with the asymptotic properties of causality tests (e.g., Sims, Stock, and Watson 1986); whereas, removal of trend information form the data may lead to low power in causality tests (e.g., Christian0 and Ljungqvist 1987). We prefer to avoid problems with the asymptotic distributions. To the extent that the resulting causality tests have low power, this biases our analysis toward the anti-monetarist view. We test in each sample period for the presence of unit roots in both levels and first differences of all variables. We use both the Dickey-Fuller (DF) test and its augmented (ADF) version.‘Both DF and ADF tests fail to reject the null hypothesis of non-stationarity in the levels; the hypothesis of a unit root cannot be rejected. But, this hypothesis is rejected for the first differences for all variables, except the price level for which only the DF test rejects non-stationarity.g Thus, we enter all regressors into our estimations in first differences. Our tests confirm Mehra’s (1989) finding that the standard deviation of money is non-stationary in levels, but firstdifferenced stationary. The minimum FPE values, the optimal lag specification (in parentheses), and the appropriate Ftests for estimating Equations 5 to 9 are reported in Table 1. The results indicate that in the 1963:i to 1979:iii and the 1970:i to 1985:i periods, the logarithm of velocity is well described by a random-walk process; whereas, in the 1963:i to 1984:ii period, the first difference of velocity follows a second-order autoregressive process,

QUABTEBLY

430 Table 1.

BEYIEW OF ECONOMICS

GRANGER CAUSALITY

BIVARIATE AND MULTIVARIA~

FPE(~3

FPEWI

AND FINANCE

FPE(v, m) FWv,g) FPIS(sp)

PPE (v, i, m, s) MuItivariate Fs for

Bivariate Fs for Sample Period

CDi

CDS

ZDln

.?IDg

GDp

1963:i-1979:iii

0.0878

0.0954

0.0849

0.0949

0.0948

uu)

(W)

1963:i-1984:ii

197O:i-1985:i

1963:i-1987:iv

1963:i-1989:i

(OJ) 5.30*

(091) 0.71

4.86*

0.05

0.06

0.1099

0.1363

0.1418

0.1474

0.1509

(2,l) 30.65**

cm 5.38*

(272) 3.65*

(292) 1.97

(291) 0.08

0.1188

0.1688

0.1712

0.1839

0.1920

(091) 30.79**

w9 5.75**

(092) 5.57**

(O>l) 3.47

(O>l) 0.87

0.1431

0.1763

0.1858

0.1875

0.1868

(1,2) 16.14**

(l>l) 6.98*

(lsl) 0.88

(1,l) 0.11

(l,l) 0.04

0.1385

0.1822

0.1808

0.1820

0.1818

(1.2) 17.19**

(1.1) 0.87

(Ll) 0.82

(l*l) 0.13

(121) 0.29

TESTS

CDi

CDm

ZDS

0.0879

(O>l)

(OJ241) 1.88

0.20

2.71

0.1113

(2,1,2,1) 2.63 0.1309

16.20**

2.08

(OA219 2.03

13.01**

1.72

0.1489 (1,2,1,1) 0.70

11.75**

0.28

0.1444 (1,2,1,1) 0.15

16.04**

0.30

Nolcs: The first live columns present the final prediction errors (FF’ES), optimal lag lengths (in parentheses), and Statistics for the bivariate Granger causality rests. For example, the Statistics in column one test whether lhe interest rate Cranger causes velocity in each of selected sample periods. The last three columns pronde similar information for the multivariate Grange1 causality ~esu. In these multixxiate regressions, the variables enter l&t with the interest rate. then the money stock. and finally money growth variability, except that the money stock enters before the interest rate in one case (indicated by a superscript a) and money growth variability enters before the money stock in another (indicated by a superscript b).

the

**means significant

at the l-percent

level.

and in the 1963:i to 1987:iv and the 1963:i to 1989:i periods, process. to In sum, the uni-variate ments are sensitive The Fstatistics sis that money 1963:i to 1984:ii, to previous Fischer

to the sample period

a first-order

processes

growth variability

autoregressive

describing

velocity move-

chosen.”

for the bi-variate tests suggest the following. does not Granger-cause

First, the null hypothe-

velocity is rejected

the 1970:i to 1985:i, and the 1963:i to 1987:iv subperiods.

studies,

our results for the 1963:i

and Serletis’s,

but inconsistent

For the 1963:i to 1984:ii period, in conflict

autoregressive

with Mehra’s.‘*

with those of Fischer

to 1979:iii

period

For the 1970:i to 1985:i period,

and Serletis;

are consistent

with Hall and Noble’s and Brocato

our results are consistent and for the 1963:i

for the

Compared with

and Smith’s.

with Hall and Noble’s,

but

our results are consistent

to 1987:iv period,

they are in

conflict with Mehra’s. Second, the null hypothesis that the money stock does not cause velocity is rejected

for the 1963:i to 1979:iii,

the 1963:i to 1984:ii,

the last result being consistent

null hypothesis

that the nominal interest rate does not cause velocity is rejected

periods.

And fourth,

cause velocity

the null hypothesis

is never

rejected.

Thus,

with Fischer

and the 19’70:i to

1985:i periods,

that real income the bi-variate

and Serletis’s. Third,

the in all

and the price level do not

tests suggest

a robust

causal

THE THOERY AND PRACTICE OF FINANCE

influence

431

for the nominal interest rate, but less robust for the money stock and the

variability of money growth. On the other hand, real income and the price level do not contribute to the temporal explanation of velocity. MultiVariate-Causality Tests

We examine, as our main objective, the aforementioned causal relationships in a multi-variate framework. As such, the significance of the causal influence of one factor on velocity occurs while holding the influences of the other factors constant. Since the bi-variate tests provide no support for a causal relationship between velocity and real income and the price level, we exclude them in our multi-variate analysis. Thus, we estimate the following autoregressive process: fit

=

a0 +

a; (L)Dv, + c&L)&

+ c&L)&

+ c$(L)Dm,,

(10)

where V, i, s, and m are the optimal number of lags for velocity, the nominal interest rate, money growth variability, and the money stock, respectively. These lags are determined following the steps outlined in the section on Methodology. Equation 10 is estimated over each sample period. In Table 1, we report the minimum FPEs, the optimal lag structure (in parentheses), and the fitatistics in the last column. The sequence of entry of variables into the autoregression, based on our selection criteria, is first the interest rate, followed by the money stock, and lastly by money growth variability, except where noted in Table 1. The Statistics suggest the following. First, in the 1963:i to 1979:iii period, the causal relationship between velocity and each manipulated variable is insignificant; the causal influences of the nominal interest rate and the money stock suggested by the bi-variate tests disappear l3 Second, the null hypothesis that the interest rate does not Grangercause velocity is rejected in all other sample periods, and that the money stock or money growth variability do not Grangercause velocity is not rejected in all sample periods. Thus, the multi-variatecausality tests indicate that over the post-october 1979 period, only the nominal interest rate directly Granger causes velocity.‘4 Our findings provide support for the hypothesis that the higher variability of velocity in the 1980s resulted directly from the increased interest sensitivity of the Ml demand for money in conjunction with financial innovations and financial deregulation, which increased the degree of substitutability between Ml balances and savingtype non-Ml deposits (Hetzel and Mehra 1989; Mehra 1987; 1989). Thornton (1983) argues that interest rate changes, financial innovations, and financial deregulation have a rather temporary effect on the growth rate of velocity; once portfolios adjust, the rate of velocity growth will resume its previous path. Since interest rate changes have a significant causal influence on velocity throughout the 198Os, it seems that, if this influence is indeed “temporary,” then portfolios must adjust slowly. On the other hand, Hetzel and Mehra (1989) suggest that the short-term interest sensitivity of the Ml demand for money has increased because of the slow

432

QUARTERLY REX’IEW OF ECONOMIC23 AND FINANCE

adjustment of the interest rate payable on NOW accounts to changing market rates. With a more interest sensitive demand for Ml in the 198Os, interest rate movements give rise to wider fluctuations in velocity than in the pre-1980s period. Our evidence seems to support Gordon’s (1990) view that in the 1980s “The rigid link between growth in Ml and inflation, so stressed by monetarists, had been broken by the money demand (velocity) debacle, which in turn was caused by financial deregulation.” (p. 531). While our results are robust, monetarists may suggest that appearances

can be

misleading. That is, while the data imply that the interest rate Granger causes velocity, rather than money growth variability, when one controls for both these and other variables, it may be that money growth variability first causes the interest rate, which then causes velocity. And thus, the effect of money growth variability through the interest rate is obscured in our multi-variate tests. To provide some insight on this issue, we also perform bi-variate Granger causality tests on the interest

rate and money growth variability. Our findings, which are

reported in Table 2, can be stated succinctly. First, money growth variability causes the

Table 2. BIVARIATE GRANGER CAU!LiLITY TESTS BETWEEN THE INTEREST RATE AND MONEY GROWTH VARIABILITY AND THE MEANS OF AND CORRELATIONS BETWEEN MONEY GROWTH AND INTEREST RATE VARIABILITY FPE (i,s) Bite Sample Period 1963:i-1979:iii

CDS

0.118

0.179

0.0055

0.0076

0.42

0.0072

0.0109

0.83

0.0081

0.0137

0.82

0.0076

0.0106

0.70

0.0078

0.0104

0.59

G3J) 17.12** 0.148

0.257

(891) 18.98** 0.126

0.172 (32) 6.22**

1963:i-1989:i

CORR (s,S)

(OJ) 0.02

(2?2) 5.98** 1963:i-1987:iv

MEANS

Fs for

0.055

0.050

(32) 19.22** 197O:i-1985:i

MEANS

ZDi

(431) 2.74 1963:i-1984:ii

FPE (~3

0.180 (3,2) 2.35

(831) 22.16** 0.283 (OJ) 7.28**

Nota: The first (second) column presents the final prediction errcm (FF’ES). optimal lag orders (in parentheses), and Faatistics for regressions with the interest rare (mon9 growth variability) as the dependent&able. Thus, the Statistics test whether money growth variability (the interest rate) G-anger causes tbe interat rate (money growth variability). The third and fourth columns report the means of s and S. where 6 is the eight-quarter moving standard deviation of the interest rav. The fifth column provides tbe simple correlations between I and 6. *‘means significant at the l-percent Icwl. *means significant at the Spercent

level.

THF. THOERY AND PRAtXICE

OF FINANCE

433

interest rate, as the monetarists may argue, during the 1963:i to 1984:ii, the 1970:i to 1985:i, and 1963:i to 1987:iv periods, but not during the 1963:i to 1979:iii and the 1963:i to 1989:iperiods.15 Second, the reverse causality from the interest rate to money growth variability is also significant in every period, except for 1963:l

to 1979:iii. In

sum, in each case where money growth variability causes velocity in the bi-variate tests, it also causes the interest rate. Thus, the multi-variate ftndings that the interest rate, not money growth variability, causes the velocity may indeed mask the role of money growth variability, at least during the 1980 to 1987 period. But, the story is more complex, since the interest rate also causes money growth variability. The bottom-line issue is whether the increased money growth variability achieved lower or higher interest rate variability. If higher, then a policy of smooth money growth would have led to less variability of both the interest rate and velocity (i.e., the monetarist position). If lower, then interest rate and velocity variability would have been higher (i.e., the anti-monetarist position). Such counterfactual experiments are difficult to implement. In an attempt to shed some light on the @sues, we calculate an eightquarter moving standard deviation of the interest rate and determine the means of, and the simple correlation

between, money growth and interest rate variability in

each of our sample periods. Table 2 reports these results. The inclusion of the early 1980s leads to higher mean money growth and interest rate variabilities. We also find a positive correlation between these two variability measures, where the highest correlations occur for samples including the early 1980s. These observations support to the monetarist position.

lend

CONCLUSION We investigate the causal relationship between the Ml income velocity and money growth variability, the nominal interest rate, the Ml money stock, real GNP, and the GNP implicit price deflator. Granger-causality tests are conducted employing both bi-variate and multi-variate models. The bi-variatecausality tests show strong support in every sample period for the nominal interest rate as an important causal factor of velocity; money growth variability and the money stock have significant causal influences in only three out of our five sample periods; and in every case, real income and the price level do not Grangercause velocity. The multi-variatecausality tests provide, in every post-1979 sample period, support for the hypothesis that the nominal interest Grangercauses velocity; whereas, the causal effects of money growth variability and the money stock cease to be significant in every case. Our multi-variate tests, therefore, suggest that the bi-variate tests may experience specification bias because of missing variables. Our evidence cannot fully confirm or deny Milton Friedman’s explanation of the variability of velocity. The multi-variatecausality tests indicate that money growth variability does not Grangercause velocity, which supports the view that the greater

434

QUARTERLY REVIEW OF ECONOMICS AND FINANCE

variability of velocity in the 1980s emanates the Ml demand for money in conjunction deregulation.

But, some of this increased

from the increased

interest sensitivity of

with the financial innovations interest

rate movement

and financial

results from the

higher money growth variability, and vice versa. In sum, we provide some support for the monetarist’s variability

contributed

to velocity variability,

position that money growth

but only indirectly

as money

growth

variability affects interest rates. Would a more stable money growth in the early 1980s have led to a more stable velocity? Maybe, maybe not. The important question

is whether

a more stable money growth would have led to higher or lower

interest rate variability. Put conversely, the fundamental money growth variability led to smoother

issue is whether the increased

or more volatile interest rate movements

the early 1980s. Simple means and correlations variability measures

counterfactual

suggest the latter, supporting

of money

growth and interest

the monetarist

in rate

view.

NOTE!3 *We acknowledge the helpful comments of an anonymous referee. 1. A careful distinction needs to be drawn between variability and instability of velocity. Agreement exists, since it is observable, that velocity variability rose after 1979. The debate focuses on whether this increasedvariability is explainable by movements in other variables (the monetarist view) or not (the anti-monetarist view). In the rest of this paper, we refer generically to velocity variability; instability is only used when the context clearly indicates the anti-monetarist view. 2.

Pierce (1984) also argues that the Federal Reserve conducts open market operations

under the false assumption that bank borrowing is determined

by a random walk, thus,

de-stabilizing money growth. 3.

Here we discuss the more “popular explanations” advanced in the literature. For more

on these and other suggested explanations, see Tatom (1983); Thornton (1983); Hetzel(l984); Judd and Motley (1984); Keran (1984); M. Friedman (1984); Pierce (1984); Miller (1986); Taylor (1986); Rasche (1987); Hall and Noble (1987); Santoni (1987); Mehra (1986); Carlson (1989); and Miller (1989). 4.

Gould et al. (1978)) employing annual data, find evidence that changes in velocity

amplify rather than offset changes in the rate of money growth. When, however, they use quarterly data,

they find

that during the postwar period, a tendency exists for changes in velocity

to offset changes in the rate of money growth; they suggest that errors-in-variables may explain this result, especially given the quieter postwar data. 5.

The variable x is strict exogenous to y if neither lagged nor contemporaneous

values

of xprovide useful information to explain y over and above lagged values of y. Cooley and LeRoy (1985) also discuss the concept of predeterminedness-the

contemporaneous

value of x does

not help to explain y, but lagged values may or may not. The issue at hand is whether money growth variability, or other variables, help explain velocity, not restricted solely to contemporaneous terms. Thus, strict exogeneity, or lack thereof, meets our purposes.

THE THOERY AND PRACTICE OF FINANCE 6.

435

In an earlier paper, McMillin (1988) considers the effects of money growth variability

on macroeconomic variables, not including velocity, using the same methodology. He concludes that money growth variability has important effects on the macro economy. 7. This methodology of vector autoregressive models and variance decompositions has, at least, one major shortcoming-the researcher must provide an initial ordering of the variables before a decomposition can be determined. The ordering of variables introduces something akin to a causal ranking. While McMillin states that several orderings were examined and that the results tended to be robust across orderings, the findings actually reported placed money growth variability first with interest rates in the middle and the velocity at the end. 8. Test statistics are reported in Fuller (1976, p. 373). 9. Inspection of autocorrelations and partial autocorrelations for the first difference of the natural logarithm of the price level suggest stationarity. The autocorrelations tail off quickly and the partial autocorrelations have a spike at lag one, which is much less than one. 10. Hall and Noble (1987) find that the rate of velocity growth follows a random walk process over the 1963:i to 1985:i period; one possible explanation of the difference with our finding may be that our data are more recent and our velocity measure is based on revised data. 11. It also appears that the process is sensitive to the frequency of the data. For instance, Fisher and Serletis (1989), using monthly data, find that in the 1970:ii to 1984:iii period, the first difference of the natural logarithm of Ml velocity is described by a first-order autoregressive process. Gould et al. (1978) find that changes in annual velocity follow a random-walk process (see also Gould and Nelson 1974, Raj and Siklos 1988); but for quarterly data, the process appears to be sensitive to the sample period. Gould et al. also find that the apparent downward historical shift in the velocity series is not statistically significant. Rasche (1987) finds that velocity in the 1980s follows a random walk with drift; and he identifies a significant negative shift in velocity movements around the third quarter of 1981. This break remains significant even when he accounts for a number of variables that may affect velocity, such as interest rates, inflation, wealth, etc. 12. Theconflictmaybedue to thefactthatMehrateststhehypothesisusingarbitnuylaglengths. 13. We also calculate the Statistic for the joint significance of the coefficients of the lagged interest rate and lagged money stock terms. The statistic [i.e., F(3,61) = 3.971 is significant at the Eipercent level. Thus, lagged interest rates and lagged money stocksjointly Granger cause velocity. 14. While these results may appear at first blush to be in conflict with those of McMillin (1991), who finds that both money growth variability and interest rates provide significant information in explaining movements in velocity in his variance decompositions. Variance decompositions consider the effect of innovations in one variable, say money growth variability, on another variable, say velocity. But, the innovations in money growth variability can have their effect on velocity through their effects on other variables, such as interest rates. Thus, the finding of significant variance decompositions for money growth variability is analogous to the bivariate causality finding. Our bivariate causality findings suggest that both the interest rate and money growth variability Granger cause the velocity, consistent with McMillin’s variance decomposition results. 15. Mehra (1987) reports similar findings from a more standard interest rate regression. To wit, he finds a positive correlation between Ml money growth variability and the one-year Treasury bill rate over the 1963 to 1986 period. Such correlation disappears if post-1979 data are excluded. Moreover, using M2 or M3 money growth variability does not produce significant correlations, even including the 1980s.

436

QUARTERLY

REVIEW OF ECONOMICS

AND FINANCE

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