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The short-run volatility of money stock targeting
Journal ot’MonetaryEconomics 10 (1983~215237. North-Holland
Publishing Company
THE .SHORT-RUN VOLATILITY OF MONEY STOCK TARGETING
P.A. TINSLEY, P. vcm zut MUEHLEN and G. FRIES* Fe&d
Remw Board, Washington,DC 20551, USA
The altered ailocationo of money market volatility akined by alternative monetary policy pmosdures are illustrated by st&astic simulations of a staff monthly model. The results indicate the nature af the tradeoff between short-run volatility in the money stock and in the
funds rate that is availnbleto money stock targetingprocedures.
In October 1979, reserves-oriented operating procedures were adopted for the execution of short-run monetary policy. The historical record of money market volatiiity in 1980 was not encouraging. As shown in fig. 1, the standard deviations of both the monthly growth rate of MI -/i and the monthly change m the Federal funds rate increased markedly during the twelve months subsequent to the alteration of procedures in contrast to the standard deviations for the preceding iwelve months. This paper explores the short-run volatility consequences of money stock targeting under current and alternative operating procedures. The focus is narrowly drawn on the feasibiiity of money stock targeting, an issue that may be considered. independently of the desirability of intermediate targeting on monetary aggregates. Two principal issues are considered: --Was the money market btieted by arypical events in 1980 or is there an inherent flaw in current operating procedures that tends to induce volatility in money markets? -‘Does there exist a well-behaved tradeoff between the volatility of deviations of i%C-- A from Ion run targets and the volatility of shorttezm interest rate der current and alternative operating procedures that may be exploited short-run monetary policy?
‘“The authors arc indebt
‘I, r’u~, B. Garrett, J. Lovin, W. Trepeta, V. for the assistuncc of I-Y
%Mcinsand C. Wilson. The views expressed hzin are solely those of the authors and do not nc~&,rily represent the’tiews of the Board of Governors or the staff of the Federal Reserve Syr;tem.
0308-3932/82,UK%4X#O/$O2.75@ 1982 North-Holland
216
P.A. ?Snsley et al., The short-run volatility of money stock targeting GtIMl-A) 40-
I i --ul(Gt)=5.9
-
-u&+)=9.3
/
--
20 -
-20
’ ’ ’ ’ ’ b ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ 80.10 79.10 78.10 .’
G,(Ml -A) - annualized growth of MI-A in month t. - standard deviation of growth rates 78.1039.09. a,(G) - standard deviation of growth rates 79.1l-80 10. ~,G) A RFF 4
I
-8 78.10
79.10
ARFF - change of Federal funds r&e in month t. rr,(dRI:F,) - standard deviation of monthly change 78.10-79.09. ~~r,(dl?FF,)- standard deviation of monthly change 79.1b8O.10.
Fig. I. Historical va.rianility in the monthly growth rate of the money stock and the monthly rhange in the Federal funds rate 1978.10-1980.10.
concept
of short-ran
stocllastic
vohility
High-frquzncy oscillations in the indicators of monetary policy may be viewed with dismay by mane) rzlarket participants, in part because t.hey
P.A. Tinsley et al., The skort-run volatilityof money stock rargering
217
obscure Ehe :,lrderlying intentions of the policy authority. However, not all kinds of meassred increaees in tht variability of money market instruments imply reduced information of policy mtentions. In the case of money stock targeti& the gr~@ v&rL:-biIityin the monthly growth rate of the money stock may be an imr@~o#ate measure sf policy performance. If the money stock is forced off 8 ,\%@eipath by an unallnticipated disturbance, the growth rate of the money stcxk must be aggressi\*ely altered in subsequent months to recover the targeted path. In this case, a more suitable measure of undesirable volatility may be the standard deviation of monthly departures from the money stock target path. Similarly, the dispersion of unexpected chanm in short-term interest rates may ba: 2 more relevant measure of undesirable interest rate volatiiity than the Rnctuations of total changes in interest rates. Thus, in this paper, undesira:Ae volatility is differentiated from gross variability where voiatility is a short-run stkchastic concept referring to the dispersion of outcomes around planneti objectives or expectations. Stochastic volatility is unavoidable in an economic environment that is subjected to unpredictable and sizable disturbances. Where that volatility is allocated within money markets depends importantly on the design of monetary :~~oiicy.Attempts to eradicate transitory variations in target variables* for example, may increase the short-run volatility of other money market variables in excharrge for little improvement in the long-run performance of the target variables. The extent of this unavoidable short-run stochastic volatility and the nature of the tradeoff allocations available to money stock targeting procedures is examined in the remainder of this paper. 3. An ecowimetric portrayal of U.S. money markets and alternative operatirbg w-
An econonurtric pnodel of mnthly financial behavior Estimates of short*run stochastic volatility in money stock targeting procedures have been c btained from stochastic simulations of an econometric model used by the staf!’ to nesate monthly econometric forecasts of money market behavior. The st astic simulation approach was adopted Ito circumvent the lack of an extensive historical track record with the new rating promdures. Stochastic simulations permit 1980 to be ‘rerun’ under alternative random disturbances or under competing policy procedures. In the current version of the model,’ twenty estimated equa.tiolts plus several accounting identities project reserve aggregates, the comlponents of ‘See the appendix for a discussion of the essential economic structure of the monthly model; a simulation characterization of monthly monetary policy, and a brief disc&on of the methodology underlying stochastic simulations. A complete description of ihie FRB staff monthly econometric model is ptovided in Farr (1980).
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M --3,and selected short-term interest rates, given judgemental projections of the monthly paths of personal income and the consumer price index (VI), and an assumed. path for the policy instrument [non-borrowed reserves (NBR), total reserves (TR), or the Federal funds rate (WF)]. Red economic activity is exogenous in this model and not
(a)
Setting
interim objective
target objective
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4.’ . . .
219
InMT
‘/
In q (X=4)
,’
/1’
/
(/
/ 1’
0
,**In rq (X=0)
P
.b
. . 1
I
2
12
t
MT -- MI - 9 target path (4.75% annual growth,, MI _=-pto_jrxtedMI-A in month 1, W -- interim MI -A target for month 2. (a) 1 =Q ndt closure of re!ative target gap (base drift), :b) I== 1; fufl closure of relative target gap in one month, 1 __ qsnthly rat=.af re-entry to annual target path (MT), In -- rraturd lop rithm. Fig. 2. Selection of interim MI -A target.
If A= 1, the policy authority plans to return to the annual target path, MT in ON month. Conversely, if A-0, the authority pEat?sto achieve an annualized monthly growth in AlI --A equal to the annuabd growth rate of ihe target ~4*~5~)but starti from the current money stock, Ml, rather thrn ihe target value for month Thus, Lr the case of 1x0, the policy authority does not uce the reilativc money stock target gap in month 2, a choice et selection, the selection of tlld:t-e-entry es the persistence of past random disturbances in the current df A,= 1, the &ect of a random disturbance rn~ney stack target gap, q/M,. in period 1 that causes the rnonzy stock, Ml, to deviate from targeted money, AK_&is elirn~~at~~din one month. Since the re-entrv rate is months in the plElnning horizon, a zero re-entcp ate in=O) ianI ~ff~~ti~~~ duration of the impact of a random isturbance is infinite since there will be no planned offset. A re-entry rate, A, can be converted to an
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P.A. 7lndey et al., The short-run volarifity of money stock targeting
implied monthly age, A, of random disturbances in the money stock tl-rget gap, as shown in table l., The typical monthly re-entry rate of cupienl targeting proce ,Jures in 1980, as estimated by Trepeta (1980), is 0.292. This Implies an average age of random disturbances in the annual money stock target gap of about three arid one-half months? Table 1 Translation of monthly re-entry rate (A)to average age (A) of money stock target miwes. Re-en r’yrate (A) -_ 1 0.333 0.292’ 0.167 -4verage monthly age Wb
1
3
3.4
6
0.111
0
9
a.I
“Estimated monthly re-entry rate of historical interim targeting prooedures 80.02-80.1J; see Trepeta (1980). bAverage age (in months) of random disturbances in the money stock target gap (In MI; - ln M,). More explicitly, A=J i i(l-I)‘-‘=1/;1. i=l
(6) Setting the policy instrument.
A. plan&led setting for the intenneeting interval (represented by the follo.+ving month in this discussion) is then selected for one of three possible policy instruments: non-borrowed reserves (NBR), total reserves (7X), or the Federal funds rate (RFF). The selection of the policy instrument setting is approximated in model simulation exercises by the following procedure: It is assumed that the projection of the money stock in the current month of the meetin sufficiently accurate so that any remaining forecast error may be ne foreCast of money market btlrhavior in the following month is then by the staff monthly model as if the interim money stosk tar mopth is the effective policy instrument. This forecast p~lu non-borrowed reserves (NBR, total reserves (TR), and the Fbderal funds rate (RFF) that are consistrnt with achieving the interim money stock tar at least in the absence of forecast errors. In some of the cases analyzb:d, the FOMC is assumed trc)impose a tw range so that the Federal funds rate cannot move by more than 308 basis 2Due to the nature of exponential decay, cornpI& elimination of the influence of a @rivcen disturbance to the money stock can be a lengthy process. FOP il==O.292,seven mwths are re+ired to eliminate WA of a given disturbance. (One month is required for ,I =LZ 1 and twenty mS3nthsfor d=O.lll.)
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221
points from the current month to the following month.3 In these cases, the funds rate constraint must be satisfied in both the ex ante policy planning; stage and in the ex poti policy execution stage (when random disturbanm are encounter4 as explained shortly). (c) Si?~iutton of s&sequent ‘history+. Following the selection of F p&q instrument setting (either non-borrowed reserves, total reserves, or the Federal funds rate) that will achieve the interim money stock targzt, M*, in the absence of random disturbanceq the model is resirnulated in the second month with non-zero random disturbances. All variables except the polis!y instrument are &&ted by the random disturbances. There are two types of stochastic simulations: (i) In psuedo-history stochastic simulations of 1980 (1980.01~1980.10), the historical monthly forecast errors of the: model are incorporated in the simulation. Thus, if the policy instrument is set at its historical path, actual monthly history would be simulated for all variables in the psecdo-history simulations. (ii) In average-history stoch;tstic simulations, random disturbances similar in pattern and size to nod-’,.. .CIIecast L* errors encountered during the I+ :: year sample period, 1971.01 through 1979.12, are incorporated.’ The purpose of averagehistory sin&&ions .is to examine the robustness of the response of alternative operating prwdures to a full spectrum of plausible random disturbance patterns. In summary, the planning stage of a monthly policy operating procedure is characterized by two components: (a) seleciion of the interim target for the money stock, AP, as determined by the rate of monthly re-entry, i., to the annual target path, MT; znd (b) selection of the policy instrument [non30nc motivationfor a tzugetrangeon au auxiliary variable,such as the Federalfunds rate in
~WUV~CI pdicy,is to provide a rough check for operatiollzi breakdownsof the a aon-borrowod
planniqjmod&If actual events move the auxiliary variableoutside the auxiliary target range, actua!eventsmay not be statistically compatible with the ex 4tlte forecast.Whr.nthis OCSWS, the pknning mxkl my be cimii~g some iagndimt in the structureof the actuai eccnomy, and the authorityUUL~ ti& to r~~&dcf plannedpolicy. Using this interpretation,the target range for tba auxiliary v viable should bear some resemblti:lceto iI confidenceinterval of the ex MC projectionof the au?itliiir ty wiabk. ‘In all policy &nuiatirlru,t. Fe&al funds rate was subject to a tloor of two percentage pointi and a c&in& of forty percentagepoints to prevent simulation of events that are far remotradfrom the sutmpk zxpetience. in simulations where a reserve aggregateis the policy inetrumsat,if the F&A Cm& rate hit a target range boundary on the monthly change or a on de kvcl, the Federal funds rate isecamethe effectivepolicy instrument am&r the execution stage of that month. bails of tie stochastic simulations reproducethe cross correlationsof the historicalihotithly’ fore&&errorsof the model, both over time and across equations in a given month. ‘I’%& stand& deviation of the monthly foreutst -or of demand deposits v as increased by about f$d to account for ex .~t informationon recent shifts in the money dc.lrand function that is’inuoprated in the mrrmt version of the model. This information is introduced into the made1 by shift piaameters whzh include rough approximations for the impact of repurchase ag.zements, the appearanceof ATS accounts and so on. poticy
P.A. Tin&y
222
et al., The short-run
volatility
qf money stock targeting
borrowed reserves (N&R), total reserves (TR), or the Federal funds rate (RFF)] that will be held invariant to incoming random disturbances throughout the subsequent month. The execution stage of monthly policy is represented by a stochastic simulation where the effect of the planned policy is evaluated by a monthly model simulation having non-zero random disturbances. The policy cycle consisting of: (a) selection of the monthly interim money stock target, (b) selection of the monthly policy instrument setting, and (c) execution of monthly policy under random disturbances. is repeated in each month of the effective policy horizon, 1980.01 to 1980.10.
4. A comparison of peado-historical PBWS .&verageperformance of current lk
annual performance af an operating policy procedure depends to a great exten; on the type of random disturbances encountered. As noted in the appendix, some policies are more vulnerable to shocks to the demand for money while others are more affected by supply side shocks. It is of interest to determine whether the intra-year deviations of the actual money’ stock, M, from the annual target path, M7: were due to some inherent flaw in the current operating procedure or whether the random disturbances encountered in the first ten months of 1980 were atypical (incorporating the impacts of unusual events such as the imposition of special credit restraints
in mid-March). Three policy ‘histories’for MI -A are presented in fig. 3: The first is actual MI -4, denoted by M. This can %e obtained by simulating, the monthly model over the first ten months of 1980 with’historical disturbances and with m.anthly non-borrowed reserves, NBR, maintained on its historical path. The two remaining ‘pseudo-historical’ paths, MS, and MS,,, are also obtaitlcd by simulations with historical disturbances, but the non-borrowed reserves paths, NBR, and NBR,,, of these simulations are obtained by werage approximations of current operating procedures. En both cases, the constant monthly rate of re-entry, L, to the target money stock path was set at the average value estimated for historical planned policy in 1980, 1=0.2X!. Also, both policies were subject tu the restrict&i “th&tthe monthly’ change. in the Federal funds rate could not exceed,.3O&basispoints. Since ‘both_the monrhiy rate of re-entry, 1, curd the effective Federal funds rate &get, range are only G:uerag@ approximat lens of historical policy; the ‘simulated results till. xcover
4y
approximationis of the consequences of actual policy.
PA. Tin&y et al., 7%~ shott-tun rdatilityqf money stock targeting
223
In the first approximation of historical procedu.res, labeled ‘MM policy (restric ‘x! ARFF)‘, the simulated policy authority selects that level of nonborrowed reserves, NBR, that will attain the interim money target, M*, in the absence of random disturbances but subject to a monthly target range of eral funds rate, RFF. When subjected to this approximation of poky, denoted NBR,, As shown in fig. 3, this policy closely mimics oney stock (M) in the first six months of 1980, more slowly to the annual target path (MT) in the
8003
80.06
80.G9
LOW -- lower boundary of 700/,confidenceintervalfor NBR policy (restricted ARFt’), M p__historicalMI-A, simulated‘history’-- h BR policy (restricted RFF) wit.h historical disturbances, MS. _yyp BR policy (BGR = BOR _ 1) with historical disturbances, AR& - simulated‘his&q’ -- EC MT .- targetMI - A (4.750/,a1lual growth 79.1G-80.1I), HKiW-- upper boundary of 70”/,confidenceintervalfor NBR policy lrcstricted dRWj.
Fig. 3. Hb;toricaland expected performanceof currentproadures.
The second approximation to current operating procedures is similar to NRR, but the simulated policy authority first selects a total reserves estimate, 7X,.. consistent with the interim money stock target. In this policy, the nonpath, NB&, is obtained by subtracting the current of borrowed res rves, MN? - 1.7 In other words, the by the policy authority a ~o~~ti~uationof current bor ent setting, AM&,= TR tic.;a of the non-borrowed “The return to target path is inhibited by the reatrictionthat the monthly RFF change must in actual history the Fe&al funds rate dropped by reserves -. that is total reserves less member beak barrnvring Fborrowing near that prevailing in :he most recent
224
P.A. Tin&y et al., The short-run volatility of money stock targeting
-BON _ 1, This policy approximation, N&R,,, is identified as ‘NB13 policy (IN% ==BOR_ J and is also subject to the restriction that the monthly target range for RFF cannot exceed six percentage points. The money stock attained by this policy under 1980 disturbances is labeled MS,,. As noted in fig. 3, the ten-month growth of the money stock of this @icy approximation is quite close to actui4 history except during April 1980 when the decrease is not as protrounced.8 The results in fig. 3 suggest that the two non-borrowed reserves policies are reasonable approximations of current operating procedures since the resultant money stocks, MS, and MSb, bracket the result of historical operating procedures, !V. To estimate the range of money stock outcomes that might have occurred under current operating procedures had 19% been an ‘average’ year, a 70% confidence interval was generated for the first approximation of current policy, MBR,.” The 70% confidence interval is obtaiued from 100 stochastic simulations of the first ten months of 1980. Random disturbances for each simulation differ but are selected to replicate the historical pattern of the forecast errors encountered by the monthly mod,! over the nine year sample, 1971.01-1979.12. After 100 simulated histories are generated by the average approximation of current operating procedures, the upper fifteen and lower fifteen of simulated money stocks in each month are removed to define the boundaries of the 70% confidence interval shown in fig. 3. As indicated, both the iactual money stock (M) and the ‘pseudo-historical’ money stocks (MS, and MS,) obtained using 1980 h&>&al disturbances fall below the 70% confidence interval in at least three of the first ten months of 19SO. Under the assumption that the relative accuracy of the model des.,ription of money market behavior is not substantially affected by the shift in operating procedures, this result suggests that the odds are at least two to one that a substantial portion of the gyrations 3f the money stock observed during 1980 can be ascribed to unusually severe disturbautis encountered in 1980 and not to instability generated by current operating procedures, 5. Expected volatility tradeoffs under alternative operating procedures This secticn examines the volatility implications of varying the monthly rate of re-entry, R, to the money stock barge! path, MT The volatihty of the *fhis policy tends to produce more modest changes in the Federal funds rat@since the simulated policy authority does not implicitly recognize the projected offset in borrowed reserves when sekcting the planned change in the supply of non-borrowed reserves. %elative to the annual target path, M?: there is a di,scemible *‘upside risk’ imp&d by the Sective midline of the 70% confidence interval. This is due, in part, to the logarithmic formulation of money demand in the monthly model. To illustrate, if the loga ithmic forecast error is normally distributed, tn M-In A.?=a, E- N(0,a2), the mean of the simulated forecasts, E(M), will exceed the certainty-equivalent (zero residual) forecast, #, E(M)= & e@*)‘.
F.A. Tin&y et ai., The short-run volatility of money stock targeting
225
Federal funds rate is rpnresented by r$e standard deviation of the monti?ly change, a(MWF). Under general conditions, this statistic can be interpreted as one-half the widzthof the ?o”/, conEdence interval for month-to-month variations in RFF. The *:olatility of money stock performance is measured by the square root of squared monthly deviations of the annualized cumulative growth rate of the money stock from the annualized cumulative growth rate of the money stock target, where the latter is 4.75% for every month in the policy horizon. The root mean square error, RMSE, penalizes persiste.nt ‘biases’ in performance @en the money stock consistently grows below or above the target path as in the case of base drift. In dl cases reported below, the mean bias is negligible (since the average random disturbance is zro) so the RMSE corresponds closely to the standarcl deviation and is approximately equal to one-half the range of the 70% confidence interval for monthly departures from 4.75% growth. It can be demonstrated that this volatility measure of monthly cumulative growth rates around 4.75% is equivalent to the RMSE of the logarithm of the annualized monthly target gap, RMSE(GAP), where GAP, = la (M c/M,) - 1200/t. in the results discussed below, a root mean square error of two, RMSE(GAP)=2.0, indicates that the annualized cumulative growth rate of the money stock in a given month will fall between 6.75% (4.75 +2.0) a:nd 2.75% (4.75 - 2.0) with approximately 707; probability.” The results that follow tabulate the expected tradeoff between target gap volatility of the money stock and the volatility of the Federal funds rate. Points on the volattility tradeoff ‘frontier’ are generated by altering the monthly rate of re-entry, il, to the money stock target path. As the monthly rate of re-entry movies from zero (base drift) to unity (full gap closure), it is of interest to determine if the frontier is ‘unstable’ (positively sloped) or wellbehaved (negatively sloped), In the case of the former, the volatility of both the money stock target gap and the Federal funds rate would increase with tht speed of monthly re-entry, suggesting that a viable tradeoff does not exist. In the latter case, an increase in the volatility of the Federal funds r;:tte can be exchanged fo: a reduction in the votatility of the monthly target gap. The volatility frontier is estimated for a particulalr policy by averagehistory simulations of the monthly econometric model. As discussed eariier, the pattern of randola disturbances of average-history stochastic simulations resembles the pattern of historical forecast errors generated b;~ the monthly mode! over the sample span, i971.01-1979.12.
Thus,
‘OThesimulation results do not include an estimate of ‘noise’ introduced by preliminary seasonal adjustment. An examination of recent work by Pierce (19801 suggests that ~~llmal~ of the target gap volatility presented below underestimate total money stock volatility by &out one percentage point.
P.A. Tin&y et al., The showrun volatility qf money std
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targeting
Four operating procedures are examined: non-borrowed reserves are selected as the policy instrument held invariant to random disturbances during the policy execution stage of each month. 0ii ?TBR (restricted ARFF) - the non-borrowed reserves policy is subject to a Federal funds target range of six percentage points. That is, the monthly change in the Federal funds rate cannot exceed three hundred basis points in either the policy planning stage, the policy exmution stage, or both. (iii) REF - the Federal funds rate is szlccted as the policy instrument held invariant to random disturbances in the policy execution stage of each month. Thus, all monthly changes in the Federal funds rate under this policy are planned changes selected in the planning stage to return the money stock to its interim target level, total reserves is selected as the policy instrument held invariant ( iv) TR to the impact of random disturbances in the policy execution stage of each month.
0i
NBR -
Tradeoffs irr the volatility of the Federal funds rate and the volatility of the money stock target gaps under the four alternative operating proadures are displayed in figs. 4-6. The horizontal axis indicates interest rate volatility as represented by the standard deviation of monthly changes in the funds rate, a(ARFF), measured in percentage points. The vertical axis provides two measures of money stock target gap volatility: The upper panel (going up from the horizontal axis) indicates the monthly volatility in money stock target gaps for all months in a sample of ten-month policy horizons. Thus, the upper panel measures month-to-month variability of the money stock target gap within a ten-month ‘year’. The lower panel (going down from the horizontal axis) measures the volatility of the terminal gap at the end of a tea-month ‘Iyear’.It is assumed that the policy authority wishes to reduce all measures of volatility: money stock target gap volatility withm a policy year, RAGE (GAP,); terminal target gap volatility, RMSB(G.4PB0 &; and funds rate volatility, a(ARFF,). However, the results indicate that this is not possible. !%esultsfor the unrestricted1 1 non-borrowed reserves policy, ‘MM policy’, are displayed on the right side of fig. 4. For the case of base drift (A=O), th upper panel indicates that a target gap volatility of about 2,26g/, is obtained by the NBR policy at the cost of a monthly funds rate volatility of about 5.9 percentage points. As the monthly re-entry rate, 1, moves toward unity, the “As noted earIier, this policy is not subject to a tic in the Federal funds rate.
t range restriction on ~~n~h~y changea
P.A. Tinsley
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uotatifity
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227
a(dRFFt) -- standard deviation of raonthly change in RFf’,
RMSE GAP,
-
root mean square error, log of annualized relative gap between targ:t mon,.y and actual money in wunth
GAPso.u, #I
-
&J of annualized @,apin last month of hoti/ -n (&O.lct), monthly rate gf re-entry to the money stock annual iatget path. Fig. 4. Re-entty tradeoff schedules, non-horrowed reserve policies.
volatility of the monthly money stock target gap is r&ced at the cost of an &muse in monthly fund:3rate volatility. Thus, the trade-of? moves in a southeasterly direction &g the reentry rate, 1, increases. At ;1= 1, the unrestricted NBR policy obtains a 600/Oreduction in monthly money stock volatility tit the cost of a 75% increase in the monthly volatility of t funds rate, RFF? As the ntsntpy rate, 4 goes to unity, the monthly money stock target gap to zltro. This is because the re-entry rate is established volatitity does not in the ~l~n~~~~~stage wi,hhout benefit of perfect foresight of the random disturbances that will be encountered during the subseqrtent month. Thus, 1.3”11,is the lowest monthly gap volatility that can be achieved by the unrestricted ,?VBRpolicy, at the cost of a monthly funds rate volatility of 10.2 ItThis may be a rel?lvely optimistic tradeoff sins:: the short-run and long-run interest rate clzsticities of the demand &tt money in the staff montXy model were the highest among models e~~rni~~d by the awjthors.
228
a(ARFF,)
RMSE GAP,
standard deviation of monthly change in RFFs - root mean square error, - log of annualized relative gap between target money and actual money in month&
-
GAP,,.to - ;bg of annualized gap in last month of horizon (80.10),
2
- monthly rate of re-entry to the money stock annual target path. Fig. 5. Rc-entry tradeoff schedules, Federal funds rate policlr.
percentage points. Note also that not much is gained in terms of a reduction in monthly money, stock volatility by moving from A=@292 (the estimated historical rate of r-e-entry) to A= 1 (planned complete closure of ‘the money stock target gapin one month). The bottom panel is roughly a mirror image of, the top panel ex?pt that the temrinal gap volatility measures for corresponding rates of r-e-entry,E,.are uniformly lower. This property was found for all policies examined and indicates that a’il policies will be more successful in attaining year-over-year targets than in maintaining close adherencze to the target’ path’ within the year. The Leftsides of the panels. ia fig. 4 indicatethe expected ,volqtiljty tradeoff for a non-borrou;red,reserv,esp&y- that js subjeot)ITV:‘d tmgy -~st&@m of.six percentage points on monthly changes in the Federal fu~~.Israte+ @‘I? This palicy is a closer approximation to current operating procedures than the unrestricted N.BRpolicy. The results in fig. 4 suggest that Vmkiian h’t6e’re~ entry rate under ,:urrent procedures is largely futile &no3 ~~o~a~~ is
PA.
Tiy
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sbt-nm
uolarility ofmoneystock targeting
228
X=0
6
.
\
X=J
3
6
a(ARFFJ -- standard devktion of monthly change, ir, RFF, RJUSE GAP,
-_ root mean square error, - log of annualizd relative gap between target money and actual money in month
GAPtW.,Q --, kg of annualized gap in last ~YMII of horizon (&O.lO), 1 =- monthly rate of re-cntry to th:: -money stock annual target path.
Fig. 6. Re-ent.y trade-off schedulen. toiui riaiarvespolicy.
domiaaeod by the imposition of the target range restriction on monthly
variationof the Fedeg;Jfunds rate, Fig. 5 indicates the expected tradeoffs for an unrestricted interest rate policy where the -Federal funds rate, RI;.F, rather than non-borrowed rves, is held catastmt during the month. Of course, the Federal funds rate is reset at the beginning of each month to obtain the interim money stock
objective, One characteristic of the unrestricted interest rate policy, RFF, is that compmb~e redwtiosrs in both monthly and terminal gap volatility are abtained at lower levels of interetit rate volatility. That is, at the historical 3 A=O.292 the monthly money stock gap volatility rate of planned non-barrowti reserves policy, NBR, is 1.6, a result uiider an unrest that @dose to the if.5 obtained for the unrestricted interest rate policy, RFF. milarly, ‘the term3ra.I gap volatility at R=0.292 is 0.56 for the unrestricted BR policy and 0.58 for the RFF policy. However, the corresponding
monthly RFF volatility measure at J =O 292 is 8.0 percen ta: P:it.\fS fc
All policy analysis is model specifr;: and the results of this paper are not exempt from this dictum. Two limitations of the existing monthly econometric model may be noted. As indicated in the a.ppendix, the economic structure and scope of the current monthly econometric model are limited. It would be desirable to incorporate a full specirum of portfolio adjustments by bank and nonbank sectors14 as well as interactions between real and financial economic activity. Efforts in these directions are impded by the limited scope of available monthly data. (ii) Stochastic simulations provide a more robust method of analysis than deterministic simulations since they account for the historical forecast error record of the model employed. Although the boundary limits of uncertainty are delineated by this method of ana!yr;is, all uncertainty in the current model is allocated to additive ex&rnal ‘surprises’. There is accumulating evidence that the essential structure of the economy is better described by allocations of forecast uncert&ty over all model (i)
13Since, as noted in the appendix, planned settings of the funds r.rte are idcnticcd under all poiicies, the results in fig. 5 could be obtained approximately by a non-borrowed reserves policy with a relatively wide target range on planned changes in the funds rate hnd tight restrictions on unplanned changes in the funds rate. Y’heoretical examination of a compiete capital account model is provides by Hadjimichalakis (1980).
coefficients, in contrast to the conventional assumption that the model structure is fixed over time. l5 Although progress in this area of inquiry is siew and tedious, it is strongI:/ suspected that the existence of stochastic policy multipliers tires pradent policy interventions if the aim of policy is to reduce, rather than increase, volatility indices of performance. 7. Sumn;pry remarks Analysis of stochastic simulations of a stti monthly money market model
---The odds are at least two to one that a substantial portion of the increased money market volatility observed in 1980 should not be solely ascribed t.o current operating procedures. -There exists a well behaved tradeoff between the volatility of money stock targeting performance and the volatility of short-term interest rates in the sense that an improvement in the performance of one objective can be exchanged for a bounded deterioration in the performance of the other. --Variations in the desired speed of monthly re-entry to the annual money stock target path, as represented by the short-run money stock objectives of the policy authority, are dominated by tight restrictions on the target range of admissible monthly variations in the Federal funds rate. ---If the target range on the Federal funds rate is suficieutly relaxed, the monthly speed of re-entry to the annual money stock target path estimated for historical procedures in 1980 is approximately efficient +I the sense that faster speeds of re-entry would yreld much larger fluctuations in the Federal funds rate with only small improvements in the volatility performance of the money stock.16 --There is some evidence tirat approximately the same money stock targeting performance can be achieved by a Federal funds rate policy as by a non-borrowed reserves policy at a lower cost in interest rate volatility if the planned zettings of the Federal Tunds rate are suficiently sggressive, Gppenrlix; Planne4I and unpla Federal funds rate I
in the money stock (fM) and the Itemative operating procedures
Table A.1 presents the ess.+ntial structure of the ctaff monthly econometric ‘%x recent empirical evidence on the allocation of uncertainty within the structure of annual and quarterly models in Swamy and Tinsley (1980) and Tin&y, Berry, Fries, Garrett, Norman, Swamy and von zur Muehlcn (1981). 16Estimation of the ‘optimal’ speed of re-entr Y is explored in von zur Muehlen and Tinsley (1!9S1),where a volatility frontier, such as those shown in figs. B.and 5, is confronted with a social indifference mapping derived from a measure of the volatility of prbate wealth.
232
P.A. Tinsley et al., The .&PWU~ volatility qf mowy
stock
targeting
modeli used in stochastic simulations described in this paper. The structure is sufficiently simple that most changes in the patterns of planned and unplanned changes in the money stock and short&m interest rate%.d~ to alterations in operating procedures can be interpreted by direct’inspection of the model as shown below. Table A. f
A skeletal money market model.
Eq.
Description
(1) AM=a,-a,ARFF (2) ARR=b,+blAM <3) AEXR=cO <4) ATR=ARR+-AEXR 65) ABOR=$+d,(ARFF-ARDIS) {6) ANBR= ATR-ABOR {7) ARDlS=e,ARFF
Money demand (stochastic) Required reserves (stochastic) Excess reserves (stochastic) Total reserves (identity) Borrowed reserves (stochastic) Non-borrowed reserves (identity) Discount rate (policy ruIe)
Variable definitions
Coefficient properties
(1) hf
-- money stock - Federal funds rate - required reserves
(0
(2) RFF (3) RR (4) EXR (5) 2-R (6) BOR (7) NBR (8) RDIS
-exessreserws -total reserves - borrowed rwerves - non-borrowed reserves - FR discount rate
el lies between 0 and 1 (iii) random disturbances (intercept coefficients\ a,, bo, co, and do have zero means and constant variances
(ii)
slope
cot@cients al, b,, and d, we all positive discount rate reaction rule
A.I. The model structure This model is a characterization of short-run behavior. Changes in variables (denoted by 8) refer to changes induced by altered settings of the policy instrument and the impacts of random disturbances. The predictions of all excluded variables (such as GNP and price inflation) are presumed invariant to sho+run changes in the policy instruments, Prediction errors of excluded variab,es are contaiued in the relevant random disturbances. For example, if GNP is overpredicted, the money demanct disturbance (ae) will include a negative component. As shown in table A-1, the skeletal model consists of seveui equations. The fast ,equation indieatesthat the denand for .money is inversely relate;d to the Federal funds rate. The next five equations comprise the effective supply of money: The second equation de5nes re+ired reserves. This equation “The complete structure of the F’RB staff monthly econometric model used in t&is study is described in Farr (1980).
PA.
233
Tinsky et d , Tire short-run zmlarility of money stock targeting
contains a random disturbance (6,) representirl,: errors in prajxting the change in required RSWWSthat is associated with a given change in the rno~~+~stock. This error term includes errors in predicting the distribution of the money W& over difkent typa of deposits and among banks of different sizes. The third equation suggests that net changes in excess reserve holdi are unplanned. The fourth equation defines total reserves, and the fiflth ates that borrowings are positively related to the spread between the Federal funds rate and the cost of borrowing. Finally, the sixth equation defines non-borrowed reserves. The seventh, and hat equation, is a characterization of discount rate p&y. The discount rate is at a give level if e, is zero; alternatively, the qmad between the &cant rate and the Federal funds rate is maintained if et is unity. Historical policy lies bcfwccn these two extremes. The historical reaction rule for the discount rate (RDIS) incorporated in th: monthly model suggests that el is about 0.25.” A.?. Pkanningand execution stages The policy authority may choose one of three variables as its policy instrument: total reserves 7’R; non-borrowed reserves NBR; or the Federal funds rate RFF. In table A.2, planned settings of variables are denoted by dp. Table A.2 Planned and utrplwned consequences of alternative operating procedures.
All policies
Change in Federal funds rate
Change in money stock
Planned
Planned
ArRFF-
-I__ - A’M~a,
Unplanned RFF policy
-
ApM Unplanned d”M,,, = a,
where O==a,h,/(a,h,
+d,(l
-e,))
-
YWwripts (g, rr, nbr) detmte policy selection. For example, A”M ,, is the unplanned chzngu in the money stock under an RFF operating procedure. Supersziipts denote planned and unplanncad changes: dPM -‘- p18nned change in M (before random disturbances), d’M unplanned change (fcwecast errar), dM - tot81 observed change (AM = APM+ A’M). cient for the first-month reaction. As fitwi, the historical react on function ‘$This is the c suggests a mean lag in adjuslment of about three and one-half months and full adjustment to an RFF change ia about nine months.
234
B.A. Tinsley et al., The short-run volatility of money stock tar@ng
To illustrate, under a funds rate procedure, the planned change in RFF is determined by the planned target objective for the money stock: APRFF= - APMftll,
where --a1 is the interest rate coefficient in the demand for money [eq. (1) in table A. 1-J. Ni*de that, in the plartnin~ stage, the planned change in the money stock (APM) sought by the policy authority can be viewed as the effective policy instrument. In this stage, the model is cast into a forecast mode by setting all random disturbances to zero (a0 = bo=co=do=O) since zero is the ‘best’ forecast of each prediction error. Given planned money change (ApM), the ..:evenequations of the model are then solved to give the planned settings of !.he remaining seven variables. IQ Since there must be only one solution of the Linear model for a given money stock target, the planned changes of all *variables must be identical under any operating procedure. (This property is explicitly indicated only for planned RFF settings in table A.24 Given the ex ante planned settings, the execution stage of policy is defined by adding nonzero values of the random disturbances (Q, bO,cO,do). Distinctions among operating procedures are determined by the selection of one variable (designated the policy instrument) that is held constant or invariant to the random disturbances encountered during the policy execution stage (however short in duration). Holding one variable constant forces the impact of the random disturbances onto the remaining seven variables (that now include the unplanned change in the money stock APM). Thus., the expected pattern of unplanned changes (denoted by A” .n table h.2) is entirely determined by: (i) the selection of the policy instrument, and (ii) the distributions or typical historical patterns of the random disturbances.2a The methodology of the stochastic simulations, and of that underlying classical econometrics and control theory in general, is that the probabilities of the random disturbances of the model structural relations a.re invariant to variations in the selected policy instruments. In other words, in the case of .II variables subject io m structural ‘laws’, the distri,butions of the random disturbances are invariant to the motion of the n-m ‘instruments’. This does not imply necessarily that the instruments are statistically independent of the realizations of the disturblances as would not be the case for feedback policies. ‘gThus ex ante policy is coherertt in the sense that it is consistent with the stru&nal fOrmsi model of’ the hypothetical policy authority. It would he misteading to characterize this as a ‘rational expectations’ policy since there is no presumption that the subi&ive world view of the policy authority iz.identical to the unobservable mechanism that generates actual events. ‘“The purpose of stochastic simuk+.:ons is to isolate and quantify the role of(i), the selection of the policy inslrument, by using random disturbance patterns similar to those observed in recent history.
PA. Tinsley et 01. The short-run volatilit_v @‘money stock inrgetin,p
235
For models with ad!ditive random disturbances, it may be argued that the stochastic volatility is mtrely allocated Roypolicy since the impact of a random disturbance may be partially or fully absorbed by an instrument without diminishing 9f magnifying the additive disturbance impact.” This would not be true for models with stochastic coefficient stcxtures where stochastic disturbaMses interact multiplicatively wit& the instrument settings. Alternative selections of policy instruments that are he!d invariant between policy intervention dates influence the ultimate destinations of random disturbances. This alteration in the allocation of volatility is a principal reaslan that apparent correlations between target variables and potential instruments (caused by the impacts of common disturbances) seem to break down when the potential instruments are, in fact, employed as policy instruments. This phenomenon, well-known in control theory, may be interpreted as the raison d’etre of Goodhart’s law: ‘Any statistical regularity will tend to collapse once pressure is placed upon it for control purposes’, Wojn.ilo\zer (1980, p. 324). A.3. Sonw utsplannedconsequences of alternative poticy procedure:
is useful to sketch some of the major diffe-ences in unplanned consequences for the money stock and the Federai funds rate under alternative policies: It
A.3.1. RFF as policy instrument
There is no wplanned change in RFF (LtRFF=B’RFF) and unplanned changes in tl;i; money stock (3”.M) are determined only by the random disturbance of the money demand schedule (a,,). A.S.2. TR as policy instrument
In counterpoint to the RFF gmky, the unplanned change in the money stock under a total reserves policy {TR) is wholly determined by two ‘supplyside’ shocks: bO, the forecast err\lr of required reserves, and cO, the forecast error of excess reserves. The rt.,~ its of stachastic simulations presented in the paper suggest that the performance of a total reserves policy is appa,iently sensitive to the accuracy of the required reserves forecast. As indicated in table A.2 the unpla.nncd change in RFF is a function of both demand (ao)l and supply (bo,co) shocks and inversely related to the interest rate. coeficient, of money demand (a,,) and ,cserve requirements (b,). Unplanne: J changes in “The allocation of uncertainty by alternative ieedback strategies and the dran atir alteration!; in projected confidence regions that may -es& arc discussed and illustrated in T.nslcjl and vort 7ur ~ueb~en (1981).
P.A. TinsJeyet al,, The short-runvoJatiJityqimoney st~k targeting
neither money nor RI;F are affected by forecast errors of borrowing (MM) or the discount rate policy (e,). A.3.3. NBR us volicy instrument In several respects, a non-borrowed reserves policy,’ NBR, -may be interpreted as a hybrid policy, mixing elements of both R The unplaaned change in the money stack, d$A&, is a wei the unplanned changes that would be observed under the That is, the weights on unplanned money stock chahges under an RFP’ policy, d”MrJ,, and unplanned money stock changes under a TR policy, BUM,,, sum to unity and are fractional for fractional el, the discount rate reaction coefficient. Thus, under a no+borrowed reserves policy, discount rate policy is an important determinant of the relative impacts of demand and supply side shocks. If larger demand shocks1are expected judgementally in the near term, g1 might be raised closer to unity; conversely, if difficulties are expected in forecasting required reserves, the response of the discount rate might be muted (moving el towards zero), NBR is the only policy where unplanned changes in both the money stock and the funds rate, RFF, may be induced by forecast errors in borrowings (do). Indeed: the presence of the borrowing projection error (do) and a discount reaction (e,) less than unity are the only elements that provide a distinction between NBR and TR policies. That is, if do =O and c1 ==1, NBR policy is identical to TR policy since ABOR, in this case, would always be zero [see eqs. (5) and (6) of table A.1). The results in table A.2 also indicate that unplanned changes in rthc funds rate will tend to be smaller under a NBR policy due to the positive Slope of the effective total reserve supply scheduie under the NB& policy (e, less than unity). Thus, under current assumptions, dispersion of total changes in the Federal funds rate will tend to be smallest under a funds rate policy, RFF, and the largest under a total reserves policy, TR,
Weferences Farr, H.T., 1980, The monthly money market model, FRB working paper, July (revi Nov.). Federal Reserve, 1984 The new Federal Rwrve tech&al proeedtrrcrr for control miIney, attachment to Chairman VoM&s testimony before the Joint Economic Corn on the 1980 EGzonomicReport of t/tie,~Presideg,Feb. 1,81-W. HadjiiW&W,’ I&X3.;_1930, ’ Pre&i& of Monet&y control &,rr,dv&M&$ comparative analysis of the reserve axld the Fe&$ ftnds oarating PTQ special studies paper 15Q. Pierce, D.A., 1980, Data revisions with moving verage !3&;snal adjustment pr of Econometrics 14,95-l 14.
P.A. Tin&y et al., The short-run uoiatdity of mney stock targeting
237
Swamy, P+A.V.B. and F’.A. Tinsiey, 1980, Linear prc&ction and estimation methods for ‘on models witilt stationary stochastic cc&icients, Journal of Econometrics 12, 103Tinsley, P. and I? van zur Muehlen, 1981, A maximum probability approach to short-run policy, Journal of Econometrics 15,31-C-8. Tins&, P.A., 3. B@r$ G. Fries, B. Garrett, A. Norman, P.A.V.B. Swamy and P. von zur Mu&&, 19881,Z’bc impact of .mcertakty on the feasibility of Humphrey-Hawkins Finamx Z%,489-4%. cksirrxi speed of return to the long-run, Mf - A target in 1980, FRB Van
m Mwh~ P. ad P. Tiusk;, 1931, A measure of the social cost of money market voratility, FM3 working paper, Jan W~jnilswer, A.M., 19Ml,The central rdt of credit crunches in recent financial history, Brooking Papns 2.277-326.
Publishing Company
THE .SHORT-RUN VOLATILITY OF MONEY STOCK TARGETING
P.A. TINSLEY, P. vcm zut MUEHLEN and G. FRIES* Fe&d
Remw Board, Washington,DC 20551, USA
The altered ailocationo of money market volatility akined by alternative monetary policy pmosdures are illustrated by st&astic simulations of a staff monthly model. The results indicate the nature af the tradeoff between short-run volatility in the money stock and in the
funds rate that is availnbleto money stock targetingprocedures.
In October 1979, reserves-oriented operating procedures were adopted for the execution of short-run monetary policy. The historical record of money market volatiiity in 1980 was not encouraging. As shown in fig. 1, the standard deviations of both the monthly growth rate of MI -/i and the monthly change m the Federal funds rate increased markedly during the twelve months subsequent to the alteration of procedures in contrast to the standard deviations for the preceding iwelve months. This paper explores the short-run volatility consequences of money stock targeting under current and alternative operating procedures. The focus is narrowly drawn on the feasibiiity of money stock targeting, an issue that may be considered. independently of the desirability of intermediate targeting on monetary aggregates. Two principal issues are considered: --Was the money market btieted by arypical events in 1980 or is there an inherent flaw in current operating procedures that tends to induce volatility in money markets? -‘Does there exist a well-behaved tradeoff between the volatility of deviations of i%C-- A from Ion run targets and the volatility of shorttezm interest rate der current and alternative operating procedures that may be exploited short-run monetary policy?
‘“The authors arc indebt
‘I, r’u~, B. Garrett, J. Lovin, W. Trepeta, V. for the assistuncc of I-Y
%Mcinsand C. Wilson. The views expressed hzin are solely those of the authors and do not nc~&,rily represent the’tiews of the Board of Governors or the staff of the Federal Reserve Syr;tem.
0308-3932/82,UK%4X#O/$O2.75@ 1982 North-Holland
216
P.A. ?Snsley et al., The short-run volatility of money stock targeting GtIMl-A) 40-
I i --ul(Gt)=5.9
-
-u&+)=9.3
/
--
20 -
-20
’ ’ ’ ’ ’ b ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ 80.10 79.10 78.10 .’
G,(Ml -A) - annualized growth of MI-A in month t. - standard deviation of growth rates 78.1039.09. a,(G) - standard deviation of growth rates 79.1l-80 10. ~,G) A RFF 4
I
-8 78.10
79.10
ARFF - change of Federal funds r&e in month t. rr,(dRI:F,) - standard deviation of monthly change 78.10-79.09. ~~r,(dl?FF,)- standard deviation of monthly change 79.1b8O.10.
Fig. I. Historical va.rianility in the monthly growth rate of the money stock and the monthly rhange in the Federal funds rate 1978.10-1980.10.
concept
of short-ran
stocllastic
vohility
High-frquzncy oscillations in the indicators of monetary policy may be viewed with dismay by mane) rzlarket participants, in part because t.hey
P.A. Tinsley et al., The skort-run volatilityof money stock rargering
217
obscure Ehe :,lrderlying intentions of the policy authority. However, not all kinds of meassred increaees in tht variability of money market instruments imply reduced information of policy mtentions. In the case of money stock targeti& the gr~@ v&rL:-biIityin the monthly growth rate of the money stock may be an imr@~o#ate measure sf policy performance. If the money stock is forced off 8 ,\%@eipath by an unallnticipated disturbance, the growth rate of the money stcxk must be aggressi\*ely altered in subsequent months to recover the targeted path. In this case, a more suitable measure of undesirable volatility may be the standard deviation of monthly departures from the money stock target path. Similarly, the dispersion of unexpected chanm in short-term interest rates may ba: 2 more relevant measure of undesirable interest rate volatiiity than the Rnctuations of total changes in interest rates. Thus, in this paper, undesira:Ae volatility is differentiated from gross variability where voiatility is a short-run stkchastic concept referring to the dispersion of outcomes around planneti objectives or expectations. Stochastic volatility is unavoidable in an economic environment that is subjected to unpredictable and sizable disturbances. Where that volatility is allocated within money markets depends importantly on the design of monetary :~~oiicy.Attempts to eradicate transitory variations in target variables* for example, may increase the short-run volatility of other money market variables in excharrge for little improvement in the long-run performance of the target variables. The extent of this unavoidable short-run stochastic volatility and the nature of the tradeoff allocations available to money stock targeting procedures is examined in the remainder of this paper. 3. An ecowimetric portrayal of U.S. money markets and alternative operatirbg w-
An econonurtric pnodel of mnthly financial behavior Estimates of short*run stochastic volatility in money stock targeting procedures have been c btained from stochastic simulations of an econometric model used by the staf!’ to nesate monthly econometric forecasts of money market behavior. The st astic simulation approach was adopted Ito circumvent the lack of an extensive historical track record with the new rating promdures. Stochastic simulations permit 1980 to be ‘rerun’ under alternative random disturbances or under competing policy procedures. In the current version of the model,’ twenty estimated equa.tiolts plus several accounting identities project reserve aggregates, the comlponents of ‘See the appendix for a discussion of the essential economic structure of the monthly model; a simulation characterization of monthly monetary policy, and a brief disc&on of the methodology underlying stochastic simulations. A complete description of ihie FRB staff monthly econometric model is ptovided in Farr (1980).
P.A. Timley et ol., The &ort-am oolatility ojmoney stock targeting
218
M --3,and selected short-term interest rates, given judgemental projections of the monthly paths of personal income and the consumer price index (VI), and an assumed. path for the policy instrument [non-borrowed reserves (NBR), total reserves (TR), or the Federal funds rate (WF)]. Red economic activity is exogenous in this model and not
(a)
Setting
interim objective
target objective
PA. Tirtsley et al., The short-run ookz‘atilityof mane! stack targeting
4.’ . . .
219
InMT
‘/
In q (X=4)
,’
/1’
/
(/
/ 1’
0
,**In rq (X=0)
P
.b
. . 1
I
2
12
t
MT -- MI - 9 target path (4.75% annual growth,, MI _=-pto_jrxtedMI-A in month 1, W -- interim MI -A target for month 2. (a) 1 =Q ndt closure of re!ative target gap (base drift), :b) I== 1; fufl closure of relative target gap in one month, 1 __ qsnthly rat=.af re-entry to annual target path (MT), In -- rraturd lop rithm. Fig. 2. Selection of interim MI -A target.
If A= 1, the policy authority plans to return to the annual target path, MT in ON month. Conversely, if A-0, the authority pEat?sto achieve an annualized monthly growth in AlI --A equal to the annuabd growth rate of ihe target ~4*~5~)but starti from the current money stock, Ml, rather thrn ihe target value for month Thus, Lr the case of 1x0, the policy authority does not uce the reilativc money stock target gap in month 2, a choice et selection, the selection of tlld:t-e-entry es the persistence of past random disturbances in the current df A,= 1, the &ect of a random disturbance rn~ney stack target gap, q/M,. in period 1 that causes the rnonzy stock, Ml, to deviate from targeted money, AK_&is elirn~~at~~din one month. Since the re-entrv rate is months in the plElnning horizon, a zero re-entcp ate in=O) ianI ~ff~~ti~~~ duration of the impact of a random isturbance is infinite since there will be no planned offset. A re-entry rate, A, can be converted to an
220
P.A. 7lndey et al., The short-run volarifity of money stock targeting
implied monthly age, A, of random disturbances in the money stock tl-rget gap, as shown in table l., The typical monthly re-entry rate of cupienl targeting proce ,Jures in 1980, as estimated by Trepeta (1980), is 0.292. This Implies an average age of random disturbances in the annual money stock target gap of about three arid one-half months? Table 1 Translation of monthly re-entry rate (A)to average age (A) of money stock target miwes. Re-en r’yrate (A) -_ 1 0.333 0.292’ 0.167 -4verage monthly age Wb
1
3
3.4
6
0.111
0
9
a.I
“Estimated monthly re-entry rate of historical interim targeting prooedures 80.02-80.1J; see Trepeta (1980). bAverage age (in months) of random disturbances in the money stock target gap (In MI; - ln M,). More explicitly, A=J i i(l-I)‘-‘=1/;1. i=l
(6) Setting the policy instrument.
A. plan&led setting for the intenneeting interval (represented by the follo.+ving month in this discussion) is then selected for one of three possible policy instruments: non-borrowed reserves (NBR), total reserves (7X), or the Federal funds rate (RFF). The selection of the policy instrument setting is approximated in model simulation exercises by the following procedure: It is assumed that the projection of the money stock in the current month of the meetin sufficiently accurate so that any remaining forecast error may be ne foreCast of money market btlrhavior in the following month is then by the staff monthly model as if the interim money stosk tar mopth is the effective policy instrument. This forecast p~lu non-borrowed reserves (NBR, total reserves (TR), and the Fbderal funds rate (RFF) that are consistrnt with achieving the interim money stock tar at least in the absence of forecast errors. In some of the cases analyzb:d, the FOMC is assumed trc)impose a tw range so that the Federal funds rate cannot move by more than 308 basis 2Due to the nature of exponential decay, cornpI& elimination of the influence of a @rivcen disturbance to the money stock can be a lengthy process. FOP il==O.292,seven mwths are re+ired to eliminate WA of a given disturbance. (One month is required for ,I =LZ 1 and twenty mS3nthsfor d=O.lll.)
P-A. IInsley et al., The short-run lmiatility of money stock far;ge!inR
221
points from the current month to the following month.3 In these cases, the funds rate constraint must be satisfied in both the ex ante policy planning; stage and in the ex poti policy execution stage (when random disturbanm are encounter4 as explained shortly). (c) Si?~iutton of s&sequent ‘history+. Following the selection of F p&q instrument setting (either non-borrowed reserves, total reserves, or the Federal funds rate) that will achieve the interim money stock targzt, M*, in the absence of random disturbanceq the model is resirnulated in the second month with non-zero random disturbances. All variables except the polis!y instrument are &&ted by the random disturbances. There are two types of stochastic simulations: (i) In psuedo-history stochastic simulations of 1980 (1980.01~1980.10), the historical monthly forecast errors of the: model are incorporated in the simulation. Thus, if the policy instrument is set at its historical path, actual monthly history would be simulated for all variables in the psecdo-history simulations. (ii) In average-history stoch;tstic simulations, random disturbances similar in pattern and size to nod-’,.. .CIIecast L* errors encountered during the I+ :: year sample period, 1971.01 through 1979.12, are incorporated.’ The purpose of averagehistory sin&&ions .is to examine the robustness of the response of alternative operating prwdures to a full spectrum of plausible random disturbance patterns. In summary, the planning stage of a monthly policy operating procedure is characterized by two components: (a) seleciion of the interim target for the money stock, AP, as determined by the rate of monthly re-entry, i., to the annual target path, MT; znd (b) selection of the policy instrument [non30nc motivationfor a tzugetrangeon au auxiliary variable,such as the Federalfunds rate in
~WUV~CI pdicy,is to provide a rough check for operatiollzi breakdownsof the a aon-borrowod
planniqjmod&If actual events move the auxiliary variableoutside the auxiliary target range, actua!eventsmay not be statistically compatible with the ex 4tlte forecast.Whr.nthis OCSWS, the pknning mxkl my be cimii~g some iagndimt in the structureof the actuai eccnomy, and the authorityUUL~ ti& to r~~&dcf plannedpolicy. Using this interpretation,the target range for tba auxiliary v viable should bear some resemblti:lceto iI confidenceinterval of the ex MC projectionof the au?itliiir ty wiabk. ‘In all policy &nuiatirlru,t. Fe&al funds rate was subject to a tloor of two percentage pointi and a c&in& of forty percentagepoints to prevent simulation of events that are far remotradfrom the sutmpk zxpetience. in simulations where a reserve aggregateis the policy inetrumsat,if the F&A Cm& rate hit a target range boundary on the monthly change or a on de kvcl, the Federal funds rate isecamethe effectivepolicy instrument am&r the execution stage of that month. bails of tie stochastic simulations reproducethe cross correlationsof the historicalihotithly’ fore&&errorsof the model, both over time and across equations in a given month. ‘I’%& stand& deviation of the monthly foreutst -or of demand deposits v as increased by about f$d to account for ex .~t informationon recent shifts in the money dc.lrand function that is’inuoprated in the mrrmt version of the model. This information is introduced into the made1 by shift piaameters whzh include rough approximations for the impact of repurchase ag.zements, the appearanceof ATS accounts and so on. poticy
P.A. Tin&y
222
et al., The short-run
volatility
qf money stock targeting
borrowed reserves (N&R), total reserves (TR), or the Federal funds rate (RFF)] that will be held invariant to incoming random disturbances throughout the subsequent month. The execution stage of monthly policy is represented by a stochastic simulation where the effect of the planned policy is evaluated by a monthly model simulation having non-zero random disturbances. The policy cycle consisting of: (a) selection of the monthly interim money stock target, (b) selection of the monthly policy instrument setting, and (c) execution of monthly policy under random disturbances. is repeated in each month of the effective policy horizon, 1980.01 to 1980.10.
4. A comparison of peado-historical PBWS .&verageperformance of current lk
annual performance af an operating policy procedure depends to a great exten; on the type of random disturbances encountered. As noted in the appendix, some policies are more vulnerable to shocks to the demand for money while others are more affected by supply side shocks. It is of interest to determine whether the intra-year deviations of the actual money’ stock, M, from the annual target path, M7: were due to some inherent flaw in the current operating procedure or whether the random disturbances encountered in the first ten months of 1980 were atypical (incorporating the impacts of unusual events such as the imposition of special credit restraints
in mid-March). Three policy ‘histories’for MI -A are presented in fig. 3: The first is actual MI -4, denoted by M. This can %e obtained by simulating, the monthly model over the first ten months of 1980 with’historical disturbances and with m.anthly non-borrowed reserves, NBR, maintained on its historical path. The two remaining ‘pseudo-historical’ paths, MS, and MS,,, are also obtaitlcd by simulations with historical disturbances, but the non-borrowed reserves paths, NBR, and NBR,,, of these simulations are obtained by werage approximations of current operating procedures. En both cases, the constant monthly rate of re-entry, L, to the target money stock path was set at the average value estimated for historical planned policy in 1980, 1=0.2X!. Also, both policies were subject tu the restrict&i “th&tthe monthly’ change. in the Federal funds rate could not exceed,.3O&basispoints. Since ‘both_the monrhiy rate of re-entry, 1, curd the effective Federal funds rate &get, range are only G:uerag@ approximat lens of historical policy; the ‘simulated results till. xcover
4y
approximationis of the consequences of actual policy.
PA. Tin&y et al., 7%~ shott-tun rdatilityqf money stock targeting
223
In the first approximation of historical procedu.res, labeled ‘MM policy (restric ‘x! ARFF)‘, the simulated policy authority selects that level of nonborrowed reserves, NBR, that will attain the interim money target, M*, in the absence of random disturbances but subject to a monthly target range of eral funds rate, RFF. When subjected to this approximation of poky, denoted NBR,, As shown in fig. 3, this policy closely mimics oney stock (M) in the first six months of 1980, more slowly to the annual target path (MT) in the
8003
80.06
80.G9
LOW -- lower boundary of 700/,confidenceintervalfor NBR policy (restricted ARFt’), M p__historicalMI-A, simulated‘history’-- h BR policy (restricted RFF) wit.h historical disturbances, MS. _yyp BR policy (BGR = BOR _ 1) with historical disturbances, AR& - simulated‘his&q’ -- EC MT .- targetMI - A (4.750/,a1lual growth 79.1G-80.1I), HKiW-- upper boundary of 70”/,confidenceintervalfor NBR policy lrcstricted dRWj.
Fig. 3. Hb;toricaland expected performanceof currentproadures.
The second approximation to current operating procedures is similar to NRR, but the simulated policy authority first selects a total reserves estimate, 7X,.. consistent with the interim money stock target. In this policy, the nonpath, NB&, is obtained by subtracting the current of borrowed res rves, MN? - 1.7 In other words, the by the policy authority a ~o~~ti~uationof current bor ent setting, AM&,= TR tic.;a of the non-borrowed “The return to target path is inhibited by the reatrictionthat the monthly RFF change must in actual history the Fe&al funds rate dropped by reserves -. that is total reserves less member beak barrnvring Fborrowing near that prevailing in :he most recent
224
P.A. Tin&y et al., The short-run volatility of money stock targeting
-BON _ 1, This policy approximation, N&R,,, is identified as ‘NB13 policy (IN% ==BOR_ J and is also subject to the restriction that the monthly target range for RFF cannot exceed six percentage points. The money stock attained by this policy under 1980 disturbances is labeled MS,,. As noted in fig. 3, the ten-month growth of the money stock of this @icy approximation is quite close to actui4 history except during April 1980 when the decrease is not as protrounced.8 The results in fig. 3 suggest that the two non-borrowed reserves policies are reasonable approximations of current operating procedures since the resultant money stocks, MS, and MSb, bracket the result of historical operating procedures, !V. To estimate the range of money stock outcomes that might have occurred under current operating procedures had 19% been an ‘average’ year, a 70% confidence interval was generated for the first approximation of current policy, MBR,.” The 70% confidence interval is obtaiued from 100 stochastic simulations of the first ten months of 1980. Random disturbances for each simulation differ but are selected to replicate the historical pattern of the forecast errors encountered by the monthly mod,! over the nine year sample, 1971.01-1979.12. After 100 simulated histories are generated by the average approximation of current operating procedures, the upper fifteen and lower fifteen of simulated money stocks in each month are removed to define the boundaries of the 70% confidence interval shown in fig. 3. As indicated, both the iactual money stock (M) and the ‘pseudo-historical’ money stocks (MS, and MS,) obtained using 1980 h&>&al disturbances fall below the 70% confidence interval in at least three of the first ten months of 19SO. Under the assumption that the relative accuracy of the model des.,ription of money market behavior is not substantially affected by the shift in operating procedures, this result suggests that the odds are at least two to one that a substantial portion of the gyrations 3f the money stock observed during 1980 can be ascribed to unusually severe disturbautis encountered in 1980 and not to instability generated by current operating procedures, 5. Expected volatility tradeoffs under alternative operating procedures This secticn examines the volatility implications of varying the monthly rate of re-entry, R, to the money stock barge! path, MT The volatihty of the *fhis policy tends to produce more modest changes in the Federal funds rat@since the simulated policy authority does not implicitly recognize the projected offset in borrowed reserves when sekcting the planned change in the supply of non-borrowed reserves. %elative to the annual target path, M?: there is a di,scemible *‘upside risk’ imp&d by the Sective midline of the 70% confidence interval. This is due, in part, to the logarithmic formulation of money demand in the monthly model. To illustrate, if the loga ithmic forecast error is normally distributed, tn M-In A.?=a, E- N(0,a2), the mean of the simulated forecasts, E(M), will exceed the certainty-equivalent (zero residual) forecast, #, E(M)= & e@*)‘.
F.A. Tin&y et ai., The short-run volatility of money stock targeting
225
Federal funds rate is rpnresented by r$e standard deviation of the monti?ly change, a(MWF). Under general conditions, this statistic can be interpreted as one-half the widzthof the ?o”/, conEdence interval for month-to-month variations in RFF. The *:olatility of money stock performance is measured by the square root of squared monthly deviations of the annualized cumulative growth rate of the money stock from the annualized cumulative growth rate of the money stock target, where the latter is 4.75% for every month in the policy horizon. The root mean square error, RMSE, penalizes persiste.nt ‘biases’ in performance @en the money stock consistently grows below or above the target path as in the case of base drift. In dl cases reported below, the mean bias is negligible (since the average random disturbance is zro) so the RMSE corresponds closely to the standarcl deviation and is approximately equal to one-half the range of the 70% confidence interval for monthly departures from 4.75% growth. It can be demonstrated that this volatility measure of monthly cumulative growth rates around 4.75% is equivalent to the RMSE of the logarithm of the annualized monthly target gap, RMSE(GAP), where GAP, = la (M c/M,) - 1200/t. in the results discussed below, a root mean square error of two, RMSE(GAP)=2.0, indicates that the annualized cumulative growth rate of the money stock in a given month will fall between 6.75% (4.75 +2.0) a:nd 2.75% (4.75 - 2.0) with approximately 707; probability.” The results that follow tabulate the expected tradeoff between target gap volatility of the money stock and the volatility of the Federal funds rate. Points on the volattility tradeoff ‘frontier’ are generated by altering the monthly rate of re-entry, il, to the money stock target path. As the monthly rate of re-entry movies from zero (base drift) to unity (full gap closure), it is of interest to determine if the frontier is ‘unstable’ (positively sloped) or wellbehaved (negatively sloped), In the case of the former, the volatility of both the money stock target gap and the Federal funds rate would increase with tht speed of monthly re-entry, suggesting that a viable tradeoff does not exist. In the latter case, an increase in the volatility of the Federal funds r;:tte can be exchanged fo: a reduction in the votatility of the monthly target gap. The volatility frontier is estimated for a particulalr policy by averagehistory simulations of the monthly econometric model. As discussed eariier, the pattern of randola disturbances of average-history stochastic simulations resembles the pattern of historical forecast errors generated b;~ the monthly mode! over the sample span, i971.01-1979.12.
Thus,
‘OThesimulation results do not include an estimate of ‘noise’ introduced by preliminary seasonal adjustment. An examination of recent work by Pierce (19801 suggests that ~~llmal~ of the target gap volatility presented below underestimate total money stock volatility by &out one percentage point.
P.A. Tin&y et al., The showrun volatility qf money std
226
targeting
Four operating procedures are examined: non-borrowed reserves are selected as the policy instrument held invariant to random disturbances during the policy execution stage of each month. 0ii ?TBR (restricted ARFF) - the non-borrowed reserves policy is subject to a Federal funds target range of six percentage points. That is, the monthly change in the Federal funds rate cannot exceed three hundred basis points in either the policy planning stage, the policy exmution stage, or both. (iii) REF - the Federal funds rate is szlccted as the policy instrument held invariant to random disturbances in the policy execution stage of each month. Thus, all monthly changes in the Federal funds rate under this policy are planned changes selected in the planning stage to return the money stock to its interim target level, total reserves is selected as the policy instrument held invariant ( iv) TR to the impact of random disturbances in the policy execution stage of each month.
0i
NBR -
Tradeoffs irr the volatility of the Federal funds rate and the volatility of the money stock target gaps under the four alternative operating proadures are displayed in figs. 4-6. The horizontal axis indicates interest rate volatility as represented by the standard deviation of monthly changes in the funds rate, a(ARFF), measured in percentage points. The vertical axis provides two measures of money stock target gap volatility: The upper panel (going up from the horizontal axis) indicates the monthly volatility in money stock target gaps for all months in a sample of ten-month policy horizons. Thus, the upper panel measures month-to-month variability of the money stock target gap within a ten-month ‘year’. The lower panel (going down from the horizontal axis) measures the volatility of the terminal gap at the end of a tea-month ‘Iyear’.It is assumed that the policy authority wishes to reduce all measures of volatility: money stock target gap volatility withm a policy year, RAGE (GAP,); terminal target gap volatility, RMSB(G.4PB0 &; and funds rate volatility, a(ARFF,). However, the results indicate that this is not possible. !%esultsfor the unrestricted1 1 non-borrowed reserves policy, ‘MM policy’, are displayed on the right side of fig. 4. For the case of base drift (A=O), th upper panel indicates that a target gap volatility of about 2,26g/, is obtained by the NBR policy at the cost of a monthly funds rate volatility of about 5.9 percentage points. As the monthly re-entry rate, 1, moves toward unity, the “As noted earIier, this policy is not subject to a tic in the Federal funds rate.
t range restriction on ~~n~h~y changea
P.A. Tinsley
et al., The short-run
uotatifity
of money stock targeting
227
a(dRFFt) -- standard deviation of raonthly change in RFf’,
RMSE GAP,
-
root mean square error, log of annualized relative gap between targ:t mon,.y and actual money in wunth
GAPso.u, #I
-
&J of annualized @,apin last month of hoti/ -n (&O.lct), monthly rate gf re-entry to the money stock annual iatget path. Fig. 4. Re-entty tradeoff schedules, non-horrowed reserve policies.
volatility of the monthly money stock target gap is r&ced at the cost of an &muse in monthly fund:3rate volatility. Thus, the trade-of? moves in a southeasterly direction &g the reentry rate, 1, increases. At ;1= 1, the unrestricted NBR policy obtains a 600/Oreduction in monthly money stock volatility tit the cost of a 75% increase in the monthly volatility of t funds rate, RFF? As the ntsntpy rate, 4 goes to unity, the monthly money stock target gap to zltro. This is because the re-entry rate is established volatitity does not in the ~l~n~~~~~stage wi,hhout benefit of perfect foresight of the random disturbances that will be encountered during the subseqrtent month. Thus, 1.3”11,is the lowest monthly gap volatility that can be achieved by the unrestricted ,?VBRpolicy, at the cost of a monthly funds rate volatility of 10.2 ItThis may be a rel?lvely optimistic tradeoff sins:: the short-run and long-run interest rate clzsticities of the demand &tt money in the staff montXy model were the highest among models e~~rni~~d by the awjthors.
228
a(ARFF,)
RMSE GAP,
standard deviation of monthly change in RFFs - root mean square error, - log of annualized relative gap between target money and actual money in month&
-
GAP,,.to - ;bg of annualized gap in last month of horizon (80.10),
2
- monthly rate of re-entry to the money stock annual target path. Fig. 5. Rc-entry tradeoff schedules, Federal funds rate policlr.
percentage points. Note also that not much is gained in terms of a reduction in monthly money, stock volatility by moving from A=@292 (the estimated historical rate of r-e-entry) to A= 1 (planned complete closure of ‘the money stock target gapin one month). The bottom panel is roughly a mirror image of, the top panel ex?pt that the temrinal gap volatility measures for corresponding rates of r-e-entry,E,.are uniformly lower. This property was found for all policies examined and indicates that a’il policies will be more successful in attaining year-over-year targets than in maintaining close adherencze to the target’ path’ within the year. The Leftsides of the panels. ia fig. 4 indicatethe expected ,volqtiljty tradeoff for a non-borrou;red,reserv,esp&y- that js subjeot)ITV:‘d tmgy -~st&@m of.six percentage points on monthly changes in the Federal fu~~.Israte+ @‘I? This palicy is a closer approximation to current operating procedures than the unrestricted N.BRpolicy. The results in fig. 4 suggest that Vmkiian h’t6e’re~ entry rate under ,:urrent procedures is largely futile &no3 ~~o~a~~ is
PA.
Tiy
et ‘al., Tk
sbt-nm
uolarility ofmoneystock targeting
228
X=0
6
.
\
X=J
3
6
a(ARFFJ -- standard devktion of monthly change, ir, RFF, RJUSE GAP,
-_ root mean square error, - log of annualizd relative gap between target money and actual money in month
GAPtW.,Q --, kg of annualized gap in last ~YMII of horizon (&O.lO), 1 =- monthly rate of re-cntry to th:: -money stock annual target path.
Fig. 6. Re-ent.y trade-off schedulen. toiui riaiarvespolicy.
domiaaeod by the imposition of the target range restriction on monthly
variationof the Fedeg;Jfunds rate, Fig. 5 indicates the expected tradeoffs for an unrestricted interest rate policy where the -Federal funds rate, RI;.F, rather than non-borrowed rves, is held catastmt during the month. Of course, the Federal funds rate is reset at the beginning of each month to obtain the interim money stock
objective, One characteristic of the unrestricted interest rate policy, RFF, is that compmb~e redwtiosrs in both monthly and terminal gap volatility are abtained at lower levels of interetit rate volatility. That is, at the historical 3 A=O.292 the monthly money stock gap volatility rate of planned non-barrowti reserves policy, NBR, is 1.6, a result uiider an unrest that @dose to the if.5 obtained for the unrestricted interest rate policy, RFF. milarly, ‘the term3ra.I gap volatility at R=0.292 is 0.56 for the unrestricted BR policy and 0.58 for the RFF policy. However, the corresponding
monthly RFF volatility measure at J =O 292 is 8.0 percen ta: P:it.\fS fc
All policy analysis is model specifr;: and the results of this paper are not exempt from this dictum. Two limitations of the existing monthly econometric model may be noted. As indicated in the a.ppendix, the economic structure and scope of the current monthly econometric model are limited. It would be desirable to incorporate a full specirum of portfolio adjustments by bank and nonbank sectors14 as well as interactions between real and financial economic activity. Efforts in these directions are impded by the limited scope of available monthly data. (ii) Stochastic simulations provide a more robust method of analysis than deterministic simulations since they account for the historical forecast error record of the model employed. Although the boundary limits of uncertainty are delineated by this method of ana!yr;is, all uncertainty in the current model is allocated to additive ex&rnal ‘surprises’. There is accumulating evidence that the essential structure of the economy is better described by allocations of forecast uncert&ty over all model (i)
13Since, as noted in the appendix, planned settings of the funds r.rte are idcnticcd under all poiicies, the results in fig. 5 could be obtained approximately by a non-borrowed reserves policy with a relatively wide target range on planned changes in the funds rate hnd tight restrictions on unplanned changes in the funds rate. Y’heoretical examination of a compiete capital account model is provides by Hadjimichalakis (1980).
coefficients, in contrast to the conventional assumption that the model structure is fixed over time. l5 Although progress in this area of inquiry is siew and tedious, it is strongI:/ suspected that the existence of stochastic policy multipliers tires pradent policy interventions if the aim of policy is to reduce, rather than increase, volatility indices of performance. 7. Sumn;pry remarks Analysis of stochastic simulations of a stti monthly money market model
---The odds are at least two to one that a substantial portion of the increased money market volatility observed in 1980 should not be solely ascribed t.o current operating procedures. -There exists a well behaved tradeoff between the volatility of money stock targeting performance and the volatility of short-term interest rates in the sense that an improvement in the performance of one objective can be exchanged for a bounded deterioration in the performance of the other. --Variations in the desired speed of monthly re-entry to the annual money stock target path, as represented by the short-run money stock objectives of the policy authority, are dominated by tight restrictions on the target range of admissible monthly variations in the Federal funds rate. ---If the target range on the Federal funds rate is suficieutly relaxed, the monthly speed of re-entry to the annual money stock target path estimated for historical procedures in 1980 is approximately efficient +I the sense that faster speeds of re-entry would yreld much larger fluctuations in the Federal funds rate with only small improvements in the volatility performance of the money stock.16 --There is some evidence tirat approximately the same money stock targeting performance can be achieved by a Federal funds rate policy as by a non-borrowed reserves policy at a lower cost in interest rate volatility if the planned zettings of the Federal Tunds rate are suficiently sggressive, Gppenrlix; Planne4I and unpla Federal funds rate I
in the money stock (fM) and the Itemative operating procedures
Table A.1 presents the ess.+ntial structure of the ctaff monthly econometric ‘%x recent empirical evidence on the allocation of uncertainty within the structure of annual and quarterly models in Swamy and Tinsley (1980) and Tin&y, Berry, Fries, Garrett, Norman, Swamy and von zur Muehlcn (1981). 16Estimation of the ‘optimal’ speed of re-entr Y is explored in von zur Muehlen and Tinsley (1!9S1),where a volatility frontier, such as those shown in figs. B.and 5, is confronted with a social indifference mapping derived from a measure of the volatility of prbate wealth.
232
P.A. Tinsley et al., The .&PWU~ volatility qf mowy
stock
targeting
modeli used in stochastic simulations described in this paper. The structure is sufficiently simple that most changes in the patterns of planned and unplanned changes in the money stock and short&m interest rate%.d~ to alterations in operating procedures can be interpreted by direct’inspection of the model as shown below. Table A. f
A skeletal money market model.
Eq.
Description
(1) AM=a,-a,ARFF (2) ARR=b,+blAM <3) AEXR=cO <4) ATR=ARR+-AEXR 65) ABOR=$+d,(ARFF-ARDIS) {6) ANBR= ATR-ABOR {7) ARDlS=e,ARFF
Money demand (stochastic) Required reserves (stochastic) Excess reserves (stochastic) Total reserves (identity) Borrowed reserves (stochastic) Non-borrowed reserves (identity) Discount rate (policy ruIe)
Variable definitions
Coefficient properties
(1) hf
-- money stock - Federal funds rate - required reserves
(0
(2) RFF (3) RR (4) EXR (5) 2-R (6) BOR (7) NBR (8) RDIS
-exessreserws -total reserves - borrowed rwerves - non-borrowed reserves - FR discount rate
el lies between 0 and 1 (iii) random disturbances (intercept coefficients\ a,, bo, co, and do have zero means and constant variances
(ii)
slope
cot@cients al, b,, and d, we all positive discount rate reaction rule
A.I. The model structure This model is a characterization of short-run behavior. Changes in variables (denoted by 8) refer to changes induced by altered settings of the policy instrument and the impacts of random disturbances. The predictions of all excluded variables (such as GNP and price inflation) are presumed invariant to sho+run changes in the policy instruments, Prediction errors of excluded variab,es are contaiued in the relevant random disturbances. For example, if GNP is overpredicted, the money demanct disturbance (ae) will include a negative component. As shown in table A-1, the skeletal model consists of seveui equations. The fast ,equation indieatesthat the denand for .money is inversely relate;d to the Federal funds rate. The next five equations comprise the effective supply of money: The second equation de5nes re+ired reserves. This equation “The complete structure of the F’RB staff monthly econometric model used in t&is study is described in Farr (1980).
PA.
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Tinsky et d , Tire short-run zmlarility of money stock targeting
contains a random disturbance (6,) representirl,: errors in prajxting the change in required RSWWSthat is associated with a given change in the rno~~+~stock. This error term includes errors in predicting the distribution of the money W& over difkent typa of deposits and among banks of different sizes. The third equation suggests that net changes in excess reserve holdi are unplanned. The fourth equation defines total reserves, and the fiflth ates that borrowings are positively related to the spread between the Federal funds rate and the cost of borrowing. Finally, the sixth equation defines non-borrowed reserves. The seventh, and hat equation, is a characterization of discount rate p&y. The discount rate is at a give level if e, is zero; alternatively, the qmad between the &cant rate and the Federal funds rate is maintained if et is unity. Historical policy lies bcfwccn these two extremes. The historical reaction rule for the discount rate (RDIS) incorporated in th: monthly model suggests that el is about 0.25.” A.?. Pkanningand execution stages The policy authority may choose one of three variables as its policy instrument: total reserves 7’R; non-borrowed reserves NBR; or the Federal funds rate RFF. In table A.2, planned settings of variables are denoted by dp. Table A.2 Planned and utrplwned consequences of alternative operating procedures.
All policies
Change in Federal funds rate
Change in money stock
Planned
Planned
ArRFF-
-I__ - A’M~a,
Unplanned RFF policy
-
ApM Unplanned d”M,,, = a,
where O==a,h,/(a,h,
+d,(l
-e,))
-
YWwripts (g, rr, nbr) detmte policy selection. For example, A”M ,, is the unplanned chzngu in the money stock under an RFF operating procedure. Supersziipts denote planned and unplanncad changes: dPM -‘- p18nned change in M (before random disturbances), d’M unplanned change (fcwecast errar), dM - tot81 observed change (AM = APM+ A’M). cient for the first-month reaction. As fitwi, the historical react on function ‘$This is the c suggests a mean lag in adjuslment of about three and one-half months and full adjustment to an RFF change ia about nine months.
234
B.A. Tinsley et al., The short-run volatility of money stock tar@ng
To illustrate, under a funds rate procedure, the planned change in RFF is determined by the planned target objective for the money stock: APRFF= - APMftll,
where --a1 is the interest rate coefficient in the demand for money [eq. (1) in table A. 1-J. Ni*de that, in the plartnin~ stage, the planned change in the money stock (APM) sought by the policy authority can be viewed as the effective policy instrument. In this stage, the model is cast into a forecast mode by setting all random disturbances to zero (a0 = bo=co=do=O) since zero is the ‘best’ forecast of each prediction error. Given planned money change (ApM), the ..:evenequations of the model are then solved to give the planned settings of !.he remaining seven variables. IQ Since there must be only one solution of the Linear model for a given money stock target, the planned changes of all *variables must be identical under any operating procedure. (This property is explicitly indicated only for planned RFF settings in table A.24 Given the ex ante planned settings, the execution stage of policy is defined by adding nonzero values of the random disturbances (Q, bO,cO,do). Distinctions among operating procedures are determined by the selection of one variable (designated the policy instrument) that is held constant or invariant to the random disturbances encountered during the policy execution stage (however short in duration). Holding one variable constant forces the impact of the random disturbances onto the remaining seven variables (that now include the unplanned change in the money stock APM). Thus., the expected pattern of unplanned changes (denoted by A” .n table h.2) is entirely determined by: (i) the selection of the policy instrument, and (ii) the distributions or typical historical patterns of the random disturbances.2a The methodology of the stochastic simulations, and of that underlying classical econometrics and control theory in general, is that the probabilities of the random disturbances of the model structural relations a.re invariant to variations in the selected policy instruments. In other words, in the case of .II variables subject io m structural ‘laws’, the distri,butions of the random disturbances are invariant to the motion of the n-m ‘instruments’. This does not imply necessarily that the instruments are statistically independent of the realizations of the disturblances as would not be the case for feedback policies. ‘gThus ex ante policy is coherertt in the sense that it is consistent with the stru&nal fOrmsi model of’ the hypothetical policy authority. It would he misteading to characterize this as a ‘rational expectations’ policy since there is no presumption that the subi&ive world view of the policy authority iz.identical to the unobservable mechanism that generates actual events. ‘“The purpose of stochastic simuk+.:ons is to isolate and quantify the role of(i), the selection of the policy inslrument, by using random disturbance patterns similar to those observed in recent history.
PA. Tinsley et 01. The short-run volatilit_v @‘money stock inrgetin,p
235
For models with ad!ditive random disturbances, it may be argued that the stochastic volatility is mtrely allocated Roypolicy since the impact of a random disturbance may be partially or fully absorbed by an instrument without diminishing 9f magnifying the additive disturbance impact.” This would not be true for models with stochastic coefficient stcxtures where stochastic disturbaMses interact multiplicatively wit& the instrument settings. Alternative selections of policy instruments that are he!d invariant between policy intervention dates influence the ultimate destinations of random disturbances. This alteration in the allocation of volatility is a principal reaslan that apparent correlations between target variables and potential instruments (caused by the impacts of common disturbances) seem to break down when the potential instruments are, in fact, employed as policy instruments. This phenomenon, well-known in control theory, may be interpreted as the raison d’etre of Goodhart’s law: ‘Any statistical regularity will tend to collapse once pressure is placed upon it for control purposes’, Wojn.ilo\zer (1980, p. 324). A.3. Sonw utsplannedconsequences of alternative poticy procedure:
is useful to sketch some of the major diffe-ences in unplanned consequences for the money stock and the Federai funds rate under alternative policies: It
A.3.1. RFF as policy instrument
There is no wplanned change in RFF (LtRFF=B’RFF) and unplanned changes in tl;i; money stock (3”.M) are determined only by the random disturbance of the money demand schedule (a,,). A.S.2. TR as policy instrument
In counterpoint to the RFF gmky, the unplanned change in the money stock under a total reserves policy {TR) is wholly determined by two ‘supplyside’ shocks: bO, the forecast err\lr of required reserves, and cO, the forecast error of excess reserves. The rt.,~ its of stachastic simulations presented in the paper suggest that the performance of a total reserves policy is appa,iently sensitive to the accuracy of the required reserves forecast. As indicated in table A.2 the unpla.nncd change in RFF is a function of both demand (ao)l and supply (bo,co) shocks and inversely related to the interest rate. coeficient, of money demand (a,,) and ,cserve requirements (b,). Unplanne: J changes in “The allocation of uncertainty by alternative ieedback strategies and the dran atir alteration!; in projected confidence regions that may -es& arc discussed and illustrated in T.nslcjl and vort 7ur ~ueb~en (1981).
P.A. TinsJeyet al,, The short-runvoJatiJityqimoney st~k targeting
neither money nor RI;F are affected by forecast errors of borrowing (MM) or the discount rate policy (e,). A.3.3. NBR us volicy instrument In several respects, a non-borrowed reserves policy,’ NBR, -may be interpreted as a hybrid policy, mixing elements of both R The unplaaned change in the money stack, d$A&, is a wei the unplanned changes that would be observed under the That is, the weights on unplanned money stock chahges under an RFP’ policy, d”MrJ,, and unplanned money stock changes under a TR policy, BUM,,, sum to unity and are fractional for fractional el, the discount rate reaction coefficient. Thus, under a no+borrowed reserves policy, discount rate policy is an important determinant of the relative impacts of demand and supply side shocks. If larger demand shocks1are expected judgementally in the near term, g1 might be raised closer to unity; conversely, if difficulties are expected in forecasting required reserves, the response of the discount rate might be muted (moving el towards zero), NBR is the only policy where unplanned changes in both the money stock and the funds rate, RFF, may be induced by forecast errors in borrowings (do). Indeed: the presence of the borrowing projection error (do) and a discount reaction (e,) less than unity are the only elements that provide a distinction between NBR and TR policies. That is, if do =O and c1 ==1, NBR policy is identical to TR policy since ABOR, in this case, would always be zero [see eqs. (5) and (6) of table A.1). The results in table A.2 also indicate that unplanned changes in rthc funds rate will tend to be smaller under a NBR policy due to the positive Slope of the effective total reserve supply scheduie under the NB& policy (e, less than unity). Thus, under current assumptions, dispersion of total changes in the Federal funds rate will tend to be smallest under a funds rate policy, RFF, and the largest under a total reserves policy, TR,
Weferences Farr, H.T., 1980, The monthly money market model, FRB working paper, July (revi Nov.). Federal Reserve, 1984 The new Federal Rwrve tech&al proeedtrrcrr for control miIney, attachment to Chairman VoM&s testimony before the Joint Economic Corn on the 1980 EGzonomicReport of t/tie,~Presideg,Feb. 1,81-W. HadjiiW&W,’ I&X3.;_1930, ’ Pre&i& of Monet&y control &,rr,dv&M&$ comparative analysis of the reserve axld the Fe&$ ftnds oarating PTQ special studies paper 15Q. Pierce, D.A., 1980, Data revisions with moving verage !3&;snal adjustment pr of Econometrics 14,95-l 14.
P.A. Tin&y et al., The short-run uoiatdity of mney stock targeting
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Swamy, P+A.V.B. and F’.A. Tinsiey, 1980, Linear prc&ction and estimation methods for ‘on models witilt stationary stochastic cc&icients, Journal of Econometrics 12, 103Tinsley, P. and I? van zur Muehlen, 1981, A maximum probability approach to short-run policy, Journal of Econometrics 15,31-C-8. Tins&, P.A., 3. B@r$ G. Fries, B. Garrett, A. Norman, P.A.V.B. Swamy and P. von zur Mu&&, 19881,Z’bc impact of .mcertakty on the feasibility of Humphrey-Hawkins Finamx Z%,489-4%. cksirrxi speed of return to the long-run, Mf - A target in 1980, FRB Van
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