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Working Paper 83-4
TEEBEHAVIOROJ?TEE
SPREAD BETWEENTREASURY
BILL RATES
ANDPlUVATEIYONEYMARKETRATES
SINCE 1978
Timothy Cook*
and
ThomasLawler*+
*Federal Reserve Bank of Richmond
and
*Federal
National Mortgage Association
December
1983
The views expressed in this paper are solely those of the authors and do not
necessarily represent those of the Federal Reserve Bank of Richmond, the
Federal Reserve System, or the Federal National Mortgage Association.
Preface
The purpose of this working paper is to present regression results
mentioned but not reported in our November/December 1983 Economic Review
article, "The Behavior of the Spread Between Treasury Bill Rates and Private
Money Market Rates Since 1978."
the end of the paper.
Review article.
To do this we simply added Section VI to
Sections I through V are identical to the Economic
THE BEHAVIOR OF THE SPREAD BETWEEN TREASURY BILL RATES
AND PRIVATE MONEY YARKET RATES SINCE 1978
The Treasury bill rate is generally viewed as the representative
money market rate.
For this reason bill rates are almost always used in
studies of the determinants of short-term interest rate levels and spreads,'
and bill rates are typically used as the index rate for variable-rate
financial contracts.z Despite this central role accorded Treasury bill
rates, they frequently diverge greatly from other high-grade money market
yields of comparable maturity.
abrupt change.
Furthermore, this differential is subject to
These aspects of the spread are illustrated in Chart 1,
which uses the three-month prime negotiable CD rate (RCD) as the private
3
money market rate.
An earlier paper by Cook [7] provided an explanation for the
spread in the period prior to 1978. According to this explanation, prior to
1978 most individual investors were unable to invest in private money market
securities because of the high minimum denomination of those securities.
1
In particular , the spread between private money rates and bill
rates is used as a measure of the default risk premium on private securities
[ZO]; the bill rate is generally used to test various hypotheses about the
effect of such economic variables as the rate of inflation or the money
supply on the general level of short-term interest rates [9, 181; and bill
rates are always used to test hypotheses about the determinants of money
market yield curves [II, 131.
2
For examule, the Treasury bill rate is often used as the
determinant of the yield on adjustable-rate mortgages. Also, many banks and
nonfinancial corporations have recently issued floating-rate notes with
rates tied to Treasury bill rates.
'The CD rate is used in this article as a representative private
money market rate. Commercial paper rates behave similarly to CD rates and
statements in this paper regarding the spread between the CD and bill rate
apply equally well to the spread between the commercial paper and bill
rates.
Chart
1
THE SPREAD BETWEEN THE CD AND T-BILL RATES
AND THE LEVEL OF THE CD RATE
Percan:age
Percent
oomts
s.o/-
20.0
I:
----
t fi cDRATE
1 I\
i A qr T Scale)
SPREAD
I-
4.0
fi
I Left Scale) \
!\I
;/
15.0
10.0
5.0
01~~II.~.I.~~I~‘~I’1II~~~~~~~1~‘.I~..I~”I..‘I~’.I”~J
1969
1971
1973
1975
1977
-.
1979
1981
1983
0
-2-
Hence, their demand for T-bills was related to the spread between Treasury
bill rates and regulated ceiling rates on small time deposits rather than to
the spread between bill rates and private money rates.
When interest rates
rose above deposit rate.ceilings at the depository institutions, the
resulting "disintermediation" and massive purchases of bills by individuals
4
caused bill rates to fall relative to private money rates.
An empirical implication of this explanation was that the spread
between private money rates and bill rates increased in periods of disintermediation when bill rates rose relative to the ceiling rates on small time
deposits.
The evidence from the earlier study provided strong support for
this implication. Because ceiling rates on time deposits were fairly
inflexible prior to 1978, this explanation also implied a positive relationship between the level of rates and the spread. As shown in Chart 1, this
was clearly true in the pre-1978 period.
Institutional and regulatory developments in 1978 eliminated the
underpinnings of this explanation by providing individuals with ways to earn
money market rates without investing in Treasury bills.
Most importantly,
that year saw the beginning of the rise in popularity of money market mutual
funds.
(Money market fund shares grew from $3.3 billion at the end of 1977
to $9.5 billion at the end of 1978 to $42.9 billion at the end of 1979.)
4
This explanation of the spread in periods of disintermediation
raises an obvious question: Why didn't other investors sell their bills and
buy private money market securities, thereby offsetting the impact of
individual purchases on the spread? In fact, other investors in Treasury
bills did react to the rise in the spread in periods of disintermediation by
decreasing their holdings of bills, but this reaction was insufficient to
eliminate the large movements in the spread caused by sharp increases in
purchases of bills by individuals. This question is discussed in detail in
171.
-3-
Also, in June of 1978 depository institutions were first allowed to offer
money market certificates in denominations as low as $10,000 with an
interest rate tied to the 6-month T-bill rate.
Chart 1 shows that since 1978 the spread has not approached the
levels reached in 1974. Nevertheless, the spread has been very large at
times and it has been even more volatile than in the earlier period.
A
number of times it has exceeded 200 basis points and then fallen sharply,
sometimes within a couple of months, to well below 100 basis points.
Also,
the spread in the post-1978 period has continued to show a tendency to move
with the level of interest rates, although a given level of interest rates
has generally been associated with a smaller spread than in the earlier
period.
This article examines the behavior of the spread in the post-1978
period using models that assume, contrary to the situation in the earlier
period, that all investors can freely choose between Treasury bills and
private money market securities. The major conclusion is that movement in
the spread can be fairly well explained in this period under this assumption
by default risk, taxes, and the relative supply of Treasury bills.
Section
I presents three models of the spread and discusses institutional
information relevant to each.
Section II looks briefly at the behavior of
two types of investors in the bill market.
results for the three models.
Section III reports regression
Section IV discusses the effect on the spread
of the introduction of money market deposit accounts in late 1982.
-4-
1.
MODELS OF THE SPREAD IN THE POST-1978 PERIOD
This section discusses three models of the spread between the rate
on private money market securities
(RMM) and the rate on Treasury bills
(RTB). All three models assume that investors can choose freely between
investing in private money market securities or bills.
The first model
focuses on default risk, while the second looks at a combination of default
risk and taxes.
Both models assume that all investors react the same to any
given RMM-RTB spread.
The third model drops this assumption.
The focus throughout is on the demand for Treasury bills as a
function of the RMM-RTB spread.
It is assumed that the relative supply of
Treasury bills is not sensitive to the spread, i.e. that the ratio of bills
to private money market securities supplied is completely inelastic with
respect to the spread.
Gaps between U.S. government expenditures and
receipts are the primary determinant of the amount of T-bills issued; while
the Treasury at times alters the average maturity of U.S. Treasury debt,
there is no evidence that such decisions are influenced by the RMM-RTB
spread.
Furthermore, it is reasonable to assume that the aggregate supply
of private money market securities is not varied in reaction to movements in
the RMM-RTB spread.
(This latter assumption is discussed below).
Default Risk Model
The simplest view of the RMM-RTB spread in the
post-1978 period is that it results solely from default risk on private
money market securities. Treasury bills are backed by the full faith and
credit of the U.S. government and are generally considered default free.
contrast,
private
In
money market securities such as CDs or commercial paper
are backed by the promise of private corporations and, consequently, there
is a general perception that default is possible on these securities.
-5-
Since investors care about expected, not promised, yields, they
demand a higher promised yield on private money securities than on bills in
order to offset the perceived risk of default and to equalize expected
returns.
Investors may also demand an additional premium for holding a
riskier asset.
The extra yield required by investors because of these
factors is called the default-risk premium.
According to the default-risk
model, the RMM-RTB spread is a direct measure of this default-risk premium
(DRP) on private money market securities:
(1) PXM - RTB = DRP
Hence, according to this model, movements in the spread simply reflect
movements in DRP.
spread.
Figure 1 illustrates the simple default-risk model of the
For any value of the default-risk premium the demand cume
for
T-bills is infinitely elastic with respect to the RMM-RTB spread. This
implies that shifts in the relative supply of bills have no effect on the
spread.
The default risk premium on private money securities is dependent
on the attitudes of investors, which are not directly measurable.
However,
the simple default-risk model of the RMM-RTB spread can be evaluated by
comparing it to yield spreads that are solely a function of default risk: if
the default-risk model is correct, the RMM-RTB spread should behave
5
similarly to these spreads.
One money market default-risk spread that has
been available since the beginning of 1974 is the spread between the
one-month medium-grade and prime-grade commercial paper rates (CPS). Chart 2
5
These spreads typically rise in periods of recession and fall in
periods of economic expansion. See Van Horne [21].
Figure 1
DEFAULT-RISK
Figure 2
MODEL
RISK AND TAX MODEL
RMM-RTB
RMM-RTB
RMM
> RMM
\
m-v---s--
DRP
RMM
/
’
/
= RMM
’
I
Aggregate
Demand
for Treaxr;
A;;regate
3111s
Figure 3
HETEROGENEOUS
INVESTOR MODEL
RMM--RIS
D
D’
Demand
‘clr Treasury
ElIIs
Chart 2
THE SPREAD BETWEEN THE CD AND T-BILL RATES
COMPARED TO CPS
Pert
Percentage
rage Points
Points
i !.O
5.0
CPS
lRighr Scale)
4.0
,y
\rr
7I
SPREAD
-1 1.5
3
3.0
i
,\
iI
I.0
!ir.
2.0
I.5
1.0
0
1975
1977
1979
1981
1993
-66
compares this spread to the RMP-RTB spread.
The chart shows that the
RMM-RTB spread does frequently move with the commercial paper rate spread.
There are periods, however, such as mid-1980 through the end of 1981, when
v than the commercial paper rate
the RMM-RTB spread behaves very differentlspread.
Tax and Risk Model
The preceding discussion assumes 'that interest
income earned on Treasury bills and private money market securities is taxed
equally, which is true at the Federal level. At the state and local level,
however, interest income on T-bills is exempt from income taxes while
interest income on private money market securities is not.
Individual
income tax rates applied to interest income range across states from as low
as zero to as high as 17 percent.
These rates are shown in Table I.7
In
some cases there are also local income tax rates; for example, in New York
City the highest marginal local income tax rate exceeds 4 percent.
Despite the exemption of T-bill interest income from state and
local taxation, there are three categories of investors who do not pay a
higher tax rate on interest income of private money market securities than
bills.
The first includes investors who are not subject to state and local
taxes, namely state and local governments and foreign investors. The second
6
The commercial paper rate spread is only available beginning in
1974 and there are no other yield series available to construct short-term
default-risk spreads. Hence the chart starts in 1974.
7
The tax rates shown are for the highest marginal tax rates.
However, in almost all states the maximum tax rate--or one very close to
it--is reached at a relatively low income. (The only exceptions are Alaska,
Delaware, Louisiana, New Mexico, and West Virginia.) Hence, one can make
the assumption that, in general, interest income on private money market
investments in a given state is taxed at the highest marginal tax rate in
that state.
TABLE I
State Individual Tax Rates on Interest Income
(As of October 1, 1979)
Alabama
Alaska
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
Florida
Georgia
Hawaii
Idaho
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massachusetts
Michigan
MXnnesota
Mississippi
Missouri
Notes:
Source:
5
14.5
8
7
11
8
0
16.65
0
6
11
7.5
2.5
2
13
9
6
6
10
5
17.5
4.6
17
4
6
Montana
Nebraska
Nevada
New Hampshire
New Jersey
New Mexico
New York
North Carolina
North Dakota
Ohio
Oklahoma
Oregon
Pennsylvania
Rhode Island
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
Washington
West Virginia
Wisconsin
Wyoming
11
*
0
5
2.5
9
14
7
7.5
3.5
6
10
2.2
*
7
0
6
0
7.75
*
5.75
0
9.6
10
0
1.
The tax rates shown are maximum rates (see footnote 7).
2.
States marked with asterik (*) have tax rates specified
as a percent of Federal income tax liability. The
percent is 18 percent for Nebraska, 19 percent for
Rhode Island, and 23 percent for Vermont.
Reproduced with permission from 1979 Edition, State Tax
Handbook, published and copyrighted by Commerce Clearing
House, Inc., 4025 W. Peterson Ave., Chicago, Illinois
60646, pp. 660-71.
-7-
includes investors that pay a "franchise" or "excise" tax that in fact
8
requires them to pay state taxes on interest earned on T-bills.
Commercial
banks in 28 states, including most of the heavily populated states, pay such
a tax.
And in 17 states there is a franchise tax on nonfinancial corporate
income.'
The third type of investor taxed equally on interest income of
T-bills and private money securities is money market fund (MNF) shareholders.
All interest earned through investment in money market funds, includ-
ing T-bill interest income, is subject to state and local income taxes.
Consequently, an investor owning shares in a money market fund that holds
T-bills must pay all applicable state and local taxes on the interest
income, even though the investor would not have to pay state and local taxes
on that income if he purchased the T-bills directly.
The implications of the wide range of relative tax rates on T-bill
versus private interest income for the determination of RMM-RTB spread will
be considered below.
For the present consider the case in which all inves-
tors are subject to the same marginal state and local tax rate of t on
private interest income; then the relationship between RMM and RTB would be
(2)
lWM(l-t) = RTB
or
(2a)
RMM - RTB = t*RMM
or
(2b)
RMM/RTB = 1/(1-t) .
8
These taxes function exactly like an income tax and were
instituted expressly to get around the prohibition of state and local taxes
on interest income of Federal securities. See [4] and [15].
9
These states are listed in [6, p. 6521.
-8-
Equation (2a) states that the RMM-RTB spread is positively related
to the level of interest rates; the after-tax yields will remain equal only
if the before-tax yield spread rises or falls in proportion to changes in
the level of interest rates.
Equation (2b) indicates that the ratio of RMM
to RTB is constant over time when taxes are the only factor affecting the
10
spread and marginal income tax rates are the same for all investors.
Chart 1 demonstrates that the RMM-RTB spread does tend to move
with the level of interest rates.
Chart 3, which plots the ratio of the
three-month CD rate to the three-month T-bill rate, illustrates that this
ratio is not constant. Although variability of the RMM/RTB ratio is inconsistent with the simple tax model, the RMM/RTB ratio in the post-1978 period
has been much less variable than the RMM-RTB spread. Moreover, the ratio,
unlike the spread, is not strongly correlated to the level of rates over
this period.
11
10
Suppose an investor is subject to a marginal Federal income tax
rate of tf and a marginal state income tax rate of ts. State taxes paid can
be deducted from Federal income taxes. Hence, if the investor pays state
income tax on private money market securities but not on Treasury bills,
then the before-tax yields on Treasury bills and private money market
securities that result in equal after-tax yields will be:
RMM (1 - tf - ts + tfts) = RTB(l-tf)
which can be reduced to:
RMM(l-ts) = RTB,
which is the formula in the text.
11
For the period from January 1979 through June 1983 the
correlation coefficient between the RMM-RTB spread and the level of the
Treasury bill rate is .520. However, the correlation coefficient between
the ratio and the level of the bill rate is only .068. (Note in Chart 3
that in the pre-1978 period the FXM/RTB ratio is as volatile as the spread
and that it is also highly correlated with the level of rates. Over the
1974-77 period the correlation coefficient between the spread and the level
Chart 3
THE RATIO Of THE CD RATE TO THE BILL RATE
COMPARED TO THE CD RATE
Rar
1.6
20.0
RATIO
1.5
t Left Scale
\
15.0
1.4
1.3
10.0
1.2
5.0
1.1
1.0
1969
1971
1
1973
1975
1977
1979
1961
191
-9-
Of course, this simple tax model is deficient in that it ignores
the effect of the default-risk premium on the spread.
The tax and default-
risk models can be joined by combining equations (1) and (2):
(3)
RMM(l-t) = RTB + DRP
or
(3a)
RMM-RTB =tRMM+DRP
or
(3b)
RMM/RTB = (1/(1-t)) + DRP/RTB(l-t)
In this tax and risk model, the RMM-RTB spread is positively associated with
the level of interest rates as in the simple tax model.
However, in
equation (3b) the RMM/RTB ratio is not constant but changes with the DRP/RTB
ratio.
Figure 2 illustrates the aggregate demand curve for T-bills
implied by the combination of the simple default-risk model and the simple
tax model. As the figure shows, at any given level of interest rates and
default-risk premium, the demand for T-bills is infinitely elastic with
respect to the after-tax RMY-RTB spread.
If RMM rises and the default-risk
premium remains unchanged, then the whole demand curve simply shifts upward
by an amount equal to the product of the tax rate times RMM.
Moreover, it
can be seen from Figure 2 that changes in the relative supply of T-bills, if
unaccompanied by changes in the level of interest rates or default-risk
premium, have no effect on the REM-RTB spread.
Chart 4 compares the RMM/RTB ratio to the ratio of the commercial
paper spread and RTB in the 1979-83 period.
The two series move fairly
closely together over the whole 1979-83 period, suggesting that the risk and
of the bill rate is .799 while the correlation coefficient between the ratio
and the level of the bill rate is .758.)
Chart 4
THE RATIO OF RCD TO RTB
COMPARED TO THE RATIO OF CPS TO RTB
Ratto
Ratio
1.6
30
1
CPSIRTB
(Right
Scale)
1.4
.20
RCD/RTB
::
1.2
.10
1S
I
1975
1977
I
3
I
1979
!
I
I
:
1981
I
,
,I
,
1983
0
- 10 -
tax model is superior to either the default-risk model or the tax model
12
alone.
Heterogeneous Investor Model
The tax and risk model assumes that
all investors bear the same relative tax rates on private money securities
and T-bills.
As discussed above, however, there are substantial differences
across investors with respect to the relative taxation of private versus
T-bill interest income; that is, investors differ with respect to the tax
rates they face.
A second source of investor heterogeneity involves various implicit returns that some investors receive from holding T-bills--i.e., returns
not measured by the stated T-bill yield.
These implicit returns arise from
various laws and regulations, many of which have changed over time.
Banks,
in particular, receive various implicit returns from holding Treasury bills.
For example, banks (and other depository institutions) can use Treasury
bills at full face value to satisfy pledging requirements against state and
local and Federal deposits.
Also, Treasury bills improve the ratio of
equity to risk assets, a measure bank regulators use to judge a bank's
capital adequacy. Moreover, prior to the Monetary Control Act of 1980,
nonmember banks in over half the states had reserve requirements that could
be satisfied at least partially--and in some cases totally-by holding
unpledged Treasury bills.
Finally, funds acquired by a bank that enters
into a repurchase agreement are free of reserve requirements if the secu13
rities involved are obligations of the U.S. or FederaS agencies.
12
In contrast, it is evident from Chart 4 that in the 1974-77
period the tax and risk model does a poor job of explaining the spread.
13These implicit returns are discussed in more detail in [7].
- 11 -
Treasury bills also provide implicit returns by virtue of their
preferred position in certain financial markets.
They are accepted without
question as collateral for margin purchases or short sales of securities.
And they can be used to satisfy the initial margin requirements for many
types of financial futures contracts, whereas private money market
securities cannot be used for this purpose.
With different tax rates and implicit returns, investors will
react differently to a particular RMM-RTB spread.
For example, even at a
large RMM-RTB spread and a very small default-risk premium, the demand for
T-bills will be positive because investors with a high marginal state and
local tax rate on private interest income and a zero-tax rate on T-bill
interest income will find it advantageous to buy T-bills instead of CDs or
commercial paper.
As the spread falls, more and more investors with smaller
differentials between the tax rates on interest income of private securities
and T-bills will find it
advantageous to buy T-bills.
14
A similar
Pledging requirements are described in [l, 10, 141, state reserve
requirements prior to the Monetary Control Act in [12], regulations on
repurchase agreements in [17], and bank capital adequacy measures in 1191.
14
An assumption in this discussion is that the possible investment
in Treasury bills by a particular investor is limited. The argument might
be made that there are risk-free arbitrage opportunites that would provide
incentives for investors to borrow funds in the bill (CD) market and lend
them in the CD (bill) market. These opportunities generally are not present
because only the Treasury can issue T-bills and only the direct holder of
T-bills receives the state and local tax exemption. For example, it might
be argued that at large values of the spread, there is an opportunity for
investors with equal tax rates on bill and private interest income to borrow
bills at a rate slightly above the bill rate, sell them and invest the
proceeds in private securities. However, investors that loan bills under
this arrangement lose the tax exemption on T-bill interest income; hence,
they need to be paat
least RTB/(l-t) to be induced to loan their bills.
This eliminates the arbitrage opportunity for the equal tax rate investor.
Conversely, suppose the spread is zero; then there appears to
exist arbitrage opportunities for investors with unequal tax rates on
- 12 -
conclusion holds for differential implicit returns.
If these vary across
investors, then a decline in the spread will induce investors receiving
lower implicit returns to buy bills.
Consequently, with differing tax rates and implicit returns, the
aggregate demand for T-bills--given some constant default-risk premium-decreases only gradually as the RMM-RTB spread rises.
When the RMM-RTB
spread is high relative to the default-risk premium, the aggregate demand
for T-bills will be relatively low; as the RMM-RTB spread declines, the
aggregate demand for T-bills will increase. When the spread falls to the
level of the default-risk premium, the demand will be completely elastic as
in the simple default-risk model.
Figure 3 illustrates the heterogeneous investor model.
The figure
shows that an increase in the level of interest rates can affect the RMM-RTB
spread because of the tax effect.
However, the effect of a rise in the
level of rates on the spread depends on the relative supply of T-bills; the
greater the relative supply of bills, the smaller the effect on the spread
of a given increase in the level of rates.
private and T-bill interest income. These investors could issue private
securities (deducting the interest paid from their taxable income) and
invest the funds in bills. However, as discussed in the text, investors
with the highest tax rate on private versus bill interest income are
individuals. They clearly are not able to and do not engage in this kind of
activity. If individual investors pool their funds to buy bills, then they
are in effect forming a financial intermediary to buy bills indirectly and
they lose the tax exemption on T-bill interest. This is precisely the
situation of money market funds (see Section II of this article). However,
in periods of very low values of the spread, there does appear to be
arbitrage opportunities for large investors (i.e. banks) in states With high
income tax rates who are not subject to excise or franchise taxes on T-bill
interest income. In periods of small spreads, one might expect to see banks
in these states issuing CDs to buy bills.
- 13 -
Moreover, changes in the supply of T-bills can have a direct
effect on the RMM-RTB spread.
For instance, if the relative supply of
T-bills falls, the RMM-RTB spread might rise, as a greater proportion of
T-bills are purchased by investors with a high marginal tax rate on private
versus T-bill interest income.
II.
INVESTMENT IN T-BILLS BY INDIVIDUALS AND MMFS
Additional evidence on the effect of differential taxation (of
interest income on bills versus private securities) on the spread in the
1979-83 period is contained in monthly data on T-bill investment by individuals and MMFs.
As discussed earlier, individuals as a group have the
largest differential between the tax rates paid on private versus T-bill
interest income.
At the other extreme are the shareholders of MMFs who are
taxed equally on the interest of T-bills and private instruments.
No data is available on individual investment in T-bills. Howev15
at weekly
er, the percentage of bills awarded to noncompetitive bidders
Treasury bill auctions is a widely used barometer of individual investment
activity in the bill market.
16
Chart 5 shows that the percent of noncompet-
itive bids at the weekly auction moves closely with the level of interest
rates.
17
15
Investors who purchase $l,OOO,OOO or less of bills at the weekly
auction can make a "noncompetitive bid," whereby the investor agrees to pay
the average price of accepted competitive bids. This amount was raised in
1983 from $500,000.
16See [5].
17
Based on Treasury Department data for 1980, 60 percent or more
of the dollar volume of noncompetitive bids at the weekly Treasury bill
auctions during that year (excluding noncompetitive bids made by Government
Chart 5
Chart 6
NONCOMPETITIVE
BIDS AT
WEEKLY AUCTION COMPARED TO
LEVEL OF RATES
TREASURY BILLS AS A PERCENT
OF TOTAL MMF ASSETS COMPARED TO
RCD-RTB SPREAD
Perter f
O:.of Total
% of Total
25 1
118
30 1
Percentace
1 3.0
20
ONCOMPETITIVE
15
10
5
(Riaht
Scale)
0
1975
1977
1979
1981
1983
III..1
1979
,.,...,..
1980
!
1981
1982
Chart 7
NONCOMPETITIVE
BIDS AT
WEEKLY TREASURY BILL AUCTION
COMPARED TO THE CD RATE
(November 1982 - February 1983 I
Percent
/ NONCOMPETITIVE
BIDS
i
10
t
CD RATE
Nov.
’
‘d
Dec.
POs?Tj
I
Jan.
Feb.
.,
.
1983
- 14 -
Chart 6 compares the bill holdings of MMFs to the RMM-RTB spread.
MMF investment in bills is negatively and strongly correlated to the
18
Hence, even though MMFs primarily buy bills tndirectly for
spread.
individual investors, their response to changes in the spread differs
markedly from that of individual investors.
The pattern of investment in T-bills by individuals and MMFs can
be explained by the different tax rates applicable to the two groups and, in
addition, strongly suggests that taxes played a role in the behavior of the
spread in the post-1978 period.
The reasoning is as follows. As interest
rates rise, at a given level of the before-tax RMM-RTB yield spread, the
after-tax yield spread falls for investors (individuals) taxed on private
interest but not on T-bill interest, inducing them to increase their bill
19
purchases.
This puts downward pressure on the bill rate and increases the
before-tax RMM-RTB yield spread.
At the same time, the increase in the
before-tax yield spread causes a comparable increase in the after-tax yield
spread for investors (MMFs)who pay equal tax rates on T-bill and private
interest income. This rise in the after-tax yield spread induces them to
accounts or the Federal Reserve) were made at the New York Federal Reserve
District, whch has by far the highest district-wide average state income tax
rate.
18
The correlation coefficient between the percent of MMF assets
invested in bills and the spread over the period in Chart 6 is -.438. In
contrast, the correlation coefficient between noncompetitive bids and the
spread is +.506.
19
It is relevant to this argument that following the growth of
MMFs in 1978 and the introduction of MMCs in that year, the effect of taxes
on the after-tax yields of these investments relative to the yields earned
by direct investment in bills was well publicized. For instance, In March
1979 the Wall Street Journal published an article entitled "Where State and
Local Taxes Hurt, Investors Can Earn More in Direct Purchases of Bills"
See also 13, 53.
r221
l
- 15 -
decrease their purchase of bills.
Hence, a rise in the level of interest
rates is followed (1) by an increase in the holdings of bills by investors
with unequal tax rates on T-bill and private interest income, (2) by a rise
in the RMM-RTB spread, and (3) by a decrease in the holdings of bills by
investors with equal tax rates on the two types of interest income.
III.
ESTIMATES OF THE SPREAD MODELS
Risk and Tax Models
Regression estimates of the alternative
20
models of the spread are presented in Table II.
The spread between the
medium-grade and prime-grade commercial paper rates ("CPS") is used as a
proxy for the default risk premium on CDs, the assumption being that the
true default risk premium is linearly related to this spread.
The coefficient of CPS in the risk equation regression, equation 1
in Table II, has the correct sign and is highly significant. In the regression equation of the tax and risk model, equation 3, the coefficients of
both the risk and tax variables have the correct signs and are highly
significant. The overall fit of the estimated tax and risk model is
20
The reported regressions follow the conventional procedure of
using the risk-free rate (the T-bill rate) as the right-hand side
(independent) variable. Actually, the tax and risk model is an equilibrium
relationship. Because of this, there is no a priori reason to use the
Treasury bill as opposed to the CD rate as the right-hand side variable in
the regression equations. The regressions were also estimated with the CD
rate as the right-hand side variable. The estimated coefficient of the
interest rate variable in these regressions (reported in Section VI) is
somewhat higher; however, none of the conclusions reached in this section
are different.
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- 16 -
considerably better than the simple risk model
21
and the value of the
autocorrelation coefficient, p, is considerably lower.
These results support the conclusion that differential taxation of
interest income on T-bills and private money securities was an important
determinant of the RMM-RTB spread in the 1979-83 period.
The tax rate
22
which is
implied by the coefficient of RTB in equation 3 is 8.3 percent,
well within the range of state individual tax rates on interest income given
in Table 1. Hence, the magnitude of the interest rate coefficient is
consistent with the tax explanation of the relationship between the level of
rates and the spread in the post-1978 period.
Heterogeneous Investor Model
The implications of the heteroge-
neous investor model discussed in Section I were that (1) the RMM-RTB spread
may be negatively related to the relative supply of T-bills and (2) the
effects of the level of rates and the relative supply of T-bills on the
spread may be interdependent; that is, the effect of an increase in the
level of interest rates on the spread may depend on the supply of bills
23
outstanding.
The supply variable used in the heterogeneous investor model
regressions is the ratio of T-bills outstanding net of Federal Reserve
holdings (TB) to total liquid assets (L), a proxy for the overall size of
21
This statement is especially true for the ordinary least-squares
summary statistics, which provide a more meaningful comparison across
regressions since they do not depend on the value of the autocorrelation
coefficient.
22
The implied tax rate is calculated from equation 2 in the text
as c/(l+c) where c is the coefficient of the Treasury bill rate.
23For previous evidence of supply effects on the spread see [161.
- 17 24
the money market.
Two regressions are reported in Table II.
The first
regression simply adds the relative supply variable to the tax and risk
model.
The variable's coefficient has the correct sign and is statistically
25
significant.
The magnitude of the coefficient implies that if the
'
relative share of T-bills in total liquid assets rises by one percentage
point, the RMM-RTB spread falls by 15 basis points.
Treasury bills range
from approximately 5.6 to 9.3 percent of total liquid assets over the period
covered by the regressions; hence, the regression results imply that supply
factors explain a relatively small part of the movement in the spread in
that period.
24
The specific form of the supply variable used in these
regressions is by necessity somewhat arbitrary. Regressions with
alternative forms of the supply variable,reported in Section VI, did not
alter the conclusion that the relative supply of Treasury bills affected the
spread in the post-1978 period. First, L, the denominator of the relative
supply variable, was replaced with two narrower measures: (1) T-bills plus
large CDs plus commercial paper plus bankers acceptances and (2) T-bills
plus large CDs. In both cases the t-statistic of the coefficient of the
supply variable rose. Second, marketable U.S. government securities of
foreign accounts held in custody at the Federal Reserve were netted out of
the numerator of the relative supply variable. When this was done, the
t-statistic of the coefficient of the supply variable rose.
25
A reasonable question regarding this result is whether the
coefficient of TB/L is affected by simultaneous equations bias, i.e. whether
a change in the RMM-RTB spread induces a response that alters the relative
supply of T-bills outstanding. We do not think this is a serious problem
because the movement in the TB/L ratio is determined mainly by the movement
in Treasury bills outstanding and the Treasury's supply of bills is clearly
not responsive to the RMM-RTB spread. Admittedly, on a priori grounds it is
possible that the supply of private securities by some agents may be
marginally responsive to the spread. (Although see footnote 14 on this
point). For example, it might be argued that at large values of the spread,
depository institutions that pay equal tax rates on bill and private
interest income would sell bills and simultaneously run down their CDs
outstanding. However, we are not aware of any evidence that the RMM-RTB
spread is an important determinant of the aggregate supply of private
short-term securities.
- 18 -
The second regression reported in Table II uses a specification
in which the effects of the interest rate and supply variables are interdependent:
Spread= a + b*CPS + c-edsTBfi-RTB,
where eis the base of the natural logarithm. This specification also
implies that the larger the relative share of bills to liquid assets (TB/L),
the smaller the effect on the spread of further increases in the share,
which should be the case if the aggregate demand for T-bills flattens out at
low levels of RMM-RTB, as argued earlier. This equation was estimated by
experimenting with different values of d and choosing that value of d for
which the sum of squared residuals in the ordinary least squares regression
was lowest. The coefficient of the interest rate/supply variable is highly
significant while the summary statistics of the regression are only slightly
better than for the regression with the linear supply variable.
The
estimate of the tax rate implied by the coefficient of RTB ranges from 6.3
26
percent to 10.1 percent over the estimation period.
While this
specification yields results that are very close to the first one, it makes
more sense a priori and for that reason should fit the data better than the
first specification in the future.
Since the bill share variable TB/L
should rise in coming years because of large budget deficits, this means
that a rise in the level of rates should be associated with a smaller rise
in the spread than in the 1979-83 period.
26
This is calculated as c*/l+c* where c* is the coefficient of RTB
in regression (4b) in Table II and is dependent on TB/L.
- 19 -
IV.
THE EFFECT OF MMDAS ON THE SPREAD
In mid-December 1982, all interest rate ceilings on short-term
deposits with minimum denominations of $2500 at depository institutions were
removed. The "money market deposit accounts" (MMDAs) that resulted from
this deregulation were very popular, reaching a level of $278 billion by the
end of February. A final question addressed here is whether the introduction of MMDAs decreased the demand for T-bills and thereby lowered the
RMM-RTB spread.
Following the introduction of MMDAs, the RMM-RTB spread fell to
extremely low levels; by March 1983 it had fallen to an average level of 16
basis points.
However, the role played by MMDAs is difficult to isolate
from other influences occurring at the time.
Specifically, MMDAs were
introduced at a time when there were major changes in the default-risk
premium and tax rate variables that would also cause the spread to fall.
Table III shows that the spread had already fallen sharply before the introduction of MMDAs in reaction to the decline in the default-risk premium and
the lower level of interest rates.
Also, as was shown in Chart 6, the
demand for bills by individuals--as measured by noncompetitive bids
at
the
weekly auction--had also fallen sharply prior to the introduction of MMDAs
in reaction to the decline in market interest rates.
Chart 7 shows the weekly data for noncompetitive bids around the
time of the introduction of MMDAs.
Noncompetitive bids dropped substantial-
ly the two weeks following the introduction of MMDAs. This occurred in a
period of stable short-term interest rates, which indicates that initially
MMDAs decreased the demand for bills by individuals. By the first weekly
auction in January, however, noncompetitive bids had returned to their
pre-MMDA
level.
Hence, there is little evidence from the noncompetitive
TABLE III
Behavior of the RCD-RTB Spread, RCD and CPS
RCD-RTB
CPS
August
1.76
1.68
10.75
September
2.61
1.68
10.81
October
1.67
1.38
9.64
November
0.72
1.26
9.07
December
0.57
0.90
8.78
January
0.35
0.76
8.48
February
0.26
0.69
8.66
March
0.16
0.63
8.81
1982
1983
RCD is the three-month prime bond equivalent prime CD rate.
RTB is the three-month bond equivalent Treasury bill rate.
CPS is the spread between the bond equivalent medium-grade and primegrade commercial paper rates.
- 20 -
bids data of a lasting effect of MMDAs on the demand for bills.
To test for
an effect on the RMM-RTB spread, a dummy variable was incorporated into the
spread regression (equation 4a in Table II).
This variable was set equal to
27
1 for the months beginning in December 1982.
The variable's coefficient
was close to zero and not significant, which reinforces the evidence from
the noncompetitive bids data.
V.
CONCLUSIONS
The volatile behavior of the RMM-RTB spread over the post-1978
period can be fairly well explained by models that assume investors can
28
chose freely between Treasury bills and private money market securities.
Variable default-risk premiums and differential taxation of interest income
on bills and private securities were found to be the two
of the spread in this period.
major
determinants
A model of the spread that allowed for
27
The dummy variable was given a value of 0.5 in December since
MMDAs were introduced December 15.
28
This raises the question of whether these models can explain the
behavior of the spread in the E-1978
period. Unfortunately, a key
variable used in this article--the commercial paper rate spread--is
available only since 1974 and the only swing in the RMM-RTB spread in the
74-77 period occurred in 1974. (In contrast there were 5 major swings in
the spread in the 1979-83 period.) However, the models discussed in this
paper clearly do a poor job of explaining what happened to the spread in
1974. This conclusion is based on Charts 2, 3, 4 and footnotes 11 and 12.
Chart 2 shows that the RMM-RTB spread fell sharply in the latter part of
1974 even though CPS stayed very high until the end of the 1974-75
recession. Chart 4 shows that the tax and risk model has the same problem.
The main implication of the simple tax model is similar to that of
the disintermediation argument: both imply that the spread is positively
related to the level of interest rates. However, the tax model clearly can
not explain the extremely high levels of the RMM/RTB ratio, shown in
Chart 3, in 1974. (Nor can the tax model explain values of the ratio
persistently above 1.2 in earlier periods of disintermediation, such as
1969-70 and 1973). Regressions for the 1974-77 period, reported in
Section VI, reinforce the comments made here.
- 21 -
investors experiencing different tax rates and implicit returns was discussed.
This model holds that the relative supply of bills can affect the
spread.
Regression results supported this contention, although the effect
of the bill supply variable was small compared to the other two determinants
of the spread.
VI.
ADDITIONAL REGRESSION RESULTS
This section reports supplementary regression results that were
mentioned in our Economic Review article (i.e. the first five sections of
this working paper) but not reported there.
five parts.
The section is divided into
The first part gives, with little or no comment, regression
results that were asserted in the Economic Review article to be very close
to those reported there.
The second part reports regression results using
different versions of the supply variable.
The third part discusses
potential problems in interpreting the coefficient of the supply variable.
The fourth part reports regression results designed to test for the effect
of MMDAs on the spread. Lastly, regression results for the 1974-77 period
are presented.
1.
Assorted Regression Results Mentioned But not Reported in the Economic
Review Article
Table IV reports the OLS regression results for the various
models.
These results are very close to the Hildreth-Lu estimates in
Table II.
Table V reports the estimates of the spread models with the CD
rate (RCD) rather than the T-bill rate used as the right-hand side interest
rate variable.
As noted in footnote 20, the results are very similar to
those reported in Table 11 using RTB.
One exception is the coefficient of
RCD in the simple-tax model, which is very high.
However, in the more
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complete models the interest rate coefficient--and, hence, the estimate of
the tax rate--is much closer to that reported in Table II.
Table VI reports regression estimates with the commercial paper
rate (RCP), rather than the CD rate (RCD) used as the private money market
interest rate.
As implied in footnote 3, the results are almost identical
to those reported in Table II.
2.
Alternative Specifications of the Supply Variable
As noted in footnote 24, the specific form of the supply variable
used in the regressions in Table II is by necessity somewhat arbitrary,
although it was the one we felt made the most sense. We also did
regressions with other specifications of the supply variable.
These
regressions are reported in Table VII.
First, marketable U.S. government securities of foreign accounts
held in custody at the Federal Reserve were netted out of the numerator of
the relative supply variable.
When this was done, the t-statistic of the
coefficient of the supply variable rose (Equation 2 in Table VII).
Second,
L, the denominator of the relative supply variable, was replaced with two
narrower measures:
(1) T-bills plus large CDs plus commercial paper plus
bankers acceptances and (2) T-bills plus large CDs.
In both cases the
t-statistic of the coefficient of the supply variable rose.
(Equations 3
and 4)
In summary, regressions with alternative forms of the supply
variable did not alter the conclusion that the relative supp>l of Treasury
bills affected the spread in the post-1978 period.
The question remains why
we chose to report regression results with TB/L as the supply variable in
the Economic Review article. With regard to the numerator of this variable,
we could not convince ourselves that foreign purchases of bills are not
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dependent on the RCD-RTB spread.
for foreign holdings of bills-the
Furthermore, the only available measure
one used above--includes all marketable
U.S. securities held in custody at the Federal Reserve, not just short-term
securities. For-these reasons we did not net out foreign holdings in the
Economic Review article.
With regard to the denominator of the supply
variable, we felt that in view of the difficulty in choosing which assets
are close substitutes to T-bills, the most logical choice was the broadest
available measure
3.
of
liquid assets, L.
Other Potential Problems with the Supply Variable
Three other potential problems with the regression results for the
supply variable are discussed in this section.
a.
Reverse causation. As noted in footnote 25, a reasonable
question regarding the result reported in Table II is whether the
coefficient of TB/L is affected by simultaneous equations bias, i.e.,
whether a change in the RMM-RTB spread induces a response that alters the
relative supply of T-bills outstanding. We argued in footnote 25 that this
is not a serious problem because the movement in the TB/L ratio is
determined mainly by the movement in Treasury bills outstanding and the
Treasury's supply of bills is clearly not responsive to the RMN-RTB spread.
However, we raised the possibility that the supply of private
securities--and, hence, L--might be marginally responsive to the spread.
In actuality this was not a problem in interpreting the regression
results because virtually all the movement in TB/L is due to movement in TB.
To show this we reconstructed L so that all its growth over the
period--which was at an annual rate of 10.7 percent--occurred at a constant
monthly growth rate.
TB/L in Chart 8.
TB divided by this variable (LTREND) is compared to
The two series are virtually identical. Regression
- 24 -
results using TB/LTRJZNDare the same as those for TB/L, as shown in equation
5 of Table VII.
Missing variable.
b.
A second potential problem, not discussed
in the -ER article, is whether a trend in the supply variable, TB/L, is
simply picking up a trend in some variable missing from the regression.
Charts 9 and 10 show the four supply variables used in the regressions in
Table VII.
The two supply variables with L as the denominator do have an
upward trend over the period.
The other two supply variables, which have
the same cyclical movement, do not have a trend.
We point to two pieces of evidence that the coefficient of the
supply variable in Table II is not simply picking up a trend in a missing
variable.
First, as shown in Table VII, when narrower measures of liquid
assets that do nothave
trends are used in the regressions the supply
variable coefficient still comes in significantly. Second, we separated
TB/L into its trend and cyclical components and did the regression with
these as the supply variables.
The results are reported in Table VIII.
The
coefficient of the cyclical component of TB/L is significant regardless of
whether or not the trend component is included in the regression.
c.
MNDA effect on supply variable.
A final question regarding
the supply variable result reported in Table II is whether it is picking up
the effect of MMDAs in the spread.
As shown in Charts 9 and 10, the supply
variable reaches its highest level at the end of the estimation period.
This raises the possibility that the coefficient of the supply variable may
be picking up the negative influence of the introduction of MMDAs on the
spread. This possibility will be discussed below.
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4.
The Impact of MMDAs on the Spread
In Section IV we noted that when we added a dummy variable set
equal to one for the months beginning in December 1982, the variable's
coefficient was close to zero and not significant. This result is reported
in Table IX.
As a second experiment we truncated the estimated period in
November 1982 to exclude the period when MMDAs were available to
29
investors.
As shown in Table X the coefficients of all the variables are
little changed from those in Table II.
The t-statistic of the supply
variable coefficient falls somewhat, but the coefficient is still
significant of the 5 percent level using a one-tailed test.
These results
provide assurance that the coefficient of the supply variable in Table 11 is
not simply picking up the effect of a missing MMDA variable.
Note that if we are right about supply effects on the RMM-RTB
spread, the implication of the surge in the supply of bills by the Treasury
is that it will lose part, if not all, of the advantage of having its debt
exempt from state and local income taxes.
The potential revenue
consequences of this loss are substantial. Currently there are about $300
billion of T-bills outstanding net of Federal Reserve holdings.
Suppose,
for example, the tax rate of the marginal investor in bills is initially
8 percent and suppose that the Treasury begins to supply so many bills that
equal tax rate investors need to be induced to buy bills. Then, at a RMM
level of 15 percent, the annual income lost to the Treasury would be $3.6
30
billion.
29
We initially did other MMDA regressions because we expected
NMDAs to affect the spread. We were surprised by the regression results,
until we looked at the weekly noncompetitive bids data discussed in Section
IV.
30The arithmetic is [.15-.15(1-.08)1*300 = $3.6.
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5.
1974-77 Regressions
In footnote 28 we asserted that the models discussed in
Sections I-III do a poor job of explaining what happened to the RMM-RTB
spread in the 1974-77 period.
As noted in the footnote a key variable used
in this article--the commercial paper rate spread--is available only since
1974 and the only swing in the RMM-RTB spread during the 74-77 period
occurred in 1974.
Table XI reports regression results for the 1974-77 period.
The
results differ sharply across equations depending on whether RCP or RTB is
used as the right-hand-side variable and depending on whether the equation
is estimated using OLS or the Hildreth-Lu procedure. When RCD is used as
the right-hand-side interest rate variable, the interest rate coefficient is
highly significant and implies a tax rate of 40 to 45 percent in both the
OLS and the Hildreth-Lu regressions. Clearly, the high magnitude of this
coefficient is inconsistent with taxes as an explanation for the correlation
between the level of rates and the spread in the 1974-77 period.
When RTB is used as the right-hand side variable, the OLS
regression result for the interest rate coefficient gives roughly the same
picture: the coefficient is very significant and too high to be consistent
with the tax explanation. When the Hildreth-Lu procedure is used, the
coefficient is no longer significant. This result is also inconsistent with
the tax explanation, because the tax explanation requires a close link
between RMM and RTB.
regression results.
That close link is not evident in the Hildreth-Lu
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