- Email: [email protected]
The demand for money in a developing economy: The case of Kenya
U’orld I)eve/ol,nnenr,
Vol.
13, No. 1011 I. pp. 1163-l
170. 1Y85. 0
Printed in Great Britain.
$3.00 + 0.00 0305-750x/85 1985 Pergamon Press Ltd.
The Demand for Money in a Developing Economy: The Case of Kenya ALI F. DARRAT” University of New Orleans,
New Orleans
Summary.
- The demand for money function occupies a central role in most theories of aggregate economic activity, especially in the formulation and execution of effective monetary policy. This paper examines the demand for money in the developing economy of Kenya. Special attention is paid to the model specification. its dynamic structure and to its temporal stability. The empirical results show that for both conventional definitions of money (the narrow and the broad), the theoretical model fits the Kcnyan data quite well. and the proposed variables arc all statistically significant and with the anticipated signs. The results further suggest. based on a battcry of tests, that the estimated money demand equations for Kenya arc temporally stable. Focus is also given to the open-economy nature of the money demand model, and the results indicate that some measure of foreign interest rates plays a significant role in the Kcnyan money demand equations as potentially in any other money demand equation of an open economy. Monetary policy in Kenya. therefore. must take into account the response of domestic money demand to changes in such external factors.
1.
INTRODUCTION
The past several decades have witnessed considerable empirical research on the money demand function due to the vital role this function plays in macroeconomic analysis, especially in regard to the formation and transmission of monetary policy. Consequently, money demand functions have been empirically estimated by many researchers for a number of developed and developing countries. ’ However, money demand function for the developing economy of Kenya has been largely ignored.’ It is the aim of this paper, therefore, to estimate an appropriate money demand function for Kenya using the quarterly data over the period lY69:I to 1978:IV. One of the central issues that this paper addresses is whether the Kenyan money demand relationship has shifted during the period of estimation. Money demand stability is in fact a prerequisite for an effective monetary policy. As Thornton (1983) pointed out on the basis of the familiar equation of exchange, the money demand is the link between monetary policy and the real side of the economy. Thus. to predict adequately the impact of money supply changes upon real output. interest rates and prices, the underlying money demand relationship must be temporally stable. In the context of economic development, it
may seem that monetary policy is irrelevant in the case of developing economies owing basically to the lack of well-developed financial and capital markets. However, as stressed by McKinnon (1973) and Bhatia and Khatkhate (lY75), monetary policy can still play a major role in mobilizing savings into real capital and promoting financial stability; this would, in turn, contribute to the development of efficient financial and markets. Indeed, the presumption capital appears to be fairly established in the literature that improvements in the intermediation process are favorable to economic development in countries like Kenya.’ The rest of the paper is organized as follows. Section 2 specifies an appropriate money demand function for Kenya. Section 3 then reports the empirical results. The stability property of the money demand equation is examined in Section 4. Finally, some concluding remarks are drawn in Section 5.
*The author would like to thank Lawrence Davidson and Elmus Wicker for their continuous cncouragcment. Thanks also go to an anonymous referee of this journal for useful comments. Any remaining errors arc, of course. the sole responsibility of the author.
1163
W0RI.D
I16-l 2.
THE
MONEY
Economic
theorv
money
balances,
DEMAND holds
($)”
I~EVtL.OPMENl
MODEL
that
dcaired
is positi\cly
related
real to
2
VXI~ variable
such as real income (X)
and nef:i-
tively
to the opportunity
of holding
related
costs
money, that is. the yields on alternative real and financial assets.’ The expected rate of inflation (JI”) is usually t&en to represent the foregone yield on real assets. and the rate(s) of interest (R) is used to rcprescnt the foregone yield on financial assets. The money demand function may
then
($=
l(X,.
bc written
as:
Another issue concerns the ~ipl”“pri;ltencss of including some measure of interest rates in the money demand equations of developing economies. Manv researchers have suggested that in these econon;ies interest rates variable should bc dropped from the money demand function. Thi\ is because financial assets in 4uch countries arc inadequate. Consequently. \ery little sub\tituability exists between money and other financial assets and the choice of asset holders is largely limited to holding either money or real good\. such as real estate or con\umc‘r durable\. Moreoc’cl-. the few interest yields available in developing
JI ;. R,)
(1)
pegged where f;
<
the theory
postulates
that f,
>
0, .I; <
0,
0.
To make equation (I) estimatable. ;I number of analytical and technical issues warrent comment. The first issue is how to define the money stock. This study, like most other empirical reports
inquiries.
the
results
from
estimating
money stock definitions, the narrow Ml definition (currency. plus demund deposits) and the broad M7 definrtion (IVI plus time and savings dcpoGts). A second issue relates to modelling the adjuatment process whereby actual real halxxxs equation
dynamically
(
1)
using
adjust
the two
to
the
conventional
desired
levels.
Re-
Koyck-lag procedure basically for its simplicity and convcnience whereby the whole adjustment process is represented simply by the inclusion of a lagged dependent variable, (f),~, Yet, as Grilichcs (1967) and others pointed out. this Koyck-lag procedure is highly biased and unduly restrictive. Therefore, this study employs an alternative and adjustment-lag procedure, superior perhaps namely the Almon procedure.” The lag structure in the Almon technique is approximated through replacing each independent variable in the cquation by ;I distributed lag variable of its own current and past values. According to this Almon scheme, the lag weights are assumed to lie along a polynomial function of a certain degree chosen by the researcher. In addition to the degree of the polynomial function. the researcher also chooses the length of the lag for each independent \~ariable. In the absence of prior knowledge. the degree of polynomial and the lag length are determined here, following Schmidt and Waud (197.1) and Giles and Smith (1977). on the basis of Theil’s (1971) residual-variance criterion. Note. however, that the Almon estimation technique is used without the endpoint constraints - as suggested by Schmidt and Waud (1973) to avoid possible biases. searchers
commonly
use
the
countries
determined
because
are
not
these
genuinely interest
market rate\
arc
by authorities.
As ;I result, most cmpiric;il studie\ on mane! demand in developing countries have solely usccl cxpectcd inflation to represent the oppo’tunit! cost of holding money. Because the ;tbo\,c argument\ seem applicable for Kenya. the interest rates variable is dropped from the Monet demand equations estimated in this paper as well.” Yet. one must further note that coaxtemporary economies are more or less open to each other. In such economies. international opportunity cost of holding money should al\o be considered along with the domestic counterpart. That is. foreign (not just domestic) financial assets ought to be considered ;I\ ;I potential alternative to holding domestic money balances in Kenya. To test this openness hypothesis. a mcasurc‘ of foreign interest rates variable is included in the money demand equation for Kenya.’ Finally. as to the specific functional form of the money demand equation. economic theory providcs no (1 priori rationale to choose between. say. the linear or the log-linear format. Neverthcless. most empirical studies. including the present one, seem to favor the log-linear functional form which is also convenient in that elasticities can bc directly
obtained
3.
TIIE
from
the estimated
EMPIRICAL
RESULTS
Based on the preceding discussion. money
demand
equation
coefficients.”
the Keynan
becomes:
(‘7)
DEMAND
FOR MONEY
where all the variables are defined as before, R’ is short-term foreign interest rates, )I, (i = 1, 2. 3,) relates to the lengths of the Almon lags, and F is a white-noise disturbance term (for the empirical definitions of the variables and sources of data. see the Appendix). As to the signs of the coefficients. the demand for money theory LI priori predicts that Zh, > 0, Zc, < 0, and X:(1,< 0. It is worth noting that as specified in equation (2). the contemporaneous values on inflation and foreign interest rates are omitted from the estimation. In developing countries like Kenya, the system of collecting and disseminating statistical data is so inefficient and slow that economic agents are likely to form their future expectations for these variables on the basis of past data alone. The omission of current inflation (the rate of change in current prices) is also meant to avoid possible spurious correlation since the dependent variable is defined as the logarithim of current money stock deflated by current prices. Equation (2) has been estimated for Kenya using the quarterly data over 196Y:l to 1978:IV.” Based on Theil’s criterion, Table 1 reports the best regression results for the two alternative definitions of money (Ml and M2). After correcting for first-order serial correlation by the Cochrane-Orcutt iterative method, the scores of the Durbin-Watson statistic suggest that both regressions do not suffer from remaining signiffirst-order serial correlation. The fit of both equations to the data is excellent as indicated by values of R’ and the standard error of the regressions do not suffer from remaining significant first-order serial correlation. The fit of both equations to the data is excellent as indicated by the goodness of fit as the two models trace quite well both the level3 and the turning points of real money demand in Kenya. The estimated equations reported in Table 1 are quite consistent with the theory u priori predictions: All of the three estimated sumcoefficients bear the correct anticipated signs and each is significantly non-zero at the conventional 5% level. Since a long-lag was found necessary for the real income variable in both equations, the empirical results then indicate that permanent (rather than current, measured) real income is the appropriate scale variable in the Kenyan money demand function. The results further show that the (long-run) real income elasticity of money demand (A41 and M2) is significantly higher than unity. These findings are consistent with other estimates reported in the literature for similar developing countries (e.g., Adekunle, 1968; Wong, 1977). Also confirmed is the hypothesis that inflationary expectations play a significant role in the
IN KENYA
1165
determination of the Kenyan money holdings implying that real goods are viewed by asset holders in Kenya as an important substitute for money. Perhaps more interesting is the evidence obtained on the significant role played by the foreign interest rates in Kenya’s money demand functions. The empirical results reported in this study indicate that foreign financial assets are also considered as attractive alternatives to holding domestic money balances in the Kenyan economy. The coefficient on the foreign interest rates variable is appropriately signed (negative) and is statistically significant at the S’!% level in both money demand equations. Moreover. this variable exerts even a stronger effect on the demand for money (Ml definition) than the traditional measure of the opportunity cost of holding money (i.e., expected inflation). This paper therefore provides empirical support for the hypothesis that foreign interest rates ought to be included in the money demand function of Kenya. as potentially of any other open economy. I” Based on the above empirical results, we may conclude that the estimated equations set out in Table 1 fit the actual data quite well and adequately describe the money demand relationship in the Kenyan economy. [Iowever. to formulate an appropriate monetary policy on the basis of these money demand results, it is essential to examine whether or not the estimated equations are structurally stable over time.
4. STRUCTURAL STABILITY OF THE ESTIMATED MONEY DEMAND EQUATIONS In the money demand empirical literature, testing for stability commonly refers to testing for the approximate constancy of the estimated coefficients over time. Such concept of stability may be formally tested through several available statistical tests. As Boughton (1981) pointed out, each stability test addresses a somewhat different aspect of stability and thus it is advisable that the researcher employs a battery of stability tests. In this paper, three stability tests are employed, namely the Chow (1960) test, the Gujarati (lY70) test, and the Farley-Hinich (1970) test. To apply the Chow test. the data set is divided into two parts at u priori date, and the two regressions over the two sub-periods are compared to the full-sample regression using an F-ratio to assess whether a significant shift has occurred in the function.” The Gujarati test
(!W/l’),
2.2
(4.SO) -i.c)Xh (K.34)
-5.0.3.i IN.3
(14,‘)s)
(S.OI) I.‘112 (3.04)
-ll.(lli
(2.11))
-0.015
(3.S7)
-O.OZI
-0. IhO (.~.40)
(I.W-l
0.951)
201.S.~
x3.41
t1.02571
I).OMi.~
0.557
-(I. 147
I .15
7.lLl
I.843 l.YI? [7.151
[4.0X] -.1x
-.I45
- .I)2
I
-.IhO
The tigure in pxcnthcse are ahwlutc \;~Iucs of i-ratios. /?’ is the cwllrcicnt ot detcrminatron corrcctccl for dcpxs (11 l’recdom, ~-v:~lue ih for tcstinp the null hypothrsk that all the right-hand sick variahlw ;I\ ;I youp esccpt the ccmstanl term have zc’r(, corllicrcnt. SE i\ the standard error 01 the regression. Q is the Cochr;m-Orcutt txtimate (11 the trial correlation coel’ficicnt. .!nd Du’ I\ the DurhrnpWntwn statktic to test for rcmarning serial correlation. Since real income variahlc in both cquatwn\. the long-run clasticitks of real money dcmnnt) and foreign mtcrcst rata wriahlc\ cntt’r lo~~~rithnlic~lll~ don, (7 with the dcpendrnt t-ratio\ arc also calculated for ditfcrence ol these elasticities with respect to thcsc two \ari;lhlea arc dtrcctlq ccvi\en hv their respective cum-c~)~rrici~nt e\tlmatc\. expectations from unity and reported in hrackct\ helow the cl;:stici;. cstimatcs. For the Ion F-run clastlcitv 01 real moncv demand wth respect to inflationary variable. which enter\ linead!. it k cnlculated a\ the product o( the estimated sum-coeiiicicnt and thi sample average 01 the inllation rate (9.69%). Both equation\ were estimated using unconstr;Gncd hlmnn twhnique with wrial correlation adjwtmcnt (PDLCOKC). Thlrtl-degree polynomial for each lay Xld II, = 4. 11~ = 4. ,I; = X for A43 equation. distribution and the l’ollown~ la? Icngth\ \st’rt’ cmpiric;ill! wperlclr: 11, -.. 12. 11: ~ s. ,I; = Y tor .\!I equation:
log
log (.MI/P),
2. I
DEMAND
FOR
MONEY
5. CONCLUSIONS
constructs a slope-dummy term for all independent variables (that is, (DZ), = DtZ, where D = 0 in the first sub-period and D = 1 in the second sub-period, and Z is any independent variable). Then using an F-ratio. one tests for a possible drift in the parameters after the inclusion of the second sub-period dummy variables. Clearly, to implement both the Chow and the Gujarati tests, a choice of sample breaking data must be made. Since no prior information is available to guide this choice, and in view of the limited number of the observations, the sample period was divided into two equal parts (each containing 20 observations). The resulting two sub-samples (196Y:I to lY73:IV versus lY74:I to lY78:IV) were then utilized for the purpose of applying the two stability tests. A third stability test, the Farley-Hinich test, is also applied. This procedure differs from the other two in that it tests for a gradual (in contrast to a single) shift in the parameters (see Farley, Hinich and McGuire, 1975). Another virtue of the Farley-Hinich test is that its implementation does not require splitting the data set at a certain point because the test is applied to the fullsample period. Thus, if a significant shift has occurred at a particular date different from the fourth quarter of 1973, the Farley-Hinich test is likely to pick it up. To apply this test, the regression coefficients being tested for structural instability are treated as linear functions of time and added to the original equation. Then an appropriate F-ratio is used to test the nullhypothesis that the coefficients on the added trend variables are jointly zero. For the narrow and broad money demand equations, Table 2 reports the calculated Fstatistics for the three stability tests. All three tests could not reject the hypothesis of stability at the 5% significance level.i2 Therefore, taken together, the evidence suggests very stable money demand functions for Kenya.
Table
1167
IN KENYA
The purpose of this paper has been to estimate an appropriate money demand function for Kenya using the narrow and the broad definitions of money. The paper has also examined the temporal stability of the estimated money demand equations. The principal conclusions of this empirical paper can be briefly summarized as follows. 1. The explanatory variables that significantly influence real money demand in Kenya are permanent real income, expected inflation and short-term foreign interest rates. As predicted by the theory, the first variable affects real money demand positively, while the latter two variables affect real demand negatively. For both definitions of money, the estimated demand equations exhibit an excellent goodness of fit. 2. The long-run elasticities of real money demand (Ml and M2 definitions) with respect to real income are significantly greater than unity (close to 2). 3. Long-run elasticities of real money demand with respect to expected inflation and foreign interest rates, although small, are significantly non-zero. Thus, the results show that both of these variables also play an important role in portfolio decisions about money holdings in Kenya. 4. Based on a battery of stability tests, the estimated money demand equations for Kenya are found structurally stable over time. 5. Perhaps a novel conclusion emerging from this study is that foreign interest rates (as a proxy for external monetary developments) exert a significant effect on domestic money demand in
2. Stability test results for the estimated Kenyan money demand eyuariorts
F-Statistics for Equation
The Chow
test
The
Gujarati
test
The Farley-Hinich
Real
Ml
demand
2.73
2.29
0.36
Real
M2 demand
2.77
2.76
1.48
For any equation,
test
a calculated F-statistic that exceeds the corresponding critical F-value at the 5% significance level suggests the equation is structurally unstable. None of the F-statistics for both equations is higher than the critical F-value.
I IhS
WOK1.I~
DEVLrl.OPhlEN’I
Kenya. Thus, neglect of such variuhlex can produce biased results. It can bc deduced that traditional money demand studies for other open economies that do not include a variable representing the influence of external factors arc potentially misspecified. The significance of foreign interest rates in the money demand function has an important implication for the cffectivenea of the Kenyan
monetary policy. Monetary policy actions aimed at stabilizing the economy and counteracting the impact of external shocks upon the domestic economy must take into account the response of domestic money demand to these external factors. If adjustments in money demand induced by external monetary influences are ignored, monetary policy actions can only generate at best uncertain results.
NO’l’tS I. For dcvcloped CounIrIcs. see’ l’or cxamplc Laidlcr and Parkin (lY70); Goldlcld (1073): Melit~ (1070); Roughton (lY7Y): and Ruttcr and Fa\e (IYSI). For developing countrie. \cc Diz ( lY70): Wong ( lY77); I‘rivedi ( IYXO): and Darrat ( IYXSa. h).
3. For further discu\slon on the Import;lncc 01 monc‘tary policy tor dcvcloping economics. \ce Eshag (lY71). 1. Note that in thi\ form. the theory impost\ the rcatrictlon that money demand ia cast in real tc‘rms. that ih. real demand for money ia homqcnous of dcgrcc Icro in prices. This is bccausc economic agents arc’ tl ,~r!orf a\\umcd rational. and thus their demand lor cii5h balances IS a demand tor real purchaslnp power. Obviously, the Almon tcchniquc i\ not without 5 drawback\. For an account ol thee prohlcm\. \ce Schmidt and Waud (lY73) and Thomas ( lY77). 0. Ncedlesa to say, that Interc\t rates arc omitted tram the money demand equations doca not necessarily imply the complete ahscncc or financial aascta 1n Kenya. 7. Of c(Iurs(c. It would appear llhcly that inllucnccs of lorcign interest rates on domc\tic money holdings
DEMAND
FOR
MONEY
IN KENYA
I I69
REFERENCES Adekunle, J. 0.. “The demand for money: Evidence from developed and less developed economies.” International Monetary Fund Stuff Papers, Vol. 15 (July 1968). pp. 22&264. Arango. S., and M. I. Nadiri, ‘
lags: A survey,” EconoGriliches, Z., “Distributed me/rica, Vol. 35 (January 1976). pp. 1649. Gujarati, D., “Use of dummy variables in testing for equality between sets of coefficients in linear regressions: A generalization,” The American Statistician, Vol. 24 (December 1970), pp. 18-22. Hamburger, M. J.. “The demand for money in an open economy: Germany and the United Kingdom,” Journal of Monetarv Economics,Vol. 3 (January 1977). pp: 25-50. . Laidler. D. E. W.. and M. J. Parkin, “The demand for money in the United Kingdom, 195667: Preliminary estimates.” Munchester School of Economic and Social Studies, Vol. 3X (September 1970), pp. 1X7-208. McKinnon, R. I., Money and Capital in Economic Development (Washington: The Brookings Institution, 1973). Melitz, J., “Inflationary expectations and the French demand for money, I959:70,” Manchester School of Economic and Social Studies, Vol. 44 (March 1976). pp. 17-41. Pathak, D. S.. “Demand for money in developing Kenya - An econometric study (1968-78);’ Indian Economic Journal, Vol. 29 (July-September 1981). pp. l&16. Schmidt. P., and R. Sickles, “Some further evidence on the use of the Chow Test under heteroskedasticity,” Econometrica, Vol. 45 (July 1977), pp. 1293-1298. Schmidt, P.. and R. N. Waud, “The Almon Lag Technique and the monetary versus fiscal policy debate,” Journal of the American Stati.sticalAssociation, Vol. 68 (March 1973). pp. 11-19. Theil, H.. Principles of Econometrics (New York: John Wiley, 1971). Thomas, J. J., “Some problems in the use of Almon’s Technique in the estimation of distributed lags.” Empirical Economics, Vol. 2 (1977), pp. 175-193. Thornton, D. L.. “Why does velocity matter’?” Federal Reserve Bank of St. Louis Review, Vol. 65 (December 19X3), pp. 5-13. Toyoda, T., “Use of the Chow test under heteroscedasticity,” Economerrica, Vol. 42 (May 1974). pp. 601-608. Trivedi, M. S., “Inflationary expectations and demand for money in India (1951-75):’ Indian Economic Journal, Vol. 28 (July 1980). pp. 62-76. Wong. C., “Demand for money in developing countries: Some theoretical and empirical results.” Journal of Monetary Economics, Vol. 3 (January 1977). pp. 59-86.
1170
WORLD
APPENDIX:
DEVELOPMEN’I
DESC’RIPTION
This study cowrs the period from 1YhY through lY7H on the basis of quarterly ohservntiona. The empirical definitions of the variables arc as follows: MI = Currency definition) MZ = Ml plus definttion) P = Consumer year X = Real Gross price\) JC = Annualized K’ = Short-term
plus time
ckmand
deposits
and savings deposit
Price Index National
with
(narrow (broad
1Y7S as the base
Product (at constant
inflation rate foreign interest rata.
1Y75
This variahlc
AND
SOURC‘ES
OF DATA
k conatructcd as the average ol quarterly short-term intcrext rates in major OECD countries. All the data scrics arc obtained l’rom various issue\ of the IMF. frrkwrrrfiord I;irw~icr/ .Stcr/i.vr~, except lor the short-term foreign interest rates which arc derived from OEC‘U Mairz Ewrzornic~ Imlicntrm (various ~asuca). Note that while the data series used in thi\ paper arc all availnhle on a quarterly hasis. data on rciil GNP are available only annually. Thus. a non-linear mathcmatd interpolatwn tcchniquc due to Diz (lY70) was cmploycd to construct the corresponding quarterly figures for real GNP.
Vol.
13, No. 1011 I. pp. 1163-l
170. 1Y85. 0
Printed in Great Britain.
$3.00 + 0.00 0305-750x/85 1985 Pergamon Press Ltd.
The Demand for Money in a Developing Economy: The Case of Kenya ALI F. DARRAT” University of New Orleans,
New Orleans
Summary.
- The demand for money function occupies a central role in most theories of aggregate economic activity, especially in the formulation and execution of effective monetary policy. This paper examines the demand for money in the developing economy of Kenya. Special attention is paid to the model specification. its dynamic structure and to its temporal stability. The empirical results show that for both conventional definitions of money (the narrow and the broad), the theoretical model fits the Kcnyan data quite well. and the proposed variables arc all statistically significant and with the anticipated signs. The results further suggest. based on a battcry of tests, that the estimated money demand equations for Kenya arc temporally stable. Focus is also given to the open-economy nature of the money demand model, and the results indicate that some measure of foreign interest rates plays a significant role in the Kcnyan money demand equations as potentially in any other money demand equation of an open economy. Monetary policy in Kenya. therefore. must take into account the response of domestic money demand to changes in such external factors.
1.
INTRODUCTION
The past several decades have witnessed considerable empirical research on the money demand function due to the vital role this function plays in macroeconomic analysis, especially in regard to the formation and transmission of monetary policy. Consequently, money demand functions have been empirically estimated by many researchers for a number of developed and developing countries. ’ However, money demand function for the developing economy of Kenya has been largely ignored.’ It is the aim of this paper, therefore, to estimate an appropriate money demand function for Kenya using the quarterly data over the period lY69:I to 1978:IV. One of the central issues that this paper addresses is whether the Kenyan money demand relationship has shifted during the period of estimation. Money demand stability is in fact a prerequisite for an effective monetary policy. As Thornton (1983) pointed out on the basis of the familiar equation of exchange, the money demand is the link between monetary policy and the real side of the economy. Thus. to predict adequately the impact of money supply changes upon real output. interest rates and prices, the underlying money demand relationship must be temporally stable. In the context of economic development, it
may seem that monetary policy is irrelevant in the case of developing economies owing basically to the lack of well-developed financial and capital markets. However, as stressed by McKinnon (1973) and Bhatia and Khatkhate (lY75), monetary policy can still play a major role in mobilizing savings into real capital and promoting financial stability; this would, in turn, contribute to the development of efficient financial and markets. Indeed, the presumption capital appears to be fairly established in the literature that improvements in the intermediation process are favorable to economic development in countries like Kenya.’ The rest of the paper is organized as follows. Section 2 specifies an appropriate money demand function for Kenya. Section 3 then reports the empirical results. The stability property of the money demand equation is examined in Section 4. Finally, some concluding remarks are drawn in Section 5.
*The author would like to thank Lawrence Davidson and Elmus Wicker for their continuous cncouragcment. Thanks also go to an anonymous referee of this journal for useful comments. Any remaining errors arc, of course. the sole responsibility of the author.
1163
W0RI.D
I16-l 2.
THE
MONEY
Economic
theorv
money
balances,
DEMAND holds
($)”
I~EVtL.OPMENl
MODEL
that
dcaired
is positi\cly
related
real to
2
VXI~ variable
such as real income (X)
and nef:i-
tively
to the opportunity
of holding
related
costs
money, that is. the yields on alternative real and financial assets.’ The expected rate of inflation (JI”) is usually t&en to represent the foregone yield on real assets. and the rate(s) of interest (R) is used to rcprescnt the foregone yield on financial assets. The money demand function may
then
($=
l(X,.
bc written
as:
Another issue concerns the ~ipl”“pri;ltencss of including some measure of interest rates in the money demand equations of developing economies. Manv researchers have suggested that in these econon;ies interest rates variable should bc dropped from the money demand function. Thi\ is because financial assets in 4uch countries arc inadequate. Consequently. \ery little sub\tituability exists between money and other financial assets and the choice of asset holders is largely limited to holding either money or real good\. such as real estate or con\umc‘r durable\. Moreoc’cl-. the few interest yields available in developing
JI ;. R,)
(1)
pegged where f;
<
the theory
postulates
that f,
>
0, .I; <
0,
0.
To make equation (I) estimatable. ;I number of analytical and technical issues warrent comment. The first issue is how to define the money stock. This study, like most other empirical reports
inquiries.
the
results
from
estimating
money stock definitions, the narrow Ml definition (currency. plus demund deposits) and the broad M7 definrtion (IVI plus time and savings dcpoGts). A second issue relates to modelling the adjuatment process whereby actual real halxxxs equation
dynamically
(
1)
using
adjust
the two
to
the
conventional
desired
levels.
Re-
Koyck-lag procedure basically for its simplicity and convcnience whereby the whole adjustment process is represented simply by the inclusion of a lagged dependent variable, (f),~, Yet, as Grilichcs (1967) and others pointed out. this Koyck-lag procedure is highly biased and unduly restrictive. Therefore, this study employs an alternative and adjustment-lag procedure, superior perhaps namely the Almon procedure.” The lag structure in the Almon technique is approximated through replacing each independent variable in the cquation by ;I distributed lag variable of its own current and past values. According to this Almon scheme, the lag weights are assumed to lie along a polynomial function of a certain degree chosen by the researcher. In addition to the degree of the polynomial function. the researcher also chooses the length of the lag for each independent \~ariable. In the absence of prior knowledge. the degree of polynomial and the lag length are determined here, following Schmidt and Waud (197.1) and Giles and Smith (1977). on the basis of Theil’s (1971) residual-variance criterion. Note. however, that the Almon estimation technique is used without the endpoint constraints - as suggested by Schmidt and Waud (1973) to avoid possible biases. searchers
commonly
use
the
countries
determined
because
are
not
these
genuinely interest
market rate\
arc
by authorities.
As ;I result, most cmpiric;il studie\ on mane! demand in developing countries have solely usccl cxpectcd inflation to represent the oppo’tunit! cost of holding money. Because the ;tbo\,c argument\ seem applicable for Kenya. the interest rates variable is dropped from the Monet demand equations estimated in this paper as well.” Yet. one must further note that coaxtemporary economies are more or less open to each other. In such economies. international opportunity cost of holding money should al\o be considered along with the domestic counterpart. That is. foreign (not just domestic) financial assets ought to be considered ;I\ ;I potential alternative to holding domestic money balances in Kenya. To test this openness hypothesis. a mcasurc‘ of foreign interest rates variable is included in the money demand equation for Kenya.’ Finally. as to the specific functional form of the money demand equation. economic theory providcs no (1 priori rationale to choose between. say. the linear or the log-linear format. Neverthcless. most empirical studies. including the present one, seem to favor the log-linear functional form which is also convenient in that elasticities can bc directly
obtained
3.
TIIE
from
the estimated
EMPIRICAL
RESULTS
Based on the preceding discussion. money
demand
equation
coefficients.”
the Keynan
becomes:
(‘7)
DEMAND
FOR MONEY
where all the variables are defined as before, R’ is short-term foreign interest rates, )I, (i = 1, 2. 3,) relates to the lengths of the Almon lags, and F is a white-noise disturbance term (for the empirical definitions of the variables and sources of data. see the Appendix). As to the signs of the coefficients. the demand for money theory LI priori predicts that Zh, > 0, Zc, < 0, and X:(1,< 0. It is worth noting that as specified in equation (2). the contemporaneous values on inflation and foreign interest rates are omitted from the estimation. In developing countries like Kenya, the system of collecting and disseminating statistical data is so inefficient and slow that economic agents are likely to form their future expectations for these variables on the basis of past data alone. The omission of current inflation (the rate of change in current prices) is also meant to avoid possible spurious correlation since the dependent variable is defined as the logarithim of current money stock deflated by current prices. Equation (2) has been estimated for Kenya using the quarterly data over 196Y:l to 1978:IV.” Based on Theil’s criterion, Table 1 reports the best regression results for the two alternative definitions of money (Ml and M2). After correcting for first-order serial correlation by the Cochrane-Orcutt iterative method, the scores of the Durbin-Watson statistic suggest that both regressions do not suffer from remaining signiffirst-order serial correlation. The fit of both equations to the data is excellent as indicated by values of R’ and the standard error of the regressions do not suffer from remaining significant first-order serial correlation. The fit of both equations to the data is excellent as indicated by the goodness of fit as the two models trace quite well both the level3 and the turning points of real money demand in Kenya. The estimated equations reported in Table 1 are quite consistent with the theory u priori predictions: All of the three estimated sumcoefficients bear the correct anticipated signs and each is significantly non-zero at the conventional 5% level. Since a long-lag was found necessary for the real income variable in both equations, the empirical results then indicate that permanent (rather than current, measured) real income is the appropriate scale variable in the Kenyan money demand function. The results further show that the (long-run) real income elasticity of money demand (A41 and M2) is significantly higher than unity. These findings are consistent with other estimates reported in the literature for similar developing countries (e.g., Adekunle, 1968; Wong, 1977). Also confirmed is the hypothesis that inflationary expectations play a significant role in the
IN KENYA
1165
determination of the Kenyan money holdings implying that real goods are viewed by asset holders in Kenya as an important substitute for money. Perhaps more interesting is the evidence obtained on the significant role played by the foreign interest rates in Kenya’s money demand functions. The empirical results reported in this study indicate that foreign financial assets are also considered as attractive alternatives to holding domestic money balances in the Kenyan economy. The coefficient on the foreign interest rates variable is appropriately signed (negative) and is statistically significant at the S’!% level in both money demand equations. Moreover. this variable exerts even a stronger effect on the demand for money (Ml definition) than the traditional measure of the opportunity cost of holding money (i.e., expected inflation). This paper therefore provides empirical support for the hypothesis that foreign interest rates ought to be included in the money demand function of Kenya. as potentially of any other open economy. I” Based on the above empirical results, we may conclude that the estimated equations set out in Table 1 fit the actual data quite well and adequately describe the money demand relationship in the Kenyan economy. [Iowever. to formulate an appropriate monetary policy on the basis of these money demand results, it is essential to examine whether or not the estimated equations are structurally stable over time.
4. STRUCTURAL STABILITY OF THE ESTIMATED MONEY DEMAND EQUATIONS In the money demand empirical literature, testing for stability commonly refers to testing for the approximate constancy of the estimated coefficients over time. Such concept of stability may be formally tested through several available statistical tests. As Boughton (1981) pointed out, each stability test addresses a somewhat different aspect of stability and thus it is advisable that the researcher employs a battery of stability tests. In this paper, three stability tests are employed, namely the Chow (1960) test, the Gujarati (lY70) test, and the Farley-Hinich (1970) test. To apply the Chow test. the data set is divided into two parts at u priori date, and the two regressions over the two sub-periods are compared to the full-sample regression using an F-ratio to assess whether a significant shift has occurred in the function.” The Gujarati test
(!W/l’),
2.2
(4.SO) -i.c)Xh (K.34)
-5.0.3.i IN.3
(14,‘)s)
(S.OI) I.‘112 (3.04)
-ll.(lli
(2.11))
-0.015
(3.S7)
-O.OZI
-0. IhO (.~.40)
(I.W-l
0.951)
201.S.~
x3.41
t1.02571
I).OMi.~
0.557
-(I. 147
I .15
7.lLl
I.843 l.YI? [7.151
[4.0X] -.1x
-.I45
- .I)2
I
-.IhO
The tigure in pxcnthcse are ahwlutc \;~Iucs of i-ratios. /?’ is the cwllrcicnt ot detcrminatron corrcctccl for dcpxs (11 l’recdom, ~-v:~lue ih for tcstinp the null hypothrsk that all the right-hand sick variahlw ;I\ ;I youp esccpt the ccmstanl term have zc’r(, corllicrcnt. SE i\ the standard error 01 the regression. Q is the Cochr;m-Orcutt txtimate (11 the trial correlation coel’ficicnt. .!nd Du’ I\ the DurhrnpWntwn statktic to test for rcmarning serial correlation. Since real income variahlc in both cquatwn\. the long-run clasticitks of real money dcmnnt) and foreign mtcrcst rata wriahlc\ cntt’r lo~~~rithnlic~lll~ don, (7 with the dcpendrnt t-ratio\ arc also calculated for ditfcrence ol these elasticities with respect to thcsc two \ari;lhlea arc dtrcctlq ccvi\en hv their respective cum-c~)~rrici~nt e\tlmatc\. expectations from unity and reported in hrackct\ helow the cl;:stici;. cstimatcs. For the Ion F-run clastlcitv 01 real moncv demand wth respect to inflationary variable. which enter\ linead!. it k cnlculated a\ the product o( the estimated sum-coeiiicicnt and thi sample average 01 the inllation rate (9.69%). Both equation\ were estimated using unconstr;Gncd hlmnn twhnique with wrial correlation adjwtmcnt (PDLCOKC). Thlrtl-degree polynomial for each lay Xld II, = 4. 11~ = 4. ,I; = X for A43 equation. distribution and the l’ollown~ la? Icngth\ \st’rt’ cmpiric;ill! wperlclr: 11, -.. 12. 11: ~ s. ,I; = Y tor .\!I equation:
log
log (.MI/P),
2. I
DEMAND
FOR
MONEY
5. CONCLUSIONS
constructs a slope-dummy term for all independent variables (that is, (DZ), = DtZ, where D = 0 in the first sub-period and D = 1 in the second sub-period, and Z is any independent variable). Then using an F-ratio. one tests for a possible drift in the parameters after the inclusion of the second sub-period dummy variables. Clearly, to implement both the Chow and the Gujarati tests, a choice of sample breaking data must be made. Since no prior information is available to guide this choice, and in view of the limited number of the observations, the sample period was divided into two equal parts (each containing 20 observations). The resulting two sub-samples (196Y:I to lY73:IV versus lY74:I to lY78:IV) were then utilized for the purpose of applying the two stability tests. A third stability test, the Farley-Hinich test, is also applied. This procedure differs from the other two in that it tests for a gradual (in contrast to a single) shift in the parameters (see Farley, Hinich and McGuire, 1975). Another virtue of the Farley-Hinich test is that its implementation does not require splitting the data set at a certain point because the test is applied to the fullsample period. Thus, if a significant shift has occurred at a particular date different from the fourth quarter of 1973, the Farley-Hinich test is likely to pick it up. To apply this test, the regression coefficients being tested for structural instability are treated as linear functions of time and added to the original equation. Then an appropriate F-ratio is used to test the nullhypothesis that the coefficients on the added trend variables are jointly zero. For the narrow and broad money demand equations, Table 2 reports the calculated Fstatistics for the three stability tests. All three tests could not reject the hypothesis of stability at the 5% significance level.i2 Therefore, taken together, the evidence suggests very stable money demand functions for Kenya.
Table
1167
IN KENYA
The purpose of this paper has been to estimate an appropriate money demand function for Kenya using the narrow and the broad definitions of money. The paper has also examined the temporal stability of the estimated money demand equations. The principal conclusions of this empirical paper can be briefly summarized as follows. 1. The explanatory variables that significantly influence real money demand in Kenya are permanent real income, expected inflation and short-term foreign interest rates. As predicted by the theory, the first variable affects real money demand positively, while the latter two variables affect real demand negatively. For both definitions of money, the estimated demand equations exhibit an excellent goodness of fit. 2. The long-run elasticities of real money demand (Ml and M2 definitions) with respect to real income are significantly greater than unity (close to 2). 3. Long-run elasticities of real money demand with respect to expected inflation and foreign interest rates, although small, are significantly non-zero. Thus, the results show that both of these variables also play an important role in portfolio decisions about money holdings in Kenya. 4. Based on a battery of stability tests, the estimated money demand equations for Kenya are found structurally stable over time. 5. Perhaps a novel conclusion emerging from this study is that foreign interest rates (as a proxy for external monetary developments) exert a significant effect on domestic money demand in
2. Stability test results for the estimated Kenyan money demand eyuariorts
F-Statistics for Equation
The Chow
test
The
Gujarati
test
The Farley-Hinich
Real
Ml
demand
2.73
2.29
0.36
Real
M2 demand
2.77
2.76
1.48
For any equation,
test
a calculated F-statistic that exceeds the corresponding critical F-value at the 5% significance level suggests the equation is structurally unstable. None of the F-statistics for both equations is higher than the critical F-value.
I IhS
WOK1.I~
DEVLrl.OPhlEN’I
Kenya. Thus, neglect of such variuhlex can produce biased results. It can bc deduced that traditional money demand studies for other open economies that do not include a variable representing the influence of external factors arc potentially misspecified. The significance of foreign interest rates in the money demand function has an important implication for the cffectivenea of the Kenyan
monetary policy. Monetary policy actions aimed at stabilizing the economy and counteracting the impact of external shocks upon the domestic economy must take into account the response of domestic money demand to these external factors. If adjustments in money demand induced by external monetary influences are ignored, monetary policy actions can only generate at best uncertain results.
NO’l’tS I. For dcvcloped CounIrIcs. see’ l’or cxamplc Laidlcr and Parkin (lY70); Goldlcld (1073): Melit~ (1070); Roughton (lY7Y): and Ruttcr and Fa\e (IYSI). For developing countrie. \cc Diz ( lY70): Wong ( lY77); I‘rivedi ( IYXO): and Darrat ( IYXSa. h).
3. For further discu\slon on the Import;lncc 01 monc‘tary policy tor dcvcloping economics. \ce Eshag (lY71). 1. Note that in thi\ form. the theory impost\ the rcatrictlon that money demand ia cast in real tc‘rms. that ih. real demand for money ia homqcnous of dcgrcc Icro in prices. This is bccausc economic agents arc’ tl ,~r!orf a\\umcd rational. and thus their demand lor cii5h balances IS a demand tor real purchaslnp power. Obviously, the Almon tcchniquc i\ not without 5 drawback\. For an account ol thee prohlcm\. \ce Schmidt and Waud (lY73) and Thomas ( lY77). 0. Ncedlesa to say, that Interc\t rates arc omitted tram the money demand equations doca not necessarily imply the complete ahscncc or financial aascta 1n Kenya. 7. Of c(Iurs(c. It would appear llhcly that inllucnccs of lorcign interest rates on domc\tic money holdings
DEMAND
FOR
MONEY
IN KENYA
I I69
REFERENCES Adekunle, J. 0.. “The demand for money: Evidence from developed and less developed economies.” International Monetary Fund Stuff Papers, Vol. 15 (July 1968). pp. 22&264. Arango. S., and M. I. Nadiri, ‘
lags: A survey,” EconoGriliches, Z., “Distributed me/rica, Vol. 35 (January 1976). pp. 1649. Gujarati, D., “Use of dummy variables in testing for equality between sets of coefficients in linear regressions: A generalization,” The American Statistician, Vol. 24 (December 1970), pp. 18-22. Hamburger, M. J.. “The demand for money in an open economy: Germany and the United Kingdom,” Journal of Monetarv Economics,Vol. 3 (January 1977). pp: 25-50. . Laidler. D. E. W.. and M. J. Parkin, “The demand for money in the United Kingdom, 195667: Preliminary estimates.” Munchester School of Economic and Social Studies, Vol. 3X (September 1970), pp. 1X7-208. McKinnon, R. I., Money and Capital in Economic Development (Washington: The Brookings Institution, 1973). Melitz, J., “Inflationary expectations and the French demand for money, I959:70,” Manchester School of Economic and Social Studies, Vol. 44 (March 1976). pp. 17-41. Pathak, D. S.. “Demand for money in developing Kenya - An econometric study (1968-78);’ Indian Economic Journal, Vol. 29 (July-September 1981). pp. l&16. Schmidt. P., and R. Sickles, “Some further evidence on the use of the Chow Test under heteroskedasticity,” Econometrica, Vol. 45 (July 1977), pp. 1293-1298. Schmidt, P.. and R. N. Waud, “The Almon Lag Technique and the monetary versus fiscal policy debate,” Journal of the American Stati.sticalAssociation, Vol. 68 (March 1973). pp. 11-19. Theil, H.. Principles of Econometrics (New York: John Wiley, 1971). Thomas, J. J., “Some problems in the use of Almon’s Technique in the estimation of distributed lags.” Empirical Economics, Vol. 2 (1977), pp. 175-193. Thornton, D. L.. “Why does velocity matter’?” Federal Reserve Bank of St. Louis Review, Vol. 65 (December 19X3), pp. 5-13. Toyoda, T., “Use of the Chow test under heteroscedasticity,” Economerrica, Vol. 42 (May 1974). pp. 601-608. Trivedi, M. S., “Inflationary expectations and demand for money in India (1951-75):’ Indian Economic Journal, Vol. 28 (July 1980). pp. 62-76. Wong. C., “Demand for money in developing countries: Some theoretical and empirical results.” Journal of Monetary Economics, Vol. 3 (January 1977). pp. 59-86.
1170
WORLD
APPENDIX:
DEVELOPMEN’I
DESC’RIPTION
This study cowrs the period from 1YhY through lY7H on the basis of quarterly ohservntiona. The empirical definitions of the variables arc as follows: MI = Currency definition) MZ = Ml plus definttion) P = Consumer year X = Real Gross price\) JC = Annualized K’ = Short-term
plus time
ckmand
deposits
and savings deposit
Price Index National
with
(narrow (broad
1Y7S as the base
Product (at constant
inflation rate foreign interest rata.
1Y75
This variahlc
AND
SOURC‘ES
OF DATA
k conatructcd as the average ol quarterly short-term intcrext rates in major OECD countries. All the data scrics arc obtained l’rom various issue\ of the IMF. frrkwrrrfiord I;irw~icr/ .Stcr/i.vr~, except lor the short-term foreign interest rates which arc derived from OEC‘U Mairz Ewrzornic~ Imlicntrm (various ~asuca). Note that while the data series used in thi\ paper arc all availnhle on a quarterly hasis. data on rciil GNP are available only annually. Thus. a non-linear mathcmatd interpolatwn tcchniquc due to Diz (lY70) was cmploycd to construct the corresponding quarterly figures for real GNP.