Demand Money Burundi

8/6/2019 Demand Money Burundi

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IDEC

The Stability of the Burundian Demand -for- Money Function:Some Further Results

Jean NDENZAKO

Institut de Dveloppement Economique

B.P. 6210. Bujumbura-Burundi

Discussion Paper

ECDI

February 1998.

The Stability of the Burundian Demand-for- Money Function :Some Further Results

Jean NDENZAKO 1

1

* An earlier version of this paper was delivered at a workshop on MoneyDemand and Monetary Policy organized by the Burundi Economic Development


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The Burundi Economic Development Institute

Summary

This paper attempts to develop specifications for the Burundian demand for

money throughout the period 1970-1995 which efficiently track actual movementsin holdings of real money balances around the long -run demand functions usingrecent techniques in the analysis of cointegrating times series relationshipsdeveloped by, inter alia Engle and Granger (1987) , Johansen (1988) andJohansen and Juselius (1990). The results indicate , once again, that the demandfor money is affected not only by changes in domestic factors such as real incomeand expected inflation, but also by fluctuations in exchange rates expectations.The evidence suggests that these variables entering into the demand for moneyequation may not form a cointegrated system as far as narrow money is concernedunless the exchange rate is included. For broad money, inclusion of the exchangerate may strengthen its stability because of the weakness of tests of cointegrationto what could be borderline stationarity when the exchange rate is excluded.Whatever the case for M2, equilibrium in the M1 demand equation requires

inclusion of the exchange rate. Furthermore, formal stability tests failed to indicateany shift in the demand for money equations over the sample period consideredand the estimated results do not allow to discriminate between alternativeformulations of the demand for money functions with broadly (M2) and narrowly(M1) defined money.Concerning the fiscal implications of inflation, the Burundian private sector adjustsat a rate of approximately 19.3 per cent per annum to any disequilibrium. Abovethis rate of inflation, the private sector systematically reduces its real holdings ofbase money more rapidly than the rate of inflation so that the real inflation taxrevenue declines.

Introduction

One of the most important recurring issue in the theory and

application of macroeconomic policy is whether or not the demand

for money is stable . In fact, for money to exert a predictable

influence in the economy so that the central banks control of the

money supply can be a useful instrument of economic policy, there

should be a stable money demand function [1].

The demand for money relation should be highly predictable in a

statistical sense as measured by the goodness-of -fit statistics,

precision of the estimated coefficients and presumably its ability to

forecast out of sample. Without predictability, the central bank

Institute in July 1998. I wish to thank workshop participants for their usefulcomments and suggestions. Of course any remaining errors are entirely mine.

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cannot know of the net expantionary or contractionary effects of a

given change in the money supply.

In an earlier paper [2], we presented some preliminary

estimates of the Burundian demand-for-money function using the

partial adjustment mechanism and concluded that current income,

expected inflation and the parallel market exchange rate are

explanatory variables for both narrow and broad definition of money

although its was more so for the narrow definition of money (M1)

than with the broader definition (M2) as far as expected inflation is

concerned.

The partial adjustment mechanism uses the Koyck-lag structure

whereby the whole adjustment process is represented by the

inclusion of lagged dependent variable. Since this structure has been

criticized on the grounds that it is highly biased and unduly

restrictive [Darrat ,(1985)], this paper attempts to refocus the issue

and presents an error correction specification which provides a more

general lag structure which nests the partial adjustment process and

does not therefore impose too specific a shape on the model [Arize,

(1989)] while allowing at the same time to avoid the spurious

regression problem outlined by Granger and Newbold (1974).

Moreover, we present a battery of specification , diagnostic

tests and additional stability tests as it has been shown that in

applied econometric research, one can estimate a totally

meaningless model and yet obtain correct signs , a high

coefficient of multiple determination and high t-values without there

being any relationships between variables whatsoever [3] . According

to my knowledge, there is no other study on money demand in

Burundi using the error correction methodology.

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The remainder of the paper is organized as follows: in section 2

a summary discussion on the model is presented, the time series

properties of the model variables using the Dickey-Fuller (DF),

Augmented Dickey-Fuller (ADF) , and the Sargan-Bargava Durbin-

Watson (SBDW) tests are presented in section 3. In section 4, we

implement recent techniques in the analysis of cointegrating time

series relationships developed by, inter alia Engle and Granger

(1987) Johansen (1988), Johansen and Juselius (1990) to determine

what variables are necessary to insure the stationarity of money

demand.

An error correction specification (using OLS estimation) which

captures the long run dynamics will be attempted when cointegration

is found to exist. The identification of a stable and well defined

demand-for-money function will allow an analysis of the fiscal

implications of inflation which depend not only on the long run

inflation elasticity of the demand-for-money but also on the dynamics

of the private sector adjustment towards its long run equilibrium.

Section 5 presents stability tests of the estimated money demand

equations and finally some concluding remarks and policy

implications are presented in section 6.

2. The Money Demand Model

The demand-for-money includes generally a scale variable

which takes into account the level of business transactions plus

variables representing the opportunity cost of holding money relative

to other assets.

The aggregate that is most commonly used as a scale variable, is

gross domestic product (GDP) which is based on the national income

accounts. There are some well known problems with such series in

Burundi. Such problems are due to changes in methodology used to

assemble the accounting data, and to potentially large errors in the

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survey data. Nevertheless, as these are the best income data

available at this time, this paper shall use the GDP series as the

measure of business transactions.

An opportunity cost variable in a demand-for-money function is

intended to measure the yield of money against other assets that

might be held. In financially developed economies, this variable is

usually the interest rate. In addition, it is also often argued that

inventories of real assets are an alternative form in which wealth can

be held, and hence the expected inflation rate should enter as a

determinant of money demand.

Given the limited range of financial assets and the pegging of

interest rate which prevailed in Burundi in most of the period under

review, physical assets represent the most common way of wealth

holding. If readily liquidable, they constitute close substitutes for real

cash balances. The return on money and on bonds become in this

case negligible. Many rechearchers haven even suggested that in

developing economies , interest rates should be dropped from the

money demand function because in such countries, they are

inadequate [ Darrat (1985)].

As a result, most empirical studies on money demand in

developing countries have solely used expected inflation to represent

the opportunity cost of holding money. Because observed interest

rates are centrally determined and remain unchanged for long

periods in Burundi, there is insufficient variation in interest rates to

enable its influence on the demand for money to be estimated with

confidence. Thus, the interest rates variable is dropped from the

money demand equation estimated in this paper.

As far as the definition of the money stock is concerned, it is

sometimes held that to be operationally useful, a money stock

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definition should comprise an aggregate that the monetary

authorities can adequately control. In financially developed

economies, this principle is sometimes adduced in support of a

narrow definition of money including currency in circulation and

demand deposits (M1), which tend to be more responsive to open

market and interest rates policies. In many developing countries,

however available policy instruments apply principally to the volume

of credit extended by the banking system. This would tend to make

the total liabilities of the banking system (M2 =M1+time deposits)

easier to control.

The last question is which measure of inflation should be used.

The GDP deflator as a general measure of prices within an economy

seems inappropriate because it captures changes in the price level of

domestic output only while the inflation measure should also include

prices of imported goods in order to be a measure of the opportunity

of holding money compared with buying goods. The consumer price

index (CPI) will therefore be used instead of the GDP deflator as the

measure of the opportunity cost of holding money balances.

The inflation variable will be defined as the rate of change in current

prices lagged one year. The omission of current inflation is meant to

avoid possible spurious correlation since the dependent variable is

deflated by current prices. The model is estimated over the period

1970-1995. Only annual data are available for all variables. A

discussion of the data sources is contained in the appendix, along

with a description of the nature of the data.

Using the following notation

md t* = (Md/P)* the stock of desired real money balances at time t

[4]

y t = a budget constraint such as real income at time t

t e = the expected rate of inflation used to represent the expected

return on physical goods at time t

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exct = the expected rate of depreciation of the parallel market

exchange rate used to represent the return on foreign money at time

t

ut= a (presumably) white noise disturbance term,

a simple econometric model of money demand can be written as

mdt* = f [ (yt) , (et), (exct )] (1)

With log linear specification, equation (1) can be written as

Ln mdt* = 0 +1 ln (yt) +2 et + 3 (exct) + ut (2)

The expected inflation and the exchange rate depreciation variables

must enter linearly since they assume negative values in some

years, in which case the logarithms are undefined.

It is generally accepted that the following conditions hold for the

partial derivatives .

mdt* / yt>0

mdt* / et > 0

mdt* / exct < 0 or > 0

Expression (2) assumes that the long- run demand for real money

balances depend positively on the income level and negatively on

the expected inflation rate. The sign of the exchange rate could be

either positive or negative. According to the currency substitution

literature, the depreciation of domestic currency leads to increase in

money demand implying a negative relationship [Cuddington (1983),

McKinnon (1982), Perera (1993)]. The effects of depreciation on

money demand could be positive through the expectations of future

depreciation thus lessening demand for domestic money (Perera,

1993).

The issue of potential endogeneity of income is first examined

using the Sargent (1976) procedure. Causality regression models for

the effects of income on both definitions of money are respectively:

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ln m1t= 0 + 1 T +i

m

=

1

2 ln m1t-i +j

n

=

1

3 ln y t-j + v t (3)

ln m2t= 0 + 1 T +i

m

=

1

2 ln m2t-i +j

n

=

1

3 ln y t-j + w t (4)

According to Grangers definition of causality, yt causes m1t or m2t if

the past values of yt taken as a group of additional explanatory

variables jointly influence m1t or m2t.

Thus the null hypothesis in (3) and (4) is that income level does not

Granger cause the Burundian money demand.

For Granger test, we apply the ordinary least squares method (OLS)

to estimate the coefficients in (3) and (4). The calculated values are

F=0.322 and F=1.526 for M1 and M2 definitions of money

respectively against a critical value of F(4,22)=2.82. The null

hypothesis that income does not Granger cause the real money

demand cannot therefore be rejected in regression models with two

lags for both narrow money and broad money. Income can thus be

considered as an exogenous variable in both money demand

equations.

To provide a comprehensive analysis of the long-run

equilibrium money demand function and the short run economic

behavior , this paper extends our previous partial adjustment model

deemed to have limited dynamics [Arize, (1992)] and uses the error

correction specification ( ECM ) which happens to be a generalization

to the partial adjustment type models and provides a more general

lag structure

In general logarithmic form, the error correction model can be

represented as follows:

A(L) log mt = B(L) log zt - (log m-log kz) t-1 +t (5)

where A (L) and B(L) are lag polynomials, z is a vector of explanatory

variables, and the second term of the right-hand size is the error

correction term which is the stationary linear ( cointegrating)

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combination of the non stationary levels of the variables log mt and

log zt, where k is a scalar.

Adopting a general to specific procedure [Hendry,1980], we begin

with an over parameterized model with liberal lags on all variables

and estimate a series of dynamic error correction models for the two

monetary aggregates. The dynamic error correction models are

based around the cointegrating vectors reported in table 2 .

These models are of the general form:

A(L) log mdt = 0+B(L) log yt + C(L) t +D(L) exct + ECM t-1 +t

(6)

where A(L) ....... D(L) are polynomials of the form A(L)=i Li in which

L is the lag operator such that Lr Xt = Xt-r, and ECM is the error

correction term.

3. Time Series properties of the model variables

Before proceeding with the estimation, we examine the time

series characteristics of the data in order to ascertain the order of

integration of the variables as to whether they are stationary or non

stationary; and therefore the number of times each variable has to

be differenced to arrive at stationarity. The stationarity of the data is

important since if times series are characterized by non

stationarities, then the classic t-test and F-test are inappropriate

because the limiting distribution of the asymptotic variance of the

parameter is infinite. [5]

Basically a series Xt is said to be integrated of order p if it

becomes stationary after differencing p times. Such a series is

denoted Xt ~ I(p). Using this terminology, a stationary series is an I(0)

series and a nonstationary series with a single unit root is I(1). Many

logarithmic macroeconomic variables are I(1) [Engle and Granger,

(1987)] but some non-stationary series are of order of 2 or higher, in

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which case the first difference or growth rate of the series will be I(1).

[Adam,1991].

To test the null hypothesis that any Xt series is integrated of

order one H0= Xt ~I(1) against the alternative hypothesis that Xt

~I(0), we apply the Dickey Fuller tests and the Sargan- Bhargava

Durbin Watson test as suggested by Sargan and Barghava (1983)

1. The Dickey Fuller Tests

The Dickey-Fuller tests for unit roots consist of estimating first a

model of the form

Xt = 0+ 1 Xt-1+j

q

=

1

jXt-j + t

Where the lag length q is set so as to ensure that any autocorrelation

inXt is absorbed, and the error term is approximately white noise.

Then we calculate a t- ratio as the ratio of the estimated 1 to its

estimated standard error.

To reject the null hypothesis of nonstationarity, i.e. the series is

stationary; the t-statistic must be significantly negative. If q=0, the

test is called the Dickey -Fuller test but if q > 0, it is termed the

Augmented Dickey-Fuller test. If we can not reject the null

hypothesis, i.e. H0= Xt ~I(1), we may conclude that the series

contains at least one unit root. Then, we test whether the first

difference is stationary that is Xt ~I(0) by estimating a model of

the form

2Xt = 0+ 1Xt-1+

j

p

=

1

j2Xt-j + t

Actually, we replaceXt with2Xt as the dependent variable andXt-1

withXt-1 as regressor and so on.

Rejection of the null hypothesis Xt ~I(1), imply Xt ~I(1). If the null

is written as Xt ~I(2), then the alternative is Xt ~I(1) and the

variable is I(1) if the null hypothesis is rejected: that is the coefficient

of the lagged first difference should be significantly less than zero.

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2. The Sargan-Barghava DurbinWatson (SBDW) test

Sargan and Barghava (1983) present a test of the hypothesis

that the errors on a regression equation follow a random walk.

Following this approach, the SBDW test regresses Xt on a constant

and tests the null hypothesis that the residuals follow a random walk.

In other words, for each series Xt , the null hypothesis is that

the first order autocorrelation coefficient is equal to one, that is the

hypothesis that the first order autocorrelation coefficient is equal to

one , that is =1 in the regression

Xt = 0+ Xt-1 + u t ; X0 = 0 u t ~ (0,2)

If the computed SBDW is larger than the critical value given in

Sargan and Barghava (1983, Table, p.157), the null H0 that the series

is a random walk

(that is non stationary) is rejected.

The SBDW test is based on the DW statistic, but it is not applied

to the residuals of the regression as usual but on level of individual

series as follows:

SBDW=t

T

=

2

(Xt-Xt-1)2 /t

T

=

1

(Xt -X)2

Unlike the DF tests, the test is against the series is I(0), in which case

the value of the DW statistic will tend toward a value of 2. If the

statistic is low then there is evidence of an I (1) series. [Adam,

1991].

The results of unit root tests discussed above are reported in table 1

Table 1: Unit root tests on annual data

Levels Differences

Variables DF ADF SBD

W

Variable

s

DF ADF SBD

WLn m1 - - 0.557 Ln m1 - - 3.212

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2.570 1.074 9.635 9.919Ln m2 -

1.799

-

0.663

0.221 Ln m2 -

6.580

-

6.965

2.584

Ln y -

2.652

-

2.650

0.758 Ln y -

7.670

-

6.061

2.868

e - -

2.556

2.511 e -

8.725

-

4.326

3.136

EXC 0.043 -

1.662

0.125 EXC -

6.117

-

6.533

2.447

The results of the DF and ADF tests as summarized in table 1

fail to reject the null hypothesis that the variables are non-stationary

and the SBDW statistic shows that they are of a random walk i.e. I (1). The results therefore indicate that the variables may not be used at

their levels in the regression equation, except in the case of

cointegrating relationships.

We therefore proceed to test for the presence of cointegration

between variables

4. Testing for cointegration

The concept of long run equilibrium economic relationship has

been discussed by Engle and Granger (1987) using the statistical

notion of cointegration.

The vector X of n dimensional times series, each integrated of the

same order, say b, is said to be cointegrated of order ( b-d ) if there

exists a vector such that W=X is I(b-d) d > 0.

If cointegration occurs it must be unique in the bivariate case. Engle

and Granger (1987) have suggested a two step procedure to test the

existence of cointegrating relationship in the bivariate case.

The test proceeds as follows:

(i) Run OLS of Xt on its explanatory variables in levels

(ii) Derive the residuals from the OLS results

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(iii) Conduct unit roots tests of the residuals and find out whether

they are integrated of order zero, or one, based on the following

equation

et= et-1 + i

k

=

0 i et-1+ vt

(iv) If et is integrated of order zero, it means that Xt and its

determinants are cointegrated of order one.

For a multiple case, Johansen (1988) and Johansen and Juselius

(1990) have developed a procedure to examine the question of

cointegration. This study shall adopt the Johansen testing procedure

as it not only allows to test for the number of cointegrated vectors

but also to estimate the cointegration vectors [Perera, 1993].

If there are N endogenous variables, each of which is first order

integrated, (that is, each has a unit root or stochastic trend or

random walk element), there can be from zero to N1 linearly

independent cointegrating vectors. If there are none, the standard

time series such as VAR applies to the first differences of the data.

If there is one cointegrating equation, the VAR will need an error

correction term involving levels of the series, and this term will

appear on the right hand side of each of the VAR equations, which

otherwise will be in first difference.

Table :2 Johansen cointegration Test

Section A: Variables in the cointegrated system: Ln m1 Ln y e

Null Hypothesis

(N of CEs)

LR Test Statistics 5% critical value

r = 0 35.46* 34.91r 1 17.40 19.96r 2 5.16 9.24

Section B: Variables in the cointegrated system: Ln m1 Ln y e EXC

Null Hypothesis

(N of CEs)


r = 0 73.36* 53.12

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r 1 37.02* 34.91r 2 19.76 19.96r 3 5.28 9.24

Section C: Normalized cointegration vector in section B

(-1 .000, 1.413, -0.446, - 0.018)

Section D: Variables in the cointegrated system: Ln m2 Ln y e

Null Hypothesis

(N of CEs)


r = 0 43.98* 34.91r 1 14.55 19.96r 2 3.39 9.24

Section E: Variables in the cointegrated system: Ln m2 Ln y e EXC

Null Hypothesis

(N of CEs)


r = 0 75.86* 53.12r 1 44.56* 34.91r 2 17.34 19.96

r 3 3.40 9.24Section F: Normalized cointegration vector in section E:

( -1.000 , 2.512, -0.136 , -0.014 )

Table 2 reports the results of the cointegration tests .The

findings reported in section A indicate absence of long -run

relationships among narrow money and its determinants, that is the

LR statistics are unable to reject the null hypothesis r = 0 with

respect to narrow money and its determinants. The LR statistics are

close to their critical values. Adding the exchange rate in section B

substantially changes the results for M1. As seen in section B of table

2, m1, y, the inflation rate and the expected depreciation of the

parallel market exchange rate form a cointegrated relation. The LR

test statistics reject the null hypothesis that there are zero

cointegrating vectors against the 5 per cent critical value and

suggest that there are at most two cointegrating vectors for narrow

money.

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The results for broad definition of money are reported in

section D and E and are different than those for narrow money. The

test statistics rejects the null hypothesis r = 0 with respect to M2 and

its determinants whether the exchange rate is included or not.

However, there is only weak evidence of cointegration between m1, y

and the inflation rate in section D. The findings for M2 reported in

section E are markedly strengthened by the addition of the exchange

rate. Moreover, the LR test statistics indicate that the hypothesis that

there are at most two cointegrating vectors is accepted for broad

money.

Section C and F report the estimated normalized cointegration vector

for the narrow money and broad money respectively. The vectors

have been normalized by dividing by the coefficient on money and

appear to be money demand equations. For both M1 and M2 real

money demand is positively related to real GDP and negatively

related to the inflation rate and the exchange rate. The negative sign

on the exchange rate in the normalized M1 and M2 vectors may

indicate currency substitution.

As market participants increase their demand for foreign currencies

relative to the Burundian franc, the Burundian franc depreciates.

The estimated long run income elasticity with respect to M1 is

1.413 and the long run inflation rate and parallel market exchange

rate elasticities are -0.446 and -0.018 respectively. Our estimated

long run elasticity with respect to M2 is 2.512 which is higher than

the income elasticity for narrow money. The long run inflation and

exchange rate elasticities with respect to broad money are -0.136

and -0.014 which are both lower that their counterparts for M1. It is

interesting to mention also that the exchange rate elasticity is

marginally lower than its counterpart for M1.

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Empirical results

In the presence of cointegrating relationships, we start the

model specification search for an appropriate ECM with an over-

parameterized autoregressive distributed model. The model was then

reduced to a more desirable specification using the information

criterion as a guide.

More specifically, our simplification involves restricting to zero

relatively small coefficients and reformulating the lag pattern in

terms of levels and changes. The results of the more preferred

specifications are presented below:

Table 2 : OLS Money Demand equation for Narrow Money (ln m1)t

Sample is 1974 to 1995

Explanatory

Variables

Coefficient Std Error T-Statistics

Constant 0.034084 0.020059 1.699185

(ln yt ) 0.536962 0.123549 4.346147

(e )t-1 -0.21774 0.083628 -2.603636

(EXC)t -1.626979 0.622512 -2.613572

(Ln m1)t-1 -0.211036 0.121590 -1.735636

(ln m1-ln m1*)t-1 -0.476739 0.170377 -2.798150

R2 adj.== 0.795 SEE=0.085 F(5,17) = 17.337 [0.0000] D.W.

=2.189

ARCH (Autoregressive Conditional Heteroscedasticity)2(1) = 0.410

[ 0.521]

Jarque et Bera test for error normality 2 (2) = 0.847 [ 0.654]

Whites heteroscedastic error test 2(10) = 6.871 [ 0.937]

Q(12) = 15.475 [0.216]

Chow Test F (13,9 ) = 1.410 [0.737]

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Ramsey RESET F (2,19) = 0.024 [ 0.975]

Farley Hinich Mc Guire F (10,16) = 2.49

Table 3: OLS Money Demand equation for Broad Money (ln m2)tSample is 1974 to 1995

ExplanatoryVariables

Coefficient Std Error T-Statistics

Constant 0.061820 0.029816 2.073336

(ln yt ) 0.769910 0.160864 4.794590

0 1(e ) -0.663275 0.294512 -4.479269

0 1(EXC)t -1.733421 1.625669 -2.146127

(ln m2)t-1 -0.438131 0.229560 -2.146127

(ln m2-ln m2*)-t-1 -0.270954 0.176005 -1.539467

R2 adj.=0.706 SEE=0.094 F(7,15) = 8.210 [0.000] D.W. = 1.964

ARCH (Autoregressive

Conditional Heteroscedasticity 2(1) = 0.193 [ 0.659]

Jarque-Bera test for error normality 2 (2) = 5.531 [ 0.062]

Whites heteroscedastic error test 2 (14) = 10.938 [0.690]

Q (12) = 5.412 [0.943]

Chow Test F (13,9 ) = 1.919 [0.221]

Ramsey RESET F (2, 17) = 0.513 [0.610]

Farley Hinich Mc Guire F (14, 12) =3.822

0 1 indicates that the shorn -run dynamics of the dependent

variable is captured by a two period lag.

The diagnostic tests reported in this paper in support of the

empirical results are the following:

RESET (Regression Specification Test) is the Ramsey (1969) test for

omitted variables and functional form misspecification.

The test augments the original regression by adding a number of

powers of the fitted values from the original regression. If these extra

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regressors have non zero coefficients, there is evidence of

specification error

Q(12) is the Box-Pierce statistic for residual autocorrelation to twelfth

order. The statistic is used to test the hypothesis that all the

autocorrelations are zero, that is, the series is white noise.

Under the null hypothesis, Q(12) is distributed as Chi-squared

with degrees of freedom equal the number of observations less the

number of estimated ARMA coefficients.

ARCH LM test is Engles (1982) test for Autoregressive conditional

Heteroscedasticity of the residuals. This particular specification of

heteroscedasticity was motivated by the observation that in working

with macroeconomic series the size of residuals appear to be related

to the size of recent residuals. The statistic provides a test of the

hypothesis that the coefficients of the lagged squared residuals are

all zero. The chi-squared statistic corresponds to a Lagrange-

Multiplier (LM) test and has degrees of freedom equal to the number

of lagged, squared residuals.

The Farley et al. test is the Farley-Hinich and McGuire test (1975) for

a gradual shift in the parameters over the full sample period. White

is the Halbert White (1980) test for general forms of

heteroscedasticity. As is well known, a key assumption in the linear

regression model is that the error term should have a constant

variance (that is, an absence of heteroscedasticity). Violation of this

assumption leads to inefficient estimates and invalidate test

statistics. The Chi-squared statistic has degrees of freedom equal to

the number of regressors and squared regressors. J.B. is the test for

normal residuals described in Jarque and Bera (1980). Under the null

hypothesis, the J.B. statistic is distributed as chi-squared with two

degrees of freedom.

As can be seen form tables 2 and 3 the statistical fit to the data

is good as indicated by values of Theils adjusted R2 and the F value

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for testing the null hypothesis that the right hand side variables as a

group except the constant term have a zero coefficient. All of the

three explanatory variables bear the anticipated signs. The short run-

run currency substitution effect is negative and significant for both

narrow and broad definitions of money indicating therein that foreign

money is considered as an attractive alternative to holding domestic

money balances in the Burundian economy, a conclusion which is

similar to the one reached earlier [Ndenzako (1998)] when we used a

more restrictive lag structure.

The estimated coefficients for real income and expected

inflation rate are also satisfactory and consistent with our a priori

theorizing.; t-ratios are significant at the 5 per cent level, indicating

both the importance of the real income and inflation variables in

explaining changes observed in the demand for money.

Values of 0.27 and 0.46 of the ECM coefficients suggests that in

the case of the broader money balances approximately about 27 per

cent of the previous disequilibrium from the long run demand for

money is corrected in one year while for the narrower M1 aggregate

the figure is closer to 46 per cent per year. This results suggest a

relatively intuitive picture in which the narrow aggregate M1 enjoys a

much faster adjustment than the broader aggregate M2 where

possibly higher transaction costs may preclude rapid adjustment.

This speed of adjustment is almost one and a half as slow as the

adjustment speed implied by our previous partial adjustment model.

In terms of the other short- run dynamic effects in the

model a number of features warrant attention. The first is the

relatively consistent short-run inflation effects for both aggregates. In

each case , the growth rate of inflation ( i.e. the acceleration in the

price level) has a significant effect on real money holdings. On the

basis of the above empirical results, and in view of the specification

and diagnostic tests employed, we may conclude that the estimated

equations in table 2 and 3 fit the actual data quite well and

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adequately describe the money demand relationships in the

Burundian economy. The diagnostic tests appear to suggest that the

error correction models fulfill the conditions of serial non-

autocorrelation, no specification error (i.e. zero disturbance mean,

homoscedasticity, normality of residuals and structural stability.

Forecasting performances

To test how the estimated equations can explain movements in

real money demand in period outside the sample, we re-estimated

the error correction models over the period 1970 through 1990 and

used the parameter estimates to forecast the period 1991 through

1995. The forecast results are reported below:

Forecasting performances for MI definition of money

(ln m1)t = 0.046 + 0.525(ln yt) - 0.210(e)t

(-1.699) (4.346) (-2.603)

-1.637 (EXC)t -0.248(ln m1)t-1 - 0.510(ln m1-ln m1*)t-1

(-2.613) (-1.861) (-2.755)

R2 adj.= 0.819 S.E.E=0.085 D.W.=2.082

ARCH 2 (1) = 0.174 [0.675]

White 2 (10) = 8.114 [0.617]

J.B. = 0.858 [0.651]

Q(12) = 7.963 [0.790]

RESET f(1,16) = 0.154 [0.700]

Chow Forecast Test: F( 5,19)=0.825 [0.556]

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Year Forecast

Errors,

percent

RMSE Theil Inequality

Coefficient

1991 0.417 0.027 0.0026

1992 0.661 0.034 0.00331993 0.890 0.048 0.00461994 0.078 0.100 0.00961995 2.778 0.143 0.0037

The Chow forecast test statistic has a value of 0.825 with a marginal

significance level of approximately of 0.556 for the M1 aggregate at

the five percent significance level. The Chow forecast test is a post

sample predictive failure test. It allows to examine whether the next

five observations have been generated by the same model estimated

for 1970-1990. Both estimated equations pass this predictive failure

test.

6. Stability of the money demand equations

As Johnston (1984, p.507) pointed out, the stability of the

parameters over various data sets is a very important indicator of the

quality of a functional specification. The approximate constancy of

the estimated coefficients over time may be tested through several

available statistical tests. This point has been emphasized by

Boughton (1981), who, along with others, argues that each stability

test addresses a somewhat different aspect of stability and thus

suggests that the researcher employs a battery of stability tests.

In this paper, three stability tests are employed, namely, the Chow

break point test, the Chow (1960) test, the Farley- Hinich- McGuire

(1975) test and the Brown-Durbin-Evans (1975) test.

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6.1. The Chow test

Breaking the sample at the midpoint after 1982, and applying

the Chow F test resulted in an F- statistic of 1.410, for M1 and 1.910

for M2 which does not allow one to reject the hypothesis of stability

at the 5 percent level. Thus, we accept the hypothesis of no

structural shift in the model and therefore conclude for the stability

of the demand for money.

In addition, by retaining the last four observations (1992-1995), we

can check for the stability of the parameters, using out of sample

information. Table 4 and 5 the forecast errors from the estimated M1

and M2 equations. Results of the post sample parameter stability test

are excellent and supportive of the Chow test. The root mean

squared errors providing a measure of the forecast accuracy also

corroborate the findings.

6.2. Time trending regressions: The Farley-Hinich-Mc Guire

test

Next we consider a test for a shift in the slopes of linear times

series model, which has been proposed by Falrey, Hinich and

McGuire [1975]. The coefficients bj of the regression equations were

augmented to

bj*=bj + t , t=1,2 .....T., j =1.....n permitting each coefficient to drift

along a linear time trend. Then an appropriate F ratio has been used

to test the null hypothesis that the coefficients on added trend

variables are jointly zero. This procedure tests for a gradual shift ( in

contrast to a single) in the parameters and it is applied to the full

sample.

When the were jointly tested from significance from zero, an

F-value of 2.49 against a critical value of 2.76 and 2.54 against a

critical value of 3.23 was obtained for the specification of M1 and M2

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respectively. None permits the rejection of the hypothesis of

parameter constancy at the 5 percent level

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6.3. Recursive estimates: The Brown-Durbin-Evans test.

The last test of stability is carried out by the Brown-Durbin-

Evans technique that, unlike Chows F-test or dummy variable

method, detects shits, if any, in a regression relationship without ant

prior knowledge about the timings of such shifts.

Basically, the Brown-Durbin-Evans residual check for testing

structural stability of regression relationship consists of calculating Sr

statistics given by Sr=(k

r

+

1

Wr2 ) (k

T

+

1

Wr2 ) r =k+1,......T.

Where K = number of explanatory variables including the constant,

T = total number of observations in the regression, and

Wr = the standardized residual for the r-th observation of the

dependent variable

The statistics Wr is obtained by standardizing the difference between

the actual and the forecasted values of the r-th observation of the

dependent variable. In forecasting the r-th observation of thedependent variable, the regression equation estimated by using r-1

observations is used. The values of Sr lies between 0 ( if r < (k+1=

and 1 if r = T).

The expected value of Sr is (r-k)/ (T-k). Given the null hypothesis that

the regression equation under consideration is stable over the period

of investigation at a specific level of significance, the plot of Sr should

lie between the pair of lines (r-k)/(T-k) c0,For T observations, k explanatory variables (including the intercept )

and given a significance level of , c0 is found by entering the table

at

m=1/2(T-k)-1 when T-k is even and interpolating linearly between

m=1/2(T-k) - 3/2 and 1/2(T-k) - 1/2 when T-k is odd (see Johnston,

1984).

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Since our study covers data from 1970 to 1995 and there are

three explanatory variables in the regression, the value of c0 in the

cusum of squares test is 0.23298 at 5 percent level of significance.

The Brown-Durbin-Evans stability test is illustrated in figure 1 and 2

for both specifications of the demand for money function.

The null hypothesis of stable demand for money function for

each specification will be accepted at the 5 per cent significance level

if the sample plot of the corresponding S r does not cross the 5 per

cent significance level.

The hypothesis of stable money demand is accepted for Burundi

during 1970-1995 for both definitions of money.

Conclusion and policy implications

There are several policy implications arising from results of this

paper. One such policy is concern over the fiscal implications of

inflation, that is the steady-state inflation capacity of the private

sector and the short run dynamics of money holdings in response to

changes in the rate of inflation.

Following Friedman (1971),and Adam(1991), standard analyses of

inflation tax derive the revenue maximizing rate of inflation as

=1/ - (g)

where is (minus) the inflation elasticity of the demand for money,

is the income elasticity of the demand for money and g is the

average rate of growth of income.

From the long-run demand function for narrow money, we

derive an average revenue -maximizing rate of inflation of 19.3 per

cent where

= -0.4466 ; =1.413 and g = 2.2% per annum. It is interesting to

note that the greater the range of substitutes for domestic base

money, and the more rapidly the private sector can adjust their real

holdings, the lower the revenue -maximizing level of inflation will be.

Above a rate of inflation of 19.3% per annum, the private

sector systematically reduces its real holdings of base money more

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rapidly than the rate of inflation, so that the real inflation tax

revenue declines.

The coefficient on the error-correction term is a direct measure of

this speed of adjustment: according to these results, the Burundian

private sector adjusts at a rate of approximately 0.47 per cent per

annum to any disequilibrium (i.e. increase in real base money).

Four other findings deserve special attention:

(i) The results indicate, once again, that the demand for money is not

only affected by domestic variables such as real income and

expected inflation, but also by fluctuations in the exchange rate

expectations.

(ii) Formal stability tests failed to indicate any shift in the demand for

money equations over the sample period considered.

(iii) The specification of the demand for money efficiently tracks

actual movements in holdings of real balances around the long-run

demand functions.

(iv) The variables entering into the demand for narrow money may

not form a cointegrating system unless the exchange rate is

included. Inclusion of the exchange rate may strengthen the stability

of M2.

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Appendix: Data Sources and Description

This study covers the period from 1970 through 1995 on the

basis of annual observations. The empirical definitions of

the variables are as follows:

M1=Currency in circulation plus demand deposits (narrow

definition)M2=M1 plus time and savings deposits (broad definition)

Y = Real gross domestic product

P=Consumer Price Index

Ex=Parallel market exchange rate ( Burundian franc per

dollar)

e=logPt-1 -logPt-2

EXC=logExt-1 -logEXt-2

All data series were obtained form issues of IMF,

International Statistics, except for the parallel market

exchange rates which were derived from Picks Currency

Yearbook as reported by J.D. Nkurunziza (1997).


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Notes

[1] John P.Judd and John Scadding, The search for a stable

money demand function: a survey of the post-1993

literature , Journal of Economic Literature, vol.XX, Sept.

1982, pp.993-1023.

[2] NDENZAKO, J. (1998) The Demand for Money inBurundi: Some Preliminary Results , RIDEC ( Revue de

lInstitut de Dveloppement Economique du Burundi), vol. 2,

n1, p.178-195.

[3] Arize, A, (1989) Exchange rates, Foreign interest rates,

and the demand for money demand in an open economy:

An empirical investigation in Korea , Savings and

Development, 3, , XIII ,p.245.]

[4] The theory imposes the restriction that money demand

is cast in real terms, that is, real demand for money is

homogenous of degree zero in prices because economic

agents are a priori assumed rational so that their demand

for cash balances is a demand for real purchasing power.

[5] Fuller,W.A., Nonstationary Autoregressive Times

Series , in Hananet al. (ed.), Handbook of Statistics,

Elsevier Publishers, Amsterdam,1985.


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Demand Money Burundi