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NOVEMBRO DE 1986. 1. INTRODUCTION. 101. Previous work on the demand for money in Brazil has concen- trated on the demand for narrow money (M1), ...
R.de Econometria

Rio de Janeiro

v.

VI

n9 2

p.

99 -130

nov

1986

AGGREGATE DEMAND FOR NARROW AND BROAD MONEY:

A STUDY FOR THE BRAZILIAN ECONOMY

(1970-1983)*

Joaquim

J . M. Gu i l h o t o**

ABSTRACT

To study the aggregate demand for narrow and broad money the Brazilian economy in its most recent period,

for

1970 to 1983,

a

basic model was developed. From this model, which is a restricted one, an unrestricted� del was derived.

Using information from both models,

the unrestri£

ted model was used to derive a common factor model as well as

a

first differences model. The best results are attained with the common factor model.

*

*'

The author wishes to thank Prof. Case M. Sprenkle� Prof. Paul Newbold� Prof. Roger W. Koenker. Manuel A. R. da Fonseca� 2nd two anonymous referees for their helpful comments o n earlier drafts of this paper. The author also ap­ preciates the help of Suzanne Wilson with the English. Financial support was provided by CAPES (Cooraenacao de Aperfeicoamento de Pessoal de Nivel Su perior). University of Illinois at Urbana-Champaign, U.S.A .



100

REVISTA OE ECONOMETRIA

RESUMO

Para estudar a de..landa agregada par moeda na sua forma restrita e mais abrangente, para a economia brasileira no de 1970 a 1983,

urn

modelo basico foi desenvolvido.

A partir deste modelo basico, que e dele nao restrito foi desenvolvido. delos, urn

0

urn

modelo restrito,

urn

urn

rno

Usanda informa�oes dos dais rna

modele nao restrito foi usado para derivar

fator comurn, assirn como

urn

modele

com

modele em primeiras diferencas.

Os rnelhores resultados sao obtidos com mum.

rnais

periodo

0

modelo do tater

co-

NOVEMBRO DE

1.

1986

101

INTRODUCTION

concen-

Previous work on the demand for money in Brazil has trated on the demand for narrow money

(M1),

and is limited to

re­

sults for the period before 1979', when (it has been suggested)



re may have occurred a structural change. This paper provides

re­

suIts for both narrow (111) and broad (M3 ) money, and tests whether the post 1978 period is different. A discussion of the theory of demand for money can be in Goldfeld ( 1973 and 1976) I and Laider ( 1977). Feige and

found Pearce

( 1977) presents a survey of empirical studies for the U.S.A.;

survey for European countries, Australia and Japan is in Pase and Kune

( 1975);

a

presented

and Barbosa ( 1978) presents a survey

of

studies made for Brazil. The methodology presented by Blommestein and Palm (1982) chosen a s the basi� Lor studying

the aggregate demand for

was money

for the Brazilian ecunomy. The choice of this work was made becau­ _ se it allows the derivation of different models from one initial mo del. These derivatior:.s are made using information from the

theory

as well as from th� data set. The methodology consists basically of the construction of

a

restricted model, £J_OiU ",hich an unrestricted model is derived.



sing information from both models,

the unrestricted model is

See Barbosa (1978). �",:. f.l("·re specifically Pastore ( 1973), da Si!va Silveira (1973). Cont;;>dor (1974), and Cardoso (1981).

used

(197 3),

REVISTA DE ECONOMETRIA

102

to derive a common factor and a first differences model.

An

ARIMA

model is also constructed for comparison with the models presented above. The period to be studied is from 1970, IV to 1983,

IV and

it

is broken down into two subperiods: 1970 , IV to 1978, IV, and 1979, I to 1983,

IV. A Chow test is conducted to test for the hypothesis

of structural change between the two subperiods. A test to verify the existence of monetary illusion in

the

aggregate demand for narrow and broad money is also conducted. The work is organized as follows:

in the next section the res

tricted and the unrestricted models are presented;

3,

in section

the empirical analysis of the models is made, and the common

fac­

tor model and the model in first differences are also derived;

con

elusions are made in section 4.

2.

THE MODEL

following

The aggregate demand for money is defined in the way (all variables are natural logarithms and the time

i

is

given

in quarters l :

M* t

(2.1)

Where: M* t

Yt

desired amount of liquidities (nominal) period

of

!.

expected income (real)

for period

!.

a representative interest rate (nominal) period

at the end

!.

at the end

of

103

NOVEMBRO DE 19B6

p�

= the expected price level at the end of period

Mt' Y£r

The unobserved variables lows:





are defined as

fol­

uses a partial adjustment process of the form:

e

yt

and

!

(Mf - M t

_

1

)

0


� :11 z

g





I,

NOVEMBRO OE 1986

123

o · ,

o · ,

" .

0 0 0 0 0

0

I

0

I

0 0 0 0 0

0

I

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0 "

0 0 0 0 0 N

0 0 0 0 0

o ·

o · ,

o · ,

o ,

o

;:

REV!STA DE ECDNDMETRIA

114

�� 0

,

·

0 ·

0 0

\

\ 0 · ·

0 0 0 0 0

0 0 0 0

.

0 0

-

i

0 0 0 0 0

.



i

0 0 0 0 0

. ,

0 0 0 0 0

0 0 0 0 0 0

. .

0 0 0 0 0 0 0

0 0 0 0

. ,

.

0 0 0 0 0

0 0 0

i

.

\

0 ·

\ \ \ \ \ \

i I i

I

0 0 0 0 0

,

0 0 0 0 0

,

0 0 0 0

.

0 0 0 0 0

0 0 0 0 0 0

0 0 0 0

0 0 0 0

g

0 0 0 0 0 0

. "

,

\

0 0

0

·

\ \ \ \

,

0 · ·

0 0 0

0 ·

"

� � 0 · ·

0 · ·

NOVEMBRO

125

DE 1986

In order to compare the prediction power of the different mo­ dels calculated for the demand function for narrow and broad mone� the models (restricted, unrestricted, common factor, first

diffe­

rences, and ARI�m) were plotted with the seasonally adjusted

va­

lues for Ml and M3. Figures 1A through 1D show the plotted values for Ml.

From

the analysis of these figures, one can see that the ARlMA model is reasonable for the first subperiod ding for the second one gression nr.

1)

{1970,IV-1978,IVI, but

and the unrestricted model (regression nr.

very close in their prediction values. model

(regression nr.

sion nr.

mislea­

(1979,I-1983,IV) . The restricted model (r�

14)

8)

Between the common

are

factor

and the first differences model (regres­

16) , one has to choose the common factor model.

This also

seems to be the best model, in terms of prediction values, of

the

several models presented in Figures 1A through 1D. In Figures 2A through 20, the values for M3 \V'ere plotted. The ARIMA model is clearly the worst in terms of predicting the values for M3. The restricted model (regression nr. ted model (regression nr.

11)

5)

and the unrestric­

have prediction values very close to

one another. A comparison between the common factor model (regres­ sion nr.

15)

and the first differences model

becomes harder than the comparison for M1,

(regression nr.

18) now

but one is inclined

select the common factor model. Indeed, this model seems to

to

per­

for� better than the other models, for M3. From the visual analysis made above, one can

automatically

discard the ARIMA models as they clearly are the ones that present the worst prediction power of the models plotted.

From the statis­

tical pOint of view, problems were seen in the unrestricted

model

(too many variables) , in the restricted model (serial correlation), and in the first differences model (the steady state velocity

va­

ries inversely with the interest rate) . The statistical tests com­ paring the different models also indicate that a reduction in

the

parameters space of the unrestricted model is the right thing

to

do (see analysis of Table 6), and that the model in first differe� ces can be rejected as being the right specification.

All of

this

information, plus the fact that the common factor model uses infor

126

REVISTA

DE ECDNDMETRIA

mation from the restricted and the unrestricted modelsi and

that

its estimates of the elasticities present the right signs,

leads best

one to believe that the common factor model is the one that explains the aggregate demand for narrow and broad money

for

the

of

the

Brazilian economy. The next paragraphs in this section make an analysis results attained in the common factor model, From regression nr.

14, for M1, one has the right sign for the

income elasticity of money, elasticities.

for M1 and M3.

as well as for the interest

and

price

If one compares these elasticies with previous

stu­

dies made for the Brazilian economy (see a survey in Barbosa, 1978), usually using M1 as >the definition for money, one can see that the value of 0.741 for the income elasticity conforms with those

stu­

dies which, in general, present values between 0. 7 and 1.0.

For

the interest elasticity, the value of -0.03 for time t and the va­ lue of -0.108

for time t-l also agree

with previous studies.

relation to the price elasticity, it presents a value This regression also shows a negative relation

(-0. 031)

quantity of money in time t-1 and a positive relation

In

0.394.

of

\..ith

the

(0. 58 )

to

its quantity in time t-2. I t should be noted that t h e coefficients of M and R are not significantly different from zero. t _1 t From regression nr. 15, for M3, it can be seen that all elasticities present the right signs. As one rarely sees a

the study

of aggregate demand for money for the Brazilian economy using M3as the definition for money, it is not possible to compare the su�ts fo� M3 with previous studies. The results attained for

re­ this

regression are: an income elasticity of 0.8 25; an interest elasti­ city of -0.073 in relation to time t and of -0.027 in relation time t-1;

a price elasticity of 0. 591; and a positive

with the quantity of money in time t-l (0.174)

relation

and in time

(0. 272) . Looking at the regression results, one sees low

to t-2

t-values

for the coefficients of M _ and R _ . t 1 t 1 A comparison between the regression results obtained for

Ml

and M3 leads one to observe that there is a closeness between

the

elasticity coefficients of both regressions. One can then conclude

NOVEMBRO DE 1986

127

that there is not much difference in measuring the aggregate deremd in terms of narrow or broad money.

4.

CONCLUSION

In this work, results were obtained for different

specifica­

tions of the aggregate demand for narrow and broad money Brazilian economy for the period 1970,IV - 1983,IVt

for

and

the

subpe-

ricds 1970tlV - 1978,IV and 1979,1 - 1983,IV. All the specifications were basically derived from an initial model, which is a restricted one. From this model an

unrestricted

model was derived. Using information from these models, a third o­ ne, a common factor model, was derived. This last model was

also

expressed in the form of first differences. Also, an ARlMA

model

was calculated for comparison with the above models. From statistical as well as graphical analysis of the

diffe­

rent models, the common factor model appeared to be best in expla� ning the aggregate demand for both narrow and broad money. The test for structural change between the two subperiods, u­ sing the restricted and the unrestricted models, showed that thehy pothesis of no structural change can not be rejected for M1,

but

can be rejected for M3. Tests also showed that the hyphothesis of inexistence of mon� tary illusion in the aggregate demand for M1 and M3 can not rejected,

be

implying that the demand for money for the Brazilian ca­

se is for real balances. It was also seen that the elasticities resulting from the cho sen model

(common factor)

for M1, do not disagree with those

ob­

tained in previous studies made for the Brazilian economy. A comparison between the elasticities in the common

factor

model, using M1 or M3 as the definition for money, shows that tiere

128

REVISTA Df

ECONOMETRIA

is not much difference in the results attained using either defini tion.

But, given that the hypothesis of no structural change

rejected for M3, the results for

M3

may be better.

was

NDVEMBRD DE

129

1986

REFERENCES

Banco Central do Brasil, Boiet�n do Banco Centnal do �ll, various issues. BARBOSA, F.R. itA Demanda de Maeda no Brasil": Uma Resenha da Evidencia Empirica". in Pe..6quiod e PR.rutejamen.to Eeonomic.o, Vol. 8, n9 1. pp. 33-82, April, 1978.

BLOMMESTEIN. H . J . and PALM, F.C. "Econometric Specification Analysis - An Ap­ plication to the Aggregate Demand for Money in the Netherlands". in Deis­ tier, M., E. Furst, and G. Schw!::ldiauer (eds.), Game., .6 Econom.i.c.6 Vynantic.&,

and T�e Se4ieo

CARDOSO, E.A.

Ana£y��, Wien; Wurzburg: Physica-Verlag, 1982.

"lima Equa(;ao para a Demanda de Maeda no Brasil". in Pe..&quioa

Ptal1ejamel1,to Ecol1.omieo, 11(3), pp. 617-636, December, 1981.

e

CONTADOR, C. R. "Desenvolvimento Financeiro. Liquidez e Substituicao entre Ati­ vas no Brasil; A Experiencia Recente", in Pe.6quLsd e. p.e.ane.jdme.ttto Ec.onamic.o. 4(2), pp. 245-284, June, 1974.

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nomic.

"The Demand for Money Revisited", in Bltooh..ing& PapVt6 o n

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"The Case of the Missing Money" J in 8Jwoh..ing6 PaP0h Ort

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Ec.o-

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REVISTA OE ECONOMETRIA

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