The Demand for Money and the Term Structure of Interest Rates in Ireland,

Transcription

1 The Economic and Social Review, Vol. 16, No. 2, Januay, 1985, pp The Demand fo Money and the Tem Stuctue of Inteest Rates in Ieland, LM KEARNEY Univesity of Loughboough, Loughboough Abstact: This pape investigates the extent to which the demand fo vaious measues of money in Ieland depends upon the tem stuctue of inteest ates. The yield to matuity cuve is fist estimated using efinements of the appoximation specification employed by Helle and Khan (1979). The estimated paametes ae then enteed as paametes into the money demand equations which ae estimated using autoegessive least squaes. Amongst othe findings is a consideably geate esponse of money demand to a unifom shift in the yield cuve than is obtained using conventional estimates which ae based on only a single inteest ate. I INTRODUCTION he extent to which the demands fo financial assets ae esponsive to changes in inteest ates constitutes a fundamental link in the monetay tansmission mechanism. The inteest elasticity of the demand fo money has been the focus of much attention in this egad. Empiical eseach has been vitually unanimous in finding a significant negative inteest ate elasticity in money demand equations. Until ecently, howeve, the existence of stong collineaity between inteest ates has hampeed eseach into the elationship between asset demands and the tem stuctue of inteest ates. This pape investigates the elationship between the demand fo money and the tem stuctue of inteest ates in Ieland ove the 1970s. The method employed is to estimate the entie yield to matuity cuve using vaious appoximation specifications and to ente the paametes as aguments into the demand equations. This pocedue follows fom the methods devised by Helle and Khan (1979) and efined by Bilson and Hale (1980), Allen,

2 Hatfield and Williams (1981) and Allen and Hafe (1983). Equations ae estimated fo the components of both naow and boad definitions of money and conclusions eached that the tem stuctue of inteest ates does indeed influence the vaious monetay measues. An outline of the pape is as follows. Section II discusses some theoetical issues aised by ou inclusion of the entie yield cuve into the estimating equations. Section III summaises the empiical esults fom estimating standad specifications of the vaious monetay aggegates. Estimates ae then pesented which include the tem stuctue of inteest ates and the esults ae compaed and contasted with the standad equations. The final section summaises the agument and daws conclusions. II THE THEORY Monetay economists have long taken the view that moe than one ate of inteest might easonably be expected to influence the demand fo money. Multicollineaity between diffeent inteest ates, howeve, has hampeed eseach into the issue. This is not to say that empiical wok on the demand fo money equation has not had a multi-inteest ate aspect fo some time. It began by compaing two inteest ates, one long and one shot ate. The esults often vaied accoding to the definition of money being employed and the county fo which the equation was being estimated. Shot ates tended to be moe significant deteminants of naow athe than boad money holdings while long ates tended to pefom bette on Bitish than on Ameican data (see Laidle (1977)). Moe ecently, Helle and Khan (1979) developed an efficient way to epesent the entie stuctue of inteest ates in tems of a few paametes. Thei appoach is to estimate the entie yield to matuity cuve using a quadatic appoximation fo each time peiod, and to ente the paametes as aguments into the money demand equation. This pocedue has the advantage of epesenting the entie yield cuve in tems of a few paametes which ae less collinea than the inteest ates themselves. In addition, the appoach allows inspection of how changes in the intecept, slope and cuvatue of the yield to matuity cuve influence the demand fo money. Thee is a cost involved in pusuing this appoach, namely, that the tem stuctue appoximation equation has an eo tem so that the fitted values may not povide a good desciption of the actual data. We shall see below, that in tems of the data employed in this study, the cost is indeed low elative to the insights which ae obtainable. A geneal desciption of the tem stuctue appoximations employed in this study 1 is as follows. 1. Honohan (1981) descibes the estimation of the yield to matuity cuve fo Ieland.

3 In Rm t = aj + a 2 In m t + a g In m 2 + a 4 In m* + Vm ( (1) whee In stands fo natual logs and Rm ( = nominal inteest ate of matuity m at time t, a ; = paametes (i = ) Vm ( = independently distibuted andom vaiable with zeo mean and a vaiance which is constant fo all values of the matuity vaiable. A numbe of vaiations on this logged cubic specification have been used in ode to intoduce the tem stuctue of inteest ates into the money demand function. Bilson and Hale (1980) set a 4 = 0 in poposing a logged quadatic appoximation and Allen and Hafe (1983) poposed an unlogged vesion of Equation (1) in ode to captue humps in the yield cuve. In the next section we povide evidence on the elationship between the demand fo money function in Ieland and the tem stuctue of inteest ates. We employ both quadatic and cubic estimates of the yield cuve and expeiment with specifications in levels as well as in logaithms. We also conside both naow and boad definitions of money and in the case of the latte we disaggegate into chequeable and time deposits in ode to uncove influences which ae not obvious in boad money demand functions. Ill EMPIRICAL RESULTS Conventional Estimates Standad specifications of the demand fo money function popose following elationship: the lnm d = 0 o +0j lny t +0 2 t +u t (2) whee m d = the desied level of eal balances, y = eal income, = nominal inteest ate, u t = a distubance tem. If actual eal balances patially adjust towads thei desied level 2 Aln m t = X(ln m d - In m M ) (3) whee X is the coefficient of adjustment and 0 < X < 1. Substituting Equation (2) into (3) yields the standad estimating equation. In m t = T 0 + Ji In y t t In m M + y 4 U { (4) 2. Milboune (1983) examines the adjustment of nominal money balances.

4 Pevious eseach on estimating money demand functions fo Ieland has examined a vaiety of altenative specifications of this equation and it is not ou pupose to duplicate these esults. 3 Ou concen hee is to captue the effects of diffeent oppotunity cost vaiables in the demand fo money equation. The coelation between seven domestic inteest ates of vaious matuities is pesented in Table 1 and highlights the poblems of multicollineaity which confont the eseache who attempts to include a numbe of oppotunity cost vaiables in the estimating equation. The table clealy shows a substantial degee of coelation among the vaious ates, deceasing slightly as the diffeence in the tem to matuity ises. It is inteesting to compae the esults of employing altenatively shot and long ates of inteest as the oppotunity cost vaiable in conventional specifications of the demand fo money function. This execise was conducted by estimating Equation (4) fo the vaious monetay aggegates (i.e., cuency, cuent accounts at banks, Ml, deposit accounts and M3 using the seven inteest ates mentioned above. All equations wee estimated on quately non-adjusted data ove the peiod 1971(2)-1981(4) with dummy vaiables (SD) included to captue the influence of seasonal tends. A full desciption of the data employed is povided in the Appendix. Table 2 povides a epesentative summay of the esults of this execise using auto- Table 1: Coelation matix fo seven ates of inteest of diffeent matuities, Ieland: l s = Cental Bank Ovenight Rate g = 3 Month Excheque Bills j = 1 Yea Rate 4 = 3 Yea Rate g = 5 Yea Rate g = 8 Yea Rate 1 7 = 15 Yea Rate Refeences ae: Bowne and O'Connell (1979), Bowne (1984), Caey (1981), and den Butte and Fase(1981).

5 egessive least squaes (ARI) to estimate the demand fo Ml balances. It shows the estimated values of the elasticities and thei associated t-atios along with the adjusted coefficients of detemination (R 2 ), the Dubin-Watson test statistic (DW), Dubin's h-statistic (DH) and the computed value of ho with its associated t-atio. Both the income and inteest ate coefficients ae coectly signed and statistically significant at the 5 pe cent level in all the equations. An inteesting patten emeges in so fa as both shot-un elasticities tend to ise with the tem to matuity of the asset whose yield is included in the equation. Also, adjustment speeds become geate as the longe ates ae included. As a esult of this, the long-un income elasticities tend to become smalle (i.e., close to one) as the tem to matuity of the competing asset ises. No clea patten of this kind emeges fo the long-un inteest ate elasticities. The oveall explanatoy powe of the equations as measued by the adjusted R 2 s tend to impove as longe ates ae employed. Simila esults wee obtained fo the naowe definitions of money measued by cuency and cuent accounts. Wide definitions such as deposit accounts and M3 balances diffeed in so fa as they wee not vey sensitive to inteest ate changes and the income elasticities did not vay with the inteest ate matuity. The fome esult concus with that obtained by othe eseaches (e.g., Bowne and O'Connell (1979) and Caey (1981)). Estimation with the Tem Stuctue The estimating fom of the money demand equation incopoating the logged quadatic appoximation of the tem stuctue is given below. A log specification of the yield cuve, as in Equation (1) above, was pefeed on empiical gounds. Use of the cubic yield cuve appoximation added little to the fit of the demand fo money equation. Hence, only esults fo the quadatic specification ae epoted hee. lnm t =7 Q +7j lny t a lt +? S tt2 t (5) o S t +y 5 lnm,.! +y 6 U t The esults of estimating Equation (5) fo the vaious monetay aggegates ae pesented in Table 3. The equations pefom as well as the conventional estimates in tems of oveall goodness of fit. Adjustment speeds ae slightly faste than the aveage obtained fom the conventional specifications. The shot un and long un income elasticities ae also compaable to those obtained using the standad specifications. This can be seen by compaing the esults fo Ml balances with those epoted in Table 2. The thee yield cuve coefficients ae all coectly signed and statistically significant at the 5 pe cent level in the equations fo cuency, cuent

6 (N ct to it CM ST»-1 i i CM CM CM to co en o oo 1 1 CM CM CM CM en CM <o <o CM 1 1 l" CM H o q IN CM CM CM CM CM CM 1 4 _, CM CM»-1 en en en en en s ^ ^ co en to it OO to o * o o q q q q l' i" M, i i' l" i i 1' "~' ~ ' ' ~ ' ' m.... m en CM CM o CM CM * CM CM oo" q co O O q q o CM O i" l' i i i" m CM ^ ^ _^ * o o US on IO to <o co <o o q O q q q CM *. CM i-j q CM q 1-( O q i' l" oo o <o CM CM o en ST -1 1 ( m o lo CM in * ID»n m" lo * i 1 i-< i i i 1 O o en i-l oo o i-i en O CM o. o o O q CM * o o en 5*^. en.. to *., to n ^ co oen men oo ^ cn even Sjco CM oo CM q CM oo oo CM -co in n s ^ t-. CN OO Ti- T)«' TJ- 2; - en.. ~.. to to.. n ^, CM ^ oen ~ cn H m ~- cno f~ in CM cn ~- i i CMi < CM i-i ooo i' ^ i * i-h i i * i ^ o

7 a: CN I as m q CN on BO q CN l" * CN O to CN co l" o lo * CN q q q -! 1 CN 1 * CN 1 I q q q co CM co cn 0 o ST o o~ ST CN ST o o 0 m O i OO 1 CN 8 t 1 CN CN 01 CN to CN CN CN O O q q O f CN l" d 1' 1 1 1" CN 3 CN m 0 CD m CN <o * o q -- q * q q 1* i < 1' CN 1 to co o >> to oo S" o" CN 1^ * co cn d 1 1 * CN 1 ^ <t< co,. >o O * 0 CD q -H" C\f ii CN d 1 if) >o m ST U0 CN o q q O q 1 1 CN 1 < d q co 1' * CN CN.. O CN lo lo o -< o ^ co to I o CN m CN If) to ^ IT) 0O If! to ^ ~ O CN CN CN.. o ~ co -- to o O CN kf) to CN to to, ^, to lo 10 ^ CN 1 ( q CN 1" d < 0. w Q

8 accounts and Ml balances. The coefficient on the intecept paamete, etj, indicates that a unifom upwad shift of the entie tem stuctue by 1 pe cent will esult in a decease of cuent accounts and Ml balances by.287 and.203 pe cent, espectively. These effects ae consideably lage than the elasticities obtained by using any of the individual inteest ates as shown in Table 2. An incease in the slope of the tem stuctue, with an unchanged intecept and cuvatue, will educe the demand fo these balances. This is consistent with the expectation that an incease in long ates of inteest with fixed shot ates will educe the demand fo money. The equation fo deposit accounts is less well detemined with espect to the yield cuve coefficients. This finding is consistent with the esults of employing standad specifications and explains the extent to which the boad money demand equation is less esponsive to the yield cuve coefficients. Indeed the small magnitude of the intecept tem in these equations is consistent with the view that boad money holdings ae best seen as detemined by inteest ate diffeentials athe than levels because, unlike the naowe aggegates, the own ate is cetainly not equal to zeo. IV SUMMARY AND NCLUSIONS This pape has examined the extent to which the Helle and Khan (1979) pocedue fo including the entie yield cuve in estimated money demand equations can be successfully employed on data dawn fom the Iish economy. The answe is in the affimative. Using this methodology, we find a consideably geate esponse of the demand fo money to a unifom upwad shift in the yield cuve than is obtained fom conventional estimates which use only a single ate of inteest. We ae also able to obtain an indication of the diffeential esponse of the demand fo money to shot and long ates of inteest. Finally, this study confims that naow measues of money ae moe esponsive to changes in the stuctue of inteest ates than ae thei boade countepats. REFERENCES ALLEN, STUART, and R. HAFFER, "Money Demand and the Tem Stuctue of Inteest Rates: Some Consistent Estimates", Jounal of Monetay Economics, Vol. 10, pp ALLEN, STUART, B. HATFIELD, and D.A. WILLIAMS, "A Cubic Estimate of the Tem Stuctue of Inteest Rates fo a Money Demand Function", Jounal of Macoeconomics, Vol. 3, No. 1, pp BILSON, JOHN F., and ROBERT S. HALE, Futhe Evidence on the Tem Stuctue of Inteest Rates and Money Demand, Repot No. 81, Cente fo Mathematical Studies in Business and Economics, Univesity of Chicago.

9 BROWNE, FRANCIS X., "The Shot-Run Demand fo Money with Exogeneous Money Ceation in an SOE", Daft Technical Pape, Reseach Depatment, Cental Bank of Ieland, June. BROWNE, FRANCIS X., and THOMAS O'NNELL, "The Demand fo Money Function in Ieland: Estimation and Stability", The Economic and Social Review, Vol. 9, No. 3, pp CAREY, PETER, "The Demand fo Money: Revised Estimates and Foecasts fo 1981", Banking Depatment, Cental Bank of Ieland, Apil. DEN BUTTER, F.A.G., and M.M.G. FASE, "The Demand fo Money in E.E.C. Counties", Jounal of Monetay Economics, Vol. 8, No. 2, pp FRIEDMAN, MILTON, "Time Pespective in Demand fo Money", Scandinavian Jounal of Economics, Vol. 79, No. 4, pp HELLER, H. ROBERT and MOSHIN KHAN, "The Demand fo Money and the Tem Stuctue of Inteest Rates", Jounal of Political Economy, Vol. 87, pp HONOHAN, PATRICK, "The Yield Cuve", Quately Bulletin, Cental Bank of Ieland, Sping, pp LAIDLER, DAVID E.W., The Demand fo Money: Theoies and Evidence, Scanton, Pa.: Intenational Textbooks. MILBOURNE, ROSS, "Pice Expectations and the Demand fo Money: Resolution of a Paadox", Review of Economics and Statistics, Vol. 65, pp O'REILLY, LIAM, AND DAVID LYNCH, "An Update of Quately National Accounts to 1980", Technical Pape 3/RT/83, Reseach Depatment, Cental Bank of Ieland. DATA APPENDIX Non-adjusted quately data fom 1971(1)-1981(4) is employed in the empiical tests epoted in the pape. Monetay Aggegates These wee obtained fom the Banking Depatment of the Cental and include the following: Bank (i) (ii) (iii) (iv) Cuency outstanding Cuent accounts Deposit accounts at Associated Banks Deposit accounts at non-associated Banks Naow money Ml is the sum of (i)-(ii) and boad money M3 includes (iii)- (iv) in addition. Inteest Rates All ates ae quately aveages and wee obtained fom the Cental Bank's Quately Bulletin. Rates ae the following.

10 Tj = Cental Bank ovenight ate 2 = 3 month Excheque Bills s = 1 yea ate 4 = 3 yea ate & = 5 yea ate g = 8 yea ate? = 15 yea ate Income and Pices These wee obtained fom the Reseach Depatment of the Cental Bank as updates on O'Reilly and Lynch (1983). Nominal GNP was deflated by the Consume Pice Index to obtain the seies fo eal income which is used in the estimated equations.