19

I

Piyu Ytte and Robert Fhsri

P/yu Yue is a research associate scholar at the /C2 Institute,University of Texas at Austin. Robert FIur/ is an economist atthe Swiss National Bank. This article was wr/tten while bothauthors were visit/np scholars at the Federal Reserve Bank ofSt. Louis. Lynn Dietrich provided research assistance.

Divisia Monetary Services In-dexes for Switzerland: AreThey Useful for MonetaryTargeting?

SOME BACKGROUND ON THESWISS MONETARY BASE

Prior to 1986, the relationship between themonetary base and economic activity in Switzer-land was quite close; this link, however, hasbroken down since then. The sudden change

Ia

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I ROM 1973 ‘TO 1989, tNFLATION in Switzer-land was roughly one-half that in the UnitedStates. For example, consumer prices in Switzer-

I land rose 3.5 percent per year during this16-year period compared with the 6.6 percentaverage annual rise in U.S. consumer prices.Similarly, Swiss wholesale prices rose at an an-

I nual rate of 2 percent during this period in con-trast to the nearly 6 percent annual averageincrease in the U.S. producer price index. In-

I deed, the Swiss inflation experience, along withthat of West Germany, is often cited as an ex-cellent example of the gains that accrue to anation whose central bank conducts monetary

I I policy by announcing—and achieving—a targetfor the growth of a monetary aggregate.

The Swiss central bank has used monetary

I L base growth rate targets since 1980. Becausethe historical relationships between monetarybase growth and economic activity have changed

I F markedly since the end of the 1980s, the Swisshave begun to reconsider the use of annualmonetary aggregate targets, and are considering

I I the potential usefulness of broader monetaryaggregates as indicators of monetary policy.

This paper develops two alternative broadermonetary aggregate measures, Divisia Ml and

M2, for Switzerland and compares their poten-tial usefulness as monetary indicators with theSwiss Ml and M2 aggregates as usually defined.First, however, we show why questions havebeen raised about the continued usefulness ofthe annual monetary base growth rate target inSwitzerland. We then discuss the methodologyunderlying the Divisia approach to constructingmonetary aggregates and use this methodologyto derive Swiss Divisia Ml and M2 measures.Next, we examine the relationship betweenSwiss inflation and the growth rates of SwissMl and M2 and the Swiss Divisia Ml and M2aggregates to determine their relative usefulnessas monetary policy indicators. Finally, we exa-mine the relationships between these variousmonetat’v aggregates and the monetary base toassess the extent to which the Swiss centralbank could control their growth.

SEPTEMBER/OCTOBER 1991

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Figure 1Inflation and Swiss Monetary Base GrowthPercenta

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can he illustrated, in part, by looking at therelationship between inflation and the growthrate of the monetary base as depicted in fig-ure 1. Until 1986, Swiss inflation movementslagged about three years behind correspondingvariations in the base money growth rate. Since1986, however, this pattern no longer holds. Forexample, the sharp drop in Swiss inflation in1986 was attributable to substantial reductionsin the prices of imported goods. Consequently,it appears that monetary base growth neithercontributed to this decline nor provided anywarning that it would occur; indeed, the growthof the Swiss monetary base was virtually cons-tant from 1984-1987.

Similarly, movement in the Swiss monetarybase from 1987-1989 (in particular, the sharpdrop in 1988) yielded neither warning nor ex-planation of the sharp rise in Swiss inflation in1989. This change followed two significant insti-

tutional innovations in the Swiss banking sys-tem. First, a new electronic interhank paymentsystem (Swiss interhank Clearing System, SIC)was introduced in the summer of 1987. Then,on January 1, 1988, reduced reserve require-ments on Swiss bank deposits went into effect.In response to these changes Swiss bankshave sharply reduced their reserve balances atthe Swiss National Bank (SNB). Swiss bankreserves dropped from more than SF8 billion(about $5.5 billion) at the end of 1987 to SF3 bil-lion (about $2.1 billion) by the end of 1989.

As a result of changes in the relationship be-tween the monetary base and inflation, the con-tinued usefulness of the monetary base as amonetary- policy indicator has been questioned.One suggestion is to rely more on broader mone-tary aggregates as monetary policy indicators.

1976 77 78 79 80 81 82 83 84 85 86 87 88 1989

FEDERAL RESERVE BANK OF ST. WUIS

I 21

MONETARY AGGREGATION

Generally, central banks worldwide use essen-tially identical procedures to construct their na-tions’ monetary aggregates. They first define thespecific aggregate—that is, they determine whichfinancial components it will include—and thenthey simply ‘add” its selected components to-gether. Not too surprisingly, these monetary ag-gregates are called simple-sum” aggregates.

Simple-sum aggregation has been criticized forfailing to distinguish between the differing de-grees of monetary (transaction) services andstore-of-value services provided by the com-ponents in the monetary aggregate. Presumably,only the former (that is, monetary or transac-tion) services should be included when a mone-tary aggregate is considered. Friedman andSchwartz (1970) have described this problem:

This [summation] procedure is a very special caseof the more general approach discussed earlier. Inbrief, the general approach consists of regardingeach asset as a joint product having differentdegrees of “moneyness,” and defining the quantityof money as the weighted sum of the aggregatevalue of all assets, the weights for individual assetsvarying from zero to unity with a weight of unityassigned to that asset or assets regarded as havingthe largest quantity of “moneyness’ per dollar ofaggregate value. The procedure we have followedimplies that all weights are either zero or unity.‘the more general approach has been suggestedfrequently but experimented with only occasional-ly. We conjecture that this approach deserves andwill get much more attention than it has so farreceived. (pp. 151-52)

As Friedman and Schwartz surmised, economicaggregation theory and statistical index numbertheory have been used to provide both theoreti-cal and empirical solutions to the problem ofmonetary aggregation.’ This research has led tothe development of alternative monetary aggre-gates, in particular, the Divisia monetary servicemeasure.2

‘See Barnett (1980).2t.ise of Divisia monetary aggregates appears in Barnettand Spindt (1982), Donovan (1978), Farr and Johnson(1985), Belongia and Chalfant (1989), among others.

of items. Well-known examples of index numbersare the industrial production index, the consum-er price index and the producer price index.These index numbers depend upon both theprices and quantities of items included in the in-dex because the values of commodities involvedare determined by their physical quantities andcorresponding prices.

Because quantities of financial assets aremeasured in terms of “dollars,” simply addingthe balances of various monetary componentswould appear to be a natural approach to mea-suring monetary aggregates. Consequently, it isnot surprising that simple-sum monetary aggre-gates have been used extensively throughoutthe world. However, economic theory suggeststhat various monetary aggregate componentsdiffer in terms of their “liquidity” and, thus,may have substantially different effects on eco-nomic activity. If this is so, the simple-sumprocedure may actually be inappropriate formeasuring “monetary service flows” in the na-tion. Instead, an alternative approach that in-volves calculation of Divisia indices may providesuperior alternatives to measuring monetary ag-gregates when compared with the traditionalsimple-sum monetary measures.

Theoretically, the Divisia index number isderived from the economic aggregation theoryand first-order conditions for utility optimiza-tion. An expanded discussion of the Divisia ap-proach appears in appendix 1 of this paper. Em-pirically, the Divisia index number is estimatedfrom a nonlinear function of the quantities andthe corresponding prices of individual com-ponents that create the aggregate. Moreover, itsgrowth rate is a linear combination of thegrowth rates of its components, where theweights (or coefficients) on the components aretheir average expenditure shares. In comparison,the simple-sum index is the linear sum of thequantities of the components in which the weight(coefficient) given to each component is unityand their prices have no effect on the index.The growth rate of the simple-sum index is alsoa linear combination of the growth rates of its

IIIIIIIIII1III1I

The Divisia Index ~~Jumber

Index numbers are widely used to provide asingle broad measure for a disparate collection

a SEPTEMBER/OCTOBER 1991

22

components, where the coefficients are equal tothe quantity shares.~

Differences between the behavior of Divisiaand simple-sum aggregates stem from the dif-ferent weights assigned to the growth rates ofthe components, which measure their contribu-tions to the monetary aggregates. Coefficientscalled “shares” are expressed by the notations

St and S~,for various components used to deter-mine the Divisia and simple-sum indexes, re-spectively, in the discussion that follows.

In calculating the Divisia index, the share ofeach component is the ratio of the expenditureson the monetary service flows it provides to thetotal expenditure on monetary service from allcomponents in the aggregate; as such, itrepresents an “expenditure share.” In contrast,shares for components in the simple-sum indexare equal to the quantities of the balances heldin each component divided by the total balancesof all components in the aggregate. In general,these two types of shares yield different valuesand move diversely over time. For example, theexpenditure share of time deposits in Swiss M2in January 1980 was 0.0856; its quantity share,in contrast, was 0.3681. In January 1988, how-ever, the expenditure share of time deposits inSwiss M2 was 0.2823, while its quantity sharewas 0.4527.

For the components of simple-sum monetaryaggregates, the only data required to computetheir respective shares are quantities of thecomponents themselves. In contrast, for Divisiaaggregates, the prices of the components—which involve their interest rates—must alsobe obtained in order to compute their expen-diture shares.

The User Costs of the MonetaryAssets

As noted above, one major problem involvedin computing Divisia index numbers for mone-tary aggregates is in determining the relevantprices of the individual monetary assets that

make up the aggregate. In economic aggregationtheory, monetary assets are treated as commod-ities and their prices are defined similarly torental prices of durable goods. In this approach,it is assumed that people receive monetary ser-vices from holding money to finance their con-sumption. In doing so, they forego higher yieldstypically available on other financial assets.While monetary services are considered con-sumed during some given period, money stock(like any durable good) is not generally con-sumed during this period. Because monetaryservices are flow variables—not stock variables—they should be evaluated by their rental pricesor user costs. Therefore, Divisia index numberscan be used to measure the monetary serviceflows provided by various monetary assets inthe economy only if the user costs of theseassets can be correctly defined and accurate-ly measured.

The appropriate user costs of monetary assetsare based on microeconomic theory and arederived by examining the representative con-sumer’s optimal intertemporal consumption pat-tern and monetary asset portfolio allocation.~These user costs are measured as the oppor-tunity costs of foregone interest associated withholding funds in different types of monetaryassets. The opportunity cost is obtained by com-paring each asset’s rate of return to that on abenchmark asset with the highest rate of return.

Under the relevant consumer theory, the ben-chmark asset is assumed to provide no liquidityor other monetary services. Because it is heldonly for accumulating and transferring wealthacross time, its interest rate is the highest in theeconomy. Consumer theory, however, does notspecify other characteristics of the benchmarkasset that would enable researchers to identifythe actual benchmark asset to be used in em-pirical studies.

Barnett and Spindt (1982) have suggested that,while human capital might best fit the theoreti-cal concept of the benchmark asset, no satisfac-tory empirical data exists on its rate of return.In their research, they found that

where S~’= mc,,/SIM, is the quantity share of the i—thcomponent. This equation shows that the growth rate ofthe simple-sum aggregate is a linear combination of thegrowth rates of its components with weights equal to thefractions of the quantities of the components to the simple-sum aggregate.

4See Barnett (1978).

3By definition, the simple-sum aggregate is denoted suchthatSIM~,= I mc,dSlM,/SIM = I (mc~,/SlMj(dmc,,/mc~)where mc~is the quantity of the i—th component. Thus,approximatelyln(SIM,) — ln(Sl M, ,) = IS,(In(mc,) — ln(mc~,—

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FEDERAL RESERVE BANK OF ST. LOUIS a

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Figure 2Selected Swiss Interest RatesPercent12.5

10.0

7.5

5.0

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0.0

R,= max[r,,,, ri,, i=1,2, .. ni

provided the best available proyy for the theo-retical benchmark rate, where rd,, is Moody’sseries of seasoned Baa corporate bond rates andr1, is the own rate of return on each of the com-ponents of L (the broadest U.S. monetary ag-gregate defined by the Federal Reserve Board).~Although Donovan (1978) used the nominal rateof return on “bonds” to compute the rentalprice of interest-bearing money for Canada,

5In the user cost formula, R, is the maximum available yieldin the economy on any monetary asset which is a uniquelydefined theoretical maximum available yield. Empirically,the proxy variable is defined by a long-term bond yieldrelative to the rates of return on all monetary components.The need for a long-term bond yield in measuring short-term holding-period yields is demonstrated by R. Shiller(1979). The Baa bond rate is used as a representative

many researchers have used the approachadopted by Barnett and Spindt.

In this paper, we use the Barnett-Spindt ap-proach to generate a proxy for the Swiss ben-chmark asset rate (see appendix 2 for furtherdetails). The benchmark asset is either the long-term Swiss bond or short-term Euro-Swissdeposits, depending on which yield is higher.Thus, as shown in figure 2, the benchmarkasset was long-term Swiss bonds before 1980,Euro-Swiss deposits during 1980-1981 (due to an

yield for long-term debts of average risk. See Barnett andSpindt (1982).

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Percent12.5

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SEPTEMBER/OCTOBER 1991

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inverted term structure of Swiss interest ratesduring this period), long-term Swiss bonds from1982 to 1987 and Euro-Swiss deposits againin 1988-1989.~

‘rhe formula for the real user costs of mone-tary assets in period t is expressed as

u~= (R, — r1j/(1 +

where u~,is the user cost of the i-th monetaryasset, B, is the nominal interest rate on the ben-chmark asset and r~,is the nominal interest rateon the i-th monetary asset in period t.’

COMPARISON OF THE BEHAVIOROF SWISS DIVISIA AND SIMPL&SUM MONETARY AGGREGATES

Divisia monetary aggregates and simple-sumaggregates for Ml and M2 were calculated us-ing the Swiss monetary data described in appen-dix 2.8 The monthly simple-sum and Divisiamonetary aggregates are indexed to equal 100

in June 1975.°Figures 3 and 4 show the 12-month growth rates of these aggregates and theSwiss consumer price index from June 1976 toDecember 1989. while Divisia and simple-sumMl indices display virtually identical growthrates in this period, the growth rates of Divisiaand simple-sum M2 indices differ substantiallybeginning in 1979 (see figure 4).

From 1980-1981, for example, the growth ofsimple-sum M2 rose rapidly while that of DivisiaM2 slowed markedly. From 1982 to 1983, incontrast, the opposite pattern can be observedin their respective growth rates. In 1989, how-ever, the divergent pattern observed from 1980-81 occurs once again.

‘these widely divergent growth rates over ex-tended periods for the simple-sum and DivisiaMa suggest that discussions about the appropri-ateness of alternative procedures used to con-

struct monetary aggregates are not merely“academic.” In general, the direction and mag-nitude of growth in monetary aggregates arepresumed to provide useful information aboutthe current stance of monetary policy and thefuture course of economic conditions. Such ex-treme differences in the growth of alternativeM2 measures (as shown in figure 4), however,may produce considerable difficulty in assessingthat information.

Simple~Sum Vs. Divisia MonetaryAggregates: What’s the Difference?

In Switzerland, Ml consists of currency (C),demand deposits with banks (DB) and demanddeposits with the postal giro system (DP). Tocompare simple-sum and Divisia Ml, we calcu-lated the shares (S,, St) for each component ofMl. For most of the period, the respectiveshares of each monetary component for simple-sum and Divisia Ml moved so uniformly thattheir respective contributions to these aggregatesare roughly equal. Therefore, the growth insimple-sum and Divisia Ml was essentially thesame over the sample period (as already notedin figure 3).

In May 1989, however, the explicit interestrate on demand deposits with the postal girosystem (DP) rose from zero to two percent,reducing the user cost of DP, U, (as shown infigure 5). Since expenditure shares depend bothon quantities of the components and their usercosts, DP’s share (St) fell, reducing its weight incalculating Divisia Ml. ‘I’herefore, since the in-troduction of explicit interest payments on DPhad no effect on its weight in calculatingsimple-sum Ml, the values St and 5, divergedafter May 1989. Since the values of St and 5,are quite small, however, the difference be-tween the growth of simple-sum and Divisia Mlafter May 1989 is trivial.

Figure 5 shows that the user costs of thethree Divisia Ml components (U1-U3) follow

°Needlessto say, such shifts in the benchmark asset raisequestions about the validity of this approach and haveresulted in criticisms of Divisia indices by a number ofeconomists. We do not address this issue in this paper.

‘The nominal user costs of monetary assets usually are ex-pressed as

u, = ~‘ [ (R,—r,j(1 —r,)

Li + RA1 — r,)

where u1, is the user cost of the i — th monetary asset inperiod t, R, is the benchmark rate in period t, r,, is thenominal interest rate on the i—th monetary asset; t, is the

marginal income tax rate, and p is the true cost-of-livingindex used to deflate all nominal quantities to real quan-tities. Since taxes are not considered here, we use thesimplified formula.

8Weak separability conditions should be satisfied first tocalculate a meaningful aggregate. However, we did notconduct weak separability tests; instead, we used the ac-tual Swiss definitions of Ml and M2 and simply assumedthat they are admissible aggregates. For details, seeBelongia and Chalfant (1989).

9See appendix 2.

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FEDERAL RESERVE BANK OF St LOUIS

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Figure 3Inflation and Ml and Divisia Ml Growth

Percent

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Figure 4Inflation and M2 and Divisia M2 Growth

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Figure 5User Costs of Currency, DemandDeposits, PGS, and Time Deposits

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similar movements from 1975 through 1989,especially for the user costs of currency and de-mand deposits %vith banks. Thus, the re/ativeuser costs for the Divisia Ml components arenearly constant, making simple-sum Ml as use-ful as Divisia Ml over this period.bo

Although the expenditure and quantity shareswere similar for the Ml components, loweruser costs for time deposits in M2 explain thedivergent patterns shown earlier betweensimple-sum and Divisia M2. We can illustratethe importance of changes in the economic en-vironment on the weights used by examiningthe different behavior of Divisia and simple-sumM2 over these time periods: January 1979 -

December 1981; January 1982 . November 1987;December 1987 - December 1989. At the begin-ning of each period, there was a significantchange in Swiss monetary policy as measuredby sharp movements in the Swiss monetarybase. During these periods, changes in theeconomic environment were reflected in thelevels of short-term and long-term interest rates.As noted earlier (in figure 2), we used thethree-month Euro-Swiss Franc rate as the short-term rate, the Swiss government bond yield asthe long-term rate and the benchmark rate wasequal or close to the higher of these two ratesin any specific period. The growth rate of theSwiss monetary base over these periods waspreviously shown in figure 1.

‘°Thisresult is consistent with Hicks’ (Hicks, 1946) conclu-sion that “when the relative prices of a group of com-modities can be assumed to remain unchanged, they canbe treated as a single commodity.”

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FEDERAL RESERVE BANK OF St LOUIS

Figure 6Simple-Sum Share S4 and Divisia ShareSX of Time Deposits and User Cost U4

The First Period: January 1979 toDecember 1981

During this period, the SNB’s response to ris-ing Swiss inflation was sharply slower growthin the Swiss monetary base (resulting in lowerinflation in 1983-84). The abrupt rise in short-term Swiss interest rates produced an invertedyield curve for the next two years. The dramaticincrease in interest rates on time deposits re-duced their user costs (U4) to nearly zero as theirinterest rates approached the benchmark rate(see figures 2 and 5).

How did this interest rate movement affectthe monetary aggregates? Asset holders shiftedfrom lower yielding securities into time deposits(TD) causing the quantity of time deposits to in-crease dramatically and the quantity of demanddeposits with banks (DB) to decrease substantial-ly. Furthermore, asset holders also shifted fundsinto time deposits from other financial assets

not included in M2. This sharp rise in the quan-tity of time deposits is indicated by the surge intheir share in simple-sum Ma, S4 (shown infigure 6).

These changes produced quite different re-sults in the Divisia Ma measure, however. As in-terest rates on time deposits increased relativeto other interest rates, time deposits had loweropportunity costs and the monetary serviceflows from a given quantity of time depositsnaturally fell. Thus, despite the large increase intime deposits, the expenditure share of themonetary service flows from time deposits ac-tually declined during this period (see St infigure 6), as did the growth of Divisia M2 (seefigure 4).

The Second Period: January 1982to November 1987

During this period, the rate of inflation de-clined to lower levels and an extended period of

I 27

Percent

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expansionary growth in the monetary basebegan in January 1982. The term structure ofSwiss interest rates resumed its normal shape,with short-term interest rates below long-terminterest rates. Figure 5 shows that the usercosts of currency, demand deposits and demanddeposits with the giro system (U,, U,, I),) beganto fall in 1982. This reflects the fact that thedifference between their interest rates and thebenchmark rate was declining, while the usercost of time deposits (U4) increased as its in-terest rate fell relative to the benchmark rate.

As noted previously, the contributions of eachcomponent to the Divisia and simple-sum M2 ag-gregates are determined by their shares. We on-ly display the quantity and expenditure sharesfor time deposits (St and S4) in figure 6 for illus-tration. In 1982, the quantity share of time de-posits (S4) fell substantially, while its expenditureshare (S) rose sharply. This resulted in the pos-itive growth of Divisia M2 and negative growthof simple-sum M2 shown in figure 4 for 1982.Divergent movements in Divisia and simple-sumM2 occurred again in 1985 when the simple-sumMa growth was positive, while Divisia M2 growthwas almost zero. During the rest of this period,Divisia and simple-sum Ma moved similarly.

The Third Period: December 1987to December 1989

Swiss inflation rose from 2 percent throughoutmost of 1988 to nearly 5 percent by the end of1989. While both short- and long-term interestrates rose over this period, short-term ratesrose relative to long-term rates. Moreover, themajor institutional changes that took place re-duced demand for the monetary base)’ In re-sponse to these events, user costs of the firsttwo components (U, and U,) rose, while the usercost of time deposits (U,) fell (figure 5); thesemovements were similar to those in the firstperiod. However, as mentioned earlier, the usercost of demand deposits in the postal giro sys-tem (U,) fell in May 1989 when the interest ratejumped from zero to two percent. Consequent-ly, the Divisia and simple-sum M2 measuresmoved in opposite directions; simple-sum M2rose sharply, while Divisia M2 fell substantially(figure 4).

28

These three episodes suggest that, at least fora monetary aggregate as broad as Swiss M2, dif-ferent aggregation procedures produce mone-tary measures that can move quite differentlyand generate very distinct interpretations forthe stance of policy and the likely course ofeconomic conditions. Therefore, it is importantto know which of the potential broader mone-tary aggregate measures are more closely re-lated to key economic conditions.

COMPARISON OF THE PERFOR-

MANCE OF THE DIVISIA AND

SIMPLE- SUM AGGREGATES

To determine whether a monetary aggregatecan be used as a monetary policy target, twoquestions must be answered. First, is there asatisfactory relationship between the monetaryaggregate and some key economic variable, suchas inflation or nominal GDP or GNP? Second, isthe monetary aggregate strongly related tosomething that is directly controllable by themonetary authority? We examine both thesequestions in this section.

Inflation and Monetary Aggregates

To evaluate the first question, the relationshipbetween selected Swiss monetary aggregatesand inflation are compared. Specifically, quarterlySwiss inflation rates were regressed on distri-buted lags of selected Divisia and non-Divisiamonetary aggregates. Because the sample is rel-atively small and because we would like to in-clude enough lags to capture the significant ef-fect of money growth on inflation, the Polynom-ial Distributed Lag (PDL) estimation techniquewas used.12

Ideally, it is desirable to use one of the com-monly used lag-length selection methods forchoosing both the lag length and the degree ofthe polynominal. However, for two of the mone-tary aggregates, simple-sum Ml and Divisia Ml,the equations exhibited significant serial correla-tion. ‘This complicates the application of theseprocedures for these aggregates. Because of this,when these aggregates were used, several speci-fications of both lag length and polynominal

I

1’See the data description in appendix 2.‘2See Batten and Thornton (1983); Thornton and Batten

(1985).

FEDERAL RESERVE BANK OF St LOUIS

degree were estimated. Specifications with rela-tively long lags and relatively low polynominaldegrees produced the highest adjusted R-square.To keep the specifications comparable with thoseof simple-sum and Divisia M2 (which were cho-sen using the FPE criteria), results with laglengths of 18 and first-degree polynominals arepresented.”

To compare the long-run relationship of themonetary aggregates on inflation, we estimatedthe selected PDL models and computed the sumof coefficients of the distributed lags to test

“The identical polynominal degree was obtained for M2 andDivisia M2 by the Pagano-Hartley technique if a T-statisticof 2.0 is used for the critical value.

29

whether the sum of the lagged money growthcoefficients was significantly different fromzero. The estimated coefficients and respectivestatistics are shown in table 1.

The results in table 1 show that monetary ag-gregates influenced Swiss inflation over periodsof up to four or more years. With the exceptionof simple-sum M2, the monetary aggregateshave roughly similar values for the sum of thecoefficients on their distributed lags. The hypo-thesis that the sum of the lag coefficients is

I

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SEPTEMBER/OCTOBER 1991

Table 2F-Statistics for PDL Models’Growth Divisia M2 Divisia M2 and M2 and M2 and

rates and Ml Divisia Ml Ml Divisia Ml

F-StatH. 0.0605 0.0726 1 8349 1.8349H, 4.0645 3.9585 7.3115 71715

At the 5 percent significance level, the critical F value is 329

I

zero was rejected in all cases at the 5 percentsignificance level.

Because Ml and Divisia Ml are included intheir respective M2 counterparts, we investi-gated whether the non-Mi components of M2themselves added significant explanatory powerin the inflation equation. Thus, we defined theunrestricted model as regressions of inflation onboth the M2 and Ml PDLs; the restricted modelswere those with regressions of inflation on theM2 or Ml PDLs, respectively. The actual F-sta-tistics and their 5 percent significance levelcritical values are shown in table 2. H, is thehypothesis that inflation can be explained byDivisia M2 or M2 alone; H, is the hypothesisthat inflation can be explained by Ml aggregatesalone. These hypotheses are tested against thecorresponding unrestricted PDL model that in-flation is explained jointly by simple-sum andDivisia M2 PDL and the Ml aggregates PDL.”

The results in table 2 show that the data failedto reject H,, but did reject H,. This result sug-gests that the broader aggregates M2 andDivisia M2 better explain Swiss inflation thandoes Ml or Divisia Ml alone.

Controllability

As noted earlier, the practical use of a mone-tary aggregate as an intermediate target dependson its controllability. Even if some monetary ag-gregate shares a close relationship with inflation

or nominal GDP, it would be of little use as a

monetary target if its growth can not be con-trolled by monetary authorities. Since the cen-tral bank controls the monetary base, the rela-tionships between it and the broader Swiss mone-tary aggregates are examined.

Because the cross correlations between thegrowth rates of monetary aggregates and thegrowth rate of the monetary base show a long-lag pattern, we used the PDL models to estimatetheir relationships. Again, because of significantserial correlation, various specifications of laglength and polynominal degree were estimated.However, they share the same qualitative pro-perties. Table 3 displays the estimates of the10-lag and first-degree PDL models.

Results show that the growth rates of Ml,Divisia Ml and Divisia Ma are statistically signif-icant in relation to the growth rate of themonetary base. However, a significant long-termrelationship between the growth rate of themonetary base and simple-sum M2 is rejected atthe 5 percent level of significance.

In addition, the contemporaneous growth rateof the monetary base is positively and signifi-cantly correlated to the growth rates of bothMl aggregates and the Divisia M2 aggregate.For simple-sum M2 growth, however, the con-temporaneous and initial lagged growth rates ofthe monetary base have negative effects on its

14The hypothesis that the sum of the lag coefficients wasunity failed to be reiected in all cases except for simple-sum M2. Thus, except for simple-sum M2, the results didnot reject a one-to-one long-run relationship between thegrowth of the monetary aggregate and the rate of inflation.The results for the monetary base are similar to those ofthe Swiss monetary aggregates; its adjusted R2 (0.4880)was lower than those displayed in table 1. As shown in thefirst part of this paper, the relationship between inflation

and growth of the monetary base slipped considerably dur-ing 1986-89 (the end of the period examined); earlier,however, there had been a close link between Swiss infla-tion and long-run growth in the monetary base. Becausethe estimation period covers 1975-89, the recent“breakdown” in the monetary base growth-inflation rela-tionship does not dominate the results.

“For both M2 and Ml aggregates, we take the samenumber of lags, 18, in the PDL models.

FEDERAL RESERVE BANK OF St LOUISa

31

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broader monetary aggregates as monetarypolicy targets.

This paper examined the potential usefulnessof Swiss Ml and M2 monetary aggregates com-pared with Swiss Divisia Ml and M2 aggregatesderived from economic aggregation theory. Weshowed that Ml and Divisia Ml generally dis-played similar movements over time and wererelated similarly both to Swiss inflation (whichjustifies their potential usefulness as a target)and to the monetary base (which means thattheir growth was potentially controllable by theSwiss National Bank).

I

IIIIIIFFFIIIIIIIIIIIII

growth. Indeed, significant positive correlationshows up only three years after the changes inthe monetary base.

These results suggest that the Swiss NationalBank can significantly influence the growth ofMl, Divisia Ml and Divisia M2 through changesin the growth of the monetary base. Long-termsimple-sum M2 growth, however, does not ap-pear to be influenced by growth of the mone-tary base.

CONCLUSION

The relationship between the Swiss monetarybase and inflation in Switzerland has becomemore uncertain in r’ecent years. This phenome-non has generated considerable interest in using

M2 and Divisia M2, ho~vever,displayed sub-stantially different behavior over time and, atcertain key times, yielded substantially differentsignals about the stance of monetary policy.

aSEPTEMBER/OCTOBER 1991

32

More importantly, M2 growth was statisticallyunrelated to the growth of the monetary base.

The results suggest that Mi, Divisia Mi andDivisia M2 would be suitable for further studyif the Swiss National Bank is interested in thepossibility of using broader monetary aggre-gates to replace monetary base targeting. How-ever, these results indicate that M2 is unlikelyto provide an adequate substitute for mone-tary policy purposes.

REFERENCES

Barnett, William A. “The User Cost of Money,” EconomicsLetters, no. 2, 1978, pp. 145-49.

______ “Economic Monetary Aggregates: An Applicationof Index Number and Aggregation Theory,” Journal ofEconometrics: Annals of Applied Econometrics 1980-3,supplement to the Journal of Econometrics (September1980), pp. 11-48.

Barnett, William A., and Paul A. Spindt. ‘Divisia MonetaryAggregates: Compilation, Data, and Historical Behavior,”Staff Study no. 116 (Board of Governors of the FederalReserve System, May 1982).

Batten, Dallas S., and Daniel L. Thornton. “PolynomialDistributed Lags and the Estimation of the St. LouisEquation,” this Review (April 1983), pp. 13-25.

Belongia, Michael T., and James A. Chalfant. “TheChanging Empirical Definition of Money: Some Estimates

Appendix 1Divisia IndexesThere are two types of Divisia index numbers:the continuous-time version and the discrete-time version. Continuous-time Divisia indexnumbers are derived from microeconomic theory;discrete-time Divisia index numbers are approxi-mations of the continuous-time version.

To understand how continuous-time Divisia in-dex numbers are derived, consider the case whereeconomic agents want a measure that aggregatesa group of n commodities in the economy. Thequantities of the goods are expressed by the vec-tor q=(q,, q,,...,q~); their corresponding pricesare denoted by the vector p=(p,, p,,.., p,).Economic aggregation theory states that theaggregator function is a utility function g(q) to bemaximized subject to the budget constraint,

(1) X q~p~= g(q)f(p) = E,

where f(p) is the price aggregator function and Eis the total expenditure on the specific goods. ‘the

from a Model of the Demand for Money Substitutes,” Journalof Political Econorrry (April 1989), pp. 387-97.

Diewert, W. E. “Exact and Superlative Index Numbers,”Journal of Econometrics (May 1976), pp. 115-45.

Donovan, Donal J. “Modeling the Demand for Liquid Assets:An Application to Canada:’ International Monetary Fund StaffPapers, Vol. 25, no. 4, (December 1978), pp. 67e-704.

Farr, Helen T., and Deborah Johnson. “Revisions in theMonetary Services (Divisia) Indexes of the Monetary Ag-gregates:’ Staff Study no. 147 (Board of Governors of theFederal Reserve System, December 1985).

Friedman, Milton, and Anna J. Schwartz. “MonetaryStatistics of the United States: Estimates, Sources, Methods:’New York, Columbia University Press, 1970.

Hicks, John Richard. Value and Capital, 2nd ed. (Oxford,Eng.: Clarendon Press, 1946).

Rich, Georg. “Swiss and United States Monetary Policy: HasMonetarism Failed?” Federal Reserve Bank of RichmondEconomic Review (May/June 1987), pp. 3-16.

“Geldmengenziele und schweizerische Geldpolitik:eine Standortbestimmung. In: Schweizerische Nationalbank:Geld, Wahrung und Konjunktur’ Quartalsheft No. 4 (Dezem-ber 1989), pp. 345-60.

Shiller, Robert J. “The Volatility of Long-Term Interest Ratesand Expectations Models of the Term Structure’ Journal ofPolitical Economy, (December 1979), pp. 1190-219.

Schweizerische Nationalbank. Revision der Geldmengen-statistik. In: Geld, Wahrung und Konjunktur. Ouartalsheft No.1, Màrz 1985.

Thornton, Daniel L. and Dallas S. Batten. “Lag-Length Selectionand Tests of Granger Causality between Money and lncome’Journal of Money Credit and Banking, (May 1985), pp. 164-78.

first-order necessary condition for utility maximi-zation is

(2) dg(q)/dq = A p,

where A is the Lagrange multiplier. Because theaggregator function is linear homogeneous, Eul-er’s equation is satisfied such that

(3) 1 (dg/dq)q = g(q).

Substituting equation 2 into equation 3 yields

A I q~p,= g(q) and

A E = g(q).

Hence, A = g(q)/E and

(4) dg(q)/dq = p,g(q)/E.

Taking the total differential of the aggregatorfunction g(q) yields

FEDERAL RESERVE BANK OF St LOUIS

I ___________________________________________

time, the continuous-time Divisia index must be

,, (5) dg(q) = I (dg/dq)dq transformed into a discrete-time version to makeit useful. The discrete time approximation of equa-Thus, substituting equation 4 into 5 yields

tion 7 is

(6) dg(q) = I pdc~g(q)/Eand (a) ln(gW) ln(g(t-l)) = I S11n(qW) - ln(q(t-l))]i—I

dg(qkg(q) = I pqdojEq.

If we set S~= p~q~/Eand call it the i-th good’s orvalue share in the total expenditure, equation 6 (10) g(t) = g(t-UEXP( I S~Un(q(t))— ln(ci(t-fl)]),

can be transformed into ‘ I(7) dtin(g(qP) = E S~dfln(q)). where S~= (5, + 5,, ~)/2,

Solving equation 7 for g(t) yields S. = pq/E = pq,/ ( I pq),

(8) g(t) = EXPI( I S(t)dEln(qW)]) di. and S~is the average expendliture share in thet%vo adjacent time periods. Equations 9 and 10 are

Equation S is the continuous-time Divisia index, the discrete-time Divisia index equations used in

Because economic variables are observed and calculating the Swiss Divisia Mi and M2

measured in discrete time rather than continuous monetary aggregates.

I I Appendix 2I Data

i’o calculate the Swiss Divisia Mi and M2 mone- Own Rates

I I tary services indexes, we used the seasonally C Zeroadjusted monthly Swiss Ml and M2 series andtheir components consistent with the definitions DB 0.25 percent

I I established in 1975 and incorporating the revision DP 1975:06 - 1989:04: Zerothat occurred in 1985 (for more details, see 1989:05 - 1989:12: 2 percentSchweizerische Natiorialbank, 1985). TI) three-month rate on time-deposits with

large banks (monthly average)

I The monetary aggregates consist of the fol-lowing assets held by individuals and non-bank Cost-of-living Indexinstitutions:

Ml: Currency in circulation (C) Monthly Swiss Consumer Price Irdex (CPI)Demand deposits with banks (DB) calculated by the Federal Statistical OfficeDemand deposits with the postal giro (Bundesamt fuer Statistik).system (DP)

M2-.Ml plus time-deposits (‘rD)Benchmark Rate

MB: Seasonally adjusted monetary base,defined as the sum of banks reserves and

The highest rate in each period from the fol-

banks notes in circulation, lowing interest rates: the secondary market yieldInterest Bates on cantonal bonds, interest rates on cash cer-tificates with the cantonal or large banks and

To compute the user costs of monetary assets, short-term Euromarket-Swiss franc interest rates.

we need the assets’ own rates of return, the Short-term rates became the benchmark rates

benchmark rate of return and the cost-of-living during 1979:12 - 1982:04 and 1988:12 - 1989:12,

index, when the Swiss yield curve was inverted.

SEPTEMSERIOCTOSER 1991—