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An exposé of disguised deposits
Journal
of Econometrics
15 (1981) 117.-137. North-Holland
AN EXPOSfi
OF DISGUISED
Pubhshmg
Company
DEPOSITS
P.A. TINSLEY
and Bonnie GARRETT* with Monica FRIAR
1. Introduction In the past ten years, product differentiation by commercial banks and other financial intermediaries has accelerated at a furious pace. New or refurbished liabilities marketed to the public have included: certificates of deposits (CD’s), Eurodollars, bank-related commercial paper, deposits in offshore branches, NOW and POW accounts, money market certificates, and immediately available funds (IF). In the case of commercial banks, each new product is designed to attract additional funds from non-bank sectors or defend existing deposits against raids by bank and non-bank competitors by paying yields significantly higher than the ceiling or statutory rates permitted on traditional core deposits. Since many of these financial innovations were initially not subject to reserve requirements, they were not exposed to the intensive monitoring associated with reservable liabilities. As a result, the proliferation of financial innovations has effected a deregulation of commercial bank borrowing that is incompletely measured and, therefore, subject to speculative analysis by government and private economists. Perhaps the most widespread circumvention of the statutory prohibition of interest payments, interest ceilings on deposits (Regulation Q), and reserve requirements (Regulation D) was accomplished by commercial bank purchases of immediately available funds (IF) from non-bank customers under both collateral (repurchase agreements)’ and non-collateral (Federal *We are indebted to C. Lucas, E. Regan, L. Rtbble, and S. Taylor for data: J. Berry and G. Frtes for computattonal assistance; and D. Hester and anonymous referees for perceptive comments. The views expressed herein are solely those of the authors and do not represent the views of the Board of Governors or the staff of the Federal Reserve System. ‘A repurchase agreement denotes a sale of U.S. government or agency securities in exchange for immediately available funds with an arrangement for the securities to be repurchased and the funds returned at a future date, usually the begmning of the next business day. Although ‘RP’ 1s used generically to describe both sides of the transaction, the borrower of funds is technically ‘selling’ securities to be repurchased by agreement whereas the lender of funds is conducting a reverse repurchase agreement, ‘buying’ securities to be resold in the future.
funds) arrangements. Propelled by high interest rates in 1973-74 and competition with government security dealers for short-maturity funds, this traditional market for interbank trading of excess reserves was transformed into a major source of funds from non-bank sectors. Net bank purchases of IF grew from $1 billion in 1967 to over $44 billion by mid-1978. This growth was accompanied by a massive overprediction by conventional transactions formulations of money demand” beginning in mid-1974 and of approximately a coincidence suggesting that traditional demand the same magnitude;3 deposits had been displaced in the portfolios of many non-bank sectors by sales of IF. The IF innovation has several unique characteristics: (i) until recently. the 1F market remained relatively unencumbered by regulatory restrictions,” (ii) except for an implicit construction provided by quarterly call reports (where final tabulation is available with about a six-month lag), there is no published measure of net IF borrowing by all commercial banks, and (iii) there has been no systematic empirical evaluation of the displacement of demand deposits by IF held by non-bank sectors.5 The aims of this paper ‘The typtcal transacttons model apectfies that real money balances demanded are a functton of a transactions proxy. such as real GNP. and nommal yrelds on one or two competing shortterm liquid assets. Hamburger (1977) suggests that the apparent overprediction is an illuston largely due to neglect of the asset demand for money. The investment motive is represented in hts analysrs by substitutmg the real yield on equtty and nominal yreld on long-term bonds in place of the short-term opportunity yrelds. Tinsley, Garrett and Friar (1978) found that adding these yields on long-term assets to the conventional transactrons formulation reduces the overprediction by only about 20”,,. ‘By mid-1978, the cumulative overpredictton of demand deposits by standard formulations had reached $44 billion, as shown later. “The Federal Reserve Board recently imposed reserve requirements on member bank IF rates, these transactions with non-member banks and non-banks. At current interest requirements increase the effective yield paid on borrowm~s from non-exempt sectors by about IO0 basts points. It is expected that this tax on membershtp will encourage the growth of nonbank financial intermediatton and increased partictpatton by member banks in unregulated International markets through foreign branches. ‘Since completton of this paper [a preliminary version appeared in Tinsley. Garrett and Friar (1978)]. several arttclcs habe discussed this issue. A detailed critique is beyond the scope of thts paper. but several ob\er\ations might highlight differences between these studies and the current paper. Although Lombra and Kaufman (197X) conjecture that demand deposits have been dtsplaced by non-bank IF sales. their sample span ends in 1974 just as the shaft began. Their measure of IF is net purchases by large weekly reporting banks (see ‘IF,‘ below) whrch exceeds the December 1976 call report measure of IF by 40”,,. Garcia and Pak (1979) employ a measure of net IF based on flow of funds data that not only exceeds the December 1976 call measure by X0”,, but is about 20”, bigger than the overprediction ‘gap’ of a conventional transactions model of money demand. Both Wenninger and Sivcsind 11979) and Porter. Srmpaon and Mauskopf (1979) add measures of collateral IF purchases or RPs (as an approximatron of IF borrowed from non-financial sectors) as well as shar-es in money market mutual funds (MMMF) to conventional money to construct an alternative dependent variable rn a transactions formulatron of money demand. The collateral IF data used by the former IS a measure of purchases by a subset of large banks (see ‘IF,,’ below) whrle the construction u\ed hy the latter 15 ba\ed. in part. on an inter-polatton usrng
P.A. Tiusley rt ul.. An exposb ofdisguixd
deposits
119
are to indicate that several incomplete measures of IF activity can be pooled to construct a measure of total commercial bank IF and that this measure can be used to provide a data-based estimate of displaced demand deposits. A construction of net IF held by non-bank sectors is discussed in section 2. An empirical model of non-bank holdings of IF and demand deposits is presented in section 3; this model reduces the errors of a standard predictor of demand deposits by about 80”:;).
2. An estimate of net immediately
available funds (IF)
Despite recent interest in the rapid growth of the IF market, there is no measure of the full extent of participation by non-bank sectors. The most comprehensive data are provided by commercial bank call reports (IF,) where the end-of-day net IF position of insured banks is reported for quarterly call dates (since 1973) and the net position of all banks is reported for semi-annual call dates (June and December).6 A more frequent monitor is provided by the weekly FR416 survey where the end-of-day net position (lF,) of some 300 large commercial banks is reported for the last day of statement weeks (Wednesday).’ Finally, the daily net IF activity of 46 of the largest commercial banks (IF,) is recorded in the FR716 reports. On the basis of some prior reasoning, it is expected that the unobserved average IF position of commercial banks will be bracketed by the reported estimates IF, s IF 5 IF; 2 IF,. IF, may understate the typical IF position of the commercial bank sector because, as suggested by Hester (1978), there may be considerable windowdressing by banks around call dates as they attempt to lower visible debt service. The FR716 measure. on the other hand, will tend to exceed IF since it includes IF purchases by daily reporters from both banks and non-banks. At the end of 1976, for example, the fifty largest banks (in total asset size) accounted for about 7036 of total IF purchases, and more than half the total purchases were interbank transactions. Similarly. it may be expected that IF, only two special surveys of large banks (in April 1974 and December 1977). Application of the analysis of liquid asset demand advanced in Tinsley, Garrett and Friar (1978) would suggest that MMMF 1s more of a substitute for savmgs deposits and that a closer competitor to demand deposits (and IF) would be found in measures of Eurocurrency deposits, an extension not attempted here. The yield on IF does not appear either as an own rate or a competing rate m any of these studies. The conceptual imprecision of reported measures of IF and the unavoidable increase In uncertainty of ‘monc)‘ demand projections due to ambiguous definitions of transactions and investment demands for hquid assets are also not discussed. bAs of the December 1977 call. there were 14,000 insured commercial banks and 94 noninsured banks. ‘There were 317 weekly reporting banks in mid-1978.
will exceed IF, if a portion of funds obtained by 416 reporters is retained and not resold to the subset of banks also reporting in FR716. The FR716 report is of special interest since it provides the only direct estimates of net sectoral positions.’ IF, = IF,, + IFd, + IF,, -IF,,
(1)
where IF,, =net unsecured IF purchased from commercial banks by 716 reporters. IF+ = net unsecured IF purchased from other depository institutions by 716 reporters, IF,, = net secured IF purchased from non-financial sectors by 7 16 reporters, IF, =net secured IF (RP’s and collateral loans) sold to U.S. government securities dealers by 716 reporters. More explicit connections between unohserwd IF and the three report measures (IF,, IF,, and IF,) are provided by the following specifications: The first approximation of net IF purchased by all commercial banks is based on the FR716 reports.
where x is a T x 1 vector of the natural logarithms unadjusted, monthly averages of daily IF. The columns Z, are zLO(t) = 1
of the seasonally of the T x 5 matrix
(unit vector),
z,,(t)=ln(IF,,+IF,,),, t=l,...,?;
~12(t)=ln(IF,,+IF,,-IF,),-~,,(r), z13(t)=RFF,. z14(t)= (RFF-RCP),.
by 716 Since ;I1 and z12 measure only the direct purchases from non-banks reporters, the yields on Federal funds and 4-6 month commercial paper are also included to explain any non-proportional movements in the remaining sales of IF by non-bank sectors. A second approximation is based on the FR416 reports, x=Z,h,+a,,
E[tr2 ti,lrr* (,j)] =a,,dij,
(2b)
E[LI, (i)tr,(j)l=a12fil.
‘Both FR416 and call reports prior to March the IF sales of commercial banks.
31, 1976 provide
limlted sectoral
detail on only
121
where the columns
of the T x 4 matrix
zzO (t) = 1
Z, are
(unit vector),
zzl(~)=~n(IF4),~ z,,(r)=ln(IF,,+IF,,-IF,+IF,,)-I,,,
t=1,...,7;
zz3 (t) = RFF,. Both zL2 and zz3 are included to capture the overstatement of IF by IF, due to the net purchases from other commercial banks also included in IF,;’ it is expected that the coefficients of both regressors will be negative.” Also, since FR416 is a one-day report, adjacent Wednesday data were averaged to provide estimates of weekly average IF before constructing the monthly averages, IF,. A reverse averaging procedure was used in the relationship between the monthly average of daily positions, IF. and the one-day call measure, IF,.
ECN3Ci)(13 (.i)l
=".?,,bij,
y=z3h3+Cx+D,a,.
(2c) E[rr,(i)Nk(j)]=O,
k=l,2.
where y is a N x 1 vector of In IF,, and C is a known N x T weighting matrix (N< T) that transforms neighboring monthly averages of IF to approximations of the one-day call estimates. * ’ The first regressor, z3, in (2~) is an approximation of the bias introduced by window-dressing in call reports and consists of the ratio of net IF recorded by FR416 reporters on call reports to the average of net IF recorded on FR416 reports in neighboring months,
The mean elasticity of this regressor, h3, is unrestricted and may be zero in the absence of detectable reporting ‘bias’; however, a random coefficient specification was selected to allow for the possibility of non-systematic over-
9Note that z,, +z12 +:22 =In IFi; this partxular format is selected to allow the possibility of equivalent elasticities for FR716 components. “As noted in Tinsley, Garrett and Friar (197X), the estimated RFF elasticity of small bank IF supply will be negative in the absence of adjustment for the loan demand of small bank customers. “The exact specification of the weighting matrix C is available on request; the row format is not systematic since call dates are not evenly spaced in calendar time.
P.A. Tinsky et ctl., .An
122
~spo,s~ of di,tguiseddepmir.~
or under-reporting. (3)
h3(t)=h3+uj(r).
Thus, D, is an N x N diagonal matrix with zj, along the main diagonal. Call dates fell at the end of statement weeks a total of nine times during the sample period December 1969 through December 1976. so it was possible to check the consistency of IF, and IF, recorded by weekly reporters for these dates. It was disturbing to observe that the average discrepancy in IF reported for the same day by FR416 banks was just under one-half billion dollars and reached a peak discrepancy of $1.5 billion. A closer examination, however, showed that only two reporting banks were responsible for 75 “/ of these two banks were the average error (and 66:;) of the peak discrepancy); subsequently dropped from the 416 measures.i2 Since IF (or X) is unobservable. the equation set (2) was transformed to an estimable format by substituting (2a) and (2b) into (2~) yielding the stacked system13 P1 Ye
Y=Zb+u.
This system (4) was estimated covariance matrix
(4) by GLS using an estimate
of the variance-
(5) where the matrix
partitions
“The two banks were not elimmated from the total call estimate IF, under the operational assumption that the call estimates were accurately recorded. “All data are seasonally unadjusted. The sample span extended from December 1969 to January 1977, including seven semi-annual calls through 1972, and quarterly calls thereafter. Several alternattve formats were estimated including (i) allowances for trend and seasonal differences between IF and the several reported measures of IF, and (ii) autocorrelation in both u, and az : the empnical results did not support the alternative formats,
123
are derived
from the definitions u, =Ca,
The variances system’”
+D_a _ 3’
of the stochastic u2
=
of the stochastic
disturbances
of (4).
C-a, + D,a,.
disturbances
were. in turn, estimated
m=Ma+e,
by the
(6)
where m is a 3N x 1 vector residuals of (4).
of products
and
cross-products
of the OLS
m’ = [m; rn; m;], m, = ri, * ii,, m2 = i2 * &, m3 = 2, * fi,, where ‘*’ denotes the element-by-element unknown ‘coefficient’ vector is
and the 31~ x 4 regressor
matrix
Hadamard
product.
The
4x 1
is
where ly denotes an N x 1 unit vector. System (6) was also estimated by GLS using OLS estimates elements of the covariance matrix of the discrepancy vector e.
to construct
(7)
where Iij = 2!C?;, CI.~=2QrrQ,2.
i=1,2,
j=l,2,
C,3=2Q,~Qr2,
~33=Qlla22-tnf2.
“Although the equation system (2) may be interpreted as a set of multiple indicators of unobservable (or. more precisely. Imperfectly observed) IF following the analysts developed by Zellner (1970) and Goldberger (1972), the estimators of the covariances of unobserved components used in this paper are similar to the approximate GLS estimators proposed for random coefficient models by Theil and Mennes (1959) and Hildreth and Houck I1968). See also discussion of and references to minimum variance quadratic estimators of variance component\ 111 Chapter 9 of Searle (1971).
124
P.A. Tins/e), C? (II.. An expo.sG of disguisrd
The specification
of the discrepancy
covariance
drposirs
is illustrated
for the case of
c 337
using the distribution
condition
E[abcd] Final estimates
that
for
zero-mean
=E[ab]E[cd]
variables
+E[u(.]E[bd]
of the equation
with
a joint
normal
+E[ud]E[b~].
set (2) are
x= -0.02+1.09z,,+1.38z,2-0.04z,3+0.11z,,+a,, (0.1) (41) (21) (6.9)
(2a’) (4.3)
r+/, =(~.163x IO 3 s= - l.20+1.19rl, (3.0) ri ,,=0.317 ~=l.l8z,+Cx
~- I.Xz,,-0.03z2,+a2,
(32)
(21)
x 10-2, (i,z=o.121
(2b’)
(4.8) x 10--2.
t/),cl,.
(2c’)
(8.9 1 c?33 =0.292 x lo- ‘. These estimates suggest that call reports underestimate net IF purchased by all commercial banks by approximately 17”,/,. However, there is considerable seasonal variation where the average underestimate ranges from OO/, for the March calls to 36 % for the December calls. Final ‘predictions’ of x (or net IF) can be obtained if estimates of the structural equation innovations a’= [a; a;] can be constructed from the residuals of the stacked system u’= [u; u;]. Unfortunately, this objective is subject to an irreducible measurement error. Although the stacked residuals u are consistently estimated, this condition cannot be met for the unobserved structural residuals a.” ISSee the discussions of the ‘uncertainty principle’ in Swamy and Tmsley 11980).
(MARL) estimator
and
the minimum
average
risk
linear
P.A. Tinsley et crl., An expost:
Unique, linear risk matrix
estimates
of disguiseddeposits
ci= Gli are provided
125
by minimizing
the average
(9)
R=E[a-Gu][a-Gu]‘,
where expectations are taken with respect expectation of u given a, and the unconditional differential of the average risk matrix is
to both expectation
the conditional of a. The total
dR=dG(-E[ua’]+E[uu’]G’)+(-E[uu’]+GE[uu’])dG’, where dG is an arbitrary perturbation about vanish if the filter gain matrix G satisfies
G. The first-order
variation
&[uu’] =E[uu’], where the variance
is defined in (5) and
1
011g::
[ 012 Thus, ‘smoothed’ covariance
(10)
E[uu’] =C,,
E[uu’] =
estimates
@C’.
of u are provided
011 012 01,
~=~(~-~)(~_q’=
i g12
022
by G;
-
with the ‘posterior’
Gc,,@,
(11)
1
where it is apparent that S does not vanish presence of u3 in u. By construction, the two predictors of X,
2,
will
as T-+m
due, in part,
=z, 6, + ci,,
to the
W-V
are equivalent at call dates CP, =CIz, but may differ in the intervening periods. To resolve this selection problem, a ‘pooled’ estimate is constructed, 2=
wi, + (I,
where the weighting
- W)f,
matrix
(13)
)
W is chosen
to minimize
the average
risk matrix
126
P.A. Tinslry
et ul., An exposP cfdisguised
&posits
Billions of dollars
1970
1971
1972
1973
I974
1975
I976
Ftg. I. Selected estimates of net IF funds supplied by non-bank sectors. 197O.lL76.1V. See text for explanatton of survey estimates (IF,, IF? and IF,) and construction of pooled estimate (I?); all data seasonally adjusted by X-l 1.
E[e,e&]
of the ‘pooled’ prediction
error
The optimal pooling matrix is defined by the appropriate ‘posterior’ covariance S defined in (I 1) above,
partitions
w=rs,,-s~llcs,l+sz2-s1z-szll-‘.
of the
(14)
The unit trace, tr (@)/-I; of the estimated pooling matrix is 0.59 indicating that the FR716 measures are assigned slightly more emphasis than the FR416 reports in the final estimate of IF.ih The final construction of net IF supplied by non-bank sectors is compared to the net IF measures of various reports in fig. 1. 3. An estimate of the displacement As indicated by Enzler, Johnson traditional formulations of money
of demand deposits (DD) by IF and Paulus (1976) and Goldfeld (1976) demand functions began to overpredict
lbThe unit trace of the pooling matrix that would minimize the average risk matrix of the poooled prediction error prior to call report measurement is 0.82. This dtstinction is of some sigmficance since the reporting lag on call reports IS about six months whereas the 1, estimate (with u*t=0) could be available with about one-day lag.
P.A. Tins/q
rt al., An exposh of disguised deposits
127
significantly in mid-1974. Since persistent overprediction was confined to demand deposits, the currency component of M, will be ignored in this discussion. The swift and thorough deterioration of the standard money demand function is illustrated by the first two equations in table 1 where the sample span of eq. (2) is only twelve quarters longer than the seventy-five quarter sample span of eq. (1). Previous analysis by the authors (1978) of the empirical structure of transactions costs indicated that the precautionary transactions demand for checking deposits in the spectrum of liquid assets might be effectively dominated by IF balances in the portfolios of large participants in the IF market. On the grounds that ‘if it looks like water and tastes like water, it might be water’, the simplest approach to restoring a traditional money demand function is to add demands for IF” and demand deposits, DD. The only modification of the standard demand format is the inclusion of an own rate on IF, approximated by the yield on Federal funds, RFF. For convenience, the approximation In (DD + IF) = In (DD) + IF/DD is also used.” A comparison of eqs. (1) and (3) in table 1 indicated that even this crude redefinition of ‘money’ recovers many of the characteristics associated with traditional money demand functions. The competing yield on passbook deposits is restored, and the long-term elasticities are similar. However, the revised demand function (3) also exhibits atypical dynamic properties : First, the mean lag of adjustment is about ten weeks, a reduction of nearly 70% from the mean lag of twenty-nine weeks implied by eq. (1). [The mean lag of eq. (2) is infinite.] Second, the strength of the positive elasticity of the own rate would reverse the usual operating rules of short-run monetary policy. It can be shown that the elasticity of the passbook rate RCBP with respect to the policy instrument RFF is negligible, and the response of the bill rate RTB is inelastic. Thus, eq. (3) suggests that RFF should be raised to increase the demand for money, and lowered to reduce demand. While this is a sensible result for IF itself, it seems improbably large for the demand for total ‘money’ since no more than 15-20% of checking deposits could have been displaced by IF. Also, it is implausible that the marginal implicit rate on
“To provide nomenclature comparable to asset demand for checking deposits, the public’s demand for IF will refer to the asset associated with the sale of immediately available funds, “As seen below, this approximation IS useful in obtaining a tractable predictor of DD. The error of approximation is elastic with respect to IF/DD so it may be expected that the estimated coefficient of the lagged dependent variable is somewhat overstated.
1ng
I”fD
0.8) [-0.1741
(1.5) [ -0.019]
-- yield on 90.day Treasury bills. - commercial bank passbook yield.
deposits.
RTB RCBP
real per capita GNP.
real per captta demand
1.000
(3.7)
0.378
(23.2)
0.0405
__-__-
[0.116]
(2.5)
-
iiInRFF
functions.”
0.55
0.53
(5.7)
zero elsewhere).
0.78 (11.6) (2.5)
(5.8)
P
-0.0719
-
-
6
RFF - Federal funds yield. - dummy shift (J= 1 for 1970.111-‘76.W; d /, - first-order residual autocorrelation. ( ) - r-ratios. [ ] - steady-state elasticities.
- 0.108
-0.0117
0.220
(3.5)
-
_
c y- 7
[xl
Ix]
10.3543
)
(3.5)
______
0.00348 (0.3
-0.0175
0.0363
(1.4)
[ -0.14471
[ - 0.0361
[0.257]
0.126
0.687 (8.5)
(3.0)
Y,
- 0.0452
1nRCBP
-0.0114 (2.8)
In RTB
0.0804 (3.4)
‘” P-N-
GNPts
I
of ‘money’ demand
(0.6)
- 1.15 (0.3)
Regressors
GNP$ P.N
P.N
DD a-_.
1955.11-76.lV
1955.W76.IV
(2)
1955.11-73.w
(I)
Y
Dependent cartable
Comparrson
Table
1.x9
2.0
1.6
DW
0.95
0.99
0.98
R2
0.00969
0.00659
0.00506
SEE
toto/ checking deposits would move closely with RFF since the owners of at least one-half of outstanding checking deposits are effectively barred, by from direct participation in the IF financial or regulatory restrictions, market. Examination by the authors (1978) of monthly IF sales by non-bank sectors indicates that sectoral demands for IF are determined by different economic indices. For example, non-financial sector IF demand is primarily influenced by a measure of income transactions rather than interest rates, whereas IF demands by financial sectors, such as thrift institutions and security dealers, are more closely related to the own rate on IF and a representative yield on a competing liquid asset. This suggests that it may be more useful to consider two unobservable components of total IF: IFY, the demand for IF on income account, and ZFP, the demand for IF on portfolio account,”
IF=IFY+IFP,
(15)
where the determinants of the components are discussed shortly. In contrast to more general formulations that incorporate investment motives for money balances, the conventional econometric money demand function features the income transactions attribute of deposits. Thus, a modification including only IF demand on income account, IFY, would be more compatible with the conventions associated with traditional money demand specifications. The design of the revised ‘money’ demand function is restricted to deviate as little as possible from the format of the standard money demand function displayed in table 1. There are two advantages of this restriction: First, it facilitates direct comparisons. Second, since the structure of the standard formulation survived for over two decades, it seems plausible that the sudden displacement of checking deposits indicates more of a problem in the measurement of ‘money’ than a shift in the requirements for transactions balances on the income account.
” Using a precautionary model of the transactions demand for liquid assets, the authors (1978) demonhtrate that both components of IF may be interpreted as rrcrmtrcrionv balances. The demand for IFY is influenced by the probability of negative net cash flows determined by variations in the level of business activity, and the demand for IFP is influenced by the distribution of cash flows determined by yields on financial instruments. Although the precautionary demand for transactions balances has a respectable theoretical lineage, many economists seem inexorably attached to a media of exchange definition of ‘money’. It is not necessary to accept the proposition that a substantial portion of IF is ‘disguised money’ in order to evaluate the displacement of demand deposits presented here, but we have argued (1978) that the proposition is theoretlcally and empirically valid.
130
P.A.
Tw~sley
et ul., AIT r.xpo.sd of‘disguised
+ h,, In RTB,+
+blh
DD In--P,N
deposits
h,41n RCBP, + b,,6,ln
+b--
RFF,
IFY DD 1 ,_, +“L
(16)
This formulationZo is identical to eq. (3) in table 1 except that total IF is now replaced by the unobservable partition, IFY, related to transactions on the income account. As noted earlier, there is evidence to suggest that IF tends to dominate checking deposits as a transactions asset for large participants in the IF market. However, as a result of the threat of withdrawals by these depositors, the implicit rate on checking deposits held by these customers will be adjusted towards the after-tax return on IF. It may be expected, however, that the elasticity of the own rate approximation, RFF, will be lower than the absolute value of the bill rate elasticity since (i) only a fraction of agents in non-household sectors actively participate in IF transactions, and (ii) the fraction did not increase significantly until late in the sample. Obviously, unless some structure is imposed on the partitioning of IF, then IFY/DD in (16) is simply an unobserved component of the stochastic ‘residual’ of the money demand function with a particular autoregressive structure resulting from the lagged demand format. It is expected that demand for liquid balances by financial business is related to IFP while IFY is more closely associated with the demand for transactions balances by non-financial business and state and local governments. These non-financial institutions increased the volume of transfers between demand deposit and IF accounts during the mid-seventies when escalating yields stimulated aggressive marketing of IF by commercial banks as a means of circumventing regulations on commercial bank borrowing and forestalling disintermediation induced by yield restrictions on deposits. This stimulus is represented by a ratchet of past peaks in the IF yield, RFFP, and the history of participation in the preceding period,
(IFY/DD),=h,,+ E,- h’ (0, ~,a1. “As
in table
h,,RFFP,+
A,,RP:‘l;,+
b2,(IFY/DD),_
1 +E,, (17)
I 7dI is a dummy shift variable that IS zero prior to 1970.111 and unity thereafter.
P.A. Tin&y
131
et ul.. An exposh of disguised deposits
IF,, as a proportion of total IF Since this is a rough approximation, borrowing by the large commercial banks, RP%,” is also included to capture uneven variations in the IF/DD mix of money not explained by the implied Koyck lag. Introduction of a possible supply influence into the demand formulation is probably unavoidable since the imposition of checking deposit requirements is likely to be more the consequence of negotiations than pure demand considerations, if the asset is dominated. The substitution of IF for dominant assets, on the other hand, will be sensitive to current yields. In the case of thrift intermediaries, the level of the yield may also be a significant determinant of the distribution of withdrawals when market yields pierce regulated ceilings on deposit yields. Thus, the format of transactions demand for IF on portfolio account, IFP, resembles a conventional ‘portfolio’ specification,
(IFPDD),
= b30 + b,, (RFF - RCP), + h,,RFF,
rt = ?/vt_ , + M’,,
+ L’,,
(18)
WI-N (0, o,,>ti. 1.
Since the standard money demand format eschews the use of wealth or the liquid asset stock as a dimensional scale, the selection of DD was based on analytical convenience. Although money markets are extremely efficient, the response to perturbations in relative yields may set off a chain of reactions as each agent attempts to readjust his portfolio. The autoregressive structure of the stochastic disturbance, u,, of this equation serves as a minimal description of this dynamic ‘rebalancing’ process. Although this set of three structural equations and one definition (15))(18) are sufficient to define four variables (DD, IF, IFY, IFP), only two of the variables (DD and IF) are explicitly measured. The two unobservables, IFY and IFP, can be eliminated by substituting (17) and (18) into the remaining equations to define the two e.stim&rrg equations for DD and IF listed in table 2. A nonlinear variant of an Aitken estimator is used to estimate this system; details are provided in appendix B of an earlier paper by the authors (1978). The most important characteristic22 of the system is that the ‘residuals’ of the estimating equations, U, and Us, are complicated functions of the three
“RPU/,= IF&F,, + IFd, + IF,, - IF,); see definitions m sectlon 2. *‘Other features of table 2 include: (i) The equations must be estimated simultaneously since two coelliclents, h,, and h,,, appear in both equations and no restrictions were placed, initially, on the simultaneous correlations of the stochastic innovations (a,,, CJ,, and rr,,). (ii) The system is also underdetermmed smce there are three unknown intercepts (h, ,+ b,,, and h,,) in the second term of (19) and the first term of (20). This problem is eliminated by the assumption that IFY/DD is zero through 1970.11.
132
P.A. Tin&y
et al., An expos4 Table
Format
Ing+6&
of the estimatmg
qf disguised
deposits
2
equations
=b,,+[h,,+b,,(l-b,,)]6,+b,,In
for DD and IF.
(19)
+h,,InRTB,+b,,lnRCBP,+h,,6,lnRFF,
+b,,B,[(RFF,-RCP,)-b,,(RFF,m,-RCP,m,)] +b,,h,[RFF,-b,,RFF,~,]+u,, u,,=‘l,+6,(tl,-b,,c,_,)
+b,,I(RFF,-RCP,)-b,,(RFF,_,-RCP,_,)]
u,,=s,+v,-b,,o,_,
stochastic innovations of the structural equations (u,, w,, E,). Elements of the from estimates of the residual covariance matrix C,, are constructed variances, covariances, and autocorrelations of the structural equation residuals.
An iterative procedure is used where (i) the coefficient vector 6 is obtained by GLS estimation of (19) and (20) given 8, and (ii) a revised 8 is provided by a Gauss-Newton estimator, given b^. This iterative estimation cycle is continued until the estimate sequences of both parameter vectors 6 and 6 converge. Using final estimates of the parameter vectors, unique ‘predictors’ of the innovations of the structural equations (a, W,E) are constructed by a MARL estimator [similar to estimator (10) in section 21 from the estimated residual vector, ri. In most cases, the results of the estimation, listed in table 3, conform to prior expectations. The broad characteristics of the demand for money (16’) are very similar to the standard money demand function, eq. (1) in table 1. The impact elasticities of the passbook rate (RCBP) and real, per capita GNP correspond closely. The impact elasticity of the bill rate increased by
P.A. Tins&
rr al., An expo.sP oJ’disgui.wd deposits
133
Table 3 Final estimates
lns+6% 1,
of ‘money’ demand
function
=-0.610-0.0226,+0.0935ln (3.7) (2.3) 10.4581
and partitioned
?!!? ( P.N
IF demand
functions.”
+0.796 lnr!$+,E 1,
(12.6) 1
- 0.0166 In RTB, - 0.03 11 In RCBP, + 0.008866, In RFF, + 9, (4.2) (2.4) (0.9) [-O.OSl] 1-0.1521 [0.043]
DD j 1-1
(16’)
~,=O.Sllr~,_,+a, (2.0) li,,, = 0.242 x IO J ,
1955.11-76.N
DW= 1.76
= -0.109+0.00932RFFP+0.0804RP~0+0.721 (3.7) (1.8) 1972.IIIL76.N
0,,=0.289
x 10-4.
(6.7)
‘Fy + E, i DD i r-1
(17’)
DW= 1.91
= 0.024 + O.O292(RFF, - RCP,) + 0.0022 1 RFF, + L’~ (2.3) (0.7)
(18’)
~1,=0.929v,-, fw,
(16.8) 1972.111-76.IV
0,,=1.154x
0.316 x 10m4, m,, = -0.122 X lo-“,
YTaw=
10-4,
0.598, P‘lw= P‘?, = - 0.425,
DW= 1.78 ( )-L-ratios, [ ] -steady-state
elasticities
46x, perhaps because of the increased liquidity of bills resulting from collateral usage in the IF market.23 The composition of ‘money’ is defined by eq. (17’). This equation is dominated by the RFF ratchet where the last peak occurred in 1974.111. Although a strict interpretation of this simple approximation of the IF market evolution should not be taken too literally, the dynamics of the equation suggest that 96% of the diffusion adjustment to the last peak was completed by 1976.IV. Z3The positive elasticity of the ‘own’ rate approximation, RFF, also conforms to prior expectation. There are a number of interesting macro implications introduced by the existence of a slgmficant non-bank demand for IF including: (i) a reduction in the net interest rate elasticity of the demand for ‘money’ and (ii) invalidation of bank reserve models based on the existence of a binding required reserves relation with ‘money’. Although a number of conjectures can be advanced on these and other issues, quantitative evaluations will be deferred to a sequel where both sectoral demand and supply schedules of IF will be embedded m a more general econometric model of economic activity.
The negative covariance of the innovation of this equation with the innovation of total money demand, c,,, is interpreted as an adjustment for aggregation. It is presumed that businesses are more efficient than households in the management of transactions balances. Thus, if corporations receive a bigger share of income, total ‘money’ balances will be lower than average, and investment in IF will be higher than average. The most notable feature of the demand for IF on portfolio account, eq. (18’) is that the variance of its stochastic innovation, o,,,,,,, is about four times larger than the variances of the two innovations that appear in the transactions demand on income account (o~~,cJ~J. Fortunately, as shown affect the constructions of the demand for below, a,,,M,does not significantly ‘money’ and its partitions. DD and IFY.24 As indicated in the last column of table 4, the partitioned ‘money’ demand system explains about SO:/;, of the cumulative error of the standard money demand forecasts. A portion of the remaining error may be attributed to other problems associated with recent measurement of ‘money’ such as the emergence of NOW and POW accounts and so on. However, much of the remaining error may be due to a mis-specification of the dynamic response to short-run variations in GNP. After differencing the entries in the third column of table 4, a large forecast error is still obtained by the partitioned demand system in 1975.1 (although it is substantially less than the corresponding error in the standard demand function). At an annual rate, the real per capita GNP dropped over 10 ;;, in that quarter alone. It is likely that the dynamic response to variations in the transactions scale is apt to be more complicated than the geometric response used in the standard money demand formulation. To provide a rough test of this conjecture, the ‘residual’ of money demand (16’) (i.e., the stochastic innovation u,) was regressed on the growth rate of real per capita GNP, ci,=-O.OOl+O.l26dln (1.4) (2.8)
L = 0.197 x 10-4.
(21)
This simple alteration in the dynamic response structure of money demand reduces both the variance of money demand, craa, by about 20”/0 and the specific forecast error in 1975.1 by over 6091. The unadjusted variance of the ‘residual’ of the money demand function of the partitioned system (16’), Ok’,,is actually about five percent lower than the variance of the standard money demand formulation, eq. (1) of table 1. Unfortunately, gno is not the variance of the one-period forecast error. The “‘It was expected that the magnitude of the cross-correlatmn between E, and IV, would indicate the degree oi mvxpecification in the partitioning of IF. Although (T_ was negative, the cross correlation was extremely low m the neighborhood of the final estimates and was set to xro to aid terminal convergence of the nonlinear estimator.
P.A. Tin&p
et al., An exposP
of disguiseddeposits
135
Table 4 Cumulative Standard Absolute error (Shill)
errors
model” Relative error (“0
in ‘forecasting’
checking
deposits,
Partitioned
modelb
Absolute error (Shill)
Relative error
(X)
1974.1-78.111.
o/0 reduction in DD forecast error by partitioned model
1974.1 II III IV
- 0.6 - 3.9 -8.1 - 14.0
1975.1 II III IV
-21.4 -22.1 -23.7 -28.5
-10 -10 -11 -13
-5.3 -3.1 -2.2 -3.4
-2 -1 -1 -2
75 86 91 88
1976.1 11 III IV
-
32.2 32.6 35.0 36.6
- 14 -14 -15 -16
- 4.8 -3.8 -4.8 -5.6
-2 -2 -2 -2
85 88 86 85
1977.1 II III IV
-31.9 - 39.3 - 39.1 - 39.4
-16 -16 - 16 -16
-5.7 - 6.6 -6.6 -7.1
L; -3 -3
85 83 83 82
1978.1 II III
-41.3 -43.x -44.5
-16 -17 -17
- 8.8 - 10.6 - 10.5
-3 -4 -4
79 76 76
“DD forecasts bDD forecasts
-0 -2 -4 -6
0.6 0.1 0.6 -1.0
0 0 0 0
3
0 103 107 93
by standard money demand equation (1) cited in table 1 above by partitioned system of equations described in table 2.
reason for this is that the unobservable residual components (u,, w,, et) and, consequently, the unobservable partitions of IF are subject to an irreducible measurement error. In a conventional regression model, it is assumed that all variables are measured without error. Then, if the regression coefficients are known, the residual of the equation is measured exactly.25 This is the case for U, and u2, for example, since all arguments of the variables in the estimating equations (table 2) are measured directly. However, this is not the case for the three residuals of the structural equations in table 3 that were constructed from the ‘exact’ measurements ui and u2. Note that increasing the sample size will not eliminate the problem since an extra unknown variable will be generated in each period.“j 25More precisely, if the unknown regression coefficients are consistently estimated, residual measurement will become more exact as the sample size goes to infimty. 2hThe use of subsequent measurements z>t to Improve the estimates of the tth period is termed smoothing.Although the variances of the smoothed estimates of the unobservable components may mtially decrease with further measurements, they will not converge to zero. For more on this topic, see the discussion of the ‘uncertainty principle’ in Swamy and Tinsley (1980).
136
P.A. Tin&y
et (II., An exposh oj disguised deposits
Under certain assumptions, it is possible to construct approximations of the moments of the distribution of the ‘true’ (unobserved) structural errors about the latest estimates.27 Denoting the discrepancy between the ‘true’ unobserved residuals and the measured errors by ii, G, t’, the one-period forecast error of ‘money’, say e M, generated by the partitioned system is
The variance
of this one-period
forecast
G6
a’(e,)-o,,+p’o-,?+-
1
-&
error is approximately 2
Or7=0.303
x 1om4,
and is about an ISo/;, increase over the ex urlte variance of one-period forecasts associated with the standard money demand function (at least prior to 1974). Thus, the cost of an operational reclamation of the money demand function is the appearance of an irreducible measurement error associated with the partitioning of IF.28
*‘See the discussion of the posterior distribution of unobservable components ‘*In the case of checking deposits. the one-pertod forecast error is
The variance
of the one-period
4,, -
forecast
error of checking
deposits
in section
2
is approximately
~0, +o,,-2~~,,+pZu$+(hZ,-b,,)Zu~=0.765x10-J,
and is about 300”/, higher prior to 1974.
than
the variance
of the one-period
forecasts
of checking
deposits
References Enzler, Jared, Lewis Johnson and John Paulus, 1976, Some problems of money demand, Brookings Papers on Economic Activity 1, 261-280. Garcia, Gilhan and Stmon Pak, 1979, The ratio of currency to demand deposits in the United States, The Journal of Finance 34, June, 7033715. Goldberger, Arthur, 1974, Unobservable variables in econometrics, in: Paul Zarembka, ed., Frontiers in econometrics (Academic, New York) 1933213. Goldfeld. Stephen, 1976, The case of the missing money, Brookings Papers on Economic Activity 3, 683 -730. Hamburger, Michael .I.. 1977, Behavior of the money stock, is there a puzzle?, Journal of Monetary Economics 3, July, 2655288. Hester, Donald, 1978, Money, velocity. interest rates and policy, Testimony before Senate Banking Committee on April 24. Hildreth, Clifford and James P. Houck, 1968, Some estimators for a linear model with random coefficients, Journal of the American Statistical Association 63. June, 548-595.
P.A. Tin&y
et ul., An exposh
of disguiseddvposirs
137
Lombra, Raymond E. and Herbert M. Kaufman, 1978, Commercial banks and the federal funds’ market: Recent development and implications, Economic Inquiry 16. Oct., 5499562. Porter, Richard D., Thomas D. Simpson and Eileen Mauskopf, 1979, Financial innovation and the monetary aggregates, Brookings Papers on Economic Activity 1, 213 229. Searle, Shayle. 1971, Linear models (Wiley, New York). Swamy. P.A.V.B. and P.A. Tinsley. 1980, Linear prediction and estimation methods for regression models with stationary stochastic coefficients. Journal of Econometrics 12, Feb., 1033142. Theil. Henri and L.B.M. Mennes. 1959. Multiplicative randomness in time series regression analysis, Report no. 5901 (Econometric Institute of the Netherlands School of Economics, Rotterdam). Tinsley, P.A., Bonnie Garrett, with Monica Friar, 1978, The measurement of money demand, Special studies paper no. 133 (Federal Reserve Board, Washington, DC). Wenninger, John and Charles Sivesind, 1979, Defining money for a changing financial system, Federal Reserve Bank of New York Quarterly Review, Spring, 1 8. Zellner, Arnold, 1970, Estimation of regression relationships containmg unobservable variables. International Economic Review 11, Oct., 441-454.
of Econometrics
15 (1981) 117.-137. North-Holland
AN EXPOSfi
OF DISGUISED
Pubhshmg
Company
DEPOSITS
P.A. TINSLEY
and Bonnie GARRETT* with Monica FRIAR
1. Introduction In the past ten years, product differentiation by commercial banks and other financial intermediaries has accelerated at a furious pace. New or refurbished liabilities marketed to the public have included: certificates of deposits (CD’s), Eurodollars, bank-related commercial paper, deposits in offshore branches, NOW and POW accounts, money market certificates, and immediately available funds (IF). In the case of commercial banks, each new product is designed to attract additional funds from non-bank sectors or defend existing deposits against raids by bank and non-bank competitors by paying yields significantly higher than the ceiling or statutory rates permitted on traditional core deposits. Since many of these financial innovations were initially not subject to reserve requirements, they were not exposed to the intensive monitoring associated with reservable liabilities. As a result, the proliferation of financial innovations has effected a deregulation of commercial bank borrowing that is incompletely measured and, therefore, subject to speculative analysis by government and private economists. Perhaps the most widespread circumvention of the statutory prohibition of interest payments, interest ceilings on deposits (Regulation Q), and reserve requirements (Regulation D) was accomplished by commercial bank purchases of immediately available funds (IF) from non-bank customers under both collateral (repurchase agreements)’ and non-collateral (Federal *We are indebted to C. Lucas, E. Regan, L. Rtbble, and S. Taylor for data: J. Berry and G. Frtes for computattonal assistance; and D. Hester and anonymous referees for perceptive comments. The views expressed herein are solely those of the authors and do not represent the views of the Board of Governors or the staff of the Federal Reserve System. ‘A repurchase agreement denotes a sale of U.S. government or agency securities in exchange for immediately available funds with an arrangement for the securities to be repurchased and the funds returned at a future date, usually the begmning of the next business day. Although ‘RP’ 1s used generically to describe both sides of the transaction, the borrower of funds is technically ‘selling’ securities to be repurchased by agreement whereas the lender of funds is conducting a reverse repurchase agreement, ‘buying’ securities to be resold in the future.
funds) arrangements. Propelled by high interest rates in 1973-74 and competition with government security dealers for short-maturity funds, this traditional market for interbank trading of excess reserves was transformed into a major source of funds from non-bank sectors. Net bank purchases of IF grew from $1 billion in 1967 to over $44 billion by mid-1978. This growth was accompanied by a massive overprediction by conventional transactions formulations of money demand” beginning in mid-1974 and of approximately a coincidence suggesting that traditional demand the same magnitude;3 deposits had been displaced in the portfolios of many non-bank sectors by sales of IF. The IF innovation has several unique characteristics: (i) until recently. the 1F market remained relatively unencumbered by regulatory restrictions,” (ii) except for an implicit construction provided by quarterly call reports (where final tabulation is available with about a six-month lag), there is no published measure of net IF borrowing by all commercial banks, and (iii) there has been no systematic empirical evaluation of the displacement of demand deposits by IF held by non-bank sectors.5 The aims of this paper ‘The typtcal transacttons model apectfies that real money balances demanded are a functton of a transactions proxy. such as real GNP. and nommal yrelds on one or two competing shortterm liquid assets. Hamburger (1977) suggests that the apparent overprediction is an illuston largely due to neglect of the asset demand for money. The investment motive is represented in hts analysrs by substitutmg the real yield on equtty and nominal yreld on long-term bonds in place of the short-term opportunity yrelds. Tinsley, Garrett and Friar (1978) found that adding these yields on long-term assets to the conventional transactrons formulation reduces the overprediction by only about 20”,,. ‘By mid-1978, the cumulative overpredictton of demand deposits by standard formulations had reached $44 billion, as shown later. “The Federal Reserve Board recently imposed reserve requirements on member bank IF rates, these transactions with non-member banks and non-banks. At current interest requirements increase the effective yield paid on borrowm~s from non-exempt sectors by about IO0 basts points. It is expected that this tax on membershtp will encourage the growth of nonbank financial intermediatton and increased partictpatton by member banks in unregulated International markets through foreign branches. ‘Since completton of this paper [a preliminary version appeared in Tinsley. Garrett and Friar (1978)]. several arttclcs habe discussed this issue. A detailed critique is beyond the scope of thts paper. but several ob\er\ations might highlight differences between these studies and the current paper. Although Lombra and Kaufman (197X) conjecture that demand deposits have been dtsplaced by non-bank IF sales. their sample span ends in 1974 just as the shaft began. Their measure of IF is net purchases by large weekly reporting banks (see ‘IF,‘ below) whrch exceeds the December 1976 call report measure of IF by 40”,,. Garcia and Pak (1979) employ a measure of net IF based on flow of funds data that not only exceeds the December 1976 call measure by X0”,, but is about 20”, bigger than the overprediction ‘gap’ of a conventional transactions model of money demand. Both Wenninger and Sivcsind 11979) and Porter. Srmpaon and Mauskopf (1979) add measures of collateral IF purchases or RPs (as an approximatron of IF borrowed from non-financial sectors) as well as shar-es in money market mutual funds (MMMF) to conventional money to construct an alternative dependent variable rn a transactions formulatron of money demand. The collateral IF data used by the former IS a measure of purchases by a subset of large banks (see ‘IF,,’ below) whrle the construction u\ed hy the latter 15 ba\ed. in part. on an inter-polatton usrng
P.A. Tiusley rt ul.. An exposb ofdisguixd
deposits
119
are to indicate that several incomplete measures of IF activity can be pooled to construct a measure of total commercial bank IF and that this measure can be used to provide a data-based estimate of displaced demand deposits. A construction of net IF held by non-bank sectors is discussed in section 2. An empirical model of non-bank holdings of IF and demand deposits is presented in section 3; this model reduces the errors of a standard predictor of demand deposits by about 80”:;).
2. An estimate of net immediately
available funds (IF)
Despite recent interest in the rapid growth of the IF market, there is no measure of the full extent of participation by non-bank sectors. The most comprehensive data are provided by commercial bank call reports (IF,) where the end-of-day net IF position of insured banks is reported for quarterly call dates (since 1973) and the net position of all banks is reported for semi-annual call dates (June and December).6 A more frequent monitor is provided by the weekly FR416 survey where the end-of-day net position (lF,) of some 300 large commercial banks is reported for the last day of statement weeks (Wednesday).’ Finally, the daily net IF activity of 46 of the largest commercial banks (IF,) is recorded in the FR716 reports. On the basis of some prior reasoning, it is expected that the unobserved average IF position of commercial banks will be bracketed by the reported estimates IF, s IF 5 IF; 2 IF,. IF, may understate the typical IF position of the commercial bank sector because, as suggested by Hester (1978), there may be considerable windowdressing by banks around call dates as they attempt to lower visible debt service. The FR716 measure. on the other hand, will tend to exceed IF since it includes IF purchases by daily reporters from both banks and non-banks. At the end of 1976, for example, the fifty largest banks (in total asset size) accounted for about 7036 of total IF purchases, and more than half the total purchases were interbank transactions. Similarly. it may be expected that IF, only two special surveys of large banks (in April 1974 and December 1977). Application of the analysis of liquid asset demand advanced in Tinsley, Garrett and Friar (1978) would suggest that MMMF 1s more of a substitute for savmgs deposits and that a closer competitor to demand deposits (and IF) would be found in measures of Eurocurrency deposits, an extension not attempted here. The yield on IF does not appear either as an own rate or a competing rate m any of these studies. The conceptual imprecision of reported measures of IF and the unavoidable increase In uncertainty of ‘monc)‘ demand projections due to ambiguous definitions of transactions and investment demands for hquid assets are also not discussed. bAs of the December 1977 call. there were 14,000 insured commercial banks and 94 noninsured banks. ‘There were 317 weekly reporting banks in mid-1978.
will exceed IF, if a portion of funds obtained by 416 reporters is retained and not resold to the subset of banks also reporting in FR716. The FR716 report is of special interest since it provides the only direct estimates of net sectoral positions.’ IF, = IF,, + IFd, + IF,, -IF,,
(1)
where IF,, =net unsecured IF purchased from commercial banks by 716 reporters. IF+ = net unsecured IF purchased from other depository institutions by 716 reporters, IF,, = net secured IF purchased from non-financial sectors by 7 16 reporters, IF, =net secured IF (RP’s and collateral loans) sold to U.S. government securities dealers by 716 reporters. More explicit connections between unohserwd IF and the three report measures (IF,, IF,, and IF,) are provided by the following specifications: The first approximation of net IF purchased by all commercial banks is based on the FR716 reports.
where x is a T x 1 vector of the natural logarithms unadjusted, monthly averages of daily IF. The columns Z, are zLO(t) = 1
of the seasonally of the T x 5 matrix
(unit vector),
z,,(t)=ln(IF,,+IF,,),, t=l,...,?;
~12(t)=ln(IF,,+IF,,-IF,),-~,,(r), z13(t)=RFF,. z14(t)= (RFF-RCP),.
by 716 Since ;I1 and z12 measure only the direct purchases from non-banks reporters, the yields on Federal funds and 4-6 month commercial paper are also included to explain any non-proportional movements in the remaining sales of IF by non-bank sectors. A second approximation is based on the FR416 reports, x=Z,h,+a,,
E[tr2 ti,lrr* (,j)] =a,,dij,
(2b)
E[LI, (i)tr,(j)l=a12fil.
‘Both FR416 and call reports prior to March the IF sales of commercial banks.
31, 1976 provide
limlted sectoral
detail on only
121
where the columns
of the T x 4 matrix
zzO (t) = 1
Z, are
(unit vector),
zzl(~)=~n(IF4),~ z,,(r)=ln(IF,,+IF,,-IF,+IF,,)-I,,,
t=1,...,7;
zz3 (t) = RFF,. Both zL2 and zz3 are included to capture the overstatement of IF by IF, due to the net purchases from other commercial banks also included in IF,;’ it is expected that the coefficients of both regressors will be negative.” Also, since FR416 is a one-day report, adjacent Wednesday data were averaged to provide estimates of weekly average IF before constructing the monthly averages, IF,. A reverse averaging procedure was used in the relationship between the monthly average of daily positions, IF. and the one-day call measure, IF,.
ECN3Ci)(13 (.i)l
=".?,,bij,
y=z3h3+Cx+D,a,.
(2c) E[rr,(i)Nk(j)]=O,
k=l,2.
where y is a N x 1 vector of In IF,, and C is a known N x T weighting matrix (N< T) that transforms neighboring monthly averages of IF to approximations of the one-day call estimates. * ’ The first regressor, z3, in (2~) is an approximation of the bias introduced by window-dressing in call reports and consists of the ratio of net IF recorded by FR416 reporters on call reports to the average of net IF recorded on FR416 reports in neighboring months,
The mean elasticity of this regressor, h3, is unrestricted and may be zero in the absence of detectable reporting ‘bias’; however, a random coefficient specification was selected to allow for the possibility of non-systematic over-
9Note that z,, +z12 +:22 =In IFi; this partxular format is selected to allow the possibility of equivalent elasticities for FR716 components. “As noted in Tinsley, Garrett and Friar (197X), the estimated RFF elasticity of small bank IF supply will be negative in the absence of adjustment for the loan demand of small bank customers. “The exact specification of the weighting matrix C is available on request; the row format is not systematic since call dates are not evenly spaced in calendar time.
P.A. Tinsky et ctl., .An
122
~spo,s~ of di,tguiseddepmir.~
or under-reporting. (3)
h3(t)=h3+uj(r).
Thus, D, is an N x N diagonal matrix with zj, along the main diagonal. Call dates fell at the end of statement weeks a total of nine times during the sample period December 1969 through December 1976. so it was possible to check the consistency of IF, and IF, recorded by weekly reporters for these dates. It was disturbing to observe that the average discrepancy in IF reported for the same day by FR416 banks was just under one-half billion dollars and reached a peak discrepancy of $1.5 billion. A closer examination, however, showed that only two reporting banks were responsible for 75 “/ of these two banks were the average error (and 66:;) of the peak discrepancy); subsequently dropped from the 416 measures.i2 Since IF (or X) is unobservable. the equation set (2) was transformed to an estimable format by substituting (2a) and (2b) into (2~) yielding the stacked system13 P1 Ye
Y=Zb+u.
This system (4) was estimated covariance matrix
(4) by GLS using an estimate
of the variance-
(5) where the matrix
partitions
“The two banks were not elimmated from the total call estimate IF, under the operational assumption that the call estimates were accurately recorded. “All data are seasonally unadjusted. The sample span extended from December 1969 to January 1977, including seven semi-annual calls through 1972, and quarterly calls thereafter. Several alternattve formats were estimated including (i) allowances for trend and seasonal differences between IF and the several reported measures of IF, and (ii) autocorrelation in both u, and az : the empnical results did not support the alternative formats,
123
are derived
from the definitions u, =Ca,
The variances system’”
+D_a _ 3’
of the stochastic u2
=
of the stochastic
disturbances
of (4).
C-a, + D,a,.
disturbances
were. in turn, estimated
m=Ma+e,
by the
(6)
where m is a 3N x 1 vector residuals of (4).
of products
and
cross-products
of the OLS
m’ = [m; rn; m;], m, = ri, * ii,, m2 = i2 * &, m3 = 2, * fi,, where ‘*’ denotes the element-by-element unknown ‘coefficient’ vector is
and the 31~ x 4 regressor
matrix
Hadamard
product.
The
4x 1
is
where ly denotes an N x 1 unit vector. System (6) was also estimated by GLS using OLS estimates elements of the covariance matrix of the discrepancy vector e.
to construct
(7)
where Iij = 2!C?;, CI.~=2QrrQ,2.
i=1,2,
j=l,2,
C,3=2Q,~Qr2,
~33=Qlla22-tnf2.
“Although the equation system (2) may be interpreted as a set of multiple indicators of unobservable (or. more precisely. Imperfectly observed) IF following the analysts developed by Zellner (1970) and Goldberger (1972), the estimators of the covariances of unobserved components used in this paper are similar to the approximate GLS estimators proposed for random coefficient models by Theil and Mennes (1959) and Hildreth and Houck I1968). See also discussion of and references to minimum variance quadratic estimators of variance component\ 111 Chapter 9 of Searle (1971).
124
P.A. Tins/e), C? (II.. An expo.sG of disguisrd
The specification
of the discrepancy
covariance
drposirs
is illustrated
for the case of
c 337
using the distribution
condition
E[abcd] Final estimates
that
for
zero-mean
=E[ab]E[cd]
variables
+E[u(.]E[bd]
of the equation
with
a joint
normal
+E[ud]E[b~].
set (2) are
x= -0.02+1.09z,,+1.38z,2-0.04z,3+0.11z,,+a,, (0.1) (41) (21) (6.9)
(2a’) (4.3)
r+/, =(~.163x IO 3 s= - l.20+1.19rl, (3.0) ri ,,=0.317 ~=l.l8z,+Cx
~- I.Xz,,-0.03z2,+a2,
(32)
(21)
x 10-2, (i,z=o.121
(2b’)
(4.8) x 10--2.
t/),cl,.
(2c’)
(8.9 1 c?33 =0.292 x lo- ‘. These estimates suggest that call reports underestimate net IF purchased by all commercial banks by approximately 17”,/,. However, there is considerable seasonal variation where the average underestimate ranges from OO/, for the March calls to 36 % for the December calls. Final ‘predictions’ of x (or net IF) can be obtained if estimates of the structural equation innovations a’= [a; a;] can be constructed from the residuals of the stacked system u’= [u; u;]. Unfortunately, this objective is subject to an irreducible measurement error. Although the stacked residuals u are consistently estimated, this condition cannot be met for the unobserved structural residuals a.” ISSee the discussions of the ‘uncertainty principle’ in Swamy and Tmsley 11980).
(MARL) estimator
and
the minimum
average
risk
linear
P.A. Tinsley et crl., An expost:
Unique, linear risk matrix
estimates
of disguiseddeposits
ci= Gli are provided
125
by minimizing
the average
(9)
R=E[a-Gu][a-Gu]‘,
where expectations are taken with respect expectation of u given a, and the unconditional differential of the average risk matrix is
to both expectation
the conditional of a. The total
dR=dG(-E[ua’]+E[uu’]G’)+(-E[uu’]+GE[uu’])dG’, where dG is an arbitrary perturbation about vanish if the filter gain matrix G satisfies
G. The first-order
variation
&[uu’] =E[uu’], where the variance
is defined in (5) and
1
011g::
[ 012 Thus, ‘smoothed’ covariance
(10)
E[uu’] =C,,
E[uu’] =
estimates
@C’.
of u are provided
011 012 01,
~=~(~-~)(~_q’=
i g12
022
by G;
-
with the ‘posterior’
Gc,,@,
(11)
1
where it is apparent that S does not vanish presence of u3 in u. By construction, the two predictors of X,
2,
will
as T-+m
due, in part,
=z, 6, + ci,,
to the
W-V
are equivalent at call dates CP, =CIz, but may differ in the intervening periods. To resolve this selection problem, a ‘pooled’ estimate is constructed, 2=
wi, + (I,
where the weighting
- W)f,
matrix
(13)
)
W is chosen
to minimize
the average
risk matrix
126
P.A. Tinslry
et ul., An exposP cfdisguised
&posits
Billions of dollars
1970
1971
1972
1973
I974
1975
I976
Ftg. I. Selected estimates of net IF funds supplied by non-bank sectors. 197O.lL76.1V. See text for explanatton of survey estimates (IF,, IF? and IF,) and construction of pooled estimate (I?); all data seasonally adjusted by X-l 1.
E[e,e&]
of the ‘pooled’ prediction
error
The optimal pooling matrix is defined by the appropriate ‘posterior’ covariance S defined in (I 1) above,
partitions
w=rs,,-s~llcs,l+sz2-s1z-szll-‘.
of the
(14)
The unit trace, tr (@)/-I; of the estimated pooling matrix is 0.59 indicating that the FR716 measures are assigned slightly more emphasis than the FR416 reports in the final estimate of IF.ih The final construction of net IF supplied by non-bank sectors is compared to the net IF measures of various reports in fig. 1. 3. An estimate of the displacement As indicated by Enzler, Johnson traditional formulations of money
of demand deposits (DD) by IF and Paulus (1976) and Goldfeld (1976) demand functions began to overpredict
lbThe unit trace of the pooling matrix that would minimize the average risk matrix of the poooled prediction error prior to call report measurement is 0.82. This dtstinction is of some sigmficance since the reporting lag on call reports IS about six months whereas the 1, estimate (with u*t=0) could be available with about one-day lag.
P.A. Tins/q
rt al., An exposh of disguised deposits
127
significantly in mid-1974. Since persistent overprediction was confined to demand deposits, the currency component of M, will be ignored in this discussion. The swift and thorough deterioration of the standard money demand function is illustrated by the first two equations in table 1 where the sample span of eq. (2) is only twelve quarters longer than the seventy-five quarter sample span of eq. (1). Previous analysis by the authors (1978) of the empirical structure of transactions costs indicated that the precautionary transactions demand for checking deposits in the spectrum of liquid assets might be effectively dominated by IF balances in the portfolios of large participants in the IF market. On the grounds that ‘if it looks like water and tastes like water, it might be water’, the simplest approach to restoring a traditional money demand function is to add demands for IF” and demand deposits, DD. The only modification of the standard demand format is the inclusion of an own rate on IF, approximated by the yield on Federal funds, RFF. For convenience, the approximation In (DD + IF) = In (DD) + IF/DD is also used.” A comparison of eqs. (1) and (3) in table 1 indicated that even this crude redefinition of ‘money’ recovers many of the characteristics associated with traditional money demand functions. The competing yield on passbook deposits is restored, and the long-term elasticities are similar. However, the revised demand function (3) also exhibits atypical dynamic properties : First, the mean lag of adjustment is about ten weeks, a reduction of nearly 70% from the mean lag of twenty-nine weeks implied by eq. (1). [The mean lag of eq. (2) is infinite.] Second, the strength of the positive elasticity of the own rate would reverse the usual operating rules of short-run monetary policy. It can be shown that the elasticity of the passbook rate RCBP with respect to the policy instrument RFF is negligible, and the response of the bill rate RTB is inelastic. Thus, eq. (3) suggests that RFF should be raised to increase the demand for money, and lowered to reduce demand. While this is a sensible result for IF itself, it seems improbably large for the demand for total ‘money’ since no more than 15-20% of checking deposits could have been displaced by IF. Also, it is implausible that the marginal implicit rate on
“To provide nomenclature comparable to asset demand for checking deposits, the public’s demand for IF will refer to the asset associated with the sale of immediately available funds, “As seen below, this approximation IS useful in obtaining a tractable predictor of DD. The error of approximation is elastic with respect to IF/DD so it may be expected that the estimated coefficient of the lagged dependent variable is somewhat overstated.
1ng
I”fD
0.8) [-0.1741
(1.5) [ -0.019]
-- yield on 90.day Treasury bills. - commercial bank passbook yield.
deposits.
RTB RCBP
real per capita GNP.
real per captta demand
1.000
(3.7)
0.378
(23.2)
0.0405
__-__-
[0.116]
(2.5)
-
iiInRFF
functions.”
0.55
0.53
(5.7)
zero elsewhere).
0.78 (11.6) (2.5)
(5.8)
P
-0.0719
-
-
6
RFF - Federal funds yield. - dummy shift (J= 1 for 1970.111-‘76.W; d /, - first-order residual autocorrelation. ( ) - r-ratios. [ ] - steady-state elasticities.
- 0.108
-0.0117
0.220
(3.5)
-
_
c y- 7
[xl
Ix]
10.3543
)
(3.5)
______
0.00348 (0.3
-0.0175
0.0363
(1.4)
[ -0.14471
[ - 0.0361
[0.257]
0.126
0.687 (8.5)
(3.0)
Y,
- 0.0452
1nRCBP
-0.0114 (2.8)
In RTB
0.0804 (3.4)
‘” P-N-
GNPts
I
of ‘money’ demand
(0.6)
- 1.15 (0.3)
Regressors
GNP$ P.N
P.N
DD a-_.
1955.11-76.lV
1955.W76.IV
(2)
1955.11-73.w
(I)
Y
Dependent cartable
Comparrson
Table
1.x9
2.0
1.6
DW
0.95
0.99
0.98
R2
0.00969
0.00659
0.00506
SEE
toto/ checking deposits would move closely with RFF since the owners of at least one-half of outstanding checking deposits are effectively barred, by from direct participation in the IF financial or regulatory restrictions, market. Examination by the authors (1978) of monthly IF sales by non-bank sectors indicates that sectoral demands for IF are determined by different economic indices. For example, non-financial sector IF demand is primarily influenced by a measure of income transactions rather than interest rates, whereas IF demands by financial sectors, such as thrift institutions and security dealers, are more closely related to the own rate on IF and a representative yield on a competing liquid asset. This suggests that it may be more useful to consider two unobservable components of total IF: IFY, the demand for IF on income account, and ZFP, the demand for IF on portfolio account,”
IF=IFY+IFP,
(15)
where the determinants of the components are discussed shortly. In contrast to more general formulations that incorporate investment motives for money balances, the conventional econometric money demand function features the income transactions attribute of deposits. Thus, a modification including only IF demand on income account, IFY, would be more compatible with the conventions associated with traditional money demand specifications. The design of the revised ‘money’ demand function is restricted to deviate as little as possible from the format of the standard money demand function displayed in table 1. There are two advantages of this restriction: First, it facilitates direct comparisons. Second, since the structure of the standard formulation survived for over two decades, it seems plausible that the sudden displacement of checking deposits indicates more of a problem in the measurement of ‘money’ than a shift in the requirements for transactions balances on the income account.
” Using a precautionary model of the transactions demand for liquid assets, the authors (1978) demonhtrate that both components of IF may be interpreted as rrcrmtrcrionv balances. The demand for IFY is influenced by the probability of negative net cash flows determined by variations in the level of business activity, and the demand for IFP is influenced by the distribution of cash flows determined by yields on financial instruments. Although the precautionary demand for transactions balances has a respectable theoretical lineage, many economists seem inexorably attached to a media of exchange definition of ‘money’. It is not necessary to accept the proposition that a substantial portion of IF is ‘disguised money’ in order to evaluate the displacement of demand deposits presented here, but we have argued (1978) that the proposition is theoretlcally and empirically valid.
130
P.A.
Tw~sley
et ul., AIT r.xpo.sd of‘disguised
+ h,, In RTB,+
+blh
DD In--P,N
deposits
h,41n RCBP, + b,,6,ln
+b--
RFF,
IFY DD 1 ,_, +“L
(16)
This formulationZo is identical to eq. (3) in table 1 except that total IF is now replaced by the unobservable partition, IFY, related to transactions on the income account. As noted earlier, there is evidence to suggest that IF tends to dominate checking deposits as a transactions asset for large participants in the IF market. However, as a result of the threat of withdrawals by these depositors, the implicit rate on checking deposits held by these customers will be adjusted towards the after-tax return on IF. It may be expected, however, that the elasticity of the own rate approximation, RFF, will be lower than the absolute value of the bill rate elasticity since (i) only a fraction of agents in non-household sectors actively participate in IF transactions, and (ii) the fraction did not increase significantly until late in the sample. Obviously, unless some structure is imposed on the partitioning of IF, then IFY/DD in (16) is simply an unobserved component of the stochastic ‘residual’ of the money demand function with a particular autoregressive structure resulting from the lagged demand format. It is expected that demand for liquid balances by financial business is related to IFP while IFY is more closely associated with the demand for transactions balances by non-financial business and state and local governments. These non-financial institutions increased the volume of transfers between demand deposit and IF accounts during the mid-seventies when escalating yields stimulated aggressive marketing of IF by commercial banks as a means of circumventing regulations on commercial bank borrowing and forestalling disintermediation induced by yield restrictions on deposits. This stimulus is represented by a ratchet of past peaks in the IF yield, RFFP, and the history of participation in the preceding period,
(IFY/DD),=h,,+ E,- h’ (0, ~,a1. “As
in table
h,,RFFP,+
A,,RP:‘l;,+
b2,(IFY/DD),_
1 +E,, (17)
I 7dI is a dummy shift variable that IS zero prior to 1970.111 and unity thereafter.
P.A. Tin&y
131
et ul.. An exposh of disguised deposits
IF,, as a proportion of total IF Since this is a rough approximation, borrowing by the large commercial banks, RP%,” is also included to capture uneven variations in the IF/DD mix of money not explained by the implied Koyck lag. Introduction of a possible supply influence into the demand formulation is probably unavoidable since the imposition of checking deposit requirements is likely to be more the consequence of negotiations than pure demand considerations, if the asset is dominated. The substitution of IF for dominant assets, on the other hand, will be sensitive to current yields. In the case of thrift intermediaries, the level of the yield may also be a significant determinant of the distribution of withdrawals when market yields pierce regulated ceilings on deposit yields. Thus, the format of transactions demand for IF on portfolio account, IFP, resembles a conventional ‘portfolio’ specification,
(IFPDD),
= b30 + b,, (RFF - RCP), + h,,RFF,
rt = ?/vt_ , + M’,,
+ L’,,
(18)
WI-N (0, o,,>ti. 1.
Since the standard money demand format eschews the use of wealth or the liquid asset stock as a dimensional scale, the selection of DD was based on analytical convenience. Although money markets are extremely efficient, the response to perturbations in relative yields may set off a chain of reactions as each agent attempts to readjust his portfolio. The autoregressive structure of the stochastic disturbance, u,, of this equation serves as a minimal description of this dynamic ‘rebalancing’ process. Although this set of three structural equations and one definition (15))(18) are sufficient to define four variables (DD, IF, IFY, IFP), only two of the variables (DD and IF) are explicitly measured. The two unobservables, IFY and IFP, can be eliminated by substituting (17) and (18) into the remaining equations to define the two e.stim&rrg equations for DD and IF listed in table 2. A nonlinear variant of an Aitken estimator is used to estimate this system; details are provided in appendix B of an earlier paper by the authors (1978). The most important characteristic22 of the system is that the ‘residuals’ of the estimating equations, U, and Us, are complicated functions of the three
“RPU/,= IF&F,, + IFd, + IF,, - IF,); see definitions m sectlon 2. *‘Other features of table 2 include: (i) The equations must be estimated simultaneously since two coelliclents, h,, and h,,, appear in both equations and no restrictions were placed, initially, on the simultaneous correlations of the stochastic innovations (a,,, CJ,, and rr,,). (ii) The system is also underdetermmed smce there are three unknown intercepts (h, ,+ b,,, and h,,) in the second term of (19) and the first term of (20). This problem is eliminated by the assumption that IFY/DD is zero through 1970.11.
132
P.A. Tin&y
et al., An expos4 Table
Format
Ing+6&
of the estimatmg
qf disguised
deposits
2
equations
=b,,+[h,,+b,,(l-b,,)]6,+b,,In
for DD and IF.
(19)
+h,,InRTB,+b,,lnRCBP,+h,,6,lnRFF,
+b,,B,[(RFF,-RCP,)-b,,(RFF,m,-RCP,m,)] +b,,h,[RFF,-b,,RFF,~,]+u,, u,,=‘l,+6,(tl,-b,,c,_,)
+b,,I(RFF,-RCP,)-b,,(RFF,_,-RCP,_,)]
u,,=s,+v,-b,,o,_,
stochastic innovations of the structural equations (u,, w,, E,). Elements of the from estimates of the residual covariance matrix C,, are constructed variances, covariances, and autocorrelations of the structural equation residuals.
An iterative procedure is used where (i) the coefficient vector 6 is obtained by GLS estimation of (19) and (20) given 8, and (ii) a revised 8 is provided by a Gauss-Newton estimator, given b^. This iterative estimation cycle is continued until the estimate sequences of both parameter vectors 6 and 6 converge. Using final estimates of the parameter vectors, unique ‘predictors’ of the innovations of the structural equations (a, W,E) are constructed by a MARL estimator [similar to estimator (10) in section 21 from the estimated residual vector, ri. In most cases, the results of the estimation, listed in table 3, conform to prior expectations. The broad characteristics of the demand for money (16’) are very similar to the standard money demand function, eq. (1) in table 1. The impact elasticities of the passbook rate (RCBP) and real, per capita GNP correspond closely. The impact elasticity of the bill rate increased by
P.A. Tins&
rr al., An expo.sP oJ’disgui.wd deposits
133
Table 3 Final estimates
lns+6% 1,
of ‘money’ demand
function
=-0.610-0.0226,+0.0935ln (3.7) (2.3) 10.4581
and partitioned
?!!? ( P.N
IF demand
functions.”
+0.796 lnr!$+,E 1,
(12.6) 1
- 0.0166 In RTB, - 0.03 11 In RCBP, + 0.008866, In RFF, + 9, (4.2) (2.4) (0.9) [-O.OSl] 1-0.1521 [0.043]
DD j 1-1
(16’)
~,=O.Sllr~,_,+a, (2.0) li,,, = 0.242 x IO J ,
1955.11-76.N
DW= 1.76
= -0.109+0.00932RFFP+0.0804RP~0+0.721 (3.7) (1.8) 1972.IIIL76.N
0,,=0.289
x 10-4.
(6.7)
‘Fy + E, i DD i r-1
(17’)
DW= 1.91
= 0.024 + O.O292(RFF, - RCP,) + 0.0022 1 RFF, + L’~ (2.3) (0.7)
(18’)
~1,=0.929v,-, fw,
(16.8) 1972.111-76.IV
0,,=1.154x
0.316 x 10m4, m,, = -0.122 X lo-“,
YTaw=
10-4,
0.598, P‘lw= P‘?, = - 0.425,
DW= 1.78 ( )-L-ratios, [ ] -steady-state
elasticities
46x, perhaps because of the increased liquidity of bills resulting from collateral usage in the IF market.23 The composition of ‘money’ is defined by eq. (17’). This equation is dominated by the RFF ratchet where the last peak occurred in 1974.111. Although a strict interpretation of this simple approximation of the IF market evolution should not be taken too literally, the dynamics of the equation suggest that 96% of the diffusion adjustment to the last peak was completed by 1976.IV. Z3The positive elasticity of the ‘own’ rate approximation, RFF, also conforms to prior expectation. There are a number of interesting macro implications introduced by the existence of a slgmficant non-bank demand for IF including: (i) a reduction in the net interest rate elasticity of the demand for ‘money’ and (ii) invalidation of bank reserve models based on the existence of a binding required reserves relation with ‘money’. Although a number of conjectures can be advanced on these and other issues, quantitative evaluations will be deferred to a sequel where both sectoral demand and supply schedules of IF will be embedded m a more general econometric model of economic activity.
The negative covariance of the innovation of this equation with the innovation of total money demand, c,,, is interpreted as an adjustment for aggregation. It is presumed that businesses are more efficient than households in the management of transactions balances. Thus, if corporations receive a bigger share of income, total ‘money’ balances will be lower than average, and investment in IF will be higher than average. The most notable feature of the demand for IF on portfolio account, eq. (18’) is that the variance of its stochastic innovation, o,,,,,,, is about four times larger than the variances of the two innovations that appear in the transactions demand on income account (o~~,cJ~J. Fortunately, as shown affect the constructions of the demand for below, a,,,M,does not significantly ‘money’ and its partitions. DD and IFY.24 As indicated in the last column of table 4, the partitioned ‘money’ demand system explains about SO:/;, of the cumulative error of the standard money demand forecasts. A portion of the remaining error may be attributed to other problems associated with recent measurement of ‘money’ such as the emergence of NOW and POW accounts and so on. However, much of the remaining error may be due to a mis-specification of the dynamic response to short-run variations in GNP. After differencing the entries in the third column of table 4, a large forecast error is still obtained by the partitioned demand system in 1975.1 (although it is substantially less than the corresponding error in the standard demand function). At an annual rate, the real per capita GNP dropped over 10 ;;, in that quarter alone. It is likely that the dynamic response to variations in the transactions scale is apt to be more complicated than the geometric response used in the standard money demand formulation. To provide a rough test of this conjecture, the ‘residual’ of money demand (16’) (i.e., the stochastic innovation u,) was regressed on the growth rate of real per capita GNP, ci,=-O.OOl+O.l26dln (1.4) (2.8)
L = 0.197 x 10-4.
(21)
This simple alteration in the dynamic response structure of money demand reduces both the variance of money demand, craa, by about 20”/0 and the specific forecast error in 1975.1 by over 6091. The unadjusted variance of the ‘residual’ of the money demand function of the partitioned system (16’), Ok’,,is actually about five percent lower than the variance of the standard money demand formulation, eq. (1) of table 1. Unfortunately, gno is not the variance of the one-period forecast error. The “‘It was expected that the magnitude of the cross-correlatmn between E, and IV, would indicate the degree oi mvxpecification in the partitioning of IF. Although (T_ was negative, the cross correlation was extremely low m the neighborhood of the final estimates and was set to xro to aid terminal convergence of the nonlinear estimator.
P.A. Tin&p
et al., An exposP
of disguiseddeposits
135
Table 4 Cumulative Standard Absolute error (Shill)
errors
model” Relative error (“0
in ‘forecasting’
checking
deposits,
Partitioned
modelb
Absolute error (Shill)
Relative error
(X)
1974.1-78.111.
o/0 reduction in DD forecast error by partitioned model
1974.1 II III IV
- 0.6 - 3.9 -8.1 - 14.0
1975.1 II III IV
-21.4 -22.1 -23.7 -28.5
-10 -10 -11 -13
-5.3 -3.1 -2.2 -3.4
-2 -1 -1 -2
75 86 91 88
1976.1 11 III IV
-
32.2 32.6 35.0 36.6
- 14 -14 -15 -16
- 4.8 -3.8 -4.8 -5.6
-2 -2 -2 -2
85 88 86 85
1977.1 II III IV
-31.9 - 39.3 - 39.1 - 39.4
-16 -16 - 16 -16
-5.7 - 6.6 -6.6 -7.1
L; -3 -3
85 83 83 82
1978.1 II III
-41.3 -43.x -44.5
-16 -17 -17
- 8.8 - 10.6 - 10.5
-3 -4 -4
79 76 76
“DD forecasts bDD forecasts
-0 -2 -4 -6
0.6 0.1 0.6 -1.0
0 0 0 0
3
0 103 107 93
by standard money demand equation (1) cited in table 1 above by partitioned system of equations described in table 2.
reason for this is that the unobservable residual components (u,, w,, et) and, consequently, the unobservable partitions of IF are subject to an irreducible measurement error. In a conventional regression model, it is assumed that all variables are measured without error. Then, if the regression coefficients are known, the residual of the equation is measured exactly.25 This is the case for U, and u2, for example, since all arguments of the variables in the estimating equations (table 2) are measured directly. However, this is not the case for the three residuals of the structural equations in table 3 that were constructed from the ‘exact’ measurements ui and u2. Note that increasing the sample size will not eliminate the problem since an extra unknown variable will be generated in each period.“j 25More precisely, if the unknown regression coefficients are consistently estimated, residual measurement will become more exact as the sample size goes to infimty. 2hThe use of subsequent measurements z>t to Improve the estimates of the tth period is termed smoothing.Although the variances of the smoothed estimates of the unobservable components may mtially decrease with further measurements, they will not converge to zero. For more on this topic, see the discussion of the ‘uncertainty principle’ in Swamy and Tinsley (1980).
136
P.A. Tin&y
et (II., An exposh oj disguised deposits
Under certain assumptions, it is possible to construct approximations of the moments of the distribution of the ‘true’ (unobserved) structural errors about the latest estimates.27 Denoting the discrepancy between the ‘true’ unobserved residuals and the measured errors by ii, G, t’, the one-period forecast error of ‘money’, say e M, generated by the partitioned system is
The variance
of this one-period
forecast
G6
a’(e,)-o,,+p’o-,?+-
1
-&
error is approximately 2
Or7=0.303
x 1om4,
and is about an ISo/;, increase over the ex urlte variance of one-period forecasts associated with the standard money demand function (at least prior to 1974). Thus, the cost of an operational reclamation of the money demand function is the appearance of an irreducible measurement error associated with the partitioning of IF.28
*‘See the discussion of the posterior distribution of unobservable components ‘*In the case of checking deposits. the one-pertod forecast error is
The variance
of the one-period
4,, -
forecast
error of checking
deposits
in section
2
is approximately
~0, +o,,-2~~,,+pZu$+(hZ,-b,,)Zu~=0.765x10-J,
and is about 300”/, higher prior to 1974.
than
the variance
of the one-period
forecasts
of checking
deposits
References Enzler, Jared, Lewis Johnson and John Paulus, 1976, Some problems of money demand, Brookings Papers on Economic Activity 1, 261-280. Garcia, Gilhan and Stmon Pak, 1979, The ratio of currency to demand deposits in the United States, The Journal of Finance 34, June, 7033715. Goldberger, Arthur, 1974, Unobservable variables in econometrics, in: Paul Zarembka, ed., Frontiers in econometrics (Academic, New York) 1933213. Goldfeld. Stephen, 1976, The case of the missing money, Brookings Papers on Economic Activity 3, 683 -730. Hamburger, Michael .I.. 1977, Behavior of the money stock, is there a puzzle?, Journal of Monetary Economics 3, July, 2655288. Hester, Donald, 1978, Money, velocity. interest rates and policy, Testimony before Senate Banking Committee on April 24. Hildreth, Clifford and James P. Houck, 1968, Some estimators for a linear model with random coefficients, Journal of the American Statistical Association 63. June, 548-595.
P.A. Tin&y
et ul., An exposh
of disguiseddvposirs
137
Lombra, Raymond E. and Herbert M. Kaufman, 1978, Commercial banks and the federal funds’ market: Recent development and implications, Economic Inquiry 16. Oct., 5499562. Porter, Richard D., Thomas D. Simpson and Eileen Mauskopf, 1979, Financial innovation and the monetary aggregates, Brookings Papers on Economic Activity 1, 213 229. Searle, Shayle. 1971, Linear models (Wiley, New York). Swamy. P.A.V.B. and P.A. Tinsley. 1980, Linear prediction and estimation methods for regression models with stationary stochastic coefficients. Journal of Econometrics 12, Feb., 1033142. Theil. Henri and L.B.M. Mennes. 1959. Multiplicative randomness in time series regression analysis, Report no. 5901 (Econometric Institute of the Netherlands School of Economics, Rotterdam). Tinsley, P.A., Bonnie Garrett, with Monica Friar, 1978, The measurement of money demand, Special studies paper no. 133 (Federal Reserve Board, Washington, DC). Wenninger, John and Charles Sivesind, 1979, Defining money for a changing financial system, Federal Reserve Bank of New York Quarterly Review, Spring, 1 8. Zellner, Arnold, 1970, Estimation of regression relationships containmg unobservable variables. International Economic Review 11, Oct., 441-454.