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.
u
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:
M£
P£
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
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and T�e Se4ieo
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e
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