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THE FED’S MANDATE:
HELP OR HINDRANCE?
Address by
ROBERT P. BLACK
President, Federal Reserve Bank of Richmond
to the
Virginia Bankers Association
Ninety-first Annual Convention
June 15, 1984

It’s a genuine pleasure to be with you today. to
discuss a few of the major problems that are confronting us at present in, the conduct of monetary
policy. I’m well aware that a discussion of a contentious topic like monetary policy may be somewhat
out of keeping with the rather idyllic setting of this
convention. At the same time, this secluded spot,
well removed from the hectic pace of everyday business life, may well be an appropriate setting for a
brief consideration of some of the broader, longer run
issues with which we’re grappling at the Fed, as
distinct from the immediate problems that receive so
much attention in the press. While I plan to mention
some of our present difficulties in passing, I want to
focus more specifically on some of these broader
issues this morning.
The Present Setting
On the surface, I suppose one could argue that the
immediate economic picture is pretty bright. After
all, we are presently in the sixth quarter of a vigorous
economic recovery. The early stages of the upswing
were powered by strong increases in both residential
construction and consumer spending. These sectors
are still reasonably buoyant, and they are now being
supplemented by increased business spending on new
plant and equipment and on inventories. The main
drag on the recovery to date has been the record
deficit in our merchandise trade balance, but even
with this deficit real growth in the economy has proceeded at an average annual rate of 6.7 percent since
the recession bottomed out in late 1982: Further, and
probably best of all, during the last two years we’ve

enjoyed the lowest sustained rate of, inflation since
the early 1970s. Indeed, my instincts tell me that
this apparent progress on the inflation front is one of
the reasons the recovery in business activity has been
so much stronger than almost anyone expected it to
be a year or so ago.
Despite this rather favorable scenario, I’m sure I
don’t have to tell you or any other knowledgeable
observers that all is not well. Since the beginning of
this year, there has been a growing uneasiness in the
business and financial communities. Especially in
recent weeks, expectations appear to have taken a
distinct turn for the worse. There are a number of
contributing factors. The discouraging failure of
Congress to come to grips with the problem of the
Federal deficit is a key element in the backdrop.
Against that backdrop the very strength of the economic advance itself becomes something of a problem,
generating as it does large increases in private credit
demands and fears of a collision between private, and
government, demands that could put sharp upward
pressure on interest rates. The potential implications
of such a collision for the international debt situation,
for the stability of the banking industry and the international financial system, and for the beleaguered
domestic thrift industry have become a matter of
increasing concern to the financial community in
recent weeks.
But most serious of all, I think, is an apparent
escalation of inflationary expectations with all its
adverse effects on financial markets. Such an expectations pattern tells us that public confidence in our
ability to cope with our problems without causing a

FEDERAL RESERVE BANK OF RICHMOND

3

resurgence of inflation is at a low ebb. Sophisticated
observers of financial markets know, as we in the
Fed know, that inflation is not a solution. Indeed it
can be a source of only more vexing, more serious
problems that could cripple our financial markets.
Nevertheless, there appears to exist an undercurrent
of fear that political and other pressures generated in
this election year climate will be too strong for the
Fed to resist.
This troubles me greatly. After all, Chairman
Volcker and others of us in the System have said
repeatedly that the Fed attaches an extremely high
priority to sustaining and extending the recent progress in reducing inflation. And I think I’m correct
in my impression that most observers, despite critical
comments, believe that our intentions are firm and
honest. But despite our much heralded “independence,” many market professionals and others believe
it will be impossible for the Fed to resist strong election year pressures to ease policy even at the risk of
reigniting inflation.
Public skepticism on this point can, perhaps, find
some support in past history, but I don’t think it captures the essence of the problem we at the Fed face
in trying to design and implement an effective antiinflationary program. The real problem, as I see it,
is not the limitations of the System’s ability to withstand partisan pressure or the ability of any of its
high officials to withstand such pressures. None of
us who choose central banking as a career expect to
win popularity contests. Rather the difficulty is the
nature of the mandate that has been given to the Fed
by the public through its elected representatives. I
have great respect for the collective wisdom of the
American people, but I have to acknowledge that I
do not believe the public has acted particularly wisely
or carefully in setting objectives for the Fed. I’d like
to spend the remainder of my time embellishing this
theme just a little bit. And in doing so I want to
emphasize that all of these views are my own personal
judgments. They do not necessarily reflect the views
of anyone else in the System.
What is the Fed’s Mandate?
Suppose I were to ask you: What is the Fed’s
mandate in the area of monetary policy? That is,
exactly what is it that the public expects the Fed to
do with monetary policy? I’ll bet that if I went
around this room and put that question to each of
you individually, I would get a wide variety of
answers. Some would probably say our principal
task is to hold inflation down. But others would
4

say it is to keep the level of real business activity
and employment high, or to prevent interest rates
from rising too much, or to keep the dollar from
becoming either too weak or too strong in the foreign
exchange markets, and so forth. Who would be
right? Well, in a sense, all of you would be right
because our mandate, in its present form, essentially
embraces all of these objectives. Section 2A of the
Federal Reserve Act, as amended, requires the Fed
“to promote effectively the goals of maximum employment, stable prices, and moderate long-term
interest rates.” Moreover, in carrying out monetary
policy, we are to "[take] account of past and prospective developments in employment, unemployment,
production, investment, real income, productivity,
international trade and payments, and prices.”
You don’t have to be a genius to know that we at
the Fed do not possess the means to achieve all of
these objectives simultaneously and singlehandedly.
In other words, the Fed’s present mandate is unrealistically general and sweeping, particularly if viewed
as a set of objectives to be achieved in the short run.
In practice, this has forced the Fed to choose among
competing objectives, or at least to make choices
regarding the weight to give any particular objective
in formulating monetary policy in the short run. At
first glance, this ability to choose among objectives
and to vary these choices over time might seem to
increase the Fed’s flexibility and hence its independence and its power. In my judgment, however, it
does just the opposite: it subjects the Fed to a relentless barrage of pressure from competing interest
groups trying to badger the Fed into giving greater
weight to their respective points of view in setting
monetary policy. Since many of these groups can
argue with some justification that the Fed is mandated to achieve their favored objectives, such pressures can, in our type of political system, paralyze
any effort of the Fed to set an attainable longer run
objective and stick to it.
I cannot emphasize this point too strongly. Far
from enhancing the Fed’s independence and insulating it from partisan pressures, it seems to me that the
lack of specificity in the Fed’s current mandate serves
to intensify these pressures, to reduce our real independence, and to prevent us from achieving any particular objective as effectively and consistently as we
otherwise might. In particular, the flexibility we are
thought to possess almost inevitably leads us to give
substantial weight to current economic and financial
conditions in deciding on current policy actions. Certainly the System should be aware of the current state
of the economy and take account of any special prob-

ECONOMIC REVIEW, JULY/AUGUST 1984

an excessive preoccupation with
current conditions can lead to policy
actions that destabilize the economy
rather than stabilize it . . . .”
...

lems in financial markets in setting policy. But an
excessive preoccupation with current conditions can
lead to policy actions that destabilize the economy
rather than stabilize it because of the long and unpredictable lags between the time policy actions are
taken and the point at which they affect particular
economic variables.

ment in living standards we would otherwise be able
to attain.
But these points alone are not sufficient to warrant
choosing price stability as the prime objective of
monetary policy. Someone else could always argue,
with perhaps equal conviction, that high rates of
unemployment are even worse than high rates of
inflation, and that if it came to a choice between the
two, the Fed should give greater weight to reducing
unemployment. It would be very difficult-if not
impossible-to resolve this kind of debate. With this
in mind, I have a more fundamental reason for
choosing price stability as the principal and maybe
even the exclusive objective of monteary policy:
namely, that price stability is the only feasible objective for monetary policy.

A Price Stability Mandate
If you’re willing to buy my argument that the allinclusive character of the Fed’s present mandate is a
problem, the obvious solution to the problem is for
the public to specify the objective of monetary policy
more narrowly and more precisely. That would mean
making a choice among competing objectives, and
obviously that choice would have to be made by the
public through the legislative process. If it’s not too
presumptuous, however, I would like to tell you what
by choice of an objective would be if the choice were
mine. My choice would be price stability, and what I
really have in mind here is a permanent return to a
very low rate of inflation. Indeed, I would go so far
as to set a goal of no inflation, after making allowance
for the effect of quality change and the like on measured inflation. Once the inflation genie gets out of
the bottle, it is very difficult to get it back in again.
You may reasonably ask why I would choose price
stability as the major objective of monetary policy
rather than some other desirable objective such. as
high employment or low interest rates. There are
several reasons. At one level, I would choose price
stability because I believe that inflation and the forces
that have created it are directly or indirectly responsible for much of the deterioration in our nation’s
economic performance over the last 20 years or so.
Inflation disrupts the. functioning of our financial
markets and discourages saving and investment. It
introduces noise into market price signals. Its volatility increases the risk associated with particular
business decisions and makes planning difficult. It
distorts incentives and leads to serious inefficiencies
in the allocation of resources. These distortions and
inefficiencies prevent us from achieving the advance-

“ . . . price stability is really the only

objective that it is feasible for the Fed to
try to achieve with monetary policy.”

This last point-that price stability is the only
feasible objective for Fed policy-is extremely important in my opinion, so let me just flesh it out very
briefly. There was a time not very long ago when
economists and others believed it was possible to
manage economic conditions very closely through
monetary and fiscal policy. The intellectual basis for
this belief was the famous Phillips Curve, which suggested that there was a trade-off between inflation
and unemployment that could be exploited profitably
by policymakers. In essence, it was thought that
policymakers could choose any particular combination of inflation and unemployment along the Phillips
Curve. If they were willing to accept a little more
inflation, they could get a little less unemployment
and vice-versa. This approach to policy and the
confidence in the manipulative power of monetary
and fiscal policy it presupposed have come to be
known as “fine-tuning.”
Over the course of the last 20 years or so, this
view of policy and the Phillips Curve doctrine that
underlies it have been subjected to an intensely critical examination by a number of leading monetary
economists. In the course of this examination, several
important ideas have been developed that seriously
challenge the validity of the fine-tuning approach.
Let me just mention a couple of these ideas very

FEDERAL RESERVE BANK OF RICHMOND

5

quickly. Like all really powerful ideas in economics,
their essence can be readily grasped by anyone.
The first is the so-called natural rate hypothesis.
What this says is that if there is in fact any trade-off
between inflation and unemployment, it is not between actual inflation and unemployment but between
that part of inflation that is unanticipated by the
public and unemployment. As long as inflation is
fully anticipated, the unemployment rate will fluctuate around its natural rate as determined by such
basic economic factors as the characteristics of the
labor force and the state of technology. For example,
if an effort is made to stimulate employment through
policies that are likely to increase inflation, and if the
public in general and workers in particular foresee
this increase in inflation, workers will demand an
increase in wages to compensate for the expected
increase in inflation, and the policies won’t cause any
permanent increase in employment. The implication
of the natural rate hypothesis for policy, then, is that
employment can be systematically fine-tuned through
monetary and fiscal policy only if the public systematically and persistently misestimates the effects of
these policies on the rate of inflation.

“ . . . the natural rate idea says that you

can fine-tune the economy through fiscal
and monetary policy only if you can fool
most of the people most of the time, and
the rational expectations idea says you
can’t do that.”

The second idea is what is known as the rational
expectations hypothesis. In the present context, this
hypothesis holds that the public, as a whole, is intelligent and perceptive and does not systematically misestimate the inflationary impact of monetary and
fiscal policies. In short, the natural rate idea says
that you can fine-tune the economy through fiscal
and monetary policy only if you can fool most of the
people most of the time, and the rational expectations
idea says you can’t do that.
The implications of these ideas for ‘monetary policy
are both obvious and profound. In essence, they say
that the Fed cannot influence real economic conditions like employment and production and real rates
of interest in any predictable way over time. This
leaves price stability as the only feasible objective for
monetary policy. I should point out that even though
6

the set of ideas I’ve just outlined and their implications for policy are not yet universally accepted, they
are embraced by a large and growing number of
economists, and I personally find them very persuasive. I might also note that they are not really
entirely new ideas but, like so many seemingly new
concepts, have roots in the classical economics that is
the foundation of our free market system.
The Matter of Implementation
I need to touch just briefly on one final point,
and that’s the matter of implementation. If one is
willing to embrace price stability as the main objective of Fed monetary policy, what’s the best way to
achieve it? In principle there are several ways that
we might go about it. For example, there have
been suggestions recently that the Fed might set
explicit numerical targets for the price level and
then react in some fairly mechanical way to deviations of actual price movements from these targets.
There might be some advantages to this kind of
procedure, but I doubt seriously that it’s the best
approach given the very long and variable lags in the
effect of Fed policy on the price level.
More fundamentally, it is not at all clear to me
that some kind of reactive mechanism is necessary.
We all know that the one sure way for the Federal
Reserve to promote price stability is to reduce, slowly
but surely, the rate of growth of the nation’s money
supply to a steady noninflationary rate and keep it
there. With this in mind, my own feeling is that the
most effective way we could attain a price stability
objective would be to rededicate ourselves to the
monetary targeting procedure we already have in
place and to take some steps to strengthen that procedure. In particular, I think there’s much to be said
for the idea of setting targets not only for the current
year but for several years into the future. Multi-year
targeting would permit the Fed to put forward an
explicit longer run strategy for achieving price stability, and it would eliminate the technical problem
known as “base drift” that is an important defect
of the current one-year targeting procedure. (This
problem arises because we always base each new
year’s target on where we ended the preceding year,
even if we missed the preceding year’s target by a
substantial amount.)
Further, I think we need to focus specifically on
controlling over the long run the measure of the
money supply known as M1 and reduce the attention
we give to broader measures of money such as M2
and M3 and aggregate measures of credit. I am well

ECONOMIC REVIEW, JULY/AUGUST 1984

aware of the debate that is going on among tech-,
nically oriented monetary specialists over whether or
not financial innovations like money market funds
and the ensuing deregulation in banking markets have
affected the demand for the various components of
M1 in an unpredictable way and therefore reduced its
usefulness as a target for monetary policy. The evidence I’ve seen suggests to me that for now M1 is
still the best target among the various alternatives
available. I don’t think there is any serious reason to
doubt that a policy of gradually reducing M1 growth
to a noninflationary rate would allow us to achieve
price stability without any excessive risk to the real
economy. Having said this, let me also say that if it
becomes evident in the future that some monetary
measure other than M1 would be a better target for
policy, I wouldn’t hesitate to change. My preference
for the use of M1 as a target is entirely practical
rather than doctrinal.

". . . the Fed’s mandate, as it is presently
structured, is so broad and general that
its value as a practical guide to monetary
policy is limited and at times may actually prevent policy from contributing as
much to our economic welfare as it otherwise might.”

Concluding Comments
I realize that I’ve covered a fair amount of ground
this morning, so let me just review very summarily
the main points I’ve tried to make. First, a case can
be made that the Fed’s mandate, as it is, presently
structured, is so broad and general that its value as a
practical guide to monetary policy is limited and at
times may actually prevent policy from contributing

as much to our economic welfare as it otherwise
might. Second, if the public should decide to narrow
the Fed’s mandate and make it more specific, the best
choice of a more limited objective for Fed policy in
my view would be price stability. Indeed, there are
very solid reasons to believe that price stability is
really the only objective that it is feasible for the Fed
to try to achieve with monetary policy. I might add
as a footnote here that restricting our mandate to
price stability should go some distance toward satisfying those of our critics who complain that the Fed
cannot be held accountable for its actions, since it
would not be unreasonable to hold the Fed accountable, for the behavior of the price level over a period
of, several years. Nor should we in the Fed fear such
accountability since our assignment would be both
feasible and unambiguous. Third and last, if price
stability were our goal, my own feeling is that we
could best achieve it by slowly but surely reducing
the growth of M1 to a noninflationary. rate under
present circumstances, but I’m enough of a pragmatist to have absolutely no objection to switching to
some other monetary handle if it is ever demonstrated
that something else has become superior to M1.
I hope you will find these comments useful as food
for thought. You in the banking industry are closer
to monetary policy than. people in most other industries, and we depend on you to consider these kinds
of questions carefully and critically and let us know
your views. I don’t claim that the changes I’ve outlined would solve all of our nation’s economic and
financial problems. Far from it. Some of these problems have very deep roots, and they Will not be resolved easily or quickly. Nonetheless, I am convinced
that the changes I have recommended would increase
our ability at the Fed to contribute to the strength
and stability of the economy. In a democracy like
ours, public institutions are guided ultimately by the
marching orders they receive from the electorate. If
we are to do our job well, it is essential that these
instructions be as clear and unambiguous as possible.

FEDERAL RESERVE BANK OF RICHMOND

7

THE TAX EFFECT, AND THE RECENT BEHAVIOUR
OF THE AFTER-TAX REAL RATE: IS IT TOO HIGH?
Yash Mehra*

I.
INTRODUCTION

Recent years have witnessed very high and volatile
interest rates. This has stirred a debate among analysts as to whether observed interest rates are high
by historical standards. Some analysts, focusing on
the before-tax real rate, argue that if the observed
nominal interest rate is corrected for the effect of
expected (or actual) inflation, the ex ante (or ex
post) real rate has been very high in recent years.
Other analysts, however, note that it is also important
to consider the effect of taxes on the behaviour of the
nominal interest rate. Since real spending decisions
in the economy are based on the after-tax real rate,
it is more appropriate to focus on the behaviour of
this latter real rate. Proponents of this view argue
that the after-tax real interest rate observed since
1980 does not appear to be too high.1
At the center of the debate is an empirical issue of
whether tax effects are fully recognized by investors.
If the nominal interest rate does fully adjust to
reflect the presence of an effective marginal tax rate
on interest income, then it is more appropriate to look
at the behaviour of the after-tax real interest rate.
The theoretical proposition that nominal interest rates
adjust to reflect the presence of taxes on interest
income is intuitively appealing. As put by Michael R.
Darby (1975), Martin Feldstein ( 1976) and Vito
Tanzi (1976), the proposition states that, ceteris
paribus, nominal interest rates will rise during an
inflation by an amount which exceeds expected inflation enough to compensate lenders both for their
expected loss of capital and for the taxation of interest income. Though this proposition is plausible,
* Economist and Research Officer, the Federal Reserve
Bank of Richmond. The views expressed are those of the
author and do not necessarily reflect the views of the
Federal Reserve Bank of Richmond or the Federal
Reserve System. Tom Hahn provided excellent research
assistance.
1

See “Rates Through Contrarian Eyes” in New York
Times, October 9, 1983, page F29.

8

early empirical work failed to provide any firm empirical support for it. More recently, however, Joe
Peek (1982) and Robert Ayanin (1983) were. able
to produce empirical evidence supporting the presence
of the tax effect on the nominal interest rate.
Despite recent empirical work implying that investors tend to adjust nominal interest rates for the
presence of taxes on interest income, the question of
whether nominal interest rates rise sufficiently to
fully insulate expected real rates from the presence
of an effective marginal tax rate on interest income
has not been adequately investigated. This is an
important issue because if nominal interest rates do
not fully adjust, then the existence of the income tax
on interest income will be another important source
of variations in the after-tax real rates of interest.
This paper has two objectives. The first is to
provide some further evidence supporting the existence of the tax effect on the nominal interest rate.
In particular, the issue regarding whether nominal
interest rates need to be fully adjusted for the presence of the effective marginal tax rate on the interest
income is investigated. More specifically, the paper
develops and applies a simple procedure to test this
issue. The second objective is to focus on the behaviour of the after-tax expected short-term real rate.
If one were to fully adjust the short-term nominal
interest rate for effects of taxes and expected inflation, would the level and range of the real rate
observed in recent years be high relative to the level
and range observed during the period 1952-1979?
This question is answered by deriving an after-tax
expected real rate series over the period June 1952 to
June 1983. In addition, to explain movements in the
level of this short-term real rate over time, an empirical model of interest rate determination is presented and estimated.
The remainder of this paper is organized as follows: Section II reviews the early empirical work
that investigated the presence of the tax effect and
led to the inference that people have not considered
the taxation of interest in determining the nominal

ECONOMIC REVIEW, JULY/AUGUST 1984

interest rate. It is argued that the conclusion regarding investor’s ignorance of taxes could have been
due to faulty interpretation of the econometric evidence. Section II also contains a discussion of the
test procedure used by economists to infer the presence of the tax effect. Section III contains a discussion of the specific interest rate model that underlies
the empirical work reported in this paper. Section IV
presents and discusses various empirical estimates
that underlie various conclusions. Section V contains
main conclusions. Finally, the Appendix reviews and
illustrates the J-test of non-nested regression models
-a statistical procedure used in the previous work to
test the presence of the tax effect on the nominal
interest rate.

BACKGROUND

The Fisher Equation and the Tax Effect
Since the studies of Darby (1975), Feldstein.
(1976) and Tanzi (1976), economists have modified
the standard Fisher relationship to incorporate the
effects of taxation of’ interest income. The standard
formulation of the Fisher equation is

where i is the nominal interest rate, r is the real rate,
This equation
postulates that given r, an increase in the expected
rate of inflation leads to an equivalent increase in the
nominal interest rate. However, since interest is
taxed, in order to leave the after-tax real interest
rate unchanged we must have

or

where r* is the after-tax real rate and T is the marginal tax rate on the interest income. Equation (2b)
tells us that the size of the theoretical coefficient on
the expected inflation rate is (1/(1-T)), and it
exceeds unity for a nonzero tax rate. That is, in the
presence of taxes on interest income, the nominal
interest rate should rise during an inflation by an
amount which, exceeds expected inflation sufficiently
to compensate lenders both for their loss of capital
and for the taxation of interest income.
It was this implication of equation (2b) that
formed the basis of the early empirical work looking

for the existence of the tax effect in the form of a
greater-than-unitary coefficient in front of the expected inflation variable.2 Moreover, in order to test
whether nominal interest rates rise enough to fully
insulate real rates from the effects of expected inflation and taxes, economists expected to find the estimated coefficient to equal the value implied by
(1/(1-T)); if the marginal tax rate on the interest
income equaled 32 percent, it implied a coefficient of
approximately 1.47, i.e., (1/(1-.32)).
However, more often than not the estimated coefficient on the expected inflation variable was found to
be close to or less than one. Initially, these empirical
findings, were interpreted as providing little or no
firm empirical support for the proposition that people
have considered the taxation of interest in determining the nominal interest rate. For example, Vito
Tanzi interpreted his estimated coefficient on expected inflation to be evidence that individuals “. . .
have failed to see through the fiscal veil and thus have
suffered from fiscal illusion” (p. 20). But the recent
contributions of Levi and Makin (1978), Melvin
(1982), and Makin, and Tanzi (1983) imply that a
unitary or less-than-unitary response of the nominal
interest rate to the expected inflation rate is not inconsistent with the presence of the tax effect. The
basic point is that the Fisher equation is a reduced
form relation. If we derive the Fisher equation from
an explicitly specified structural macro model, the
coefficient’ in front of the expected inflation variable
is a function of several structural parameters, and it
Gill be equal to (1/(1-T)) only under specific restrictions on those parameters. In the absence of
such restrictions, the response of the nominal interest
rate to expected inflation is expected to be less than
(1/(1-T)). (Section III demonstrates this in the
context of a specific macro model that underlies the
empircial work reported here.)
In fact, a more general analysis of the channels
through, which expected inflation may influence the
nominal interest rate suggests that it is very difficult
to infer the presence of the tax effect by ‘looking at
the size of the estimated coefficient on the expected
inflation variable in the interset rate equation based
on equation (2b). The coefficient in front of the
expected inflation variable may reflect, among other
things, the influence of all or some of the following:
(i) the Fisher effect, whereby the nominal interest
rate rises by the full amount of a rise in expected
inflation; (ii) the tax effect, whereby the nominal
2

See Cargill (1977), and Tanzi (1980).

FEDERAL, RESERVE BANK OF RICHMOND

9

interest rate must rise by more than the rise in expected inflation to maintain a constant expected aftertax real return; (iii) the portfolio effect, whereby a
rise in expected inflation, by raising the opportunity
cost of holding money, causes people to shift from
money to interest-bearing financial assets thereby
restricting the rise in the nominal rate; and (iv) the
Feldstein-Summers effect, whereby a rise in anticipated inflation depresses the expected after-tax profits and causes investment to fall. This latter effect,
like the portfolio effect, tends to depress the real rate.
In sum, tax-effects move the coefficient in front of
expected inflation above unity, while the portfolio
effect and the Feldstein-Summers effect both push it
below unity. The net impact of all these on the coefficient in front of expected inflation is uncertain. 3
Hence the size of the estimated coefficient in front of
the expected inflation proxy variable can not be used
to reveal the presence or the degree of “fiscal illusion.”

expected real returns are equalized on the after-tax
basis. These considerations imply that in equilibrium, expected real returns must satisfy the following
relationship :

nominal dollar rate of return on the alternative use of
funds; Ta = marginal tax rate on income from the
alternative use of funds. We can also express equation (3a) in the following way :

The equations (3a) and (3b) imply that even though
after-tax expected real returns are equalized on the
alternative uses of funds, nominal returns differ due
to the interaction of differential tax rates and the
inflation premium. If we augment the basic Fisher
equation (1) with this “tax-differential” term, we
get the following equation :

The Fisher Equation and the Magnitude
of the Tax-Adjustment
or
Even if one focuses on the simple Fisher equation
as formulated in equation (2b) and assumes the
existence of the full Fisher effect, a general analysis
of the tax effect on nominal interest rates suggests
that there is no reason the market will always adjust
the nominal interest rate for effects of expected inflation and income taxes by the full amount given by
(1/(1-T)). Milton J. Ezrati (1982) points out
that the tax effect on interest rates depends upon the
tax status of market participants and the tax burden
imposed on alternative uses of funds. The taxadjusted inflation premium for nominal interest rates
will equal (1/(1-T)) as suggested in equation (2b)
only in the special case where the tax rate on alternative uses of funds equals zero and the tax rate on
interest income is greater than zero.
In order to explain these results, let us explicitly
discuss the alternative investment available to market
participants. This alternative investment option pays
some rate of return that can be compared with the
interest rate. Markets are in equilibrium when the
after-tax expected real returns are equal on these
investment alternatives.4 When these returns are not
equal, wealth-maximizing investors will reallocate
funds among these investment alternatives until the
3

See Makin and Tanzi (1983).

4

To be realistic, these perceived returns should be adjusted for risk.

10

where 1 in (4b) can be viewed as the inflation
premium coefficient without tax considerations and
c = the tax-differential adjustment = ((T-Ta)/
(1-T)(1-Ta)).
From equation (4a), it is clear that if the two tax
rates are equal (T=Ta), or if holders of funds are
entirely tax exempt (T = Ta = 0), then the tax
differential term is zero, and there is no tax effect in
response of the nominal interest rate to expected
inflation. This tax-differential term becomes positive
when returns on the alternative uses of funds are
taxed at a lower rate than returns on financial securities. We will get the tax-adjusted basic Fisher equation (2b) in the case where Ta equals zero, and T is
greater than zero; in this special case, the taxadjusted inflation premium equals (1/(1-T)).
In general, not all market participants in securities
markets are tax exempt. There are taxless options
open to individuals in “consumption” and to many
investors in the purchase of tax-free securities ; in
these cases, the tax rate on alternative investments
falls short of the rate applied to interest income.
Investment in real plant and equipment also offers
relative tax breaks accorded by accelerated depreciation schedules, investment tax credits, etc. In view
of these considerations, the estimated coefficient in
front of the expected inflation variable even in the

ECONOMIC REVIEW, JULY/AUGUST 1984

simple Fisher equation (2b) may turn out to be
smaller than (l/(1--T)). But that result in itself
will not be indicative of the presence of “fiscal
illusion”.
An Alternative Test of the Presence
of the Tax Effect
In view of the discussion in the previous two
sections, it is clear that the test based on the magnitude of the estimated coefficient in front of the expected inflation variable could not be relied upon to
reveal the presence of the tax effect on the nominal
interest rate. Aware of this difficulty, Peek (1982)
and Ayanin (1983) used tests not contingent on the
magnitude of the estimated coefficient in front of the
expected inflation variable. Peek finds evidence for
the tax effect by showing that the forecasting performance of the nominal interest rate equation estimated to allow the full adjustment of the nominal
interest rate for the presence of taxes is better than
that of the same equation estimated ignoring the
presence of taxes. Moreover, he also uses the nonnested J-test to reveal the presence of the tax effect
(see Appendix for details).
In order to explain these tests as well as to motivate the empirical work reported in this paper, the
Fisher equation could be written as

estimation of the interest rate equation (5b) should
proceed by dividing all the explanatory variables by
(1-T) or not. Equivalently, should, the estimation
of equation (5b) be carried out by setting k to zero
or k to one? He shows that the forecasting performance of the tax-adjusted Fisher equation (equation
(5b) estimated setting k to one) is better than that of
the standard Fisher equation (equation (5b) estimated setting k to zero).5
However, the general analysis of the tax effect
presented in the previous section implies that the
nominal interest rate may only partially adjust for the
presence of the effective marginal tax rate on interest
income. In order. to investigate this possibility, the
empirical work in this paper treats the taxadjustment parameter k as an unknown parameter
and estimates it along with other parameters. Since
the parameter k is hypothesized to take values ranging from zero (no tax-adjustment) to one (complete
tax-adjustment), the empirical procedure employed is
to search for that value of k that minimizes the standard error of the regression. An estimated value of k
which is less than one but greater than zero, could be
interpreted to imply an incomplete adjustment of the
nominal rate to the presence of taxes.

III.
THE MODEL OF INTEREST RATE DETERMINATION

the inflation premium coefficient not necessarily equal
to one ; u = the random error term; k = the taxadjustment parameter. The procedure used in the
early empirical work to test the presence of the tax
effect could then be characterized as follows: estimate equation (5b) setting the parameter k to zero
and then examine whether or not the estimated coefficient on the expected inflation variable is greater
than one. Moreover, under the assumption that the
population parameter b equals one, examine whether
or not the value of this estimated coefficient exactly
equals the value given by (1/(1-T)), where T is
the average marginal tax rate on interest income. As
observed before, more often than not the estimated
coefficient on the expected inflation variable was
found to be less than one.
In his empirical investigation of the tax effect,
Peek argues the crucial question is really whether the

As observed before, the Fisher equation (5b)
should be viewed as a reduced form relation. In
order to estimate it, we need a model to help identify
the important determinants of the expected real rate
and the expected inflation rate. Therefore, this section presents a simple IS-LM-Aggregate Supply
model 6 which can be seen as providing the basis for
the nominal interest rate equation (5b) estimated in
this paper.
The linearized version of this model could be expressed as

5

The procedure used by Ayanin (1983) is entirely different; he does not estimate the Fisher equation. Instead,
through regression technique, he examines the yield
spread between taxable and tax-exempt bonds. He finds
that the nominal yield on taxable bonds has risen sufficiently to compensate the lenders for the presence of an
effective marginal tax rate on the interest income; his
results imply an effective average marginal tax rate in the
neighborhood of 40 percent.
6

This macro model is in essence similar to the ones given
in Peek (1982), Wilcox (1983), and Peek and Wilcox
(1983).

FEDERAL RESERVE BANK OF RICHMOND

11

where all the variables except i and Z are in natural
logs and where Y is actual real output, Y n is the
natural real output, X is the exogenous component of
real demand, M is the nominal money stock, P is the
price level, P e is the expected price level, i is the
SS is a supply shock variable measuring things like
oil price disturbances, Z is the percentage change in
the real output lagged one period, and T is the
average marginal tax rate on interest income.
Figure 1 presents graphs of IS, LM, and aggregate
supply (AS) equations. Equation (6) is the equation of the IS curve showing an inverse relationship
between the after-tax nominal rate i(1-T) and real
output* (Y-Y”) ; its position depends upon the
exogenous component of the real demand X, the
income Z, and the supply shock variable SS. Equation (7) is the equation of the LM curve showing a
positive relationship between the after-tax nominal
rate i(1-T) and real output (Y-Y n ) ; its position
depends upon the price level P and the nominal
money stock M. Equation (8) is the equation of the
aggregate supply curve implying a positive relationship between the price level and real ouput; its position depends upon the expected price level Pe and the
supply shock variable SS. The model as formulated
above enables one to consider the short-run behaviour
of the nominal interest rate as the economy deviates
from its natural real output level.
Equation (6) through (8) can be combined to
yield the following nominal interest rate equation:

9

In the empirical section of the paper, M1 is proxied by
the variable LIQ; the latter is defined as the current
growth rate of the nominal money stock relative to its
most recent trend growth rate. See Wilcox (1983).

Figure 1

IS AND LM CURVES

AGGREGATE SUPPLY AND
AGGREGATE DEMAND CURVES

7

The demand equation for real money balances underl y i n g t h e L M c u r v e i s a s s u m e d t o b e ( M - P - Yn) d =

money supply equals the money demand, we can solve
the equilibrium expression for the after-tax nominal
interest rate to get equation (7) of the text.
8

Actual real output is measured relative to its natural
level.

12

ECONOMIC REVIEW, JULY/AUGUST 1984

IV.

nal interest rate responds positively to an increase in
expected inflation (A1 > 0), exogenous components
of real demand (A 2 > 0), and real income (A 5 >
0). All of these variables lead to an upward shift in
the IS curve and therefore to a rise in the nominal
interest rate. The supply shock variable has a priori
an uncertain effect. on the nominal interest rate
in the relative price of energy, is assumed, at least
in the short run, to reduce the demand for capital
because capital and energy are complements in the
production process. This reduction in the demand
for capital implies reduction in investment which
effect, by itself, tends to cause a decline in the nominal
interest rate (see eq. (6)). However, an adverse
supply shock at the same time tends to raise input
costs and in so doing shifts upward the aggregate
supply curve (see eq. (8)): This shift raises the
price level, reduces the real money supply and thereby causes a rise in the nominal interest rate. The net
impact of an adverse supply shock on the nominal
interest rate, therefore, depends upon the relative
importance of the investment effect and the input cost
effect. 10 The coefficient in front of the monetary
variable is expected to be negative (A4 < 0).
The interest rate equation (9) yields two interesting implications. First, the presence of taxes on the

EMPIRICAL RESULTS

This section reports the evidence on the existence
and the magnitude of the tax effect. The procedure
employed here is to search for that value of the taxadjustment parameter k that, produces the lowest
standard error of the estimated interest rate equation.
For different values of k between zero and one, the
nominal interest rate equation (9) is estimated multiplying all the right hand side explanatory variables by
(1/(1-kT)), where T is replaced by the actual
values of the average marginal tax rate on interest
income.
Table I reports the standard errors of the estimated interest rate equation for the full period 19521979 and for two subperiods. 1952-1970 and 19711979. It is clear that the nominal interest rate equation estimated under the assumption of the full taxadjustment (assumed by setting k equal one in
(1/(1-kT))) yields the lowest standard error of
the regression (compare the standard errors of the

T a b l e I

EVIDENCE ON THE MAGNITUDE OF
THE TAX-ADJUSTMENT IN THE
INTEREST RATE EQUATION
semiannual

data

the parameter in front of the expected inflation variable but also other parameters in the interest rate
equation. Hence important changes in the tax policy
can bring about changes in the response of the nominal interest rate to the determinants of the real rate
and the expected inflation rate. Second, as mentioned
above the coefficient in front of the expected inflation
rate will equal (1/(1-T)) only under some special
assumptions about the structure. This parameter,
given in equation (10.1), can be expressed as

In the context of this simple structural model, this
coefficient will equal (1/1-T)) only if either b 2 o r
is horizontal). In general, this coefficient will be
less than (1/(1-T)). Therefore, the presence of
the tax effect is not inconsistent with the findings of a
smaller-than-unitary coefficient in front of the expected inflation variable.
10

For details, see Wilcox (1983).

The entries in column (1) through (3) above list standard
Note:
errors of the regression of the nominal interest rate equation
estimated for different, sample periods under various hypothesized values about the magnitude of the tax-adjustment
factor k (see note in Table II for a description of the interest
rate equation estimated).

FEDERAL RESERVE BANK OF RICHMOND

13

estimated interest rate equation in Table I). 11 This
empirical result can be interpreted to imply that the
nominal interest rate fully adjusts for the presence of
an effective marginal tax rate on interest income.
These findings support the assumption of complete
tax-adjustment made by Peek (1982).
Table II presents estimates of the nominal interest
rate equation (9). Row 1 presents estimates obtained
ignoring the presence of income taxes on interest
income (k=0), and row 2 presents estimates obtained assuming the full tax-adjustment (k=1). The
estimates presented in rows 1 and 2 imply that all the
explanatory variables have the expected influence on
the behaviour of the nominal interest rate. That is,

rises in expected inflation, exogenous components of
aggregate demand, and lagged real income growth
raise interest rates while positive supply shocks and
accelerations in money growth lower them (see coefficients on PE12, X, SS, LIQ, and Z in Table II).
Given the above empirical results, Chart 1A graphs
the behaviour of the after-tax short-term real rate
for the period June 1952 to June 1983. The solid line
displays the actual ex ante real rate and is computed
The dotted line displays the
behaviour of the after-tax real rate predicted by the
nominal interest rate equation. For the period June
PE12, where î is the predicted value of the nominal
interest rate equation estimated over the period 19521979. For the period June 1980 through June 1983,
the predicted values are the simulated values from
the interest rate equation estimated over the period
1952-1979.
This chart suggests some interesting inferences.
The after-tax real rate that was positive in the ’50s
and ’60s turned negative in the ’70s. The level of
the after-tax real rate observed during the period
June 1981 to June 1983 is again positive but it is
within the range observed in the ’50s and the ’60s.
Therefore, when judged against that range, it cannot
be considered unusually high. However, the real rate
does appear high relative to the negative levels observed in the ’70s.

11

This result about the existence of complete taxadjustment seems fairly robust with respect to the measure of inflation used and the estimation procedure employed. If some right hand side explanatory variables in
the interest rate equation (9) are not strictly exogenous,
then the ordinary least squares estimation procedure will
provide inconsistent estimates of the parameters including
k. Therefore, the nominal interest rate equation was
also estimated by the instrumental variable estimation
procedure treating both Z and LIQ as right hand side
endogenous variables. Even here, the nominal interest
rate equation estimated by setting k equal one in
( 1 / ( 1 - k T ) ) yielded the lowest standard error of the
regression. Similarly, considering the possibility that the
Livingston survey measure of inflationary expectations
(PE12) may contain measurement errors and thereby
produce biased estimates of the regression parameters, a
two-step procedure as outlined in Lahiri (1976) was
employed to estimate the nominal interest rate equation
(9). Again, this estimation procedure yielded the same
conclusion about the presence of the complete taxadjustment. These results are available upon request
from the author.

Table II

REDUCED FORM ESTIMATES FOR THE INTEREST RATE EQUATION
semiannual data, 1952-1979
Coefficient on
Z

SER

PE12

X

SS

LIQ

1. Non-tax-adjustment
k = 0

.81
(20.4)

7.70
(3.2)

- 2.84
(-4.5)

- 17.1
(-2.9)

14.9
(2.5)

.7339

.891

2. Full tax-adjustment
k=1

.55
(20.7)

5.81
(3.6)

- 2.52
(- 5.9)

- 11.9
(- 2.9)

10.2
(2.5)

.6996

.981

Note:
The nominal interest rate equation estimated and reported above is from the text (equation 9) and can be expressed, using proxy
variables, as

where i is the average market yield on a one-year Treasury bill, X is the normalized value of real exports and real government
expenditure, SS is the ratio of the deflator for imports and deflator for GNP adjusted for changes in the exchange rate, PE12 is
the Livingston survey forecast for inflation over the 12-month horizon, LIQ is the annualized growth rate of the nominal money
stock (M1B) over the last six months minus its annualized growth rate over the last three years, T i s t h e s e r i e s o n t h e a v e r a g e
marginal tax rate prepared by Joe Peek (1982), and Z is the lagged value of the rate of growth of the real GNP. The time series on
the average marginal tax rate was kindly provided by Peek, and the one on PE12 by the Federal Reserve Bank of Philadelphia. The
interest rate equation is estimated using semiannual observations corresponding to the Livingston survey data collected each June and
by the ordinary least squares estimation procedure.

14

ECONOMIC REVIEW, JULY/AUGUST 1984

Chart 1A

REAL AFTER-TAX INTEREST RATES
ACTUAL AND PREDICTED

Chart 1B

EFFECT ON THE AFTER-TAX REAL RATE
OF CHANGING EXPLANATORY VARIABLES

FEDERAL RESERVE BANK OF RlCHMOND

15

These observations on the level of the after-tax
short-term real rate raise one important question.
Why did the after-tax real rate turn negative in the
1970s? In order to suggest an answer to this question, Chart 1B displays the effect on the after-tax
real rate of changing explanatory variables like the
expected inflation rate (PE12), predetermined components of aggregate demand (X and Z), supply
conditions (SS), and money growth rate (LIQ).
Each plotted series traces the impact of an explanatory variable on the after-tax real rate and is calculated as the product of the variable and its estimated
coefficient from row 2 (in Table II), less the value
of that product for the first observation of the sample.
Thus, each measure’s movement of the after-tax expected real rate is due to that explanatory variable
from the June 1952 base. Consider the solid line
depicting the effect on the real rate of changing
expected inflation (PE12). The solid line shows that
the effect of expected inflation has been to depress
the real rate, and the magnitude of this depressing
influence has been changing over time. Thus, the
steadily rising expected inflation drove down the real
rate by almost 2 percentage points from the early
’50s until the end of the ’60s. The magnitude of this
depressing influence increased as the expected inflation rate accelerated in the late ’70s; it reduced the
real rate by almost 5 percentage points by the end of
the ’70s. In the early ‘80s, the reduction in the expected inflation rate did decrease the magnitude of
this depressing influence. Other lines in Chart 1B
can be similarly interpreted.
Overall, Chart 1B shows the rising expected inflation rate to be the most important factor that contributed to depress the real rate in the 1970s. The
adverse supply shocks of the 1970s were another
factor contributing to low real rates in this period
(Wilcox (1983)). Both of these factors were responsible for producing excessively low real rates of
interest in the 1970s.
Even though the interest rate model estimated
here reasonably explains the behaviour of the aftertax real rate during the period 1952-1979, it does not
explain very well the behaviour of the after-tax real
rate in the post-1979 period. The recent drastic
reduction in the level of inflationary expectations and
the recent stability in oil prices were among the
important factors contributing to the recent increase
in the after-tax real rate; however, they alone cannot
explain all of the recent rise in real rates (see Chart
1A). This suggests that an important change might
16

have occurred in the response of nominal and real
rates to various explanatory variables in the post1979 period.

V.

SUMMARY REMARKS

One of the important issues arising as a result of
the recent appearance of high and volatile real interest
rates concerns the existence of the tax effect on the
response of the nominal interest rate to expected
inflation. Those who ignore the effect of taxes on the
nominal interest rate tend to focus on the before-tax
real rate of interest. The before-tax real rate may
appear high by historical standards. However, there
is growing evidence that the tax effect does exist,
and this paper presented some further evidence on its
full existence. The empirical results reported here
imply that investors have fully recognized the effect
of income taxes in reducing the after-tax expected
real rates of interest and therefore have adjusted
nominal interest rates to insulate real rates from the
effect of taxes. In view of this, it is more appropriate
to focus on the behaviour of the after-tax real rate of
interest.
Several analysts, focusing both on short- and longterm real rates, have expressed the view that real
rates are excessively high by historical standards.
This view may not be entirely correct. For the evidence from an estimate of short-term real interest
rates presented in this paper shows that the range of
the after-tax real interest rate observed in recent
years is not different from the range observed in the
’50s and the ’60s. The after-tax real interest rate was
positive during the years 1952-1970 and turned negative in the ’70s. Recently, it has been positive. Since
the real rate has been positive in recent years, it does
indeed appear excessive when compared with the
negative real rate observed in the ’70s. However, the
level is well within the range experienced during the
period of positive real yields.12
The simple interest rate equation reported and estimated in this paper suggests that accelerating expected inflation and, to some extent, adverse supply
12

The result concerning short-term real rates does not
imply that long-term real interest rates may not be high
by historical standards. However, the evidence on the
existence of the tax effect reported in this paper does
imply that it might be appropriate to adjust long-term
nominal interest rates for effects of expected inflation
and taxes.

ECONOMIC REVIEW, JULY/AUGUST 1984

shocks produced abnormally low real rates of interest
in the late ’70s. Recent years, however, have witnessed a drastic reduction in the expected inflation
rate and considerable stability in oil prices. These
two factors together caused the real rate to rise from
its severely depressed level of the late-‘70s. However,

the interest rate equation reported in this paper still
cannot explain all of the recent rise in the real rate.
But this observation notwithstanding, the level of the
after-tax real rate observed in recent years falls well
within the range experienced during the ’50s and the
‘60s.

APPENDIX

THE J-TEST OF NON-NESTED REGRESSION MODELS: REVIEW AND AN APPLICATION

This Appendix reviews the J-test of non-nested
regression models proposed by Davidson and MacKinnon (1981). This test is used by Joe Peek
(1982) to prove the presence of the tax effect on
nominal interest rates.
In applied econometric work, researchers very
often face the problem of testing the specification of
an econometric model in the presence of one or more
other models which purport to explain the same
phenomenon. The conventional techniques for hypothesis testing (such as the F-test) allow one to test
the validity of a particular specification of an econometric model by testing restrictions on an alternative
specification more general than the one being tested,
conditional on the more general specification being
valid. Since the specification whose validity is being
tested (called the null hypothesis) can be obtained
by imposing restrictions on the more general specification (called the alternative hypothesis), such hypotheses are said to be nested, i.e., the null hypothesis
is nested within the alternative hypothesis.
However, in many cases, the alternative specifications suggested by economic theory are non-nested,
meaning that any given specification whose validity
we might be interested in testing is not nested within
the alternative specification and could not be obtained
by imposed restrictions on the latter. This is usually
the case when each competing specification of the
econometric model is characterized by the presence of
some explanatory variables which are unique to that
specification. Since the competing specifications are
non-nested, the conventional F-test is not directly
applicable. Recently, more powerful tests of nonnested hypotheses have been proposed,13 and the Jtest is one of them.

In order to illustrate how the J-test differs from the
conventional F-test and how it is implemented, consider the simple model of interest rate determination
discussed in the text. The nominal interest rate equation suggested by this model can be expressed as

where all variables are defined as before and u 1 is the
error term. Suppose one wants to test the hypothesis
that one or more explanatory variables (say, Z and
SS) suggested by the above model (A1) have no
influence on the nominal interest rate. The conventional F-test sets up the following as the null (H0)
and the alternative (H1) hypotheses

and then tests whether the restrictions implied by
(A2) are correct, i.e., whether A3 = A5 = 0 in
(A3). Note that the alternative specification (A3)
is more general than the one being tested (A2) and
that the latter is nested within the former.
Now suppose one wants to test the hypothesis that
there is no tax effect on nominal interest rates. As
explained in the text, the issue here is whether we
should estimate equation (A1) by multiplying all the
right hand side explanatory variables by (1/(1-T))
or not. So, the two competing specifications suggested by the tax issue can be expressed as

13

Pesaran and Deaton (1978), Davidson and MacKinnon
(1981), Pesaran (1982), and Davidson and MacKinnon

FEDERAL RESERVE BANK OF RICHMOND

17

where the starred variables in (A5) are derived by
multiplying the corresponding variables in (A4) by
(1/(1---T)). Since the average marginal tax rate on
interest income varies over time, we have entirely
different values of the explanatory variables appearing in (A5). Therefore, one can view (AS) as an
interest rate equation with a different specification of
the right hand side explanatory variables. The specification (A4) implies that it is appropriate to estimate the interest rate equation ignoring the presence
of taxes on interest income. The specification (A5)
implies that it is appropriate to take into account the
presence of an effective marginal tax rate on interest
income and that tax effects are complete.
We can now see why the conventional F-test in this
case is not directly applicable to the problem of
testing the validity of a given specification (A4)
(that there is no tax effect) against the alternative
specification (A5) (that there is the full tax effect);
the null hypothesis (A4) is not nested within the
alternative hypothesis (AS) as the latter contains an
entirely different set of explanatory variables. The
alternative hypothesis here does not include the variables suggested by the null hypothesis, and one could
not test the restrictions implied by the null hypothesis.
However, there exists several non-nested test procedures which can be employed to test the validity of
the alternative specifications of an econometric model.
The important point in the methodology of nonnested testing is that there is no presumption about
the validity of any specification; each specification is
on an equal footing with every other specification.
This is so because the alternative specifications are
non-nested by assumption and can not be ranked by
the level of generality as can be done when the models
are nested. To follow the non-nested test procedure,
one takes the alternatives one at a time, assuming
each one in turn to be true and inferring from the
behaviour of the alternatives against the data whether
or not the temporarily maintained or working alternative can or cannot explain the behaviour of the
phenomenon one is interested in. One thus makes
pair wise tests of each pair of alternatives and asks
the question, is the performance of an alternative j
against the data consistent with the truth of an alternative i?
In the present case, we have two alternative specifications (A4) and (A5). If one’s working or currently maintained hypothesis is that (A4) is true,
then one tests whether the performance of (A5)
against the data is consistent with the truth of (A4).
Similarly, if one’s maintained hypothesis is that (A5)
is true, then one tests whether the performance of
18

(A4) against the data is consistent with the truth of
(A5). In this procedure, it is conceivable both alternatives may be rejected, or that neither may be rejected. It is also conceivable that one may be rejected
and the other may not be, in which case one would
presumably want to choose the latter over the former.
The case in which both specifications are rejected is
interesting; it implies that there is some element of
truth in both specifications, and that the researcher
should expand the model to incorporate the important
factors suggested by these competing non-nested
specifications.
The J-test proposed by Davidson and MacKinnon
(1981) can be implemented in two steps. The first
step generates estimates of the regression parameters
in (A4) and (A5) by using an estimation procedure
that provides consistent estimates of the parameters.
Since the error terms in (A4) and (A5) are assumed
to be serially uncorrelated, homoscedastic, and uncorrelated with the right hand side explanatory variables,
consistent estimates of the parameters of (A4) and
(A5) are provided by the ordinary least squares estimation procedure. The estimated regression equations are then used to generate the within sample
predictions of the dependent variable under the two
alternative specifications. The second step consists
of estimating two expanded regressions which can be
expressed as

where î and î, respectively, are the predicted series
for the dependent variable i from equations (A5)
and (A4) estimated in step one. In the estimating
equation (A6), the maintained hypothesis is (A4);
one is testing the truth of it given the performance
of the alternative (A5) against the data. If the
specification (A4) is true, then the true value of y
is zero. As shown by Davidson and MacKinnon
(1981), one may validly test whether y=0 in (A6)
by using a conventional t test or, equivalently, a likelihood ratio test. Thus, by testing the significance of
the parameter y in (A6), one tests the truth of the
maintained hypothesis (A4) given the performance
of the alternative hypothesis (A5). The process is
reversed in the estimating equation (A7); the maintained hypothesis here is (A5) and one tests the
truth of it given the performance of the alternative
(A4) against the data. Therefore, one tests the truth

ECONOMIC REVIEW, JULY/AUGUST 1984

of (A5) given the alternative (A4) by examining
the significance of the parameter y in the estimating
equation (A7).
Since the J-test uses t statistics from the expanded
regression equations (A6) and (A7) to draw inferences about the truth of the alternative specifications,
it is imperative that error terms in these regressions
satisfy the important assumptions of the classical
linear regression model, i.e., zero mean, homoscedastic variance, absence of serial correlation, and no
correlation with the right hand side explanatory variables, etc. It is well known that t statistics are biased
if error terms fail to possess some of these properties. 14
Table III presents results of performing the J-test
along the lines suggested above; it shows estimates
of the relevant parameter y and the associated tstatistic from the estimating equations (A6) and
(A7). Two sets of estimates are reported; the first
set (labelled as y1 and t-statistic 1 ) is based on the
ordinary least squares estimates of equations (A6)
and (A7) and the second set (labelled as y2 a n d
14

See Davidson and MacKinnon (1983) and McAleer,
Fisher, and Volker (1983) for an extension of the nonnested tests to cover the issues raised by the violation of
some of these assumptions.

t-statistic 2) is based on the estimation of equations
(A6) and (A7) assuming the presence of the first
order serial correlation. Since the nature of serial
correlation can differ across the alternative specifications, we let the serial correlation coefficient differ
in equations (A6) and (A7).
Since the t-statistic is biased if the error term is
serially correlated, we focus on the second set of estimates. These estimates are consistent with the following inferences : In the estimating equation (A6),
the maintained hypothesis that there is no tax effect
on the nominal interest rate is rejected (y2 is significantly different from zero as evidenced by a significant t value) given the performance against the data
of the alternative that the tax effect does exist. However, in the estimating equation (A7), the maintained
hypothesis that the tax effect does exist is not rejected
( y2 is not significantly different from zero) given the
performance against the data of the alternative that
does not allow tax effects. These results together
then imply that the specification of the interest rate
model, which allows the existence of the full tax
effect on the nominal interest rate, is the preferred
specification when judged against the one which completely ignores the existence of taxes on interest
income.

Table III

RESULTS OF THE J TEST
Sample

Period

1952-1979

* Significant at the .05 level; the two-tailed test.
Note: See the Appendix for on explicit description of various equations.
(A6) and (A7) are estimated by the Hildreth-Lu estimation procedure.

FEDERAL RESERVE BANK OF RICHMOND

19

References
Ayanin, Robert. “Expectations,, Taxes and Interest:
The Search for the Darby Effect.” American Economic Review (September 1983), pp. 762-65.
Cargill, Thomas F. “Direct Evidence of the Darby Hypothesis for the United States.” Economic Inquiry
(January 1977), pp. 132-34.
Darby, M. R. “The Financial and Tax Effects of
Monetary Policy on Interest Rates.” Economic
Inquiry (June 1975), pp. 266-76,
Davidson, Russel, and James MacKinnon. “Several
Tests for Model Specification in the Presence of
Alternative Hypotheses.”
Econometrica (May
1981), pp. 781-93.
. “Testing the Specification of Multivariate
Models in the Presence of Alternative Hypotheses.”
Journal of Econometrics (December 1983), pp. 3011 3 .
Ezrati, Milton J. “Inflationary Expectations, Economic
Activity, Taxes, and Interest Rates: A Comment.”
American Economic Review (September 1982), pp.
854-57.
Feldstein, Martin S. “Inflation, Income Taxes, and the
Rate of Interest : A Theoretical Analysis.” American Economic Review (December 1976), pp. 809-20.
Lahiri, Kajal. “Inflationary Expectations : Their
Formation and Interest Rate Effects.” American
Economic Review (March 1976), pp. 124-31.
Levi, Maurice, and John Makin. “Anticipated Inflation
and Interest Rates.” American Economic Review
(December 1978), pp. 801-12.

20

Makin, John H., and Vito Tanzi. “The Level and Volatility of Interest Rates in the United States: The
Role of Expected Inflation, Real Rates, and Taxes.”
NBER Working Paper No. 1167, July 1983.
McAleer, Michael; Gordon Fisher; and Paul Volker.
“Separate Misspecified Regressions and the U. S.
The
Long-Run Demand for Money Function.”
Review of Economics and Statistics (November
1982), pp. 572-83.
Melvin, M. “Expected Inflation, Taxation, and Interest
‘Rates: The Delusion of Fiscal Illusion.” American
Economic Review (September 1982), pp. 841-45.
Peek, Joe. “‘Interest Rates, Income Taxes and Anticipated Inflation,” American Economic Review (December 1982), pp. 980-91.
Peek, Joe, and James A. Wilcox. “The Postwar Stability of the Fisher Effect.” The Journal of Finance (September 1983), pp. 1111-24.
Pesaran, M. H., and Angus S. Deaton. “Testing Nonnested Non-linear Regression Models.” Econometrica (May 1978), pp. 677-94.
. “Comparison of Local Powers of Alternative Tests of Non-nested Regression Models.”
Econometrica (September 1982), pp. 1287-1305.
Tanzi, Vito. “Inflation, Indexation and Interest Income
Taxation.” Banca Naz. Lavoro Quarterly Review
(March 1976), pp. 54-76.
. “Inflationary Expectations, Economic
Activity, Taxes, and Interest Rates.” American
Economic Review (March 1980), pp. 12-21.
Wilcox, James A. “Why Real Rates Were So Low in
the 1970’s.” American Economic Review (March
1983), pp. 44-53.

ECONOMIC REVIEW, JULY/AUGUST 1984

A REVIEW OF BANK PERFORMANCE
IN THE FIFTH DISTRICT, 1983
F. Ward McCarthy Jr.

The profitability of Fifth District banks improved
dramatically in 1983. The .98 percent return on
average assets and 15.2 percent earned on average
equity capital were well above the average returns of
recent years. With interest rates well below prevailing yields of the previous few years and loan
demand that lagged the increase in business activity
by several months, most banks found it difficult to
generate a strong stream of interest revenue. Consequently, noninterest revenue sources and cost reductions contributed more to increased profits than did
growth in interest income. Despite changes in liability structure and lower market rates, which caused
a significant decrease in average interest expenses,
net interest as a share of average assets still fell 17
basis points. A strong gain in noninterest income
offset most of the decline in net interest margins,
however. Reductions in provisions for loan loss and
losses on securities transactions, and lower noninterest expense growth were major factors in increased
net earnings.
The cost structure of Fifth District banks was
strongly influenced by deposit deregulation. The
Garn-St. Germain Depository Institutions Act of
1982 authorized banks to offer a money market deposit account (MMDA). MMDAs became available
on December 14, 1982 and permitted the public to
earn market rates of interest on deposits with limited
transactions features. MMDAs are available to all
customers and carry a reserve requirement of 3
percent on nonpersonal accounts, but no reserve
requirements on personal accounts. The Depository
Institutions Deregulation Committee (DIDC) also
authorized banks to offer a Super-NOW account on
January 5, 1983. Super-NOWs are fully transactional accounts that pay unregulated interest rates on
initial and maintained balances of at least $2,500.
Super-NOWs carry transaction account reserve reValuable research assistance was provided by John
Walter. Part of the data base was developed by Nancy
Bowen of the Board of Governors of the Federal Reserve
System.

quirements of 12 percent and are available to a
limited clientele including nonprofit organizations,
households and government agencies. Fifth District
banks attracted over $15 billion in MMDAs and
Super-NOWs. In doing so, these banks altered the
structure of liabilities and greatly increased the yield
sensitivity of deposits. This recomposition was
instrumental in reducing interest expense since a
large volume of the funds that flowed into these deregulated consumer accounts were shifted from higher
cost-managed liabilities or longer term deposits.
Banks of all sizes expanded revenue from noninterest sources and reduced loan-loss provisions and
noninterest expense. In spite of the increase in
aggregate profitability, cash dividends declined 3
basis points as a percent of average assets. Retained
earnings, however, increased almost 45 percent. As a
consequence, both the rate of retained earnings and
internal equity growth also increased substantially.
Nonetheless, asset growth outpaced equity growth so
that leverage increased for the third consecutive year.
Table I summarizes the main components of income
and expense relative to average assets for all Fifth
District banks for the years 1979-83.
Interest Revenue
The gross return on assets, which is the ratio of
gross interest revenue to average assets, declined for
the second year in a row. In the aggregate, Fifth
District banks collected 9.58 percent for each dollar
of assets compared with 10.86 percent in 1982. This
reduction in gross returns is a reflection both of prevailing market yields that remained substantially
below the average yields of the past few years (see
Chart 1) as well as the pattern and composition of
asset growth over the year. While banks of all sizes
expanded loan and investment security portfolios,
security holdings grew substantially faster than loans
until the fourth quarter. As a consequence, banks
were less successful in generating current interest
income than in expanding the asset base. Approximately 70 percent of Fifth District banks reported

FEDERAL RESERVE BANK OF RICHMOND

21

Table I

INCOME AND EXPENSE AS A PERCENT OF AVERAGE ASSETS
FIFTH DISTRICT COMMERCIAL BANKS, 1979-1983

year-end 1983 interest earnings in excess of the
previous year’s figure. Of those that reported higher
interest earnings, few were able to accumulate interest revenue proportionally to asset growth.
The sharpest deterioration in gross returns occurred at banks with $750 million or more in assets.
As a group, these large banks experienced a 141 basis
point reduction in the interest revenue average assets

Chart 1

SHORT- AND MEDIUM-TERM RATES
(1981 - 1983)

22

ratio (see Chart 2). None of these institutions reported an increase in gross return on assets. An
inability to generate a stream of interest revenue
commensurate with asset growth characterized banks
in all size categories, however. Only 6 percent of the
banks with less than $750 million in assets recorded
an increase in the gross return on assets. In contrast,
over 70 percent of all banks in the Fifth District
reported an increase in interest revenue scaled to
average assets in 1982.
As indicated in Table II, the effective yield on
gross loans declined 176 basis points on average.
The reduction in loan yields at banks with less than
$100 million in assets was more modest. Specifically,
these small banks reported a decline in loan yields
of 89 basis points. Because of a relatively high
incidence in small bank portfolios of fixed-rate
consumer loans and mortgages bearing the high
yields inherited from the past, the average yield at
small banks was partially insulated from the reduction in market rates. Conversely, the decline in the
return on loan portfolios was steepest at the large
banks because these institutions are more vulnerable
to interest rate fluctuations. Short-term and floatingrate loans with yields that are sensitive to market
conditions account for a large fraction of large-bank
loan portfolios. Medium-sized banks with loan port-.
folios similar in character to large bank portfolios

ECONOMIC REVIEW, JULY/AUGUST 1984

Table II

AVERAGE RATES OF RETURN ON SELECTED INTEREST-EARNING ASSETS
FIFTH DISTRICT COMMERCIAL BANKS, 1979-1983

also reported a significant deterioration in average
loan yields. Medium-sized banks are banks with less
than $750 million in assets but more than $100
million.
The share of Fifth District bank assets allocated
to loans rose by approximately one percent. There
was significant variation in the pattern and rate of
growth of different loan categories during the year
(see Table III). Only the volume of commercial real
estate loans grew steadily throughout the year, although consumer credit activity accelerated over the
last three quarters after a lethargic first quarter.
Consumer mortgage and commercial and industrial
(C&I) loan extensions were considerably more
erratic. Growth in all four major loan categories

Chart 2

GROSS INTEREST RATIO*

Table III

QUARTERLY GROWTH RATES IN
SELECTED LOAN CATEGORIES IN 1983

peaked in the fourth quarter. The expansion in C&I
loans and consumer credit occurring after September
exceeded 40 percent on an annual basis. C&I loan
growth over that period was even stronger for the
large bank group.
Returns from securities portfolios at all banks declined 7 basis points. This decline reflected the lower
yields on federal treasury and agency securities and
the enormous volume of these investments which
banks purchased. Fifth District banks added almost
$6 billion of these investments to asset portfolios.
This growth in federal security holdings was especially strong over the first three quarters but tapered
off in the fourth quarter to coincide with the resurgence in loan demand.
Interest Expense

*Interest revenue divided by average assets.

With market rates remaining substantially below
the average level of recent years, the average cost of
interest-bearing liabilities declined 186 basis points
(see Table IV). In response to the ongoing deposit
deregulation, banks of all sizes expanded their holdings of rate-sensitive liabilities and reported sub-

FEDERAL RESERVE BANK OF RICHMOND

23

Table IV

AVERAGE COST OF FUNDS FOR SELECTED LIABILITIES
FIFTH DISTRICT COMMERCIAL BANKS, 1979-1983

stantial reductions in the average cost of funds.
Interest expense per dollar of average assets, the
interest expense ratio, declined from 6.93 percent to
5.82 percent, on the average. The decline was most
pronounced at the large banks where interest expense
ratios declined 120 basis points (see Chart 3). Reductions in interest expense were evident at banks of
all sizes, however. District-wide, 97 percent of the
banks reported lower expense ratios and 65 percent
lower total interest expenditures than in 1982.
Most categories of interest-bearing liabilities
showed an average cost decline of at least 250 basis
points compared with 1982. The decline in the effective interest rate paid on certificates of deposits
(CDs) and balances of foreign offices was markedly
steeper. Because a substantial portion of CDs bearing
high interest rates matured and were repriced at the
relatively lower yields that prevailed in 1983, the
average cost of CDs decreased almost 4.5 percentage
points; the 5.06 percentage point decline in the average cost of the highly liquid and rate-sensitive foreign
office, deposits was also due directly to the lower
market rates. On the other hand, the average interest
expense associated with subordinated notes and debentures was virtually unchanged because of the fixed
interest rates and relatively long maturities which
these liabilities carry. The average effective rate paid
on “other” deposits is a weighted average of the
interest expense on deposits such as savings and
small time deposits, negotiable order of withdrawal
(NOW)
accounts,
Super-NOW
accounts
and
MMDAs. The relatively small decline in the average
cost of these funds reflects the net effect of lower
market rates and a shift from fixed or low interest
24

deposits, such as savings deposits and NOW accounts, to MMDAs and Super-NOWs, which carry
market rates.
Both MMDAs and Super-NOWs were very successful, in attracting funds and both stimulated a
major restructuring of Fifth District bank liabilities.
The growth of MMDAs was especially dramatic
(see, Table V). The weekly flow of funds into
MMDAs averaged well over $1 billion for the first
month that the deposit was offered. By early March,
however, the weekly flow had decelerated to about

Chart 3

INTEREST EXPENSE RATIO*

*Interest expense divided by average assets.

ECONOMIC REVIEW, JULY/AUGUST 1984

Table V

MONTHLY BALANCES IN
MONEY MARKET DEPOSIT ACCOUNTS
AND SUPER-NOW ACCOUNTS’
(in millions of dollars)
D a t e

MMDA

Super-NOW

12/15/82

287.1

12/29/82

3,530.2

-

1/26/83

7,581.8

452.8

2/23/83

9,360.7

643.1

3/30/83

10,523.3

799.1

4/27/83

10,975.8

897.3

5/25/83

11,629.6

951.2

6/29/83

12,084.8

1,003.7

7/27/83

12,369.1

1,064.1

8/31/83

12,613.1

1,139.9

9/28/83

12,772.3

1,154.9

10/26/83

13,140.7

1,219.9

11/30/83

13,646.9

1,270.5

12/28/83

13,850.7

1,314.6

1

Does not include balances at banks with less than $15 million
in deposits.

$500 million but still remained at a greater than $100
million pace throughout the first half of the year. By
midyear, MMDAs comprised more than one quarter
of all savings and time deposits. By year end, they
made up approximately 28 percent of these deposits.
This share was about ten percentage points lower, on
average, at small banks, however.
The growth of Super NOWs was less spectacular
than that of MMDAs. However, Fifth District banks
accumulated approximately $1.3 billion in SuperNOWs. By December, Super-NOW balances comprised almost 20 percent of all checkable deposits
other than demand deposits, such as NOW, ATS
and Super-NOW accounts, and 6 percent of traditional demand deposits. At small banks, however,
Super-NOW balances comprised well over 30 percent
of other checkable deposits and 14 percent of demand
deposits by the end of the fourth quarter.
Rates available to MMDA depositors were substantially higher than yields on Super-NOWs
throughout the year (see Chart 4).1 Because of the

broad transactions features of Super-NOWs, these
accounts carry transaction account reserve requirements and are more costly to service than MMDAs.
MMDAs have at most a small reserve requirement
and lower service costs than Super-NOWs because
they have limited transactions features. The positive spread between MMDA and Super-NOW yields
is associated with the different costs of the two accounts. This rate differential was also influenced by
marketing strategies, however. The widest spread
between MMDA and Super-NOW rates occurred in
January when banks were still competing aggressively for MMDAs, in some cases with promotional
rates that were out of line with other short-term
rates. The spread narrowed to as little as 108 basis
points in March and April before rising again in the
second half of the year and leveling off at around
140 basis points.
In spite of the higher average return associated
with MMDAs, Super-NOW depositors maintained
average balances that were substantially above the
minimum required to avoid a ceiling on the interest
rate paid on the account. Through August, SuperNOW balances exceeded the minimum requirement
by an average of almost $12,000.2 Depositors who
maintained such large Super-NOW balances rather
than shifting excess funds to an MMDA, forfeited
interest at the average annual rate of 1.3 percentage
2

Based on a stratified sample of Fifth District banks.
Data are not available after August 1983.

Chart 4

SPREAD BETWEEN MMDA
AND SUPER-NOW RATES

l

Yields on MMDAs and Super-NOWs are based on a
stratified sample of Fifth District banks and are weighted
averages. Constituting the weights are the balances of
the individual institutions.
FEDERAL RESERVE BANK OF RICHMOND

25

points. Assuming average excess Super-NOW balances of approximately $12,000 per account were
maintained throughout the year, then these depositors
sacrificed approximately $150 in interest per account.
Net Interest Margins
Net interest income, that is, the difference between
interest income and interest expense, declined 1 7
basis points relative to the average assets of Fifth
District banks. Banks in different. size categories,
however,, reported markedly different experiences,
experiences that are obscured by the aggregate figure
(see Chart 5). Only 13 percent of the banks with
$750 million or more in assets recorded increases in
net interest margins from 1982. The ratio of net
income to average assets declined 21 basis points for
these large institutions as a group. Net interest
margins expanded 5 basis points at small banks as 55
percent of banks with less than $109 million in assets
reported increased margins. While margins also
increased at a majority of the medium-sized banks,
the net income average assets ratio declined 4 basis
points for these banks as a group because of the relatively steep declines registered at some of the larger
banks in this asset category.
With aggregate interest income virtually unchanged
and the ratio of interest income to average assets
declining at 95 percent of Fifth District banks, the
ability to control interest expense was a critical de-

26

terminant of the level and pattern of change in net
interest margins during 1983. On the average, banks
with expanded net interest margins managed to generate only 1.1 percent more interest income in 1983
than in the previous year; banks with contracted
margins reported a .l percent. decline in interest
income (see Table VI). Differences in interest
expense were more significant. Interest expense
declined 7.2 percent and 3.4 percent, respectively, for
banks reporting expanded, or conversely, contracted
net interest margins. Banks with increased net margins were able to reduce interest costs more rapidly
than banks with unchanged or depressed margins
because these institutions held a higher proportion of
liabilities bearing, market yields.
Noninterest Revenue and Expenses
Provisions for loan loss decreased relative to average assets for all banks. This decline accounted for a
3 basis point increase in aggregate profitability. The
reduction in loan loss provisions relative to average
assets was of approximately the same magnitude at
large and small banks and was associated with an
improvement in loan quality due to the cyclical
expansion.
Cash losses net of recoveries declined approximately 12 percent. Relative to average assets, loan
losses decreased most rapidly at the small banks, but
were lower at banks of all sizes. Actual loan chargeoffs declined 3 percent in the aggregate, while cash
recoveries grew by over 22 percent.
Increases in noninterest revenue outpaced growth
in assets, as noninterest income rose by over 26 percent in 1983. This dramatic increase in noninterest
earnings reflects the more widespread use of explicit
pricing of services and a greater dependence on noninterest income as a source of profit. For example,
revenue from credit card fees, loan service fees and
other miscellaneous fees rose by over 30 percent.
Service charges on deposits increased by 19 percent.
The increase in deposit service fees is associated with
the growth of deposits bearing market interest rates.
The largest banks registered the largest increase in
deposits service charge income.
The ratio of noninterest expense to average assets
declined at banks of all sizes. Increases in wages and
salaries were almost 20 percent lower than in 1982.
This deceleration in the rate of growth of labor costs
accounted for three quarters of the 8 basis point contraction in noninterest expense ratios. Increases in
other operating and occupancy expenses were in the
order of 10 percent.

ECONOMIC REVIEW, JULY/AUGUST 1984

Table VI

CHANGES IN NET INTEREST MARGINS IN RELATION TO INTEREST INCOME AND
INTEREST EXPENSE GROWTH RATES AND LIABILITY COMPOSITION IN 1983
Total Assets
($ millions)

Number
of Banks

Interest
Income
Growth

Interest
Expense
Growth

Percent of
Rate-Sensitive
Liabilities1

Percent
Change in
Net Margin

Less than 100
Increased margin

269

3.8

- 5.4

59.4

10.6

Others

228

4.1

2.4

57.4

- 8.0

51

1.9

- 6.6

59.4

9.8

38

.9

- 1.7

57.0

- 8.8

6

- .8

- 8.4

61.2

2.1

28

- .7

- 4.2

59.5

- 8.9

100 to 750
Increased margin
Others
750 and over
Increased margin
Others
All banks
Increased margin

326

1.1

-7.2

60.3

6.2

Others

294

- .1

- 3.4

59.1

- 8.8

1

Rate-sensitive liabilities include deposits in foreign offices, fed funds purchased, i n t e r e s t - b e a r i n g d e m a n d n o t e s
issued to the U.S. Treasury and other liabilities for borrowed money, a n d a l l t i m e a n d r o v i n g s d e p o s i t s e x c e p t :
NOW accounts, ATS accounts, savings deposits subject to federal regulatory ceilings and IRA and Keogh plan accounts.

Profits and Dividends
Before-tax profits edged up 7 basis points to 1.22
percent of average assets in 1983. The improvement
in profitability was twice as great at small banks.
However, an increase in taxes relative to average
assets offset more than half of the gains in before-tax
returns. In the aggregate, taxes increased 4 basis
points as a share of average assets. The increase in
the tax average asset ratio was almost 6 basis points
at small banks.
Banks of all sizes reduced losses on securities transactions. Small and medium-sized banks broke even
on the year. While large banks registered some
losses, these banks did report a substantial improvement in the performance of security operations. In
the aggregate; reductions in securities and extraordinary losses contributed to an 8 basis point improvement in net returns.
Net income as a percent of average assets rose to
.98 percent, an improvement of 11 basis points over
1982. The gains in average returns were equally
impressive at both large and small institutions; gains
in earnings rates at medium-sized banks were more
modest (see Chart 6). The average return on equity
rose by an impressive 2.09 percentage points (see
Table VII). The increase in the return on average
equity exceeded the improvement in the earnings
rate on average assets due to the increase in aggre-

gate leverage. Aggregate leverage measures, such as
the average assets/average equity ratio, have increased every year in the Fifth District since 1980.
In spite of the increased profitability, cash dividends on common stock were virtually unchanged
from last year and declined 3 basis points relative to

Chart 6

RETURN ON ASSETS*

1979

1980

1981

1982

1983

*After-tax net income divided by average assets.

FEDERAL RESERVE BANK OF RICHMOND

27

Table VII
Chart 7

RATES OF RETURN AND LEVERAGE FOR
FIFTH DISTRICT COMMERCIAL BANKS1
Assets/
Equity

RETURN ON EQUITY*

Year

Return on
Assets

Return on
Equity

1979

.94

x

14.37

=

13.51

1980

.89

X

14.35

=

12.79

1981

.86

x

14.56

=

12.56

1982

.87

X

15.06

=

13.12

1983

.98

X

15.53

=

15.21

1

The return is net income; assets and equity ore averages. Discrepancies in calculations are due to rounding error.

average assets in the aggregate. Dividend policies
differed significantly at large institutions and banks
with less than $750 million in assets. Most of the
increase in income at small and medium-sized banks
were distributed to stockholders, as, cash dividends
increased 15 percent and expanded relative to average
assets while retained earnings’ kept pace with asset
growth. On the other hand, large banks decreased
cash dividends and increased retained earnings by an
average of 80 percent. Consequently, retained earnings scaled to average assets increased 150 percentage
points for the large bank group. In the aggregate,
retained earnings relative to average assets rose 14.5
basis points.
Equity capital was expanded by $853 million in
1983, $300 million more than in 1982. Nonetheless,
the capital growth rate of 10.3 percent was 2 percent
slower than asset growth, and the aggregate leverage
ratio, defined as average assets divided by average

*After-tax net income divided by average assets.

equity, increased by 47 basis points. This increase
in leverage accounted for approximately 20 percent of
the 209 basis point increase in the return on equity
(see Table VII). The increase in profitability was
responsible for the remaining 167 basis point increase
in return on equity.
The rate of internal equity growth rose 2.5 percentage points in 1983 and, at an annual rate of 9.96,
‘was higher than it has been in a number of years (see
Table VIII). As a consequence, the discrepancy
between asset growth and internal equity growth narrowed. Asset growth has exceeded internal equity
growth since 1980, contributing to the increase in

Table VIII

INTERNAL EQUITY GROWTH RELATIVE TO ASSET GROWTH
FOR FIFTH DISTRICT COMMERCIAL BANKS
Internal
Equity
Growth

Rate of
Retained
Earnings 2

Asset
Growth

Internal Equity
Growth Asset Growth

Year

Return on
Equity1

1979

13.51

x

.6819

=

9.21

5.19

4.02

1980

12.79

X

.6418

=

8.20

9.43

-1.23

1981

12.56

X

.6116

=

7.68

10.12

-2.44

1982

13.12

X

.5695

=

7.47

11.54

-4.07

1983

15.21

X

.6547

=

9.96

12.30

-2.34

1

2

28

S e e Table VII,

footnote 1.

The rate of retained earnings is the ratio of net retained earnings to net income.,

ECONOMIC REVIEW, JULY/AUGUST 1984

aggregate leverage over that period. The increase in
the rate of retained earnings and greater profitability
contributed about equally to a higher rate of internal
equity growth. The rate of retained earnings in 1983
was higher than in any year since 1979. Nonetheless,
the increase in equity capital from retained earnings
declined substantially (see Table IX). Banks raised
$80 million in equity from sources other than income
retention such as the equity markets.
Summary and Conclusions
The profitability of Fifth District banks improved
significantly in 1983. Dollar profits rose more than
25 percent, and the 98 percent earned on average
assets was an 11 basis point improvement over the
.87 percent earned in 1982. Moreover, the rate of
return on average equity capital increased 209 basis
points to 15.21 percent, as asset growth exceeded
equity growth for the third consecutive year. This
district-wide increase in leverage occurred even
though the rate of retained earnings and the rate of
internal equity growth increased.
Because market interest rates were below the average levels of the previous few years and loan growth
lagged the economic expansion, few banks were able
to expand the gross return on assets. As a consequence, the level and pattern of change for net interest
margins were strongly influenced by the ability to
control interest expense. Banks with a cost structure
that was relatively sensitive to changes in market
conditions were the most successful in reducing

interest expense and increasing net interest margins;
many of these low-cost institutions attracted a substantial volume of funds in MMDAs and SuperNOWs. Aggregate profitability was enhanced. by a
large increase in noninterest revenue and reductions
in noninterest expense and provisions for loan loss.
Given the continued strength in the economy,
growth in loan demand and the upward movement in
market interest rates, Fifth District banks should be
able to expand the flow of interest revenue and increase the gross return on assets in 1984. Since
deposit deregulation has led to an increased sensitivity of the commercial bank cost structure to
changes in market rates, net interest margins and
profitability in general will depend on the ability to
contain interest expense should interest rates rise as
the year progresses., Net interest margins are likely
to be more volatile. Consequently, Fifth District
banks must also attempt to increase the revenue flow
from noninterest sources and control noninterest
expense, especially labor costs, in order to maintain
profitability.
References
Furlong, Frederick T.
“New Deposit Instruments.”
Federal Reserve Bulletin (May 1983), pp. 319-26.
McCarthy, Ward, and Walter, John.
“A Review of
Bank Performance in the Fifth District, 1982.”
Economic Review, Federal Reserve Bank of Richmond (July/August 1983), pp. 3-11.
Opper, Barbara Negri. “Profitability of Insured Commercial Banks in 1982.” Federal Reserve Bulletin
(July 1983), pp. 489-507.

Table IX

RATE OF RETAINED EARNINGS AND SOURCES OF TOTAL EQUITY CAPITAL
FOR FIFTH DISTRICT COMMERCIAL BANKS
(1)

(2)

(3)

Net Income
Year

Net Retained
Earnings

($000)

($000)

Rate of
Retained
Earnings1

(4)

(5)

Increase in
Equity Capital
($000) 2

Increase in
Equity Capital
from Retained
E a r n i n g s2,3

1979

758,804

517,398

.6819

557,787

.9276

1980

788,145

505,872

.6418

542,487

.9325

1981

840,834

514,278

.6116

558,561

.9205

1982

944,785

538,068

.5695

545,990

.9855

1983

1,179,971

772,571

.6547

852,862

.9059

1

2

3

S e e T a b l e V I I I , footnote 2.
The figures for 1979-1982 have been adjusted to correct for data error.
The increase in equity capital from retained earnings is calculated by dividing column (2) by column (4).

FEDERAL RESERVE BANK OF RICHMOND

29


Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102