A divisia system approach to modelling monetary aggregates

Economics Letters North-Holland

A DIVISIA SYSTEM APPROACH Tran

365

17 (1985) 365-368

TO MODELLING

MONETARY

AGGREGATES

VAN HOA

Unruersity of Melbourne. Received

Parkuille,

Vict. 3052. Australra

3 July 1984

A complete system of Divisia partial adjustment asset equations based on the augmented-price expectations Baumol-Tobin inventory and transactions postulates is used to study the dynamic behaviour of monetary aggregates and their components in Australia during 1969.111 to 1983,IV. The system provides a new and useful approach to modelling demand-for-money functions for effective monetary policy controls and targetting.

1. Introduction Although crucial for controlling monetary aggregates in ISLM analysis and for predicting the induced flows or the exchange rate in the monetary approach to balance-of-payments studies, the behaviour of money supply and particularly demand has not been very successfully modelled in empirical causal or statistical investigations. The problem arises to a large extent from the fact that most monetary models are single-equation demand-for-money specifications [see for example, Van Hoa (1982)] and that the relevant methodologies used involve essentially simple-sum aggregation in which perfect substitutability between component assets is assumed. Attempts at alleviating some of these difficulties include the work by Barnett (1983) in which a Divisia monetary index based on a complete system of three goods in the Laurent series approximation form with the user-costs of the component assets as prices was computed for the U.S.A. for the period 1961.1 to 198O.IV. This index appears to be superior to the simple-sum index but the local conditions for monotonicity and concavity restrictions of the underlying utility function and its exact aggregation properties are yet unknown. Another recent work involves the time-series approach to monetary aggregates [see Pierce (1983)]. As is well-known, the time-series approach is statistical and not model-based and, in the particular case of the X-11 and other similar empirically based adjustment procedures, the same seasonal adjustment filter is applied to series with possibly differing characteristics. In this paper, we provide an alternative approach to modelling the dynamic behaviour of the monetary aggregate M3 or its subsets M2 and A42 by proposing a complete system of differential component demand-for-money functions in which M3, M2 or MI are all defined as ultimate Divisia monetary indexes. Each component demand-for-money function in this case is of partial adjustment form and satisfies the traditional economic postulates of the ‘inventory’ and ‘transactions’ approaches suggested by Baumol (1952) and Tobin (1956) and augmented by anticipated inflation. Within the framework of this multi-equation monetary model, estimates of the monetary aggregates are full-information maximum-likelihood (FIML) system estimates with testable hypotheses concerning the adjustment process and the elasticities of macro policy variables. The model is then fitted to Australian time-series data for the period 1969.111 to 1983.IV to study the short-run dynamic behaviour of M3 and its component monetary assets. 0165-1765/85/$3.30

0 1985. Elsevier Science Publishers

B.V. (North-Holland)

2. A monetary

model in differential

form

We consider a model of m component assets M, (i = 1.. , m) in which, for convenience, each M, is uni-directionally related to the exogenous macro-economic vaiables, say, R (90-day commercial bill rate), Y (real GDP) and P (expected inflation rate) by an arbitrary but continuously differentiable function. ’ Then, in terms or the rates of change d M,. d R. etc., we have [see Allen (1960)] dM,/M,

= E,,dR/R

+ E,,dY/Y+

E,,dP/P.

i=l

. . . ..m.

(1)

in which E,,, E,,, E,,, are, for the ith component asset, elasticities of R, Y and P, respectively. For small changes however, the differentials can be approximated by log-changes [Theil (1980)]. Thus, at the data point t, (1) can be written as

(2) or, more compactly, dlogM,,=

E,,dlogR,

+ E,,dlogY,+

Above, the model consists the endogenous monetary

(3)

E,,,dlogP,.

of m structural or reactional functions for M, which are the components aggregate M. We therefore close the model by introducing the identity

dlogM, = $ U’;,dlogM,,, ,=I

of

(4)

where q, is the average monetary share of the i th component asset at t and t - 1. As is well-known, (4) is the aggregate Divisia monetary index in which differentials are approximated by finite log-changes. Recent applications of the Divisia index in system analysis in economics include the work by Theil (1980), Barnett (1983) and Van Hoa (1984). The linearized form (1) provides a convenient computable basis for a class of Johansen functions and is popular in applied general equilibrium analysis [see, for example, Dixon et al. (1982)]. With the addition of appropriate stochastic error terms, (3) and (4) constitute a complete model of monetary aggregates in differential or log-change form, with (m + 1) endogenous variables and, in the present study, three exogenous variables. Assuming a partial adjustment process, the model also includes m predetermined variables. Within this information set in which all stochastic variables and disturbances are assumed to be jointly and normally distributed, the model can be conveniently estimated by the FIML system estimation procedure to give asymptotically consistent and efficient estimates of the growth rates of the monetary aggregate M.

3. Some empirical

evidence

The model (2)-(4) in stochastic partial adjustment data for the period 1969.111 to 1983.IV and the FIML

form has been fitted to Australian quarterly results are given in table 1. In the model, the

’ The assumption of exogeneity for R, Y and P in demand-for-money functions is. although tenuous. widespread in economic literature. An attempt at establishing multi-directional causal relationships between M and R, Y and P using Australian data was reported by Van Hoa (1980).

monetary aggregate M is identified as M3 and its four component assets M, (i = 1,. . . (4) are (a) currency or public’s holdings of notes and coin (CUR), (b) current deposits with trading banks (C‘DP), (c) fixed deposits and certificates of deposits with trading banks (ODP), and (d) deposits with savings banks (SDP). As is well-known, using simple-sum aggregation, MI = CUR + CDP, M2 = CUR + CDP + ODP. and M3 = CUR + CDP + UDP + SDP. All data are quarterly volumes of money in unadjusted form and deflated by the consumer price index. The series R denotes 90-day bank-accepted/endorsed commercial bill buying rate, Y real GDP and P the anticipated inflation rate computed as P, = lOO( DEF,_, - DEF,_,)/DEF;_, in which DEF is the GDP implicit deflator [see Van Hoa (1982) for an earlier use of this measurement of anticipated inflation]. From table 1. uniform results in terms of the negative sign of the short-run elasticity estimates are obtained for commercial bill rates R on all four component assets. These estimates are statistically significant only for current deposits (CDP) and fixed deposits and certificates of deposits (ODP); the former component has an elasticity of -0.14 and the latter of -0.07. The effects of real GDP are, however, positive and significant for currency (CUR) and current deposits (CDP) having the short-run elasticity estimates of 0.19 and 0.25, respectively. The findings regarding the partial adjustment process appear to be rather mixed. Here, the adjustment period for current depostits (CDP) is about four quarters while an instantaneous adjustment is observed for ODP and SDP. In all four equations, no firm conclusion can be made about the effects of expected inflation on the demand for monetary assets, a result we found earlier in the Box-Cox transformation analysis of the aggregate demand-for-money for Australia [see Van Hoa (1982). The above findings indicate that, within the traditional framework of the demand-for-money postulates, barren money (CUR) and especially current deposits with trading banks (CDP) appear to be the only component assets significantly affected by commercial bill rates (R) and real GDP. These two component assets define, however, the monetary aggregate Ml. It is clear that, for effective monetary policy controls or targetting in the Australian case, the monetary aggregate the authorities should pay attention to is MI and not M2 or M3. In this context, our Divisia system approach is capable of providing, in addition to the superior differential monetary index in which the mean shares of the component assets play an important part [see Barnett (1983) for further details], statistical evidence to discriminate among u priori competing monetary aggregates for effective controls and targetting.

Table 1 A Divisia model of monetary aggregates. likelihood function = 534.77).”

Australia

1969.111 to 1983.1V: full information

estimates

DW

SSR

0.194 (6.47)

- 0.003 (0.31)

1.34

0.030

- 0.144 (2.21)

0.245 (2.20)

- 0.008 (0.20)

2.1-l

0.137

0.002 (0.01)

~ 0.74 (1.75)

~ 0.098 (0.86)

0.010 (0.23)

1.95

0.159

0.215 (1.11)

-0.016 (0.96)

- 0.040 (0.83)

0.002 (0.08)

2.00

0.021

Constant

Lagged dependent variable

dlogR

dlogCUR

0.011 (2.29)

- 0.306 (2.79)

- 0.020 (0.59)

dlogCDP

0.002 (0.24)

0.696 (3.45)

0.014 (1.62)

0.003 (1.07)

dlogSDP

likelihood

dlogP

Assets

dlogODP

maximum

A The complete model includes the dlogM3 identity son statistic; SSR: Sum of squared residuals.

(4). Estimated

dlogY

mean/standard

error in parentheses.

DW:

(log of

Durbin-Wat-

368

T. Van Hoa / Divisia system, modelling monetrrry aggregates

References Allen, R.G.D., 1960, Mathematical analysis for economists (MacMillan, London). Barnett, W.A., 1983, New indices of money supply and the flexible Laurent demand system, Journal of Business and Economic Statistics 1, 7-23. Baumol, W.J.. 1952, The transactions demand for cash: An inventory theoretic approach. Quarterly Journal of Economics 66. 545-556. Dixon, P.B., B.R. Parmenter, J. Sutton and D.P. Vincent. 1982, ORANI: A multisectoral model of the Australian economy (North-Holland, Amsterdam). Pierce, D.A., 1983, Seasonal adjustment of the monetary aggregates: Summary of the Federal Reserves Committee report. Journal of Business and Economic Statistics 1, 37-42. Theil. H., 1980, The system-wide approach to microeconomics (University of Chicago Press, Chicago, IL). Tobin, J., 1956, The interest-elasticity of transactions demand for cash, Review of Economics and Statistics 38, 241-247. Van Hoa, Tran, 1980. Traditional demand for money functions in Australia: Stability and causality, paper presented at the 9th Conference of Economists, 25-29 Aug. (University of Queensland, Brisbane). Van Hoa, Tran, 1982, Extended power modules transformations of the demand-for-money function for West Germany and Australia: An international comparison, Review of World Economics 118, 563-570. Van Hoa, Tran, 1984, Distributional effects of true economic indexes Economics Letters 16, 185-189.