The monetary base or M1? results from a small macromodel

Baseor Ml? Resultsfrom a

R. W. Wafer

This auticle investigates the issueof whether Ml cotthe monetarybase should be used as an intermediate target for planetary p&q. Because the target variable should be reliably related to fW-2 economic activity, exh aggregate is used in estimating a small ma&mmodel which consistsof a nominal GlWgn~& equaticinand an inflation sytciflcation The empirical tntlts indicate that Ml better explains GNP growth and inflation for the period 1960-1980. Forecasterrors of GNP growth fnmr 19704980 are reducedwhen Ml is used

instead of the adjusted base, although there is little difference between inflation forecasts. Based on the evidence presented in this study, Ml is preferxd as the intermediate target variable.

I. lntmduetion

of

A question continuing Interest to monetary policymakers concerns the choice of the appropriste intermediate target for the conduct of policy.’ 1~ choosing the intermediate target. two important questions must be addressed: First, how well does the variable proiect the future path of economic activity? Second, to what degree can the Federal Reserve Board control the intermediat? target variable? Previous analyses have focused on examining the first of these two questiopls. because there is substantial evidence that the growth of the narrow definition of money (M I ) is better related to monetary base (hereafter base) grctwth than is the broader MZ money measure. Furthermore, M 1 has been shown to be statistically superior to M2 in explaining GN P growth.’ Thus the general conclusion is that M 1 is preferred to M2 ;1s an intermediate target. Some have argued that, because of slippages (contra’ errors) between the base tind Ml via the multiplier, the Federal Reserve Board st juld focus tjn controlling base growth. One study, by Andersen and Karnoskv ’ 477). showed that in predicting nominal GNP growth, thtire is no statistical differcc: between the results obtained tjj usrny base, MI, or M,.7 P’:1m;t(lW2) has recently argued that ;ontroI of base growth

R \I/ tiafer IS !hlor Economist. Federal Reserve Bank of St. Lou~r. St I.o~rs. Mlssourl Address reprrnr requests IO R. W. Hafer. Federal Rewrte Rank of St LOUIS. St Lout\. ‘bl~sst)urI

Journalof Economicsand Bmmss _36.85-9? t 1984)

314&6195/84/W3 al

gives a more direct control over inflation tilan does controlling the monetary aggregates. In addition, Fama shows that base growth is no; related to the growth of real GNP, whereas M 1 growth is. The resultins policy scenario suggested by Fama is that controlling base, not M I, will lead to better control of inflation while not affecting real GNP growth. Most empirical analyses have focused solely on the money-GNP link to investigate the relative properties of base and M 1 in explaining economic activity. The procedure followed in this paper is to compare the relative merits of base and Ml in a smr~ll macroeconomic model consisting of ;I nominal GNP and inflation specification. The comparison of the base and M 1 equations is done on several statistical criteria: insample predictive performance, stability, and out-of-sample predictive performance. The next section presents the model and the in-sample estimates using base and M 1. Section III examines the question of stability and out-of-sample performance. Concluding remarks are presented in Section IV.

II. The Model and In-Sample Results ThL model used in this paper is based on Tatom (1981). It consists of a St, Louis-type reduced-form nominal GNP equation that accounts for energy price effects and an inflation equation that is based on Karnosky (1976) with energy price effects incorporated. Real GNP is determined implicitly as the difference between the nominal GNP growth and inflation estimates. The model, then, consists of the following specifications:

and i

-’

()

j=

I

+ s, Dl + s, D2 + ‘jr where

Y= nominal GN P; AI = the money measure E = tiigtt-employment

he

or M 1;

ftderd cxpencliturts;

P” = relative price of energy.‘; S = strike variabteJ;

’ The relative price of energy variable is constructed by defhiting the private business sector energy price component by the C.WP deflator. * Th: strike varlablc is used tocapture the impact on GNP growth due tc days of work loss. The variable is constructed as the chrsnge in the quarterly average of days lost due to strkes deflated by the civilian labor force See Tatorn (IS 1) and Andersen (1975) for further &cusslon of tt is vanable.

P =GNP deflator (19?2= 100) Dl. DZ=dummy variables for price control period+ The dot (_)above the variables denotes annual rate of change; l, ar,d 4, are error terms.

Equations (I) and (2) are estimated using ordinary least squares (OU), unlike previous estimations that have relied on the Almon lag estimation procedure. The reason for this choice is the continued unertainty that is associated with applying, a p&k. the numerous restrictions incorporated i.1 the Atmon technique. Although one may test for thess restrictions individually, i.e., degree of polynomial, lag length, and endpoint restriction, one cannot test for them jointly-thus our use of OLS estimates? In estimating equations (1) and (2). we have used the basic format provided in Tatom (1981). since preliminary ewminations sf v&ous lag lengths for M 1 or base did not alter the results.

The 1960/l- 1980/N estimates of equation (1) using M 1 and base (B) are (absolute value of t statistics in parentheses) 2.04

1.107 4 1 m,_,A&_i “=(2.,0)+(6.77, ;zzO 0.063 4 z 44 +(0&a) )“Q

R2=0.540

0.056 pc 7(l_H) ’

SE = 2.705

DW = 1.95

(3)

SE = 3.02.;

DW = 1.96

(4)

and

k?z = 0.426

’ The dummy variables are used tocapture the influence of the imposltior and subsequent removal of wsge 0 otherwise. and D2= I for 1/1971-1/19T5, 0 and price controls. Specifically, Dl = 1 for 197!/111-l/1973, ~1 herwise. Thus Dl is used to represent the control period and D2 is used to capture the impact of the ensrgy price controls. See Tatom (1981). especially fcotnote : 4. ’ For a previous examination of this type of equation using OLS see Carlsoq and Hein (15380)

R. W. H&r where f7 2 is the adjusted coeffkient of determination, SE is the standard error of the equation and DW is the Durbin- Watson test statistic.’ Comparing the regression results, we see that Ml and base growth both have significant and lasting impacts on nominal Gi\l P growth. Although the summed effect of M 1 is slightly less than that of the base, each coefficient is not statistically different from unity. The relevant r statistics for the Ml measure is 0.65 and for base it is 0.91, each well below an acceptable critical level. ?,respective of the monetary definition, the fiscal variable shows no lasting or significant effect on GNP growth. One result of changing the monetary definition is a reduction in the number of lagged energy price coefficients: a contemporaneous and five lagged terms are used in the M 1 equation, and only three lagged terms are used in the base equation. This change gives the relative price of energy a la,*ger negative influence ( 4.16) in the base equation relative to the effect in the Ml version (-0.02). Similar to previous studies, the outcome of comparing the statistical properties of equations (3) and (4) is to favor the equation employkg Ml to explain movements in nomnnal GNP growth. This is apparent in the superiority of R ’ in equation (3) to that of 17’ in equation (4): using Ml yields about a 27 percent improvement in explanatory power over the equation using base growth. Next we compare the 1960/l 1980/1V estimates of inflation (equation 2) using M 1 rend the base. These results are (absolute value of I statistics in parentheses’

2o . 0.013 p:‘-,+ 0.042 p, z (2057) 0.934 c1 ‘n, , ML”(0,74) (1.95) P; 2 I 0 0.03 1 0.062 p (’ 1.918 1.134 l?Z P: q+ -(1.23) (3.29) r -4-(3.38) D1 +(?.I I) 172 =0.814

-

SE = 1.214

DW = 1.75

(5)

0.02 1 1.976 1.800 p:’ ‘+(1.15) p I’ 4-(3.0N) D1 +(2.91) 02 (0.54) ‘0.0 I 2

iis &cl1 ;ts in the Jumnik

1,ariables.

The most striking

%

and important difference is found

unity (t = 1.45) at the 5 percent level of significance. The sum coefficient on the base variable, however, is statistically dinrerent from unity at the 1 percent level of significance (I =3.83). Assuming that the lag structures are being measured appropriately. this result suggests that an increase of 1 percentage point in the base growth rate will, after 5 years, result in an increase of only 0.85 percentage point in inflation, while the same increase in Ml will lead to an equilivent rise in inflation. Lookmg at the summary statistics, the inflation estimates indicate that, as with the GNP equations, M 1 growth is preferable to base growth in explaining movements of inflation during the 1960/l--1980/N period.

Ill. Stability Tests a d Forecasting Results If one were to chose between base and Ml at this stage, the evidence presented thus far would favor selecting M 1. Such a decision, based on parameter estimates for a ZQ-year sample period. may be based on unstable parameter estimates. To examine the stability properties of equations (3&(6). the sample period was split at 1970/ll.R

Stdthiht)

ikSt.5

The subperiod estimates for the GN B and inflation equations are prese ted in Tables I and 2. respectively. Looking first at the Ml-GNP equations. there appear to be significant changes in the estimated coefiicients across the two subperiods. This is especially true for the summed coefficient on the high-employment fec!e,al expenditure variable and several of the lag coeffkients on the energq price variable. The general statistical insignificance of these variables during each subperiod suggests, however, that these differences wilt have little impact on the overall stability of the equation. Even the summed coefficient on Mt indicates a slight increase during the second subperiod. This increase is. however. Hithin the confidence region of the first subperiod estimate. Indeed, testing the stability of the overall relationship between Ml growth and GNP growth using the Chow test yields an F statistic of F ( 18.48) = 0.40, less than the critical value at the 5 prcent level of significance. Turning next to the base/GNP equations. the findings reported in Table 1 indicate a substantial shift in the estimated coeficients on the cumulative impact of base growth on GNP growth. For example. during the period 1960/l 1970/U, thti estimated sum coefficient for base is0.96. This iscompared to the 1970/111--1980/W estimateof 2.20, a value over twice the size oft he pi evious period estimar : c -6 significantly different from unity at the 5 percent level. The sum coefficient on tht: fiscal \2abte displays a marked change, increasing almost sevenfold bctwcen the two yubperiods. Moreover. the sum coerlcient on the fiscal actions measure achieves statistical significance (at the 19 percent level) during the 1970s. Again using the C‘how test, we formally tested for structural stability of the base/GNP relationship. Inlterestingly. the resulting F value. F ( t 8.48) = I .46, does exceed the 5 percent critical :alue. Thus, WCcannot reject the hypothesis of stability. This result IS somewhat stirprising. given the rather Iawe deviation in the sum coefficients. 8Stability testsnccevsarily involve :, degree of arbitrariness m selecting the hypothestzed break pomt The selection of 1970/Uthe midpoint of trru sample -was done to maximize the power of the Chow test On this point, see Farley Hinich and McGulre (1975).

R.W.H&r

T&iIe 1. subpcriodEstimatesfmEqurttion(1p 1970/111-l 980/W

19dO/I-1970/H Variable

Ml

Bzse

Ml

Base

--

_1___1_Constant

-9.85 (1.72)

2.31 (1.92)

3.98 (3.66)

0.955 (3.42)

1.142 (3.31)

2.1?1 (2.99)

1.36 1 (2.92)

(0.66)

-0.130 (1.03)

0.453 (1.87)

0.269 (0.96)

G-2

0.134 (1.23) -0.097 (0.92) -0.181 (1.75)

q-3

0.089 (0.82)

- 9.038 (0.28) 0.03 1 (0.27) -0.059 (0.54) 0.060 (0.56) 0.265 (2.40) 0.136 (1.20) -0.159 (0.58) 0.479 2.320 1.46

- 1.63 (0.46)

4

4

-0.069

ei F

rr.e

PF-1

q-4 5-5

-0.695 (2.54) 0.468 2.345 1.65

S & SE DW

-0.070 0.027

( 1.47)

-0.052 0.095 0.026 -0.073 -0.042 0.079 -0.636 0.469 2.992 2.46

(0.46)

0.03’ (0.64) -0.197

(4.21)

- 0.767 (2.48) 0.460 3.018 2.71

(1.10) (1 .SS) (0.42) (1.11) (0.66) (1.38) (2.08)

--.

-

a 4bsolute value of 1 statistics appear in pa; entheses. R2 is the adjusted coefficient of determination, SE is the regression standard error and D\S is the Durbin-Watson test statistic.

T&k

_-__-

2. S&period Estimates for Equation(2~

111-W

1960/I-1970/11

. _~___--_eI_-.Variable

Base

0.848 (11.51)

p:_

1

q_> & @;-L$

- 0.034 (0.64)

--v-e

-__ ---

Ml

0.942 (9.38) -0.128

0 Absolute Table 1.

_ -__-__l_l-

-- -e__

BW

1

0.749 (10.88)

0.972 ( 1I .82)

(2.04)

0.004 (0.12)

0.004 (0.13)

0.013 (1.69)

0.059 (1.48)

0.030 (0.73)

---0.093 (1.91)

- -0.138 (2.00)

0.032 (0.47)

0.67 1 1.002

0.737 0.836 1.40

-0.0 11 (0.28) 0.035 (1.04) -3.621 (3.18) -1,568 (1.06) 0.504 1.593 1.91 -_._--

-0.034 (0.94)

0.032 (0.65)

1.65

value of t statistr.cs appear in parentheses.

-

_M

0.010 (0.21)

Dl DZ R2 SE DU

s-c1970/111-l 980/N

0.073 (2.65) -3.190 (4.02) I.355 (2.10) 0.68 1 1.278 2.19 I

--

-

.---

R ‘-2, SE, and ItW are defined In footnotes

ta

To investigate the stability& the base/GNP relationship more closely. the following test was used: legged base growth terms were dunked out for each subperiod. This equation was estimated for the 1960/i-1980/W period and compared by means of an F test with the ful!-period regression results reported ir: the text. In this way, we can statisticall:; assess the usefulness of dichotomizing the effects of base growth across the

Tllt_BrreaMl?

91

two periods. The result of the compaison is an %statistic of F(5,61) =0.72, a value well below any acceptable significance level. Thus, a:; ;lough the sum coeficients for base in Table 1 appear to be quite different, statistically we cannot reject the notion that, as a group, they are the same. The inflation subperiod results are reported in Table 2. Interestingly, the cumulative irnm of Ml and base growth on inflation are statistically the same during each subperiod. For example* during the period I/196&II 11970, the sum coefficient on M 1 is 0.942 (I =9.38b, an3 the sum coeffrcknt for Ml across the t970/11--1980/I!/ period IS 0.972 (t = 11.82). This evidence suggests a stable relationship between M 1 and inflatior, across the full sample per&cd,ceteris p&bus. Indeed, the results from the chow test support this contention: the calculated F value of F (27,3(I)= 1.33 is well below the reievant 5 percent critical vaiue. Thus, like the M 1 /GNP relationship, the M 1 /inflation specification is stable across the 1960/l-1980/N sampie period. The base-inflation results presented in Table 2 indicate that there is only a small change in the cumulative efkcts of base growth on inflation across the two yriods. For example. the sum c&ficient for the 1960/l-1970/U pcrlod is 0.848 (t = 1 ISI), *vhiJethe v&e of the ccdcient declines in the 197Q/ltl-198OflV period to 0.749 (t= 10.88). In each instance, the estimated coeefrrcientsare statistically different from unity. The relativeiy minor changes in the base cocfftclents-clearly the most statistically important variable in explaining movemer + in inflation-suggest that the overall relationship will be stable. The results of tha: Chow test support this notion: the calculated F value F=(27,30)=0.80 is less tharh the 5 percent critical value. Thus, as with M 1. we cannot reject the stability hypothesis.

Forecast Rest&s TO analyze further the relative merits of base and M 1, the following experiment was conducted. The respective GNP and inflation specification: were estimated from 1960/I to 1970/11’ and four-period-ahead forecasts were made The estimation period then was extended through 1971 /lV and forecasts were made si,r the four quarters of 1972. This procedure was continued until forecasts for the year 1980 were obtained. The averages of the quarterly projections, along with summary statistics, are prese:lted in Table 3. The first two colt [mns of Table 3 report the forecast perf, rmances for the <;N P equation using base Jnd M 1. Over the 10 years reported, M 1 txtters the base forccast 60 percent of the time. Moreover, the record using base suggests a slight underprcdiction, on the average, of GNP growth. while MI indicates that, on the average. t:le forecast error is essentially zero (0.04 percentage points). Compared with base. M 1 improves the average GNP forecasting performance almost five times. The summary statistics also reveal lhat M 1 is better in predicting GNP growth than is base: the rootmean-squarred error (RMSE) for Ml is 4.12, or about IO percent lower than the 4.52 RMSE for base. Moreover, the Theil Lr statkic indicates that the average performalIce of M 1 growth in predicting GNP Rrowth OSsuperior to that of base The third and fourth columns of Table 3 present the inflation forecasting records for the two monetary agdregates. Here the overall performances are illuch closer than with GN P. Still, M 1 growth provides a smaller forecast error in 7 of the 10 years studied in addition to an average error that is less than half the average error using base growth. he differences in the: RMSE and Theil V statistic> suggest that there ma:! be only

R.W.Hda

92 T&k

3. Post-Sample Fbdiction Emrs fix GNP and Inflatim Infation

GNP -Period

Base

Ml

1971 3.07 1.62 1972 -1.48 -0.16 1973 --4.74 -4.60 1974 2.07 2.52 1975 4.99 3.56 1976 -0.10 -0.53 1977 --2.37 -1.23 1978 --I.37 -1.69 1979 --0.11 1.12 1980 -- 1.85 -0.18 ME -0.19 0.04 RMSE 4.52 4.12 u 0.46 0.41 - ___I__--__-. _---a Errors reported are four quarter averages for years shown,

BW

hll

-0.79 0.04 -2.01 --1.34 1.20 2.3 1 0.92 -1.58 -1.17 -2.30

-0.76 0.03 -2.36 -2.31 1.96 1.61 0.27 -2.10 -0.08 0.67 -0.2 1 2.04 0.30

-0.47

2.02 0.30

actual minus pwdkted.

ME is the mean

error, RMSE is the root mean squared error, and U is the Thei: U Statistic.

ditrerences between the capabilities of the two measures in predkting inflation, on the average. It is interesting to note, however, that during the 1974 IQ80 period :>frapid inflation, the M 1 forecast errors average about 2 percentage points less than those from the base equation. Moreover, while the Ml equation slightly overpredicted inflation from 1974 to 1980 (0.02 percentage points), the base equation yielded inflation predictions that were less than actual inflation (I.95 percentage points).

marginal

1V. Conchsion The perennial question that monetary policymakers and their economic advisors must address is. Which variable should be used as an intermediate target’? In this paper. WC have examined the estimation, stability. and foxcasting properties of base and M 1 in ci smrrlt, reduced-form macroeconomic model that consists of u nomin 1 GNP growth equation and an inflation specification. The M 1 measure provided better in-sample results for both GN P growth and inflation repressions. M 1 was also the better measure III predicting GNP growth from 1970 to 19X0.Thus, from the tes: results presented in this study. the cvidcncc indkatcs that M 1 is prcferrcd ;IS the mtcrmcdiute targcr ~fiahk k)vt’r the txisc nlt’;:;suTe.

References Andersen, L. C., June 1975. A monetary mmlel of nominal income determination. Sr. Louis Federal Resewe Bunk Review 9- I G. Anckson, L. C. and Kamosky , D. S . Sept. 1977. Some Lonsideration in ?*:e use of monetary aggregates for the implementation of monetary policy. St. Louis Federal Reserve Bunk Review 2-7.

Eirunnef. Karl, ed. 1969. Targets ond Indhrors Publishing, Co.

of Monetary Policy. San Francisco: Chandler

TbtMonccrybWMI?

93

Ckmbs, C. M. lur. 191#).Fakral Itslrxvehtmnaliatc

taqps: Money or the monemy base? Km

CiryFe&miResmdhk~RIvirw3-15. Gilbat, R. A. Xkc. 1980. Rcv&nt of dw St. L&s F&d Reserve’s @ustai mnctary base. St. lmisF&mfRmmelbnkRhew3c10. Hafet, R. We Oct. 198 1. Much ado about M2. St. Louis F ederof Reserve Bank Rsvh 13- 18.

Hatnbwger, M. I. May 11970.idiom of ~io~yt~lly policy: ‘Ik arguments and the evidence. Amdun Ekmtdc Revkw 32-9. Karnosky, D. S. I1976. ‘I’k link kiwaca money and prices: 1970-76. St. Louis f’edkruf Reserve Bd Rev&v 17-23. L&n, F. 1. 1934. Tk srkcriosr of a mmetary indicatoc Some hxther empirical evdeace. In ~~Aggngcttrscad~~Policy.NewYorltFedcrplRescrveBanlr.pp.35-39. Schalmk, F. C. 1974. An unpirid wroach to the &f&ion of money. In Monetrvy Aggregates d~~Poli~.NewYorlrFadcnlRescncBmk.QQ.28-34. Tmm, J. A. Jan. 1981. Enc%y prices and shcwt-wr economic perfonxunce. St. Louis Federal Rese~&mLRev~~~I7.

7’kil.H

1966.ApplirdEmumic

Accxptcd 25 January 1983

Fonccuting. Amstedam: North HolIandPIlblishingCo.