Monetary anticipations and the demand for money: an application for the South Asian region.
Ahmed, Ather Maqsood ; Rafiq, Mohammad
1. INTRODUCTION
While there are a number of issues in economics which are
frequently scrutinized, the most important of them probably is the
determination of a stable money demand function. Other issues in this
regard relate to the choice between (i) broad vs narrow definition of
money; (ii) measured vs. permanent income; (iii) short-term vs.
long-term interest rate; and (iv) inclusion of a variable for inflation
or expected inflation.
Quite recently, a new dimension has been added to the demand for
money function. It is now argued that unanticipatory changes in the
nominal money supply also affect the real demand for money. Darby (1972)
has proposed that unanticipatory nominal money supply behaves as a
shock-absorber in the money demand function. Initially, Laidler (1980)
and then Carr and Darby (1981) formulated a shock-absorber model in
which they have shown empirically that unanticipatory shocks in money
supply positively affect the demand for money. Inclusion of this shock
variable was justified by Darby (1972) on the ground that money balances
serve as a buffer stock or shock-absorber which temporarily absorbs
unexpected variations in income, especially the transitory income, until
an adjustment is reached in adjusting the portfolio of securities and in
consumer durable goods. The shock-absorber model of Carr and Darby is
based on the following two hypotheses:
(i) Changes in money supply which are fully anticipated will be
reflected in price level expectations and, therefore, in nominal demand;
and
(ii) Changes in money supply which are unanticipated will
temporarily be stored in bank accounts. The adjustment in interest rates
and the price level will not be so quick, so that money demand equals
money supply. Therefore, these unexpected changes in money supply will
affect real money balances with positive sign.
The second hypothesis was tested by Carr and Darby (1981) for eight
industrial countries. Their results show that unanticipated money supply
changes always positively affect the real demand for money. Furthermore,
this particular result is insensitive to the estimation techniques.
Mackinnon and Milbourne (1984), while commenting on the Carr and
Darby paper have shown that the econometric technique used by them yield
severely biased estimates. Mackinnon and Milbourne (1984) arrived at
this result after making a number of algebraic manipulations to the
original model. However, in a later article Carr, Darby and Thornton
(1985) refuted the comments of Mackinnon and Milbourne on the grounds
that the economics used by the later to clarify their position was
wrong. In the process, Carr, Darby and Thornton (1985) not only proved
their second hypothesis as correct, they also proved that their first
hypothesis was also correct. An attempt similar to the above was also
made by Khan (1980). In this article a monetary anticipation model was
estimated for a developing economy.
The present exercise is taken up with a view to put the hypotheses
of the Carr-Darby Model to further empirical testing for developing
countries of the South Asian region. For this purpose, time-series data
have been collected for the relevant variables for Pakistan, India, Sri
Lanka and Bangladesh. (1)
The plan of the paper is as follows. The paper is divided into four
parts. After the introduction and a brief review of literature, the
second part outlines the proposed model. The third part reports the
methodological issues and the results of estimation, while the last part
concludes this study.
II. THE PROPOSED MODEL
The conventional real money demand function as given by Cagan
(1956) is usually expressed as a Cobb-Douglas type function of a scale
variable (usually current or permanent income) and one or more interest
rate variables. The general form of the equation where all the variables
are real and are expressed in logarithmic form is given as follows:
[m.sup.d.sub.t] = [[varies].sub.0] + [[varies].sub.1] [y.sub.t] +
[[varies].sub.2] [r.sub.t] ... ... ... (1)
where
[m.sup.d.sub.t] = [M.sub.t] - [P.sub.t] = logarithm of real money
demand;
[y.sub.t] = [Y.sub.t] - [P.sub.t] = logarithm of real income;
[r.sub.t] = logarithm of interest rate;
[P.sub.t] = logarithm of price level; and
[M.sub.t] = logarithm of nominal money demand.
We assume that there is a tendency of partial adjustment of actual
to the desired level of money stock. The partial adjustment model as
proposed by Chow (1966) is
[m.sub.t] = [m.sub.t-1] = [lambda]([m.sup.d.sub.t] - [m.sub.t-1])
... ... ... (2)
Combining Equation (2) with Equation (1), we get the usual real
money demand equation where there is a lagged dependent variable along
with other exogenous variables. The new equation, after substitution, is
the following:
[m.sub.t] = [[beta].sub.0] + [[beta].sub.1] [y.sub.t] +
[[beta].sub.2] [r.sub.t] - [[beta].sub.3] [m.sub.t-1] ... ... ... (3)
As stated by Darby and Carr (1981), the Chow model is also
consistent with contemporaneous changes in expected nominal money supply
and price level, but it does not work so well when there are nominal
money shocks. To incorporate this type of expression, they have
developed the following relationship. Assume that [M.sup.s.sub.t] is the
logarithm of nominal money supply and [M.sup.a.sub.t] is the
anticipatory value of [M.sup.s.sub.t]. The hypothesis states that real
money holding is not simply related to real money demand as in Equation
(3) but it also includes a term for unanticipated value of money as in
the extended Equation (4), i.e.,
[m.sub.t] = [[beta].sub.0] + [[beta].sub.1] [y.sub.t] +
[[beta].sub.2] [r.sub.t] + [[beta].sub.3] [m.sub.t-1] + [varies]
([M.sup.s.sub.t] - [M.sup.s.sub.t]) (4)
The second type of modification in the original model as proposed
by Carr and Darby is the addition of a term for transitory income. The
reason for the inclusion of this variable as suggested by Darby (1972)
is that all unexpected variations of income, especially the transitory
income, are absorbed by money balances until there is final adjustment
in the portfolio of securities.
Finally, the new proposed model can be differentiated from Equation
(3) by making a choice for permanent income in place of current income.
Therefore, after introducing the two changes, i.e. the choice of
permanent income in place of measured income and by adding the
transitory income in Equation (4), we get the following expression;
[m.sub.t] = [[gamma].sub.0] + [[gamma].sub.1] [y.sup.p.sub.t] +
[[gamma].sub.2] [y.sup.T.sub.t] + [[gamma].sub.3] [r.sub.t] +
[[gamma].sub.4] [m.sub.t-1] + [varies] ([M.sup.s.sub.t] -
[M.sup.a.sub.t]) (5)
where
[y.sub.t] [equivalent] [y.sup.p.sub.t] + [y.sup.T.sub.t]
[y.sup.p.sub.t] = logarithm of permanent income; and
[y.sup.T.sub.t] = logarithm of transitory income.
III. METHODOLOGICAL ISSUES
Before we could proceed with the ultimate results of Equation (5),
it may be important to clarify some of the steps that we have undertaken
while estimating the model. The first step was the estimation of an
unanticipated money supply variable. To calculate this variable, the
first requirement was to estimate some kind of money demand function. In
Carr and Darby (1981) a univariate ARIMA process was used. However,
Mackinnon and Milbourne (1984) used only the lagged values of [M.sub.t]
to find out the value of anticipatory money supply. They later on showed
that the empirical results of these two estimation techniques did not
change the conclusions to be drawn therefrom.
In the present study, the extrapolative predictors were obtained by
regressing the actual money demand on its own past values. The number of
lags were different for every country. We continued to add lags until
the explanatory power of the equation ([[bar.R].sup.2]) declined. This
kind of prediction is regarded as 'partly rational' a term
introduced by Sargent (1973). After adopting the above procedure, we
first calculated the anticipatory values of money supply, i.e.,
[M.sup.a.sub.t], and, in the second step, the unanticipatory money
supply value was calculated by the relationship [M.sub.t] =
[M.sup.s.sub.t] - [M.sup.a.sub.t], i.e. this is the residual in the
above equations, which will now be used as a proxy for the shock
variable in Equation (5). (2)
The second problem related to the estimation of permanent income.
For this Purpose we used the methodology which was suggested by Rausser
and Laumas (1976) and later on was used by Mangla (1979). Here the
permanent income was defined as the weighted average of current and past
income, (3) i.e.,
[Y.sup.p.sub.t] = 0.4 [Y.sub.t] + 0.3 [Y.sub.t-1] + 0.2 [Y.sub.t-2]
+ 0.1 [Y.sub.t-3]
The transitory income can now be calculated from the relationship
given below:
[Y.sup.T.sub.t] = [Y.sub.t] - [Y.sub.p.sub.t]
where
[Y.sup.T.sub.t] is logarithmic transitory income;
[Y.sub.t] is logarithmic current income; and
[Y.sup.p.sub.t] is logarithmic permanent income.
The final problem relates to the estimation of Equation (5) itself.
We have initially estimated this equation by the Ordinary Least Squares
(OLS) technique. Since many variables like ([M.sub.t], [T.sup.p.sub.t]
and [Y.sup.T.sub.t] are all simultaneously determined, there is a
possibility that the estimated results of OLS have a simultaniety bias.
To overcome the problem of simultaniety, we used the instrumental
variable estimation technique. (4)
IV. ESTIMATION RESULTS OF THE MODEL
Although there are a number of studies especially for Pakistan,
India and Sri Lanka where the conventional money demand function is
empirically tested, however, the focus of attention in almost all of
these studies has revolved around testing alternative specifications.
(5)
The results of the proposed shock-absorber model in Table I show
that the money shock variable has a positive sign in all the equations.
The OLS estimates for this variable are significant at the 95 percent
level for Pakistan, India and Bangladesh. For Sri Lanka, the coefficient of the money shock variable is significant at the 90 percent level. The
instrumental variable estimates show that once again this variable
enters positively in all the equations. However, now it is significant
only for Pakistan and India. (6)
Table 1 also shows that the coefficient of transitory income has
also appeared with the correct positive sign for all the countries
except for Bangladesh. This is true both for the OLS and instrumental
variable estimates. The variable of transitory income is significant at
the 95 percent level for India and it is significant at the 90 percent
level for Sri Lanka. Finally, the coefficient of the lagged dependent
variable is also significant and its size is less than unity in all the
four cases. This result is consistent in the presence of the partial
adjustment model.
In the same table, alternative specifications for the four
countries are also reported. Instead of making any distinction between
permanent income and transitory income, we have used measured income as
a scale variable. (7) The results of the equations have not changed the
complexion of the earlier story as the money shock variable has not only
appeared with a positive sign, it is significant as well. All other
variables also have the correct sign. However, the explanatory power of
the alternative equations is slightly less.
As far as fully anticipated changes in money supply are concerned,
according to Carr and Darby (1981) these will be reflected in the price
level expectations and, therefore, in nominal money demand. This
hypothesis could not be verified in the present study. It may be
important to note that the empirical verification of this hypothesis was
not even reported by Carr and Darby (1981) in their original work.
However, in their rejoinder to Mackinnon and Milbourne (1984) they have
successfully attempted this.
V. CONCLUSIONS
In this paper an attempt has been made to empirically test the
hypothesis that changes in money supply which are not fully anticipated
affect the real money balances with a positive sign. Although this
hypothesis was verified for eight industrial countries by Carr and Darby
(1981), nevertheless, it required further empirical tests especially for
the economies of developing countries. Here we have shown that in a
shock-absorber model for countries of the South Asian region, the shock
variable enters in all the equations with a positive sign. Furthermore,
the coefficient of the transitory income is also positive and greater
than zero for all except one case. This confirms that all unexpected
variations of income, especially the transitory income, are absorbed by
money balances until there is a final adjustment in the portfolio of
securities. Towards the end it may be noted that the hypothesis that
fully anticipated changes in money supply affect nominal money supply
could not be verified in the present exercise.
Comments on "Monetary Anticipation and the Demand for Money:
An Application for the South Asian Region"
The paper is a successful attempt to apply the Carr-Darby model to
some of the Asian countries. Three major comments on the paper
concerning its theoretical basis, specification of the model and the
empirical estimates are in order:
1. The hypothesis, that unanticipated changes in money supply
affect real money balances rather than the interest rate and price
level, was tested by Carr-Darby for eight industrial countries. To put
this hypothesis to further empirical testing for developing countries,
the authors needed to establish the relevance for doing so by convincing
the readers about the following queries:
(i) Are there really some changes in money supply which remain
unanticipated in the developing countries?
(ii) If yes, how large is the size of such changes, i.e., are these
changes significant enough to be considered separately in the demand for
money?
(iii) Do the capital markets in the developing countries really
provide a portfolio adjustment mechanism in the same fashion as they do
in the case of industrial countries?
(iv) Do the communities in developing countries really have a feel
for distinction between anticipated and unanticipated parts of money
supply changes?
2. The unanticipated changes in money supply have been approximated
in the paper by the residual of the equation regressing money supply on
its past values alone. Estimates of this equation for all the four
countries considered in the study turn out to be unstable as the
coefficients of [M.sub.t-1] exceed unity. Moreover, the residual thus
derived would be biased if there had been large money creation for
budgetary support purposes mainly because a part of such money creation
is anticipated. In view of this, it would be desirable to include in the
equation, some measure of money creation required for federal financing
needs. Barro (1977) used for this purpose, actual federal expenditure in
excess of normal federal expenditure. As an alternative, actual
budgetary support in excess of some average of the sample period may be
used.
3. In specifying the demand for money equation, the authors, simply
follow the Carr and Darby specification and without realizing the
difference of the money markets between the developed and developing
countries, have used, inter alia, interest rate, transitory income, and
unanticipated money supply. In developing countries, interest rates are
often timed by the monetary authorities and remain fixed over a fairly
long period. In these circumstances it is not correct to use the
interest rate as the market price of holding money. Secondly, if there
is any such thing as unanticipated money supply at all, it would be
highly correlated with the transitory income and, thus, the use of both
the variables as regressors simultaneously, as has been done by the
authors, seems highly unwarranted. The mis-specification of the model is
manifested in the insignificant coefficients of both the interest rate
and transitory income in most of the equations; transitory income is
insignificant for all the countries except India and, similarly, the
interest rate is insignificant for all the countries except Bangladesh.
Shaukat Ali
Ministry of Finance, Islamabad
REFERENCE
Barro, R. J. (1977). "Unanticipated Money Growth and
Unemployment in the U.S ". American Economic Review. Vol. 67, No.
1.
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(1) Data in this study covers a period from 1960 to 1982. The
authors are thankful to Mr Muslehuddin, Staff Economist, PIDE for
providing the necessary data for this study.
(2) Alternative specifications using dummy and fiscal variables
were also tried, but unfortunately, neither of these worked well.
(3) Permanent income can also be measured by alternative
methodology which can be found in the studies of Friedman (1959);
Goldfeld (1973) and Laidler (1977). The choice between these
alternatives is purely arbitrary.
(4) The choice of instruments in this study differs not only from
Cart and Darby (1981), it also slightly differs from Mackinnon and
Milbourne (1984). Here we have used the procedure which is quite close
to that of McCallum (1975).
(5) See for example Abe et al. (1975); Akhtar (1974); Mangla
(1979); Khan (1982); Gujrati (1968); Gupta (1970) and Singh (1970) for
India, Wong (1977) and Khan (1982) for Sri Lanka and Naqvi et al. (1984)
for all the four countries.
(6) The equations estimated by OLS and also by instrumental
variable technique are corrected for serial correlation by applying
Cochrane-Orcutt technique, if and when it was present. 7 In order to
save ourselves from any problem that may arise out of the use of the
simultaneous [Y.sup.T.sub.t] and [M.sup.u.sub.t], we have also tried
alternative specification for every country.
ATHER MAQSOOD AHMED and MOHAMMAD RAFIQ, The authors are Research
Economist and Computer Programmer respectively at the Pakistan Institute
of Development Economics. They are grateful to Prof S.I. Cohen for
helpful suggestions on an earlier draft of this paper.
Table 1
OLS and Instrumental Variable Estimate of Demand for Money
Coefficient of
Techniques
of [y.sup.p. [y.sup.T.
Country Estimation Constant sub.t] sub.i]
1. Pakistan OLS -0.62 0.23 0.14
(-0.44) (0.93) (0.24)
INST -0.42 0.22 0.14
(-0.39) (0.61) (0.18)
OLS -1.07 -- --
(-1.71) -- --
INST -1.25 -- --
(-1.72) -- --
2. India OLS -2.48 0.56 1.33
(-2.57) (2.36) (3.15)
INST -1.30 0.26 1.80
(-1.01) (0.79) (3.17)
OLS -5.85 -- --
(-1.86) -- --
INST -2.29 -- --
(-1.89) -- --
3. Bangladesh OLS -12.86 1.55 -0.99
(-3.01) (4.07) (-1.83)
INST -12.87 1.46 -1.08
(-2.79) (3.59) (-1.62)
OLS -5.02 -- --
(-1.01) -- --
INST -6.83 -- --
(-1.05) -- --
4. Sri Lanka OLS -1.02 0.20 2.71
(-0.36) (0.47) (1.51)
INST -2.06 0.36 3.16
(-0.57) (0.64) (1.54)
OLS -7.55 -- --
(-1.39) -- --
INST -0.40 -- --
(-0.007) -- --
Coefficient of
Techniques
of
Country Estimation [y.sub.t] [r.sub.t] [m.sub.t-1]
1. Pakistan OLS -- -0.15 0.83
-- (-1.24) (2.97)
INST -- -0.12 0.83
-- (-0.83) (2.33)
OLS 0.19 -0.16 0.93
(1.68) (-3.13) (8.57)
INST 0.33 -0.18 0.79
(1.92) (-2.99) (4.86)
2. India OLS -- -0.02 0.77
-- (-0.71) (6.74)
INST -- -0.01 0.92
-- (-0.30) (5.83)
OLS 0.72 -0.07 0.52
(1.83) (-1.34) (1.77)
INST 0.56 0.01 0.73
(1.93) (0.19) (5.06)
3. Bangladesh OLS -- -0.52 0.57
-- (2.69) (3.79)
INST -- -0.52 0.68
-- (-2.50) (3.90)
OLS 0.66 -0.21 0.76
(1.68) (-0.91) (4.10)
INST 0.82 -0.28 0.77
(1.58) (-0.94) (2.95)
4. Sri Lanka OLS -- 0.07 0.86
-- (0.33) (3.59)
INST -- 0.50 0.79
-- (0.22) (2.60)
OLS 1.23 -0.03 0.42
(1.63) (0.13) (1.28)
INST 0.11 0.14 0.86
(0.12) (0.59) (1.80)
Coefficient of
Techniques
of [m.sup.u. [[bar.R]
Country Estimation sub.t] .sup.2] SER D.W.
1. Pakistan OLS 0.85 0.90 0.041 1.61
(2.61)
INST 0.89 0.89 0.041 1.57
(1.76)
OLS 0.95 0.98 0.044 0.96
(9.64)
INST 0.50 0.97 0.051 1.02
(1.09)
2. India OLS 0.83 0.99 0.036 1.91
(2.47)
INST 1.38 0.99 0.041 2.37
(2.30)
OLS 0.81 0.96 0.480 1.80
(1.93)
INST 1.08 0.98 0.062 2.13
(2.05)
3. Bangladesh OLS 0.73 0.81 0.108 2.34
(2.01)
INST 0.64 0.80 0.112 2.75
(1.08)
OLS 1.01 0.65 0.146 1.79
(2.12)
INST 1.62 0.61 0.154 1.49
(1.51)
4. Sri Lanka OLS 0.51 0.96 0.109 1.49
(1.70)
INST 0.33 0.96 0.111 1.49
(0.66)
OLS 0.44 0.86 0.104 1.65
(1.82)
INST 0.65 0.96 0.113 1.66
(0.81)
Notes: (1) The figures given in the parentheses are t-values.
(2) The variables are defined as follows:
[y.sup.p.sub.t] = Logarithm of permanent income;
[y.sup.T.sub.t] = Logarithm of transitory income;
[Y.sub.t] = Logarithm of current income;
[r.sub.t] = logarithm of interest rate;
[M.sup.u.sub.t] = unanticipated money demand variable
Last two equations of each country is the alternative specification.