RDP 8703: Money Demand, Own Interest Rates and Deregulation Appendix D: Calculation of the own rate on M3 and BM

An assumption frequently made in studies of the demand for money is that the pecuniary (and/or non-pecuniary) return to holding money assets is either zero or constant. The motivation for calculating own rates for M3 and BM is that this assumption has become less and less tenable for the broader money aggregates, especially during the relaxation of monetary controls in Australia over the last decade.

Complete details of the calculation procedures for R_M3 and R_BM are given in notes by J. Lynne Evans (1986) “A Series for the Own Rate of Money: M3”, and S. Thorp (1986) “The Own Rate of Return on M3 and Broad Money”.

The own rates on M3 and BM used in estimations reported in this paper are simply weighted averages of pecuniary returns to the asset components of M3 and BM. Data on interest rates and detail on different deposit types needed for the calculations were not complete, so simplifying assumptions were made. The final products are thus best regarded as “representative” of the true own rates.

Both R_M3 and R_BM were constructed as monthly rates using data taken mostly from the Reserve Bank Statistical Bulletins. Table D.1 shows the components of M3 and the Statistical Bulletin tables from which data are drawn for the calculation of R_M3. The pattern of calculation is identical to the method of Evans (1986).

(a) Zero interest components

Zero interest rates were attributed to all trading bank current deposits, all cheque accounts with savings banks, “other” accounts with savings banks and fixed deposits with savings banks, in the absence of more complete information. This assumption probably leads to some systematic underprediction of the M3 own rate in recent years.

(b) Certificates of deposit

A weighted average of interest rates on certificates of deposit is available from Table J3 of the RBA Bulletin. The rate is weighted by the share of certificates of deposit in total M3.

(c) Trading bank fixed deposits

A breakdown of fixed deposits into categories greater than and less than $50,000 was supplied by internal RBA sources. The midpoint of the range of interest rates available for “small” fixed deposits was used as a representative rate for those categories. The weighted average rate for deposits over $50,000 (Table J3) was multiplied by the appropriate share and employed in calculation.

(d) Savings bank deposits

On the basis of two annual observations, Evans split total savings bank Passbook accounts into those “less than” and those “greater than” $4,000 in the ratio of 45:55. The interest rates on large and small Passbook deposits (J3) were weighted in line with that ratio.

The necessary breakdown of savings bank deposits into the categories listed in Table D.1 was supplied by internal sources. “Statement” and “investment” account interest rates were thus weighted by their share in total M3. As noted above, the fixed deposits, interest bearing and non-interest bearing cheque accounts and “other” categories are assumed to earn zero interest.

Having weighted each interest rate by the share of each deposit type in total M3, the rates were summed to form the R_M3 series. The monthly series from – January 1974 to June 1986 is set out in full in Thorp (1986).

The M3 own rate was employed as the representative rate for the M3 component of Broad Money. An own rate similar to R_M3 was also constructed for the non-bank financial institution (NBFI) component of BM, then each own rate (R_M3 and R_NBFI) was weighted according to the shares of M3 and NBFI's in Broad Money. The sum of the weighted R_M3 and R_NBFI then gave the BM own rate.

The problem of data availability was compounded for the construction of R_NBFI. The NBFI component of Broad Money includes borrowings of permanent building societies, credit co-operatives, finance companies, authorised money market dealers, pastoral finance companies, money market corporations, general financiers and cash management trusts. Of these categories, interest rates were available only for building societies, finance companies, money market corporations and cash management trusts. Institutions for which rates were not available were given zero weight in R_NBFI – implicitly assuming that the final weighted average rate is representative of the true return to holding assets of the excluded institutions as well as the included ones. Despite the exclusions, about 85 per cent of the total NBFI borrowings in Broad Money were given positive weighting in R_NBFI.

Volumes of borrowings by NBFI's were netted of cash, bank deposits and balances with other NBFI's (strictly, Financial Corporations Act corporations) to avoid double-counting. The details of these calculations are set out in Thorp (1986). Details on the selection of interest rates for each institution are set out below.

(e) Money market corporations – interest rates

A complete range of 24-hour call rates was supplied by internal sources and used in calculations. The 11.00 a.m. call rate was initially preferred as a representative rate, but was not available as far back as August 1976, where the broad money series begins. (Note that this series is different from the 24-hour call rate reported in the RBA Bulletin.)

(f) Finance companies

The mid point of the two year and three year debenture rates (from RBA Bulletin table J4) was selected as representative of finance company borrowing rates. The Bulletin series was unavailable prior to April 1980, so rates were collected from the Stock Exchange Fixed Interest Offerings for the period August 1976 – April 1980. (See Thorp (1986) for details.)

(g) Building Societies

Since no breakdown of Building Society deposits into call and term components is at present available, the midpoint of the range of rates on call deposits and 12-month fixed-term shares was selected as the single representative rate on Building Society borrowings. In this case, rates from the RBA Bulletin were supplemented with rates supplied in December 1983 Economic Digest of the Permanent Building Societies Association (NSW).

(h) Cash Management Trusts

The weighted average net yield to unitholders of cash management trusts (Bulletin Table J4) was selected for calculation.

Once interest rate and borrowings data had been collected the process of calculating the interest rate was simply a matter of weighting the interest rates and summing them to produce a single series.

As noted above, all components of broad money for which interest rate series were unavailable were given a zero weighting, so the weighting for the building society rate, for example was:

where

BS is net borrowings of building societies

FC is net borrowings of finance companies

MMC is net borrowings of money market corporations

CMT is net borrowings of cash management trusts

WBS is weight given to the building society interest rate in R_NBFI

Similar weights were constructed for the other components, multiplied with the appropriate interest rate, and the weighted rates were summed to a single R_NBFI. R_M3 and R_NBFI were then weighted and summed to form R_BM.

The monthly BM series is presented in full in Thorp (1986).