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Federal Reserve Bank of Dallas

VIEWS: 3 PAGES: 49

  • pg 1
									       Federal Reserve Bank of Dallas
                                                   presents


                          RESEARCH PAPER

                                              No. 9339


               Searching for a Stable M2-Demand Equation


                                                         by


                      Evan F. Koenig, Research Department
                        Federal Reserve Bank of Dallas




                                                                                                 October 1993


This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org)
                  Searching a StableM2-Demand
                          for              Equation




                               EvanF. Koeng'
                                         i
                     Senior Economist         icy
                                      and Po1 Advisor
                             Research Department
                       Federal ReserveBankof Dallas
                            2200 l{. Pearl Street
                              Dallas TX 75201




                               September
                                       1993




*       King provided excellent and patient research assistance. John Duca
  .Anne
and HarveyRosenblum offered heipful'suggestions. The views expressed  are my
ownand not necessarily those of'the Fei;rai Reserve Bankof Dallas or the
Federal ReserveSysteml
ABSTRACT:

The Federal Reserve  Board's error- correcti on modelof 142  dernand fails to
explain nuch of the recent weakness noneygrowth, By sl igh y generalizing
                                      in
the Board^mode1 , however,its performance    rilt[ prior to and iuriirg-the recent-
episode of "missing money"  can be substantially' improved. The reiults suggest
that weakness. l,l2growth has beenprimarily due to a long-run trend towiid
               in
more efficient use of M2 balancestolether with a normal rEsponse a growing
                                                                       to
gap between  long-tern interest rates-and l.l2deposit rates.
          0ver the period from 1964through 1989, there is a very high comelation
 between the incomevelocity of the M2monetaryaggregateand the opportunity
 cost of holding M2 balances,wherethe 'l atter js measured the difference
                                                         by
 betweenthe 3-monthTreasurybill rate and the averagerate of return on M2
deposits. Since 1990, however,this relationship appearsto have brokendown:
the velocity of 142
                  has beenrising even as M2,s opportunity cost has been
falling.         S e eF i g u r e 1 .     S i m i l a r l y , t h e F e d e r a lR e s e r v e o a r d , sm o d e lo f l , l 2
                                                                                             B
           ,
d e m a n dw h i c h a s s u m ea s t a b l e l o n g - r u n r e l a t i o n s h i p b e t w e e n e l o c i t y a n d t h e
                                s                                                                 v
T-bi11-deposit-rate spread, has systematicalty overpredictedthe growth rate

of ll2 in recent years. The apparentbreakdown the historical linkages
                                            of
betweenM2 and the economy
                        has led the Federal 0pen l.larket committee (FOMC)
                                                                         to
downwardly
         revise its 1993ilz target growth ranges and deemphasize in the
                                                               l,|2
p o l i c y m a k i n g r o c e s s( G r e e n s p a1 9 9 3 ) .
                       p                             n
          T h i s p a p e re x a m i n e t h e s t a b i l i t y , p r e d i c t i v e p e r f o r m a n c ea n d f i t o f
                                         s                                                                  ,
two modified versions of the l.l2-demand
                                      model used by the Federal Reserve
Board- The modified modelsexplain significanily moreof the movement l,l2
                                                                 in
than does the Boardmodel This improvement evident both before and during
                       .                is
the recent period of missing money. Indeed, the missing moneyproblemlargely
d i s a p p e a r s s i n g t h e m o d i f i e dm o d e l s , F u r t h e r m o r ei,n t h e m o d i f i e dm o d e l s ,
                  u
u n l i k e t h e B o a r dm o d e l ,t h e r e i s l i t t l e   evidence f structurai instability.
                                                                          o
         The modified modelsdiffer from the Boardnodel in two key respects:
( l ) t h e y a l l o w f o r a q u a d r a t i cr a t h e r t h a n a l i n e a r t r e n d i n t h e r e l a t i o n s h i p

betweenthe velocity of H2 and l4Z,s opportunity cost and (2) they allow
substitution between and non-lil2
                    M2          assets to be driven not just by the
difference betweenTreasury-bi1l rates and l'lz deposit rates but, also, by the
difference betweenlong-term bondrates and l4z deposit rates,                                           In addition,
one of the modelsuses househoid
                              expenditureson non-durablesand services,
 r a t h e r t h a n G N P , s a l o n g - r u n s c a l e v a r i a b l e . I m p o r t a n t l y ,b o t h t h e
                           a
 coefficient on the squareof time and the weight attached to the long-tenn
 b o n dr a t e a r e s t a t i s t i c a l l y s i g n i f i c a n t e v e np r i o r t o t h e p e r i o d o f m i s s i n g
 moneyI .
           The results reported here suggestthat the recent weakness lrl2growth
                                                                   in
 has been primarily due to a long-run trend toward more efficient use of lil2
 balancestogether with a normal responseto a growing gap bethreen
                                                                long-term
 interest rates and l,l2deposit rates.                           Other factors--such as the activities of
 t h e R e s o l u t i o nT r u s t C o r p o r a t i o n R T C ) ,d i s i n t e r m e d i a t i o n ,a n d h o u s e h o l d s ,
                                                         (
 evident aversion to debt--have played at most a secondaryrole in sluggish trl2
 growth. The bottom line is that it has not beenthe behavior of H2 that has

 been unusual in recent years so muchas it has been the behavior of long-term
 interest rates relative to short-term and deposit interest rates.
           Feinman
                 and Porter (1992) take an approachsimilar to that adoptedhere,
modelingltl2's opportunity cost as the difference between weightedaverageof
                                                         a
competinginterest rates and a weightedaverageof own interest rates, where
both sets of weights are estimated along with the rest of the money-demand
equation.2 unfortunateiy, data Iimitations force Feinman
                                                       and porter to use a
money
    demand
         equation that has been stripped of its short-run dynamics.
Furthermore,Feinman
                  and Porter do not allow for any long-term trend in the

               I n c o n t r a s t , M e h r a( 1 9 9 2 ) - - u s i n g m o d e lt h a t d i f f e r s f r o m t h e B o a r d , s
                                                                      a
    .
p r i n cIi p a l l y i n t h a t i t i s f i r m u l - a t e d n - r e a l r a t h e r t h a n n o r n i n a t e n n s - - f i n d s
                                                                i                                             l
t h a t , t h e l 0 - y e a r - r e a sr y b o n dr a t e h a s a s t a t i s t i c a l l y s i g n i f i c a n t e f f e c t o n
                              T          u
the demand           for M2 oniy whenthe sampleperiod extendsjnto-the 1990s. llore on
                                     -
Mehra'smodel l ater.
          )
         - _ . lhe
                      competing.       rates include the yields on S-year Treasury notes and
jf-rear lreasury bonds,.                  and the interest rate chargedon 4g-month                              auto loans,
 Ine own rates include the rates of return availab'le on other checkable
d e p o s i t s , s a v i n g sa c c o u n t s n d m o n e y a r k e td e p o s i t a c c o u n t s ,c e r t i f i c a t e s o f
                                              a                m
o e p o s l [ , a n d m o n e y a r k e tm u t u a lf u n d s .
                                 m
 money-demand
           equation they estimate. As a result of these omissions, the
 Feinman
       and Porter mode'l
                       exhibits clear synptoms structural instability.3
                                             of
           S e c t i o n I p r o v i d e sa q u i c k o v e r v i e w f t h e B o a r d , sM 2m o d e la n d
                                                                     o
 demonstrates
            the model's inabil ity to account for the recent weakness IrlZ
                                                                    in
 growth. section 2 presents the modified modelsand compares
                                                          their performance
 to that of the Boardmodel
                         .                      section 3 discussesthe role of RTCactivity,                               the
                 n
 s l o w d o w in c o n s u m eb o r r o w i n g ,a n d d i s i n t e r m e d i a t i o n n e x p l a i n i n gt h e
                               r                                                         i
 cuffent episodeof missing money. section 4 examines
                                                   whetherthere rnight not
 have beena missing-money
                        episode in the early 1960s. A summary major
                                                            of
 r e s u l t s , w i t h p o 1 c y d i s c u s s i o n , c o n c l u d e sh e p a p e r .
                             i                                           t


 I.    THECORPUS
              DELICTI
          A detailed description of the Federal ReserveBoard,s M2 demand
                                                                       model
can be found in l4oore, Porter, and Small (1990). Briefly, the model assumes
that there is a stable long-run relationship betweenthe incomevelocity of il2
and M2's opportunity cost, where the latter is measured the difference
                                                      as
betweenthe yield on 3-monthrreasury bills and the averagerate of return on
ll2 deposits. M2 growth tends to accelerate whenvelocity is aboveits long-
r u n e q u i l i b r i u mv a l u e a n d t o d e c e l e r a t ew h e nv e l o c i t y i s b e l o wi t s l o n g - r u n
equil ibrium value. Honeygrowth is also influenced by near-termmovenents
                                                                       in
M2's opportunity cost and consumer
                                 spending,and by regulatory changessuch as
the introduction of money
                        market deposit accounts (in December
                                                           lgga) and
c r e d i t c o n t r o ls ( 1 9 8 0 ) .


         3 Feinnan Porter,s
                         and                 estimates intercept anderror-correct on
                                                          of                                          i
coefficients change.by               nore than two standard         errbrs when       they extendihe end
                          p
o f . t h e i r s a m p l e e r i o df r o m1 9 8 9 : Qt4 1 9 9 2 : Q 2 . s t i m a t ev a i u e so f s e v e r a l
                                                        o               E              d
interest-rate welghtsalso change morethan two standard
                                                    by                                  errors.
           Formal the Boardmodeltakes the form:
                ly,



                     Azm.= 6r^993Ql crrD83Q2 c..DC0N c4(vt_r - V *a - , )
                                  +        +       +
                                 + csAoct+ c.(Ax. - Amt-l) + c*(Ax.-' - A m . - 1 )
                                 + c., (Ax._, - Am._, + e.
                                                    )                                                      (l)


                     vl = co + ct t + caDMl.,lDAt c3ocs ,
                                               *                                                          (2)


                     oct=ln(R3Mot-RMzt)                                                                   (3)


where A and A2 are fi rst -di fference and second i fference operators,
                                                -d
r e s p e c t i v e l y , e . i s a randomerror term,

                    m = 1n(nominal
                                 l'12)
                    D83Ql= dummy
                               equal to I in 1983:Ql to control for MMDAs
                         =
                    083Q2 dunmyequal to I in 1983:Q2 control for lrlMDAs
                                                    to
                       =
                    DCON I in 1980:Q2whencredit controls imposed
                         -l in 1980:Qafter credit controls lifted
                                     3
                    v = l n [ h ( G N P G N p - ' ' ) / ( n o m i nH Z ) ]
                                      +                            al
                        =
                    R3140 yield on 3-monthTreasury bills
                        =
                    Rl.l2 averageinterest rate paid on MZbalances

                    x = 1 n ( n o m i n ap e r s o n a lc o n s u n p t i o n x p e n d i t u r e s )
                                         l                                  e
                             :
                    D M M D Ad u r n m yq u a l t o I b e g i n n i n gi n 1 9 8 2 : Q 4 ,
                                      e

and where it is presumed
                       that c. and co are both positive.                                            In practice,
equations 2 and 3 are substituted direc                             y into equation l, and then the
              d
c o m b i n e e q u a t i o ni s e s t i n a t e d u s i n g o r d i n a r y l e a s t s q u a r e s .
           The secondand third coiumnsof Table I present estimates of the Board
 nodel over the period from 1964:Qlthrough 1986:Q4
                                                 and the period from 1964:Ql
 t h r o u g h1 9 8 9 : Q 4r,e s p e c t i v e l y . a I n b o t h c o l u m n s t h e c o e f f i c i e n t o n v . _ , ,i s
                                                                                 ,
 statistically significant andof the expected ign, jndicating that money
                                            s
 growth does, indeed, tend to acclerate whenvelocity exceedsits long-run

 e q u i li b r i u m v a l u e . T h e n e g a t i v ec o e f f i c i e n t o n o c t - l i n d i c a t e s t h a t , a s
 expected, long-run velocity is an increasing function of llZ,s opportunity

cost.        ( T h e i m p l i e d l o n g - r u ne l a s t i c i t y o f v e l o c i t y w i t h r e s p e c t t o c h a n g e sn
                                                                                                                                i
                                                            8
t h e o p p o r t u n i t yc o s t i s - , 0 1 0 4 , / . 1 7= - . 0 5 8 o v e r t h e s a m p l e e r i o d e n d i n gi n
                                                                                                 p
 1 9 8 6a n d - . 0 1 0 7 / . 1 9 1 - . 0 5 6 o v e r t h e s a m p l e e r i o d e n d i n g i n 1 9 8 9 . ) T h e
                                   =                                  p
coefficient attached to the time variable suggeststhat the velocity of Flz has
exhibited a small upwardtrend after controling for movements l,l?,s
                                                           in
opportunity cost.

          llhen the sampleperiod is extendedthrough the end of 1992, problens
beconeapparent. Thus the coefficients of oc.-, and v.-' reported in the
fourth columnof Table t differ from their counterparts in the secondand
third columnsby morethan two standarderuors. The sameis true of the

constant term. The fit                  of the equation markedlydeteriorates.                               llhen an
additive dummy
             variable is introduced into the noney denandequation over the
post-1989sample,as ih the fifth                                of
                                                         co'lumn the table, the coefficient
a t t a c h e dt o t h e d u m miy h i g h l y s . i g n i f i c a n t . T h e m a g n i t u d e f t h i s
                                 s                                                             o
coefficient indicates that money
                               growth has beenover three percentagepoints
per year lower in the post-1989period than can be accountedfor by the Board


  . _-0.-.The ,      starting date for the sample that customarilyis                               usedby the Board
s t a f f ( l 4 o o r ee t . a l , 1 9 9 0 ) . B e c a u sIe u s ea f t e r - t a x r a t h e r t h a n pre-tax
i n t e r e s t r a t e s i n c a l c u l a t i n g h e o p p o r t u n i t y o s t o f h o l d i n gM 2balances, the
                                                   t                        c
coefficient estimates                reportid in Tible I arir trivially- diff6rent from those
reportedby, for example,                   Duca(1993,forthcoming).
     .
 model

           As a further test of the structural stability                                of the Boardmodel the
                                                                                                        ,
 modelwas re-estimated after including a dummy
                                             variable for each observation
 s i n c e t h e b e g i n n i n g f 1 9 9 0 . I f t h e m o d e li s s t a b ' l e , t h e d u m mv a r i a b l e s
                                  o                                                                y
 s h o u l d f a i l t o b e j o i n t l y s i g n i f i c a n t ( D u f o u r1 9 8 0 ) . l t o r e g e n e r a l l y , b y
 exanining the pattern of coefficients attached to the dunrmy
                                                            variables, one can
get someidea whether the Eoardmodelhas been consistently off target, or has

 failed only in one or two quarters. Results are reported in Table Z.

          The hypothesisthat the coefficients of the dummy
                                                         variables are equal to
zero is rejected at the one-percentsignificance level .                                         The coefficients are
c o n s i s t e n t l y n e g a t i v ei n s i g n ,   Individualcoefficients are statistical ly
s i g n i f i c a n t i n 1 9 9 0 : Q 4 n d f r o m 1 9 9 1Q 3 t h r o u g ht h e e n d o f 1 9 9 2 . T h e i m p l i e d
                                      a                   :
shortfal'l in M2 growth is fairly small in 1990 (just under 2.0 percent,
a n n u a l i z e d ) ,b u t r i s e s t o o v e r 7 . 0 p e r c e n t i n 1 9 9 2 .

          Takentogether, these results provide compellingevidencethat the
Federa] ReserveBoard's ll2 demand
                                model has broken down. The model has been
o v e r p r e d i c t i n g 2g r o w t hs i n c e t h e b e g i n n i n go f 1 9 9 0 - - s i g n i f i c a n i l ys o s i n c e
                           M
the middle of 1991. The prediction errors have, if anything, gotten larger

t h r o u g ht i m e . 5


                Resu1ts      very similar to those reportedin TablesI and Z for the Board
modelare also obtainedusingMehra,s                                mohel real ll2 growth(llehra1992,
                                                                            of
1 9 9 3 ) . l l h e n . p o s t - 1 9 8d u m m y r i a b l ei s i n t r o d u c e d; t o M e h i a , s o d e l i t
                          a                    9        va                                 i                      m      ,
i s . n e g _ a t i a e ds t a t i s t i c a l l y s i g n i f i c a n t a t w e l l u n d e rt h e l - p e r c e n tl e v e l.
                        v  n
Individual_Dufour               dummy       variiblei are consisten y negative,ahd are
s t a t i s t i c a l l y s i g n i f i c a n t a t t h e S - p e r c e nl t v e l i r o m - 1 9 9 1 : Qh r o u g h 9 9 2 : Q 4 .
                                                                            e                             t3         1
collectively, the_Dufour                     dummy      varihblesare significantly riifferenl from zero
a t t h e 5 - p e r c e nlte v e l, T h u s l e h r a , s( 1 9 9 2 ) l i i m t h a t h i s m o d ed o e sn o t
                                                      l                       c                                 l
d i s p l a y s i g n i f i c a n t p o s t - 1 9 8 l n s t a b i li t y i 3 q u i t e s e n s i t i v et o t h e s a m p l e
                                     .                 9
                        r
p e r i o d . o v ew h i c ht h e m o d e i s e s t i m a t e d . ( l . l e ' h r a a r t s h i s s a m p l en i g s g : Q t
                                                   l                                  st                           i
llg^elqs.it             i n 1 9 9 2 : Q 2 . ' t ys a m p l p e r i o db d g i n si n 1 9 6 4 : Qa n di u n s t h r o u g h '
                                             l              e                                          l
        2 .
1 9 9 : Q 4)
2.    THEIIODIFTED
                 I'IODELS
2.1 The GenerallzedIncome-Vel ty llodel
                           oci
        The recent unusually slow growth in 142
                                              has been accompanied a growing
                                                                 by
gap betweenlong-term interest rates and lil2deposit rates, and by large flows
of cash into the stock and bondmarkets. (For a plot of the long-terrnbond
rate less the M2 deposit rate, see Figure Z,)                Thesefacts suggestthat
households
         mayview stocks and longer-tenn bondsas substitutes for ll2
deposits. To allow for this possibility, I introduced he rate of return on a
                                                     t
long-term security into the formu'lafor the opportunity cost of holding
N2.6'7 In the generalizedmodel equation 3 is replaced by:
                             ,


                oct = tnlpRloyRt (l - F)R3Mot Rl42sJ,
                               +            -                                        (3',)


whereRI0YR
         denotes
               the after-tax rate of return on lO-yearTreasurybondsand
where is a parameter be estinated. Notethat equation3' reduces the
    B              to                                        to
Board's pecification hen = 6.
      s            w   p
        Equations and2 werealso generalized. To al low for t h e p o s s i b i l i t y
                I
that the short-rundynamic
                        impactof the newopportun cost variable might
                                               i ty-
differ from that of the old opportun cost variable, an additional lagged
                                   i ty-
change the opportunitycost was introduced
     in                                  into equationl.                          Thus,equation


       6 An alternative
                        approach to expandthe existing M2 aggregateto
                                is
include bond market mutual funds or stock and bond markei mutfai f-unds                       _
Interestingly, adjusting M2 for bond and stock funds does not, by itself,
eliminate very muchof the recent H2-growth        shortfall (Duca19931
forthcoming). For further discussion-of the propertiei of an exfanded
aggregate, see Feinman  and Porter (1992) and the Appendix.
       7 Hamburger 977,1983)
                   (1
   .                           w a sa n e a r l y a d v o c a t e f i n c l u d i n g r a t e s o f
                                                                o
return on long-term securities as right-hand-side variables in m-oney                       demand
         i
e q u a to n s ,
 I wasreplacedby


                    Azm.= 6*Pg3Ot* czB083Q2+ czcDC0Nc4(vt-r - v*t-r)
                                                   +
                               + crAoc.+ claoc._',cu(Ax. - A n . - 1 )
                                               +
                               + c6A(axt-l - A m . - 1 )+ cr, (Ax.-, - A r n t - l + e t .
                                                                               )                            (1')


A 1 s o , t o a l l o w f o r t h e p o s s i b i l i t y t h a t t h e p a c eo f f i n a n c i a l i n n o v a t i o n( a s

measured trend growth in MZ's velocity) might be accelerating, the I inear
       by
time trend incorporated into the Boardmodelwas replaced with a quadratic
tine trend.          Forma1ly,equation Z was replaced by




                   vl = co + c,t + cit2 + crDI'lMDAtcaoct
                                                  +                                                        (z',)

         Table 3 presents estimates of the generalizedM2rnode'l The fonnat of
                                                             .
t h e t a b l e i s s i m i l a r t o t h a t o f T a b l e l , e x c e p tt h a t t h e e s t i m a t e d a l u e s o f
                                                                                                          v
three additional coefficients are reported.

         In a1l respects, the perfornanceof the generalized modelappears
superior to that of the original Boardmodel The R2,s of the generalized
                                          .
equations are substantially higher than those of their counterparts in Table
l.   The weight attached to the lO-year bondrate in the opportunity cost term
andthe coefficient of time squared re significant--both statistically and
                                  a
economically--even sampleperiods that end we'll before the emergence the
                 in                                                of
missing ltl2. Moregenerally, parameterestimates appearto be quite stable
across sampleperiods: estinates are alwayswithin two standard errors of one
another and are usually within one standarderror.                                              variable is
                                                                                   llhen a dummy
                   d                            9
 i n t r o d u c e o v e r t h e p o s t - 1 9 8p e r i o d( c o l u m n ) , i t s c o e f f i c i e n t i s
                                                                       5
 s t a t i s t i c a l l y i n s i g n i f i c a n t , T h ep o i n t e s t i m a t e f t h i s c o e f f i c i e n t i s o n l y
                                                                                    o
 one third the size of that reportedin Table l:                                     the generalized
                                                                                                  model
 underpredicts growthby only aboutl-percent per year since 19g9,as
             f.l2
        with an over 3- percentper-yearshortfall using the Board
 compared                     -                                 model
                                                                   .
                      performance the generalized
           The improved         of              modelis also reflected in
 Tab'le whichreports results from an estimationthat includesa sequence
      4,                                                             of
 Dufourdummy
           variab'les. Notethat the Dufourdurmies
                                                are nowboth
 i n d i v i d u a l l ya n dj o i n t l y i n s i g n i f i c a n t . T h e i r e s t i m a t e d o e f f i c l e n t sa r e ,
                                                                                                 c
 however,
        consistentlynegative,andthere is still                                         sonetendency
                                                                                                  for their
magni.tudes increase
         to         with time.


2.2 UsingConsumptlon the Long-Run
                  as            ScaleVariable
          As notedearl ier, the Board,s modela'llows
                                      l,l2         movements consumption
                                                          in
to havea short-run impacton noney
                                growth, but usessmoothed as its long-
                                                       GNp
run scale variable. Thefact that the recent slowdown ll2 growthhas been
                                                   in
accompanied unusually
         by          weakconsumption
                                  spending
                                         suggests
                                                that the
assumptionthat it is GNPrather than somemeasure consumption
                                                of           that drives
'long-run
        money denand merits closer examinaffon.s
                                               Accordingly,I estinateda
variant of the generalized demand
                         1rl2   modelin whichnominal
                                                   household
expenditure non-durables serviceswasusedas both the long-runand
          on           and




            For evidenceof the slowdown consumptlon,      in                         see Blanchard(1993) and
P e r r y a n d S c h u l t z e( 1 9 9 3 ) . F o r a n i c e d i s c u s j i o n o ? t h e practical and
theoretical reasonsfor bel ieving consumption                            rnight be a better scale vari able
than GNP, eeHankiw ndSurnmers-(1996),'
                s                 a
  s h o r t - r u n s c a l e v a r i a b l e . e R e s u l t sa r e r e p o r t e d i n T a b l e 5 .

            The frz's reported in Table 5 are only slighily below those reported in
 Table 3' and remainwell abovethose obtained using the Board model Again,
                                                                 .
 the estimated coefficients of the lO-year bondrate and of time squaredare
 e c o n o m i c a l l y n d s t a t i s t l c a l l y s i g n i f i c a n t e v e ni n r e l a t i v e l y e a r ' l ys a m p l e
                       a
 periods. Parameter
                  stabil ity appearsto be excellent--better even than that
 o b t a i n e di n t h e i n c o m e - v e l o c i t v e r s i o n o f t h e g e n e r a l l z e d o d e l . l . t i t h
                                                      y                                            m
                    n
 c o n s u m p t i oa s t h e l o n g - r u n s c a l e v a r i a b l e , n o c o e f f i c i e n t e s t i r n a t e a r i e s b y
                                                                                                                     v
 even as muchas one standarderror across samples. The estinated coefficient
 o n t h e p o s t - 1 9 8 9 u m mv a r i a b l e i s i d e n t i c a l i n T a b l e s3 a n d 5 :
                           d      y                                                                            bothmodels
.accountfor about two-thirds of the money
                                        growth left unexplainedby the Board
 m o d e.l I n T a b l e 5 , a s i n T a b l e 3 , t h e c o e f f i c i e n t o n t h e d u n r m y r i a b l e i s
                                                                                                  va
 s t a t i s t i c a l 1 y l n si g ni f i c a n t .

           The consumption-velocity
                                  version of the generarizedmodelperforms
particularly well in the Dufour dununy
                                     test.                                  As shownin Table 6, not only are
the dumny ariables both individually andcollectively insignificant, they
        v
exhibit Iittle             o r n o t e n d e n c y o g r o w i n m a g n i t u d e s t h e s a m p l ei s e x t e n d e d ,
                                                 t                               a
The dumrny
         coefficients are, however,consisten y negative in sign.
           There are several notable differences betweenthe parameterestimates in
Table 5 and the conespondingestimates in Table 3.                                        The error-correct i on
coefficient (co), for exampre,is sma er in the consumption-velocity
                                                                  version
o f t h e g e n e r a l i z e d o d e lt h a n i n t h e i n c o m e - v e l o c i t y e r s i o n . 0 n t h e o t h e r
                               m                                                     v


            flg val_idityof th.eerror                                i on approach
                                                                                 hingesupon
s,t a.t .t n a r i t y o f t h e t e r m ( y . _ r- v.correcte q u a f i o n. T h 6r e s i d u thef r o ma
        io                                            . . _ , , )i n           l               als
regression the log of thi'consuription
                   of                                                veiocity or money viilautes rrom
                                                                                     on-
the risht-hand-side equation iie inieea-ititioniiv." ilationiiiii cannot
                                 6f                 z;
be rejected evenin the iase where                        the coirricieni oi-time;qu;;;;-i;"
constrained be zero. to

                                                                10
 hand, the long-run interest e1asticity of the demand        is
                                                    for money somewhat
 larger in magnitude the consumption-velocity
                    in                      model than in the income-
 velocity model
              .10 The sameis true of the weight, F, attached to the long-
 run interest rate.


 2.3      A l{ore Detalled Look at the l'lodel Recent performance
                                             s,
            Table 7 compares
                           the meanemors and root nean square errors generated
 by the Boardmodelover the post-1989period with those of the general
                                                                   ized
 income-velocityand consumption-velocity
                                       models. Two sets of results are
 presented: one baseduponmodelestimates over a sampleperiod extending from

.1964:Qlthrough 1989:Q4,
                       and the other uponmodelestimates extendingfrom
 1 9 6 4 : Q lt h r o u g h1 9 9 2 : Q 4 .A c c o r d i n g o c o l u m n h r e e o f t h e t a b 1 e , w h e n
                                                           t             t
 estimated over the 1964:Ql-1989:Q4
                                  sampleperiod the Boardmodeloverpredicts
moneygrowth frorn 1990 through 1992 by an average of over one percentagepoint
 per quarter. 0ver the sane period, the generalized income-velocitymodel

overpredicts moneygrovrth by betweenfour and five tenths of a percentage
point per quarter, and the generalizedconsumption-velocity
                                                         modelover
predicts money
             growth by only a third of a percentagepoint per quarter. l,lhen
the sampleperiod over which the nodels are estimated is extendedto the end
of 1992' the performance the generalizedmodelsimprovesfurther relative
                       of
to that of the Boardmodel: the Boardmodeloverpredicts money
                                                          growth by an
averageof about 1.5 percentagepoints per year, as compared an average
                                                         to


          to
  -                f h . . l o n g - r u n .n t e r e s t e l a s t i c i t y i s f o u n db y d i v i d i n g t h e c o e f f i c i e n t
                                           i
o f . 9 . , - . , |b y - t h e c o e f f i c i e n t o f v . - , . ( T h e i a t t e r c o e ? f i c i e n t i s , o f c o u r s e , a n
estimate of cn--the^error correction ioefficient.)                                           In the incorne-velocity
m o d e l ' e s t i m a t e so f t h e l o n g - r u n i n t e r e s t e l a s t i c i t y r a n g ef r o m - . 0 1 6 4 / . 1 - 9 9
= - . 0 8 ? t o - . 9 1 ! 9 l . l q 3 = - . 0 9 2 . I n t h e c o n s u m p t i o n - - v e l o i im o d e l e s i i m a t e s
                                                                                                               ty    ,
r a n g ef r o m - . 0 1 3 ? / . 1 3 0 - . 1 0 2 t o - . } t Z B / . 1 2 0 = - . 1 0 7 .
                                             =

                                                                   il
 overprediction of less than .3 percentagepoints per year using the
 generalizedmodels. The generalizedmodelsaccountfor over 80 percent of the

 nissing money.

          The root meansquareerrors displayed in the secondand fifth                                               columnsof
 Table 7 provide an alternative measure the perfornanceof the modelsover
                                      of
 recent quarters.              In both columns,the root meansquare enor of the
 generalized income-velocitymodel is over 50 percent smaller than that of the

 Boardnodel.            The root meansquareerror of the generalized consumption-
velocity model is over 70 percent sma'llerthan that of the Boardmodel
                                                                    .
          Finally, Table 8 presents results from encompassing
                                                            tests basedon the
recent performance the money
                 of        demand
                                models, llodel A is said to encompass
ModelB if forecasts obtained from l'lodelA contain useful information that is
not contained in the forecasts of ModelB.                                 If llodel A encompasses
                                                                                               llodel B and
l'lodel B fails to encompass
                           ModelA, then l.lodelA is clearly superior to lilodel
B. As a practical nratter, to determinewhetherl4odelA encompasses
                                                               l.lodelB
one can regress lrlodel B's forecast errors on the difference betweenthe
forecast errors of lrlodelB and the forecast errors of Hodel A.                                             If the
coefficient on the differenceln errors is statistically significant, then
ltlodelA encompasses
                  ModelB. similar'ly, if a regression of ModelA,s forecast
errors on the difference between
                               the forecast errors of                                          odels A and B yields
a s t a t i s t i c a l l y s i g n i f i c a n t c o e f f i c i e n t , t h e n l . l o d e B e n c o m p a s s ms d e lA . 1 1
                                                                                              l                   eo
         The first        two rows of Table 8 showthat the generalized income-velocity
nodel encompasses Boardmodelover the period of the missing money,
               the
whereasthe Eoard modelfails to encompass generalized income-velocity
                                       the


       F o r a d e t a i l e d d e s c r i p t i o n o f t h e e n c o m p a s s i ne s t u s e d h e r e , s e e
                                                                                   tg
Chongand Hendry(1986).

                                                               t2
model That is, the forecasts of the generalized income-velocitymode'l
    .                                                               are
unambiguously
           superior to those of the Boardmodel over the three-year period
f r o m 1 9 9 0 : Q l h r o u g h1 9 9 2 : Q 4 . S i m i l a r l y , t h e r e s u l t s d i s p l a y e di n t h e t h i r d
                    t
and fourth rows of Table 8 showthat the generalized consumption-velocity

modeldominatesthe Boardmodel
                           .                            Finally, the fact that the difference in
errors betweenthe incone-velocity and consumption-velocity
                                                         modelshelps to
explain the errors of the incorne-velocity
                                         modelbut not the errors of the
consumption-velocity
                   modelshowsthat the forecasts of the consumption-
velocity model are unambiguously
                              superior to those of the income-velocity
nodel.
                    judging between
          In summary,              the modelssolely on the basis of their
recent performance,
                  the generalized consumption-velocity          denand
                                                     model of 142
significantly outperformsthe generalized income-velocitymodel
                                                            ,                                               Both the
generalized consumption-velocity
                               model and the generalized income-velocity
model signiflcantly outperformthe current Federal ReserveBoardmodel
                                                                  .


3.    OTHER          ()F
          EXPUI}IATIONS THEIIISSINGI{OT{EY
         Duca (1993, forthcoming) has suggested
                                              that Resolution Trust Corporation
(RTC)activity may be responsible for muchof the weakness M2growth since
                                                       in
1989, There are two reasonswhy RTCactivity might have an adverseimpact on
t h e d e m a n f o r M 2 d e p o s i t s . F i r s t , w h e na t h r i f t
                d                                                                i s , , r e s o 1 v e d ,i't,s
depositors are forced to reallocate their portfolios sooner than would
otherwise have beenthe case. In an environment
                                             where interest rates on nevf
bank deposits have fallen, nany of those who have deposits at a resolved
thrift    wi'll chooseto shift assets out of lrl2and into the stock and bond
markets. Second,as more and more thrifts                             are resolved, people beconeaware

                                                             t3
 t h a t t h e r e i s a c a l l r i s k a s s o c i a t e d i t h b a n kt i m e d e p o s i t s . T h i s n e w l y
                                                           w
 perceived call risk reducesthe attractiveness of bank time deposits for any
 given spreadbetweenmarket interest rates and bank deposit rates,
           During 1992, there was an additional special reason for weakM2 growth:
 for a time, the floor rate of return on 6-monthsavings bondsexceeded
                                                                    the
 r a t e o f r e t u r n a v a i l a b l e o n s h o r t - t e r mT r e a s u r yb i l l s .     This yield gapmay
 h a v er e s u ' l t e di n d i s i n t e r m e d i a t i o n - - a l b e i d i s i n t e r r n e d i a t i o nn d u c e d y a n
                                                                             t                                 i           b
 artificial         floor on the return from an asset competitive with bank deposits
 rather than by an artificial                     c e i l i n g o n b a n kd e p o s i t r a t e s t h e m s e l v e s ,
           Ducafinds that of several possible alternative measures RTC
                                                                 of
 activity'        the measure
                            that best accountsfor the missing M2 is the changein
 the quarterly averagecumulatedstock of resolved deposits. He measures
                                                                     the
 i n c e n t l v e f o r d i s i n t e r m e d i a t i o n s i n g a v a r i a b l e t h a t e q u a l se i t h e r z e r o o r
                                                         u
the floor yield on 6-monthsavings bondsminus the yield on 6-monthrreasury
bllls,      whicheveris greater.                   Table 9 reports estimates of the Boardmodel
                                                                                             ,
the generalized income-velocitymodel and the generalized consumption-
                                   ,
velocity model each expanded include Duca's RTCand disintermediation
             ,             to
variables (denoted0RTCand DISINTER,
                                  respectively).
          Results displayed in the secondcolumnof rable 9 confirm that both the
RTC ariable andthe disintermediation ariable are highly significant, andof
   v                               v
the expectedsign, whenaddedto the Boardmodel
                                           .                                                  whenthe same
                                                                                       However,
v a r i a b l e s a r e a d d e dt o t h e g e n e r a l i z e d o d e l s ,t h e i r e s t i m a t e dc o e f f i c i e n t s
                                                               m
a r e s t a t i s t i c a l l y i n s i g n i f i c a n t a n d c o n s i d e r a b l y e d u c e d n m a g n i t u d ec o l u m n s
                                                                                      r            i                  (
three and five).               In contrast, the coefficient of time squaredand the weight
placed uponthe lO-year bondrate in the opportunity cost formula are both

s t a t i s t i c a l l y a n d e c o n o m i c a l l y i g n i f i c a n t i n e v e r y r e g r e s s i o ni n w h i c h t h e y
                                                      s


                                                                t4
 are i ncl uded.

           Q u ailt a t i v e l y s i m i l a r r e s u l t s a r e o b t a i n e dw h e nt h e R T C a r i a b l e i s
                                                                                                     v
 replaced by a variable designedto capture the incentive for households
                                                                      to
 reduce debt by drawing downll2 deposit balances. The spread betweenthe
 interest rates chargedon consumer
                                 loans and the interest rates paid on il2
 d e p o s i t b a l a n c e s a s b e e nu n u s u a l l yw i d e i n r e c e n t y e a r s . t . T h e p h a s e - o u o f
                             h                                                                                           t
 the tax deduction for interest on consumer
                                          installment loans has contributed
 t o t h e w i d e n i n go f t h i s g a p , a s h a v er i s i n g c o s t s o f d e p o s i t o r y
 i n t e r m e d i a t i o n . I t s e e m s l a u s i b l e t h a t h o u s e h o l dw o u l dr e s p o n d o t h i s
                                           p                                          s                     t
 unusually wide gap by using some the funds that they would normally have
                                 of
 placed in a bank accountor certificate of deposit to reduce their outstanding

 credit-card balances, makelarger-than-usual dovrn
                                                 payments newcars and
                                                        on
other consumer
             durables, and pay downtheir home-equity
                                                   loans.     In effect, a
                    debt night serve as a substitute for a high 'level of l.l2
low level of consumer
balances. In an effort to incorporate this rnarginof substitution into the
m o n e y e m a n m o d e l s ,e q u a t i o n3 ' w a s g e n e r a l i z e d o a l ' l o wt h e o p p o r t u n i t yc o s t
        d         d                                                         t
of holding money depend
                to     uponthe averageinterest rate on consumer
installment debt, in addition to the yields on 3-rnonthrreasury bills and l0-
year Treasury bonds. The estimatedweight attached to the consumer
                                                                loan rate
is listed as T in the third andfifth columns f Table9.r3 Thereported
                                           o
r e s u l t s i n d i c a t e t h a t , l i k e t h e R T C n dd i s i n t e r m e d i a t i o n a r i a b l e s , t h e
                                                           a                                   v
c o n s u m el r a n r a t e i s s t a t i s t i c a l l y i n s i g n i f i c a n t w h e ni n c l u d e d i n t h e
               o

         12 See
                         F e i n m a n n d p o r t e r ( 1 9 9 2 ) ,C h a r t 3 ,
                                      a
         t3.
               . I n . t h " r e g r e s s i o n s e p o r t e d i n T a b l e 9 , t h e c o n s u m elr a n r a t e i s
                                                 r                                                     o
a s s u n e do h a v e a z e r o w e l g h t - p r i o r t o t h e p e r i o d o f m i s s i n gm o n e y i . e , p r i o r
               t                                                                                                (
t o 1 9 9 0 : Q l ) . H o w e v e rv e r y s i i n i l a r r e s u l t s ' a r e o b t a i n e dw h 6 nt h e - c d n s u m e r
                                          ,
 l o a n r a t e i s a l l o w e dt o h a v ea n o n - z e r o e i g h t b e g i n n i n gi n 1 9 7 2 ,w h e n
                                                                     w
c o n s u m el r a n r a t e d a t a f i r s t b e c o m a v a i l a 6 l e .
                  o                                               e

                                                              15
 generalized noney-denand
                        model
                            s.
           Although the RTC,d i s i ntermedat i on, and debt-paydown
                                          i                        variables are
 s t a t i s t i c a l l y i n s i g n i f i c a n t i n t h e g e n e r a l i z e d o d e l s ,t h e i r c o e f f i c i e n t s h a v e
                                                                                   m
 t h e e x p e c t e d i g n s . I n c l u d i n gt h e s e v a r i a b l e s i n t h e r e g r e s s i o n s o m e w h a t
                      s                                                                                     s
 improvesthe nodels' post-1989fit.                              (Compare meanerrors and root mean
                                                                       the
 square errors reported at the bottom of columnsthree through six in Table g
 to the corresponding
                    errors reported in Table z.)                                        Furthermore,the inclusion
 of RTC' disintermediation, and debt paydown
                                           variables sometimes
                                                             improvesthe
 stability       of key parameters, Increasedparameterstabi'lity is particularly
 noticable in the income-velocityversion of the generalized money
                                                                demand
m o d e.lr a A c c o r d i n g l y ,o n e c a n n o t r u l e o u t t h e p o s s i b il i t y t h a t R T C ,
disintermediation, and debt paydown
                                  effects have contributed to the recent
weakness lil2 growth. Any contribution from these sources has obviously been
       in
dwarfed, however, by the cornbined
                                 effects of a long-run tendency towaro more
efficient use of M2 balancesand a growinggap betweenlong-term interest
rates and M2 deposit rates,


4. tt0RE
       [Issl]tc ]i0NEY?
         As noted above, the Board staff typically uses a 1964:Qlstarting date
for estimation of its [12model However,
                             .        consistent l.l2data are available all
the way back to the beginningof 1959. lrlhen
                                           the sampleperiod used to
estimate the Boardmodel is extendedto include the pre-1964data, evidenceof

        1a
     ,                              the
            -For-examp]g! error-correct on coefficient (the coefficient of
                                                                i
                   frop-_.-f9-2,to in Tabte3 as the end of ihe sample
                                        .163
Yr-,t)f.Jlif r o m . _ 1 9 8 9 : Q 4 - t o                                                                period is
extended                                 1 9 9 2 : Q 4 . l i t h R T C d i s i n t e r m e d i a t i o ra,i d d e b t
                                                       l               ,                                i
paydown      variables includedin the regression,the same                               coefficient only drops
t o ' l 8 4 . o r _ . 1 8 6 T a b l e9 , c o l u m nts i e e a n df o u r ) . I n c r e a s e s t a b i l i t ! i s '
                           (                           h                                             d
also notabie in the estimates the interest-raie weightingparameterl and
                                                of                                                                 p,
t h e c o e f f i c i e n to f t i m e s q u a r e d .

                                                                l6
 a p o s t - 1 9 8 9 r e a k d o win t h e m o d e lr e m a i n ss t a t i s t i c a l l y s i g n i f i c a n t ,
                   b               n
 liloreover,tests indicate that the Boardmodel seriously over-predicts H2
 growth prior to 1964. Thus, using the Boardmodel, there are two periods of

 m i s s i n gn o n e y - - o n en t h e e a r l y 1 9 9 0 s n d t h e o t h e r i n t h e e a r l y 1 9 6 0 s . I n
                                i                           a
 contrast, the ll2 growth predictions of the generalized income-velocityand
 general
       ized consumption-velocity   s
                               model are without significant bi as.
           T o t e s t t h e s e n s i t i v i t y o f t h e p o s t - 1 9 8 9 i s s i n gm o n e y o a c h a n g e n
                                                                             m                    t                i
the starting date used in estimating the Boardmodel two regressionswere
                                                  ,
run.       Oneof these regressions included Dufour dummy
                                                       variables extending from
 1990:Qlthrough 1992:Q4,and the other included a single durnmy
                                                             variable equal
t o o n e f r o m 1 9 9 0 : Q l h r o u g h1 9 9 2 : Q 4 . R e s u l t s a r e d i s p l a y e di n T a b l e 1 0 .
                              t
l r l h i l e o n l y f o u r o f t h e D u f o u rd u r n m y r i a b l e s a r e i n d i v i d u a l l y s i g n i f i c a n t ,
                                                            va
every Dufour coefficient is negative, and the hypothesisthat all the
coefficients are equal to zero is reJected at the S-percentsignificance

level .       The single dummy
                             variable has a coefficient that is negative and
s i g n i f i c a n t a t t h e l - p e r c e n t l e v e l.   T h u s , o u r e a r l i e r c o n c l u s i o nt h a t t h e
Boardmodelbreaks downafter 1990 is not sensitive to an extension of the
     p
sample eriod to includepre-1964 ata.15
                              d
          The secondand third columns Table 1l present evidencethat the Board
                                     of


          15
                  I c o n d u c t e d i m i l a r e x e r c i s e s( w i t h s a m p l e e r i o d s b e g i n n i n gi n
                                    s                                                   p
 1959    :Q4).-forthe general zed i ncome-velbci and coisumpti
                                         i                               ty                        on-vi l oci t-y mode'l        s,
 and for Mehra'smodelof real 142                         growth. Dufour dummy                variables thal run fr6m
 1 9 9 0 : Q l h r o u g h1 9 9 2 : _ Q 4 _ a r e t h e r i n d i v i d u a l l y n o r i o l l e c t i v e l y s i g n i f i c a n t
                t                                nei
 i n t h e . g e n e r a l i z e d o d e l s . A d u m mv a r i a b l e t h i t e qw h eso n e f r o i r l g i 0 : Q l
                                  m                             y                       ' ual n
t h r o u g h1 9 9 2 : Q 4s a l s o s t a t i s t i c a l l v i n si q ni f i c a n t
                             i                                                                   i n t r o d u c e di n t o t h e
g e n e r a l i z e d o d e l s . A l l f o u r 1 9 9 2D i r f o u rd u m m i ea r e s t a t i s t i c a l l y
                      m                                                              s
s i g n i f i c a n t a t t h e S - p e r c e n tI e v e l i n l , l e h r a , s o d e l a n d t h e F s t a i i s t i c f o r a
                                                                               m
j o i n t t e s t o f t h e e n t i r e s e t o f D u f o u rd u m mv a r i a b,i e s i s s i g n i f i c a n t a t t h e
                                                                              y
10-percentlevel (but not the S-percenttev6l). When dumnr!                                  a              variable that
e q u a l so n e o v e r t h e e n t i r e i n t e r v a l f r o m 1 9 9 0 : Q l h r o u g h1 9 9 2 : Q 4s i n t r o d u c e d
                                                                                   t                           i
i n t o l 4 e h r a ' s o d e,l i t i s s i g n i f i c a n t a t w e l l u n d e rt h i l - p e r c e n t l e v e l .
                       m

                                                                 l7
modelbreaks down, not just after 1990, but also prior to 1964. Again, two
 regressionswere run, one with Dufour dummies each quarter from 1959:Q4
                                            in
through 1963:Q4,and the other with a single dunrny
                                                 variable equal to one from
 1959:Q4
       through 1963:Q4. The coefficients of the Dufour dunrmies
                                                              are
c o n s i s t e n t l y n e g a t i v ei n s i g n , a n d n a n ya r e s t a t i s t i c a l l y s i g n i f i c a n t .   The
hypothesisthat the Dufour coefficients are al1 equal to zero is reJected at
the S-percent significance level .                          The coefficient of the s.ingle dummy
v a r i a b l e i s n e g a t i v ea n d s t a t i s t i c a l l y s i g n i f i c a n t a t t h e l - p e r c e n t 1 e v e .
                                                                                                                             l
Its point estimate indicates that the Boardmodelover-predicts money
                                                                  growth
by over 3 percent per year, on average, in the pre-1964period. This
shortfall is a]rnostidentica'l to that generatedby the Board model in the
p o s t - 1 9 8 9 e r i o d ( T a b l el , c o 1 5 ) .
                p                               .
         As shownin columnsfour through sevenof Table ll,                                          whenDufour dummies
are introduced into the generalized income-velocityand consumpt -vel oci ty
                                                             i on
models, individual coefficients are rarely significant.                                          Onecannot reject the
hypothesisthat the Dufour coefficients are, collectively, equal to zero.
l'lhena single dummy
                   variable is introduced into the models, it too is
insignificant.            T h u s , t h e g e n e r a l i z e d o d e l s u c c e e dn e x p l a i n i n gt h e p r e -
                                                              m          s          i
1964nissing money
                muchas they succeedin explaining the post-19g9missing
money,

         The superior performance the generalizednrodelsin the pre-1964
                                of
period is confirned by encompassing
                                  tests.                                  As shownin Table lZ, the
difference betweenthe errors of the Boardmodeland the errors of the
generalized income-velocitymodelhelps to explain the errors of the Board

nodel but not the errors of the generalized income-velocitymodel That is,
                                                               .
the forecasts of the general
                           ized income-velocitymodel are unambiguously


                                                                I6
 superi0r to those of the Boardmodelover the pre-1964sanple period. The
 forecasts of the generalized consumption-velocity
                                                 model are also unambiguously
 superior to those of the Boardmodel 0n the other hand, the ranking of
                                   ,
 general
       ized consumption-vel
                         ocity and general
                                         ized incorne-velocity    s
                                                              model
 r e l a t i v e t o o n e a n o t h e ri s u n c l e a r .


 5.    SU}II'IARY I}IPLICATIO}IS
                AIID
          Growthin the lilz monetaryaggregatehas beenweakerthan is consistent
with widely usedmodelsof the demand money. The results presentedhere
                                  for
s u g g e s tt h a t n e a r l y a l l o f t h i s r e c e n t w e a k n e sis a t t r i b u t a b l e t o a l o n g - r u n
                                                                             s
trend toward more efficient use of M2 balancescombined
                                                     with a normal response
to the growinggap betweenlong-tenn interest rates and l'12deposit rates,
Apart fron its impact on the will ingnessof banks and other savings
institutions to narrow the interest rate gap, the thrift                                     resolution process
has played at most a minor role in depressinggrowth in the dernand M2
                                                                 for
b a l a n c e s . s i m i l a r l y , i n s o f a r a s h o u s e h o l drse g a r d a l o w l e v e l o f d e b t a s a
substitute for high l.l2balances, the incentive to reduce debt by drawing down
M2 deposits appearsto be adequate'ly
                                   captured by the spread betweenlong-term
bond rates and M2 deposit rates.

          Both the presenceof a quadratic trend in l.lz velocity and the influence
of long-term interest rates on 142    are discernable in sampleperiods
                                 demand
that end well before the "missing l,l2',emerged a problem. This fact
                                              as
provides somereassurance
                       that the roles played by the trend and the Iong-terrn
i n t e r e s t r a t e i n e x p ' l a i n i n g h e m i s s i n gm o n e y r e n o t s p u r i o u s . N e v e r t h e l e s s ,
                                                t                          a
time trends inevitably carry with them an aura of ad hockery, In future
research, analysts mayweli wish to experiment
                                            with other, more direct proxies

                                                              l9
 for the effects of financial innovation on the demand noney.16
                                                     for
         The fact that a rnonetary
                                 aggregateis explainable does not necessarily
meanthat it can be used successfully as an intermediate target.                                         To serve as
 an intennediate target, it is desirable that a monetaryaggregatebe both
controllable and close'ly linked to a measure economic
                                            of       activity that is of
 interest to pol icy makers. Insofar as the demand
                                                 for M2dependsuponthe
spreadbetweenlong-term interest rates and deposit rates--as results obtained
here strongly suggest--andthis spread is subject to unpredictablemovements,
t h e u s e f u l n e s s f M 2a s a n i n t e r m e d i a t e a r g e t i s c a l l e d i n t o q u e s t i o n .
                         o                                   t
Addingto doubts about the usefulnessof MZtargeting are results suggesting
that the demand
              for l.l2maybe more rel iably linked to a subcategory
                                                                 of
consumption
          spendingthan to total output.
         The fact that a rnoney
                              aggregateis explainable also does not necessarily
meanthat it can be used successfully as a leading indicator.                                       However,
Feldstein and stock (1993) find that forecasts of economic
                                                         activity improve
whena noney-demand-enor-correcti term is included in the forecasting
                             on
equation. This result suggeststhat the better are our modelsof the demand
for money,the better will be our ability to predict the economy.




     16. Siklos_(1993)
                       reports somesuccessusing the ratio of non-bank
trnanclal assets to total financial assets and fhe cuffency-money
                                                                ratio to
capture long-term trends in velocity.
 APPEI{0IX: l{0uLDADDING
                       BOilDFUNDS ilz l,tAKE
                                r0         tit0vE}tEilTs t'ta EASIER
                                                       IN           To
 EXPLAIII?

          It is sometimes
                        easier to expandthe definition of money
                                                              than to model
 the forces that are driving households
                                      awayfrom traditional monetaryassets.
 For example,lil2 largely replaced Ml as a guide to nonetary policy after the
 introduction of i nterest- bearing checkingaccountsblurred what had hitherto

 been a fair'ly clear-cut distinction between
                                            transactions balancesand savings
 balances (Hetzel and lilehral9B9), Ear'l
                                        ier, the definition of l,l2had itself
 been broadened include money
              to            narket mutual funds (simpsonl9g0).                                          The
 evident breakdown the Federal ReserveBoard,s M2 model together with large
                 of                                  ,
-recent inflows into stock and bondnutual funds, has stimulated economists
                                                                         to
consider whether the current definition of M2 ought to be expanded include
                                                                 to
 somesubset of stock and bondmutual fund assets (Duca1993, forthcoming;
Feinman
      and Porter 1992).
         one issue addressed this literature is whether an expanded
                           in                                     lil2
aggregateis more "explainaflg', than M2 as curuen y defined.lT Ouca
(forthcoming) argues that an M2 aggregateexpanded include household
                                                to                bond
funds (exclusive of IM and Keoghaccounts) is more explainable than cument
ll2.    In his analysis, Ducauses the Federal ReserveBoard,s standardmoney
demand
     model adjusted to control for RTCand disintermediation effects.is
         ,
Results presentedhere suggest, however,that the Board,s money    model
                                                            demand
can be improvedupon. It is natural to wonderwhether bond-fund-adjusted
                                                                     i,l2

       17 Relatedissues
                                  are whether       monetary      aggregates
                                                                           -ano other than l.l2are
superior indicators of future movements-out-p-ut lnriaiion, andwhether
                                                            in
alternative monetary         aggregates suffiCieniiy underthe FedeialReserve,s
                                              are
contror to serve as intermediate                 targets. As yet, no consensus apparent        is                on
t h e a n s w e rts t h e s eq u e s t i o n s .
                   o
       18 Duca lso a     i n c r u d e s y i e l d - c u r v e a r i a b l ei n s o m e f h i s r e g r e s s i o n s .
                                       a                      v                       o
                                                        2l
remainsmoreexplainable than conventionalI',|2 the context of the improved
                                            in
m o d e l s . B r i e f l y , t h e a n s w e ri s " n 0 . "

           Evidencethat adding bondfunds to H2 does not yield a more explainable
aggregateis shownin Table Al .                          The top half of the table presents root-mean-
squarederrors obtained from modelsthat exclude Duca,s RTCand
d i s i n t e n n e d i a t i o n a r i a b l e s . T h e b o t t o mh a l f p r e s e n t ss i m i l a r r e s u l t s f o r
                                 v
m o d e l s h a t i n c i u d e t h e s e v a r i a b l e s . M o d e l s h a t a r e e s t i m a t e du s i n g D u c a , s
           t                                                            t
bond-fund-adjusted have a ,'M28,'
                 M2                            -meansquaredeffors
                               designation. Root   -

calculated over the entire sampleand calculated only over the period of

            are presentedfor each model
missing money                         .

                                                        better job of
          As noted by Duca, the Boardmodeldoes a somewhat
e x p l a i n i n gg r o w t h i n M Z B h a n i t d o e so f e x p l a i n i n gg r o w t h i n M 2 . T h i s
                                        t
superior performance especially evident over the period from 1990:Q3
                   is
through 1992:Q4,
               and is obtained regardless of whetheror not RTCand
d i s l n t e r m e d i a t i o n a r i a b l e s a r e i n c l u d e di n t h e r e g r e s s i o n s .
                                v
          Results are rather different in the context of the generalized incone-
v e l o c i t y a n d g e n e r a l i z e d o n s u r n p t i o n - v e l o c imy d e l s e v e l o p e dn t h i s p a p e r .
                                          c                                    to        d              i
0ver the period of the missing money,both of the generalized modelsdo a
s u b s t a n t i a l l y b e t t e r j o b o f e x p l a i n i n gg r o w t hi n c o n v e n t i o n a M 2 t h a n i n
                                                                                                        l
explaining growth in bond-fund-adjusted
                                      M2. Over the sampleas a whole, the
generalizedmodelsdo as well explaining movements conventionalM2 as
                                              in
                                      l.lz. Even ln the bond fund- adJusted
explaining movements bond-fund-adJusted
                  in                                       -
M2 regressions, the generalized income-velocityand generalized consumption-
velocity modelsyield root -meansquarederrors that are nuch lower than those
                              -

obtained using the Eoardmode'l the Boardmodel supplemented
                             or                          with RTCand



                                                               22
 d i s i n t e r m e d it i o n v a r i a b l e s ( a , l a D u c a ) . l e
                      a
           The findings presentedin Table Al do not establish that MZshould not
 be expanded include assets held in bondrnarketmutual funds. However,
           to                                                       the
 case for expanding to include bond funds cannot be basedon an argunent
                   li12
 that l.l2Bis more explainable than fi2.                            Instead, it must be basedeither on
 evidencethat ll2B is morecontrolable than l4z, or upondirect evidencethat
      is
 Itl2B a better indicator of future movements output or inflation than is
                                           in
 M2.




     . _ l e . P o i n t e s t i n a t e s o f t h e c o e f f i c i e n t s c h a n g ei t t l e i n t h e g e n e r a l i z e d
                                                                                       l                     -As
nodels whenconventionall,l2 is replaced by bond f-und- usted HZ.                 -        adj                         before,
the coefficient of time squaredaird the wiight attacheO-io itre iO-yeir-
Tfeafu^Ty         bond in the opportunity cost formuia are highly statistic;lly
s i g n i f i c a n t . T h e c o e f f i c i e n t s b f t h e R T C n d d i s i n t E r m i d i a t i o nv a r i a - b l e s r e
                                                                         a                                                   a
i n s i g n i f i c a n t i n t h o s e r e g r e s s i o n s n w h i c ht h e y a r e i n c i u d e d .
                                                             i
 TITERATURE
         CITEO
 Blanchard,0livier.            and             of
                    "Consumption the Recession 1990-1991.,'AEC.Iie.Le
 EconomicReview.Paoersand Proceedinqs (ilay 1993), ?70-14
                                    83
 Chong,Yock Y. and David F. Hendry. ',EconometricEvaluation of Linear l4acro-
 Economic
        ltlodels," Reviewof Economic Studies 53 (August 19g6), 671-90.
Duca, John V. "ShouldBondFundsbe Included in M2?"Journal of Bankinqand
Finance ( forthcomi )
                  ng
            'RTCActivity and the 'Missing
=                                               Ee!-ng4j!.8_La!!ers. (1993), 6Z-
                                          1,12,.',               4t
71.
Dufour, Jean-Marie. "Dumm5r                Variables and Predictive Tests for Structural
C h a n g e . E c o n o m i cL e t t e r s 6 ( 1 9 8 0 ) , Z 4 l - 4 7 .
          "                  s
Feinman,JoshuaN. and Richard D. Porter, ,'TheContinuing l,leakness 142.',
                                                                 in
Financeand Economics
                   DiscussionPaper#209, Board of Gov6rnors the Federal
                                                             of
ReserveSystem(September 1992).
Feldstein, Martin and James Stock. ',TheUse of HonetaryAggregate
                           H.                                     to
Target NominalGDP.' National Bureauof Economic        iloi[i n! paper No.
                                              Research-
4304 (llarch 1993).
Greenspan,
         A1an. "Statement the Congress." Federal ReserveBulletin 79
                        to
(September
         1993), 849-55
Hamburger,
         l4ichael J. "RecentVelocity Behavior, the Demand Money,and
                                                          for
Monetary_Policy.n Conference Monetary
                            on          Targeiing and Velocity, Feiiral
ReserveBankof San Francisco, 1983.
        nBehavior the Money
                  of          Stock: Is There a puzzle?', Journal of
HonetaryEconomlcs (Ju1y 1977), 265-9g
                  3
                                        ',TheBehaviorof iloneyDemand the
lglzel , Robert L. and Yash P. t'lehra.                              in
I980s." Journal of l,lonev,Credit and Bankino2l (November   iSAS;, +SS-OS.
llankiw'_N-.Gregory Lawrence summers. "Money
                                and                   H.                                         and
                                                                                     Demand the Effects of
F i s c a l P o l i c i e s . " J o u r n a l o f l 4 o n e vC r e d i t a n d B a ; k i n q l g ( N o v e m b e r 8 6 ) ,
                                                             .                                                 19
415- 9.2
!4ehra,Yash P. "The Stabil ity of the M2 Demand
                                              Function: Evidencefrom an
Error-Correcti on Flodel Journal of Honey.Credit and Bankinq25 (August
                                  .',
1 9 9 3 ,P a r t l ) , 4 5 5 - 6 0 .

      "Has M2 DenandBecomeUnstable?,' Federal ReserveBankof Richmond
Economic                      l99Z), 27-35.
       Review( September/0ctober




                                                            24
lloore, George . , R i c h a r d0 . Porter, and D a v i d H . S n a l l . " M o d e l i n g h e
              R                                                                           t
Dis       ted Demands ile and lrll: The U , S . E x p e r i e n c en t h e 1 9 8 0 s". I n
                         for                                             i
edi              Hooper,                                                     ,Da                     S€J '
Richard  P o r t e r , a n dR a l p h r y o n ,p p . 2 l - 1 0 5 . U a s h i n g t o n ,. C , , B o a r d f
                                     T                                               0                  o
Governors the FederalReserve
        of                                System,     1990.
Perry, George andChar1es Schultze. "l{asThis Recession
                     L.                      L.                                                Different? Are
T h e y l l D i f f e r e n t ? " B r o o k i n qP a p e r o n E c o n o mAc t i v i t y ( l : 1 9 9 3 ) , 1 4 5 - 9 5 .
       A                                         s         s              i c
S i k l o s , P i e m eL . " I n c o m Velocity and Institutional Change:
                                        e                                   Sone  l{ewTime
                                        '
S e r i e sE v i d e n c e1 8 7 0 - 1 9 8 6 .Journal of Monev. Credit and Bankino 25 (August
                           ,
1 9 9 3 ,P a r t 1 ) , 3 7 7 - 9 2 .
Simpson,        Thomas     D. "The Redefined             l'lonetaryAggregates.
                                                                             "          Federal Reserve
B u l l e t i n ( F e b r u a r y9 g 0 ) , 9 7 - 1 1 4 .
                                l




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     cl,
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     ot
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    (r)
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           o
           o
    t\
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O   t\
    i\
    (o
    l-
    F
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    ct
    t-
    F
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    €
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                                           o
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               ____ _ _-_'-7>-             E
                                           C!
                                           E
                                            I
                                           -o
                                           e
     --.'=-=.---         :--r:--:-----::
                                     -E
                                     .8
                                     "E
                                     s
                                     F
                                     F
                                     E
gg gg gg ggEsEHs g
  gggg g g    ggg
         .
 T A B LIE     Estimates the FederalReserve
                       of                             l.lodel
                                          Eoard,s Demand
                                                 M2
                                                        Sample      Period
Variable                   6 4 : 0 I - 8 6 : 0 4 4 : 0 1 - 8 9 : 0 4 4 : 0 1 - 9 2 : 0 4 4 : 0 1 - 9: 0 4
                                                6                  6                   6            2
Constant                   l. to7"            1 .t 9 4 . '          .64?"               . g30"*
                           (.182)             (.164)              (.1s2)              (.1s6)
Timexl0-3                  -.108t'            - .t22--            -.0971**            -. lo3-*
                           (.032)             (.030)              (.0333)             (.031)
DMHDA                       .00400             .00409'             .00206              .00383
                           (.00208)           (.00les)            (.00217)            (.00204)
D83Q
   I                           .o3os"           .o3oz"              .0 3 1 7 "               l
                                                                                       . 0 3 1"
                           (.0046)            (.0044)             ( .00s0)           ( .0046)
083Q2                      -.00393            -.00309             - .00979           -.00830
                           (.00s32)           (.00s05)            ( .00s57)          (.00s1s)
DCON                       -. 01oo"           -. ol04"            - .o l 1 6 "       - .0109-'
                           ( .0036)           (.0034)             ( .0038)           (.003s)
oct-t                      -.0104**           - . OloT'*         -.00521"            - .00763"
                           (.001s)            (.0014)            (.00u6)             (.00121)
Vt-l                        .179"              .l9l*'              , 102**            .148'-
                           (.02e)             (.026)             ( .024)             (.024)
Aoc.                      -.00763"            -.00783"           - , 0 0 6 6 1 * ' - .00720"
                          (.00144)            (.00133)           (.00r47) ( .00136)
(Ax. - Am._1)               .267-'             .256'"              .204"              .2?7-'
                           (.070)             (.064)             ( .068)             (.063)
(Ax.-.,- Am._1)            . t98"             .2t7"               .106                 .136'
                          (.072)             (.065)              (.070)              ( .05s)
(Ax,-, - Arn._,
             )                 .0927           .0770               .0608              .0702
                          ':::"':::"                             ( .060e)            (.0s62)
       y
D u n m9 0 : Q l - 9 2 : Q 4                                                         -.00806*'
                                                                                     ( .00187)
ssE                            .00146        .00158                .00233             .00197
                               .00436        .00421                .00481             .00443
$$tr                           .653          .665                  .531               .600
* S i g n i f i c a n t a t 5 %l e v e l
** Significant at I% level
Standarderrors appear in parentheses.


                                                          26
    2.
TABLE DufourTest of the Structural Stabil ity of the Board's M2 l,lode'l
         e
S a m p lP e r i o d : 1 9 6 4 l Q l - 1 9 9 2 : Q 4
Date             Coefficient Stnd. Emor
 1990:Ql         -.0017            .0044
1990: 2
   Q             -.0050            .0043
1990:Q3          -.0037            .0044
1990:Q4          -.0099-           .0044
l99l:Ql          -.0042            .0045
1991:Q2          -.0041           .0044
l99l:Q3          -.0135"          .0044
l99l:Q4          -.Oll8.          .OO4O
1992:Ql          -.0130"          .0048
1992: 2
   Q             -.0211"          .0047
1992:Q3          -.0208.'         .0049
1992:Q4          -.0196"          .O0Sz

F Test                  =
                   Frz,ss 3'521"

*    Significant at 5%I evel
**   Significant at l% I evel




                                                       27
    TABLE
        3.        Estimates the Generalized Demand
                                of                            l'l2            lilodel  with Income        as
                  L o n g - R u nc a l eV a r ia b l e
                              S
                                                 Sample od  peri
    V a r ia b le                                4      - 8 9 : 0 46 4 : 0 1 - 9 2 : 06 4 : 0 1 - 9 2 : 0 4
                             6 4 : 0 1 - 8 6 : 06 4 : 0 1                              4
    Constant                   l.lz5"            1.146*'           .951.-            t.olo*-
                               (.251)            (.225)           (.20s)            (.20e)
 Timexl0-5                      .7tg'            .s??-             .rzg'*            .603-'
                               (.333)           (.231)            (.18s)            (.211)
DI'IMDA                        .00974-' .oo8t7..                   .00918** .00836".
                              (.00208) (.002s2)                   (.0027s) (.00282)
D83Ql                          .0333'-           .0322-.           .0327'-           .032?'*
                              (.0046)           (.0042)           (.0041)           (.0041)
D83Q2                         -.00550           -.00371           - .00591 -.00535
                              (.00510)          (.00478)          (.004s2) (.004s3)
DCON                          -.00960"          - . 0 0 9 6 6 . . - .00885-'        - .00887'-
                              (.00344)          (.00327) (.00314)                   ( . 0 0 3 1)
                                                                                               2
oct-l                         -.0164"           -.0161.'          - . ol50--        - .0154"
                              (.0037)           (.0032)           (.0032)           (.0032)
vt-i                           .199--            .192..            . 163*'           .l7l'-
                              (.042)            (.037)            (.035)            (.035)
Aoc.                          -.0124'*          -.01I8'.          - . 0120"        - .0118"
                              (.0030)           (.002s)           ( .0025)         ( .0024)
(Ax. - Am.-,,
           )                   .250"             .257'-            .24s"             .251-'
                              (.067)            (.062)            (.0s7)           ( .056)
(Ax,-,' - Am,_1)               .200'-            .236..            . l g5*'          . 196"
                              (.068)            (.062)           ( .0s7)           ( .0s7)
(Ax._, - Am.-'


Dumrny
             )

    90:Ql-92:Q4
                             ':::"'::1"
                               .0764             .0840            .0941
                                                                 (.0s02)
                                                                                     .0946
                                                                                   ( .0s00)
                                                                                   -.0027?
                                                                                   ( . 0 0 2 1)e
timezxl0-5                   -.365'            - .273--          -.360--           -.303-'
                             (.154)            (.104)            (.084)            (.0e6)
Aoc._.,                      -.00398           -.00382           -.00723*          -.00638'
                             (.003s0)          (.00306)          ( . 00318)        (.0031r)
p                              .zg7*"           .z5o'-            .326"             .307"
                             (.0e6)            (.074)            (.057)            (.0s8)
       E
T A B L3 . C o n t i n u e d

ssE                     .00123   .00132     .00143   .00141
BtlsE                   .00408   .00392     .00383   .00382
R'                      .697     .710       .702     .704
* S i g n i f i c a n ta t 5 %l e v e l
* * S i g n i f i c a n ta t 1 %l e v e l
Standard      errors appear parentheses.
                                   in




                                      29
 TABLE
     4.          Dufour Test of the Structural Stability of the Generai
                                                                      i zed H2 Demand
                 llodel with Income the Long-Run
                                   as                         a
                                                  Scali V a r i b l e
 Sample eriod: 1964:Ql-1992:Q4
      P
 Date                Coefficient Stnd. Error
 1990:Ql             -.0011             .0042
 1990:Q2             -.0028             .0042
 1990:Q3            -.0016              .0043
 1990:Q4            -.0068              .0043
 1 9 9 1Q l
       :            -.0012              .0044
1991:Q2             -.0009              .0045
1 9 9 1Q 3
      :             - .0070             .0046
l99l:Q4             -.0040              .0048
1992:Ql             -.0042              .0050
1992:Q2             -.0098              .0053
1992:Q3             -.0086             .0055
1992:Q4             -.0073             .0055

F Test                 Fp,r5 = .S9l

*    S i g n i f i c a n t a t 5 %| e v e l
**   Significant at l% I evel




                                                30
    TABLE
        5.    Estinates of the Generalized Denand          M2             Modelwith Consumption the  as
              S c a l e V a r ia b le
                                               Sample     peri od
    Variab'le             6 4: 0 1 - 8 6 : 0 4 4: 0 1 - 8 90 4 6 4 :0 1- 9 2 :0 4 6 4 : 0 1 9 2: 0 4
                                              6            :                              -
    Constant               .839"           .829-'         .787"          .8lg*'
                          (.22?)          (.213)         (.les)         (.lee)
    Ti mexl0'l             .551             .671*         .822"          ,717"
                          (.347)          ( .?67
                                               )         (.225)         (.242)
    DH]4DA                 .00661           .0066s'       .00793"        .00712-
                          (.00337)        ( . 00296
                                                  )      (.00265)       (.00274)
    D83Ql                      .0284t-     .0284--       .0293"          .0286"
                          ( .0046)        (.0043)       (.0041)         (.0041)
 D83Q2                    - . 0129'      - .0120'       -.0131"         -.0126-.
                          ( .00s2)       ( .004e)       (.0046)         (.0046)
DCON                      - .00688       -.0o7ol'       -.oo54t'       -.00643'
                          (.00346)       ( .00338)      (.003r3)       (.00312)
oct-t                     - .0137"       - . o132'"     -.0128"        -.0133-'
                          ( .0038)       (.0035)        (.0033)        (.0033)
vt-r                        .l3l'-         .130**        .lzo*'          .lz9**
                          ( .034)        ( .033)        (.030)         (.031)
Aoc.                      -.00941"       - .00969'- - . 0 0 9 5 7 "    -.00945**
                          ( .00300)      (.00?72) (.00262)             (.00256)
(Ax. - Amr-,,
          )                .350**         .3?2-'         .346"          .349'-
                          (.llt)         (.10s)         (.0e0)         (.0e0)
(Ax.-' - Am._1)          -,130           -.105          -.137          -.131
                         (. r23)         (.115)         ( .r00)        (.100)
(Ax.-. - Am._,)            .268'"         .268'*         .259-'         .261.'
                         ( .0es)         (.08e)         (.078)         (.078)
        y
D u m n9 0 : Q l - 9 2 : Q 4                                           -.00272
                                                                       (.00222)
timeaxl0'5               - .354'         - .365"        -.430"         -.385"
                         (. r64)         (.126)         (.10e)         (.116)
Aoc.-',                  -.00649         - .00809.      -.00993-. -.00886.-
                         ( .00376)       ( . 00343
                                                 )      (.00327) (.00323)
F                          .356-'         .358-'         .404."        .383.t
                         ( . 118)        (.086)         (.068)        (.06e)
                                                   5l
    5.
TABLE Continued

ssE                .00125     .00141       .00146   .00143
RMS E              .00412     .00404       .00385   .00384
R-,                .691       .691         .698     .700
* S i g n i f i c a n t a t 5 %l e v e l
** Significant at l% level
Standarderrors appearin parantheses.




                                     32
 TABLE
     6.         Dufour Test of the Structural S t a b i li t y o f t h e G e n e r a l i z e d Demand
                                                                                             142
                l4odelwith Consumption the Scale Variable
                                       as
 Sample eriod: 1964:Ql-199?:Q4
      P
Date               Coefficient Stnd. Error
 1990:Ql            -.0000             .0044
 1990:Q2            -.0028             .0044
 1990:Q3            -.0014            .0044
1990:Q4            -.0061             .0045
1991:Ql            -.0040             .0046
l99l : Q2          - .0023            .0047
l99l:Q3            -.0043             .0048
1991:Q4            -.0029             .0048
1992:Ql            -.0026             .oo5l
1992:Q2            -.0045             .0053
1992:Q3            -.0055             .0053
1 9 9 2Q 4
      :            - .0032            .00s4

F Test                Fp,s = .254

* S i g n i f i c a n ta t 5 %l e v e l
* * S i g n i f i c a n ta t l % l e v e l




                                                33
TABLE Comparing Recent
    7.        the     performance the Alternative Models;
                                 of
       RootMean
              Square
                   Errors andHeanErrors from 1990:Q1-1992:Q4
             M o d e l s s t i m a t e6 4 : Q l - 8 9 : Q 4l o d e l sE s t i m a t e E 4 : Q l - 9 2 : Q 4
                       E              d                   l                           d
ilodel       @@
Board       .01247         .01053                        .00540          .00378
Incorne
Velocity    .00553         .00447           St.Sy,       .OOZ37 .00069                   gt.7%
Consunpti
        on
Velocity .00371            .00332           68.5%        .00145         .00067           gZ.3%


* Percentage
           reductionin mean
                          error relative to the Boardmodel
                                                         .




TABLE
    8.     Comparing       the Recentperformance the Alternative Hodels:
                                                              of
           F o r e c a s tE n c o m p a s s i f rg m 1 9 9 0 : Q l - 1 9 9 2 : Q 4
                                              no
      le
Sarnp'Period: 1964:Ql-1992:Q4
Indenendent
          Variable            Dependent
                                      Variab'le                    T Statistic
     €s - €r                           e8                          7,glg.'
                                       er                          1.703
     €e - oc                           eB                          9.149"
                                       ec                          1.149
     €r - €c                           er                          4.zgl"
                                       ec                           .105
Notes:
     e, = residuals      from Boardmodel
     er = residuals      from generalized income-velocitymodel
     ec = residuals      from generalizedconsumption-velocitymodel
     *- Significant      at S%-evel
                               I
     ** Significant      at l% level



                                                   34
 TABLE9.           Important
               HoI,,       are RTC, si ntermedi on, and Debt-Paydown
                                  Di         ati                   Effects?
 S a m p l e e r io d : 1 9 6 4 : Q l - I 9 9 2 : Q 4
           P
Variable                   BoardMode
                                   l             Income-Vel tv
                                                         oci                  Consumpt -Ve ocity
                                                                                    i on l
Constant                   1.074'*           1.093-'         1. 104-'           .827*-     .851--
                           (.rs7)            (.21?)          (.216)           (.ree)      (.201)
Timexl0-3                  - .116"            .552**          .586*            .696-'      .715.-
                           (.030)            (.204)          (.2r7)           (.242)      (.?42)
DMMDA                       . o04ol-           ,00822"         .00855"         .00694*     .OO7r?'
                           (.001e6)          ( .00277
                                                    )        ( .0 0 2 8 1 )   (.00274)    (.00273)
D83Ql                        .0310"          .o32?'.           .0324"          .0286'*     .0287*
                           ( .0044)         (.0041)          ( .0041)         (.0041)     (.0041)
D83Q2                      - .00519         -.00427          - .00438         -.0124"     -.012s'.
                           ( . 00s03
                                   )        (.00454)         ( . 00460
                                                                     )        (.0046)     (.0046)
DCON                       -.0106"          - ,0ogo7** - . 0 0 8 7 8 - ' -.00663*         -.00627'
                           (.0034)          (.003r0) (.00312) (.00313)                    (.00314)
oct-i                     -.00922"          -.0160--         - .0161"         -.0133"     -.0136*-
                          (.00128)          ( .0031)         (.0031)          (.0033)     (.0033)
Vt -'t                      .172-*            .184"           .186"            . t30*      .133'-
                          ( .02s)    ( .o3s)                 (.036)           (.031)      (.031)
Aoc.                      - . oo7s8" - . o 1 2 0 "           -.olt7"          -.00976'-   -.00936*.
                          ( .00r31) ( . 0 0 2 4 )            ( .0024)         ( .00256)   {.002ss)
(Ax. - Am.-''
           )               .24t-'            .258'.           .265"            .349"       .362'*
                          (.061)            (.057)           (.0s7)           (.0e1)      (.oet)
(Ax.-' - Am._,
             )              .t75"             .2ll"            . e04"         -.123       -.146
                          ( .063)           ( .057)          ( .os8)          (.101)      (.100)
(Ax.-, - Am.-'
             )             .0909             .0993.           .lo2'            .289"       .zlg"
                          (.0s44)           (.04e8)          ( .oso)          (.07e)      (.07e)
DRTCxl0-5                 - .3 1 5 "       -.148                              -. 132
                          (.07e)           ( .088)                            ( .0e0)
DISINTER                  -.0?07"          - .00834          - .00536         -.00460     -.002?5
                          (.004s)          ( .004s4)         (.00404)         (.00436)    (.00387)
T                                                             .0269                        .0396
                                                             (.02s4)                      (.030s)


                                                        J5
       E
T A B L9 . C o n t i n u e d

t i mezxl0-5                     -.283-.     - .300-*   - .376-*     - .386"
                                 (.0s2)      (.0e8)     (.116)       (.11s)
Aoc.-,                           -.00510     -.00493    -.00848*" - . 0 0 8 1 2 *
                                 ( .002e8)   ( .00301
                                                    )   (.003221 (.00322)
p                                  .279"'     .246"      .374"         .328--
                                 ( .060)     (.077
                                                 |      (.072)       ( .0e0)
ssE                     .00180    .00137     .00140      .00142       .00143
RMS                     .00426    .00378     .00381      .00385       .00386
F                       .6 3 1    .709       .704        .699         .697
l.lE90:Ql-92: Q4  .00047          .00001     .0001e      .00007       .00002
Rl.lSE90:Ql-92:Q4 .00390          .00?02     .00238      .00122       .00127
* S i g n i f i c a n t a t 5 %l e v e l
** Significant at l%'level
Standarderrors appear in parentheses.




                                        36
 TABLE
     10. Dufour Test of the structural Stability of the Board's M2llodel
 Sample eriod: 1959:Ql-1992:Q4
      P
 Date                      Coefficient Stnd. Error
 1990:Q1                   -.0019            .OO4T
 I990:Q2                   -.0053            .0047
 1990:Q3                   -.00?7            .0047
 1990:Q4                   -.0080            .OO4t
 l99l:Ql                   -.0024            .0049
 1991:Q2                   -.0019            .0048
1991:Q3                    -.oll3'           .0048
1 9 9 1Q 4
      :                    -.0085            .0049
1992:Ql                    -.0079            .0050
1992:Q2                    -.0164"           .0049
1992:Q3                    -.0143"           .O0Sl
1992:Q4                    -.010t           .0053

F Test                      F r z , r o= 1 . 9 6 1 *
                                       c

Single Dumqy
9 0 : l- 9 2 : 4
    Q        Q             -.0065'-         .0019

*    S i g n i f i c a n t at 5%I eve'l
**                              '|
     S i g n if i c a n t at l% evel




                                                       37
 TABLE
     ll.          Testingthe Pre-1964
                                    Structural stabil ity of Alternative l4ode'ls
          e
 S a m p lP e r i o d : 1 9 5 9 : Q l - 1 9 8 9 : Q 4

 Date =--=.-9ryE..--=- Er.
      coefficient Stnd.                     = GqrleralizedIncome        Generalized Consumption
                                                                                        -$=
                                            Coefficient Stnd.En         Geffint     StnA.
 59:Q4 - . 0 1 6 8 - -       (.0047)        -.0060           (.0051)    - .0073     (.00s1)
 6 0 :Q l   -.or02'         (.0047)           .0000          (.00s0)    - . 0012    (.00s1)
 6 0 :Q 2 - . 0 1 6 0 . .   (.0049)         -.0078           (.00s0)    - .0085     (.00s1)
60:Q3 -.0112*               (.00s1)         -.0049           (.0050)    - .0002     (.00s3)
6 0 :Q 4 - . 0 1 5 8 "      (.0050)         -.0094           (.004e)    -.0148"     (.0051)
6l:Ql       -.0080          (.0048)         -.0007           ( .0048)   -.0035      (.00st)
6l:Q2 -.0081                (.0046)         -.0011           ( .0046)   - .0067     (.00s0)
6l:Q3 -.oll2'               (.0046)         -.0044           (.0046)    - .0068     (.004e)
6 l : Q 4 - .0122'          ( .0047)        - .00s9          ( .0047)   - .0075     (.0050)
6 2 :Q I - . o l l o *      (.0047)         -.0056           (.0047)    - .0021    (.004e)
62:.QZ - . 0 1 4 2 *        (.0047)        -.0102'           (.0046)    -.0094'    (.0047)
6 2 :Q 3 - . 0 1 7 4 "      (.0048)        -.0143'*          (.0046)    -.0119'    (.0047)
62:Q4 -.0105'               (.0047)        -.0067            (.0048)    -.0043     ( .0048)
6 3 :Q l - . 0 0 6 s        (.0046)        -.0039            ( .0044)   -.00?2     (.0046)
63:Q2 -.0048                (.004s)        _.0ol8            (.0043)    -,0026     ( .004s)
63:Q3 - . 0 0 3 6           (.0044)        _.0014            (.0042)    -.0026     (.0044)
63:Q4 -.0008                (.0044)          .0018           (.0042)    .0030      (.0044)

F Test         Fr,n = 2.071'                     Ftr,r, = I .055           Ft7,ro= I .098

Single Dunnny               -.0093-'                         - .0033               -.0037
59:Q4-63:Q4                 (.o0Zl)                          (.0023)               ( .0024)

* Significant at 5%level
** Significant at l% level
Standarderrors appearin parentheses.

                                                        38
    12. Companing Past performance the Alternative Models:
TABLE             the              of
                           from 1959: - 1963Q4
        Forecast Encompassing       Q4     :
Sample eriod: 1959:Ql-1989:Q4
     P
Indeoendent
          Variable        Deoendent
                                  Variable       T Statistic
         €o - €r                eB               2.149*
                                er               -.889
         €r - €c                eB               2.395*
                                ec               -.703
         €r - €c               e,                1.367
                                                 - .805
                               ".
Notes:
         es = residua'ls fron Boardmodel
         er = residuals from generalized income-velocityrnodel
         ec = residuals from generalizedconsumption-veiocitymodel
         *- Significant at S%-evei
                               I




                                      39
 TABLE .
     Al       DoesAdding BondFundsto MZ Yield a ltloreExplainableAggregate?
 Sample i od:
       Per        1964:Ql-1992:Q4


l'lodel Excl udi ng RTCand
      s
Disi ntermedi on Effects
              ati
Board M2.'                                           .0047                .0057
Board ll2B"                                          .0045                .0056

General
      ized Income-Velocity
                         lil2                        .0036                .0026
General
      ized Income-Velocity
                         M2B                         .0035                .0029

General
      ized Consumpti
                  on-Vel ty M2
                       oci                           .0035               .0015
General
      ized Consumption-Vel ty lt2B
                       oci                           .0036               .0018


l,lodel Incl udi ng RTCand
       s
Dis i ntermedation Effects
             i
Board M2'*                                           .0041               .0044
Board M2B"                                           .0040               .0040

General
      ized Income-Velocity
                         M2                         .0035                .002?
General
      ized Income-Velocity
                         ilZB                       .0035                .0025

Generalzed Consumption-Veloci M2
      i                   ty                        .0035                .0013
General
      ized Consumpti
                  on-Vel
                       ocity il28                   .0035                .0016


Notes
    :
        Root   -mean - squared       errors are not correctedfor degrees of freedom
        l o s t i n e s t i m a t i n gh e m o d e l s .
                                      t
        As reportedin Duca(forthcoming).




                                        40
               RESEARCH PAPERS OF THE RESEARCH DEPARTMENT
                     FEDERAL RESERVE BANK OF DALI,AS

                   Available, at no charge,from the ResearchDepartment
                     Federal ReserveBank of Dallas. P.O. Box 655906
                                  Dallas, Texas 75265-5906

9201 Are Deep RecessionsFollowed by Strong Recoveries? (Mark A. Wynne and
     Nathan S. Balke)

9202 The Case of the "Missing M2" (John V. Duca)

9203 Immigrant Linl<s to the Home Country: Implications for Trade, Welfare and
     Factor Rewards(David M. Gould)

9204 Does Aggregate Outpur Have a Unit Root? (Mark A" Wynne)

9205 Inllation and Its Variabiliry: A Note (Kenneth M. Emery)

9206 Budget Constrained Frontier Measures of Fiscal Equality and Efficiency in
     Schooling(ShawnaGrosskopf,Kathy Hayes,Ilri Taylor, William Weber)
       'the
9207      Effects of Credit Availability, Nonbank Competition, and Tax Reform on
       Bank ConsumerI-ending (John V. Duca and Bonnie Garrett)

9208 on the Future Erosion of the North American Free Trade Agreement (williarn
     C. Gruben)

9209 Threshold Cointegration(Nathan S. Balke and Thomas B. Fomby)

9210 cointegration and rests of a classical Model of Inllation in Argentina, Bolivia,
     Brazil, Mexico, and Peru (Raril Anibal Feliz and John H. Welch)

9211 Nominal FeedbackRules for Monetary Policv: Some CommentsCEvanF.
     Koenig)
       'the
9212          Analysisof Fiscal Policy in Neoclassical
                                                     Models' (Mark Wynne)

9213 Measuringthe Value of Schooleuality (tori Taylor)

9214 ForecastingTurning Points: Is a Two-state characterizationof the Business
     Clcle Appropriate? (Kenneth M. Emery & Evan F. Koenig)

921,5 Energy Security:A Comparisonof Protectionistpolicies (Mine K. yricel and
      Carol Dahl)
9276 An Analysisof the Impact of Two Fiscal Policieson the Behavior of a
     Dlnamic Asset Market (Gregory W Hutrman)

9301 Human Capital Externalities,Trade, and Economic Growth
     (David Gould and Roy J. Ruffin)

9302 T\e New Face of Latin America: Financial Flows, Markets, and Institutions in the
     1990s(John Welch)

9303 A General Two Sector Model of Endogenous  Growh with Human and
     PhysicalCapital (Edc Bond, Ping Wang, and Chong K. yip)

9304 The Political Economy of School Reform (S. Grosskopf,IC Hayes,L. Tayloq
     and W. Weber)

9305 Money, Output, and Income Velocity (Theodore Palivosand Ping Wang)

9306 Constructing an Alternative Measure of Changesin Reserve Requirement
     Ratios (JosephH. Haslag and Scott E. Hein)

9307 Money Demand and Relative PricesDuring Episodesof Hyperinflation
     (Ellis W' Tallman and Ping Wang)

9308 On Quantity Theory Restrictionsand the SignallingValue of the Money
     Multiplier (JosephHaslag)

9309 The AJgebraof Price Stability (Nathan S. Balke and Kenneth M. Emery)

9310 Does It Matter How Monetary Policy is Implemented? (JosephH. Haslag and
     ScotrE. Hein)

9311 Real Effects of Money and Welfare Costs of Inflation in an Endogenously
     Growing Economy with Transactions Costs (Ping Wang and Chong K. Yip)

9312 Borrowing Constraints,
                          HouseholdDebt. and Racial Discrimination in Loan
     Markets (John V. Duca and Stuart Rosenthal)

9313 Default Risk, Dollarization, and CurrencvSubstitutionin Mexico
     (William Grubenand John Welch)

9314 TechnologicalUnemployment(W. Michael Cox)

9315 Output, Inflation, and Stabilizationin a Small Open Economy;EvidenceFrom
     Mexico (John H. Rogers and Ping Wang)
9316 Price Stabilization, Output Stabilization and Coordinated Monetary Policy Actions
     (JosephH. Haslag)

9317 An Alternative Neo-Classical
                                Growth Model u'ith Closed-FormDecision Rules
     (Gregory W. Huffman)

9318 Why the CompositeIndex of Irading Indicators Doesnt Irad
     (Evan F; Koenig and'Kenneth'M. Emery)

9319 Allocative Inefficiency and l-ocal Government: Evidence Rejecting the Tiebout
     Hypothesis (I-ori L. Taylor)

9320 T}e Output Effects of Government Consumption: A Note (Mark A Wynne)

9321 Should Bond Funds be Included in M2? (John V. Duca)

9322 Recessionsand Recoveries Real Business
                              in              Clcle Models: Do Real Business
     Clcle Models Generate Clclical Behavior?(Mark d Wynne)

9323* Retaliation, Liberalization, and Trade Wars: The Political Economy of
      NonstrategicTrade Policy (David M. Gould and Graeme L Woodbridge)

9324 A General Two-Sector Model of EndogenousGrowth with Human and Physical
     Capital: Balanced Growth and Transitional Dynamics (Eric W. Bond, Ping Wang,
     and Chong K. Yip)

9325 Growth and Equity with EndogenousHuman Capital: Taiwan's Economic Miracle
     Revisited (Maw-Lin I-ee, Ben-ChiehLiu, and Ping Wang)

9326 Clearinghouse Banks and Banknote Over-issue (Scott Freeman)

%n    Coal, Natural Gas and Oil Markets after World War II: What's Old, What's
      New? (Mine K. Yiicel and Shenryi Guo)

9328 On the Optimality of Interest-BearingReserves Economiesof Overlapping
                                                 in
     Generations(Scott Freemanand JosephHaslag)

9329* Retaliation, Uberalization, and Trade Wars: The Political Economy of
      NonstrategicTrade Policy (David M. Gould and Graeme L. Woodbridge)
      Reprint of 9323

9330 On the Existence of Nonoptimal Equilibria in Dynamic StochasticEconomies
     (JeremyGreenwoodand Gregory W. Huffman)

933I The Credibility and Performanceof Unilateral Target Zones: A Comparisonof
     the Mexican and Chilean Cases(Raul A. Feliz and John H. Welch)
9332 Endogenous Growth and International Trade (Roy J. Rutrin)

9333 Wealth Effects, Heterogeneity and Dynamic Fiscal Policy (Zsolt Becsi)

9334 The Inefficienry of Seigniorage
                                   from Required Reserves(Scott Freeman)

9335 Problems of Testing Fiscal Solvencyin Higb Inflation Econorries: Evidence
     from Argentina, Brazil, and Mexico (Johrf H. Welch)

9336 Income Taxes as Reciprocal Tariffs (W. Michael Cox, David M. Gould, and Roy
     J. Ruffin)

9337 Assessing Economic Cost of Unilateral Oil Conservation(StephenP.A Brown
               the
     and Hillard G. Huntington)

9338 Exchange Rate Uncertainty and Economic Growth in latin America (Darryl
     Mcl-eod and John H. Welch)

9339 Searching for a Stable M2-Demand Equation (Evan F. Koenig)

								
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