MUSHTAQ AHMAD Unioersity of Wisconsin

Menusha, Wisconsin

ASHFAQUE H. KHAN Pakistan Institute of

Development Economics

Zslamabad, Pakistan

A Reexamination of the Stability of the Demand for Money in Pakistan*

This paper examines the stability of the demand for money function in Pakistan (1959-60 to 198G87) using a fairly robust econometric technique which permits parameters to vary over time. The results show that the money demand function was stable with both MI and Ma definitions of money for the period 1959-80 to 1980-81 and became unstable thereafter. It is also found that multiple interest rates are preferred explanatory variables and lend stability to the demand for money function (especially M,).

1. Introduction The stability of the money demand function is important for

the conduct of effective and meaningful monetary policy. In addi- tion to an understanding of the factors that affect the demand for money, knowledge of stability of the demand for money function is important for implementing sound monetary policy for economic development. The stability of the demand for money has been ex- tensively studied in developed countries, but relatively few at- tempts have been made in developing countries to examine this issue, even though it is equally important for these countries.’

Although various issues relating to the demand for money (such as the appropriate definition of money, the relevant-scale variable, the variable representing the opportunity cost of holding money, monetization, etc.) have been studied extensively for Pakistan,’ the

*The authors are thankful to two anonymous referees for several helpful com- ments and are also grateful to Professor Prem S. Laumas for his valuable comments and suggestions on the earlier drafts of this paper. Any errors or omissions are the sole responsibility of the authors.

‘To the best of our knowledge, Laumas (1978), Mahajan (1979), and Ram and Biswas (1983) tested the stability of the money demand function for India.

*See, for example, Khan (1980, 1982a, 1982b, 1982c), Akhtar (1974), Abe et al. (1975), Mangla (1979), and Nisar and Aslam (1983).

Journal of Macroeconomics, Spring 1990, Vol. 12, No. 2, pp. 307-321 307 Copyright 0 1990 by Louisiana State University Press 0184-0704/90/$1.50

Mushtaq Ahmad and Ashfaque H. Khan

issue which receives relatively less attention is the stability of the money demand function. Only Khan (1980, 1982a) tested the sta- bility of the function using the Chow test covering a time period from 1959-60 to 1977-78 and found the function stable. The lim- itations of the Chow test are well known, and perhaps the major limitation is that this test considers the constancy of the regression coefficients over different time periods as a test of stability. How- ever, even if the estimated coefficients remain constant over dif- ferent sample periods, this does not guarantee that data are gen- erated from the same population. Furthermore, several important events relating to the exchange rate and financial system have taken place during the post 1978 periods which, we contend, may have significant effects on the stability of the demand for money function in Pakistan.

The main purpose of this paper is to reinvestigate the stability of the demand for money in the light of several recent develop- ments covering a time period from 1959-60 to 1986-87 using a fairly robust technique that permits parameters to vary (see Cooley and Prescott 1976). The Chow test is not a reliable technique be- cause the change in coefficients may be temporary. On the other hand, the varying parameter technique divides the change into transitory and permanent parts, and instability implies that the un- derlying functional relationship has changed permanently. Besides the structural change in the economy that took place in 1971 when the Eastern part of the country (East Pakistan, now Bangladesh) gained independence after the civil war, the following major events provided additional motivation for this study.

First, a partial interest-free banking system was introduced in 1981 in accordance with the teachings of Islam. Separate interest- free counters were opened in all branches of the commercial banks along with the traditional interest-based counters with the stated objectives of a gradual movement toward complete Islamization of banking and of financial sectors.3 Two types of deposit schemes, namely, Profit-Loss Sharing (hereafter PLS) savings deposits and PLS term deposits, were started for investment by the public on the basis of participation in profit and loss under the interest-free sy-

‘It may be pointed out that interest rate (or ‘Riba’ as it is called in Arabic lan- guage) is strictly forbidden in the financial transactions in the Islamic religion. In- stead of abruptly eliminating the prevalent interest-based system, the government announced that during the initial phase the traditional interest-based system will continue to exist parallel with the interest-free system.

308

Reexamination of the Stability of the Demand for Money

tem.4 Public response to the new system was overwhelming. On the very first day of the PLS deposit schemes, commercial banks received Rs. 92.7 million in the PLS account. The growth of PLS deposits has been quite impressive, and by the end of fiscal year 1983-84 it stood at Rs. 20,738 million which was 17.8% of total deposits. Since our definitions of money (Mr or M,) do not include PLS deposits, the impressive growth in PLS deposits in a short interval of time may have been caused by the substitution of Cur- rency-in-circulation for PLS deposits. The statistics show that the contribution of Currency-in-Circulation to the growth of monetary assets fell from 58.2% in 1980-81 to 24.4% in 1981-82, while the contribution of demand deposits remained the same. Such a drastic substitution of Currency-in-Circulation for PLS deposits can cause instability in the money demand function.

Second, prior to 1981, a fixed exchange rate system was op- erative in Pakistan and the Pakistani rupee was linked with the fate of the U.S. dollar. During the early 198Os, the U.S. dollar started rising against the major world currencies, and, since the rupee was linked to the U.S. dollar, it began to have an adverse effect on Pakistan’s exports. As a result, the government announced a policy of delinking the rupee from the U.S. dollar in December 1981 and adopted the system of managed floating exchange rates. This policy led to a 36.4% depreciation of the Pakistan rupee against the U.S. dollar from Rs. 9.90 = U.S. $1.00 in December 1981 to Rs. 13.50 = U.S. $1.00 at the end of fiscal year 1983-84. The depreciation of the Pakistan rupee due to the change in the exchange rate re- gime led to a sharp increase in workers’ remittances horn U.S. $2225 million in 1981-82 to U.S. $2,886 million in 1982-83. The 30% growth in workers’ remittances in 1982-83 compared with only 5.1% in 1981-82 led to an unprecedented growth in monetary assets. The monetary assets (M, definition) grew at the rate of 25.3% dur- ing 1982-83 compared with 11.4% in 1981-82 and 13.2% in 1980- 81. It is our view that this drastic expansion in money supply due to the change in the exchange rate regime could also create insta- bility in the money demand function.

The above-mentioned factors provide enough justification to reexamine the issue of the stability of the demand for money in

‘For more on this issue and particularly on the working of tbe interest-free banking, see Government of Pakistan, Paki.stan Economic Suroey 1980-81. Isla- mabad: Ministry of Finance, 1981, p. 94.

Mushtaq Ahmad and Ashfaque H. Khan

Pakistan. With this purpose at hand, we employ a robust technique to test the stability of the function which allows parameters to vary. Unlike the Chow test, this technique does not require any prior knowledge of the point in time when shifts in the parameters of the equation might have taken place. The plan of the paper is as follows: Section 2 discusses methodology and explains the data sources. The results are reported in Section 3, while the final sec- tion contains the summary and concluding remarks.

2. Methodology and Estimation Method Following the standard practice, the money demand function

is specified for estimation purposes in logarithmic form as

In M, = PO + PI ln Y, + p2 In R, + U, , (1)

where

M, = the desired real money balances (M, or M,), Y, = real income,’ R, = interest rate (RC for inter-bank call money rate and RT for

weighted average of time deposit rate).

The variable ut is the structural disturbance term, which is assumed to have a zero expected value. The other stochastic properties of u, are specified in Cooley and Prescott (1976) and Rauser and Lau- mas (1976). Equation (1) is an equilibrium relation, and it is im- plicitly assumed that adjustment between the actual and desired money balances is achieved within a single time period (in this case it is one year).

Since our main interest lies in testing the stability of the de- mand for money relation, we argue on the assumption that changes in the exchange rate regime and in the financial system, besides political events, may have caused parameters &,, PI and pz in Equa- tion (1) to vary over time. To allow for the possibility of varying regression parameters, Cooley and Prescott (1973) suggest the vary- ing parameter regression model. This model derives maximum like-

5We do not use the permanent income because earlier studies (Khan 1980, 1982~) found no significant difference between the estimated coefficients of permanent and measured income. Hence, for our analysis we use only measured income.

310

Reexamination of the Stability of the Demand for Money

lihood estimates of the parameters under the general assumption that the parameters are adaptive in nature and may be subject to permanent and transitory changes over time. The estimates of the parameters are then used to test the hypothesis that the regression parameters are subject to permanent variation over time. The f&c- tion is considered stable if the parameters are not subject to per- manent change over time. tie Laumas (1978), Mahajan (1979), Ram (1982), and Ram and Biswas (1983) we also use the varying param- eter technique suggested by Cooley and Prescott to test the sta- bility of the money demand function. Since this technique has been discussed in great detail elsewhere, we try to be very brief in our presentation here. 6 We may write Equation (1) in the matrix no- tation as

M = XP, > (2)

where M, represents the logarithmic values of two definitions of money, MI or Mz for the tth observation, and X, is a vector of explanatory variables In Y, and In R, and a constant with unit value for the tth observation. The variable pt is a vector of unknown pa- rameters, subject to both permanent and transitory changes such as

PF = PF-‘-l + u, , t=l,2 ,..., T, (3)

where p denotes the permanent component of the parameters. The stochastic terms e, and v, are assumed normal, identically and in- dependently distributed with mean vector zero and covariance structures known up to scale factors that may differ. After imposing the normalization aI = u’;~ = 1, the convenient parameterization, the covariance structures of e, and u, are of the form

Cov (e,) = (1 - ~)a’ Z, ,

cov (u,) = yc? C” . (4) For the above specification, the parameters to be estimated are Pt,

‘For detailed discussion see Cooley and Prescott (1976), Rausser and Laumas (1976).

311

Mushtaq Ahmad and Ashfaque H. Khan

u2, and y. The latter parameter indicates the rate at which the regression parameters are adapting to a structural change, therefore y represents a measure of model stability. Since y is the fraction of parameter variation due to permanent changes, it is restricted to fall within the range (0,l). Given that y is the measure of stability, we construct a test of the null hypothesis y = 0 versus the alter- native hypothesis y # 0 and then use the asymptotic standard nor- mal 2, that is, Z = 9/S,. If y = 0, we cannot reject the null hy- pothesis, and our estimated relation is stable but stochastic.

To apply the varying parameter regression model, the matri- ces Z, and XV must be specified a priori. Since there is no reason to supect that permanent changes are more or less important than transitory changes, the identical structure of 2, and C, is assumed. Furthermore, we also assume that random changes in the param- eters are uncorrelated. Given these two assumptions and the nor- malization ayl = a;, = 1, we use four alternative specifications of the covariance matrices (Z, = Z, = 2):

& = diag(l.O, 0.0, . . . , 0.0))

&=diag(l.O,O.l,. . . ,O.l),

X3 = diag(l.O, 0.5, . . . , 0.5))

X4 = diag(l.O, 1.0, . . . , 1.0).

The first specification is useful in correcting the auto-corre- lation problem, while the remaining specifications allow an appro- priate range of the standard errors of the parameter vector. We believe that the above specifications are rich enough to provide a range of variation on the variance of the parameters to include the true values of the covariance of the parameters.

The maximum likelihood estimates of the unknown parameters (&, y, and a2) reported in this study are conditional upon the value of the parameter process at time (T + l), referred to here as the base point, since this is the value needed for prediction for the first post-sample period.

Before we close this section, a few words regarding data and their sources are in order. Two definitions of money are used in this study, namely, Mr, which consists of currency in circulation and demand deposits, and M2, which consists of M1 plus time de- posits. The data for the period 1959-60 to 1970-71, pertaining to

312

Reexamination of the Stability of the Demand for Money

Mr and M,, are taken from Kemal et al. (1980) and thereafter from various issues of the Pakistan Economic Survey and International Financial Statistics (ZFS).7 The data for the GNP representing in- come variables are taken from the Pakistan Economic Survey 1987- 88. Both money and GNP data are deflated by the implicit GNP deflator with 1959-60 = 100. Based on earlier studies (for example, Khan 1980, I98Zb, 1982c) we use the weighted average of interest rates on time deposits as the relevant opportunity cost variable. In addition, we also use an interbank call money rate. These data are taken from Naqvi et al. (1983) for the period 1959-60 to 1979-80 and thereafter from the Monthly Bulletin of the State Bank of Pak- istan, April 1988. Both money and GNP data are deflated by the implicit GNP deflator with 1959-60 = 100.

3. Results The results corresponding to both definitions of money (M,

and M2) with alternative interest rates as relevant opportunity cost variables are reported in Tables l-4. First of all, a weighted av- erage of interest rates on time deposits (RT) is used as an oppor- tunity cost of holding money. The estimation results reveal that the money demand function with both M, and Mz definitions of money were unstable for the sample period 1959-60 to 1986-87. To find out exactly when the demand for money function became unstable due to structural and institutional changes that took place in the 1970s and the 1980s we first estimated the model corresponding to both definitions of money covering the period from 1959-60 to 1968-69. The sample size was then increased by one fiscal year each time up to the year 1986-87. It is found that the money de- mand function corresponding to the M1 definition of money became unstable after 1970-71. However, the money demand function with the Mz definition of money remained stable up to the period 1979-80 and thereafter became unstable. The results with the M, definition of money are reported in Table 1. Since the results for other spec-

‘It should be noted that money supply statistics are not available for West Pak- istan (now Pakistan) and East Pakistan (now Bangladesh) separately prior to 1970- 71 in any government or international publication. Hence, money supply estimates for M, and M2 for the period lS59-60 to 1970-71 used in this study are taken from Kemal et al. (1980). Details on methodology and data sources are available upon request from Ashfaque H. Khan.

313

TABL

E 1.

M

axim

um

Like

lihoo

d Es

timat

es

of M

2 M

oney

De

man

d Fu

nctio

ns

for

Pak

ista

n u&

h V

aryi

ng Par

amet

ers

1x1

M,

= a,

+ a,

In Y,

+

a2 I

n R,

+

qr

x Re

gres

sion

coeff

icien

ts an

d (

) sta

ndar

d err

ors

b2

Y Z

Sam

ple

Perio

d:

1959

-60

to 19

79-8

0 z,

In M,

=

-9.00

9 +

1.86

0 In

Y -0

.510

In RT

0.

0073

2 0.0

0.0

(2

.574)

(0

.286)

(0

.230)

(0

.008)

Sam

ple

Perio

d:

1959

-60

to 19

80-8

1 z,

In MZ

=

-4.16

5 +

1.39

8 In

Y -0

.496

In RT

0.

0079

9 0.

98

4.30

(4.32

5)

(0.44

7)

(0.35

1)

(0.22

4)

Sam

ple

Perio

d:

1959

-60

to 19

81-8

2 5

In M,

=

-3.18

1 +

1.28

8 In

Y -0

.425

In RT

0.

0078

3 0.9

8 4.4

7 (4

.087)

(0

.418)

(0

.335)

(0

.219)

Sa

mple

Pe

riod:

19

59-6

0 to

1982

-83

Cl

In M,

=

-3.96

4 +

1.37

1 In

Y -0

.458

In RT

0.

0076

7 0.9

8 4.5

8 (3

.916)

(0

.400)

(0

.329)

(0

.214)

Sa

mple

Pe

riod:

19

5940

to

1983

-84

& In

M2

= -3

.304

+ 1.

293

In Y

-0.31

9 In

RT

0.00

744

0.98

4.67

(3.69

1)

(0.37

1)

(0.30

4)

(0.21

0)

Sam

ple

Perio

d:

1959

-60

to 19

84-8

5 1,

In M2

=

-2.93

1 +

1.25

4 In

Y -0

.371

In RT

0.

0071

4 0.9

8 4.7

6 (2

.553)

(0

.284)

(0

.229)

(0

.206)

Sa

mple

Pe

riod:

19

59-6

0 to

1985

-86

2, In

M2

= -2

.534

+ 1.

208

In Y

-0.33

0 In

RT

0.00

687

0.98

4.85

(3.07

7)

(0.29

8)

(0.25

4)

(0.20

2)

Sam

ple

Perio

d:

1959

-60

to 19

86-8

7 Xl

In

MZ

= -1

.531

+ 1.

085

InY

-0.17

2 InR

T 0.

0067

6 0.9

8 4.9

5 (2

.759)

(0

.248)

(0

.145)

(0

.198)

Reexamination of the Stability of the Demand for Money

ifications of E were similar, to conserve space, only one set of re- sults is reported in Tables l-4.

When an inter-bank call money rate RC (a short-term rate) was used as a relevant opportunity cost variable, the demand for the money function corresponding to the Mr definition remained stable up to the period 1980-81, and thereafter it became unstable. It may be noted that this function was stable only prior to 197O- 71, when time deposit rate was used as an opportunity cost of hold- ing money. The results corresponding to the M, definition with the inter-bank call money rate are reported in Table 2. The demand for money function corresponding to the M, definition with the in- ter-bank call money rate remained unstable. To conserve space we did not report the results for M, definition of money.

The above findings suggest that the inter-bank call money rate is a more relevant opportunity cost variable with the M, specifi- cation because it lends stability to the function. With the Mz spec- ification, however, the time deposit rate appears to be the relevant opportunity cost variable.

The results corresponding to both of the definitions of money along with multiple interest rates (RC, RT)’ as opportunity cost variables are reported in Tables 3 and 4. It can be seen from the results that the money demand function corresponding to the Mr definition remained stable up to the period 1980-81, while for the M2 definition it remained stable up to the period 1978-79. These results support the conclusion reached by Mahajan (1979) that, for India, multiple interest rates lend stability to the demand for money function.

4. Concluding Remarks The purpose of this paper has been to test the stability of the

demand for money in Pakistan for the period 1959-60 to 1986-87 using a fairly robust technique that permits parameters to vary over time. During these periods, the country experienced structural and institutional changes besides the change in the exchange rate re- gime. Such events were expected to have a profound effect on the stability of the function. The results of this study show that, with a long-term rate (average rate on time deposits), the money demand function with the Mz definition of money remained stable until I980- 81. However, with respect to the Mr definition, the money demand

‘We are grateful to one of the referees for bringing this point to our attention.

315

TABL

E 2.

M

axim

um

Like

lihoo

d Es

timat

es

of

M,

Mon

ey

Dem

and

Func

tions

fo

r Pa

kist

an

with

Va

ryin

g Pa

ram

eter

s

h M

, =

(Ye

+ (Y

~ In

Y,

+ ct

2 In

R

C,

+ qt

z R

egre

ssio

n co

effic

ient

s an

d (

) st

anda

rd

erro

rs

12

u Y

z

Sam

ple

Perio

d:

1959

-60

to

1980

-81

h M

, =

-3.9

84

+ 1.

293

h Y

-0.

214

In R

C

0.00

955

0.0

(1.3

15)

(0.1

46)

(0.1

24)

(20,

)

Sam

ple

Perio

d:

1959

-60

to

1981

-82

In M

I =

0.77

2 +

0.82

8 In

Y -

0.11

1 1n

RC

0.

0095

3 0.

9800

(3

.631

) (0

.336

) (0

.122

) (0

.219

)

Sam

ple

Perio

d:

1959

-60

to

1982

-83

In M

I =

0.52

4 +

0.85

4 In

Y -

0.11

9 In

RC

0.

0089

2 0.

9800

(3

.409

) (0

.312

) (0

.115

) (0

.214

)

Sam

ple

Perio

d:

1959

-60

to

1983

-84

In M

I =

0.70

5 +

0.83

4 In

Y -

0.11

7 In

RC

0.

0086

2 0.

9800

(3

.332

) (0

.304

) (0

.113

) (0

.210

) 4.

67

Sam

ple

Perio

d:

1959

-60

to

1984

-85

In M

I =

0.33

5 +

0.87

0 In

Y -

0.12

0 In

RC

0.

0082

9 0.

9800

4.

76

(3.1

27)

(0.2

82)

(0.1

10)

(0.2

06)

Sam

ple

Perio

d:

1959

-60

to

1985

-86

In M

1 =

0.34

1 +

0.87

0 In

Y -

0.12

0 In

RC

0.

0079

5 0.

9800

4.

85

(2.9

95)

(0.2

68)

(0.1

05)

(0.2

02)

4.47

4.58

Sam

ple

Perio

d:

1959

-60

to

1986

-87

In M

I =

0.19

1 +

0.92

6 In

Y -

0.14

0 In

RC

0.

0075

8 0.

9400

4.

43

(2.8

55)

(0.2

54)

(0.1

20)

(0.2

12)

TABL

E 3.

M

axim

um

Like

lihoo

d Es

timat

es

of

M,

Mon

ey

Dem

and

Func

tions

fo

r Pa

kist

an

with

Va

ryin

g Pa

ram

eter

s

In

M,

= a0

+

a1 I

n Y,

+

a2 l

n R

C,

+ a3

In

RT,

+

qr

z R

egre

ssio

n co

effic

ient

s an

d (

) st

anda

rd

erro

rs

A2

u Y

z

Sam

ple

Perio

d:

1959

-60

to

1980

-81

In M

I =

-5.3

61

+ 1.

446

In Y

-0.

166

h R

C

-0.1

71

In R

T 0.

0099

4 (2

.877

) (0

.320

) (0

.154

) (0

.315

) (K

O7)

0.

0

Sam

ple

Perio

d:

1959

-60

to

1981

-82

In M

I =

-2.3

11

+ 1.

178

In Y

-0.

058

In R

C

-0.3

79

In R

T 0.

0088

1 0.

8800

3.

48

(4.3

68)

(0.4

53)

) (0

.150

) (0

.437

) (0

.253

)

Sam

ple

Perio

d:

1959

-60

to

1982

-83

In M

1 =

-2.5

97

+ 1.

207

In Y

-0.

063

In R

C

-0.3

86

In R

T 0.

0082

7 0.

8600

3.

40

(4.1

24)

(0.4

28)

(0.1

43)

(0.4

25)

(0.2

53)

Sam

ple

Perio

d:

1959

-60

to

1983

-84

In M

I =

-0.9

86

+ 1.

026

In Y

-0.

082

In R

C

-0.2

28

In R

T 0.

0084

8 0.

9200

4.

00

(3.9

63)

(0.4

02)

(0.1

38)

(0.3

91)

(0.2

30)

Sam

ple

Perio

d:

1959

-60

to

1984

-85

In M

I =

-1.3

41

+ 1.

064

In Y

-0.

081

In R

C -

0.25

0 In

RT

0.00

798

0.9o

oo

3.88

(3

.560

) (0

.358

) (0

.135

) (0

.369

) (0

.232

)

Sam

ple

Perio

d:

1959

-60

to

1985

-86

in M

I =

-0.8

36

+ 1.

007

In Y

-0.

082

In R

C

-0.2

03

In R

T 0.

0077

8 0.

9200

4.

14

(3.2

64)

(0.3

19)

(0.1

31)

(0.3

34)

(0.2

22)

Sam

ple

Perio

d:

1959

-60

to

1986

-87

In M

, =

-0.6

16

+ 0.

983

In Y

-0.

085

In R

C

-0.1

77

In R

T 0.

0075

7 0.

9400

4.

43

(2.8

85)

(0.2

60)

(0.1

16)

(0.1

75)

(0.2

12)

TABL

E 4.

M

axim

um

Like

lihoo

d Es

timat

es

of

M2

Mon

ey

Dem

and

Func

tions

fo

r Pa

kist

an

with

Va

ryin

g Pa

ram

eter

s In

M,

= a,

, +

a,

In

Y,

+ up

In

RC,

+ a3

In

RTt

+ ,rj

i

B Re

gres

sion

coef

fcien

ts an

d (

) sta

ndar

d er

rors

CP

Y Z

sam

ple

Perio

d:

1959

-60

to 1

978-

79

- In

Mn

= -1

2.13

+

2.20

4 In

Y -

0.19

3 In

RC

-0.5

63

In R

T (2

.65)

(0

.29)

(0

.13)

(0

.W

Sam

ple

Perio

d:

1959

-60

to

1979

-80

In M

, =

-2.6

55

+ 1.

211

In Y

-0.

264

In R

C -0

.009

In

RT

(4.1

4)

(0.4

3)

(0.1

3)

(0.4

1)

Sam

ple

Perio

d:

1959

-60

to

1980

-81

In M

g =

-2.7

48

+ I.2

26

In Y

-0.

254

In R

C -0

.056

In

RT

(4.0

7)

(0.4

2)

(0.1

3)

(0.3

9)

Sam

ple

t’erio

d:

1959

-60

to

1981

-82

In M

2 =

-2.0

41

+ 1.

146

In Y

-0.

263

In R

C -0

.007

In

RT

(3.8

0)

(0.3

9)

(0.1

2)

(0.3

7)

Sam

ple

Perio

d:

1959

-60

to 19

82-8

3 In

MS

= -2

.274

+

1.17

0 In

Y -

0.27

2 In

RC

-0.0

10

In R

T (3

.63)

(0

.37)

(0

.12)

(0

.W

Sam

ple

Perio

d:

1959

-60

to 19

83-8

4 In

Me

= -2

.069

+

1.14

6 In

Y -

0.27

6 In

RC

-0.0

35

In R

T (3

.36)

(0

.34)

(0

.11)

(0

.32)

Sam

ple

Perio

d:

1959

-60

to

1984

-85

In M

2 =

-1.8

56

+ 1.

123

In Y

-0.

277

In R

C -0

.048

In

RT

(3.0

6)

(0.3

1)

(0.1

1)

(0.3

1)

Sam

ple

k’erio

d:

1959

-m

to

1985

-86

In M

e =

-1.5

13

+ 1.

084

In Y

-0.

277

In R

C -0

.084

In

RT

(2.7

9)

(0.2

7)

(0.1

1)

(0.W

S

ampl

e Pe

riod:

19

59-6

0 to

19

86-8

7 In

M2

= -1

.887

+

1.12

91n

Y -0

.264

In

RC

- 0.

013

In R

T (2

.45)

(0

.22)

(0

.10)

(0

.14)

0.00

580

0.0

0.00

ww

0.00

710

0.98

00

4.28

(0

.229

)

0.00

688

0.98

00

4.38

(0

.224

)

0.00

663

0.98

00

4.47

(0

.219

)

0.00

633

0.98

00

4.58

(0

.214

)

0.00

604

0.98

00

4.67

(0

.210

)

0.00

577

0.98

00

4.76

(0

.206

)

0.00

554

0.98

00

4.85

(0

.202

)

0.00

533

0.98

00

4.94

(0

.198

)

Reexamination of the Stability of the Demand for Money

function remained stable only up to 1970-71. When short-term rate was used (call money rate) as a relevant opportunity cost variable, the function corresponding to M1 remained stable up to 1980-81, while the function was found unstable with MP. With multiple in- terest rates in the money demand equation, Mr was found stable up to 1980-81, and M, remained stable up to 1978-79. These re- sults imply that multiple interest rates are preferred explanatory variables, rather than a single rate, and that they lend stability to the demand for money function (especially M,).

In general, the money demand function was found unstable after 1980-81, corresponding to both (M, and M,) definitions of money. This instability might have been caused by the institutional changes in the banking sector, such as the introduction of partial interest-free banking, and the change in exchange rate regime caused by the policy of delinking the Pakistani rupee from the U.S. dollar. Both of these events took place around 1981.

Finally, in this paper we have assumed a log-linear form of the demand for money function. However, functional form could be an important issue. We agree with Ram (1982) that “the main lesson seems to be that functional instabilities and parameter shifts can be of various types, may show up in different ways, and it is useful to conduct several tests to detect these instabilities since ex- clusive reliance on a single procedure might be hazardous.”

These results are in accord with our expectations. Due to the introduction of the interest-free banking system and due to the de- linking of the Pakistani currency, we expected the demand for money function to become unstable. However, from this, one should not infer that the demand for money function for Pakistan will remain unstable in the future as well. It may become stable again after the impact of these innovations has been fully assimilated in the econ- omy and the concept of money has been broadened to incorporate the specific needs of the banking system based on Islamic Law.

Receioed: Febmary 1987 Final version: July 1989

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321