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MONEY, THE MONETARY BASE,
AND NOMINAL GNP
William

The relationship
financial

between

innovations

the monetary

money

and nominal

notwithstanding,

base and nominal

E. Cullison

GNP has been generally

although

the relationship

GNP has been slightly

Recently,
a number
of influential
policymakers
have argued that innovations
in the means of making
payment have changed past relationships
between the
‘money supply and aggregate
income (see, for example, Morris
[18], Solomon
[20], and Wallich
[21]),
These policymakers have asserted that financial innovations
such as NOW
accounts,
money
market mutual funds, customer
repurchase
agreements, and deposit-sweeping
arrangements
obscure
the relationship
between a narrowly
defined monetary aggregate such as M11 and money balances held
for transactions
purposes.
The apparent plausibility
of this view has spawned the corollary notion that
Ml should be replaced as a primary
intermediate
target2 for monetary policy. Frank Morris, President
of the Federal Reserve Bank of Boston, for example,
advocates total liquid assets (L) as an “intermediate
goal” [18, p. 9]. Others have simply advocated that
the FOMC be flexible in choosing which aggregate
to target.
The first purpose of this paper is to investigate
whether financial innovations
have indeed obscured
the relationship between narrow monetary aggregates
and nominal income.
On the basis of the empirical
evidence, the article shows that contrary to popular
opinion, financial innovations
did not have a substantive effect on the relationship
between M1 and
GNP over the period examined,
1959 to 1981 (except possibly for the three-year period from 1975 to
1978).

stable,

between

more predictable.

This is, of course, not to say that financial innovations might not change the historical relationship
of’
M1 to GNP at some future date. But even if that
relationship changed, there is another money/income
relationship, namely that between the monetary base3
and GNP, that is thought to be relatively immune to
financial innovations
(see Meltzer [17] for a succinct explanation
of this assertion).
Therefore,
a
second purpose of this paper is to examine the monetary base to see whether it has potential as an intermediate target for monetary policy.
Several recent
studies have tended to dismiss the monetary base as
an intermediate
target on the grounds that M1 has
borne a closer empirical relationship
to GNP over
the years than has the monetary base. This article
reexamines the evidence and concludes that the base
actually bore a slightly more predictable relationship
to GNP than did M1.
Narrowly
Defined Monetary
Aggregates
As Targets for Monetary
Policy
Milton Friedman
has
argued that “. . . the monetary authority should guide
itself by magnitudes
that it can control, not by ones
that it cannot control” [7, p. 486]. Broad aggregates
like total liquid assets are not (in practice)
controllable through the reserve base, whereas narrowly
defined aggregates
can be controlled
through
the
monetary authority’s control over bank reserves, the
basis for monetary
expansions
and contractions.4

defined to include currency and coin,
demand deposits, traveler’s checks, and NOW accounts.
This sum was named M1B in 1981. For simplification,
whenever
M1 is referred to in this article, the current
definition will be relevant.

3 The monetary
base is defined as the sum of reserves
held at the Federal
Reserve
and currency
and coin
outside the Federal Reserve System and the Treasury.
It is adjusted for changes in reserve requirements.
In all
subsequent discussion of the monetary base in this article,
the figure referred to will be the monetary base as constructed by the Federal Reserve Bank of St. Louis.

2 Under current operating
procedures,
nonborrowed
reserves are used as the operating target.
M1, therefore, is
called an intermediate
target-i.e.,
intermediate
between
nonborrowed
reserves and nominal GNP.

4 See Goodfriend
[10] for an analysis of this issue. Contemporaneous
reserve accounting,
of course, is a necessary precondition
for direct control of money through the
reserve base.

1 M1 is currently

FEDERAL RESERVE BANK OF RlCHMOND

Broad

monetary

aggregates

are (in practice)

con-

trollable, if at all, only through measures designed to
affect interest rates. As a result, they are subject to
considerably
larger targeting
errors than are narrowly defined monetary
aggregates.
Also, in attempting to stabilize a broad aggregate by reacting
to changes in the demand for credit, the monetary
authority may actually destabilize the economy. This
perverse outcome may come about because the monetary authority
may misperceive
the lag between a
policy action and the subsequent impact of that action
on the economy.
Friedman
[7] has noted that, for
this reason, past Federal Reserve actions designed to
stabilize the economy have nearly always proved to
be destabilizing.
The argument that financial innovations
can cause
loss of control of monetary aggregates
is not new.
On the contrary, it represents a resurrection
of the
well-known
Gurley-Shaw
thesis [12] that was discussed widely in the economics literature in the late
1950s.
This thesis held that near-monies
such as
deposit liabilities
of savings and loan associations,
savings banks, and other financial intermediarieswhich were outside the jurisdiction
of the Federal
Reserve System-rendered
monetary
policy per se
useless as an anti-inflationary
weapon. In particular,
Gurley and Shaw argued that the Federal Reserve
could not stop inflation because it could not control
nonbank financial intermediaries
and thus could not
limit the creation of near-monies
that were regarded
as effective substitutes
for Ml.
Accordingly,
the
issue in the fifties was, as it is today, whether monetary control is feasible in a financial system that can
produce an endless array of money substitutes,
i.e.,
whether an easily controllable
monetary
aggregate
such as Ml (or the monetary base) could be used to
control the entire credit superstructure
and therefore
total spending.
Both the Gurley and Shaw thesis and the current
financial innovations
argument can be tested empirically. Both propositions
imply that the relationship
between money and nominal GNP is extremely variable and unpredictable.
Equivalently,
the financial
innovation
theses imply that the income velocity of
money, far from being stable, is a will-of-the-wisp.
(By definition, MV = GNP, where M is a monetary
aggregate and V is the income velocity of that monetary aggregate.)
The simplest and most straightforward
way of
examining the relationship between money and GNP
is to regress the percentage change in GNP on the
percentage
change in the monetary
aggregate
(see
Friedman
and Meiselman
[8]).
This method is
4

ECONOMIC

employed below. Before presenting the model, however, a word of caution is in order.
Results from
single-equation
regression models are always subject
to potential statistical difficulties.
Even so, the evidence reported below is sufficient to demonstrate
that (1) the relationship
between Ml and GNP has
been generally stable except for one three-year period, and (2) the monetary base has also borne a stable
relationship
to GNP.
The analysis will proceed by
first examining
the relationship
of Ml to GNP and,
subsequently
the relationship of the monetary base to
GNP.
The Relationship
of Ml to GNP:
The Empirical
Evidence
Countless
analyses
of GNP and Ml
have been undertaken
for different
reasons since
Friedman
and Meiselman.
One recent analysis performed by Richard
Davis
[5] is shown below.
Davis used a single-equation
model of the form,

where g is the percentage change in nominal GNP
and m is the percentage change in M1. This model
is employed in the present article.5
Parameter
estimates in a model such as this will
be influenced by the state of the economy at the end
of the estimation period. As Friedman concluded on
the basis of an extensive historical study, “. . . income
velocity tends to rise during cyclical expansions when
real income is rising and to fall during cyclical contractions when real income is falling”
[6, p. 329].
Consequently,
in order to minimize possible bias from
that source, the regression coefficients for this study
were always estimated over a period from one quarter
before the peak of one business cycle (as defined by
the NBER)
to one quarter before the peak of another.6
The results of the regressions
estimated
(with
quarterly data) from 1959-IV to 1969-W, 1959-IV
to 1973-III, and 1959-IV to 1979-IV are shown in
Table I. In-sample
results by themselves, while of
some interest, cannot give much information
about
Thus, the
the long-run
stability of M1 velocity.
equations were simulated dynamically from the fourth
5 The Davis equation was used as a model for the analysis because he concluded that M1 was more closely
related to GNP than was the monetary base. This article
subsequently examines that question, as noted before,
and his form of the equation will be used to evaluate his
The equation was estimated with unconconclusion.
strained

lags.

6 See Cullison

[4] for an example

be associated with disregarding

REVIEW, MAY/JUNE

1982

of the pitfalls that can
Friedman’s advice.

Chart

GNP AND OUT-OF-SAMPLE SIMULATIONS OF GNP FROM
M1 AND M1 ADJUSTED FOR THE 1975 - 1978 VELOCITY SHIFT

quarter of 1959 through fourth quarter of 1981.7
Chart 1 shows the resulting out-of-sample
forecasts
(from 1959-69 and 1959-73 data) plotted against
actual GNP. As is apparent, the equations predicted
nominal GNP fairly accurately until the second quarter of 1975, when velocity growth rose as the econThe simulation
omy moved out of the recession.
began to track the changes in the actual GNP again
in 1978,8 although simulated GNP was at a lower
level.
After an ad hoc adjustment
was made to simulated
GNP to account for the 1975-78 velocity shift, the
forecasts came back on track.
The adjustment
involved adding 0.5 percent per quarter to the percentage change in nominal GNP over the period from
1975-11 to 1978-11. Chart 1 also shows the out-ofsample simulation of GNP forecasted from M1 with
7 In the dynamic simulations,
the regression
equation
predicts the percentage
change in nominal GNP. Actual
GNP in the beginning
period is used as the base and
never again enters the simulation.
*Thanks
me.

are due Stephen

Hale for pointing

this out to

that adjustment,
and Table II reports the forecast
errors in the out-of-sample
period.
As the table
shows, the simulations adjusted for the velocity shift
missed actual fourth quarter 1981 GNP by only $34.1
billion (1.1 percent)
in the simulation from the parameters estimated from 1959-69 data and only $2.3
billion (0.08 percent)
in the simulation
based upon
1959-73 data. Considering
that these were dynamic
simulations
with the only actual GNP data entering
the forecasts coming in 1959-IV (the beginning of the
simulation),
the closeness of the forecasts to actual
GNP in the post-sample period is striking.
During

1981, nationwide

NOW

account

owner-

ship was authorized and NOW accounts, a component of M1, grew rapidly.
At the same time, the
economy experienced
an immense increase in outstanding
shares of money market
mutual
funds.
Money market mutual fund shares, while checkable
(under certain restrictions),
are not included in M1.
Could the relationship
of predicted to actual GNP
have remained so close in 1981 if financial innovations had obscured the relationship
of M1 to GNP ?

FEDERAL RESERVE BANK OF RICHMOND

ment was faulty and that M1 (then M1B) continued
to be the appropriate
measure of transactions
accounts.
One explanation
may be that money market
mutual funds were absorbing
funds designed for
savings
whereas
NOW
accounts
were absorbing
The
1981
experience
does
transactions
balances.
illustrate that financial innovations
have made monetary targeting more difficult.

During 1981, the Federal Reserve paid close attention to a monetary aggregate denoted shift-adjusted
M1B-i.e.,
MI adjusted to remove any shifts from
time and savings deposits into NOW accounts.
That
aggregate was also tested in the simulations
of GNP
in 1981. The NOW-shift
adjusted simulation gave
considerably
poorer results than did the simulation
based upon actual M1.9 This result was somewhat
puzzling, for it implied that the NOW-shift
adjust-

These simulation results, in any event, are not consistent with an unstable and unpredictable
relationship between M1 and GNP.
Therefore, econometric

9 The root mean squared error for 1981 of GNP simulated from Ml was $44 billion compared to $76.5 billion

money

for GNP simulated from M1 adjusted for the shift into
NOW accounts. ‘Additionally,
the geometric averages of
the quarterly percentage
changes in actual GNP and the
GNP simulations
for 1981 were 9.69 percent for actual
GNP, and 10.2 percent for GNP simulated from M1, but
only 7.5 percent for GNP simulated from “shift-adjusted
M1B.”

demand

predictable
Hafer

equations

that are unstable

may

well

be misspecified.

and Hein

[13]

and

Hetzel

similar

conclusions

using

different

Marvin

Goodfriend

[11]

has shown

[14]

and un(See also
who reach

methodology.)
that

there

Table I
RESULTS

OF REGRESSIONS

(All variables

are represented

OF GNP ON THE ST. LOUIS
as quarter-by-quarter

percentage

MONETARY

changes.

BASE AND M1*

All lags are unconstrained.)

(M is equal to M1)

ECONOMIC

REVIEW, MAY/JUNE

1982

1.60

0.0072

1.88

0.0076

1.80

0.0083

are

Table II

OUT-OF-PERIOD

FORECASTING

QUARTERLY
SIMULATIONS

Date Forecast
Began

GNP FROM
ENDING

ERRORS

FOR

DYNAMIC

IN 1981-IV**

Actual
1981-IV GNP
Number of
Less
Out-of-Sample
Estimated GNP
Quarters
$ billions

Root Mean
Squared
Error
$ billions

1970-l
176.7

119.9

M1 Adjusted†

M1 (Eq. 1)*

34.1

29.3

Monetary Base
(Eq. 4)*

57.3

31.2

Monetary Base
(Eq. 7)*

43.8

35.0

- 446.3

156.0

Trend Alone
1973-w
M1 (Eq. 2)*

142.0

98.5

M1 Adjusted†

- 2.3

23.0

47.1

36.9

45.6

41.2

- 374.8

147.4

Monetary Bore
(Eq. 5)*
Monetary Base
(Eq. 8)*
Trend Alone
1980-I
M1 (Eq. 3)*

-37.8

34.7

Monetary Base
(Eq. 9)*

-21.5

32.9

- 158.5

41.6

Trend Alone

* Equation numbers refer to regression equations in Table I from
which simulations were made.
**All
dynamic simulations began on 1959-IV.
Forecast errors,
however, include only those errors that began after the estimation
period.
† Adjustment on the M1 simulations adds 0.5 percent (2 percent
annual rate) per quarter to the simulated change in GNP over
the 1975-II to 1978-II time period.

sound theoretical reasons to believe that conventional
money demand equations are indeed misspecified.
There remains, however, the troublesome fact that
the rate of growth of income velocity of M1 apparently did increase in the 1975-78 period.
One can
adjust for such shifts on an ex post basis, but if an
aggregate is to be an appropriate
target for monetary policy, such shifts should be predictable
ex
ante. Fortunately,
there is another narrowly defined
monetary
aggregate
whose relationship
to nominal
GNP did not shift through the fourth quarter of
1981-one
that is amenable to control by the monetary authority.
That variable is the monetary base.

The Relationship
of the Monetary
Base to GNP
Three Federal Reserve articles have recently considered the monetary base as a policy target (John
Carlson [2], Richard Davis [5], and Carl Gambs
[9]).
Their conclusions were generally unfavorable
toward the base, although all agreed that the base
could be better controlled than other monetary aggregates, even under current institutional
arrangements.
All three articles concluded that the empirical evidence weighed against using the monetary base as a
policy target because it was not as closely related to
nominal GNP as was M1. In addition, the studies
enumerated
several theoretical
reservations
against
targeting the monetary base. This article will focus
primarily
on the empirical
arguments
against the
base, although the theoretical reservations
voiced in
the articles will be discussed.
The Davis and Gambs studies (which contained
the empirical work) reach the conclusion
that the
base is less closely related to aggregate demand by
comparing the correlation
coefficients of regressions
of nominal GNP on money with those of GNP on the
monetary base. There are slight variations
in techniques, but each used current and lagged values of
the monetary variables to estimate his single-equation
model. As is shown in Table I, this article’s regressions of GNP on the base and on M1 were consistent
with the result found by Davis and Gambs, namely
that the multiple correlation
coefficients of the M1/
GNP regressions were higher than the multiple correlation coefficients
of the base/GNP
regressions.
Both papers, however, gave insufficient attention to a
very important criterion, forecast performance in outof-sample simulations.
That omission is illustrated
in Chart 2.
Chart 2 shows actual GNP and two dynamic simulations of GNP in out-of-sample
periods.
One is
based upon a regression
of GNP on M1 (without
adjustment
for the 1975-78 velocity shift).
The
other is based upon a regression
of GNP on the
monetary base. The chart shows out-of-period
forecasts from parameters
estimated
from 1959-IV to
1969-IV, and from 1959-IV to 1973-III.
GNP
simulated
from M1 began to go off track in the
second quarter of 1975, but GNP simulated from the
monetary
base continued
to track nominal
GNP
through the fourth quarter of 1981.
This result
contradicts
Davis and Gambs’s conclusion
that the
monetary base is less closely related to GNP than is
M1. Note that this contradiction
occurs even though
the multiple correlation coefficients were consistently
higher for the regressions
of GNP on M1 than for
the regressions of GNP on the base.

FEDERAL RESERVE BANK OF RICHMOND

Chart 2

GNP AND OUT-OF-SAMPLE

SIMULATIONS

OF GNP FROM M1 AND THE MONETARY

Table II provides measures of the dynamic tracking ability of the out-of-sample
simulations.
As the
table shows, GNP simulated from the monetary base
always ended up closer to actual fourth quarter 1981
GNP than GNP simulated from M1 (not adjusted
for the velocity shift). The root mean squared error
a measure of overall forecasting
error
(RMSE),10
reported in Table II, also shows smaller errors for
the simulations
derived from the monetary
base.
The monetary
base/GNP
equation was specified
to conform to Davis’s analysis.
Having no further
need of this specification,
the monetary
base/GNP
relationship
was reestimated
using a different lag
structure.
This preferred equation regresses the percentage change in GNP on percentage changes in the
monetary base over the two previous quarters.
The
results are reported in Table I, and simulations from
them are evaluated in Table II.
10 The RMSE is defined as the square root of the sum
of the squared forecasting
errors divided by the number
of forecasted periods.
The squaring procedure not only
prevents
negative errors from offsetting
positive errors
in the summing up, but it also penalizes large errors more
than proportionately.

ECONOMIC

This particular

BASE

lag structure

was chosen because it

avoids current period relations between the base and
GNP, and it is relatively uncomplicated.
Avoidance
of contemporary
relationships
between GNP and the
base is predicated upon the assumption
that changes
in the monetary base affect GNP only after a lapse
of time. As can be seen from Table I, in the preferred lag form the bulk of the effects of changes in
the base on GNP take place with a two-quarter
lag.
The out-of-sample
forecasting errors (in percentages) of the simulations
of GNP from the preferred
monetary
base equation, from M1, and from M1
adjusted for the velocity shift are shown in Chart 3.
(The relative accuracy of the forecasts is more apparent from percentage errors than from levels.)
GNP
simulated from M1 adjusted for the velocity shift
outperformed
GNP simulated
from the monetary
base during the 1973-76 period, although they were
virtually identical before and after.
The simulation
from the monetary base, however, substantially
outperformed the simulation from unadjusted
M1. Thus,
the simulation from the base did not predict the 197375 recession, while the simulation from M1 did not

REVIEW, MAY/JUNE

1982

pick up the changing
1975-78 period.

trend in income velocity

in the

The failure of the base to predict the 1973-75 recession represents a shortcoming in its feasibility as a
target for monetary policy. Note, however, that the
base came back on track after the recession with no
ad hoc adjustment,
and it did not mispredict the other
out-of-sample
recessions.
The explanation
may lie
in the character
of the 1973-75 recession,
which
began with the oil embargo
and was influenced
throughout
by energy supply effects.
If, as many
economists
believe, the base is less influenced
by
feedback from GNP than is M1,11 M1 might be
expected to show the effects of the 1973-75 recession
11 This paper’s regression
results reported
in Table I
indicate that the contemporaneous
relationship
between
M1 and GNP was more pronounced than the relationship
between the base and GNP.
The result is consistent
with, but no proof of, the explanation advanced above.

Chart

PERCENTAGE ERRORS IN PREDICTING
GNP FROM M1 AND THE MONETARY BASE
SAMPLE

PERIOD

1959-l\/ to

1969-IV

more closely than would the monetary base.12 The
failure of the base to predict the 1973-75 recession,
however, should provide a caution to anyone relying
solely upon it as a forecasting tool.13
Chart 4 shows actual GNP plotted against simulations of GNP from the preferred
monetary
base
The chart
equation and from GNP’s own trend.
clearly shows that GNP simulated from the trend
extrapolation
is subject to substantially
higher forecast error than GNP simulated from the monetary
aggregates.
Table II, which reports the out-of-period
forecasting statistics, confirms this visual observation.
Are Monetary
Aggregates
Endogenous
or Exogenous?
The empirical.
relationship
between
the
monetary base and GNP has been dismissed by some
analysts on the ground that the base is endogenous
to GNP (i.e., that the base responds to changes in
GNP rather than vice versa).
This contention
is
difficult to resolve.
Like the money supply, the
monetary
base has passed statistical causality tests
that indicate that the monetary aggregates add some12If adjustment
of currency holdings is more costly than
adjustment
of demand deposits, the result can also be
consistent with a transaction
cost analysis of the demand
for money that distinguishes
between
transitory
and
permanent
input variable
changes
(see, for example,
Goodfriend
[11]).
Such analysis would seem to be able
to rationalize why M1 should track transitory
changes in
income better than the monetary base.
Finally, the explanation
might be advanced
that inherent technical problems related to the composition
of
the base caused the base to mispredict the 1973-75 recession. It is indeed true that a trend toward a larger proportion of currency in the base seemed to begin somewhere around 1973. As a result, currency increased from
65.8 percent of the base in the fourth quarter of 1973 to
68.8 percent by the third quarter of 1976, a rate of inThis
crease of approximately
0.4 percent per quarter.
trend in the currency composition
of the base has continued since that time, however, although at a slower 0.2
percent per quarter rate.
Given, however, that the predictions from the base came back on track of their own
accord even though the composition
of the base was
continuing
to change; and given that the parameters
of
the equations
from which the simulations
were made
were estimated during a period in which there was very
little change in the composition
of the base (0.06 percent
per quarter),
compositional
changes
seem an unlikely
explanation of the miss in the 1973-76 period.
13In comparison
to the forecasters
reported by Stephen
McNees [15] in his article evaluating forecast performance over the 1976-11 to 1980-111 period, however, the
simple base equation estimated over the 1959-IV to 1973III period (Equation
8 in Table I) performed
respectIn terms of one-quarter
forecast
horizons,
the
ably.
average absolute error from the base equation turned out
to be 3.27 percent, measured at a compound annual rate,
which was lower than nine of the sixteen average forecast
errors reported by McNees.
Using the base equation- to
forecast two quarters out (this could be done by assuming that the rate of growth of the base in time period
t-1 was the same as in t-2, which would be known),
the average absolute error turned out to be 2.4 percent,
which was as low as that of any forecaster
reported in
McNees’s article.

FEDERAL RESERVE BANK OF RICHMOND

with concurrent
increases in the monetary base and
M1. A monetarist would argue that these contemporaneous changes in the monetary aggregates
would
have feedback effects on GNP that would show up a
few months later.
The endogeneity
argument provides an additional
reason to prefer a base/GNP
regression that avoids
the contemporaneous
relationship.
It must be acknowledged,
however, that avoidance
of the contemporaneous
relationship does not answer the endogeneity charge, for the one- and two-quarter
lags
could be providing a proxy for concurrent
changes.
Some simple tests were run to show that the fit of
the regression of GNP on GNP lagged one, two, and
three periods was substantially
improved by adding
the base lagged one and two periods, and that the fit
of a regression of the monetary base on the monetary
base lagged one period was not significantly improved
by adding GNP lagged one and two periods.
The
results of these regressions
are reported in the appendix, along with measures of their out-of-sample
forecasting accuracy. These results are all consistent
with a causal relationship running from the monetary
aggregates to GNP. Other studies have come to similar conclusions
(see Cagan [3], Hetzel [14], Mehra
[16], and Sims [19]).
Because of the contemporaneous relationship between GNP and the monetary
aggregates, however, the direction of causation cannot be conclusively demonstrated
by analyses such as
these.

Chart 4

GNP AND OUT-OF-SAMPLE
SIMULATIONS OF GNP FROM TREND
AND THE MONETARY BASE
SAMPLE PERIOD

1959-IV TO 1973-III

thing to predicting GNP whereas GNP adds little or
nothing to predicting the monetary aggregates.
The
power of these tests is somewhat limited, however, for
there is a contemporaneous
relationship between both
aggregates and GNP (although
Table I shows the
contemporaneous
M1/GNP
relationship
to be more
pronounced).
To illustrate
this problem,
suppose the Federal
Reserve System were using an interest rate target
while nominal GNP and hence demands for liquidity
were rising rapidly. In this case, interest rates would
be under upward pressure,
so the System would
provide reserves to keep short-term rates down. Increases in nominal GNP would thus be correlated
10

ECONOMIC

Conceptual
Reservations
to Using the Base As a
Target
for Monetary
Policy
The conceptual
reservations
to targeting
the monetary
base, mentioned earlier, are related to the definition
of the
monetary base. The base is defined as the sum of
(1) currency outside the Federal Reserve System
and the Treasury
and (2) bank deposits at the
Since currency accounts for over
Federal Reserve.
70 percent of the base, many economists argue that
currency
changes would be given disproportionate
weight if the monetary base were the target for monetary policy.
This is particularly
true since a dollar
of bank reserves can support multiple
dollars of
money and credit.
The argument
continues
that if the Federal Reserve System were to react to changes in the demand
for currency by making offsetting changes in bank
reserves, the resulting effects on the economy would
As a result, targeting
total (or
be destabilizing.
nonborrowed
reserves)
and excluding currency has
often been suggested as an alternative
to targeting
the monetary base.
Advocates of targeting the base answer that cur-

REVIEW, MAY/JUNE

1982

rency is included in the monetary base because it,
along with bank reserves, is a balance sheet item (liability)
for the Federal
Reserve
System.
Thus,
changes in the total base measure changes in the asset
side of the Federal Reserve balance sheet and, hence,
measure
Federal
Reserve
open market
actions.
Therefore, the argument goes, no distinction
should
be made between the components of the base.

Chart 5

GNP AND OUT-OF-SAMPLE
SIMULATIONS OF GNP FROM THE
MONETARY BASE, CURRENCY HOLDINGS,
AND BANK RESERVES
(Bank Reserves Adjusted for Changes in
Reserve Requirements by St. Louis Method)

To test this proposition,
regressions
were run of
GNP on currency and on total reserves (adjusted for
reserve requirement
changes) from 1959-IV to 1973III, and the results were simulated
dynamically
through the fourth quarter of 1981. Both simulations,
shown in Chart 5, went off track. Moreover, both of
the component
simulations
underpredict
nominal
GNP; the differences were not offsetting.
This result
implies that the monetary base as a whole is more
closely related to GNP than is its components.
And
that result, if correct, would seem to contradict the
conceptual
argument
advanced against the base at
the beginning
of this section (i.e., that currency
changes are given disproportionate
weight by the
base).
Phillip Cagan [3] recently provided another analysis of the currency issue. He also thought that currency was a questionable
indicator of economic activity.
He argued that reserves and checkable deposits are highly correlated
and both provide the
same information
about the economy, implying that
the reserve portion of the monetary
base was the
more important indicator of the effects of money on
GNP. Using a modified Granger-Sims
test, he found
that “. . . when concurrent values are omitted, neither
set of growth rates [of checkable deposits or the
monetary
base] can be shown by this test to add
significant
information
not contained
in the other”
[3, p. 29]. His test pertained to in-sample data over
the period from 1953-III to 1974-IV.
Using the methods outlined
previously
in this
article, the percentage change in GNP was regressed
on lagged values of the percentage change in checkable deposits over the 1959-IV to 1973-III period.
The simulations
therefrom
are shown in Chart 6
compared to actual GNP and GNP simulated from
the monetary
base.
The out-of-sample
simulation
from checkable deposits did not track nominal GNP
at all well.14
14 The equation form specified for Chart 6 was similar
to that for the “preferred base” simulation (Equations
6,
7, and 8 in Table I), having checkable deposits lagged
one and two quarters.
An alternative
specification
was
also tried, using checkable
deposits
with five lagged
quarters, but the simulation results were not appreciably
different from those illustrated in the chart.

These last results combine with simulations
from
currency and reserves to favor those who recognize
no distinction between the components
of the monetary base. This conclusion deserves further testing,
however.
This article presents
statistical
reConclusion
sults demonstrating
that the trend in income velocity
of the monetary base remained remarkably
constant
from 1959 to 1981 and that the trend in income velocity of M1 also remained remarkably
constant except
for the three-year period from 1975 to 1978.

FEDERAL RESERVEBANK OF RICHMOND

Chart 6

GNP AND OUT-OF-SAMPLE
SIMULATIONS OF GNP FROM THE
MONETARY BASE AND FROM
CHECKABLE DEPOSITS

indeed rendered money/income
relationships
meaningless, so the argument goes, then narrow monetary
aggregates should be scrapped as targets for monetary policy.
The analysis in this article suggests,
however, that (except possibly for M1 during 197578) the much heralded financial innovations
had no
substantial impact upon the relationships
between the
narrow
monetary
aggregates
and nominal
GNP
through the fourth quarter of 1981.

References

1. Andersen,

Leonall,
and Karnosky,
Denis. “Some
Considerations
in the Use of Monetary Aggregates
for
the Implementation
of Monetary
Policy.”
Review, Federal Reserve Bank of St. Louis (September 1977).

2. Cagan, Phillip. “The
gregates
as Targets.
Policy.”
A paper
Enterprise
Institute
in the Conduct of U.
ton, D. C., February

Choice Among Monetary
Agand Indicators
for Monetary
presented
for the American
Conference
on Current
Issues
S. Monetary Policy, Washing4-5, 1982.

Base, the Econ3. Carlson, John B. “The Monetary
omy, and Monetary
Policy.”
Economic
Review,
Federal Reserve Bank of Cleveland
(Spring 1981).
4.

Cullison, William. “Monetarist
and Tax Cuts:
Comment.”
(January
1981), pp. 173-75.

Econometric
Economic

Models
Inquiry

“The Monetary
Base as an Inter5. Davis, Richard.
mediate Target for Monetary
Policy.”
Quarterly
Review,
Federal
Reserve
Bank
of New York
(Winter 1979-80).
6. Friedman,
Milton. “The Demand for Money: Some
Theoretical
and Empirical
Results.”
Journal of
Political Economy (August 1959), pp. 327-51.

These results imply (1) that the demand for money
(M1) has been generally stable since 1959 but that
(2) the monetary base has borne
and more predictable
relationship
trend in GNP than has M1.15

“The
Role of Monetary
Policy.”
American
Economic
Review
(March
1968) ; reprinted in Smith, Warren
L., and Teigen, Ronald
L., eds. Readings in Money, National Income, and
Stabilization
Policy.
Rev. ed.
Homewood,
Ill.:
R. D. Irwin, 1970, pp. 476-88.

Friedman,
Milton, and Meiselman,
David.
“The
Relative
Stability
of Monetary
Velocity
and the
Investment
Multiplier
in the United States, 18971958.” In Stabilization
Policies, prepared
for Commission on Money and Credit.
Englewood
Cliffs,
N. J.: Prentice-Hall,
Inc., 1963, pp. 165-268.

a slightly closer
to the long-run

As noted at the outset, the argument
has often
been made that financial innovations
such as retail
repurchase
arrangements,
money
market
mutual
funds, Eurodollars,
and NOW accounts have obscured past relationships
of monetary aggregates to
nominal income.
And if financial innovations
have
15 See also Andersen and Karnosky [1], who reached a
similar conclusion using somewhat similar methodology
in 1977.
12

Reserve Intermediate
Tar9. Gambs, Carl. “Federal
gets:
Money or the Monetary
Base.“’
Economic
Review,
Federal
Reserve
Bank of Kansas
City
(January
1980).
10.

Goodfriend,.
Marvin.
“A Model of Money Stock
Determination
with Loan Demand and a Banking
System Balance Sheet Constraint.”
Economic Review, Federal
Reserve Bank of Richmond
(January/February
1982).

11.

“Transaction
Cost, Dynamics,
and
the Specification
and Estimation
of Money Demand.”
Federal Reserve Bank of Richmond Working Paper 82-1, forthcoming.

ECONOMIC REVIEW, MAY/JUNE 1982

12. Gurley,
John,
and Shaw,
Edward.
“Financial
Intermediaries
and the Saving-Investment
Process." Journal
of Finance (May 1956), pp. 257-66.
13. Hafer,
R. W., and Hein, Scott.
“The Shift in
Money Demand:,
What Really Happened.”
Review, Federal Reserve Bank of St. Louis (February 1982).
14. Hetzel, Robert.
“The Stability of the Demand for
Money in the 1970’s.” Unpublished
paper in process, Federal
Reserve
Bank of Richmond,
April
1982.
16.

McNees, Stephen.
“The Recent Record of Thirteen
Forecasters."
Corrected
reprint
of article
published in New England Economic Review, Federal
Reserve Bank of Boston (September/October
1981).

17.

Meltzer, Allan.
The Wall Street

18.

Morris, Frank
E. “Do the Monetary
Aggregates
Have a Future
as Targets
of Federal
Reserve
Policy?”
New England Economic Review, Federal
Reserve Bank of Boston (March/April
1982).

19.

Sims, Christopher.
“Money,
ity.”
American
Economic
1972), pp. 540-52.

20.

Solomon, Anthony.
“New Strategies
for the Federal Reserve.”
Challenge
(March/April
1982),
pp. 19-24.

21.

Wallich, Henry C. “Government
and InflationPart of the Problem or of the Solution.”
A paper
presented
at the annual meeting of the American
Economic Association,
Washington,
D. C., December 28, 1981.

16. Mehra, Y. P.
“Is Money Exogenous
in MoneyDemand Equations?”
Journal of
Political Economy (April 1978), pp. 211-28.

“Avoiding
the Monetary
Shoals.”
Journal, May 9, 1979, p. 20.

Income,
Review

and Causal(September

APPENDIX

ILLUSTRATION

OF. NECESSARY

FOR THE MONETARY

(BUT

NOT

BASE TO BE EXOGENOUS

(sample period from 1959-IV

Form of Equation

SUFFICIENT)

CONDITIONS

TO NOMINAL

GNP

to 1973-III)

Multiple Correlation Coefficients
(uncorrected for degrees
of freedom)

Root Mean Squared Errors
(forecast period from 1973-W
to 1981-IV, 33 observations)

0.310

$ 39.87

0.142

Definitions:
g = percentage change in nominal GNP, ß
=
regressions with unconstrained lags, estimated by ordinary
F test for significance of differences
and Company, 1971), p. 371.

in multiple

For Eq. 1 versus Eq. 2, F(2,50) =

6.09*

For Eq. 3 versus Eq. 5, F(2,52)

0.63**

For Eq. 4 versus Eq. 5, F(3,51)

1.31**

* Significantly
**

different

correlation

146.45

0.59

3.71

0.61

3.25

0.50

4.21

percentage change
least squarer.

coefficients

in St: Louis monetary

from Kmenta,

base.

Equations

Elements of Econometrics (New

York:

are

linear

Macmillan

at 0.01.

Not significantly different

at 0.10.

FEDERAL RESERVE BANK OF RICHMOND

DETERMINANTS
OFINDIVIDUAL
TAX-EXEMPT
BONDYIELDS:A SURVEY
OFTHEEVIDENCE
Timothy

The distinctive
feature of the market for taxexempt bonds is its heterogeneity.
The features of
specific tax-exempt
bonds, the characteristics
of the
issuers, the scope of the market for the bonds, and the
conditions
under which the bonds initially are sold
all vary greatly across individual bond issues.1 As a
result, the yields of different tax-exempt bonds issued
at a given point in time cover a wide range. A substantial amount of recent research has attempted to
explain the effects of different tax-exempt bond characteristics on a bond’s yield.2
The purpose of this article is to describe in some
detail characteristics
of tax-exempt
bonds and the
tax-exempt
bond market and to survey the evidence
on cause and effect relationships
between variations
in these characteristics
and variations in the yields of
individual
tax-exempt
bonds.
Table I identifies the
factors that have. been analyzed as determinants
of
the yields on individual
tax-exempt
bonds.
The first group of characteristics
are those related
to the issues themselves.
These are call provisions,
coupon setting practices, and issue size. Most taxexempt bonds have call provisions
that permit the
issuer to redeem the bond prior to its maturity.
Newly issued tax-exempt
bonds frequently
have
coupons that differ substantially
from their yield-tomaturity.
As a result, these bonds sell at prices above
or below their par value. Finally, the size of a taxexempt issue can range anywhere from less than $1
million to over $200 million.3

Q. Cook

The second source of diversity in the tax-exempt
bond market relates to the issuers of the bonds. Most
tax-exempt
bonds are classified either as “general
obligation”
or as “revenue”
bonds.
General obligation bonds are issued by state and local governments
and are secured by the taxing power of the issuing
government.
Revenue bonds, in contrast, are usually
secured solely by the revenues of the project they are
issued to finance.
Typically, revenue bonds are sold
by an authority, commission, special district, or other
government
entity created for the specific purpose.
A major focus of studies of tax-exempt
yields has
been on the risk of issuer default as a determinant
of
Default risk of general
obligation
bonds
yields.
depends on economic and fiscal conditions
of the
government
issuing the bonds while default risk of

Table

EXPLANATORY
VARIABLES
USED
STUDIES OF THE DETERMINANTS
ON INDIVIDUAL

call dummy variable
other call provision variables

BONDS*

coupon variables

Issuer Characteristics
4.

rating category

dummy variables

5. issuepurpose dummy variables
other measures of default

Marketing

2 There have been at least 25 regression
studies of the
determinants
of individual tax-exempt
bond yields. These
studies are enumerated
and described briefly in the references at the end of this article. A preliminary
version of
one of these studies by Broaddus and Cook [8] was done
for the Federal Reserve System’s Ad Hoc Subcommittee
on FullInsurance
of Government
Deposits
[28].
The
data collected for that study is used extensively
in this
article.

10.

ECONOMIC

MUNICIPAL

1 Sources of information
on tax-exempt
bonds and the
tax-exempt
bond market are Lamb and Rappaport
[37],
Peterson
[43],
Public
Securities
Association
[44],
Rabinowitz
[45], and Robinson [47].

IN REGRESSION
OF THE YIELDS

Issue (Bond) Characteristics

3 In this brief overview
issue size and revenue
bond
versus genera1 obligation status are discussed in the issue
and issuer categories, respectively.
However, alternative
theories as to how size and revenue bond status affect
yields relate them to other categories
as well.
Consequently, later in the article they are discussed separately
as shown in Table I.

(Underwriter

number of bids

dispersion of bids

negotiated

risk

Competition)

dummy variable

bank eligibility dummy variable

Regional Market

Conditions

11.

pledging variables

12.

other demand variables

13.

supply variables

Other
14.

revenue bond versus general

15.

size of issue

obligation

16. other

* Excluded are variables
the time of issue.

REVIEW, MAY/JUNE

1982

to pick up national

market conditions at

revenue
bonds depends primarily
on the income
generated by the project financed by the bonds.
The marketing
process by which new issues of taxexempt bonds are sold is a third broad area considered as a source of variation
in individual
taxSome small issues are sold
exempt bond yields.
directly to local banks.
Other issues are generally
sold through the process of underwriting
and syndication, in which a group of dealers join together in a
“syndicate”
to purchase
an entire issue of bonds
from a governmental
unit for the purpose of reselling
them in the retail market at a slightly higher price.
Commercial
banks are prohibited by law from participating in the underwriting
of some types of revenue bonds.
Bonds are purchased from the government
unit by
dealers either through negotiation
or through competitive bidding.
In the case of negotiation the issuer
chooses a syndicate with which it negotiates the purIn the case of competitive
chase price of the bonds.
bidding the issuer solicits bids from syndicates and
sells the bonds to the highest bidder. The number of
bids received varies greatly across issues.
Two features
of the underwriting
process are
worth noting.
First, prior to offering a price to the
issuer for bonds, the underwriting
syndicate
canvasses potential buyers to get a firm idea of the price
the latter will offer for the bonds.
Because of the
great diversity of tax-exempt
issues, this process is
widely believed to help identify those willing to pay
the highest price-i.e.,
receive the lowest yield-for
the bonds. Many studies have specified this information as a determinant
of tax-exempt
yields.
The second important
characteristic
of the marketing process is the method by which the winning
bid is chosen.
In most cases the winning
bid is
determined on the basis of the syndicate offering the
lowest net interest cost (NIC)
to the issuer.
NIC
is defined as
total interest

payments

+ discount

(or -- premium)

bond year dollars
where bond year dollars is simply the amount of
bonds outstanding
over the time they are outstanding.
A drawback of NIC is that it ignores the time value
of money. Hence, payments made by the government
in early years count the same as payments in later
years even though the present discounted
value of
the later payments is much lower.
Although
most bidding is done on
NIC, some bonds are awarded on the
lowest true interest cost (TIC).
TIC
discount rate that equates the present

the basis of
basis of the
is the single
value of all

future payments by the issuer to the price received
from the syndicate.
Conceptually
it is a far superior
measure of yield than NIC. Both NIC and TIC are
calculated from the issuer’s point of view, so they
reflect not only the payments to the bond holders,
but also the payment to the underwriter
(called the
“underwriter’s
spread”).
A third yield concept is the reoffering yield to
maturity
the investor
earned bywho purchases a taxexempt bond from the underwriter.4
It is the discount rate that equates the present value of the
stream of payments received by the investor to the
price he pays the dealer for the bond.
The fourth broad area that has received some
attention as a source of variation in individual taxexempt bond yields is regional market conditions
where the issue is sold.
For reasons that will be
explained
in detail below, the argument
has been
made that the demand for at least some tax-exempt
issues is largely regional in character.
If true, the
yields on these tax-exempt
bonds may be influenced
by regional supply and demand factors.
The methodology
employed by all the studies of
individual
tax-exempt
bond yields discussed in this
article is multiple regression analysis, which regresses
the dependent
variable,
a measure
of tax-exempt
yield, on various subsets of the independent
or explanatory variables listed in Table I. Some of the
variables listed have been included in virtually all of
the studies while others have been included in only a
The references at the end of this
small number.
article indicate the set of explanatory
variables in
each of the studies surveyed, using the same format
as in Table I.
While the basic approach
followed by all the
studies is similar, an important
difference
among
them is the choice of the yield to be used as the
dependent variable.
Municipal
bonds are generally
sold in serial issues that include securities of several
maturities.
Most studies employ as the dependent
variable a composite measure of the yields on all of
the bonds in the serial such as net interest cost
(NIC)
or true interest cost (TIC),
both of which
are measures of issuer cost. The studies then attempt
to specify independent
variables that are representative of the entire serial issue.
This use of a composite
yield measure
has a
number of disadvantages.
First, treating the entire
serial as the analytical unit makes it difficult and in
some cases impossible to analyze the effect on yields
4 In the rest of the article this is called
yield, yield-to-maturity
or, simply, yield.

FEDERAL RESERVE BANK OF RICHMOND

the reoffering

of particular
bond (as opposed to issue) characteristics. For example, serial issues often include shortterm bonds that are not callable and some longer
term ones that are, It is therefore very difficult to
measure differences in call provisions
across entire
serial issues.
Second, this approach precludes analysis of the effect of a particular factor on bond yields
of differing maturity.
A third disadvantage
of using
aggregate yield measures
such as NIC or TIC is
that these variables include both the compensation
to
the underwriter
and the return
to the investor.
Hence, in some cases it is difficult
to interpret
whether an estimated regression
coefficient reflects
the behavior of one or both of these groups.
As a result of the disadvantages
of using NIC and
TIC, a small number of studies have used instead
reoffering yields as the dependent
variable in taxexempt bond yield regressions.
Broaddus and Cook
[8] estimated separate equations for four separate
maturities:
5 years, 10 years, 15 years, and 20 years.
Where appropriate,
the independent
variables were
defined differently for each maturity.
In addition to the variables
shown in Table I,
virtually all of the studies include one or more independent variables
to capture the effect of current
“national market conditions”
on a bond yield. If the
dependent variable is the reoffering yield for a specific maturity,
then the national
market condition
variable chosen is always the reoffer yield on highgrade general obligation bonds for that maturity.
If
the dependent variable is NIC or TIC, capturing national market conditions
is much more complicated
because the dependent variable is affected not only by
the level of general yields in the market but also by
the average muturity
of the serial issue and the current slope of the yield curve.5 Different studies have
specified one, two, or three variables to capture these
three effects.6
A final background
comment
on the regression
studies is that conceptually
they are cross-section
studies that attempt to measure how variations
in
characteristics across
tax-exempt
issues influence
their yields.
In practice, however, the studies use
5The yield curve in the tax-exempt market is generally
Hence, for a given level of market
upward sloping.
interest rates the NIC of a serial issue will be higher the
Similarly, for a given
greater the average maturity.
average maturity the NIC will be higher the steeper the
The problems and possible
slope of the yield curve.
pitfalls of using national market conditions variables in
NIC and TIC regressions are discussed in Broaddus and
Cook [8].
6 For example, see Hendershott and Kidwell [15] who
include variables for market yield, average maturity of
issue, and slope of the yield curve.
16

ECONOMIC

data gathered over periods from three months or less
to ten years or more.
Lengthy data periods create
two potential problems.
First, the effect of a given
value of an explanatory
variable may vary over time
due to changes
in national
economic
conditions.
Second, inflation
over the data period may cause
nominal values of variables to change, which makes
it important to specify whether a theory calls for an
explanatory
variable to be measured in nominal or
real terms.
The remainder
of this article is divided into five
sections corresponding
to the five categories shown
in Table I. In each section the relevant characteristics of tax-exempt
bonds are described.
Next the
theories linking these characteristics
to bond yields
Finally, the results of the empirical
are outlined.
studies are presented.

I.
ISSUE

CHARACTERISTICS

Coupons
Coupon Setting
Practices
When state and local
governments
solicit bids on new issues, they set constraints on the coupons (i.e., annual interest payment) that the bonds can carry when they are resold
by underwriters
to the public.
Occasionally,
the
bonds are required to carry coupons at each maturity
More
equal to their reoffering yield to maturity.
commonly, however, underwriters
are allowed a great
deal of flexibility in setting coupons.
As a result of
this flexibility, and for reasons that will be described
immediately
below, the winning bids on tax-exempt
issues often specify coupons for at least some maturities that differ considerably
from their yield to
maturity.
Specifically, new short- and intermediateterm bonds often carry a coupon above their yield to
maturity while long-term
issues often, but less frequently, carry a coupon below their yield to maturity.
When a bond has a coupon above its yield to maturity
it is sold at a “premium,”
i.e., at a price above its
par value.
Conversely,
when a bond has a coupon
below its yield it is sold at a “discount.”

Table II shows the different coupon-setting
practices on the winning bids for ten tax-exempt
issues.
As the table illustrates, sometimes the coupon is set
well above the yield to maturity at the 5-year maturity, about equal to the yield to maturity
at the
15-year maturity,
and well below the yield to maturity at the 20-year maturity.
This pattern is shown
in issues 3 and 6 and to a lesser extent in issues 4
and 10. In other cases such as issues 1 and 9 the

REVIEW, MAY/JUNE

1982

Table II

COUPONS AND YIELDS TO MATURITY

OF SELECTED TAX-EXEMPT

ISSUES

Bond issue

1. Plano, Texas
(3-14-77)
2. Columbia, Missouri
(3-30-77)
3. Anderson Co.,
Tennessee
(3-31-77)
4. State of Hawaii
(4-5-77)
5.

Nebraska Public
Power District
(4-5-77)

6. Miami, Florida
(4-14-77)
7. Carroll co.,
Maryland
(4-20-77)
8. New Jersey
Housing Finance
(4-28-77)
9. Alaska Municipal
Bond Bank
(4-27-77)
IO. Mecklenberg Co.,
North Carolina
(5-3-77)

coupon is set well above the yield to maturity at the
early maturities but does not fall below the reoffering
yield

at the longer

maturities.

A third

group

issues, such as issues 5 and 8, have coupons equal to
yields throughout
the entire range of maturities.
Coupons
shorter

are never set below yield to maturity
maturities

or above it at the 20-year

Table III shows the spread
yield to maturity at the shorter

at the

maturity.

between coupon and
maturities for all the

issues included in the Broaddus-Cook
study [8].7
At the 5-year maturity,
745 out of 885 issues had
coupons above their yield.
Of these, the difference
between coupon and yield was greater than one percentage point for 392 bonds and greater than two
percentage
points for 146 bonds.
The number of
bonds with large premiums dropped sharply at the
10-year maturity
maturity.

and was negligible

at the 15-year

Table IV shows the distribution
of issues with
coupons below yield to maturity at the 15- and 20year maturities.
At the 20-year maturity, 318 of the
issues in the sample had coupons below their yield.
Of these, however, only 33 had coupons more than
one percentage
point below yield.
At the 15-year
maturity, 181 were sold at a discount; but in all cases
the difference between yield and coupon was quite
small.
Explanation

for

and

Possible

Costs

Coupon-

The coupon setting practices illustrated above occur because, as noted earlier, winning
bids on most serial municipal bonds are determined
on the basis of net interest cost (NIC).
NIC bidding
creates incentive for underwriters
to set high coupons
at the shorter maturities
and low coupons at the
longer maturities:8
Setting

Practices

Because
investors place time value on coupons,
coupons on early maturities can be sold by the

7 Data from the study by Broaddus and Cook [8] is used
for description
throughout
this section.
Bonds used in
the study were almost all those for which reoffering
yields were reported
in Moody’s
Bond Survey from
March 1977 through the end of 1978.

8 This explanation
is given in more detail in Robinson
[47] and Hopewell
and Kaufman
[32, 33].
Robinson
(Appendix
B) and Public Securities
Association
[44,
Appendix]
give examples.

FEDERAL RESERVE BANK OF RICHMOND

Table III

PREMIUM

BONDS

Distribution of Bonds by Spread Between
Coupon and Yield to Maturity
(number of bonds)
Spread:
(percentage points)

5-year
maturity

Equal to 0 (or negative)

Source:

306

622

123

332

207

230

129

142

104

885

Broaddus

and Cook

15-year
maturity

140

1
Total

10-year
maturity

901

851

The question remains as to why investors might
demand a higher yield to maturity
for bonds that
carry “high” or “low” coupons.
For bonds with low
coupons there is a powerful reason for this relating
to the taxation on income earned on discount bonds
versus income earned on bonds selling at par. Par
bonds are not subject to any Federal taxes because
all the income is tax-exempt
interest income.
However, investors in low coupon discount bonds generally have to pay capital gains taxes at maturity on the
difference between the par value and purchase price
of the bond.10
Consequently,
a higher yield is required on a discount bond in order to earn the same
after-tax yield as a par bond.

[8].

underwriters
at higher
prices
than coupons
on
later
maturities
summing
to the same
dollar
amount.
Yet, under NIC, these coupons do not cost
the underwriter
any extra.
Thus, to maximize
their revenues
from the sale of the bonds, the
underwriters
are encouraged
to place the highest
coupons on the earliest maturities.
The placing of
large coupons on the early maturities
is referred
to
as frontloading.
To obtain a low NIC, compensating low coupons are placed on the most distant
maturities
[32, p. 534].

9 Hence, the lowest TIC bid under NIC bidding may be
higher than the lowest TIC bid that would occur under
TIC bidding.
This is distinct from the first possible
cost of NIC bidding, which is that the issuer may not
select the lowest TIC bid.
10 The question of whether
the discount on new taxexempt issues is subject to capital gains tax is very confusing. According to a 1973 publication of the Securities
Industry Association
[26, p. 9]:

There are two possible limitations to the ability of
underwriters
to set coupons that differ from a bond’s
yield to maturity.
The first is that investors may
purchase bonds with such coupons only if compensated by a higher yield than on an otherwise similar
par bond. At some point this could offset the advantage to an underwriter
in achieving a low NIC of
setting high coupons at shorter maturities
and low
coupons
at longer maturities.
The second limitation
may be imposed by issuers who specify constraints
on the type of coupon they will accept.
Hopewell and Kaufman
[32, 33] identified
two
possible costs to municipal governments
of awarding
bonds sold competitively to underwriters
on the basis
of NIC bidding as opposed to true interest cost
(TIC)
bidding.
The first cost is that the lowest
NIC bid may not be the same as the lowest TIC bid.
In other words the government
may accept the wrong
18

ECONOMIC

bid. The second potential cost of using NIC bidding
is that, for reasons to be discussed below, investors
may only purchase bonds with coupons that are above
or below their yield to maturity at a lower price than
bonds that have coupons equal to their yields and
that are otherwise equal in all respects.
If this were
the case then all bids (in terms of the prices offered
by underwriters)
under NIC bidding would be lower
than under TIC bidding because under NIC bidding
the bonds would be worth less to the ultimate investors.9

Issue discount
is recognized
as being interest
in
substance
and as “interest”
on a tax exempt bond
such issue discount is tax exempt. . . . This is true
only where the bond is issued at a discount and does
not apply where bonds which were originally sold at
par or at a premium are subsequently
re-offered at a
discount. Where an issue of serial bonds is purchased
from the issuer by a dealer at a single unallocated
price of not less than their total par value (face
amount)
and some of them are re-offered
by the
dealer at a discount, they are not issued at a discount.
This statement clearly implies that if an underwriter
purchases an entire serial issue of bonds at a single price not
less than their total par value and some of the bonds are
reoffered by the dealer at a discount, the capital gain is
not tax-exempt.
However., a just-published
article ("The
Tax Treatment
of Municipal
Discount
Bonds: Correction of a Fallacy” by Ronald C. Braswell, Walter J.
Reinhart, and James R. Hasselback,
Financial Management,
Spring
1982) states unequivocally,
citing IRS
Revenue Ruling 73-112, that if an investor buys a new
discount
bond from an underwriter,
the discount
is
treated as tax-free interest income regardless
of the circumstances
under which the underwriter
acquired the
bond from the issuer. In any case the regression results
discussed in this section present convincing evidence that
at least in the 1977-78 period investors viewed new issue
discount bonds as subject to capital gains tax.

REVIEW, MAY/JUNE

1982

Table IV

DISCOUNT

BONDS

Distribution of Bonds by Spread Between
Yield to Maturity and Coupon
(number of bonds)

20-year
maturity

Spread:
(percentage points)

15-year
maturity

Equal to 0 (or negative)

670

317

181

272

0
851

Total
Source:

Broaddus

1
635

and Cook [8].

Hopewell
and Kaufman
argued that even after
adjusting for tax differences investors may require a
higher yield on discount bonds than on par bonds for
two additional reasons [33, pp. 284-285]. First, since
low coupon bonds have longer duration
than par
bonds of comparable maturity investors might, to the
extent that liquidity premiums
increase with duration, demand a higher yield on low coupon bonds.11
Second, discount bonds may be less marketable than
par bonds and consequently
investors might demand a
higher yield.
The major argument
Hopewell and
Kaufman presented for the effect of high coupons on
yields is that high coupon bonds may subject investors to greater reinvestment
risk [32, p. 535].
Empirically,
Hopewell
and Kaufman
concluded
that both high and low coupons raise yields, although
the effect of high coupons was much smaller.12 They
also concluded that in most cases, capital gains tax
liability by itself is insufficient
to explain the magnitude of the additional
yield required
on discount
bonds.
Regression Results
Of the regression studies on
the determinants
of tax-exempt
yield only the
Broaddus-Cook
study attempted to estimate the effect
of high and low coupons on yields to maturity.
The
study calculated a data series for high coupon bonds
11Duration is a weighted average of times in the future
when payments are to be received.
12Hopewell
and Kaufman
did not use the regression
technique common to the studies surveyed in this article.
Hence, their results are not discussed in detail here. See

[33].

by taking the difference between coupon and yield
and a similar series for low coupon bonds by taking
(In both
the difference between yield and coupon.
cases the values were set equal to zero if they were
negative.) These series were then entered as explanatory variables in the four maturity regressions.
The
regression
results strongly supported the view that
low coupons raise yields to maturity.
At the 20-year
and 15-year maturities the estimated effects were 19
and 36 basis points, respectively, for each percentage
point difference between yield and coupon.
These
estimates support Hopewell and Kaufman’s contention that the effect of low coupons on tax-exempt
bond yields was greater than could be explained by
the capital gains tax factor alone.13
A possible explanation
for the larger estimated
effect on yields of selling discount bonds at the 15year maturity than at the 20-year is that it reflects
the greater role of commercial bank behavior at the
15-year maturity.
According
to Hobby [31], bank
holdings of tax-exempt
bonds fall off sharply after
10- to 15-year maturity
range.
Since commercial
banks have a higher capital gains tax rate than individuals, who are the second largest group of investors
in tax-exempt
securities, one might expect the marginal investor at the 15-year maturity
to have a
higher capital gains tax rate than the marginal investor at the 20-year maturity.
This would push up
the coefficient of the low coupon variable in the 15year regression relative to the coefficient in the 20year regression.
The evidence from the regressions for an effect of
high coupons
on yields to maturity was very weak.
The coefficient in the regression for the 5-year maturity was less than 2 basis points and was significant
only at the 10 percent level. The coefficients of the
high coupon variables in the 10- and 15-year maturity
regressions were not significant.
These results indicate that discount bonds constitute by far the greatest cost to governments
in terms
of the additional yield required to induce investors to
buy them. The small number of large discounts in
the 1977-78 period indicate that most governments
have realized this and have put constraints
on the use
of low coupons in NIC bidding.
13In order to make this judgment
the estimated coefficients of the low coupon variables
were compared
to
hypothetical
coefficients
calculated under the assumption
that only the capital gains effect was at work. The calculation used the 48 percent capital gains tax rate of the
commercial banking sector, which is the largest investor
in the tax-exempt
market and which has the highest
capital gains rate.
Hence, the hypothetical
coefficients
were the maximum expected if capital gains taxes were
the only force pushing up the yield on discount bonds.

FEDERAL RESERVE BANK OF RICHMOND

Call Provisions
The Extent and Nature of Call Provisions on TaxExempt
Bonds
Most tax-exempt
bonds have call
provisions
that permit the issuer to redeem them
prior to maturity under certain conditions.
For example, in the Broaddus-Cook
data sample 58.5 percent of the general obligation
issues and all of the
revenue bond issues were callable.
Call
exempt

provisions
vary substantially
across taxissues.
To illustrate,
the provisions
of ten

issues are shown in Table V. The call provisions
typically include the date of first call, the price the
issuer must pay per $100 at the time of first call, and
the changes in call price between first call and maturity.
It is also generally
indicated
whether the
bonds in a serial issue are callable “inversely,”
i.e.,
in reverse order of maturity.
On the right-hand
side of Table V specific characteristics of the call provisions
are extracted from
the summary statements of the issuer.
The number
of years to first call is specified for the whole package, rather than for individual maturities, so that it is
the same for all maturities.
The table illustrates that
while the most common number of years to first call
is ten, there is a great deal of variation.
The summary data on years to first call for the
issues used in the Broaddus-Cook
regressions
is
shown in Table VI. These data show that although a
particular serial issue may be “callable,” some of the
bonds that comprise the issue may in fact mature
before the first call date.
Only 0.7 percent of the
callable issues at the 5-year maturity had an initial
call date prior to maturity.
This figure rises to 10.6
percent for the lo-year maturity,
88.1 percent for
the 15-year maturity, and 98.2 percent for the 20-year
maturity.
The examples-shown
in Table V also illustrate the
variation in call price provisions across different bond
issues.
These provisions
typically indicate the call
price at the time of first call and specify how it declines to par in between the time of first call and
maturity.
The provisions are specified for the issue
as a whole but the call price at a given point may or
may not be the same for bonds of different maturity
with a given issue.
Call price schedules generally
fall into two categories. Some issues specify a specific
price covering all maturities
for each point in time.
For instance, the call price of issue 8 is $104 per
$100 at the time of first call and then drops sharply
Other issues specify a
to $100 four years later.
formula.
For instance issue 2 specifies the call price
for any maturity as 100 plus ¼ percent for each 12
20

ECONOMIC

months or fraction thereof between date of redemption and date of maturity.
In this instance the price
at time of first call would be $101.25 for the 15-year
maturity and $102.50 for the 20-year maturity.
Some
issues that specify formulas indicate an upper limit
for the call price.
For instance, the cap for any
maturity in issue 2 is $102.50. Issue 1 has the same
formula as issue 2, but without a cap. The examples
shown in Table V also illustrate
that in some instances the call price drops quite slowly while in
others it drops sharply to 100.
Table VII shows the call price at the first call date
for the bonds in the 15-year maturity Broaddus-Cook
regression.
The table, which includes only those
issues

in the regression

that

are callable

maturity,
shows that while a price
time of first call is most common,
over a wide range including $100.

prior

of $103 at the
call prices fall

The Predicted Effects of Call Provisions on TaxExempt
Bond Yields
Callable tax-exempt
bonds
may have higher yields to maturity than otherwise
similar non-callable
bonds because they expose the
investor to the risk of having to invest his money at a
lower interest
rate between the time of call and
maturity.
In compensation
for this risk, investors
may demand
on callable

a higher

“promised”

than on non-callable

yield to maturity
bonds.

The effect of call risk on the yield of a bond should
depend on two broad factors.
The first is the expected pattern of interest rate movement over the life
of the bond. Ceteris paribus, the lower interest rates
are expected to fall relative to current rates between
the first call date and maturity, the greater the probability that the issuer will find it profitable to call the
issue.14 The second factor consists of the call provisions specific to that bond. The longer the years to
first call for a bond of a given maturity the lower the
one would exexposure to call risk. Consequently,
pect the effect of call risk to vary inversely with the
number of years to first call. Also, the higher the
call price the lower the probability
that the market
price of the bond will rise enough for the issuer to
find the call option attractive.
Consequently,
one
would expect increases in the call price to decrease
the risk of call and thereby
callability on a bond’s yield.

decrease

14 The risk of interest rates falling to
tax-exempt
bond will be called may be
tion of the expected change in interest
function of the expected variation in
regression study [8] that attempted to
used a proxy for the expected change

REVIEW, MAY/JUNE

1982

the impact

a level where the
viewed as a funcrates and/or as a
rates.
The only
capture this effect
in rates.

Table V

CALL PROVISIONS OF SELECTED TAX-EXEMPT ISSUES
Call Price 3 Years After
Time of First Call

Call Price at Time of
First Call (Per $100)
Bond issue

Call provisions specified by issuer

Years to
first call

S-year

maturity

Call Price
6 Years After
Time of
First Call

IO-year
maturity

15-year,
maturity

20-year
maturity

15-year
maturity

20-year
maturity

1. Montebello Comm. Redevel. Agency
(5-10-77)

Callable as a whole or in port inversely
and by lot within a maturity from any
available funds on any interest date
beginning April 15, 1984 at 100 plus
¼ percent for each year or fraction
thereof between date of redemption
and date of maturity.

not
callable

100.75

102

103.25

101.25

102.50

101.75

2. Philadelphia, Pennsylvania
(5-24-77)

Callable as a whole on any date, or in
part inversely and by lot within a
maturity on any interest date, beginning
Sept. 15, 1987 at 100 plus ¼ percent
for each 12 months or fraction thereof
between date of redemption and date
of maturity, premium not to exceed
2½ percent.

not
callable

1.25

2.50

100.50

101.75

101

3. State of California
(6-7-77)

Callable beginning June 1, 1992 or any
interest date thereafter at 100.

not
callable

100

4. Birmingham, Alabama
(7-26-77)

Callable as a whole, or in part inversely
on any interest date beginning Aug. 1,
1987 thru Feb. 1: 1989, 103½; 1991,
103; 1993, 102½; 1995, 102; 1997,
101½; 1999, 101; thereafter 100.

not
callable

103.50

103

102

5. Kentucky Hous. Corp.
(8-18-77)

Callable as a whole or in part at any
time beginning July 1, 1987 thru
June 30: 1988, 103; 1989, 102; 1990,
101; thereafter 100.

not
callable

n o t
callable

103

100

6. Hennepin Co., Minnesota
(9-13-77)

Callable as a whole or in part inversely
on any interest date beginning Jan. 1,
1987 at 100.

not
callable

100

7. Mera, Arizona Utility
(10-3-77)

Callable as a whole or in part inversely
on any interest date beginning July 1,
1983 at 100 plus ½ percent for each
year between date of redemption and
date of maturity, premium not to exceed
3 percent.

not
callable

102

103

8. Anchorage Alaska Electric
(11-8-77)

Callable as a whole or in part inversely
and by lot within a maturity on any
interest date beginning May 1, 1988 to
Nov. 1: 1989, 104; 1990, 103; 1991,
102; 1992, 101; thereafter 100.

not
callable

104

102

100

Source: Moody’s Municipal and Government (News Reports), 1977; Moody’s Bond Survey, 1977,

100

Table VI

DISTRIBUTION

OF BONDS

BY YEARS

TO FIRST

CALL

(number of bonds)
5-year
regression

* Bonds below the solid line ore not callable
Source:

glomeration of bonds among which call risk may vary
greatly.
Hence, like the analysis of coupon effects,
the analysis of call provisions must focus on individual bonds, not serial issues.
Second, while the protection offered by years to first call is fully captured
by one number, the call price at a given point, such
as the first call date, is only a rough proxy for the
price over the whole period between years to first

Table VII

BONDS

OF FIRST

IN 15-YEAR

CALL FOR

REGRESSION*
Number of
issues

Call price
Equals 100

112
25
104
246
20

greater

than

104

Total

20-year
regression

because call date is not prior to maturity.

call and maturity.
Third, in general, the difference
between the call price and the price of the bond represents the gap that has to be overcome by falling
interest rates before the market price of the bond
rises to its call price. The larger the gap, the greater
the decline in interest rates necessary to make call
profitable to the issuer and, hence, the lower the risk
of call. The size of this gap, however, depends not
only on the call price but also on the initial price of
the bond, which is frequently not par. Consider the
case of a discount bond selling at $95 with a call price
of $103. In this case interest rates have to fall enough
to raise the market price of the bond from $95 to
$103. The point here is that coupon effects complicate
the analysis of call risk.
A final complication
in analyzing the effect of call
provisions
on tax-exempt
yields is that they are
interdependent.
That is, call risk for a particular
issue depends jointly on interest rate expectations,
years to first call, call price, and initial price of the
bond. Consider the case where interest rates are at a
cyclical low and are expected to rise in the future.
Then investors
may have little fear that callable
bonds will be called. In such a period variations
in
call price or years to first call across bonds of a given
maturity may have little effect on yields.

516

* Includes only bonds callable
15 yews.
Source:

15-year
regression

Broaddus and Cook [8].

Before reporting
the regression
results on the
effect of call provisions
on tax-exempt
bond yields,
several complications
should be mentioned.
First, as
discussed above, a given tax-exempt
issue is a con-

CALL PRICE AT TIME

10-year
regression

Broaddus

in less than

and Cook [8].

ECONOMIC

Regression Results
The approach used in all but
one of the eighteen regression studies that attempted
to capture the effect of call provisions on tax-exempt
REVIEW, MAY/JUNE

1982

bond yields was to include either a dummy variable
set equal to one for callable issues or a variable for
the number of years to first call.15 The predicted sign
of the call dummy variable coefficient
is positive
while the predicted sign of the years to first call
coefficient is negative.
These studies have generally
had poor results in estimating the effect of call provisions. Only in four studies [15, 19, 20, 22] did all
reported regressions have statistically significant call
variable coefficients with the predicted sign.16
Of
those studies reporting significant coefficients for the
call dummy variable, the coefficients with one exception ranged from 11 to 35 basis points.17
The unexpectedly
poor results of these studies stem
from the complications
discussed above.
First, the
dummy variable technique forces the effect of call
risk to be constant over the whole period covered by a
study’s data sample.
It is clear, however, from the
reasoning above and from evidence in the corporate
bond market (see Yawitz and Marshall
[51] for
example) that this should not be the case. Second,
12 of the 17 studies used the whole issue as the unit
of investigation
and NIC or
TIC as the dependent
variable.
As noted above, this approach cannot accurately estimate call effects, because a given callable
serial issue in fact is a conglomeration
of bonds, only
some of which are callable. And even among callable
bonds within a given serial issue the effect on yield
of a given set of call provisions may vary.
The Broaddus-Cook
study attempted to deal with
these problems by analyzing the effects of call risk
on yields to maturity at three different maturities:
10, 15, and 20 years. In each case rather than use a
simple call dummy the study used an interest rate
expectations proxy that allowed the effect of call risk
to vary over time as expectations varied. This proxy
was the spread between the 20- and 7-year U.S.
government
bond yields.18
The assumption
under15 An exception within this group is Kidwell [18] who
tested for other call features.
However, years to first call
is the only call feature that had a significant coefficient
with the predicted sign in any of his regressions.
16 In seven studies [4, 11, 12, 17, 18, 23, 24] the results
were mixed and in six studies [3, 6, 7, 14, 16, 21] there
were no statistically
significant call variable coefficients.
17 Specifically, references
[4, 15, 19, 20] reported coefficients of .346, .148, .110, and .137, respectively.
Reference
[24] reported a coefficient of .198 for general obligation
issues and a coefficient of .995 for all issues.
18 An implicit
assumption
is that the adjustment
to
changing interest rate expectations
is made solely through
the yield on callable bonds.
This in turn assumes that
state and local governments
do not alter years to first
call and call prices to offset the effect of changing
interest rate expectations
on callable bond yields.
Both
Kidwell [36] and Broaddus and Cook [8] present evidence that supports this assumption.

lying the use of this proxy is that in 1977 and 1978
changes in the U. S. bond yield curve were determined by changes in interest
rate expectations.19
This proxy was set equal to zero if years to first call
of a particular issue were greater than the maturity
of the bond in question.
The study made the effect of years to first call and
call price on a bond’s yield dependent on the interest
The specific call price
rate expectations
proxy.
variable used was the difference between the call
price of a bond at the time of first call and its price
at the time of first call calculated using the initial
reoffering yield of the bond. (The gap between these
two prices is a proxy for the amount rates have to
fall below the initial yield before the bond’s market
price at first call rises to its call price.)
The study found a highly significant
relationship
between interest rate expectations
and the yield on
callable tax-exempt
bonds at the 15- and 20-year
maturity.
The coefficient of the 10-year maturity
was only significant
at the 10 percent level.
The
study also found a significant
negative relationship
between years to first call and the effect of call risk
on yield.
The coefficient of the call price variable
did not have the expected sign in any regressions and
it was concluded that the call price at the first call
date is simply a poor proxy for the call price over
the whole span between years to first call and maturity.
The estimated call effect for a 20-year bond
with 5 years to first call ranged from 8 to 22 basis
points over the 1977-78 period.
For a bond with 10
years call protection, the effect was only 3 to 9 basis
points.
These effects are fairly small compared to
those reported in corporate bond studies.
However,
the 1977-78 period was one of low tax-exempt
rates
relative to the previous three years and one might
consequently
expect call risk to be relatively small in
this period.
II.
ISSUER

CHARACTERISTICS:

The Expected Effect of Default
Tax-Exempt
Bond Yields

DEFAULT

RISK

Risk on

Yields on tax-exempt
bonds are calculated using
the promised interest payments of the bonds. Default
risk refers to the possibility that an issuer of a bond
may not make these payments or may not make them
19 The specific variable used was (call dummy) (1/eSPR)
where the call dummy indicates whether or not the issue
is callable and SPR is the spread between 20- and 7-year
U. S. government
bond yields. This functional form has
the feature that as the spread gets very high the effect
of call risk approaches zero.

FEDERAL RESERVE BANK OF RICHMOND

on time. Default risk may affect the yield to maturity
on a bond in two ways.
First, a higher promised
yield to maturity
is necessary
to achieve a given
expected yield. Second, the investor may demand a
higher expected yield on a risky bond, relative to the
yield on a risk-free bond in compensation
for the risk
involved.20
Default Risk Explanatory
Variables Used
Tax-Exempt
Yield Regression
Studies

Cross-Section
Variables
In discussing
the explanatory variables designed to capture the effect of
default risk on tax-exempt
yields, it is useful to
distinguish between “cross-section”
and “time-series”
explanatory
variables.
While tax-exempt
bond yield
studies are conceptually
cross-section
studies, they
frequently use data that cover a long period of time.
As a result, the effect of default risk on yield may not
be totally captured by cross-section
variables.
The
cross-section
and time-series
variables
used in the
various studies are summarized
in Table VIII.
Regression
studies of the determinants
of taxexempt bond yields have used one of two approaches
in attempting to capture the effect of default risk at a
given time on yields.
A small number of studies,
interested primarily in default risk, have specified the
20 In studies of yield relationships
these two effects are
generally combined and called “default risk premiums.”
Strictly
speaking
the first is a “default”
premium
to
compensate
for the expected loss of holding a risky bond,
while the second is a “risk” premium to provide additional compensation
for holding
a risky asset.
See
Lawler [38].

economic and fiscal characteristics
of the issuer believed to influence risk premiums and entered them
The much more
directly into yield regressions.
common procedure is to instead include dummy variables that are presumed to be related in some way to
the underlying
economic and financial characteristics
of the issuers.
As shown in Table VIII, by far the
most widespread
practice in this regard is to enter
dummy variables for the various rating categories
employed by one or both of the two major rating
agencies, Moody’s and Standard and Poor’s.
It has
been argued in a number of articles that the rating
category dummy variables do not adequately capture
cross-section variations in default risk. In particular,
the argument
has been made that within a given
rating category, default risk of revenue bonds varies
systematically

by purpose

of issue, i.e., whether

Time-Series
Variables
Default risk variables that
change over time have been entered as explanatory
variables in tax-exempt
bond yield regressions
primarily to allow for the possibility that the relationship between the default risk premium on a bond and
This
its rating category might change over time.
might happen if economic and financial conditions of
an issuer change but the rating agencies do not
change, or are slow to change, their ratings.
Or, risk

Table VIII

DEFAULT

RISK

EXPLANATORY

TAX-EXEMPT

VARIABLES

BOND YIELD

USED

REGRESSIONS

Cross Section Variables

Time Series Variables

direct measurer

1. economic and fiscal characteristics of issuer
[9, 10, 13, 24]

indirect measures

1. rating category dummy variables
[1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 14, 15,
16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

1. rating category dummy variables weighted
by spread between Moody’s low- and highrated bond yield series at time of issue
[8]

issue purpose dummy variables
[4,* 6, 7, 14, 16,* 19,* 20,* 22, 23*]

percentage change in real GNP
[5, 19, 20, 21]

location dummy variables
[8, 10]

annual dummy variables

Proposition 13-related
and time trends

[6]
dummy

[2]
* In these studies the individual

purposes were

grouped

into aggregate

ECONOMIC

the

bond is
issued to finance
universities,
hospitals,
schools, etc., (for example, see [6, 22]).
Issue
purpose dummy variables have been included to capture this effect. A third cross-section
dummy variable tested in a small number of studies has been the
location of the issuer.

“high-”

REVIEW, MAY/JUNE

and “low-”

1982

risk purpose categories.

variables

premiums
might change over time for reasons not
directly related to the condition of the issuer.
In an
attempt to deal with these possibilities, one study [8]
used a variant of the dummy variable method in
which the dummy variables were weighted by yield
spread series from Moody’s.
For instance, the Aa
dummy variable was weighted by the spread between
Moody’s Aa and Aaa yield series.
This forces the
risk premium on all Aa-rated bonds in the sample to
conform with the risk premium implied by Moody’s
yield series at the date of issue. As shown in Table
VIII, other approaches to this problem have been to
include the percentage change in real GNP or simple
annual dummy variables.
Regression

Results

Cross-Section
Variables
In two articles, Browne
and Syron [9, 10] tested for the effect of numerous
economic and financial characteristics
of big cities on
the yields of their general obligation bonds.
They
found that a city’s unemployment
rate, its volume of
short-term debt per capita, its ratio of pension benefits to assets, and its location were significant determinants of the yield on its bonds. The characteristics
used by Hastie [13] to capture the effect of default
risk on the yields of general obligation bond yields of
local governments
included default history, the ratio
of overall debt to true property values, and a measure
of economic diversification.
Virtually
all the studies that used the indirect
dummy variable approach found the rating category
of the issuer to be the most important determinant
of
variations
in yields across tax-exempt
bonds.
For
instance, the Broaddus-Cook
study included dummy
variables for bonds rated Aa, A1, A, Baa1, and Baa.
(The omitted category was Aaa-rated bonds, so the
coefficients of the dummy variables are interpreted
as the increased yield relative to the going Aaa-rated
bond necessary to sell the bond.)
Over the sample
period covered by the study (1977-1978)
the estimated risk premiums for bonds at the lo-year maturity with these five ratings were 12, 33, 37, 55,
and 75 basis points, respectively.
The studies that included issue-purpose
dummy
variables generally concluded that issue purpose for
revenue bonds was associated with variations
in default risk premiums
among revenue bonds having
the same rating.
Of particular interest here are the
studies of Bierwag, Hopewell, and Kaufman
[6] and
Sorenson [22] both of which included over ten issuepurpose dummy variables.
Both studies found that
within a given revenue bond rating category, hospital,
university,
and housing had above average default

risk premiums
while non-university
schools, roads,
and utilities had below average risk premiums.
Sorenson reasoned that the important difference between
the two groups of revenue bonds was that the first
group of issuers compete with other suppliers
of
similar products or services and, as a result, their
“future revenue flows are subjected to the uncertainties of future market share."21
Time-Series
Variables
In all those studies using
it, the percentage change in real GNP had a significant and negative effect on a bond’s yield relative to
This is consistent
with the
the going Aaa yield.
widely observed phenomenon
that risk premiums on
bonds of a given rating category tend to widen in
periods of economic weakness.
Similarly, the Broaddus-Cook regressions
were modestly improved with
the rating category dummy variables weighted by
Moody’s yield spread at the time of issue. Beebe [2],
using time trends and dummy variables
that took
on a value of one after certain points in time, found
that the effect of Proposition
13 on the risk premiums
of California municipal bonds varied according to the
type of bond (general obligation, revenue, tax allocation, or lease-purchase).
Default Risk and Maturity
An area of concern
related to default risk is the relationship
of default
risk premiums
to term-to-maturity.
One view of
this relationship
is that default
risk premiums
demanded
by investors on
the bonds of an issuer
with a given rating category
may increase
with
term-to-maturity
because of the greater uncertainty
associated with promised payments further out into
An alternative
view is that-at
least
the future.
for low-rated issues-risk
premiums may be larger
the shorter the term-to-maturity
of bonds of a givenrated issuer because of a “crisis-at-maturity.”
The
rationale
for the crisis-at-maturity
effect on risk
premiums for lower grade bonds is that “for these
grades, the probability of default may increase as the
final redemption date grows nearer and the company
is unable to improve its financial condition”
[49, p.
166].
Van Horne [49] surveyed the evidence from three
studies on the relation between risk premiums
and
maturity
in the corporate bond market and found
that evidence from two of the three supported
the
notion that the lower the grade of the bond, the
higher short-term
default risk premiums are in relation to long-term risk premiums, consistent with the
21 If this argument is valid, the puzzle remains as to why
these differences are not captured by the rating agencies.

FEDERAL RESERVE BANK OF RICHMOND

notion of a crisis-at-maturity.
He emphasized that
the relationship
between risk structure and maturity
can change over time, especially during economic
downturns
when crisis-at-maturity
may grow in
importance.
There is relatively little evidence on the relationship between risk premiums and maturity in the taxexempt market.
Looking at data for the 1940s and
1950s, Robinson
[47] concluded that the differential
between the yields of Baa-rated and Aaa-rated bonds
widened as maturity lengthens.
This finding is not
consistent with crisis-at-maturity
in the tax-exempt
market in the years studied by Robinson.
To estimate the relationship
between risk and maturity,
the Broaddus-Cook
study ran regressions
using data only for general obligation
issues that
offered bonds at each of the 5-, 10-, 15-, and 20-year
maturities.
Also for the purposes of this exercise
the default risk dummy variables alone were used so
that the coefficients across rating categories and maturities could be easily compared.
The coefficients
for the five categories of lower than Aaa-rated bonds
are graphed
in the accompanying
chart
across
the four maturities for which regressions
were estimated. In every case the coefficients of a particular
rating category increase with maturity.
In particular,
risk premiums rise at least as much from the 5- to

10-year maturity for the low-grade
for the high-grade
bonds.
Also,

bonds as they do
the slopes of the

term-to-maturity
risk premium curves generally are
(Only from
steeper the lower the rating category.
Baa1- to Baa-rated
is there a slight drop in the
slope.)
While there was no recession during the study’s
sample period, risk premiums did move over a wide
range especially at the beginning
and end of the
period.

As a second

test of the crisis-at-maturity

effect, the sample was divided up into two subsets,
one for the relatively “high risk” period and one for
the “low risk” period, and regressions were run for
both subperiods.22
This second test also provided no
support for the existence of a crisis-at-maturity
for
the lower rated issues. There was very little difference in the slopes of the term-to-maturity
curves for
the five risk categories over the two subperiods.
Both
were very close to the slopes for the total sample
regressions shown in the chart.
In summary,
exempt market

the available evidence
is that the relationship

premiums

maturity

and

is positive

from the taxbetween risk
over

the whole

range of maturities.
Hence, there is no evidence of a
crisis-at-maturity
effect in the tax-exempt
market.
However, the evidence is by no means overwhelming
since the only regression study to address this issue
did not include a recession.
Also, the relationship
between risk premiums
and maturities
of less than
five years was not studied.
The Effect of New York City Default on Big City
Tax-Exempt
Bond Risk Premiums
A final question
related to default risk that has received some attention from a small number of the studies is whether or
not the financial crisis of New York City in 1975 had
an effect on the risk premiums,
and hence on the
yields, of bonds issued by similar Northern industrial
cities. This question arose when the crisis spawned
numerous
reports (for example [42]) that the concurrent
unfavorable
publicity
was pushing
up the
borrowing
costs of other Northern
industrial
cities.
Three of the studies addressed
this question by
doing regressions with data from the period following
Browne and Syron [9] found that an
the crisis.
equation with economic and financial conditions
as
explanatory

variables

understated

the yields

of four

22 Specifically,
the “high-risk”
period covered all time
periods when Moody’s (Baa-Aaa)
spread was greater
than or equal to 78 basis points and the “low-risk” period
was when the spread was less than 78 basis points.
The
cut-off point of 78 basis points was chosen arbitrarily
to
divide the sample roughly in half.
26

ECONOMIC

REVIEW, MAY/JUNE

1982

Northern industrial cities in 1976 by at least 90 basis
points each. They leaned towards the conclusion that
the market demanded
a premium
on the yields of
these cities’ securities because of the intense publicity
following the New York crisis.
Browne and Syron
[10] conducted a follow-up study using 1978 data
and an implication
of this study was that the unexplained risk premium in the yields of the bonds of
Northern industrial
if not disappeared.

cities had declined

considerably,

Broaddus and Cook [8], using data from 1977-78,
attempted to analyze the question by incorporating
a
dummy variable set equal to one for the issues of six
large Northern
industrial
cities:
Boston, Chicago,
Cleveland, Detroit, Philadelphia,
and Pittsburgh.
The
dummy variable had a highly significant coefficient of
about 60 basis points. They also ran regressions with
separate dummy variables for the issues of each of
the six cities individually
and in each case reported
positive and significant
coefficients.
Broaddus and
Cook attempted to gain insight into the cause of this
result by comparing
Moody’s ratings at the end of
1981 for the 30 Northern
industrial
city issues in
their sample to the ratings at the time of issue, reasoning that if there were a change in the economic
and financial conditions of these cities not reflected in
Moody’s ratings at the time of issue, one would expect that eventually
Moody’s would lower their
ratings.
In fact, the ratings of 15 of the 30 issues
were lowered subsequent
to their issue date, none
were raised and 15 were unchanged.
The ratings of
the cities of Boston, Chicago, Cleveland, Detroit, and
Pittsburgh
were all lowered, although the ratings of
some of their associated districts were unchanged.
On balance, it was felt that the only conclusion that
could be drawn from these results was that much, if
not most, of the “unexplained”
risk premiums
on
issues of Northern
industrial
cities in the study reflected the relatively slow reaction of Moody’s, as
compared with investors, to deteriorating
conditions
in those cities.
Finally, a study by Kidwell and Trzcinka
[20]
using data from the summer of 1975 concluded upon
analyzing the residuals of their regressions that these
results “provide marginal support that the New York
City crisis by itself led to higher borrowing costs for
other municipalities
(Detroit,
Philadelphia,
Cleveland).”
In summary, there is some evidence from the
regression studies that the New York financial crisis
had a temporary effect on the yields of securities of
similar Northern
industrial
cities.
However, there
is no evidence of a lasting effect.

III.
UNDERWRITER

Underwriter

COMPETITION

Conditions

Almost all of the regression
third potential source of variation
yields, namely

the marketing

studies consider a
in tax-exempt bond

conditions

of the bond.

As noted earlier, most tax-exempt
issues are sold
initially by the issuer to an underwriter
who in turn
sells them to the public. Bonds can be sold by issuers
to underwriters
via competitive bidding among numerous underwriting
syndicates or through negotiation

with

only one syndicate.

Almost

all general

obligation bonds are required by law to be sold via
competitive
bidding, while revenue bonds are sold
both by competitive

bidding

and through

negotiation.

If a bond is sold competitively
it may receive as
many as ten bids or as few as one. Table IX shows
the number of bids received by the 793 competitively
sold issues in the sample used by Broaddus and Cook
[8]. The median number of bids received was four.
Table IX also shows the number of bids received by
rating category,
illustrating
that the lower rated
issues tend to receive fewer bids. The dispersion of
bids received by an issue as measured by the variance
or range of bids also varies greatly.
An issue, for
example,

that receives four bids may have these bids

Table IX

NUMBER

OF BIDS

ON COMPETITIVE

ISSUES

IN SAMPLE
(Moody’s Ratings)
Number

Number

113

184

136

113

greater
than 10

Source:

793

124

215

142

186

Broaddus and Cook [B].

FEDERAL RESERVE BANK OF RICHMOND

all come in close to the winning bid or the bids may
be scattered over a wide range.
Table X shows the
range of bids for all the issues in the sample that
received four bids.
Another underwriter
competition
characteristic
is
the issue’s eligibility to be underwritten
by banks.
Prior to 1968, the Glass-Steagall
Act of 1933 prevented banks from underwriting
all revenue bonds.
Hence, revenue bonds could be used as a proxy for
bank eligibility to underwrite
a given issue.
The
Housing and Urban Development
Act of 1968, however, permitted banks to underwrite
municipal revenue bonds issued to finance housing, university,
or
dormitory projects.
Further, the Comptroller
of the
Currency may rule that a municipal revenue bond is
in effect a general obligation
bond eligible to be
underwritten
by national banks if the bond is backed
by the full faith and credit of the issuer. According
to the Public Securities Association
[44], 40 percent
of the revenue bonds issued in 1979 were eligible for
bank underwriting.
This discussion points to four underwriter
conditions that vary across issues:
(1) method of sale,
i.e., competitive bidding versus negotiation;
(2) the
number of bids received by competitive
issues; (3)
the dispersion
of bids; and (4) bank underwriter
eligibility.
Various
studies have included
one or
more of these variables as explanatory
variables in
tax-exempt
yield regressions.
Before proceeding with a discussion of why underwriter conditions are thought to influence tax-exempt
yields, it is useful to recall that many regression
studies have used measures such as NIC or TIC
which represent the total cost to an issuer of selling

ISSUES

BY RANGE
RECEIVING

Range of bids

Regression
Results and Search
Possible Explanation

Theory

as a

Kessel’s Paper and the Number
of Bids as a
"Determinant”
of the Reoffer Yield on Competitively
Sold Bonds In early 1971, Kessel [17] presented an
argument
explaining
why underwriter
competition
affects reoffering yields to maturity.
He also presented evidence from a regression model in support
of his argument.
His major empirical finding was
that the number of bids on competitively
sold issues
is negatively related to reoffering yields. This result
has held up remarkably
well in subsequent
studies,
and, until recently, his rationale for this relationship
For this reason, it is useful to
was widely accepted.
begin with a discussion
of Kessel’s theory.
The
criticisms of his explanation
will be discussed below.
Kessel employed George
search and the economic

Stigler’s thesis regarding
value of information
to

argue that an increase in the number of underwriters
bidding on an issue would reduce the reoffering yield
at which the issue could be sold to investors.23
Specifically, Kessel hypothesized
that information
regarding potential buyers of a new municipal
issue

Table X
DISTRIBUTION

bonds, including
both the underwriter
spread plus
the yield earned by the investor.
This is a complication in interpreting
the coefficients of the underwriter competition
variables
because there are a
priori reasons, confirmed by empirical evidence (for
example, see Kessel [17]), to expect that these variables affect not only yields to maturity
but also
underwriter
spreads.
Hence the coefficients of these
variables may reflect the behavior of the underwriter
or the investor or both. For that reason, when possible, the focus in this section is generally on those
studies that used reoffering yields to maturity.

OF BIDS

FOUR

BIDS

Number of
issues

varied across

underwriters.

Each underwriter

knew

some prospective
buyers not identified
by other
underwriters.
On this basis, Kessel suggested that
the number

of bids was a proxy

for the extent

which prospective final buyers
identified and informed about

of an issue had been
an issue:
the larger

the number

the search and there-

fore the lower the reoffer

of bids, the greater
yield.

4
4

23 An earlier study

by West [SO] concluded that large
issues receiving one and, to a lesser extent, two bids have
higher reoffering
yields because of monopsony
in the
underwriting
and distribution
of these securities. However, West also concluded
that the number
of independent buyers necessary to assure most of the benefits
of competition
is quite small and issuers, in any case, can
take precautions
to protect themselves
from monopsonistic behavior by underwriters.

5
4
greater than .40
Total
Source:

7
136

Broaddus and Cook [8].
ECONOMIC

REVIEW, MAY/JUNE

1982

The magnitude of the effect of the number of bids
on reoffering yields implied by Kessel’s regression
results is substantial.
His coefficient for the natural
logarithm of bids was -.14, which implies that issues
receiving five and ten bids carry reoffer yields 23
and 32 basis points lower, respectively, than an issue
receiving only one bid. In all subsequent
studies in
which the number of bids has been tested it has been
found to be a significant
determinant
of reoffering
yields, even though these studies have covered widely
varying

time periods

ported coefficients
Kessel’s.

[5, 8, 11, 12, 20].24

The re-

have been equal to or greater

than

Dispersion of Bids
In an attempt to extend the
Kessel thesis, Benson [4] argued that the number of
bids captures only part of the total effect of underwriter search on municipal bond yields. Specifically,
he argued that the intensity of underwriter
search
varied across issues receiving the same number of
bids due to variations in underwriter
expectations of
the benefits and costs of search.
Benson assumed
that the intensity of search varied inversely with the
dispersion of bids. On the grounds that more intense
search should uncover buyers
yields, Benson hypothesized

willing to accept lower
a positive correlation

between municipal yields and the variance of bids.
His findings supported his hypothesis in the case of
general obligation bonds, but not in the case of revenue bonds.25 One other study [8] included a measure of the dispersion of bids-the
range of bids--as
an explanatory
variable.
The coefficient had the
correct (i.e., positive) sign and was highly significant
in each of the full sample regressions.
Negotiated
versus Competitive
A third underwriter competition variable tested in a limited number
of studies including both competitively
sold and negotiated issues is a dummy variable denoting
the
bond’s sale through negotiation.
Of the three studies
reporting

regressions

with a negotiated

dummy

vari-

able [2, 8, 14], only Broaddus and Cook [8] found a
significant
relationship.
The coefficients of the negotiated dummy variable ranged between 11 and 15
basis points

in the full sample

regressions.

tween 1970 and 1976 and found that the mean 10year reoffering yield for negotiated issues exceeded
the corresponding
mean yield for competitive
issues
by 23 and 27 basis points, respectively, in the case of
general obligation and revenue bonds.26 They found
this difference in yields consistent with the hypothesis that monopoly powers may exist with issues sold
through negotiation.
An alternative explanation
following the search thesis, is that underwriters
that
do not go through the competitive
bidding process
might conduct a less thorough search for buyers than
competitive
underwriters.
(A third interpretation
will be given below.)
Bank Eligibility
A fourth underwriter
competition
variable that has been tested in a small number of
studies of revenue bond yields is bank eligibility to
underwrite
eligibility

the bond.
to have

yields of negotiated
search

theory

Cagan

[11, 12] found

a negative
revenue

to explain

effect

bank

reoffering

issues and used Kessel’s
this

result.27

Bierwag,

Hopewell, and Kaufman
[6], however, argued that
bank eligibility
is correlated
with issue purpose
among revenue

bonds and that Cagan’s result largely

reflected the absence of issue purpose variables in
his regression.
When they introduced issue purpose
dummy

variables

into Cagan’s regressions,

the coeffi-

cient of bank eligibility was no longer significant.
an earlier study, Hopewell and Kaufman
[16]
ported a negative coefficient significant
percent level for bank eligibility.
The Attack

on Search

Theory

While search theory is perhaps
ible explanation

at the

In
re-

an intuitively

of the correlation

between

plausunder-

writer competition
variables and reoffer yields, its
application is vulnerable
to criticism because it fails
to explain why
others.
Critics

some issues receive more bids than
argue that on this point the search

theory explanation
writer

competition

for the correlation
variables

between

and reoffer

under-

yields

falls

Joehnk and Kidwell [34] analyzed a sample of 730
paired competitive
and negotiated
bonds issued be-

26 Sorenson [23] argued that the effect of negotiation
on
yields differs according
to the riskiness
of the bond.
Specifically, Sorenson estimated that negotiation
actually
reduced the NIC of lower rated issues.

24 Not discussed here are those studies that used NIC
or TIC as the dependent variable. All 13 of these studies
that included the number of bids also reported a significant coefficient.
These studies are listed in the references.

27 The literature on the effect of bank eligibility on revenue bond yields is voluminous and this article was unable
to deal with the issue in any depth. Major combatants
in
the debate
are Bierwag,
Hopewell,
Kaufman,
and
Leonard [6, 7] and Mussa [40, 41] on the side that bank
eligibility does not lower yields and Cagan [11, 12] and
Silber [48] on the side that bank eligibility does reduce
yields.

25 Benson’s dependent

variable

was TIC.

FEDERAL RESERVE BANK OF RICHMOND

apart.

The

argued
ment

that

criticism

has

the number

quality

two

parts.

of bids

First,

is related

it is

to invest-

theory

to investment
point

Table

that

quality,

the

the number
the critics

information

IX that higher

rated

issues,

second

part

variations

in default

risk are crude

to differentiate

between

quality.

to capture

gressions
categories

shown

The

in “intrinsic

Mussa
quality

differences
when

Broaddus
periods

and
when

series

relatively

low.28

natural
.1885

28 These

logarithm
while

the

regressions

ran

spread

bid-ask

dealer

spread

bonds

with

as $5 per

poor

needing

in terms

theory
bonds

argue
with

of
that

differ-

not captured

larger

to sell such

lack

plausible

that

search-and
by underwriters

the case, then
positively
crude

ables.

with

sub-

Baa

and when
period

in Section

Since
at

to capture
of bids

best

the

may

and
the
very

effect

be capturing

argue

that

proponents
should

of the

specify

“missing

appropriate

would

bid-ask

spreads),

whole

reason

have been
native

be difficult

direct

especially

the

rating

characteristics

yields

essentially

would

result.
on the basis

for

competition
ex

post

The reader
of which

(i.e.,
and

the

variables

is that the alter-

economic

explanations

underwriter
are

dummy

studies

issuer

issues,

and financial
be

extremely

In any case, both the search

variables

between

the

new

categories

the number

exempt

earlier

regressions

is to ‘use dummy

to the rating

ences

with

great

in detail

contention.29

is essentially

A second
argument

variable”

reported

Mussa’s

with

risk.

is correlated
are

results,

argument

default

“missing

of bids

on average,

of the criticism
yield

basis

with

marketability,

in tax-exempt

ent

of search

shown

included

way

These

of bids is correlated

bids.

The

was .1005.
are consistent

The above

of the contention

is related

[8],

[41]:

. . . underwriters
will undertake
costly search and
marketing
activities
only if they are adequately
compensated
for the costs incurred
in such activities. For some bond issues, the search and marketing costs will be low. These will typically be issues
of well known borrowers
with impeccable
credit,
particularly
general
obligation
bonds issued
by
states and localities with high credit ratings.
On
intuitive grounds, one might expect that such issues
would attract
a large number of bids because the
cost of marketing
is low. For such issues, the potential bidder does not need to engage in a costly
search for potential
customers
in advance of making his bid. As one of many bidders his costs must
be low because his chance of winning
is also low
and he runs the risk of failing to recover these costs
if he is a losing bidder. In contrast,
issues by less
well known or less credit worthy
borrowers
are
likely to attract
fewer bids because the costs of
ascertaining
a reasonable
bid for such issues is
greater than for issues with a ready market.
In support

period

the
was

low-risk

II.

ECONOMIC

30 Actually Mussa also seems to imply this. Hastie
uses number of bids as a proxy for marketability.

[13]

31 The argument here is for number of bids. However, it
could also be applied to the negotiated
dummy variable
and the dispersion
of bids.
In particular,
it has been
reported that negotiated
sales are often used by “lesser
known” issuers [44].
If so, negotiated
issues would in
general have poorer marketability
than competitive issues.

REVIEW, MAY/JUNE

1982

IV.
REGIONAL

MARKET

CONDITIONS

The Argument
for an Effect of Regional
Conditions on Tax-Exempt
Bond Yields

Market

A small number of studies have considered regional
market conditions
as a determinant
of tax-exempt
yields.
(For reasons explained below, in all cases
the region focused on is the state.)
A priori, one
would expect arbitrage by investors to eliminate all
but very temporary
differentials
between the yields
to maturity on comparable bonds issued in different
regions.
The essence of the argument that arbitrage
may not eliminate all interregional
yield differentials
is that investors
inside and outside a region are
subject to different costs, taxes, and other considerations that create a gap between the observed yield
to maturity on a region’s bonds and the true yield
earned by investors inside versus outside the region.32
Specifically, there are three factors which may affect
in-state
investors
differently
from out-of-state
investors : information
costs, differential
taxes, and
commercial bank pledging requirements.
Information
Costs The first and most widely cited
reason why regional market conditions
may affect
tax-exempt
bond yields is information
costs.
As
noted earlier, many municipal bond issues are relatively small and are handled by local or regional
underwriters
that sell primarily
in local or regional
markets.
The cost to an investor of obtaining information about, say, a local sewer bond issued in a
different state might be considerable.
Similarly, the
cost to an underwriter
(and hence to an issuer) of
searching for and identifying
distant buyers for the
bond might also be considerable.
If these costs are
significant, then the yields on bonds in a region could
deviate from the “going” yields on similar bonds outside the region without triggering interregional
arbitrage.
Taxes
The second reason why in-state investors
are willing to accept lower yields on in-state bonds is
that income from a municipal bond is typically exempt from state and local income taxes within the
state of issue but not in other states.
As a result
the true after-tax
yield on a bond with a given
before-tax yield is different for in-state and out-ofstate investors.
This creates the incentive for investors to buy tax-exempt
bonds issued within their
32 The theory behind the existence of “regional market
segmentation”
in the tax-exempt
bond market has not
been rigorously formulated. This explanation is from [8].

own state. The tax rates applicable to individual investors in each state vary over a great range from 0
to over 15 percent,33
In Virginia, for example, an
individual investor earning 7.6 percent on an in-state
issue would require over 8 percent on an out-of-state
issue to get the same after-tax yield. Hence, if the
out-of-region
yield were 8 percent, yields in Virginia
would have to fall below 7.6 percent before Virginia
investors
would be induced
to buy non-Virginia
bonds.
Conversely,
if the yield on Virginia
bonds
were 7.6 percent the yield on out-of-region
bonds
would have to rise above 8 percent before Virginia
investors
would be induced to buy non-Virginia
bonds. This creates a range of 40 basis points over
which Virginia bond yields could move in response
to regional market conditions without inducing interregional arbitrage.
Pledging Requirements
A third factor that may
permit regional market conditions to affect individual
bond yields in a given state is the effect of state and
local “pledging”
requirements
at commercial
banks
against state and local deposits in that state.
Some
states require banks to hold securities equal to 100
percent or more of the value of their deposit liabilities
to the state and its political

subdivisions.

Other

states

have less stringent requirements,
and still others have
Those
no requirements.
or very low requirements.
states that impose such requirements
invariably
accept as eligible collateral U. S. government
and
agency securities and securities issued by the state in
question and its political subdivisions.
Most states,
however, do not accept out-of-state municipal securities as eligible collateral [28]. Hence, banks in states
with high pledging requirements
must purchase substantial amounts of in-state issues or Federal securities if they wish to acquire public deposits.34 Consequently, banks may be willing to accept a lower yield
on in-state bonds than on out-of-state bonds in order
to gain the return associated with attracting
public
deposits.35
In summary,
information
costs, differential
state
income tax treatment of in-state and out-of-state municipal bond interest, and differential
treatment
of
in-state and out-of-state municipal bonds for pledging
33 See[27].
34 Studies that have examined
the effects of pledging
requirements
on bank behavior are [1, 28, 29, 46]. Most
recently, Ratti [46] found that the demand by banks for
state and local securities
is greater as a result of the
presence of pledging requirements.
35
The
pledging requirements
in the various
1979 are summarized
in [28].

FEDERAL RESERVE BANK OF RICHMOND

states

as of

purposes may have created a range over which a
given region’s yields move in response to regional
supply and demand factors without inducing
arbitrage activity.
This phenomenon
has often been
referred to as “market segmentation”-a
term that
explains little and that conjures up the image of investors too lazy, ignorant, or irrational
to arbitrage
away interest rate differentials
across regions.
The
point here
taxes, and

is that information
pledging
regulations

costs,
may

state income
prevent
this

arbitrage by creating gaps between the true after-tax
yields earned by investors inside and outside a region
on that region’s
Regression

bonds.

Results

Before proceeding with the results of the studies
that have incorporated
regional variables, a few preliminary
comments are necessary.
First, as noted
above, in all these studies the “regional” market used
was the state. This is because the pledging and tax
arguments relate specifically to the state and because
“regional’: data are available only on a state basis.
Second, the argument
has been made that, to the
extent that regional conditions influence tax-exempt
yields, the effect should be inversely related to the
size of the issue [15]. The essence of this argument
is that unit information
costs decline as issue size
rises because the relatively fixed costs of acquiring
information
about an issue in another region are
spread over more dollars and the effect on yield is
smaller.
Third, the argument
has also been made
that the effect of regional variables--especially
those
related to the pledging effect-might
vary inversely
with maturity
[8]. This is because banks which are
the major holder of tax-exempt bonds, purchase primarily short- and intermediate-term
bonds with maturities generally not exceeding 15 years.
Demand Variables:
theory, if the pledging

The Pledging
Effect
In
requirements,
state income

taxes, and information
costs create a situation
in
which yields in a region can move over a range without triggering
interregional
arbitrage, then anything
affecting the demand for or supply of bonds in a
given region might affect yields in that region relative to the “national”
yield.
In practice, the only
demand variable that has been tested in the taxexempt yield regressions
is bank demand related to
pledging requirements.
Two studies have examined
this effect on tax-exempt yields. The first [1] which
was part of a larger study of public deposit insurance
for the Advisory Commission on Intergovernmental
32

ECONOMIC

Relations
(ACIR),
included dummy variables constructed to measure the pledging effect. The pledging
dummies were based on a classification of states into
“high-pledge,”
“moderate-pledge,”
and “low-pledge”
categories.
The results of the analysis suggested that
pledging requirements
reduced NIC of general obligation bonds in the high-pledge
states by 5 to 20
basis points relative to those in the low-pledge states.
Further, the effect appeared to be more consistently
significant in the latter part of the 1966-1974 period
covered due to the apparent substitution
of municipal
for Treasury
and agency securities as collateral for
public deposits by banks in the late 1960s and early
1970s.
The dummy
variable
included
to measure
the
pledging
effect in the ACIR
study differentiated
among states only on the basis of the character of
their pledging requirements,
It took no account of
differences in the proportion of short-term assets held
by state and local government
units solely in the form
of bank deposits. However, both the stringency
of
pledging requirements
and the relative share of government funds held in bank deposits are relevant.
For this reason Broaddus and Cook [8] used the percentage of total deposits in a state subject to pledging
requirements.
This pledging variable worked well in
the full sample and general obligation bond regressions. Its coefficients had the expected sign and were
highly significant at the 5-, 10-, and 15-year maturities. The coefficient was much smaller and was not
significant in the 20-year regressions.
This pattern
was not unexpected
since banks are less important
participants
at the long end of the market.
The
pledging variable was not significant
in any of the
revenue bond equations.
This result may reflect the
ineligibility
of revenue bonds as collateral in some
states with high pledging requirements.
The Broaddus-Cook
study also tested for the effect
of size by adding a multiplicative
term of the pledging variable

times

the logarithm

of the size of the

issue. This multiplicative
term had the expected sign
and was significant at the 5-, 10-, and 15-year maturities in the full sample and general obligation
equations, where the basic pledging effect exists. The
results suggest that at the 10-year maturity, for example, relatively high pledging requirements
reduce
reoffer yields on the order of 30 basis points for small
issues to 10 basis points or less for issues exceeding
$200 million.
Supply Variables
Three studies have tested the
effects of regional supply variables
on tax-exempt
bond yields and all three found them to be significant

REVIEW, MAY/JUNE

1982

on yields.
Hendershott
and Kidwell [15] used the
standard regression model (with NIC as dependent
variable) to estimate regional supply effects on yields
of bonds issued in Indiana between 1970 and 1974.
Their supply variable was the recent volume of new
municipal
securities issued by Indiana
government
units relative to the recent volume of new issues in
the national market.
They also included the supply
variable multiplied
by the logarithm
of issue size.
The supply variable coefficient was positive and the
coefficient on the multiplicative
term was negative.
Both were significant at the one percent level. They
concluded that a regional supply effect existed, but
that the effect was inversely related to issue size.
Both the ACIR
studies

included

currently

as a supply

outstanding

to state personal
variable

[1] and the Broaddus-Cook
variable

[8]

the ratio of the

stock of state and local bonds

income.36

was significant

In the ACIR

study this

and had the expected

positive

The coeffialso had the

expected positive sign and were highly significant in
all of the full sample equations.
Since this variable
measures
the outstanding
stock of regional bonds
rather than the flow of new issues, these results imply
that an increase in the supply of regional issues has a

Size of Issue37
Theories of the Effect of Issue Size on Reoffering
Yield Issue size has been included as an explanatory
variable in about three-fourths
of the tax-exempt
yield regression studies (see references).
However,
only a handful of these studies have attempted
to
articulate the expected relationship between issue size
and tax-exempt yields and even these few studies offer
diverse hypotheses of the relationship.
Tanner
[25]
argued that supply effects would drive up yields on
large issues because the demand curve for any particular issue is downward sloping.
Benson, Kidwell,
Koch, and Rogowski
[5] agreed that these supply
effects exist, but they argued

that the size of issue is

also a proxy

for marketability.

marketability

increases

They

will accept a lower yield in return
ability.

Hence,

argued

that

with issue size and investors
for greater

the marketability

market-

effect of size on

yield is the opposite of the supply effect.

They postu-

lated that the marketability
effect initially
would
dominate, but that at some issue size the supply effect
becomes dominant.
Hence, “the expected relationship between

yield and size may be U-shaped.“38

Problem in Interpreting
Size
Before summarizing

the Coefficient of Issue
the regression
results of

permanent effect on the yields of new regional issues
as long as the increase is reflected in a rise in the

encountered

ratio of the stock of regional issues to regional
come.
This implication
differs somewhat from

should be discussed.
First, size of issue is generally
viewed as being a determinant
of underwriter
spread

results of Hendershott
and Kidwell’s
was inconclusive on this point.

analysis,

inthe

which

the effect of issue size on yields two problems

which
use

OTHER

VARIABLES

EMPLOYED

YIELD

Two

obligation
versus
used in numerous
yields has either

in those

NIC

coefficient
IN TAX-EXEMPT

or TIC

of NIC

and

tax-exempt

yield

as the

dependent

of issue size may reflect

underwriters

or the behavior

that are

the coefficients

TIC.

of size

Conse-

regressions
variable,
the behavior

that
the
of

of investors.39

REGRESSIONS

This section will discuss a small number of variables that do not fit easily into the above four categories.

is a component

quently,

in interpreting

these-issue

size

and

general

revenue bond status-have
been
studies, yet the expected effect on
generally
not been discussed,
or

remains a matter of controversy.
Also, there are a
couple of recent articles that have argued for the
existence of market segmentation
by type of bond
that will be discussed briefly at the end of the section.

36 Actually, in the ACIR study this variable was interpreted as both a regional supply variable and a default
risk variable [1, p. 520].

37 This discussion is concerned exclusively with the direct
effect of issue size on yield. Size may also effect yields
through
its interaction
with regional market variables.
See Section IV.
38 A third rather tenuous
hypothesis
was offered by
Kessel [17] who found an unexpected
negative relationship between size and yield, and argued that the relationship reflected a weakness in the use of number of bids as
a proxy for underwriter
search.
Specifically,
he argued
that, ceteris paribus, larger underwriters
do more search
than smaller underwriters.
Also larger underwriters
tend
Hence, issue size captures the
to bid on large issues.
additional search on a given issue as opposed to a smaller
one with the same number of bids.
39 To complicate
things further, issue size is also used
as an explanatory
variable in equations
attempting
to
explain the number of bids received by a competitively
sold issue. Hence, issue size is thought to affect underwriter spread both directly and indirectly
through
its
effect on the number of bids. (See Kessel [17].)

FEDERAL RESERVEBANK OF RICHMOND

The second problem in interpreting
the coefficient
of issue size is that, in all but one of the regression
studies, size is measured in nominal terms.
This is
relevant because the theories of the relationship
between size and yield are implicitly theories of the
effect of size relative to the size of other current new
issues. If a data sample covers an extended period of
time, size measured in nominal terms may be incompatible with theories of how size is supposed to affect
yield. This problem is aggravated by the fact that,
due to inflation in the 1960s and 1970s, issue size
has an upward trend in the period covered by virtually all the regression studies.
The longer the data
period covered by a regression,
the greater is the
risk that the coefficient of size is picking up some
spurious correlation between the trend in size and in
An example
of this is
the dependent
variable.
Kessel’s study which used data covering a nine-year
period.
Over this period there was a significant
downward trend in the spread between lower rated
and Aaa-rated
bonds.
Kessel’s regression
shows a
negative and highly significant coefficient on size but
this may simply reflect correlation
between the upward trend in size and the downward trend in risk
premiums over the period.40
Regression
Results
The regression
results for
issue size show a division depending on whether the
dependent variable was (1) reoffering yield or (2)
NIC or TIC.
Of the nine studies that found a significant relationship
between size and NIC or TIC,
all but one found a simple positive relationship
[2,
3, 4, 6, 7, 15, 19, 24].
The one exception was the
ACIR study [1], which found a negative relationship
for small issues and a positive one for large issues.
Conversely, of the four that found a significant relationship between size and reoffering yield, two [17,
21] found a simple negative relationship
and none
found a simple positive relationship.41
Unfortunately,
the two studies that found a significant negative
relationship
between issue size and
reoffering yields used data series covering nine years
and measured size in current dollars. Thus, they are
subject to the criticisms discussed above.
Benson,
Kidwell, Koch, and Rogowski [5] corrected for the
trend in size by measuring
it in price-deflated
(i.e.,
40 Tanner

[25]

pointed

out this

problem

with

Kessel’s

study.
41 This would seem to imply that the net effect of issue
size on underwriter
spread is positive.
However,
the
behavioral interpretation
of the result is not clear because
issue size is thought to affect underwriter
spread both
directly and indirectly through its effect on the number

of bids (see footnote 39).
34

“real”) dollars. They tested a quadratic specification
for issue size and concluded that increased size reduced reoffering
yield up to a certain point ($26
million in 1972 dollars) after which further increases
in size raised reoffering
yields.
As noted, they
attributed
this pattern to a combination
of marketability and supply effects. Broaddus and Cook [8],
who used data covering a period of two years, tested
various forms of issue size and found that the quadratic specification worked best.
In summary, even though issue size has been used
as an explanatory
variable in 22 regression studies of
tax-exempt
yields, there is no generally
accepted
theory of how issue size should affect reoffering
yields. A common and perhaps intuitively
plausible
belief is that issue size is a proxy for marketability
and that consequently
it should have a negative effect
However, none of the regreson reoffering yields.
sion studies have provided any evidence of the link
between issue size and bid-ask spreads.
Studies
using reoffering
yield as the dependent
variable
found a negative relationship
between size and yield
but these studies are subject to the criticism that they
measure size in nominal dollars over an extended
period of time. One study dealt with this problem by
measuring
size in constant
dollars and found increases in issue size exert a downward
impact on
yields up to a point and an upward effect thereafter.
Revenue

versus

General

Obligation

Bonds

Almost all of the studies using data for both general obligation
and revenue bonds have included a
revenue bond dummy variable to capture any systematic difference between the yields on general obligation and revenue bonds not captured by the other
explanatory
variables.
In all cases, the coefficient of
the revenue bond dummy variable has been positive
and significant.
Explanations for the Positive Relationship Between
Revenue Dummy Variable and Yields
Virtually all
the studies that have included a revenue bond dummy
variable fail to specify the predicted effect of this
Consequently,
the
variable on tax-exempt
yields.
explanations
are basically ad hoc attempts to explain
a statistically
significant
result.
Three explanations
have been offered for the positive coefficient of the
revenue bond dummy variable.
Hopewell and Kaufman [16] argued that the positive effect of revenue
status on yields reflects a perception on the part of
investors that revenue bonds carry a higher default
risk than general obligation bonds of equal rating.
Broaddus and Cook argued that an equally plausible

ECONOMIC REVIEW, MAY/JUNE 1982

explanation
is that the revenue bond coefficient reflects the relatively poorer marketability
of revenue
bonds.
Revenue bonds generally have poorer secondary markets and higher bid-ask spreads than
comparable
(in size and rating)
general obligation
bonds.42
Investors
would therefore be expected to
demand a somewhat higher yield on revenue bonds in
compensation
for the greater loss experienced if those
bonds are sold prior to maturity.
Since none of the
tax-exempt
yield regressions
include a variable that
directly captures the effect of marketability
on yield,
the revenue bond dummy variable may capture some
of this effect. Finally, Silber [48] has suggested that
the revenue bond dummy variable picks up the effect
on yields of bank ineligibility
to underwrite
most
revenue bonds.
Regression Results
Ten of the regression studies
included a revenue bond dummy variable and all of
these reported a positive and statistically
significant
coefficient.
Six used NIC or TIC as the dependent
variable and four used reoffering yields (see references).
There is no systematic
difference in the
magnitude of the coefficient between the two sets of
studies.
Kessel [17] estimated that revenue status raised
reoffer yields, approximately
8.5 basis points.
Although Kessel offered no explicit rationale for the
inclusion of the revenue bond dummy variable in his
specification,
Silber argued that the coefficient captures a direct effect of bank ineligibility
on reoffer
yields.
This interpretation
is possible since Kessel
used pre-1968 data, when virtually all revenue bonds
were ineligible.
The coefficients of the revenue bond dummy variable in the Broaddus-Cook
regressions,
all of which
are significant, indicate that revenue status increases
yields from about 6 basis points at the 5-year maturity to about 10 basis points at the longer maturities. These results are quite close to Kessel’s estimate.
The coefficients of the revenue bond dummy variable
in the other studies were generally higher, in some
cases over 20 basis points [15, 19, 20, 21].
In summary, it seems clear that the yields on revenue issues are systematically
higher than comparably
rated general obligation bonds.
However, it is not
clear whether this reflects (1) default risk not cap-

42 This statement
was confirmed by discussions
with
underwriters.
Also, some indirect evidence on this point
comes from a 1973 Municipal Finance Officers Association Survey [39], which reported that a new revenue
issue has an average marketing
cost per $1,000 about
twice as large as that of a new general obligation issue
($3.84 versus $1.98).

tured by the rating category dummy variables,
poorer marketability
of revenue bonds, or (3)
ineligibility
to underwrite
most revenue bonds.
mately, the only way to answer this question
include as explanatory
variables more explicit
sures of default risk, marketability,
and bank
bility.43
Segmentation

by Class

(2)
bank
Ultiis to
meaeligi-

of Bond

Benson, Kidwell, Koch, and Rogowski [5] argued
that because of regulation and liquidity needs, banks
purchase
primarily
high-quality
tax-exempt
bonds
and that, consequently,
changes in commercial bank
demand for tax-exempt
bonds should influence the
relationship
between the yields on high- and lowrated bonds.
To test this theory they ran the standard tax-exempt yield regression model with the ratio
of bank net purchases
of tax-exempt
securities
to
total net issues as an additional explanatory
variable.
The regression
supported their hypothesis
that increases in commercial bank demand for tax-exempts
increase the differential
between the yield on lowrated bonds and the, yield on high-rated
bonds.
Using the same type of reasoning,
Kidwell and
Koch [19] argued that the markets for general obligation and revenue bonds might be segmented.
To
test their hypothesis they included, in addition to the
revenue bond dummy variable, a number of terms
constructed by multiplying
the revenue bond dummy
variable by other variables.
They concluded that the
differential between the yields on revenue bonds and
those on high-grade
general obligation
bonds increases as commercial banks increase their purchases
of net tax-exempt
securities and as the supply of
revenue bonds increases relative to the total supply
of new tax-exempt
bonds. They also concluded that
the spread between revenue and general obligation
yields varies inversely with the GNP growth rate.
Summary

and Conclusions

This article has surveyed the evidence from 25
regression studies on the determinants
of individual
tax-exempt
bond yields. There is general agreement
among the studies as to why coupon, call provision,
and default risk variables should affect tax-exempt
bond yields.
The variables used in the regressions
fit the underlying
rationales fairly well, although the
complexity of call price schedules has made it difficult, if not impossible, to devise an accurate proxy

43 In the case of bank eligibility
been done. See Section III.

FEDERAL RESERVE BANK OF RICHMOND

that has in some

cases

to capture call price effects. The regression results
for these variables are fairly good.
Many studies,
however, have had difficulty estimating the effect of
call risk for the reasons discussed earlier.
The relatively few studies that have included regional market conditions variables have found them
to have the predicted effect on tax-exempt
yields.
The basic idea underlying the inclusion of these variables is that because investors inside and outside a
region face different taxes, costs, and regulations,
yields within a region can move over a limited range
in response to regional market conditions
without
inducing interregional
arbitrage.
This theory, while
plausible, has not been given a rigorous theoretical
formulation.
Hence, the specific choice of variables
used to test it has been somewhat arbitrary.
The
same limitation
applies to testing for the effects of
segmentation
by class of bond.
Also, the rationale
for this type of segmentation
seems to be weaker
because it does not rely on differential
taxes and
information
costs.
The regression results for the underwriter
competition variables, especially the number of bids, are
remarkably consistent across studies. There is strong
disagreement,
however, on the ability of search theory
to explain the correlation between these variables and
tax-exempt yields. In particular, a number of recent
studies (especially
[40, ,41]) have argued that the
underwriter
competition
variables
are picking up
differences in intrinsic quality and marketability
not
captured by other variables in the regression,
The
basic problem is that the search theory explanation
in its present state does not clearly link the underwriter competition variables to aggregate underwriter
search.
The problem with the issue size and revenue bond
dummy variables is that they are not clearly related
to the theories that have been used to justify their
inclusion in tax-exempt yield regressions.
As noted,

ECONOMIC

the appropriate
include

solution

variables

underlying

theory.

point would
marketability.
spread

to this problem

that

are

be a variable
The
measure

that

logical

would be to

Most important

in the secondary

an accurate

directly

to the

from this standaccurately

choice

market.44

is the

reflects
bid-ask

In the absence

of marketability,

the interpre-

tation of the coefficients

of issue size and the revenue

bond

(and,

dummy

underwriter

variable
competition

for

variables)

that

matter,
will

the

remain

clouded.
In conclusion,
the regression
studies surveyed in
this article provide much information
on the determinants of individual tax-exempt
bond yields.
In a
couple of instances further evidence might be obtained
cation
seems
shed
bond

through the inclusion or more careful specifiof a variable.
More generally,
however, it
unlikely that additional regression analysis will
new light on the determinants
of tax-exempt
yields. Rather, the need is for a more rigorous

and clearer articulation
of the theories underlying
the
variables employed.
Most important
in this regard
is a theory convincingly
linking the underwriter
competition variables, especially the number of bids, to
aggregate search.
Also, in the case of market segmentation by region (or by class of bond) it would
be desirable to have a more rigorous theory of how
heterogeneous
investors
confronted
with different
taxes, costs, and regulations can lead to a situation in
which regional market conditions affect the relative
yields on tax-exempt
bonds.

44 There is no bid-ask spread for new issues but a reasonable proxy would be the bid-ask spread on other outstanding bonds of the issuer or the bid-ask spread of the
new issue after it begins to trade in the secondary market.
The difficulty
here is that there is no comprehensive
published
data on bid-ask spreads
in the tax-exempt
market, so this data would have to be gathered through
the dealer community.

REVIEW, MAY/JUNE

1982

References with Tax-Exempt

Bond Yield Regressions

References with Tax-Exempt

Bond Yield Regressions

(cont.)

Other References
39.

Municipal
Finance
Officers
Association.
Costs
Involved in Marketing State/Local
Bonds: Survey.
Chicago:
Municipal
Finance
Officers Association,
September
1, 1973.

40.

Final Report and Recommendations
of the Ad Hoc
Subcommittee
on Full Insurance
of Government
Deposits.
September
4, 1979. (Mimeographed.)

“Competition
and Borrowing
Cost
Mussa, Michael.
in the Municipal
Revenue Bond Market:
An Appraisal of the Evidence.”
Securities Industry
Association, January
1979.

41.

Haywood,
Charles
F.
“The Pledging
of Bank
Assets:
A Study of the Problem of Security
for
Public Deposits.”
Chicago : Association
of Reserve
City Bankers, 1967.

“Interest
Savings from Bank Underwriting of ‘Municipal Revenue Bonds:
What Have
We Learned from the Recent Debate.”
University
of Chicago:
January
1980. (Mimeographed.)

42.

“Other Cities Suffer Pains in Bond Market from
New York Woes.”
Wall Street Journal, June 19,
1975, p. 1.

43.

Peterson, John. Changing Conditions in the Market
for State and Local Government
Debt:
A Study
Prepared for the Use of the Joint Economic Committee of the United States.
Washington,
D. C.:
Government
Printing
Office, April 16, 1976.

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