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A NEOCLASSICAL MODEL OF

THE TAX-EXEMPT BOND MARKET

By

Phillip H. Allman, III

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1982

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ABSTRACT

A NEOCLASSICAL MODEL OF
THE TAX-EXEMPT BOND MARKET

BY

Phillip H. Allman, III

The intent of this dissertation is to construct a
model of the tax-exempt bond market which reveals the
behavior underlying the decisions that determine tax-exempt
bond demand and supply. Neoclassical theory is used to
accomplish this goal. A secondary objective has two parts:
first, to solve the supply equal demand system of estimated
equations for the equilibrium rate of return and quantity
of tax-exempts outstanding; and second, to examine how
exogenous shocks affect these equilibrium values.

The model observes tax-exempt demand as one of several
asset demands in investors' portfolios. The assets held
depend on many variables, the main ones being the rate of
return on each asset and the tax structure. The model is
further divided into two private sectors --bank and non-
bank.

Bank behavior is hypothesized as dependent on long run
profit maximization, where safety is an important constraint.

A bank equation is specified in which bank officers trying

Phillip H. Allman, III

to maximize long run profits choose their portfolio mix
based on their expectations of future economic conditions.

The non-bank specification is similar to other Tobin-
like asset demand models, except it has two important
extensions. First, the tax rate applied to the rates of
return is the tax rate of the investor who is indifferent
between tax-exempts and corporate bonds. Second, the income
of investors in tax brackets exceeding that of the marginal
investor is an important variable.

Since there are two kinds of tax-exempt bonds --each
with a different behavioral motivation behind its issue-—
the bond supply model is correspondingly broken into two
parts.

General obligation bonds are usually issued upon voter
approval, hence a neoclassical model of voter choice is
formulated here.

The decision—maker in the revenue bond supply model is
an elected official; a city manager must determine whether
or not the revenues from future user fees will cover the
repayment of revenue bonds.

With all of the sources of demand and supply estimated,
an analysis of the model as a demand equal supply system is

presented.

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ACKNOWLEDGMENTS

It is with a heavy heart that I squeeze out the last
words of this fulfilling undertaking. It has been my full—
time companion for the last four years, and I will miss it
sorely. Unfortunately, others, who have shared this com-
panionship, must also bid it adieu. At least they will
receive some compensation for this loss in the credits below.

Of course the greatest thank you goes to Robert Rasche
--the Chairman of the committee. His use of the Socratic
method in guiding the progress of my dissertation I found
highly productive. Many of the discoveries I made while
attacking the tasks he put to me will be of great benefit
in future research endeavors. I now feel, my next disser-
tation will be twice as good as this one.

The other committee members were also enormously help-
ful. Aaron Gurwitz supplied the original idea and motiva—
tion. Dan Saks provided many useful insights to the early
drafts and from beginning to end was a constant morale
booster. James Johannes, through a thorough and critical
reading of the paper, forced me to rethink and reinvestigate
some of my hypotheses and the empirical methodology of cer-
tain parts of the study. These suggestions were useful in

the thesis and will be of further use as I continue to

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refine the model. Chris Amsler must not only be thanked
for her evaluation of the thesis and useful remarks, but
also for putting up with my so-called sense of humor.

Several colleagues also contributed generously to the
effort. Coburn Ward provided extensive computer programming
help and mathematical advice. In return he asked only for
a homemade pasta meal. Kerry Doherty was always willing to
discuss technical snags with me. In return he asked only
for my shirts. Hub Segur provided late night motivation.
In return, he asked only that I support farm workers.
Philip Hanser also discussed some technical issues with me.
In return, he asked only that I not eat so much dessert at
his house. Finally, Mark Haas, fellow student, suggested
some Econometric methods which I later used. In return, he
asked only that I never come back to Michigan.

In typing various drafts, fantastic people became
available. My mother, Daisy, typed the early drafts. In
return, she asked only that I be a good boy and not be such
a violent father. Kathy Yoon volunteered to type the mid—
period drafts. In return, she asked that I carry her to a
major mixed-doubles tennis championship. After several
unsuccessful attempts, it is now beginning to look like
this may be a lifetime endeavor. Mary Gambatese, typed
the final drafts. In return, she asked only for money. The
final copy was skillfully done by Jan Wright. In return,

she has not yet had a chance to ask for anything. However,

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she is in a position to make me pay for many things for a
long time.

Phillip H. Allman, Jr., my father, drafted all of the
figures and diagrams which appear in the final draft. He
was also a motivational force. In return, he asked only
that I finish. Max Allman, my son, provided the ultimate
motivation. He bet me that he would finish his dissertation
before me. This time the return goes to me. He owes me
his allowance for a whole year.

Finally, Celeste Allman, Max's mother, contributed
infinite outside support, sacrifice, motivation, and ”nec-
essary" threats. ,In return, she asked only that we do

"everything" we did not do in the last four years.

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TABLE OF CONTENTS

LIST OF TABLES
Chapter
I. INTRODUCTION .
II. REVIEW OF THE LITERATURE
Descriptive Studies
. Empirical Studies
State and Local Government Models

III. A NEOCLASSICAL MODEL OF DEMAND FOR
TAX-EXEMPT BONDS . . . . .

The Theoretical Model
The Variables . . .
The Equations . . . . .
Solution to the System .
Wealth Effects . . .
Empirical Specification
Bank Demand

Specification
Results

Non-Bank Private Demand

Specification . . . . .
Results . . .

Total Demand .

IV. A NEOCLASSICAL MODEL OF STATE AND LOCAL
GOVERNMENT BOND SUPPLY . . .

General Obligation Bonds

Page
vii

19
27

35
36

39
50

58
66
71

71
84

92

92
101

103

105

110

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Chapter

The Theoretical Model—-A Model of
Voter Choice . . . .

The Utility Function

The Budget Constraint .

The Optimal Level of State and
Local Goods . . .

The Optimal Tax Rate .

On Balancing the Budget . .

The Optimal Capital Stock and
Price of State and Local
Capital Services .

The Optimal Level of General
Obligation Bonds

A Discussion of the Dynamics

Institutional Constraints

Summary

The Empirical Specification

The Desired Capital Stock .

The Fraction of Capital Financed

by Debt . . .
General Obligation Bond Supply
Results . .
Revenue Bond Supply
Specification
Results
Summary
V. THE DEMAND-SUPPLY SYSTEM .
The System of Equations
The Multipliers
Examination of the Multipliers
VI. CONCLUSION .
APPENDIX

BI BLIOGRAPHY

vi

Page

110

111
114

119
125
126
127
131
134
135
138
139
139
144
145
147
150
150
160
163
166
166
174
176
196
207

209

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Table

LIST OF TABLES

Bank Demand Estimates Using Ordinary
Least Squares . . . . .

Bank Demand Estimates Using the
Cochrane-Orcutt Method .

Bank Demand Estimates Using Real Bank
Income . . . . . . z . . . . . .

Non-Bank Private Demand Estimates

Equilibrium Supply and Rate of Return

Rate of Return Multipliers Computed for

the Years 1964-1977

Quantity Multipliers Computed for
the Years 1964-1977

vii

Page

85

85

87
102
175

180

186

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CHAPTER I
INTRODUCTION

Federal tax law permits state and local governments to
issue bonds with interest payments which are tax-exempt
(26 U.S.C. Sec 103, 1913). Because of this law and the
kinds of participants evoked by this financial investment,
the tax-exempt bond market is characterized by several
features which clearly differentiate it from other financial

markets. As in most financial markets, its chief function

is to raise investment capital for its issuers. Tax-exempt
bond issuers, however, behave differently than other

issuers because capital financed with tax-exempt debt is

for public purposes. Consequently, the decision-makers who
supply the financial markets with tax-exempts do not attempt
to achieve the same objectives as decision-makers who sup-
jply private debt. The distinguishing characteristic of
tax-exempt debt on the demand side is the tax shelter it

13rovides to its holders. Holders of tax-exempts are con-

£3equently those individuals or entities with potentially

high tax payments.

To appropriately analyze the tax-exempt bond market, a

t'Ilnancial model must be constructed which incorporates the

a--l:)ove distinctions. It is the purpose of this dissertation

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to construct such a model. The model, although it focuses
on the tax—exempt market, observes this specialized market
within the context of a complete neoclassical asset demand
system. Similarly, on the supply side, a neoclassical
model of supply is assembled. This approach to the model
allows a deeper theoretical and empirical view of the
economic behavior underlying the tax-exempt bond market

than previous models have been able to achieve.

There has always been particular interest in state and
local debt because the tax-exemption has created political
controversy, as well as criticism from the economics pro—
fession. The model set forth in this dissertation should
further aid in the evaluation of the political consequences
and criticisms of the tax-exemption.

The political controversy has historically centered on
the immense losses in revenue absorbed by the Federal
government as a result of the exemption. The state and
local governments are the beneficiaries of about two-thirds
Of these revenue losses, since their interest payments are
lower than on comparable taxable bonds. (Huefner, 1972,

I). 2). Naturally state and local governments want to
retain this advantage at the capital markets. Furthermore,
E3‘tate and local governments seem to stand on firm consti-
't11tiona1 ground in demanding the preservation of their tax

a~dvantage, and what they consider unfettered local control

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Some economists believe that the state and local
governments should, on economic grounds despite consti-

tutional guarantees, enter the capital markets on equal

footing with other capital fund pursuants. They contend

that the exemption distorts the proper allocation of
resources within and between the private and public

sectors. (Peckman, 1966; Rabinowitz, 1969). Other

economists attack the exemption further. They find in-
efficiency and inequity because holders of tax-exempts
with high marginal tax rates (the rich) receive a subsidy
twice --once from the municipality which pays a rate high
enough to induce investors with low tax rates to hold their
bonds, and again from the Federal tax payment they escape.
Recently, several compromises have been proposed
whereby state and local governments might receive subsidies
or guarantees in lieu of the tax-exemption advantage
(Kennedy-Reuss Bill, 1975; William Simon proposal, 1975;
thyors Plan, 1975). The political force behind these come
jpromises can be assessed to some degree through the
IDarameters determined in the model developed below. In
Short, the model helps answer some major questions such as;
thaw committed are economists to the concept that the
ekemption significantly distorts resource allocation; how
‘1C> Federal grants affect the allocation of resources; and
hcw strong a political contingent of tax-exempt bond

hc>lders is and will be present in the future. The first

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two questions must come from an analysis of how supply side
decisions are made. The third question comes from the
demand side where one must ask how do economic conditions
such as inflation affect the desire of middle income groups
to hold tax-exempt bonds. These questions and other less
far-reaching questions can be analyzed with the model.
Another political consideration which this model
addresses is the recent series of municipal fiscal crises.
These crises are the result of many fiscal difficulties and
some financing errors by municipal government officials.
One of these errors has been the overextension of revenue
bond issues to the point that some municipalities have
failed to meet the required debt payments. These failures
have been primarily on revenue bonds because the legal re-
quirements restraining their issuance are more lenient than
old-fashioned general obligation bonds which are paid back
through taxes and generally require voter approval. The
model developed here examines these two kinds of bonds
separately. This is an important distinction which has
been ignored in all other tax-exempt bond models constructed
to date. The offering decisions and effects on fiscal sol-
‘Vency differ widely between these two types of bonds. A
IWealistic View of the effect bond issues have on fiscal
c"auditions requires a separate analysis of revenue bonds.
The remainder of this study will proceed as follows.

IP‘irst the economic literature on tax-exempt bond markets

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will be reviewed, and the deficiencies in these models will
be noted, then the present model will be formulated and
described. The demand side will be examined first. The
general theoretical model presents tax-exempt demand as one
of many asset demands in investors' portfolios. The assets
held depend on many variables, the main ones being the rate
of return on each asset and the tax structure. The model
is further divided into two private sectors --bank and non-
bank. This division enriches the model considerably. It
enables non-bank investors to place part of their funds
with intermediaries, and shows that intermediaries choose
asset mixes which differ from the choices of other indi-
viduals or households.

The demand model is then explicitly specified. The
bank demand specification makes a marked advance over pre-
vious bank specifications. Bank behavior is presumed to be
based on long run profit maximization where safety is an
important constraint. In this model, to maximize long run
profits, bank officers choose their portfolio mix based on
their expectations of future conditions.

The non-bank specification is similar to previous
models with two important extensions. First the tax-rate
applied to the rates of return is the tax rate of an in-
vestor whose after tax rate of return on corporate bonds is
equal to the rate of return on equal quality tax-exempt

bonds. Second, the amount of income in tax categories

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equal to and exceeding the tax rate mentioned in the last
sentence is one of the determinants of tax-exempt demand.

The supply model is described next. In formulating
this model, a major effort was made to feature the state
and local government behavior underlying the supply of
state and local debt obligations. As the literature review
discloses, no previous model has made a rigorous attempt
to achieve this objective. Because of this void in the
literature, the literature review chapter includes a dis-
cussion of previously formulated state and local government
models which are related to the behavioral derivation of
bond supply found in the present undertaking. Since there
are two kinds of tax-exempt bonds, each with a different
behavioral motivation behind its issue, the bond supply
chapter is correspondingly broken into two parts.

General obligation bond supply is modeled first.
These bonds are usually issued upon voter approval, hence a
theoretical model of voter behavior is devised. The
empirical specification consequently contains behavioral
variables. This specification permits analyses which were
previously difficult or impossible to examine, such as the
effects of grants on state and local capital demands or the
effect of voters' rates of time preference or the means
used to finance local capital.

The revenue bond model follows. This is a particularly

interesting means of state and local government finance

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where this researcher has uncovered no significant economic
inquiry. The procedure involved in issuing revenue bonds
is unique for two reasons. First, the decision-maker is
usually an elected official with an unknown time horizon in
a management position. Second, the budget constraint
facing this manager is difficult to determine. These two
conditions have made research in this area difficult since
few economists deal with models concerning the behavior of
politicians, and most economists prefer researching areas
where there is measurable data and quantitative conclusions
can be derived. Thus the model presented here is a first
effort. The difficulties encountered and final compro-
mising results will be fully discussed.

With all of the sources of demand and supply estimated,
an analysis of the model as a demand equal supply system is
presented.

Finally, a concluding chapter connects the model to
its political and economic implications, reiterates some of
the innovations of the model, and discusses how this model

fits into future inquiries of the tax-exempt bond market.

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CHAPTER II

REVIEW OF THE LITERATURE

A literature review of the tax—exempt bond market can
be very broad. Most of this work is of a descriptive
nature. Theoretical and empirical analyses of the tax-
exempt bond market on the other hand have not received
extensive attention. The earliest econometric analysis
specifically designed to study the tax-exempt bond market
appeared in Harvey Galper and John Peterson's "An Analysis
of Subsidy Plans to Support State and Local Borrowing"
(1971). This analysis was followed by Peter Fortune (1973),
and Patric Hendershott and Timothy Koch (1977). Hendershott
and Koch subsequently made further refinements (1980). The
review shows that none of these empirical pieces adequately
model the supply side of the market, since they all fail to
develop the behavioral relationships entailed in bond
supply decisions. It is essential to formulate a model of
tax-exempt bond supply which considers how decisions to
purchase and finance state and local goods are determined.

With these observations in mind, the review of
literature is broken into three parts. First, the major
descriptive studies of recent tax-exempt market conditions

will be summarized. (Robinson, 1960; Huefner, 1972;

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Peterson, 1976; Rosenbloom, 1976). Second, the empirical
works cited previously will be critically examined. Third,
several state and local government models relevant to the
tax-exempt bond supply model which will be developed here

are reviewed.

Descriptive Studies

In the descriptive analyses conditions are observed in
the market over a specified period of time, and then condi—
tions for the next three to five years are predicted.
Generally, their prognoses foresee state and local gover-
ments headed for difficult times, as local officials
attempt to float their bonds at rates significantly below
the after-tax market rates on taxable bonds. In other
words, they perceive greater and greater debt needs for
local governments and an unstable group of buyers.

Peterson's paper (1976) is the most recent of this
kind of study. The tax-exempt bond market is viewed
through a short-run perspective only.

Peterson lists the important characteristics of the
current market, especially those characteristics which have
undergone recent changes. This list along with some comment
is as follows: 1) The current U.S. experience is one of
tight money conditions. This is of course a problem for
all borrowers, so should not necessarily be perceived as a

special situation. 2) The composition of tax-exempt buyers

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is changing. Again, however, if this is seen as a problem,
it would be myopic to judge the problem as permanent. If
tax-exempts are worthy investments, the market will uncover
participants. If not, then eliminating the instrument
should not be viewed as a problem. 3) There has been a
large influx of special purpose bonds —-bonds liquidated
with user fees from specific projects-- and short-term
bonds which obviously are not used for the traditional tax—
exempt bond purpose of financing local capital. 4) The
above increase in non-traditional tax-exempt bonds in
addition to fiscal crises in several urban centers has
created new concerns over tax-exempt bond quality and
riskiness; hence many new issues require higher risk
premiums which impose further fiscal burdens. Soothsayers
of doom would judge the situation as a vicious spiral lead—
ing to market collapse. In reality, if recent actions by
local governments cause some insolvencies, retrenchments
will necessarily occur. Similar situations frequently
exist in private markets. Private capital-seekers often
embark on aggressive actions which get them into financial
trouble. When this happens, some appropriate reaction is
attempted. Local officials can do the same.

With the problems created by conditions 1, 3, and 4 in
the list above, Peterson looks to the ”changing pattern in
demand" --condition 2—— to see if some potential resolution

rests here. A great deal of the research on the tax-exempt

-- ~—¢._-._»-

11

bond markets has been concentrated in this area. Peterson
notes that the major buyers of tax—exempts have been
individuals in high marginal tax brackets and commercial
banks. Since World War II, the fraction of tax-exempt
issues held by each has varied depending on cyclical condi-
tions --"annual net purchases of municipal bonds...shows a
fascinating contrapuntal motion between changes in bank
holdings and those of the household sector. The relation—
ship is particularly evident in the tight credit years."
(Peterson, 1976, p. 35) Peterson warns, however, that as
larger banks expand their leasing and foreign branch
activities, their tax-exempt demand will fall, leaving only
smaller banks to provide funds for increasingly needy local
governments.

A similar warning is advised concerning fire and
casualty insurance company demand. They are currently de-
.pressed and reducing asset holdings across the board.

Households, the other group supplying state and local
funds, then must of necessity pick up the slack if the cur-
rent market is to be saved. The household sector consists
lmainly of individuals, trusts, and bond funds. The average
umrginal tax rate for tax-exempt bond holders has been
estimated at about 55% (Galper and Peterson, 1973). It is
suggested that inflation and the progressive income tax
system will systematically push more investors into this

‘bracket, consequently raising demand in this sector. The

empirical model developed here will investigate this pos-
sibility. Up to now there is no empirical evidence that
this ”bracket effect” (A.W. Sametz, et.al.,NYU Paper No.
24) influences household demand.

Peterson concludes by observing that despite the cur-
rent problems in marketing tax-exempts and the criticism
for allowing tax-exemptions on state and local securities
both on equity and efficiency criterion (Huefner, 1972 and
Fortune, 1973), state and local governments still strongly
favor the current legal provisions on state and local bor-
rowing. Presumably, most local governments do not deem the
current problems as pervasive or permanent. On a micro
level, individual localities feel confident in their own
long run ability to market debt in its present condition
and have little interest in new Federal regulations or new
ikinds of subsidies.

If Peterson's list does not trouble the individuals
nmking the decisions, it must not contain even a moderate
‘basis upon which to study tax-exempt bond market behavior.
In fact, the entire discussion offers no model or framework
upon which to base an analysis.

Rosenbloom formulates a simplified theory through
'which to gauge tax—exempt bond market conditions
(Rosenbloom, 1976). Given rN is the rate on a tax—exempt
bond and rC is the rate on a corporate bond of equal

quality, an investor with the marginal tax rate t is

13

indifferent between the tax-exempt bond and the corporate
bond when rN = (l-t)rC. Investors who are in tax brackets
greater than t will prefer the tax-exempt to the corporate
bonds. Rearranging terms: t = 1-rN/rC. Knowledge of

r reveals the tax rate at which an investor will re-

N/rC
arrange his/her portfolio. This ratio has been historically
quite volatile and considered a reasonable estimate of tax-
exempt bond market conditions. Rosenbloom examines tax-
exempt supply and demand to disclose what makes this ratio
vary.

Rosenbloom notes that supply increases have paralleled
inflationary increases since 1960. These increases have
shown no "apparent relationship to the business cycle"
(Rosenbloom, p. 12). Hence the yield ratio fluctuations
are not believed to emanate from the supply side.

As all other descriptive studies, Rosenbloom traces
the demand history of each sector. He goes another step,
however, as he adopts a theory of bank demand. He asserts
that banks primarily strive to fill their portfolios with
loans and to meet liquidity needs. Only the leftover or

"residual" funds are invested in tax-exempts (p. 14). He

notes through observation of Flow of Funds data that there

 

is an inverse relationship between the fraction of deposits
placed in loans and the fraction placed in tax-exempts.
Both fractions fell in 1974 and 1975. This short run trend

led Rosenbloom, as Peterson, to foresee trouble ahead.

14

1980 Flow of Funds data reveal the deep fears of demand
slippage were too hasty. Total bank demand for tax-
exempts, total deposits, and bank loans have all risen
markedly.

Rosenbloom points out that individual demand is
expected to pick up when banks leave the market. A fall in
bank demand raises rN/rc, which lowers t, and causes more
individuals to become subject to tax rates higher than tax
rate t, the rate of marginal investors. Rosenbloom does
not attempt to measure the strength of this effect.

Similarly, he notes but does not quantify the
strengths of the fire and casualty insurance company
Sector. Unlike Peterson, Rosenbloom finds this sector a

Stable and strong source of demand. Current Flow of Funds

 

data show Rosenbloom correct.

In concluding Rosenbloom takes a pessimistic view of
the future market. In 1975 with bond demand falling,
insurance companies making low profits, debt needs rising
steadily, and rates subject to the vagaries of the business
CYcle, he sees municipalities facing an enormous marketing
effort. A more general model might foresee future markets
developing on their own. In fact, recent experience shows
a. considerable expansion in municipal bond funds and in—
creased buying of tax-exempts by thrift institutions.

Beyond Rosenbloom another group of analysts has looked

t0 the Federal government to stabilize the tax-exempt

15

market. The empirical literature on tax-exempt markets was
initiated to show how Federal subsidies and supply limita-
tion policies would improve tax-exempt bond market condi-
tions. Among those involved in this movement are Robert
Huefner, Susan Ackerman, David Ott, Peter Fortune, Harvey
Galper, and John Peterson.

Drawing on the work of Huefner, Ackerman, and Ott,
Peter Fortune outlined a formal, yet elementary, theory of
the tax—exempt bond market (Ackerman and Ott, N'_I‘_J_, 1970;
Huefner, m, 1970; Fortune, m, 1973). This theory
underlies the early theoretical and empirical work done on
tax—exempt bonds. The foundation of this theory is embedded
in Figure 2-1. The tax-exempt to taxable bond yield ratio
discussed in Rosenbloom is on the vertical axis. Recall
I‘N/rC is equal to l-t. The volume of tax-exempt bonds
issued is on the horizontal axis. To induce more indi-
Viduals to purchase tax-exempts, the t value must fall,
this means rN/rC must rise as shown by the positive slope
of the demand curve. For simplicity of exposition it is
a«Ssumed in Figure 2-1 that debt issues are independent of
interest rates, therefore an inelastic supply curve is
Shown.

Figure 2-1 indicates that in order to sell all their
b0nds, municipalities must set rN/rC = .7 so that for the

indifferent investor t =.3.

l6

 

I‘N/rc

.60

.USO

 

.70 ——

 
   

I
I
l
I
I
I
I
I
I

S'

 

 

 

 

I
D I
I
l
I s
0 $1,000 $1,500 $2,000 tax-exempt
bonds
issued ($)
\

 

Figure 2-1

 

 

"000.

no.

o...~

‘1.
4p

‘10

1")

H

17

Fortune employs the model because it is useful in
"pointing out the problems created for the municipal bond
market by using tax-exemption to subsidize the interest of
municipalities... . The chief problems are: (1) The
special sensitivity of the interest rates to monetary
policy; (2) The inefficiency of tax-exemption as a means of
subsidizing municipal debt issues; and (3) the windfall
income which accrues to individuals with higher tax rates
than the tax rate of the last purchaser of municipal bonds."
(p. 21)

The model can also be used to examine the possibility
Of a long run collapse in the market. Both supply and
demand shift right as income and wealth rise. The crucial
Question in the long-run is which curve shifts faster, or
will the shifts in supply exceed those in demand to the
extent that rN/rc becomes too high for local governments to
Withstand. This poses a particular problem to Fortune
because it exacerbates the problems he mentions above.

Figure 2-1 is redrawn in Figure 2-2. Area B is "paid
twice", once by the municipality to inframarginal investors
and once by the Federal government in lost tax receipts or
tax expenditures. According to Fortune, here lies the
SOurce of inefficiency and inequity resulting from the tax—
exemption. No general equilibrium models have emerged to
cOunter this argument. Whether or not a general equilibrium

InOclel would alter Fortune's conclusions is irrelevant to

18

 

 

 

 

 

 

Figure 2-2

I'N/rc
S!
1400-— ____________________ w
A
D!
(70
ID
S tax-exempt
bonds
issued ($)

 

‘-r

c~.-

.F
..v

u _
sin

.n»

nu.

 

19

this paper. But it is important to note that the early
empirical models are constructed to compare efficiencies in
the above sense when different Federal subsidy options are

offered to local governments to replace the tax-exemption.

Empirical Studies

 

Galper and Peterson present the first empirical
zxnalysis of the tax-exempt bond market (Galper and Peterson,
1&371). The Galper-Peterson (G—P) model consists of a tax-
exempt bond supply equation, a non—taxable bond supply
quuetion, a household demand equation for tax-exempts, and
11 household demand equation for other bonds. Other
=sectoral demands for tax-exempt bonds are assumed exogenous.
SDecification of the demand equations are in line with the
Ihosenbloom and Fortune theory delineated previously.
Ifiousehold purchases of tax-exempts depend mainly on the
ratio of the tax-exempt bond yield to the taxable bond
IYield. Bank demand for tax-exempts is regarded as
GXOgenously determined; it comes out of the residual funds
left over after loan demand is exhausted and liquidity
‘needs are met.

Peter Fortune broadens the 0-D model (Fortune, Ell,
1973). His goal, like G—P, is to show the economic
:”Superiority of direct subsidies over tax-exemption.
3Fortune's model has five markets --tax—exempt bonds,

Private securities, U.S. bonds, thrift deposits, and bank

(1-

,5-

Yu-

~“

5‘

20

time deposits. This allows tax-exempt purchases to sub-
sstitute for deposits or U.S. bonds, not just private
ssecurities as in G-P's model. More significant, Fortune
fiilly specifies a bank demand equation with tax-exempt
demand dependent on the rate differential between tax-
eaxempts and long term corporate bonds. However, he doesn't
rweject the residual theory; the choice of what kind of long
term bonds to buy is made _a_f_t_e_r_ the total amount of long—
term purchases is determined, which depends on bank loan
and liquidity demands. Fortune makes his model a residual
‘theory by scaling the yield ratio by the change in total
Ihong term bond purchases. Despite the additional attention
‘to bank demand, the R2 for Fortune's equation is .85 and
‘the D.W. is .80. It appears that there are serious auto-
correlation problems.

The household demand equation is similar to that in
(i—P with independent variables being the aforementioned
IYield ratio, the change in household purchases of all kinds
(Bf bonds and a list of definitions which allow Fortune to
test the efficiency of different subsidy plans. Despite
the complexity of this equation, its usefulness is ques-

tionable. The R2 is .17 and the D.W. is .83. G—P also had

poor R2 and D.W. statistics although not as poor as Fortune.
3Fortune suggests the problem may be in his data, not his

sPecification.

"I

0-.”

in“

- _
u.._

(I)

V.

‘.
.4.

(1‘

C)"

‘1.

’r 1

21

Both G-P and Fortune attempt to show a behavioral
relationship between local government decisions and tax-
exempt bond supply. G-P note that borrowing depends on
local construction demand, which is assumed to be a linear
function of GNP. Gross tax-exempt bond supply over con-
struction demand is their dependent variable. The only
major independent variable is the rate of return on tax-
exempts. The equation has an R2 of .66 and D.W. of 1.45.

Fortune's supply equation is no more explanatory
than G-P's equation. Net issues of tax-exempt bonds is the
dependent variable. To measure the demand for state and
local capital goods, Fortune simply inserts disposable
income as an independent variable. He also attaches net
State and local government receipts to the equation. No
rationale for its inclusion is given and there is probably
a great deal of multicollinearity between net receipts and
disposable income. The R2 is .66 and D.W. statistic 1.79.
The obvious inadequacies of these models led to the
Hendershott and Koch study (1977).

Hendershott and Koch (H—K) have constructed the most
Clolnprehensive economic model of the tax-exempt bond market
to date. On the demand side, they have delineated a full
behavioral model. Bank and insurance company tax-exempt
b0nd demands depend mainly on profits. Household demand
depends mainly on the relative rate of return on a full

portfolio of assets. Their supply model offers possibly a

n
i“

(II

(‘I

22

slight improvement over the other models; an accounting
:framework is used to restate the same variables found in
‘the equations of earlier studies.

H—K, in taking a profit maximizing approach to bank
tzax—exempt bond demand, put forward a more general, long—
Iweaching model. H—K maintain that a certain base stock of
'taxeexempts must be held to obtain the long run income or
Iprofits which the banks expect to acquire. Discounting
(expected future income by the average rate on tax-exempts
«determines this base stock demand. From this base, H-K
begin augmenting their equation. Other tax shelters and
a-Ininimum level of taxable assets to avoid legal harass-
!nent are subtracted from the base stock.

Two adjustments for short run deviations are then
*entered. When actual profits exceed expected profits, more
“tax-exempts are demanded because more income must be
'Shielded from taxation. To show this effect, the dis-
‘counted difference between actual and expected profits
becomes a variable.

When the rate of return on tax-exempts relative to the
rate on taxable securities is abnormally high, tax-exempt
demand goes up to take advantage of these conditions. Con-
versely, when the relative rate on tax-exempts is abnormally
low, tax-exempt demand falls. To capture this effect, H—K
use a moving average of past ratios of tax—exempt rates to

taxable rates as a proxy for the normal rate ratio. The

23

difference between the current ratio and the normal ratio,
scaled by profits, becomes an additional independent
variable in the equation.

In their actual specification, H-K have observed data
and decided to enter the independent variables alone and
with two truncated time trend factors. The regression re-
sults show R2 = .997 and D.W. = 2.04. This observor
believes that these highly supportive results come about
because of the time trend factors. H-K used their model
to forecast future demands. Their second time trend factor
follows a fall in demand over the later years of their
observation period. Hence future forcasts are likely to be
understated. In fact, their 1979 prediction is $10 billion
short of the actual amount of tax-exempts held by banks.
This is not to suggest that their model should be rejected,
but a model with less manipulation of data and more des-
criptive power can surely be constructed.

H—K's use of the profit motive as the underlying
characteristic of tax-exempt demand is noteworthy. The
model put forward in this paper will begin with the same
premise when reconstructing a bank demand equation. How-
ever, H—K's method of making profits a determinant of tax-
exempt demand is peculiar. It seems unrealistic for bank
managers to have some expected profit level in mind to
which they adjust their tax-exempt bond holdings. Bankers
adjust their portfolios on a daily basis in anticipation of

market conditions and changing expectations of future rates

 

pru-

v.14-

3“ .

It:

N‘s

at,

I"
(I)

1"

’1

J

'C’

(j

24

of return on many competing assets. A more descriptive
profit maximization model should observe the behavior of
bank asset managers and how they adjust their portfolios in
an unending effort to maximize short-run and long-run
profits —-keeping in mind that short-run and long-run
profit maximization may require conflicting portfolio
choices.

H—K also model Property Insurance Companies and in a
later article (1980) model the demand of thrifts. These
models follow the commercial bank model outlined above as
no significant changes in methodology are made.

To model the household sector H-K utilize standard
portfolio theory. The demand for tax-exempts depends on
the own rate of return, the after tax rates of return on
U.S. government bonds and equities, and the total value of
asset holdings.

H-K's empirical estimates immediately run into prob-
lems. The coefficient on the tax-exempt yield is unac-
ceptably low and the D.W. statistic is low. H-K attribute
the low coefficient to "simultaneous-equation bias." The
rates must adjust for the demand of each asset market to
clear the existing supply. Although they ignore the
possibility, their method of choosing the proper tax rate
could also have damaged their results.

To resolve their problem, H-K make the tax—exempt rate

of return the dependent variable but find that the rate of

.34“
an.

inn...

9...

Vin.

-.

«A

v.4“.

n»-
.0...

..\\

rah
r.-

25

return on taxable bonds overshadows all other relationships.
Thus, they make further adjustments and reestimate house-
hold demand as a function of the original variables. The
results show R2 = .768 and D.W. = 1.38, still statistically
weak.

To model tax-exempt bond supply, H-K employ an
aggregate state and local government sources-equal-uses
statement. Simple algebra yield issues of tax-exempt
bonds equal to uses of funds minus the sources of funds
other than tax-exempt bonds. These categories of uses and
sources are redefined and a linear function is expressed:
tax-exempt bond issues = 80 + 81 (structures) - 82 (federal
grants) - 83 (net of all other sources and uses). H-K
implicitly assume that structures and grants are the
variables whose relationships with tax-exempt bond issues
are the most important to uncover.

Structures are deemed important because most states
have legal debt limits allowing debt to be issued only for
special purposes, such as capital financing, or requiring
current operating budgets to balance. Grants are important
because they provide state and local governments a sub—
stantial source of funds, which offer numerous additional
options to state and local government finance. H-K expect
grants to be negatively related to tax-exempt issues, as

this relationship follows from the accounting identity.

5‘.
va

It:

"I‘

u-

I
on,

. .

‘u.

(D
(I)

0-

‘v

r?

L).
(D

26

To the three regressors from the accounting relation-
ship, H-K adjoin a ten year tax-exempt rate "in an attempt
to capture this permanent portfolio response” (p. 39). As
a final regressor, they try to reveal short run supply
variations in reaction to the tax-exempt rate by observing
deviations of the present rate from a "normal" rate. They
foresee state and local managers adopting regressive
expectations of future rates --i.e. local government
managers think the rate will return to its normal level
which is an average of previous rates.

H—K have merely added ornamentation to G—P and Fortune.
There is essentially no behavioral analysis involved in
this equation. Statistically, the results are excellent,
but they should be inasmuch as the explanatory equation is
based on an accounting identity of the variable being
estimated. The dollars spent on structures and received
from Federal grants are obviously involved in the decision
to issue bonds, but these dollars do not hold a direct
causal relation with bond issues. All of the variables
found in the accounting relationship are ex post; these
numbers appear after the important decisions have been made.
Local governments agree upon some method of choice to de-
termine the structures they need, the taxes they are willing
to pay, how they will use grant money, and the amount of
debt they want. Embodied in these decisions are the effects
of borrowing rates, which H—K tack on to their accounting

structure. Only on an accounting sheet should it

.II...
6—4'

an
I [I

' I
0‘!!-
a.....

' .
15“ y.
cc. \
I‘ .
. .I>\

C)‘
.,7
C 4

"h
1“,:

1"
l.
)

27

unquestionably hold that Federal grants reduce state and
local bond issues. Grants can lead to larger volumes of
local debt because matching grants make local public

services relatively cheaper than private services. H-K's

model misses these behavioral relationships.
State and Local Government Models

The literature related to the model developed here
utilizes standard household optimization procedures to
derive an expression of demand for state and local services.
Although the entity whose welfare is maximized may vary
slightly from model to model, the optimizing variables are
quite similar.

A pioneer article using this approach was formalized
by James Henderson (1968). "It is postulated here that the
resultant public expenditure and tax decisions can be ex-
plained as if they were the result of maximizing a social
welfare function subject to a social budget constraint, both
defined in expenditure space" (p. 156). The community wel-
fare function is W==(a0 + alY + a2R + a3P) logeG + X, where
Y is per capita personal income, R is per capita grant
money, P is the community's population, G is per capita
local public spending, and X is all other uses of income.

The community budget constraint is: Y-X = T = b(G-R),
where T is per capita local taxes and b is a fixed propor-

tion of the difference between local spending and grants.

28

Hence l-b of each expenditure dollar is financed with debt
issues.

Henderson maximizes the welfare function subject to
the budget constraint and generates an expression of ex-
penditure demand. As in all maximization problems, he
regenerates the budget constraint when taking the derivative
of W with respect to the Lagrange multiplier. Unfortunately,
however, he then rearranges the budget constraint to
isolate X, which he interprets as the demand for private
goods.

Henderson's initial idea is creditable, but his method
fails to catch the whole picture. First, note the form of
W --when taking the derivative of W with respect to X, X
drops out. Second, the budget constraint is a constraint
on G spending only, while W, the variable being maximized,
allows for X spending as well. A proper constraint would
bind all spending, not just certain appointed kinds of
spending. Finally Henderson neglects the production side
of the problem entirely. Borcherding and Deacon rectify
many of these defects as they present a broadened model in
a later article (Borcherding and Deacon, 1972).

Borcherding and Deacon (B-D) consider their model the
first non-3d hog construction, as their model is based on
the accepted theory of collective decision making (Bowen,
1943; Arrow, 1963; Black, 1948; Downs, 1957; Buchanan and

Tullock, 1962). B—D follow the original Bowen argument

29

that the provision of local goods is set where the marginal
benefit of the median voter is equal to the marginal tax
price of the median voter. B-D further assume that log-
rolling is inefficient and not done; and they assume
bureaucracy does not create productive inefficiency, so
local goods are produced with least cost methods. Finally,
the production function is assumed to be a Cobb-Douglass
type.

B—D derive a marginal cost function which with its
Cobb-Douglas properties is horizontal. The amount of the
local good consumed by the median voter depends on the
degree of rivalry inherent in the good. B-D posit this
consumption as total production over community population
taken to an exponent which reveals the good's degree of
rivalry. They further assume that the marginal tax price
of the median voter is equal to the marginal cost of the
good divided by the community's population level.

From this point B—D take a large leap. They postulate
a median voter's local good demand function; it is log-
1inear and depends on the median voter's marginal tax price,
previously derived, and the median voter's income. B-D use
this form because it offers a highly tractable empirical
specification, which is subsequently estimated.

B-D have also passed over some crucial pieces of
theory. The median voter must optimize with limited

resources, but the choices and resources available are

30

ignored. Hence the demand function B-D posit has an
unknown base from which to emanate. There is no reason to
accept their demand schedule. Second, the financing de-
cisions are not clear. These decisions are embedded some-
where in the marginal tax price, but there is no mention
of where.

B—D have, however, broadened the model to include pro-
duction, and the idea that a median voter chooses between
public and private goods with a constraint on all choices.
Bergstrom and Goodman in an article following shortly after
B-D attempt to clarify the relationship between the demand
schedule and the optimizing behavior of the median voter
(Bergstrom and Goodman, 1973).

Bergstrom and Goodman (B-G) note a utility function
whose arguments are public goods and private goods. The
median voter maximizes utility subject to a budget con-
straint where income is equal to the price of private goods
times the number of private goods purchased plus the
marginal tax price -—as explained in B-D-- times the
quantity of public goods produced. B-G assume that the
demand schedule derived from this procedure is very similar
to the demand curve postulated by 8-D. B—G, as did B-D,
then go about estimating their log-linear equation.
Although they have been openly vague about the proper form
of the median voter's utility function, B-G have taken

another step toward a complete median voter model.

31

At about the same time as B-G, Gramlich and Galper
(G-G) came out with another utility maximization state and
local government model (Gramlich and Glaper, 1973). The
entity whose utility is maximized is unclear, but we are
given some "objectives" of state and local decision-makers.
These objectives are the arguments of the utility function
G—G posit. This utility could belong to the community, as
in Henderson. It could belong to the median voter, or
possibly to the officials themselves. It could even be some
combination of official and community welfare as perceived
through an unstated procedure of collective action. In any
event, the local decision-makers attempt to maximize this
utility subject to the localities budget constraint.

The objectives of state and local government are: (1)
higher current expenditures; (2) higher disposable income;
(3) greater flows of services from the capital stock; and
(4) greater flows of services from the stock of financial
assets. The budget constraint ensures that any rise in
lgggl spending is matched by a grant, taxes, or the sale of
financial assets. Just like Henderson, this constraint
only binds certain variables in the utility function. The
choice between private goods and local goods must be made,
before the model becomes operable; i.e. objective 2 above
is not bound by the state and local government budget con-

straint —-it must be exogenous or predetermined.

on

.u-

1.“.

lo

32

As a tool in developing a state and local debt model,
the G-G model is further deficient in that it does not
allow expenditures to be financed with debt ——not even the
expenditures on capital. G-G do, however, advance the state
and local model by suggesting that services flow from cur-
rent accounts and capital accounts. This distinction is
useful in developing a bond supply model. Ott and Ott con-
sider this distinction in an even more comprehensive state
and local government model presented a couple of years
later (Ott and Ott, 1975).

Following the work of Buchanan and Tullock who assert
"collective action, along with private action, is motivated
by individually-conceived ends, and all action proceeds
only after a mental calculus is performed by some indi-
vidual or individuals" (Buchanan and Tullock, p. 316), Ott
and Ott (O-O) adopt the median voter approach to state and
local government decision-making behavior. Similarly to
Borcherding and Deacon, O-O assume that majority rule leads
to a combination of choices in line with the optimal choice
of the median voter.

O-O affirm that the median voter in choosing public
and private consumption within his/her budget must be
restricted to current account purchases only. "It is
impossible to specify the appropriate 'tax price' for the
services of state and local capital, and even if it were

possible, the necessary data on state and local government

 

33

stocks of capital and flows of services would still be
lacking" (p. 12). Hence O-O only use the median voter
approach to analyze the current account, while they take
an EQ.E2£ approach to analyze the capital account.

For their current account model, O-O adopt the assump-
tions laid down by B-D. Their utility function contains
a basket of state and local goods and a basket of private
consumption, savings, and Federal goods. Each of these
goods is expressed with a population variable taken to an
exponent to express, just as B-D and B-G, the degree of
rivalry in consumption.

The budget constraint is the price of private and
Federal goods times the quantity of private and Federal
goods purchased plus the tax price to the median voter
times the quantity of local goods purchased set equal to
the median voter's income, assumed to be the mean of com—
munity income.

The first order conditions yield an expression of
demand for each of these goods. They are a function of per
capita income, the tax price, the price of private goods,
and population. In estimating these demands 0-0 make
assumptions limilar to B-G.

O-O then move to the capital account or "structures"
side of their model. They point out that capital provides
a flow of capital services, "the median voter demand is for

a flow of capital services during a given period" (p. 17).

34

I disagree. The median voter wants a flow of local govern-
ment services. Providing these services requires capital.
In fact, the government services described by 0-0 earlier
on the current account can only partially be provided with-
out the services of capital.

O-O dismiss capital from their central model because
they perceive inequalities in the payment flows and benefit
flows of capital services from one time period to the next
since the services of capital extend over such a long time
span. They express an uneasiness about the high probability
that "the price of capital services the median voter is
willing to pay may not be equal to debt retirement plus
interest" (p. 18).

In the final segment of their model, O-O pronounce a
bond supply specification. It is a function of construc-
tion expenditures minus grants, the tax-exempt bond rate,
and the previous period's asset to debt ratio. This speci-
fication has the same deficiencies referred to during the
discussion of Hendershott and Koch, and Fortune, etc.

There is no behavioral motivation behind the specification.
The bond supply decision must be made contemporaneously
with the decision of how many local goods to produce and
the choice of inputs necessary for this production.

In the next two chapters a model will be developed

which addresses the deficiencies discussed in this review.

CHAPTER III

A NEOCLASSICAL MODEL OF

DEMAND FOR TAX-EXEMPT BONDS

In this chapter a model of tax-exempt bond demand will
be delineated. The theoretical model is cast in a modified
”capital account" framework (Tobin, 1969). Tax-exempt bond
demand is considered within a whole portfolio of competing
assets, where a vector of rates of return and other
variables adjust to equilibrate the supply and demand of
every asset in the portfolio. Observing tax—exempt bond
demand within a portfolio of financial assets and liabil-
ities, rather than in isolation, insures that no relevant
variables are neglected; every asset demand function con—
tains the same interrelated variables.

With the above variables determined, the model's
empirical specification of tax-exempt bond demand is
expressed in a partial equilibrium framework. The desired
fraction of assets placed in tax-exempt bonds becomes the
dependent variable and the endogenous variables from the
general equilibrium system become in equilibrium the
independent variables of the regression equations. This
implicitly assumes that the endogenous variables in the

general equilibrium system adjust quickly to equilibrate

asset demands with asset supplies.

35

36

The Theoretical Model

 

The theoretical model of tax-exempt bond demand
formulated for this analysis departs from previous studies
in two ways. First, tax-exempt bond demand is observed
within a general equilibrium system comprised of two
sectors and seven financial markets.

Second, the relative after tax rates of return on
financial assets depend directly, via the tax structure, on
the level of nominal wealth. (Unlike the capital account
approach adopted in this analysis, the "balance account
approach" (Brunner and Meltzer, 1963, 1972, 1973) asserts
that wealth changes do alter the yield and price structure
of assets. However, they are not altered in the systematic
way put forward in this model.)

To depict fully the demand for tax—exempt bonds within
a comparative static framework, it is necessary to construct
a model which places several financial markets and two sec-
tors into a general equilibrium system. Such a system
shows the interrelationship between tax-exempt bond demand
and other financial asset demands, and displays the inter-
sectoral activity which determines total tax-exempt bond
demand. In particular, it is important to separate the
financial sector from other sectors, since the activities
of financial intermediaries heavily influence the allocation

of the economy's wealth.

37

The requisite sectors of the model are the banking and
household sectors; they have historically combined to fill
80 to 90 per cent of total tax-exempt bond demand. Insur-
ance companies have held most of the remaining 10 to 20
per cent. The dominance of these two sectors results from
a lack of alternative tax shelters which insulate other
upper income entities from high marginal tax rates. The
two sectors appearing in the model are "banks" and "non-
bank private," where non-bank private includes the house-
hold sector agg private business enterprise. Business is
included in this sector because businesses and households
share in the demand for the assets observed in the model,
and because businesses supply corporate bonds which are
close substitutes for tax—exempt bonds in the household's
portfolio. Most businesses are not interested in tax-
exempts because they can obtain more profitable ways to
avoid taxes, such as depletion allowances, investment
credits, depreciation deductions and other businesses
expenses. Insurance companies, lacking some of these tax-
sheltering opportunities, have been the major buyer of tax-
exempt bonds among businesses.

The financial assets relevant to the portfolio deci-
sions of the two sectors are (in real terms) equity capital
(qK), high-powered money (M/P), federal government
securities (S/P), non-taxable bonds (N/P), corporate bonds

(C/P), bank deposits (D/P), and bank loans (L/P), where P

38

is the price level. (Note: the q in qK is taken from
Tobin's model --the price of existing capital over the
price of new capital (Tobin, 1969).)

The basic model is formulated at a single point in
time, where the general price level and flow variables are
exogenously determined. This formulation is used since
financial assets are stock variables which can be measured
only at a particular moment. An economic unit can either
accumulate or depreciate its wealth over time, but at each
instant that a portfolio decision is made, the unit's desire
to hold assets is constrained by a given legacy of wealth.
This technique of analysis as alluded to previously is
termed the "capital account approach" (Tobin, 1969).

The amount of an asset held by either sector depends
on the rate structure, real wealth, and several other
variables which will be discussed later. According to the
capital account approach, the desired amount of each asset
is homogeneous in wealth --that is, if the rates of return
do not change, an increase in real wealth will bring about
a proportional increase in the desired amount of each asset.
This will occur if there is a proportional increase in all
asset supplies.

Unlike the standard capital account approach, in this
model a proportional increase in all assets directly changes
the relative after tax rates of return on the assets. This

direct effect occurs because as nominal wealth rises, none

 

39

of the additional nominal income earned on additional tax—

exempt bonds is lost when investors move into higher income

tax brackets.

At the same time the added nominal income

earned on the other assets is subject (due to the progres—

sive income tax law) to higher marginal income tax rates.

This model follows the capital account approach, neverthe-

less, in that decisions to save are independent of asset

portfolio allocations. This independence is retained in

the model developed here. (The direct effects of wealth

on the rate structure will be examined in greater detail

later.)

The Variables

The nominal rates of return in the model are:

the rate of return on equity capital

the rate of return on currency and reserves

the rate of return on treasury securities
the rate of return on tax-exempt securities
the rate of return on corporate securities
the rate of return on bank deposits

the rate of return on bank loans

Federal Reserve discount rate

is the Xector (rK, rM, rs, rN, rC, r

rL,

40

The real after tax rates of return on assets held by

the banking sector are:

r3 the real after tax rate of return on free
reserves and required reserves

r; the real after tax rate of return on
treasury securities

rs the real after tax rate of return on
tax-exempt securities

r: the real after tax rate of return on
bank loans

d real Federal Reserve discount rate

rD the real rate of return on bank deposits,

a liability, hence requiring no tax rate

11 u
u d,

s' rN’ rL’ 1'

. u
13 the vector (rM, r D).

The rates of return on capital and on corporate bonds
are not entered into the banking vector, as banks are
legally prohibited from investing in most types of corpo-
rate stock, and very few banks invest in corporate bonds.

rD is also constrained by government regulations; legal
ceilings have been placed on the nominal rates of bank
deposits. With the exception of large certificates of
deposit, in recent years the market rates on deposits have
rarely fallen below the ceiling rates. Consequently, bank
supplies of total deposit offerings to the public have been
very elastic.

The discount rate, d, is important because when it
goes down relative to the rates on bank assets, it becomes

profitable for banks to borrow from the Federal Reserve and

41

invest in the income earning assets. This means the level
of non-interest bearing assets held by banks should decrease.
In short the fraction of bank assets held in free reserves
should fall. This conclusion cannot be asserted unequi-
vocally, however, since it is not certain how excess
reserves will change in response to a change in d. His-
torically, the level of excess reserves has remained
relatively stable when compared to the level of borrowed
reserves. (Historical Chart Book, 1978). The argument is
often made that many banks attempt, quite successfully, to
keep their excess reserves close to zero. This would sug—
gest that most of the fluctuations in free reserves in
response to changes in d occur through the effect of d on
borrowed reserves, where there is a clear negative rela-
tionship. Thus when d rises, the demand for borrowed
reserves falls and the demand for free reserves rises.
Furthermore, free reserves may be held in case reserve
requirements cannot be met when d is prohibitively high.
The after tax real rates of return on assets held by
the portion of the non-bank private sector supplying funds

(i.e., lending) are:

r; the real after tax rate of return on
equity capital

r; the real after tax rate of return on
currency

r; the real after tax rate of return on

treasury securities

42

r; the real after tax rate of return on
tax—exempt securities

ré the real after tax rate of return on
corporate securities

r3 the real after tax rate of return on

bank deposits.

The real rates on liabilities to the non-bank sector are:

the real rate of return on corporate

C securities
rL the real rate of return on bank loans.
At . t t t t t t
r is the vector (rK, rM, rs, rN, rc, rD, rC, rL).

d is not included because only banks can borrow from the
Fed. With the introduction of inflationary expectations,
taxes, and the price of existing capital, the after tax
real rates of return can be more precisely defined. The
symbols involved and their rationale are described below.

n* is the expected rate of change in the price level.
In choosing a time series for this variable the literature
has been thoroughly reviewed. The time series data chosen
was produced by John Scadding whose series is in close touch
with the current state of the art on the subject of
inflationary expectations (Scadding, 1979):

This paper (John Scadding) presents a model of

how individuals might rationally extract information

about the underlying inflation rate from observed

price changes, and how they might use that informa—

tion to forecast future prices...

Traditionally, economists have assumed that
economic agents form their expectations about future

events adaptively, i.e. the forecast for next period
is forméd by adjusting this period's forecast by some

43

fraction of this period's forecast error. Price

expectations are commonly modelled this way, although

the adaptive model is in part ill-suited for this
purpose because it leads to chronic underprediction

of prices if prices are growing. The reason is fairly

obvious. The adaptive model implies that forecast

prices are a weighted average of current and past
prices, which will always be less than the current
level when prices are growing. The forecasting

model developed in this paper represents a generaliza-

tion of the adaptive model that allows for systematic

growth in prices and therefore avoids the problem of
chronic underprediction. The model has the added
attraction of being derived from optimizing behavior,
rather than adduced on an 3d hoc basis as is typically

done (Scadding, 1979, p. 7).

It is also important to note that although the price
level is fixed and acts as a constraint at the moment of a
decision, expected price changes do enter into the decision-

:0:
making process. In short n injects a dynamic element into
a static decision-making model.

u is a weighted average of the marginal corporate
income tax rates facing a bank in a given year. Each rate
is weighted by the fraction of bank income which is taxed
at its rate. These rates have periodically changed.

T = T(y*(W), P*, T*) is the expected income tax rate
applied to investors who are indifferent between tax-exempts
and corporate securities. y is the real income derived from
the human and non-human wealth of these marginal individuals;
so y* = y(1 + (the expected growth rate of y)).

P* = P(l+n*) is the expected price level. T* is the expec-
ted tax structure, which is assumed to be realized. Here

again a dynamic element is placed within the static frame-

work. When P* or y* rise, the number of investors in tax

44

categories greater than or equal to T rises.

q as previously noted, is equal to the market price of
ownership claims to existing capital divided by the repro-
duction price of new capital (the general price level).
Allowing the value of equity capital to be a proxy for all
financial claims to existing capital, an old car has market
value included in qK under the general title of equity
capital. The variable q enriches the model, as it allows
the general price level (the price of new capital) and the
price of existing capital to diverge. This divergence in
relative prices causes financial portfolio rearrangements
discussed below.

rk = R/q; this simplified form for the real pre-tax
rate of return on equity capital assumes that capital does
not depreciate and has an infinite life. R is the marginal
product of capital which in equilibrium is equal to the
rental cost of capital (RC) divided by P. Since Pq is the
amount an investor must pay for a claim to a unit of
existing capital, r' ° Pq = RC or r' = RC/Pq; and since

K K
RC/P = R, then rk = R/q.

If the depreciation and lifetime assumptions are
dropped, the inverse relationship between rk and q still
holds. For instance, if the price of existing capital
rises relative to the price of new capital (q rises), then

rk falls because it costs more to buy the existing capital

used to produce a steady return to its owner.

45

There are two effects as a result of a fall in rk.
The first is financial; when the rate on equity changes,
all rates must change in order to restore equilibrium in
the market for each asset. The second effect is real; if
new capital costs less per unit than old, then it pays for
the investor to invest in new capital —-that is, increase
the level of the capital stock. This of course requires
time and causes W to change. Thus a link is provided from
the financial markets to a short-run flow model of income
determination. At the end of each period W will be dif-
ferent, but fixed for the moment, and rk, as well as the
rates on other assets, must adjust in order to induce
financial investors to hold the existing stock of each
asset.

Although it is an essential part of this study to
understand the theoretical relationship between the rate of
return on equity relative to the rate of return on tax-
exempts (especially during inflationary periods), the com-
ponents of the variable R/q are difficult to measure and
apply to practical use. Efforts to measure R and q have
been conducted (Brainard and Tobin, 1968), but these
methods require a great deal of approximation. A simple,
more practical measurement of rk should serve the purposes
of the present undertaking. Keeping in mind that the price
of equity is used as the general price of a claim to all

existing capital, a standard definition for the real rate

of return on equity is employed --rk = (nominal earnings per

 

46

period, E) e (the value of stock prices at the period's
beginning, SP) minus the expected rate of inflation at the
beginning of the period, n*; rk = E/SP - n*.

The revised definition is easily related to the pre-
vious one. When the price of new capital or the marginal
product of capital rises, E should rise --when prices rise,
nominal earnings rise, and when productivity rises, real
earnings should rise. Changes in stock prices reflect
changes in the price of existing capital. Since E is the
nominal return, n* must be subtracted to get the asset's
real rate of return. With this rationale, the changes in
rk can be viewed as the result of changes in q or R. With
these relationships established, the list of after tax

real rates of return can be further explained.

u
M

required or free reserves, so there is no income earned or

r = - n*. There is no nominal interest rate on
tax placed upon them, but there is an anticipated loss in
purchasing power shown by the expected rate of inflation.
r: = (l-u)ré — n*. (l—u) is the fraction of income
derived from federal securities which is not taxed away,
and again n* shows the expected loss in real buying ability.
u = r' - n*. There is no tax rate applied to the

N N
nominal return of state and local bonds, as they are tax—

r

exempt. This rate is not precisely correct, but making it
correct would require redefining other rates in a way which

is impossible to do when using aggregate rates.

 

47

When measuring the after tax return on an asset, to be com-
pletely correct, the tax reduction associated with the tax
deductions from interest payments on funds borrowed to
purchase the asset should be added to the after tax return
of the asset. Correspondingly, the after tax rate of
return should be modified by adding to the rate of return
a fraction equal to the borrowing rate times the indi-
vidual's tax rate. Of course determining this rate is
impossible to do on the aggregate, since not everyone bor-
rows to invest, and borrowers acquire their funds from
different sources with different rates of return. However,
this concept is still relevant to tax-exempt bond demand
because the Internal Revenue Service does not permit
individuals to deduct interest payments on funds used to
purchase tax-exempts. Since bank funds come from a general
source which may be invested in any number of assets, banks
can still deduct the full value of their interest payments
from taxable income. This law then provides banks with a
greater incentive to invest in tax-exempts than it does
individuals; the banking sector's rate of return should
additionally include ur', while for individuals, interest
deductions in taxes would not be included in the rate of
return for tax-exempts.

rD = rb - n*. rb is a weighted average of the rates
on demand deposits, savings deposits, and time deposits.
Some of these rates are legally fixed at a level below their

unregulated rate.

 

48

r = (l-u)ri - n*.

d = d' - n*. Since banks borrow from the Fed, n* is
an expected gain because the banks pay off their debt with
money which has less purchasing power.

r; = (E/SP)(l-T) - n*. This variable has an upward
bias because it overlooks the double taxation of corporate
income. At the same time it has a downward bias because T
(the marginal investor's tax rate) may be greater than the
corporate tax rate for most investors and the tax advantage
of capital gains on equity is ignored. Obviously, a perfect
measurement of the aggregate after tax rate of return of
equity is impossible to uncover, but using T as a rate
applied to corporate earnings puts the after tax rate on
equity more closely in line with the after tax rates on
other assets.

r; = - n*. n* is the inflationary loss of holding
currency. Not included in rt is the shoe leather cost of

M
trying to keep currency holdings at a minimum.

t: .. '-*

rS (l T)rS n .

t:'-*

rN rN n .

rt = (l-T)r' - n*

C C '

r; = (l-T)rb - n*. r5 is influenced by regulation Q.
The weighted component of r' referring to demand deposits

D
is equal to zero (until recent decontrols). Thus when n*

rises, rb cannot adjust fully to the desired real rate of

49

return, so r; falls relative to the rates on other assets
and the desired amount of bank deposits is reduced.

rL = rt - n*. Loans are a liability to this sector.

Other symbols used in the model are:

fip-—the fraction of wealth which the non-bank private
sector wishes to hold as asset i.

fib--the fraction of loanable bank assets (which equals
their deposit liabilities minus required reserves) the banks
desire to put into asset i.

K is a weighted average of the legal reserve ratio on
time deposits and demand deposits.

Y/W denotes the transactions need for money --currency
or demand deposits. Conventional theory of money demand
says as income rises, more money must be readily available
to make the greater volume of purchases allowed by the
higher level of income. With the level of W fixed, there
must be a corresponding decrease in the fraction of public
wealth desired in other assets. If W rises by the same
proportion as Y rises, more money can be held for transac-
tion's needs, without changing the fraction of wealth held
in money balances. Similarly, if W rises by a greater pro—
portion than Y, more money can be held while the fraction
of wealth held in money balances decreases.

pol represents changes in banking portfolio policy

(similar to a "taste” variable as an argument in the demand

for a real good). This variable reflects the degree of

50

bank aggressiveness or caution when choosing between
profitable (illiquid) and safe (liquid) assets.

NS stands for new forms of tax shelters for banks.
The most important of these is leasing operations which
gives banks all the investment tax credits and deductions
allowed to companies employing physical capital. Another,
though less important shelter is foreign activities. The
advantage here is that the United States allows tax credits
on foreign profit taxes.

These last two variables are essentially shift

variables in the sense of Brainard (Brainard, 1964).

The Equations

With the variables listed and discussed, the static
financial asset model can be formally stated.

The definition of real private net wealth is:

w = qK + (N + M + S)/P

The balance equations for the capital account are:

 

Banks Non-bankgpgivate
(l) flp(£t’ Y/W)W = qK (equity capital)
(2) RD + f2b(£“, pol; NS)D(l-k) + f2 (ft, Y/W)W - M/P (high-powered
p money)
(3) f3b(;u, pol; NS)D(l—k) + f3 (9‘, Y/W)W = S/P (federal
p securities)
(4) f4b(§“, pol; NS)D(l-k) + £4P(Et, Y/W)W = N/P (tax-exempt

bonds)

51
(5) f5 (Pt, Y/W)W = 0 (corporate
p bonds)
(6) f6b(£u’ pol; NS) + f6p(£t’ Y/W)W = 0 (bank deposits)

Definition: D = f6p(£t’ Y/W)w

(7) f (Pu, pol; NS)D(l-k) + £7p(£t, Y/W)W 0 (bank loans)

7b

In each line the private demand for that line's asset
is to the left of the equal sign. To the right of the
equal sign is the net supply of the asset. If the net sup-
ply is equal to zero, total debts equal total credits
leaving no he: supply. If the net supply is greater than
zero, as in the equity equation, assets exceed liabilities
in the private sector; or, as in equations 2, 3, and 4, the
government is a net debtor leaving net assets in the private
sector. This implies the wealth equation above, W is equal
to the sum of the net asset supplies. The sum of all banks'

asset demands equals total bank deposits less required

reserves --f2b + f3b + f4b + f7b = 1. And the sum of all
7

non-bank private asset demand is equal to W -- 2 fip = 1.
i=1

Further note that all variables relevant to a sector
are included in 21231 equation. This is necessary because
the demands are constrained by wealth; so if a variable in
an equation changes, causing its demand to go up, the change
in the variable must also make a corresponding decrease in
the demand for some other variable or variables in order to

remain within the wealth confines.

52

Mathematically, this means:

Eafib/a(any functional argument) = 0, and

zafip/a(any functional argument)

Also, implicit in the

equations must sum to W, therefore

not independent.

II
O

system is Walras' Law. All of the

at least one equation is

In addition, all assets are assumed gross substitutes

so that the following restrictions

derivatives:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

t t
aflp/arK > 0, aflp/ari7eK <

u u
Bbe/arM:>0, abe/ari#u<:

t t
afzp/arM>0, afzp/ari*M<

u u
afsb/arsz>0, af3b/3ri$8<

t t
afsp/ars:>0, 3f3p/3ri$S<

u u
8f4b/arN:>0, 3f4b/3rifN‘:

t <

iaIN

at /art>o 8f /art <
5p C ' 5p ifC

t
8f4p/arN:>0, 3f4p/ar

t t
3f6p/3rDI>0. afep/Briyn“

u u
3f7b/3rL:’O' 3f7b/3ri¢L<

are placed on the partial

0, Bflp/8(Y/W)<<0
0, Bbe/Bd:>0

0, afzp/3(Y/W):>O
0.

0, stp/3(Y/W)<<0
0.

0, 3f4p/3(Y/W)<:0
0. afsp/8(Y/W)<10
0. 3f6p/3(Y/W)3>0

0, 3f7b/ad<:0

Most obvious when observing these partials is that the

partial with respect to an assets own rate of return is

always positive,

and the partial with respect to the rate

53

of return on any other asset in the decision-maker's port-
folio is always negative. The assets are gross substitutes
within each sector. This is consistent with the adding up
requirement discussed in the last paragraph. The partial
with respect to Y/W is positive for the two money assets
and negative for the other assets; this is also consistent
with the last paragraph.

Finally, it is assumed the partial of free reserve

demand with respect to the discount rate is positive:

3(FR/D)/8d = l/D - BFR/Bd, since D is constant,

1/0 - BER/3d - l/D - aBR/ad, since FR

excess reserves (ER) - borrowed reserves (BR).

BER/3d is negative, as a higher discount rate discourages
borrowing. It is not certain what ER will do in reaction to
d, but it is reasonable to assume an increase in d will
indicate to banks that restrictive monetary policy is being
undertaken, so they should expect a contractionary future.
Under these circumstances banks will want to hold at least
the same level of ER and probably increase ER in anticipa-
tion of contractionary withdrawals of deposits. Under this
reasoning both terms, BER/3d and BBB/3d, signify 3FR/3d=>0.
This result implies that the partial of some other asset or
assets with respect to d must be negative. The demand for
treasury securities and tax-exempts are probably not
affected greatly by d, but loans should rise significantly

when d falls. It becomes more profitable to borrow more

54

and lend more at the higher borrowing-to—lending differen-
tial, thus the partial listed above for loan demand with
respect to d is negative. No partial is listed for tax-
exempts or treasury securities. It is clear, however, that
if the partial of FR does not equal the partial of loans,
tax-exempt or treasury security demand must change in some
way for the wealth constraint to be preserved.

A brief discussion of the balance equations will com-
plete the static model's description.

The first balance equation, showing the demand for
equity capital, has no demand function for banks since, as
previously mentioned, banks are legally restricted from this
kind of investment. However, in recent years banks have
begun leasing operations. One is tempted to place such
activity into the capital equation under the banking sector.
For now, however, this activity will be included as part of
NS (new shelters). These operations are becoming increas-
ingly attractive to banks because they offer sizable tax
loopholes, which means leasing investment is a likely future
substitute for non-taxable bonds.

The second equation shows the total demand for high-
powered money --i.e., bank demand for free reserves plus
required reserves plus non-bank private demand for currency.
The third equation shows total demand for short-term
government securities, and the fourth equation shows total
demand for tax-exempt bonds. Both the banking and non-bank

private sectors hold a large share in the demand for each

55

of these assets. The fifth equation shows net demand for
corporate securities. The banks are insignificant in this
market. Both the liabilities and assets of this debt
instrument are held by the non—bank private sector. Since
demand for the asset must equal the demand for its
liability (i.e., negative demand), the two must sum to
zero.

Even though corporate securities are not part of net
private wealth or the liabilities of banks, it is important
to include this equation because it has an impact on the
rate structure of the system.

Equation six shows the demand for bank deposits (D) and
the willingness to accept these deposits as liabilities
(f

(Note f is not a fraction.) For the deposit

6b)' 6b
assets of households to equal deposit liabilities of banks,

D + f must equal zero. Banks generally provide a highly

6b
elastic supply of deposit liabilities because of the rate
ceilings.

Equation seven is the bank loan demand and non-bank
private loan supply equation. f7b D(l-k) is an asset to

the banks and f W a liability to the non-banking private

7p
sector. These also must sum to zero to maintain the
equality between borrowing and lending.

Of these seven equations the fourth and seventh have

the greatest direct effect upon the demand for non-taxable

bonds. Equation four is obviously important, while equation

56

seven is closely associated with bank demand for tax-exempt
bonds. Banks attempt to keep the volume of their loans as
high as possible within the limits of safety --i.e., mini-
mizing high risk loans and maintaining liquidity needs.
Bank profits are highest when they are able to make these
loans without suffering from liquidity crises or excessive
losses on bad loans. Skilled managers will move in and out
of certain uses of funds depending on the prevailing condi-
tions of the time. When few auspicious loan prospects
exist, the funds tend to go into tax-exempt bonds where
after tax returns are normally better than other invest—
ments. When this occurs, rfi falls, and the quantity of
tax-exempt bonds demanded by the non-bank private sector
declines. On the other hand when banks anticipate favorable
loan prospects, f4b falls and rfi rises, which induces a
greater quantity of tax-exempt bonds demanded by the non-
bank private sector.

It should be noted that the movement of funds from
tax-exempts to loans is not frictionless. Tax-exempts and
loans are not highly liquid assets, so it might involve
time and risk to move strictly from one to the other. Con-
sequently, banks also hold short term treasury securities
which allow them to bridge this transition with greater

safety and profitability. The dynamics of these activities

will be detailed in a later section.

57

Essentially, however, bank managers observe the 22223
lag rate of return differential between tax-exempt bonds
and loans; if r: = (l-u)r£ — n* exceeds r; = rfi - n* plus a
risk premium (which accounts for liquidity needs and the
quality of competing assets), then the banks put their
funds into loans. If not, the funds go into tax-exempt
bonds. Naturally, phenomenon occurring in the remainder of

the system also exerts feedback into tax-exempt bond demand,

but the interplay is not as strong.
Solution to the System

In solving the system, recall the wealth equation,
seven balance equations, and thirteen rate of return equa-

tions, together totalling twenty independent equations.

T = T(y*. P*. T*). Y. M. S. K. N. rfi. w*. P. d'. k. u. p01.
and NS are exogenous variables, while q, W, rE, r3, rfi, ré,
u t , u t , t , u t , u t

rs, rs, rN, rN, rN, rc, rC, rD, rD, rD, rL, rL, rL, and d

are twenty endogenous variables determined by the simul-
taneous solution of the independent equations. If rfi is
exogenous, because of a legal ceiling Eb, then there are
nineteen endogenous variables. The number of independent
equations also becomes nineteen since the bank deposit equa-
tion is no longer an equation since banks cannot get all

the deposits they would like at the legal ceiling. If a
product market equilibrium and a labor market equilibrium

is added to the system of equations, they Y and P can also

58

be determined endogenously. All of this implies that for
any set of exogenous variables, only one set of values for
the endogenous variables exists which equates the demand

for tax-exempt bonds with their supply.

Wealth Effects

A complete model which includes saving and the growth
of real income requires specification of the ”real" side of
the economy and a growth mechanism. The "financial" side
of the economy formulated above is easily related to the
real side via the variable r'

K
1y, is one of the determinants of real investment. (This

which, as explained previous-

link between the real and financial sector is one approach
to studying the transmission mechanism. Of course, there
is a whole literature concerning this controversial link-
age (Tobin, 1969; Friedman, 1970; Fand, 1970; Teigan,
1972)). The growth of income increases saving and consump-
tion. When saving increases, total wealth increases, and
unless the rate structure of assets is perverse (returns on
private financial assets are higher than the returns on
government assets of equal quality), net wealth will rise.
Thus it can be expected that real wealth goes up nearly
every period since income in recent years has risen every
period. The magnitude of these increases depends not only
on income, but the real return from saving, the level of
real per capita wealth, and general rate of time preference

among savers.

59

Changes in wealth can also occur when q changes, as
this will change the real value of equity capital. Similar
to this change, although not explicitly shown in the model,
is a change in N caused by a change in the price of munici-
pal bonds. This detail is left out of the model to avoid
over-complication. Neither of these wealth effects, how-
ever, is systematically related to time, as saving has been
in recent years. Given this glance at wealth dynamics, the
earlier assumption --wealth accumulation and wealth alloca-
tion decisions are independent at a point in time-- remains.
Recall this means the desired amount of each asset is
homogeneous in wealth.

The adding-up requirements of the static framework
provide a link from wealth changes to the balance equations

and consequent changes in asset demands. More precisely:
zafib/3D(l-k) = l, and zafip/aw = 1.

W, as a dynamic link, plays an important part in the
analysis of tax—exempt bond demand since greater wealth
permits more investment in all assets. Of particular
interest, households, although their relative demands may
change, are potentially able to place more of their savings
into N without reducing their holdings of other assets.
Additionally, the non-bank private sector can increase the
amount of deposits available for investment by the banking

sector which may further raise tax-exempt bond demand.

60

In the absence of outside interference, given the
homogeneity assumption, an increase in wealth raises the
demand for each asset in proportion to the wealth increase.
However, the progressive income tax system disturbs these
homogeneous adjustments. Assuming that prices do not fall,
the additional income earned on the added wealth is subject
to a higher tax rate. This would not notably modify the
relative after tax rates of return among assets if the
income earned on all assets was taxed equally. However,
the income earned on certain assets is tax-free, thus
creating a marked rearrangement in the relative after tax
rates of return and a consequent asset reallocation.

The above phenomenon can be illustrated by utilizing a
simple geometric version of mean-variance portfolio selec—
tion theory —-demonstrated in Figure 3—1 (Tobin, 1965). ER
is the expected after tax real return of an asset, and OR

is a measure of asset riskiness. Assuming the investor is

risk-averse, ER is a good and o is a bad, so that IC

R 1
represents an indifference curve on a risk-averse investor's
utility surface. In this illustration, there are three
assets, A, B, and C, where B and C are taxable, and A is
tax-exempt. At an initial level of real wealth, point A
shows the (0R, ER) combination available when all wealth is
placed in asset A; point B does the same for asset B; and

point C gives the risk-return combination for asset C. The

line DC denotes the efficient opportunity locus of (OR, ER)

61

 

 

ER

--..._--..-.._..-.. .‘A’k

 

 

 

 

 

Figure 3-1

 

62

combinations corresponding to every possible allocation of
wealth between assets A, B, and C. This drawing assumes
the correlation between the returns on the assets is close
to zero. APC shows the opportunities between assets A and
C, and BEP shows the opportunities between asset B and
blend P of assets A and C. The utility maximizing investor
divides his/her wealth between assets A, B, and C so that
he/she has the (OR, ER) combination at point E. CP*/CA* is
the fraction of assets A and C held in asset A. B*E*/B*P
is the fraction of wealth held in assets A and C. There-
fore, the fraction of wealth held in A = CP*/CA* . B*E*/B*P.
If nominal wealth increases in the same proportion as
prices increase, real wealth will not change, but with the
progressive tax structure, the after tax rates of return on
taxable assets will fall. A similar result will occur if
all asset supplies increase proportionately. Figure 3-2
shows the opportunity loci following either of these events.
(Note that the utility achieved is per unit of wealth;
hence a proportional increase in all assets which raises
total utility will not necessarily increase utility per
unit of wealth.) After the shift in the desired portfolio
mix, C'P'*/C'A* is the fraction of assets A and C held in
asset A. B'*E'*/B'*P"* is the fraction of wealth held in
A or C. So the fraction of wealth held in A becomes
C'P'*/C'A* - B'*E'*/B'*P"*. Observing Figure 3-2, it can be

seen that C'P'*/C'A*:>CP*/CA* and B'*E'*/B'*P"*I>B*E*/B*P.

63

 

 

A*

------—------‘

 

 

I

 

 

 

Figure 3-2

64

Therefore, C'P'*/C'A* - B'*E'*/B'*p"*:>CP*/CA* - B*E*/B*P.
The events above cause the fraction of assets held in A
(the tax-exempt asset) to rise.

A simpler illustration depicted in Figure 3-3 again
shows the same concept. In this example, it is assumed
that there is perfect positive correlation between the
returns of each asset. BC is the initial opportunity locus
for an investor, when asset A is dominated by asset B and
not in EEiE investor's portfolio. (This is not to say that
asset A is not in the portfolio of another investor in a
different tax category.) The proportional rise in nominal
wealth and prices moves B and C to B' and C', as the
expected after tax real rate of return of these two assets
decreases. With the increase in nominal wealth and rise in
nominal income generated by this added nominal wealth,
holders of assets B and C are pushed into higher income tax
brackets. Since asset A is tax-free, it does not experience
this tax loss in ER, and the situation depicted in Figure
3-3 can arise, where B' is below A. Asset B is now
dominated by asset A, and the opportunity locus becomes AC',
with asset B no longer included in the investor's portfolio.
To maximize utility, wealth is allocated between asset A
and asset C with a (0R, ER) combination at point E'.

(Again this only means EEEE investor drops B from his/her
portfolio; investors in lower tax-brackets may still hold

asset B.)

65

 

 

ER

 

Blo

1C1

102

 

 

Figure 3-3

 

66

As shown above, an important wealth effect is inflation.
A rise in P reduces the real value of N or any other finan-
cial asset. This means, as previously mentioned, that for
the real supply and demand of tax—exempt bonds to be main-
tained at their pre—existing level, nominal supply and
demand increases must be commensurate with price increases.
The effect of a price increase without commensurate nominal
wealth increases can also be demonstrated with the use of
portfolio selection theroy. The asset reallocation results
are similar to the results analyzed above, however, total
utility, as well as per unit utility, will fall.

With the above theoretical model of demand laid out,
it remains to construct the empirical model associated with

it.

Empirical Specification

The total demand for tax—exempt bonds is composed of
three sectoral demands: individuals, commercial banks, and
casualty insurance companies. The non-bank private sector
presented in the theoretical section consists of casualty
insurance companies and individuals which in turn includes
households, trusts, unincorporated businesses, and municipal
bond funds. The variables delineated in the theoretical
system affect these sectoral demands in different ways. At
the same time each sectoral demand influences the values of

variables in other sectors. Figure 3-4 provides a schematic

67

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68

picture of this interaction. Income, inflation, the tax
structure, savings, and certain rates of return influence
individual demand. The savings of individuals, leasing
operations, inflation, and the loan market affect commercial
bank demand, which in turn affects the rates of return
relevant to the non-bank private sector and its ultimate
demand.

Figure 3-4 suggests that the tax-exempt demand of the
insurance sector is not as responsive to economic conditions
and the behavior of other sectors as are the banking sector
and household sector. The data shown in Figure 3-5 shows
that fire and insurance companies as a group are the most
stable source of demand in the market. Industry profits,
which have generally risen steadily, are the major deter-
minant of demand in this sector (Rosenbloom, p.15). Conse-
quently, there will not be a separate specification for
insurance company demand. This demand, since its percentage
of the total remains essentially constant, will appear in
the constant coefficient in the non-bank private sector
demand equation, which will be specified later.

As indicated in the theoretical section, only one set
of values for the internal variables in the general system
of asset demand equations will establish equilibrium. An
estimate of demand for tax-exempt bonds can be made without
estimating the demand for other assets, as each equation

has common variables which must adjust across all asset

69

 

 

PERCENT OF STATE AND lOCAL DEBT HElD BY
EACH DEMAND SECTOR COMPARED TO Ila/Re

 

 

    

 

 

 

Percent
N
70
w b-
e"
50 " Commercial Bank: _ V “‘M-.
’.e.\ .I’ K
._,--’ \a’
.’
n I-
N .. Individuals
w and Individual Trust:
20 in
fire and Caeuahy Insurance Cee.
IO -
Life Insurance Cos. N f' . I C
.v. /‘-.,_,_/ on manna erps.
c: = K . v.3, “r. ~. 1..

 

19“ I962 19“ I,“ 196. 1970 I972 1974

sources: IeerdefGevemereefcheFederalleeerVeSye-
tern, "an e! Fonda: U. 3. Treasury OW.
Treeeery whole: Solemn Brothers. Aeelyrkel
leeerd e0 Yield: and Yleld Spreede. J

 

 

Figure 3-5

70

demands to establish equilibrium in every asset market.
Thus, specification of the relevant variables in the tax—
exempt bond equation, while ignoring other asset demands,
will generate a valid approximation of tax-exempt bond
demand. It is still important, however, to begin the
analysis from a general equilibrium framework so that all
of the variables relevant to tax—exempt bond demand are
considered.

Recall that in the theoretical framework, equilibrium
demand was obtained upon the adjustment of the endogenous
variables to clear the existing asset supplies. Now, it is
assumed that equilibrium occurs rapidly in financial markets
so that equilibrium bond demands are observed in response
to equilibrium values of demand-determining variables.

Thus the endogenous variables of the theoretical model will
be exogenous variables in the empirical specifications.

Finally, the demand functions in the Theory were
general; they will now be expressed as specific functions.
And since the theoretical model expresses asset demands as
a fraction of total net private wealth, the empirical
equations below estimate this fraction.

Bank demand will be specified first. Comparative
static equations are specified, and then equations allowing
for dynamic stock adjustments are specified. Non-bank pri-
avate demand will then be specified. Similarly, a com-
parative static specification is made, followed by a

specification with the stock adjustments.

71

Bank Demand

Specification

 

According to the theoretical model, banks place their
deposit liabilities into required reserves, free reserves
(a safety asset), and three income earning assets --loans,
tax-exempt bonds, and Federal securities. In the static
model where the amount of deposits is observed at a single
point in time, the fraction of these deposits which banks
wish to hold as tax-exempts at that moment must be deter-
mined in order to find the dollar value of the banking
sector's tax-exempt bond demand. To accomplish this, two
alternative dependent variables are tested: first,
Ng/D(l-k), the fraction of deposits not held as required
reserves which are invested in tax exempts; and second,

Ng/D(l-k) - f2bD(l—k) = Ng/D(l-k)(l-f the fraction of

2b)’
deposits not held as required 2E free reserves which are
invested in tax-exempts. Two dependent variables are
estimated because, as discussed earlier, there is no

a priori relationship between the discount rate (d) and tax-
exempt bond demand. The discount rate is specified in
equations determining the first variable. Equations esti-
mating the second dependent variable are based on the
premise that the level of free reserves is determined prior
to and independent of the amount of tax-exempt bond invest-

ment. Since the level of free reserves is pre-determined,

the discount rate does not appear in specifications related

72

to this variable.

More than two equations are specified below because
desired bank holdings of tax-exempts depend upon the
economic events expected by bank officers. Since no single
variable can always reveal the expectations of a decision-
maker, several slightly different equations are posited and
tested. Before listing these equations, however, a short
discussion of the banking theory behind their specification t
must be considered.

The required reserves of a bank (denoted by kD) must
be considered a highly illiquid asset, as bankers cannot
rely heavily on these funds during an emergency because
they must stay with the Fed or in a vault. Consequently,
excess secondary reserves are maintained to meet sudden
deposit outflows or unexpected loan demands. These are
mostly short-term assets which mature quickly at par value
with only a slight risk of a capital loss. The remaining
funds are placed in loans or investments. Most modern
aggressively run banks attempt to place most of their assets
in loans. There are two reasons for this. First, banks
gain goodwill and hold onto depositors. Second, loans
usually pay a higher rate of return. Even if the face rate
on a loan is lower, the effective rate is probably higher
because the loan might be paid off in installments or the
borrower may be required to hold compensating balances.

Thus funds going into U.S. government securities and tax—

 

73

exempts are only received when loan demands are low. When
loan demand is up, investment officers generally sell their
assets and turn the funds over to loan officers.

Funds become available to investment officers during
recessionary periods. As all bank officers, the investment
officer's goal is to maximize bank profits. When he or she
invests during a recession, bond prices are high and rates
of return low; hence the crucial decision to be made is
whether to invest long at higher rates of return or short
where the investment can be easily converted into a loan,
if and when the opportunity arises. If the investment
officer expects a recession to persist, then investments
will be placed long (tax-exempts). If the recession is
expected to end soon, funds will be put into short—term
securities (U.S. government securities), where there is
less chance of capital losses due to falling bond prices
at the time the banker liquidates investments to acquire
loanable funds.

With expansionary expectations, investment officers
must be ready to provide funds for the loan officer. Often
this is done at a capital loss since rates of return have
already begun to rise and bond prices to fall, but invest-
ment officers will gladly take capital losses on investments
as long as the expected gains from loans exceed the capital
loss and forgone returns of investments. The better the
investment officer is at predicting the waves of the

economy, the higher bank profits will be. He or she will

74

tend to invest long (tax-exempts) when loan demand is not
imminent and short when loan demand is at the horizon.

To summarize, the theory of banking investment

presented above is a theory of investment officer expecta-

tions.

The specifications are:

f4b = Ng/D(l—k) = 80 + 81d + 32x25 + BBXSSM
+ B4YBP61 + g;

f4b = Ng/D(l-k) = 80 + 81d + 82X25 + 83x35M
+B4YBP61 + BSLOP + e;

f4b = Ng/D(l-k) = 80 + Bld + Bzxzs + B3X35M
+B4YBP61 + BSLOP + B6DUNLR + e;

f4b = Ng/D(l-k) = 80 + 81d + 82X25 + 83X35M
+ B4YBP61 + BSLOP + BGDDUNLR + e;

f4b = Ng/D(l—k) = 80 + 81d + 82X25 + B3X35M
+ 84YBP61 + BSLOP + 86n* + e;

f4b/l-f2b = Ng/D(l—k)-FR = 80 + le25 + 82X35M

+ B3YBP61 + e;
f4b/l-f2b = 30 + 81x25 + 82X35M + B3YBP61

+ B4LOP + E;

(1)

(2)

(3)

(4)

(5)

(6)

(7)

75

f /l-f = B + slxzs + 82X35M + BBYBP61

4b 2b 0

+ B4LOP + BSDUNLR + e; (8)
f4b/1_f2b = 80 + 81X25 + 82X35M + 83YBP61

+ B4LOP + BSDDUNLR + e; (9)
f4b/l—f2b = 80 + 81X25 + 82X35M + BBYBP61

+ B4LOP + 85n* + e. (10)

Since this estimate is the fraction of D(l—k) desired in
tax-exempts, it must be multiplied times D(l-k) (the real
value of non—required deposits) to get the real value of
tax-exempt bond demand.

Nb is the real value of tax-exempt bonds desired by
banks.

D(l-k) is real total deposits less real required
deposits.

d is the real value of the Federal Reserve discount
rate. It equals the nominal Federal Reserve discount rate
(d') minus the expected rate of inflation (n*). d falls
when d' falls or n* rises. As discussed earlier, when d'
falls banks will probably borrow more, reduce their free
reserves, and place more funds into income earning assets.
If loan demand exists, the funds will be placed in loans.
If the fall in d' is seen as a move by the Fed which will
shortly lead to greater loan demand, the funds will
probably go into short term securities. If little future

loan demand is expected (bankers see the decrease in d' as

 

76

a futile attempt to stimulate demand), the borrowed funds
may go into tax-exempts. Similarly, the response of bank
demand for tax-exempts to a rise in d' will depend upon
bankers' perceptions of how the d' increase will affect
credit demands.

A rise in n* usually signals that loan demand is rising.
Consequently, tax-exempt demand will fall, either directly
replaced by loans or shifted into short—term securities in
anticipation of future loan demand. In general, one could
expect bank demand for tax-exempts to fall as d falls.

Conversely, a rise in d' will reduce borrowing and
loans, while instilling an atmosphere of expected loan
decline. Some bank officers may decide to begin converting
loans into tax-exempts as soon as possible in order to buy
while their prices are still low. Similarly, a fall in n*
is a sign of contractionary expectations and will raise
tax-exempt demand. In summary, a rise in d, is expected
to raise tax-exempt demand, unless bankers judge the Fed's
policy as too weak to slow down demand.

Equations 6 through 9 drop d as a variable, because
of the possible ambiguity concerning its effect on tax-

exempt demand and other asset demands.

4
g u _ u _ u _ u , u .
X25 (rN rL) (11:1(rN rL)-i)’ where rN IS the

real after tax return on tax—exempts, r: the real after tax

rate of return on commercial loans, and i quarterly obser-

4
vations. & Z (r
i=1

1.1 r11)

N - L _1 represents a proxy for a normal

 

77

rate of return differential. Several lag structures were
tested for the normal rate differential with a one year
moving average minimizing the regression equation standard
error.

X25 is an important variable in the determination of
the fraction of bank assets which go to commercial loans.
Since bankers view loans as their primary profit source,
they react quickly to indications that loan demand may be
picking up. When X25 falls, bank officers try to take
advantage of the rise in the loan rate relative to the tax-
exempt rate and begin taking funds out of tax-exempts and
Treasury securities so they can be used to make loans.
Conversely, when X25 rises, it is hypothesized that bankers
will sense a drying up of loan demands and will begin
placing funds in tax-exempts and Treasury securities before
their prices begin to rise significantly. Thus bank offi-
cers react to current rates relative to the normal rates
not only to acquire current profits, but also with an eye
on future profits since X25 can be an indicator of future
loan demand, as well as current demand.

In summary, it is hypothesized that when X25 rises,
bank officers adopt adaptive expectations, so tax-exempt
demand rises. Similarly, when X25 falls, bankers reduce
their demand for tax-exempts and acquire more loans.

4 u

_ u _ u _ u _ . u .
X35M - (rN rs) (ii:i(rN rS)-i)’ where rS is the

real after tax rate of return on three to five year U.S.

Se

9X

ta

78

4
government securities, and i Z (rg - r
i=1

11
s)-

1 is a proxy for
the normal rate differential again with a lag structure
which minimizes the standard error.

X35M provides an indication of how funds are distrib-
uted between tax-exempts and Treasury securities. Unlike
the bank officers' behavior with respect to X25, it is
hypothesized that the investment officer adopts regressive
expectations with respect to X35M. This kind of behavior
is likely to occur because investment managers know that
their investments may be temporary, since they plan to
convert investments into loans when loan rates exceed
investment rates plus capital losses on investment sales.
The rates on securities are lower than on tax-exempts, but
normally the capital losses upon their sale are also lower.
Furthermore, U.S. securities can usually be liquidated
faster than tax-exempts. Hence, when loan demand is expec-
ted to rise, investments will be placed into short term
U.S. securities, where the transactions cost of converting
securities to loans is lower; and when loan demand is
expected to diminish, investment funds are shifted into
tax-exempts, where they can be stored with greater prof-
itability. This hypothesis can be clarified by investi-

gating the mechanics of X35M changes.

When X35M falls, r§ must decrease more than r;
decreases, or r; must rise faster than rfi rises. When r§

u
decreases more than r

S decreases, two signals of possible

mo
fa
ma
Dr

It

12

re

ix

79

future events are suggested to the investment officer.

0 D D I u
First, a deep rece851on is coming because rN

despite possible Fed policies to lower r

is falling

u u
faster than r8 8'

With a deep anticipated recession, the investment officer

will want investments safely consigned to the more

u
N

falling faster than rg, the price of tax-exempts is rising

profitable long-term asset, tax-exempts. Second, with r

faster than the price of U.S. securities. If the investment
officer wants to get into the more profitable tax-exempts
without taking a large capital loss upon the eventual tax-
exempt bond sale, he/she will buy tax—exempts quickly, be-
fore the price rises even further.
When r; rises faster than r§,
officer receives signals of the probable future. Tight

again the investment
money policy is very likely succeeding, as r; is rising
fast. Hence an economic downturn is imminent, which will
make the return on loans fall. Therefore, it may be
profitable to begin moving funds into tax-exempts while
their price is still low.

In summary, when X35M falls, it is hypothesized that
tax-exempt demand should rise.

Conversely, it is hypothesized that when X35M rises,

tax-exempt demand falls. X35M rises when r; falls at a

slower rate than rg, or r; rises faster than rg. A rapid
fall in r; suggests to the investment officer a future of

recovery and falling tax-exempt bond prices, as the

increase in their prices have already begun to slow down.

80

Consequently, managers begin shifting into U.S. securities,
where they are in a more liquid position and suffer lower
capital losses when loan needs arise. When r; rises faster

than r the investment officer perceives prolonged expan-

u
S’
sion. Loans and long-term investments are still in demand
and the Fed has not cut credit to the extent that rg is
rising faster than other rates. Hence any investment funds
available will stay in U.S. securities to insure meeting
loan needs.

YBP61 is real annual bank income. As nominal income
rises, more banks enter the higher corporate income tax
bracket, creating a greater need for tax shelters, such as
tax-exempts. Real income is the variable specified, rather
than nominal income, because the effects of the inflation-
ary part of a rise in nominal income should be accounted for
by other variables in the equation. Nevertheless, the
equation will be tested with nominal income as a variable,
and the results of this test will be discussed in a later
portion of the paper.

Other studies have implicitly suggested that a positive
relationship between bank income and tax—exempt bond demand
exists (Fortune, 1972, Talley, 1972). Fortune did an
empirical study showing that the larger the bank the more
banks will replace U.S. securities with tax—exempts. Since

bank income has grown at a much greater rate than has the

number of banks, it can be safely concluded that the number

81

of large banks has risen with overall bank income growth.
Talley studied the behavior of bank holding companies and
found they tend to invest more heavily in the riskier tax-
exempts than the safer U.S. securities. Again it can be
concluded that higher income allows a greater risk cushion
and therefore more tax-exempt demand.

LOP is a dummy variable indicating the years in which
bank leasing operations have become a popular alternative
to tax-exempt bonds as a tax shelter.

DUNLR is the change in the unemployment rate. This is
another expectations-variable. When the unemployment rate
is rising, bank officers expect a recession and begin con-
verting funds into tax—exempts. When the unemployment rate
is falling, they expect favorable loan prospects.

DDUNLR is the rate of increase or decrease in the
changing unemployment rate. This is probably a better
expectations-variable than the Simple change in the unem-
ployment rate. When the unemployment rate is rising at an
increasing rate, the banker expects a deep recession coming
and this signals him/her to put funds in tax—exempts.
However, when the unemployment rate is rising at a decreas-
ing rate, the recession may have bottomed out and an expan-
sionary period with greater loan demand may be coming soon.
So the investment officer might predict that greater prof—
its can be made by converting tax-exempts into U.S.

securities, while tax-exempt bond prices are still high.

as
de
Or:

Dr

eC

in

82

Similarly, if the unemployment rate is falling at a
decreasing rate, the bank officer may anticipate the end of
an expansion and think it more profitable to buy tax-exempts
while their price is low. In summary, there should be a
positive relationship between DDUNLR and tax-exempt bond
demand.

n*, the expected rate of inflation is a possible sub-
stitute for DUNLR or DDUNLR as another expectations-variable.
When n* is low, a recession is usually expected and tax-
exempt demand is up. Most of this variable's effects may
be captured in d' - n*, so it probably does not strengthen
.the model as much as DDUNLR. Even in the equations where
d' - n* is dropped, many of the n* effects should be captured
by variables X25 and X35M.

Note, all variables relevant to every asset demand of
the banks are specified in the tax-exempt demand equation.
This is important because whenever a variable affects any
asset demand, this effect requires some adjustment in the
demand for tax-exempts. A tax-exempt demand equation which
omits variables affecting other asset demands would thus
present an incomplete picture of the tax—exempt bond market.

The static equations above have only limited use since
economic units normally do not adjust their portfolios
instantaneously to equilibrium. Extending the model to.a
dynamic setting, specifying an equilibrium adjustment
mechanism, will further enrich the model. Again, as in the

static model, no variables should be omitted since the

83

adjustment process of other bank assets will affect the
adjustment towards equilibrium of tax-exempt bond demand.
Since banks cannot immediately adjust their desired
level of an asset to the actual level of the asset, a par-
tial-adjustment model is adopted here to capture the
disequilibrium behavior of bank investment managers.
f45t is the desired fraction of bank assets placed in

a:

tax—exempts. So f4bt - f4bt-l is the de51red change and

f4bt - f4bt-l is the actual change. Since the actual

change is only a fraction of the desired change:

at

4bt ‘ f

f - f = 6(f

4bt 4bt-1 4bt-1)’

*
where f is the static equation (1) and 0.<5::1. So,

4bt
f4bt - f4bt_1 = 5(80 + 81d + 32x25 + 83X35M
+ B4YBP61 - f4bt_1 + at), (11a)
and
r4bt = 580 + 681d + aezxzs + 683x35M + 684YBP61
+(1’5)f4bt-1 + et’
= Y0 + Yld + y2X25 + y3X35M + Y4YBP61
+ Y5f4bt—l + et’ (11b)

where Y0 = 680, Y1 = 681, Y2 = 662. Y3 = 683, Y4 = 684,

A A

Y5 = l - 6. Therefore, 6 = l - Y5’ 80 = YO/l - Y5,

- Yl/l _ Ysr 82 = Y2/1 _ Y5: 83 = Y3/1 - Y5:

m
H
I

Y4/1 - Y5'

84

Equations 12—20 analogously follow from the static equations
2-10.

Although this stock adjustment technique adds another
dimension to the model, Brainard and Tobin ("Pitfalls”) warn
of a potential problem which may arise. The adjustment
speed toward equilibrium of an asset within a general sys-
tem of assets varies, depending upon what exogenous variable
causes the disequilibrium disturbance and is driving the
system to a new equilibrium. The adjustment parameter (6)
estimated when using time series data must necessarily
result from some combination of several economy-driving
exogenous variables. As a predictive tool this adjustment
speed coefficient may be a good predictor on the average,
but when observing the cyclical adjustment process created
by a change in a particular exogenous variable, the

coefficient loses predictive accuracy.

Results

The 20 equations above were estimated using ordinary
least squares. The results of six of the equations are
shown in Table 3-1. Each cell contains a regression
coefficient and its associated t-statistic. Note in equa—
tions 7, 8 and 9, where the dependent variable is not
lagged, that the Durbin-Watson statistic is low, which sug-
gests serial correlation. In equations 17, 18 and 19, where
the dependent variable is lagged, the DW statistic is

within the indecisive range when checking for serial

85

 

 

 

 

 

 

 

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88

correlation. However, as discussed in Maddala (p. 371),
when there is a lagged dependent variable on the right side
of the equation, there is danger of accepting the hypothesis
that there is insignificant serial correlation when in fact
a serious serial correlation problem may exist. He warns
that the DW test may not be applicable in these models.
Maddala also points out that the coefficient on the lagged
dependent variable is overestimated, thus distorting the
estimated speed of adjustment.

To allow for serial correlation the Cochrane-Orcutt
procedure is adopted. Using the Cochrane-Orcutt procedure,
the 20 equations are again estimated. These results are
shown in Table 3-2.

The constant term is positive and significant in all
20 equations. There is no a_priori or post test basis for
not retaining it in the equation.

As suggested previously, the discount rate might be
dropped from the equation. The t-statistics in equations
1 through 5 and 11 through 15 indicate a possible weak
negative relationship between the two variables. Since the
a priori and post test grounds for retaining this variable
are weak, it is dropped, leaving only equations 6 through
10 and 16 through 20 to investigate.

Another variable which could be omitted is LOP. The
a priori sign on this coefficient is negative, as leasing

operations are an alternative to tax-exempt bond investments.

V3

St

st:
ta:

buI

89

However, the coefficient is positive and has a high level
of significance in every equation. This suggests the dummy
variable is a poor measure of leasing operation effects on
banking behavior. However, on statistical grounds, the
variable should not be discarded from the equation. Equa-
tion 16 is estimated without LOP as an explanatory variable.
The coefficients of the other explanatory variables are
nearly the same as the coefficients of equation 19, where
LOP is included. Hence it is clear that LOP does not dis-
tort the conclusions about the other variables. In fact,
the inclusion of LOP strengthens these conclusions. The
t-statistics associated with these coefficients are markedly
more significant in equation 19.

In equations 7 through 10 and 17 through 20 the
variables C, X25, X35M, and YBP61 are in almost all cases
statistically significant, and always in agreement with
a priori relationships discussed earlier. These results
strongly substantiate the hypothesis that bank demand for
tax-exempts depends not only on current rates of return,
but expected future rates as well.

The distinguishing variable in each equation is an
economic-outlook variable. Choosing one static and one
adjustment equation containing an economic-outlook variable
which best characterizes the tax—exempt bond demand of
banks is a difficult task from a statistical point of view.
However, from an economist's viewpoint, one equation may

provide a better analysis of a certain situation than

90

another equation. Furthermore, the equations can be
ranked based on the best combination of statistical sig—
nificance and economic description.

Among the static equations equation 8 clearly has the
greatest statistical significance. All t-statistics are
significant and its R2 value is the highest of the four
equations. However, on the grounds discussed previously, I
view DDUNLR in equation 9 as being a better descriptive
variable than DUNLR in equation 8. As far as statistical
significance is concerned, equation 9 ranks second; the LOP
t-statistic is significant at the 10% level of confidence,
while the remaining t-statistics are 5% or better. The
coefficients of both equations 8 and 9 are almost the same,
and it should make little difference which of these two
equations one might use for predictive purposes. Equation
7 ranks third statistically; the t-statistic associated
with X25 is only significant at the 10% level. From an
economic standpoint, all the effects of forecasting done by
bank managers must be shown by the coefficients of X25 and
X35M; hence equation 7 is not as descriptive as 8 and 9.

In equation 10 the t-statistic for X25 is the lowest of the
4 equations, barely significant at 10%. The coefficient
for n* is insignificant and positive, while the expected a
priori sign is negative. Obviously, this equation should
be discarded.

Among equations 17 through 20, equation 19, for the

same reasons as applied to equation 9, is ranked first on

 

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91

an‘a priori basis. Furthermore, statistically, equation 19
is ranked first. Every variable in equation 19 has a high
t-statistic and it has the highest R2 of all 20 equations.
Equations 17 and 18 also have statistically strong results.
In fact, they are almost identical and either could inter-
changeably be a good predictor. It should be noted, how-
ever, that they model the adjustment process differently
than equation 19. According to equation 19, .383 of the
adjustment occurs each period, while equations 17 and 18
allow more than twice this pace. The slower paced equation
19 could be deemed more realistic since the t-statistic con-
comitant to the lagged dependent variable has a far more
significant t-statistic in equation 19 than in either
equation 17 or 18.

As for equation 20, the coefficient for W* has the
expected sign, and the t-statistic is nearly high enough to
signify a 10% confidence level. This equation is weaker
than the other three both statistically and descriptively,
but if one is explicitly interested in inflationary effects
in the tax-exempt bond market, this equation may be the
most useful of the four. Also note that the rate of
adjustment in equation 20 is almost identical to the rate
in equation 19. Finally, Table 3~3 shows as expected,
when nominal bank income replaced real bank income in an
equation, the t-statistic was never significantly high.

Since real bank income was a significant variable in every

92

equation and there was solid a priori grounds for this
significance, it can be concluded that the effect of
inflationary increases in bank income on tax-exempt bond
demand is accounted for by the other variables.

To find the absolute amount of bank demand for tax-
exempts, the demand for bank deposits must be determined.
Bank deposits are a financial asset of the non-banking
private sector. Hence the non-bank private sector's demand
for a financial asset must be analyzed when determining
bank demand for a financial asset. After discussing non—
bank private demand for tax-exempts and bank deposits, the
discussion will turn to total bank demand for tax-exempt

bonds.

Non-Bank Private Demand

Although there is a whole menu of financial assets
available to the non—bank private sector, only tax-exempt
demand and bank deposit demand is examined here. The other
assets, however, are not completely ignored in this partial
equilibrium analysis since the variables important to the
demand for every asset are contained in each demand equa-
tion --tax-exempt bond demand and bank deposit demand in-

cluded.

Specification

 

Since the level of real net wealth (W) is momentarily

fixed. the fraction of this wealth which the non-bank

93

private sector wishes to hold in a certain asset is the
important variable to determine. As explained in the
theoretical section, the demand for an asset depends on the
after tax rate of return on itself and alternative assets,
and on the transactions demand for money. Rather than
entering these independent variables into the estimated
demand equations and trying to contend with multi-
collinearity and oversimplification, the independent
variables will be redefined in a way that avoids high cor-
relation among independent variables and more closely
portrays the behavior of asset holders.

Looking first at the tax-exempt bond market, the
closest substitute for the tax—exempt is the corporate bond.
They are equally desirable when rfi - n* = (l-T)ré - n* or
T = l - rfi/ré, where T is the marginal tax bracket in
which investors are indifferent between tax-exempts and
corporate bonds; rfi is the nominal rate of return on tax-
exempts; and ré is the nominal rate of return on corporate
bonds. When rfi/ré rises, T falls, making the after tax rate
of return on tax-exempts higher than on corporate bonds for
more investors.

Figure 3-6 helps show the primary behavior occurring
in the tax-exempt market. As discussed above, when rfi/ré
rises, T falls, and the tax-exempt demand of households

rises; this is represented by a movement up the ND curve.

This illustration also helps in seeing the interaction of

94

 

 

 

 

 

r'N/r'C
= 1-T N
2
N D
N11)
0
C
0
N

 

 

Figure 3-6

 

95

bank demand with non-bank demand as shown in Figure 3-4.
If bank demand drops from 0A to OB, rfi/ré must rise from OC
to OD to reestablish equilibrium. In so doing, non-bank
demand rises from AE to BE, while T falls. When T falls,
the after tax rate of return on tax-exempts is higher than
on corporate bonds for more investors.

When looking at the bank deposit market, it should be
recalled that banks generally will accept all the demand
deposits and passbook savings they can get at the going
rate, which has typically been the ceiling rate. Time
deposits without ceilings are more inelastic, but in total
the supply of deposits available from the banks as a way
for the non-bank sector to hold assets can be viewed as
highly elastic at the going real bank depost rate --r =

D

rb - n*, where rb is a weighted average of the rates on

demand deposits, savings deposits, and time depostis. This

is shown as D in Figure 3-7. D is the demand for bank

S D
deposits by the non-bank private sector.

With these ideas in mind equation 21 specifies non-bank
private demand for tax-exempt bonds, and equation 22 spe-

cifies the demand for bank deposits.

f4p = Np/W = 80 + BlTYBIL + 82(Y/W)
t
+ 83(r; - ré(l-T)) + e4(r§ - rD) <21)
f6p = D/W = 80 + BITYBIL + 82(Y/W)

+B3(rfi - ré(l-T)) + 34(rfi - r3) (22)

96

 

 

rI)

  
 

.------ ---------------

 

 

r*D

 

 

Figure 3-7

97

The independent variables are the same for every asset
demand function. The specification of an asset demand
which omits a variable whose major impact is on the demand
for some other asset will attribute the equal offsetting
impact of this variable to the unwritten equations. Hence
all relevant variables must appear in every asset demand
function.

Np is the real demand for tax-exempt bonds by the non-
bank private sector.

TYBIL is the amount of taxable income in tax categories
:_T = l - rfi/ré. When TYBIL rises, more taxable income is
anticipated, so tax-exempt demand goes up, too. This could
be the most important variable in the equation; it causes
non-homogeneity between f4p and wealth.

The value of TYBIL depends on three factors: tax laws
which change the marginal tax rate corresponding to each
income level; rfi/ré which fluctuates with banking conditions
and the volume of bonds offered; and income. Tax laws,
which have frequently changed to adjust for inflation, have
historically reduced TYBIL. Income growth raises TYBIL.
Banking conditions either raise or lower TYBIL: when bank
demand for tax-exempt bonds rises, rfi/ré falls, T rises,
TYBIL falls, and the quantity demanded by individuals
declines; and when bank demand falls, similar events occur
in reverse directions. All of these forces, which are sub-

sumed into the variable TYBIL, have a net effect upon f4p.

98

Also imbedded in this variable is an implicit wealth
effect, even though wealth at the moment does not change.
(This effect is discussed in the Theory with use of the
risk-variance model.) At each point in time a new level
of wealth is observed which in turn depends on past income
and corresponding saving decisions. Recall from the
theoretical discussion that as wealth rises with rising
income, the progressive income tax first distorts the allo-
cation of assets in favor of tax-exempts, and second,
reduces the saving rate, holding future levels of wealth
lower than they would be with a proportional income tax.

The relationship between f and TYBIL picks up the allo-

4p
cative impact of progressive taxation --at any given moment
the absolute value of W by way of its income-earning capac-
ity and corresponding level of taxable income in itself
affects tax—exempt demand.

TYBIL should also affect the fraction of assets placed
into deposits. Since certain deposits earn interest income

which is taxable, a rise in TYBIL should reduce f with

6p’
the funds being shifted from deposits (as well as other
assets) into tax-exempts.

Y/W, as indicated in the Theory, is the ratio of income
to wealth. When Y/W rises, the transactions demand for
bank deposits rises. With the exception of tax-exempts,
the rise in bank deposit demand will cause an offsetting

fall with the demand for other assets. The tax-exempt

demand for the non-bank private sector may also rise when

99

Y/W rises because, as discussed earlier, during expan-
sionary periods when income is rising, the bank demand for
tax-exempts tapers off and the non-bank private sector
replaces this demand. Consequently, when Y/W is used as a
measure of the transactions demand for bank deposits, the
cyclical effect of income on tax-exempt bond demand cannot
be avoided.

rfi - ré(l-T) is specified because the rate of return
on U.S. securities, relative to tax-exempts and corporate
bonds, must be included in order to pick up offsetting
effects of adjustments occurring in the U.S. security
market. Since ré is related to rfi in the TYBIL variable,
offsetting effects of U.S. security market adjustments
would also be picked up by the variable rfi - ré(l-T) in a
corporate bond demand function; although this function is
not explicitly specified here.

When rfi - ré(l-T) rises, tax-exempt demand should also
rise, as the after tax rate of return on tax-exempts rises
relative to the rate on U.S. securities. The effect of
this variable on bank deposit demand is uncertain.

t t

1K ' rD’

return on equity and on bank deposits, is important in both

the difference between the after tax rate of

equations. Equity offers an attractive substitute to the

tax-exempts, especially in the face of inflation. r; is
much more volatile than r3, thus the investor's reactions

t changes are reflected by the variable rt - rt When

to TX K D.

.55
rd

510

pa

Ii

100

t . . t t t .
rK rises relative to rN (usually when rK - rD rises), f4p
should fall.

r; is important in the bank deposit equation, as well

as the other equations, because it represents the Tobin
rate of return which links the monetary to the real side of
the economy. The relationship between r; - r; and f6p
should be negative, since the opportunity cost of holding
money rises as r; - r; widens.

Individuals in the non-bank private sector, similarly
to individuals in the banking sector, cannot adjust their
portfolios to the desired level immediately. Again a

partial-adjustment model is adopted to determine disequi-

librium behavior. The specifications become:

f4p - f4pt_l = 5(30 + BlTYBIL + 82(Y/W)
I I t t
+ 83(rN - rs(l-T)) + 84(rK - rD)
_ f4pt_1 + at) (23a)

f4pt = (Np/pmt = yo + leYBIL + y2(Y/W)

t
+ Y3(rfi - ré(l-T)) + Y4(r§ - rD)

+ Y5f4pt-1 + at (23b)

f6pt - f6pt_l = 5(30 + BITYBIL + 82(Y/W)

+ 83(rfi - ré(l-T))

t t
+ 84(rK - rD - f6pt-l + at) (24a)

101

f6pt = (D/W)t = YO + leYBIL + Y2(Y/W)
+ Y (r' - r'(1-T)) + (rt - rt)
3N 3 Y4 K D
+ Y5f4pt-l + at, (24b)

where 5 = the adjustment parameter (0<I6:;1), Y0 = 080,

Y1 = 681! Y2 = 682: Y3 = 583; Y4 = 084, Y5 = 1 - 0. There-
fore, 6 = 1 - Y5! 80 = YO/(l-Y5)) 81 = Yl/(1_Y5)r 82 =
Yz/(l-Ys). 83 = Y3/(1-y5), and B4 =Y4/(l-Y5).

Again, as discussed earlier, the potential problems
admonished by Brainard and Tobin (”Pitfalls") are still

present.

Results

Table 3-4 summarizes the results. ‘In all four equa-
tions, the R2 and F statistics are high, while the Durbin—
Watson statistics signify no serial correlation problems.
The adjustment parameter for both tax-exempts and bank
deposits is very close to one, indicating rapid portfolio
adjustments by non-bank investors. In fact this adjustment
is so fast that there is little difference between the
regression coefficients in the static models and in the
partial adjustment models. The lagged dependent variable
is significant for both assets, and the R2 is higher in the
lagged equations. Consequently, equations 22 and 24 prob-

ably depict the asset demand more accurately than equations

21 and 23.

102

 

 

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103

The only variable not significant in equation 22 is
t t
rK - rD.

in this equation, as its effects should be felt more

This variable is not expected to be significant

strongly in the demands for other assets --particularly
equity. The regression coefficients of all variables,
however, have the expected a priori sign.

In equation 24 again rt - rt

K D
possesses the expected a priori sign. Although this

is not significant, but

variable might be deemed important in a Tobin IS-LM model
("General Equilibrium Approach to Monetary Theory," 1969),
non-significance is not surprising because this is not a

simple capital-money model, so most of the effects of the

. t t
variable rK - rD

assets. Also insignificant in equation 24 is rfi - ré(l-T).

can be felt in the markets for other

This lack of significance is not surprising since the

effects of rfi

only pick up small offsetting and often conflicting adjust-

- ré(l-T) on the demand for deposits should

ments from U.S. security, tax exempt, and corporate bond
market activities. Y/W is strong and with the predicted
sign, as is TYBIL which offsets a rise (fall) in tax-exempt

demand when TYBIL rises (falls).
Total Demand

An estimate of the total demand for tax-exempts can be
determined by combining the banking sector estimate of the

fraction of non-required deposits placed in tax-exempts

K.)

104

with the non—bank sector estimate of the fraction of net
wealth it places in tax—exempts, and applying net private
real wealth (W) to these fractions.

To complete the model, the supply of tax-exempt bonds
must be determined. This is the intent of the next

chapter.

CHAPTER IV

A NEOCLASSICAL MODEL OF

STATE AND LOCAL GOVERNMENT BOND SUPPLY

As revealed in the literature review, most studies of
government bond supply observe a governmental unit's
balance sheet statement, where the difference between
expenditures and revenues is equal to the amount of bonds
issued during the fiscal year. This kind of analysis is
severely lacking in economic content, as most of the
behavioral relationships involved in the decision to issue
bonds are overlooked. In fact, many state and local
governments generate a surplus nearly every year, yet still
issue bonds. A model which studies the behavior of these
economic units, rather than their balance sheets, will
explain conditions such as the one above where bonds are
issued while surpluses show up on the balance sheets. The
intent of this chapter is to construct a model of state and
local government bond supply which reveals the decision-
making behavior involved in determining the amount of state
and local government bonds issued.

Such a model requires an analysis of conditions under
which citizens demand state and local goods, how much of

these goods will be demanded, and the variables which deter-

105

106

mine how these goods will be paid for. When making these
decisions, citizens are simultaneously deciding the amount
of state and local government debt that best satisfies
their constrained wants. Since the model involves more
than a simple determination of bond supply, it has other
uses as well. Some of these uses will be mentioned as the
model is developed, and one use will be discussed at some
length.

To analyze how well consumer wants are met, conven-
tional neoclassical theory employs individual utility as a
measure of an individual's economic welfare. Further,
economic efficiency is attained when an individual citizen's
income is allocated between state and local goods and other
goods in a way that maximizes his/her utility. The model
of state and local government good production formulated
here is based on the premise that state and local govern—
ments spend their revenues in a way which attempts to
achieve the above-stated standard of economic efficiency.

When private markets fail to produce wanted goods and
services efficiently, the production of these goods by state
and local governments is justified. Justified, of course,
on the presumption that governments, acting in behalf of
the will of their constituents, can and will produce these
goods efficiently. The causes of market inefficiency can
be broken down into two general categories. First, some

goods (or bads), once produced, are by their mere presence

107

shared by many individuals, with or without payment for the
positive (or negative) services they afford --parks,
streets, and garbage, for example. Second, certain goods
are deemed ”natural" monopolies, and in private hands are
considered detrimental to the local welfare of the citizen-
ry --too little of the good will be produced at too high of
a price.

Since goods in the first category (public goods) run
into free-rider difficulties, market pricing signals are
disrupted and inefficient levels of these goods are pro-
duced. Therefore, some means other than private markets
must be used to determine the optimal amounts of state and
local goods to be produced. To uncover citizen wants,
while avoiding free-riders, local governments have their
citizens vote for the amounts of public goods desired.

This method of local public good allocation is not optimal
to every citizen, but will reveal the efficient amount of
production better than the pricing mechanism. Production
of state and local goods often requires a large initial
capital outlay, which must be financed. State and local
bond issues are used to acquire a large fraction of the
money necessary for capital outlays.

Voter behavior then has a large influence on the amount
of state and local bonds issued. In fact most states
require voter approval of all bonds whose principal and

interest must be covered out of local taxes. This kind of

108

bond is called a general obligation bond. Voter rejection
or approval of a general obligation bond referendum is
actually a means of expressing the amount of local public
goods desired. Therefore, the ensuing model of general
obligation bond supply is based on voter behavior.

For the second category of market inefficiency --
natural monopolies-- state and local officials must deter-
mine where natural monopolies exist. Once this deter-
mination is made, it is up to the officials to insure that
production of this good is executed like an efficient non-
profit enterprise. Generally, the enterprise is expected
to be run with zero profits --average cost pricing rules
are used. Bonds to help defray the capital expenditures
for these goods have few legal limitations, since as in
private enterprise, revenues from users of the good are ex-
pected to cover interest payments and eventually retire the
bonds. Such bonds are called revenue bonds. The amount of
revenue bonds issued depends on the number of revenue pro-
jects local officials regard as being in the public
interest. Officials are interested in the public interest
because satisfying voters will keep officials in office,
which gives utility to officials. Therefore, the utility
of local officials is observed in deriving a model of
revenue bond supply.

Neither of the above categories can be perfectly de-

fined. Public goods have degrees of publicness, as some

109

non-payers can usually be excluded from using the good. In
such cases local officials may decide to produce this good
as a self-supporting endeavor, or voters may reject govern-
ment production of the good entirely. Determining where
natural monopolies are present and require government inter-
vention is an important and imprecise decision of local
government officials, one which to a large extent circum-
scribes the scope of state and local government. This
decision, of course, also greatly influences the size of
total revenue bond issues.

Offering revenue bonds can itself be a further means
of extending the scope of government. Although general
obligation issues and revenue bond issues are treated
independently in this study it should be understood that
revenue bond issues depend to some degree on general obli—
gation issues. When public officials feel committed to
issue bonds, while general obligation bond issues are con-
strained by legal limitations, officials may look for
reasons to issue revenue bonds and thus circumvent lending
restrictions. (Maxwell and Anderson, 1977, p. 212).

Although achieving efficient economic solutions is
generally considered the central responsibility of state
and local governments, distributional objectives are also
present in these decisions. Even perfect private markets
do not account for income inequality. Thus many state and

local governments feel a social responsibility to provide

110

some goods for distributional purposes. Furthermore, they
tend to promote tax systems which contain an ability to pay
component, a component which is not neglected below.

A full description of the model will proceed as
follows. First, a theoretical voting model of general
obligation bond supply is posited. Some extensions beyond
bond supply are discussed. The empirical specification of
the model is set forth. And the empirical results are
shown and evaluated. Similarly, a revenue bond model is
constructed, specified, and its results evaluated. The

model's implications will be examined in a later chapter.

General Obligation Bonds

The Theoretical Model-u-A Model of Voter Choice

As mentioned above, general obligation bonds are
issued to help purchase capital needed to produce state and
local public goods which have been sanctioned by referenda.
Therefore, general oblibation bond supply can be construed
as a means of financing capital which is a derived demand
resulting from voter demand for state and local public
goods. The first step in constructing a theoretical model
of general obligation bond supply is to develop a voting
model which reveals the amount of state and local public
goods demanded by a locality's citizens. The production of
the voter-approved amount of local public goods requires a

corresponding amount of capital. Determining this amount of

 

 

111

capital and the means of financing this capital completes
the model.

As a result of local government defaults during the
Great Depression, most states have placed constitutional
and statutory restraints upon the ability of localities to
issue general obligation bonds. One of the most common
restrictions is a referendum requirement for all general
obligation issues. In an effort to preserve public choice
and fiscal solvency all but eight states impose this
requirement (ACIR, 1977, pp. 92-93). This suggests that a
voting model will show, better than other models, how
decisions to issue general obligation bonds are made.
Since voters determine, by passing or turning down bond
issues, now much of a public good will be produced, the
utility of the individual voter is the building block of
this kind of model. In short, an individual votes for the
amount of local public goods which maximizes his/her income

constraint.

The Utility Function

A well known theory of individual behavior involved in
the choice of local public goods is the Tiebout hypothesis
(Tiebout, 1956). According to the Tiebout hypothesis,
citizen voters, as a mechanism of registering their pref-
erence for local public goods, move into locations where
their preferences are best satisfied. Thus, voters tend to

move into jurisdictions where their neighbors will have

112

similar utility functions. If, after searching all com-
munities, the members of a community find that they still
have markedly different preferences from their neighbors,
they will undertake efforts to influence the tastes of one
another. This process tends to homogenize preferences
within a community, even when a family is initially unable
to move to a community providing the local goods they
desire (Brown and Saks, 1978). The income of each member
of the community, however, may vary greatly. Allowing this
similarity in the preference patterns of voters within a
community, the utility function postulated here is assumed
to be the same for all members of a certain community.

The utility function of each community is initially
assumed to have the following general form:
U = Axagbn-C; a>0, b>0, caO; where g is the amount of
state and local public goods consumed, x is all other goods
consumed (these goods are provided by the private and
federal government sectors), and n is the number of people
in the individual's community. c indicates a loss in the
publicness of g or the degree in which the consumption of
others affects an individual's consumption of g; these
might be called density or congestion effects. When there
are no congestion effects, c = 0; and if congestion
eliminates all individual utility, c approaches infinity.
a is the utility elasticity with respect to x, and b is
the utility elasticity with respect to the individual's

consumption of the local public good. It is assumed in the

113

initial analysis that every member of the community has the
same a and b. a and b can differ among communities, how-
ever.

If c = 0, population size has no effect on individual
utility. If c is greater than 0, congestion creates inter-
dependent utilities and population growth and concentration
reduces indivdual utility. Congestion-created exter-
nalities, which reduce individual g consumption and utility,
also motivate greater demand for public good consumption
--i.e., the demand for goods which alleviate the problems
of congestion. This relationship is evident in the utility
function. If U and x are held constant, there is a positive
relationship between n and g. It is important to remember,
however, that although population growth necessitates an
increase in g or x consumption in order to maintain an
individual's utility at its pre-growth level, additional
population potentially carries additional income. This
potential allows more g to be available to all and the pos-
sibility of maintaining or raising prior utility levels.

Another demographic variant, the age composition of a
community's population, can also affect the demand for g;
this would reflect a shift in the taste parameters. Com-
munities with many young or old residents would be expected

to have a higher 2 to a ratio than mediumeaged populations.

(J

n

(I)

114

The Budget Constraint

 

With the utility function understood, it is necessary
to look at the constraint on this utility. Since g is a
public good, it is either partly shared (it may not be a
pure public good) or provided equally to all community
members. This means the income of the whole community
should be a component of the individual's income constraint.
As is well known in public finance theory, it is difficult
for each member to receive the amount of g desired because
some members of the community will not pay for the amount
of g they desire. They count on someone else to make the
payment, while everyone shares in g's consumption. There-
fore, showing just how community income enters into the
income constraint of an individual can be a diffcult task.

Theory gives an indication of where to start. The
familiar Pareto-optimum condition for a public good
specified by Samuelson is that the sum of the marginal rates
of substitution for all members must equal the marginal
rate of transformation between other goods and the public
good (Samuelson, 1954). This condition can be broken down
further --the sum of the individual demand prices for the
public good must equal the marginal cost of the public good
and the individual demand price must equal the individual
marginal cost for every individual. This normative criteria
takes a strict benefit approach to the optimal payments for

a public good, just as in the payments for private goods.

115

It is only a first step, however, because even with the
distribution of community income constant, the Samuelson
condition still allows an infinite number of Pareto
efficient solutions. Hirofumi Shibata demonstrated this
result in his article "A Bargaining Model of the Pure
Theory of Public Expenditure” (Shibata, 1971). Shibata
shows that from an initial income distribution point, prior
to sharing the cost of a public good, there exists an "area"
of Pareto preferred points and a contract curve of "Pareto-
preferred Pareto optima." Only the Pareto-preferred Pareto
optima meet the efficiency standard set forth earlier in
this paper. Even within these efficiency confines, the
marginal cost of each individual is subject to game
theoretic strategies, i.e., political contests which deter-
mine the tax system. Theoretically, local governments
strive to achieve one of the efficient solutions, and at
the same time reach an agreement as to which of these
solutions is best.

In so doing, a locality must determine via a tax
system the distribution of costs among its citizens. A
valid voting model must come close to revealing the desired
production of g and at the same time include a tax system
which delivers the revenues necessary to purchase the
desired amount of g. The locality can only hope that the
desired amount of production is a Pareto—preferred Pareto
optimum, and that the costs of production are equitably

distributed.

116

Most voter models adopt the benefit approach to the
provision of public goods and try to find out how close the
voter-model solution is to the Pareto optimality solution
(Bowen, 1943; Black, 1948, Barlow, 1970). Even when these
voting models' solutions are not near an optimal solution,
they are recommended as good studies in positive economics.
Bowen's model is the earliest and probably best known of
these models. This model reduces the efficient solution
set to one solution by imposing the same per-unit tax on
all voters --the marginal cost of the public good divided
by the number of individuals in the community is equal to
the marginal cost to the individual. This payment scheme
is Bowen's assumption of what a locality might consider an
equitable distribution of local public good payments. Each
voter has a different demand for the local public good be-
cause of different preferences or incomes. Bowen concludes
that the amount of g produced is where the marginal cost of
the voter with the median demand curve is equal to the
demand price of the voter with the median demand. This may
or not be the efficiency solution, but it is considered
much closer than a private provision of g could achieve.
Most subsequent voter models have been extensions of Bowen's
model. The model used in this analysis is to some degree
also an extension of Bowen's model. The basic benefit
approach is used, but an ability to pay element is placed

in the taxing scheme of localities (the result of political

t6}

pa:

Th.

th

3.8

1‘8

WI]

Ut

SC

to

117

contests), and the level of individual incomes are explic-
itly considered.

A local government, acting in accordance with con-
stituent wants, taxes its citizens not only on benefits de-
rived from the local goods, but also on an individual's
ability to pay for the goods, i.e., his/her personal income
or wealth. Henry Aaron has found that on the average, local
taxes are proportional to income (Aaron, 1975, p. 38).
Theoretically then, it is assumed in this model that a
locality's concept of an individual's ability to pay in
terms of equal sacrifice is "equal proportional" --tax—
payers give up utility in proportion to their utility.

This assumption provides an outcome to the infinite range
of Pareto efficient distributions of tax payments. It is
the final result of political contention. With this
assumption, a unique Pareto efficient amount of g can
result which meets both the efficiency and equity standards
which localities ostensibly wish to attain.

According to Musgrave equal proportional sacrifice re-
quires a proportional tax rate if as income rises, the
marginal utility decreases at the same percentage rate as
the average utility (Musgrave, 1959, Ch. 5). Given the
utility function postulated above, the appropriate tax
scheme for the locality is a tax which is proportional

to the level of income. This can be easily proved:

118

dU/dg = bn‘CAxagb'l, U/g = n'CAxagb’l, a 1n (dU/dg)

d In (U/g) = b(b-l)n-chagb_2/bn-CAxagb-l

(b-1)g"1dg, %AMU = %AAU = (b—l)%Ag.

Having established conditions where a proportional income
tax is desirable, the amount of g to produce and the cor—
responding proportional income tax rate can be determined.
Since government goods are socially produced, no profit
should be derived from their consumption. The total amount
paid by the community and through federal grants should
equal the production cost. It should also be noted, how-

ever, that this budget is only balanced on a current account,

 

not on a capital account. With this in mind,

n n
C = t ; yi + mC or t = C(l-m)/ 2 y.; where C is the total
i=1 i=1 1

cost of local government goods; t is the proportional tax
rate; yi the income of consumer i, m the fraction of state
and local expenditures paid for by Federal grants, and n the
number of voters in the community. The actual value of t is
still unknown, since the amount of g is not yet determined.
The value of m of course is not a specific rate for a
specific project. The Federal government extends many
grants, each with its corresponding matching rate. Rates
may range from zero to one --no grant for a project to a
fully subsidized project (a project which is completely
financed via a block or unconditional grant). When aggre-
gating all of these projects an average rate on matching

grants results; this is the m value observed above. Even

119

as an average, however, m should cause both substitution
and income effects on the consumption of g.

In order to determine the amount of g desired by an
individual voter, the voter's per unit cost or price of g
(Pgi) must be known. Allowing constant returns to scale in
the production of g, the average cost of g becomes a con-
stant equal to marginal cost. As discussed in further de-
tail later, the production function of g is assumed to be a

Cobb-Douglas production function. So C = AC ° g, where

AC is constant. With this assumption, the total cost to

n
indiVldual l 15: C1 = tyi or C1 = C(1-m)yi/i:1yi =
n
ACg(l—m)yi/ Z yi. So the per unit cost of g to individual 1
i=1
n
is: Pgi = A—(l-m)yi/ Z yi. Letting the price of good X
i=1

citizen i becomes: y. = Pxx. + P .g = Pxx. +
n
(45(1—m)yi/.Z

y.)g.
1-1 1

The Optimal Level of State and Local Goods
With the utility function and budget constraint de-
fined, it now remains to optimize the citizens utility.
Holding n-c (the demographic parameters) constant, the
a b -c

utility function stated previously, U = Ax g n , can be

maximized subject to:

120

The interior solution is:

b a-l a b-l -c
n

A = aAg x n_c/Px = be g /P

’

gi
or

ag/Px = bx/Pgi' So x = (Pgia/be)g.
Substituting into the income constraint:

y1 = Pgig + Px(Pgiag/be) = Pgi(l+a/b)g.

Substituting into Pgi yields:

11
vi - (1-m)ACyi(l+a/b)g/ 2 vi.
i=1
01‘
n —
2 Vi = (l-m)AC(1+a/b)g.
i=1
SO
n —-
g* = X yi/(l-m)AC(1+a/b)- (1)
i=1

Note that this solution for g* is the same for every
voter of the community, regardless of his/her income --yi

and x are not present in the g* solution. Further note

i
that this is the Pareto efficient solution since each voter
is paying the amount he/she is voluntarily willing to pay
in order to consume g* of g. Figure 4-1 illustrates with

n = 3. The three straight lines are the income constraints
of the three voters. Voters with more income can operate
within a higher budget line. As income rises, however, the
slope of the budget line, -Pgi/Px, becomes steeper; this is
n

because as income rises, yi/ Z yi rises, which in turn makes
i=1

121

 

 

Y3

 

 

 

 

 

 

 

 

 

 

 

gs
Figure 4-1
Pgi n
= (l-m)ACyi/ Z yi
i=1
D1
8*

Figure 4-2

 

 

122

Pgi go up. In short an income effect on the consumption of
g is exactly offset by a substitution effect. As for
Pareto optimality, it can be observed that at g*, every
voter maximizes his/her utility, each subject to his/her
respective income constraint.

Figure 4-2 shows a second illustration which is similar
to the model described by Bowen. Again, demand goes up as
income rises --D1 to D2 to D3, but the rise in Pgi
associated with the income increase exactly counter—
balances the increased demand. Pareto optimality is also
demonstrated since the demand price is equal to the supply
price for every voter at g*.

If we now relax the assumption that all members of the
community have the same utility function --the a and b
parameters differ among the citizenry-- then in a majority
voting model, the median voter again gains prominence.
(Remember, however, with a proportional income tax, as pre-
viously defined, individual income doesn't determine the
optimal amount of g for the individual; it is determined by
the parameters of the utility function and production
function, and the amount of EEEEl community income.)

When voters are not alike, a large common utility
group, a median utility individual, or a common utility
group in the median range will determine g*. Figure 4-3
illustrates. There are 3 income classes --A, B, and C—-

where yA > yB > yC and PgA > PgB > ch. There are five voters

123

 

 

 

 

 

 

 

DII

 

 

DIV

 

gred

*
9 white

gblue

PgC

 

Figure 4-3

 

124

and three utility groups --red, white, and blue. Voter I
is in income class A and utility group white; II in class
B and group red; III in class B and group white; IV in

class B and group blue; and V in class C and group white.

The white group, which is the median utility group,
determines g. Voter II, in the red group, will not vote
for more than gred since beyond this amount his/her demand
price is less than his/her supply price. Voters I, III,
and V, of the white utility group, will vote for all amounts
of g up to and including g* since their demand price
exceeds their supply price up to level g* where their de-
mand price equals their supply price. Voter IV will vote
in favor of all amounts up to gblue' So there is a clear
majority of votes (4/5 approval) at g*. So with different
utility functions, the model is no longer Pareto optimal
(the supply price does not equal the demand price for
voters II and IV). It does retain a sound operational
character, and provides g at a level closer to optimal than
the private sector can accomplish.

Members of the white group will also get the propor-
tional tax rate which they consider optimal. Any member of
this group, regardless of his/her income level, can be the
central individual whose behavior determines local govern-
ment output. It happens in this illustration that Voter III
is in the middle income class as well as the median utility

group, but this need not necessarily be true.

 

125

Throughout the remainder of the analysis, whenever the
determination of g* is of interest, it is assumed that all
community members have the same utility function or that
the utility function of the median voter is observed. These
assumptions provide a rationale for an optimal or near-
optimal provision of local public goods. Further work
could be done with this voting model and the g* associated
with it. For instance, a/b could be estimated for different
communities, or the calculation of t could be examined
under various assumptions of individual utility. These
kinds of analyses, however, do not serve the purpose of the
present undertaking. g* is important in this analysis,
because it affects the amount of state and local debt
issued to partly finance the capital stock necessary to
generate the capital services that must be employed to

produce g*.

The Optimal Tax Rate

 

With voter i knowledgeable of his/her per unit tax
rate (Pgi) --which is related to his/her relative income--
g* as shown above can be determined. The value of g* in
turn allows authorities to calculate the proper income tax

rate to place upon each individual. Since g is equal to g*,

n
C* = K—g* and t* = C*(l-m)/ Z yi, the desired proportional
i=1
___ n
income tax rate is: t* = g*A (l-m)/ Z yi'
i=1

A sidelight of this result is that t* can be used to

126

find the ratio of the utility elasticities: substituting

for g*, t* = 1/(1+a/b); a

/b = (l-t*)/t*.

Finally, notice the tax rates yield a Pareto optimal
solution when it is assumed that all members of the com-
munity have the same utility function. If they have dif-
ferent utility functions (and they should not be too
different according to the Tiebout hypothesis), then the

median voter obtains an optimal amount of x and g for every

time period.

On Balancing the Budget

 

Debt, as has been discussed, is important to the pro-
duction of g*, since the cost of debt is part of the cost
of the capital needed for production. This cost is implicit
in AC, one of the variables determining g*. The total cost
of g* (using least cost production methods) is C*, while
the cost to state and local governments is (l-m)C*; so
n

n
total local taxes equal t* 2 y = Z P .g* = (l—m)C*, state
i=1 1 i=1 31

and local expenditures on public goods.

The above result, that taxes equal expenditures, gives
the impression that the budget is balanced; suggesting
there is no debt. The model does assume there is a bal—

anced budget on the current account, but one of the costs

 

in this current account is debt service. This service
includes interest payments and repayment of principal at a

rate equal to the rate of capital depreciation.

127

The total value of state and local capital and any debt
issued to pay for the original outlay of capital is not of
central interest to the taxpayer; of more concern is the
amount he/she must pay each time period to obtain the
services of capital needed to produce g*. In short, a
locality may borrow to buy capital needed to produce g*,
but the total value of this debt does not appear on the
current account, only the amount to be paid each period.
The Optimal Capital Stock and Price of State and Local
Capital Services

The level of capital services needed to produce g*
using least cost production techniques is denoted k* and
can be determined if the local public good production
function is known. The previously assumed Cobb—Douglas
production function is again postulated here to look at the
main determinants of the desired state and local capital
stock. To determine the optimal level of capital services,
it is necessary to minimize C = PCSk+WL, subject to
g* = Dquq-l, where w is the wage rate, L labor, k the real
value of capital services per period, and D and q production
parameters of the postulated Cobb-Douglas production
function.

Pcs is the real price of capital services or cost of
capital to a locality. In defining the price of capital
services, the approach taken by Dale Jorgenson "The Theory

of Investment Behavior" in Determinants of Investment

 

 

128

Behavior (1971) will be used. Jorgenson's presentation
operates in competitive private markets where the value of
the marginal product of a unit of capital can be directly
observed. A local voter when making a local capital
investment decision does not have this advantage when com-
pared to a private firm making a similar decision. However,
recall the voter had to choose between private goods with a
market price and value and government goods with a price
based on costs, income, and grants. Given this non-market
"price" for government goods, the voter still decided how
much in private goods he/she must sacrifice to obtain the
desired amount of local government goods. In obtaining the
final unit of capital needed to produce local goods, some
market value of private goods was given up. This in effect
is the value of the marginal product of local capital in
the same sense that private firms purchase capital to the
point where its rental cost is equal to the value of its
marginal product.

Rather than acquiring capital to the level where the
value of the marginal product of capital equals its rental
cost, the utility maximizing voter will allocate capital so
that its marginal value in each use is equal. Since the
marginal value of capital in local good production is equal
to its marginal value in private use, the marginal value of
state and local capital also equals the rental cost of

capital.

SE!“

it
a?
pa
fo
ra
ri
co
an

ch

129

This rental cost is called the price of capital
services (RC). When deciding upon how much capital to pur-
chase, the voter will weigh the price of a unit of capital,
Pm, with the benefits generated by the capital in the
future. A unit of capital purchased for Pm dollars will
deteriorate at the rate 1/Z each period and what remains
will produce the value of its marginal product = RC in each
future period. In equilibrium, the price of a unit of
capital will just equal the present value of the future

rentals it generates, or:

t

Pm = RC(l+l/Z)-t

IIM8

(1+r )-
l N
RC 2 (1+rN)‘t(1+1/Z)‘

t=1

t
t

The annual rental RC is discounted by the rate r to bring

N

it to a present value. r the rate on tax-exempts, is the

N’
appropriate discount rate since this is the rate voters must
pay to borrow financial capital. It is also a good proxy
for the opportunity cost of investing in local capital
rather than other assets, as the after tax return on equally

risky assets tends to equalize with r RC is also dis-

N'
counted at the rate 1/Z which reflects capital depreciation
and corresponding amortization of any debt issued to pur-
chase the local capital.

The infinite sum of (1+r _t(1+1/Z)-t equals

N)

1/(rN+1/Z+rN-l/Z). If rN-l/Z is ignored then this reduces

130

to l/(rN+l/Z) and one obtains RC = Pm(rN+1/Z). The real

price of capital services --%E = P -- thus becomes P =
m cs cs

rN+1/Z. This simple expression offers the best practical
definition for the real price of state and local capital
services. The depreciation rate could be somewhat modified
if expressed in a way showing how debt will be repaid.
However, this would be vastly complicated.

From this point forward, the analysis of Pcs is far
simpler than it was for Jorgenson. State and local govern-
ment investors do not have to deal with taxes, hence the
PCS is not complicated by taxes as it is when considering
private investment. Jorgenson must bring in a series of
taxes which lowers his private Pcs' (Of course, in
equilibrium the Pcs for state and local capital is equal to

N
of return on private securities adjust until they are

the PCS of private capital since r and the after tax rate

equal.)
PCS is implicit in the AC used to determine g* in the
voting model. This can be seen by observing the first order

conditions resulting from the cost minimization procedure

which yields:

k* = g*ql‘qwl‘q/D<1-q>1‘qPCSI—q (2)
and

AC = Pcsw1-q(l—q)q-1/qu. (3)

131

Returning to equation (1) and substituting equation

(3) makes
n q q 1- q—1 a
g* = z yi Dq /(1—m)Pcs s q<1~q> (1+ /b),
i=1
SO
n l— 1— 1- -1
k* = 2 y.-quq qw q/(l-m)p qw q(l-q)q
i=1 1 cs
(1+a/b)D<1-q)1‘qp “‘1
CS
n a
= .2 yieq/(l—m)(1+/b)pcso (4)
i=1
n
and, (l-m)Pcsk* = 2 yi/(b+a)/aq, (4a)

1 l
which means aq/(b+a) is the average fraction of community
income which voters agree to put into state and local
capital during each pay period over the lifetime of the
capital in order to get the flow of local public goods they
desire.

With the optimal flow of state and local goods, optimal
flow of state and local capital services, and the optimal

tax rate determined, the optimal level of debt can also be

determined.

The Optimal Level of General Obligation Bonds

To complete the model of general obligation bond
supply, the median voter must determine h --the fraction of
non-Federally funded state and local capital stock which is
financed by state and local debt. To determine h, the
median voter's preference pattern of x and g over many time

periods must be recognized. When considering the use of

 

132

capital with a lifetime of Z years, the median voter will
try to maximize his/her utility over Z periods of time. At
the moment the maximization decision is made, all con—
straints must be observed and all parameters assumed con-
stant in order to simultaneously find the optimal value for

each variable; that is citizen 1 maximizes

U1 - Ui(x1,x2, ,xz, g1, g2,...gZ, h1,h2,...,hz)
Z Z Z
subject to 2 y.. = Z P .x.. + Z P ..g.
j=1 1.] j=1 XJ 1.] j=1 g1.) Jr
and
1-q q-1 q n
P .. = P .w. 1- D 1- . .. Z ..
glJ ( as; J ( q) / q ) mJ)le/i=1ylJ
for j = 1,2,...,Z.

Determining a solution to this problem would require
an explicit utility function and strenuous mathematical
effort, but it is clear that optimizing values for
x1*,x2,...,xz*,g1*,g2*,...,gZ*,h1*,h2*,...,hZ*, are
determinant.

For each gj*, there is a cost minimizing capital
services requirement --kj*. An expression showing kj*
desires would be like the expression shown in equation (4),
except that rate of time preference parameters must also
appear in the expression. For any desired kj*' there is
also a requisite amount of state and local capital —-Kj*.

The relationship between these two variables is typically

some straightforward technical correspondence --possibly

133

linear. In fact it is not unusual to View this relation-
ship as linear.

Given a relationship between capital services and the
capital stock, the relationship between desired state and
local capital services and the desired general obligation
bond supply can be determined. If hj* = l, for j =
1,2,...,Z, then Kj* will equal Nj* --the desired supply of
tax-exempt bonds. Of course, as is evident from the
utility function, hj does not equal 1. Local citizens feel
uncomfortable financing all of their capital needs with
debt. Fear of insolvency and other subjective factors
frequently pressure local citizens to pay more in captial
expenses out of current revenues than is necessary. Each
period, a utility maximizing hj is found. The optimal
value for hj is found where an/th = 0. When this con-
dition is met prior to hj = 1, then current-period capital
expenses will exceed interest payments on debt plus depre-
ciation. (l-h§)(l-mj)AKj* becomes a current capital
expense, (h? being the new debt issue to new capital expen-
diture ratio for period j aaly).

Given hj*’Nj* = hj*(l-mj*)Kj*; where mj* is the Z-year
average rate on Federal grants, weighted by AKj*/Kj*. This
result can be simply demonstrated: since hj* =
Nj*/(l-mj*)Kj*,(Nj*/(l-mj*)Kj*)(l-mj*)Kj* = Nj*' We have
thus arrived at one of the ultimate objectives --a value for

the desired supply of general obligation bonds.

134

A Discussion of the Dynamics

 

It is unlikely in reality that the Z—dimensional g*
vector will not change throughout the lifetime of the
capital stock going into the production of the g* vector.
New capital must be financed every year since the capital

n
a

from past decisions wears out, and Z yi, m, /b, or AC
i=1

might change. There will be a corresponding change in the
need for the productive services of inputs. When the
median voter wants to raise the g* vector, he/she is
expressing a willingness to pay gaaa taxes during each pay
period in order to acquire more services from state and
local government labor, capital, and materials. The

additional tax money volunteered to capital services is

 

((l-m)(rN+1/Z)hc+(l-m)(l-hc)) (k*—k*_l) for the current
period and (l-m)(rN+1/Z)hc(k*-k*_1) during each period for
the remaining lifetime of the new capital. (l-m)hc*(K*—K*_l)
of state and local debt would be approved by a referendum.
If voters decide they want less g*, fewer capital ser-
vices will be demanded, or k*<k*_1 and (l-m)Pcs(k*-k*_1)<0.
There is a restriction on this inequality: voters are not
so myopic in their decisions to employ capital services
that future capital demands will diminish faster than
capital depreciates --K*_l—K*:(l/Z)K_1. Such a restriction
is not unrealistic; voters can closely approximate future
income and wants, and make the public spending decision in

the same way they make private spending decision. This

 

135

information is then allowed for when making current deci-
sions. With this restriction, the adjustment of the actual
captial stock to its desired level could take place very

quickly. There are, however, other constraints on behavior.

Institutional Constraints

 

Most states place legal constraints other than
referendums on the amount of bonds a locality can issue.
If (l-m*)h*K* exceeds a legal limit, g must be cut back.
This constraint of course creates a non-optimal provision
of x and g. The voter would gain more utility with more
state and local debt, and more g. Assuming that the
Ireferendum constraint on local government behavior is
strictly enforced, this argument submits that the added
constraint of bond issue limitations is suboptimal and
unnecessary. Nevertheless, these limits are real and must
be accounted for when analyzing tax-exempt bond supply.

Other than the referendum requirement, the most common
legal restriction on state and local bond issues is a
ceiling on the nominal rate of return on state and local
government bonds (Ffi'). Under conditions where the ceiling
is above the market rate, conventional wisdom asserts there
is a negative relationship between r ' and N. If borrowing

N

needs or inflation lead voters to expect rN' = rN+n* to

rise above the ceiling, they may want to borrow before the

rate required to get funds is legally unacceptable. On the

other hand, once a rise in n* has pushed rN' above rN',

136

voters have waited too long to borrow, debt finance must
wait until the ceiling is raised, the inflation rate falls,
or the market pushes rN' back down.

Figure 4-4 illustrates. Beginning at point A, if n*

rises, bond supply will shift to S'. So ceteris paribus

 

(voters attempt to beat the inflationary impact on the
demand for tax—exempts) the quantity of bonds supplied will
rise to point B, where further supply is legally restrained.
However, eventually the rise in n* will also cause tax-
exempt bond demand to decrease to D'. So when voters pro-
crastinate, the volume of issues falls to point C. Further—
more, should the market seek a rate above the ceiling, such
as point D, bond suppliers can not respond by offering
higher rates.

In review, a negative relationship is expected to
exist between rN' and h, but the ceiling sometimes creates
distorted non-market rates where the relationship may
appear temporarily positive (due to a n* increase), or the
relationship may appear to blow-up above the ceiling rate.
This ceiling, of course also can create sub-optimal levels
of debt.

Disregarding the legal limitations on borrowing, the
mere fact that the price of capital is expected to rise
with inflation gives a further incentive to buy capital as

soon as possible. If current funds are not available, the

capital expenditure must be debt financed. In a similar

137

 

 

I

’1
2
II

rN+17*

 

 

 

ceiling
rate

 

 

Figure 4-4

 

138

vein, if revenues cannot keep pace with this inflation,
more borrowing is necessary. Too much of such borrowing
can cause severe consequences on fiscal finances. Greytak
has done a thorough study on this impact, showing borrowing
needs rising, as the differential between capital expendi-
tures and revenues has risen because of inflation (Greytak

and Jump, 1975).

Summary
In summar , e uilibrium h.* = h.* 1r.*, r .+n.*, I"
y q J J ( J NJ J NJ
the voter's rate of time preference); and
n a
* = _. + . '
kj qillyij/(l mj)(l /b)Pcsj The de81red amount of

general obligation bonds outstanding if the legal con-
straints are not binding is: Nj* = (l-mj*)hj*Kj*. If the

legalities are constraining, N.*>N_ (where N_ is the
rNrj rNr

bond supply when the ceiling rate is binding).

To recapitulate, a voting model has been developed to
explain the determination of general obligation bond supply.
The central thesis is that voters decide how much of their
income will be spent on state and local capital services
during each period. This involves not only choosing the
size of the state and local capital stock, but also the
method of financing the capital stock. This formulation of
a tax-exempt bond model differs from formulations where
bond supply is a consequence of a balance sheet where

expenditures exceed revenues. Much economic behavior is

139

overlooked in these earlier models, as the capital stock is
seen simply as an independent variable determing debt needs.
More important is the determination of capital needs as a
derived demand for state and local government services.
This model provides a linkage from individual demand to

capital needs to bond supply.
The Empirical Specification

Specification of tax-exempt bond supply involves two
equations. The state and local capital stock (K) must be
specified; and the fraction of state and local capital

financed by debt (h) must be specified.

The Desired Capital Stock

 

The theoretical value for the desired flow of state
and local capital services, as determined previously is:
n

k* = (.3 yi)q/(1-m)(1+a/b)Pc

S )
i=1

n

where X y. is net state and local income, and m is the
i=1

matching rate on Federal grants. This rate is an aggregate
average of all rates across the country. On a Micro basis,
there are a whole range of rates which range from project
specific to general grants. General grants are really
transfers of income, but these grants enter into this
variable as a 100% matching rate. At the same time some
projects are completely unfunded by Federal money and add

to the aggregate average at a 0% matching rate.

140

q is a production parameter, and a and a are utility
parameters. Recall, however, k* is based on restrictive
assumptions --1) the utility function and production func—
tion of a representative locality have been given specific
functional forms which may or may not be correct; 2) in the
aggregate, a, b, and q must be the same in every locality;
and 3) demographic variants are held constant. Given these

restrictions, the model implies that the elasticity of k*

n
with respect to Z yi equals 1, and with respect to (1—m)
i=1

and Pcs equals -1. Testing the null hypothesis that these
elasticities are l and —l is not a constructive exercise,
however, because it is unrealistic to maintain the afore—
mentioned restrictions.

A more constructive empirical test is to retain the
basic theoretical structure, but relax the restrictions and
estimate the sensitivity of k* to its most important
determinants. To do this, the following equation is posed;

n 81 82 B3 B4 85

k* = 80‘ z yi) d 1 e/(l-m) P
i=1

cs
Provision of capital services requires a capital stock, K*,
which is assumed to be roughly proportional to the desired
flow of capital services; hence K* depends on the same

variables as k* times a constant. The above expression of

k* suggests a specification for K* of the form:

8 B B B e
l 2 3 4 5
i d l e/(l-m) pcs .

ME!

K*=B y
0.
i=1

141

e is an error term in which large errors are associated
with large values of K. The production and utility param-
eters (q/(l+a/b) are now subsumed into the constant term
80, and alternative forms of the utility function and pro—
duction function are permissible since the elasticities of
K* are not postulated at unity. The sensitivity of K* with
respect to each of the independent variables can easily be
estimated by the 8's, as this functional form is easily
converted into a linear model:

n

*=
ln K 1n BO+Bl ln( 3

1 Yi)+82 1n d+B3 1n 1

l
-84 1n (1-m)—35 1n pcs+ 1n 8.

The variables 1 and d reintroduce demographic
variables into the model. As total population rises, more
people must share the local public good, so g must also
rise to keep utility standards up. Presumably, this is

possible because each individual has some income, so as

n
total population rises, Z yi also rises. Since public
i=1

goods can be partly shared without a loss in consumption to
each individual (with a pure public good, there is no
individual loss in consumption due to sharing), a rise in
total population does not raise K* as much as it would if g
could not be shared. The degree of sharing depends on the
inherent publicness of state and local goods and upon the

intensity of congestion which can diminish individual

142

participation in the consumption of state and local goods.
To account for the demographic impact on K*, a density dummy
and an age-composition factor are used. This allows for
demographic adjustments without seriously altering the
theoretical formulation.

d is a dummy variable --1 from 1959 to 1970 and 2 from
1971 to 1977. This dummy is necessary for several reasons.
As a proxy for density, the dummy separates the years where
the country's fifteen largest SMSA's had some population
growth from the years they had zero or negative population
growth. Secondly, this falling growth rate among large
SMSA's was accompanied by several fiscal crises, which made
it more difficult for municipalities to find city investors.
Also in the 70's the price of construction rose faster than
the general price indices. In reaction to these events,
many local governments turned to leasing rather than pur-
chasing local capital. Sometimes local governments out and
out returned certain services to the private sector.

1 is a population factor for school age children. It
is equal to the current year's annual fraction of the total
population older than 4 years and younger than 16 years
divided by the same fraction in 1963. When 1 rises, demand
for state and local goods should also rise since this group
requires more state and local public services. Thus 1 to

some extent also reflects changing tastes over time.

144

Since the actual level of capital cannot be immediately
brought to the desired level of capital, the specification

is revised further:

Kt/Kt-l = (Kt’k/K )A

t-l

where the left isde is the actual ratio of present state
and local capital over the level in the previous period,
and the right side shows the degree to which the desired
ratio has adjusted to the actual ratio. A, the adjustment
parameter, is greater than zero and less than one. The
value of A is somewhat distorted in reality since the level
of the capital stock cannot be reduced by more than the
amount that it depreciates.

Given Kt* previously obtained,

n B B B B B
_ 1 2 3 4 5 l
Kt/K,_1 - (80(iilyi) d 1 e/(l—m) Pcs Kt_1> . (7)

and taking logarithms transforms to

n

1n Kt-ln Kt-l = 1 ln BO+181 ln (illyi)+182 ln d+l83 ln 1
-184 1n (l-m)-).B5 1n PCS-1 ln Kt—l
+1 ln 6t (8a)

and

n
1n Kt = Y0+y1 In E

-Ys 1n PC +y6 In K +8 . (8b)

S

144

The Fraction of Capital Financed bnyebt

It is also necessary to determine what fraction of the
non-Federally funded capital stock is financed by state and
local debt. Several variables, discussed in the theoretical
section, contribute to the size of this fraction, denoted
h. Several linear estimating equations involving these

variables are proposed below:

ln h = ln 80+81 1n (g/y)+62 ln rN'+e (9)
1n h = 1n 80+81 1n (g/y)+82 1n rN+83 1n n*+c (10)
h = 80+Bl(g/Y)+82rN'+€ (11)
h = 80+Bl(g/Y)+82rN+83n*+e (12)

g/y is the ratio of state and local expenditures to
permanent income (a weighted average of past incomes).
This variable is employed to capture the tastes of voters.
More explicitly, the fraction of income they al§a_to place
in state and local goods as opposed to private goods and
Federal goods is estimated with this ratio. Permanent
income is more relevant than current income because, as
stated in the theory, current decisions affect consumption
over many time periods. The relationship between g/y and h
is possibly non-linear. At some point voters will no longer
wish to sacrifice private goods for more state and local
good consumption, hence greater consumption of state and
local goods must be funded almost exclusively through

debt --h would then begin to rise exponentially as g/y rises.

145

rN', discussed earlier, is the tax-exempt bond rate.
Recall, there is a ceiling on this rate. h is expected to
fall as rN' rises. Once the market rate begins to rise
above state and local ceilings, h will probably fall
dramatically, as many localities lose their legal borrowing
rights. This situation is not completely predictable since
localities modify their behavior in many ways in order to
deal with the disequilibria created by the rate ceiling.

rN and n*, discussed previously, breakdown the rN'
component of the equation. Beyond this breakdown, n* on
its own has potential effects on h. These effects were
discussed in the theoretical section. Unfortunately, for

measuring purposes, n* can have effects which counter one

another.

General Obllgation Bond Supply

 

Combining the equations specified in the last two

sections, general obligation bond supply can be estimated:

= _ *
N0t (1 mt )htK

t'
Note that l-m plays a part in the determination of K*.
Once K* is determined, Federal grants pay for l-m of the
capital expenditure, so l-m enters the picture again, only
as a simple fraction which shows which part of the capital
expenditure the state and local governments need not pay.
Figure 4-5 illustrates. K * is the amount of state and

1
local capital desired if no grants are offered. The state

146

 

 

K*other

 

.---_--..- /.....

 

N
*

O

N
H*------

 

Figure 4-5

 

147

and local governments must pay K * for this capital. If

1
grants are offered, the state and local governments desire
KO* of state and local capital. They must pay (l-m)KO* for
this capital. K1* and (l-m)KO* are not necessarily equal.
The grant affects the amount state and local governments
are willing to pay.

Finally, K is the real value of capital, so the N

solved for is the real desired supply of general obligation

bonds.

Results

Equations 8 - 12 are estimated using the method of
ordinary least squares. Since the h equation and K equa-
tion have no independent variables in common, identification

is not a problem. The estimates are:

n
ln Kt = -.265846 + .124876 1n 2 yi - .0184991 1n a + .0562207 1n 1
i=1
- .0375442 1n PCS - .0353040 In (l-m) + .896869 1n Kt_1 (13)
(-1.47) (-.27) (16.85)
R2 = .9998 F = 9979.58 0w = 2.20
In h = .00969004 + .479134 ln(g/y) - .219280 1n rN' (14)
(.04) (3.68) (-9.74)
R2 = .9220 F . 70.97 0w = 2.14

1n h = -.687951 + .224856 ln(g/y) - .0147338 ln rN - .129184 1n n*
(15)
(-2.00) (1.31) (—1.14) (-7.24)

50
II

.8943 F = 31.04 DW = 1.18

148

h = .211842 + .928104 (g/y) - .0126417 rN' (16)
(5.74) (3.45) (-10.17)

R2 = .9253 F = 74.37 0w = 2.07

h = .237376 + .693258 (g/y) - .00977768 rN - .0121014 n* (17)
(5.36) (1.97) (-3.23) (9.00)

R2= .9320 F = 50.24 0w = 1.74

All of the coefficients in equation 13 have the
expected a priori sign with reasonably strong t-statistics.
The F statistic is significant, the R2 is exceptionally
high, and the DW statistic is acceptable. The coefficient
associated with In Kt-l is nearly .9, indicating that A,
the adjustment parameter, is about .1. Capital stock
adjustment to its desired level is not particularly rapid,
which is not a surprise since the political process of set-
ting up voting procedures requires time.

Of further note In (l-m) tests with a weak negative
significance --its t-statistic is —.27. This weak sign is
probably due to a shift in tastes. In recent years many
people feel they have become satiated with public goods.
They view many public goods as inferior. Consequently,
more and more grant money is used to reduce state and local
taxes, and thus total real state and local capital spending.
A shift in tastes has probably caused a clear relationship

between Federal grants and state and local capital spending

to look weaker than it really is. (Approval of Proposition

149

13 in California is the kind of voter behavior that suggests
public attitudes towards state and local public goods has
been changing.)

Equations l4, l6, and 17 are statistically strong on
every count, while equation 15 has a low DW statistic. All
coefficients show the expected a priori sign and strong
supporting t-statistics.

It was suspected that a strong negative relationship
between rN and h might not result because of the disequi-
librium behavior induced by the rate ceiling. An increase
in the n* component of rN' clearly causes rN' to go over
the ceiling, and thus reduce h. Conversely, when n* falls,
r ' might then fall below the ceiling rate, allowing h to

N

rise. rN in the meantime may rise or not change, but the
withheld desire to issue tax-exempts that may build up
while rN' exceeds the rate ceiling is unleashed when n*
falls. Hence a rising h might be associated with a rising
rN. This effect has not proved out to be important. But

splitting rN' into rN and n* helps to isolate this possible
effect, even though it is minor.

Finally, the results show that the linear specifica-
tion estimates h more accurately than the logarithmic
specification. Possibly the rate ceiling to some extent
linearizes the relationship.

These estimates can be used to predict total tax-exempt

bond supply, after estimates of revenue bond supply are

obtained.

150

Revenue Bond Supply

 

Specification

The winds of public feeling toward the size of govern-
ment have a subjective influence on public officials' View
of the number of natural monopolies present and the amount
that local governments should spend in the operation of
these industries. In periods or locations where there is
discontent with private provisions of important community
goods, then public enterprises should be popular, and the
number and level of public enterprises sizeable. These
goods usually are not public goods and can be supplied on a

quid pro quo basis; allocative efficiency precludes ability

 

to pay as a revenue rationale for these endeavors. Thus,
local governments, theoretically, try to produce Pareto
efficient amounts of these goods; an objective the private
sector cannot accomplish. This means consumers should pay
the average cost for a unit of good. A local official then
must --just as the manager of a private monopoly-- determine
optimal production methods and optimal amounts of produc-
tion. Unlike private managers, the local officials do not
try to maximize profits; they attempt to maximize their
office holding capacities.

Revenue or non-guaranteed bonds are used to help
finance the investment projects of natural monopolies run

by local governments. Since revenue bonds are supposed to

151

be retired out of the revenues earned from the project they
finance, statutory or constitutional limitations, including
voter approval, are not required prior to their issuance.
Therefore, non-guaranteed bonds can be issued by elected
officials without directly representing the will of their
constituency. The issuance of non-guaranteed bonds is
essentially a discretionary action by local officials. It
is the utility of local officials then that is critical in
the decision to issue this kind of bond.

Presumably, financial prudence and acumen are present
in this decision, although in practice the utility of an
official may direct him/her away from sound financial
undertakings. For this model, it is assumed that local
government officials do not intentionally make reckless
decisions; they borrow to undertake projects only after
they have received sound financial advice and fully expect
future earnings to cover costs. But the primary charac-
teristic of an official's utility is the desire to be re—
elected. This usually means supplying many government
services which satisfy his/her electorate, while holding
taxes down. If he/she blatantly fails to accomplish one or
both of these conflicting objectives, he/she need not be
concerned about future government services since someone
else will be in office. Hence we should expect at the time
a borrowing decision is made that local officials favor

present consumption of government services above future

152

consumption. On this basis, determining the amount of non-
guaranteed local government bonds issued is a simple utility
maximization problem.

In reality the present versus future consumption
decision extends over many time periods; here, for simplic-
ity of exposition, only two time periods are analyzed.
Nevertheless, the model retains the essence of a multi-
period model. The utility function of an elected official

can be expressed:

a b
U = Ag1 g2

where a2>b since officials prefer current consumption to
future consumption. g1 and g2 represent real government
services in time periods one and two respectively. g1 is

the average amount of public enterprise production per year

 

over the next two years. Incumbent officials place high
priority on this production since most local officials have
at most two years to act before they are up for re-election.
g2 is the average amount of production per year across the
official's desired time in office. Most officials hope to
be in office possibly ten more years, but cannot realis-
tically put too much value on public enterprise production
beyond that point.

Scrupulous officials look at actual time spans when
observing predicted project returns, even though their

interests do not necessarily coincide with this span of

153

time. Still, choosing a set time limit for all public
enterprises, in this case ten years, simplifies the model
considerably, especially when designing an empirical
specification.

The expenditures on g1 and g2 are eventually paid for

out of user fees. The official's budget constraint is:

H
+

4 4
1 12/(1+rN) + m(gl+gZ/(1+rN) )
= 81 + gz/(1+rN)4, which reduces to

I1 + 12/(1+rN)4 = (l-m)g1 + (1-m)g2/(1+rN)4; (18)

the present value of the expected returns must equal the
present value of state and local expenditures on these
projects, with I1 and I2 being the real expected returns
from the project. User fees during the current year
measure returns during the first period. Expected user
fees four years hereafter are used to measure the average
income during the course of the succeeding eight years.
The fourth year is used since it is the median year of the
projected eight year time span which the officials are
assumed to base their present decisions upon.

rN (the real rate of return on tax-exempt bonds) is
the discount rate used since this is the rate that must be
paid to borrow for public enterprise projects. Again m is
the matching rate on Federal grants. Note that the budget

constraint implicitly assumes that officials expect the

future matching rate to equal the current rate.

154

As long as an official acts within this constraint,
his/her behavior must be considered prudent. This is not
to say his/her rate of time preference is the same as the
body he/she represents.

Maximizing the official's utility function with respect

to the budget constraint yields the following condition:
_ 4
A = ag2 - bgl(l+rN) . (19)

a standard rate of time preference condition. Substituting
this expression into the officials' budget constraint
yields the desired amount of local government services

derived from public enterprises over the current period

[_a_] [_a_]

a+b I a+b I

g1* = ——————l + 2 4 . (20)
(l-m) (1-m)(1+r)

 

This expression can be used to corroborate the earlier
hypothesis that a:>b. Letting B = a/a+b, the following
regression equation would follow:

* I I

g1 = B 1 + 2 + E, (21)

(l-m) (1-m)(1+r)4

 

 

where 11’ 12, m, and r are exogenous variables. To support
the hypothesis that a1>b, then 32>é. However, it is not
the purpose of this effort to uncover the exact utility
function of public officials; hence the B in equation 21 is

not estimated.

155

It is important to show how public officials' behavior
affects revenue bond supply. The volume of revenue bond

issues resultant from the desired spending above is:

* *

*
ANf — g1 - mgl - I1 = (l-m)g1 - I1. (22)

In estimating AN the (l-m) which appears in equation 22

f
will not cancel out the (l-m) component of gl*. Such a
cancellation is proper only if the previously postulated
utility function of local officials is correct. This
correctness of course has not been determined. Thus (l-m)
may be wrapped up in the preference parameters of some

alternate utility function.

*
Thus substituting g1 into equation 5 yields:

 

ii. _a_
a+b,I1 a+b I9

ANf = (l-m)-——————— + ‘ 4 — I1. (23)
(l-m) (l-m)(l+r)__

As discussed above, if the utility function is correct, the

B of equation 21 would provide the information needed to

estimate ANf. However, the above relationship among the

exogenous variables and utility parameters is conditional
and not confirmed. But it is clear that these variables

in some functional form determine AN or:

f,

ANf = ANf(I1, 12, (l-m), (1+r)4, utility parameters).(24)

A linear specification of this function is as valid as any

other proposed and it can be easily estimated.

156

Hence:

AN = 8 + 8 I + Sol

4
1 1 - 2 + 83(l-m) + 84(1+r) + e. (25)

where the utility parameters are embodied in the betas.
Since the remainder of the complete model observes
total bonds outstanding rather than net issues, it follows
that the revenue bond component of the model should do the
same. This modification is easily accomplished by using

the inter-period change identity:
N = AN + N . (26)

The major potential difficulty expected when estimating
either equation 21 or equation 25 is the calculation of a
macroeconomic measurement of the expected future returns
derived from user fees placed on public enterprise projects.

The following method of measurement is proposed.

12 = 11.(1+(LY_LY_1)/LY_1)4/(1+r*)4 (27)

where I1 again denotes current user fees, LY denotes local
income, and n* shows the expected rate of inflation. This
variable is based on the idea that the flow of user fees
grows at the same rate as local income. If it does not
accurately reflect expected income, then an alternative
specification may be called for.

A possible indicator of future user fees, which is not

itself a measure of user fees, is the interperiod change in

157

user fees. Thus equation 25 can be respecified with changes
in user fees substituted for I2. This formulation retains
the preceeding theoretical basis, but avoids measuring and

specifically defining expected future returns which may be

an impossibility:

AN = B + B I + BZAI

4
0 1 1 + 83(1-m) + 84(1+rN) + e. (28)

1

I1, as equation 23 shows, may be positively or nega-
tively related to revenue bond issues. High levels of user
fees can spawn higher demand for public enterprise projects
which create more financing needs, and high levels of user
fees mean there is more current income available to govern-
ment enterprise projects, thus reducing debt needs. The
net effect depends upon how much the level of current user
fees affects demand for new projects.

I and its relationship with revenue bond issues is

2

also shown in equation 23. When future income is expected

to be high relative to current income, officials will feel

 

safe in raising the amount of bond issues; hence a positive
relationship is clear. Since a macro-measure of expected
future income is typically based on current measures, this

variable can present problems because it is the relative

 

relationship between current and future income that is

important. The substitution of AI into the equation is an

1
effort to overcome this difficulty.

158

All is expected to be positively related to revenue
bond issues. Local officials, often newly-elected, in their
quest for local government services and voter satisfaction
tend to be optimistic in their estimates of future income.
Consequently, they perceive increases in user fees to be a
sign of rising public demand for local services -—a rising
demand which will produce even greater revenues in the
future.

r is expected to have a negative relationship with

N
revenue bond issues. When borrowing costs rise, less bor-
rowing is feasible. This negative relationship may,
however, be contaminated by an interdependency between
general obligation bonds and revenue bonds. As bond rates
begin to exceed the legal ceiling on general obligation
bonds, officials may shift their funds to general obliga-
tion projects and borrow to cover their revenue project
needs.

The relationship between l-m and revenue bond issues
is indeterminant. When l-m rises, due to a drop in the
matching rate on Federal grants, local public expenditures
become relatively more costly than private expenditures;
hence private goods or Federal goods are substituted for
local goods. If the elasticity of demand of local officials
for public enterprise projects is low, total expenditures
will rise creating greater debt needs. If the elasticity

is high, total expenditure will fall and debt needs may be

159

eased. A rise in l-m also means fewer current funds are
available to purchase whatever level of local expenditures
is desired; hence more local debt may be needed to replace
the lost Federal payments. The net result of these two
opposing results depends upon the officials' elasticity of
demand. Clearly, if the elasticity is low, l—m is inversely
related to revenue bond issues. But if the elasticity is
high, a reduction in expenditures consequent to a rise in
l-m may outweigh the loss in Federal money and thus reduce
debt issues.

The model as it stands does not directly estimate the
demand elasticity of local officials. However, if the
regression coefficient of l-m in the above model is negative
and significant, it strongly suggests that the elasticity
is high. If the coefficient is positive, either the elas-
ticity is low; or the elasticity is high and a loss in
Federal money outweighs a reduction in expenditures --the
model can not conclusively reveal which of these circum-
stances occurs. An insignificant coefficient suggests two
possibilities. One, the elasticity is neither high nor low
--a rise in l-m lowers desired local purchases by an amount
approximately equal to lost Federal money, so no bond issues
are called for. Second, Federal grants do not influence
revenue bond issues.

Recalling equation 22, it was noted that with the

originally postulated utility function, l-m cancelled out

160

of the analysis completely. This occurred because the
utility function had no elasticity components for local
goods versus other goods; the parameters showed only the
rate of time preference for local goods. However, in this
context, the debt needs arising from the effects of grants
on desired local expenditures may be exactly offset by the
amount of Federal funding available. Consequently, the
model will also be tested after dropping l-m from equation
25.

Although several specifications are posed to estimate
revenue bond supply, the foundation of each specification
is the same. The amount of present and potential future
user fees are important variables. The borrowing rate is
important, and the rate on Federal grants might influence
debt decisions. Finally, either explicitly or implicitly
embedded (depending upon the specification) in a set of
coefficients is the officials' rate of time preference,
which is expected to boost revenue bond issues above the
amount issued if officials were indifferent between present

and future state and local government goods and services.
Results

Equation 25, not unexpectedly, was not statistically
strong. There are two possible reasons for this lack of
strength. First, as mentioned before, finding a good

measurement of expected future income earned on public

161

enterprises is quite difficult, maybe even impossible with
the data limitations on state and local government aggre-
gate financial time-series statistics. Second, state and
local government officials may not behave rationally, or in
any consistent pattern from which a general relationship can
be demonstrated; there may be no stable utility function
for them.

In either event the independent variables proposed in
these equations do appear to influence revenue bond supply.

The results from equation 25 are shown below:

ANf = 12575 - .716395I1 + .301847I2

(.26) (-.385) (2.83)
+ 11635.3(l-m) - 7558.60(1+r)4,

(.28) (-.37)

R2 = .6569, F = 4.31, DW = 2.26

Dropping l-m, the results are as follows:

ANf = 24990.8 - .7389991l + .28420712 - 8926.65(l+r)4,

(1.12) (-4.43) (3.53) (-.45)

R2 = .6537, F = 6.29. ow = 2.24

118

negative which suggests that when current fees are high, the

All of the a priori relationships are corroborated. B

correspondingly high amounts of local expenditures are

covered with these fees, rather than with debt issues.

A

82 is positive --local officials borrow when they foresee

162

A

high future returns. 83 is positive, but insignificant,
which means the elasticity of demand for local services is

A

probably not high. 84 is negative as expected; its t-
statistic, however, is low, but this is no surprise. The
interdependency with general obligation bond issues, as
previously discussed, has most likely reduced the strength
of this relationship. Finally, the R2 and F statistics do
not verify that the model as a whole is highly descriptive.
The respecification set forth in equation 28, however,

does lend strong support to the basic foundation of the

model. Its estimates are:

AN = 136593 - .653335I + 1.90052AI

r 1 l
(2.16) (-2.13) (16.04)
- 72476.9(1—m) - 54581.0(1+rN)4
(-.94) (-l.83)
2 = 90.93, 0w = 1.86;

R = .9732, F

and dropping (l-m):

ANf = 84256.9 .39557111 + 1.88611611 - 69536.1(1+rN)4

(2.81) (-2.86) (16.13) {-2.77)

R2 = .9709, F

122.21, DW = 1.65;

and finally simplifying (1+rN)4 to observe the direct rN

relationship:

163

AN = 79509.9 - .6507341 + 1.89812AI

f 1 1
(1.12) (-2.15) (16.23)
- 69452.5(1-m) - 2311.92rN (29)
(-.91) (-1.93)
R2 = .9740, F = 93.48, DE = 1.85.

The respecified model, which does not use a prior
growth rate as an indicator of future user fee income,
tests statistically strong. All a priori relationships are
as expected, and the R2 and F statistics suggest a well-

fitted model.
Summary

The interesting aspect of the revenue bond model when
compared to the general obligation model is the amorphous
nature of the budget constraint in the revenue bond model.
The budget constraint is an outlook of future income
variable with a heavy political bias to overpredict,future
income levels. The independent variable All estimates the
relationship between revenue bond supply and local political
bosses' views of future user fee income and present needs.
Since there is no specific budget constraint underlying
this relationship, there is no guarantee that revenue bonds
can be paid off when their time comes. We have then in
revenue bond equation 29 an estimate of bond supply with a

high potential for fiscal insolvency. In the literature

search, this researcher was unable to find any empirical

164

studies specifically relating to revenue bonds and the
ability of local governments to redeem them when due. Work
is scant possibly because, as already noted in developing
the present model, obtaining reliable data presents a
severe problem. Nevertheless, more study in this area
would be of immense practical value.

Finally, it should be noted that in this model non-
guaranteed bonds can be used to finance current expenditures
other than capital expenses. Therefore, they are riskier
than general obligation bonds. Additionally, if returns
from user fees are not as high as expected, officials are
tempted to raise taxes to cover repayment of debt and thus
maintain the locality's credit rating. This is a dangerous
kind of situation which localities should avoid since it
may lead to a fiscal crisis and the loss of voter control
over local government finance. This kind of situation is
also difficult to capture in an economic model since con-
straints are broken, and the rules of rational economic
behavior are not necessarily followed. Nevertheless, this
model still offers a good approximation of how £2321 tax-
exempt bond supply is determined --the supply of general
obligation bonds is determined by the median voter (h*K*
decision); and the supply of non-guaranteed bonds is
determined essentially by the rate of time preference of

local officials.

165

The model with all of its components provides a
behavioral analysis of aggregate tax-exempt bond supply.
With these estimates established, the following chapter

will trace through the effects of changes in the exogenous

variables.

CHAPTER V

THE DEMAND-SUPPLY SYSTEM

So far the demand and supply of tax-exempts have been
analyzed independently. Equally necessary is an analysis
of the workings of the municipal bond market model as a
demand—supply system. In short, the equations estimated in
the previous chapters must be supplemented by an identity
which states that the sources of demand equal the sources
of supply. This system of equations can then be solved for
the quantity of bonds outstanding and the real rate on tax—
exempts given the values of the exogenous variables. With
these equilibrium values established, multipliers of the
quantity of municipal bonds outstanding and the real rate of
return on tax-exempts with respect to the exogenous
variables can be determined. A discussion of these multi-
pliers allows the display of the model's operation as a

demand-supply representation of the municipal bond market.

The System of Equations

 

The system contains five equations --two demand-side
equations, two supply-side equations, and a demand equal
supply identity. Each of the sectoral equations includes

the real rate of return on tax-exempts plus several

166

167

exogenous variables. More formally:

Household demand = NDH(RRNA, exogenous variables 1);

Bank demand = NDB(RRNA, exogenous variables 2);

General obligation supply = NSO (RRNA, exogenous
variables 3);

Revenue supply = NSR(RRNA, exogenous variables 4); and,

NDH + NDB = NSO + NSR.

Hence the system is composed of 5 equations and 5 unknown
-—NDH, NDB, NSO, NSR, and RRNA.

Using the estimated regression equations, the system
is explicitly stated in Chart 1 with symbols denoted in
Chart 2. Lines 1 — 4 show household demand; lines 5 - 10
show bank demand; line 11 shows other demand; line 12 shows
revenue bond supply; and lines 13 - 15 show general obliga-
tion bond supply. Since the Cochrane-Orcutt method was
used to estimate the demand equations, they contain lagged
values and the constant value rho which is .9665051 in the
non-bank equation and —.l679364 in the bank equation. The
equations have also been somewhat modified in order to
locate and isolate RRNA.

Recall from Chapter 3 that the non-bank public demand
equation contains the variable TYBIL (observed in equation
22, Table 3-4, Chapter 3). TYBIL is the amount of taxable
income for all individuals in marginal tax brackets greater

than or equal to tax bracket T, where T is the marginal tax

168

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Chart 2.

F4PH5

TYBIL

RRNA
RC

EXPA

TRSD5

DRKRD3

RST

DRNRS

W5X3R

F4BNOF

WTU

RLU

CALCl

RSMU

CALC2

YBP61

169

Glossary to Chart 1

the fraction of non-bank wealth placed in tax-
exempts.

taxable income in tax brackets where the marginal
tax rate is greater than or equal to that tax
rate in which investors are indifferent between
tax-exempts and corporate bonds.

the real rate of return on tax—exempts.
the rate of return on corporate bonds.
the expected inflation rate.

the tax bracket where investors are indifferent
between corporate bonds and tax—exempts.

the income to wealth ratio.

the difference between rate of return on capital
and rate of return on deposits.

the real rate of return on long-term Federal
securities (after taxes).

the difference between the rate on tax-exempts and
the rate on Federal securities.

the real value of net private wealth.

the fraction of bank deposits placed in tax-
exempts.

the tax rate for banks times the weighted rate
of return on deposits.

the real after tax rate of return on bank loans.

4
i z (RRNA + WTU - RLU)_.
i=1 1

the real after tax rate of return on medium—term
Federal securities.

4
k 2 (RRNA + WTU - RSMU)
i=1

the real bank income.

170

Chart 2 (cont'd.)

LOP
DDUNLR

RDEPMR

D3

DRUSR

M1

M13

RUSR
RNSR
RLINC
EDUM12
OSPOPF
AEXLI

the leasing operation dummy.
the second difference of the unemployment rate.

the real value of bank deposits less required
reserves less free reserves.

other bank demand.

the change in the real value of state and local
user fees.

1 — the matching rate on Federal grants.

the average of M1 over lifetime of capital;
weighted by the capital stock contribution of
that year.

the real value of state and local user fees.
the real value of revenue bonds outstanding.
real state and local income.

the exponential value of the density dummy variable.

the age-distribution population factor.

the ratio of state and local government spending
to local income.

171

rate at which an investor is indifferent between tax-exempts
and corporate bonds. T is determined in the following way.
When the nominal rate of return on tax-exempts —-RNA-- is
equal to the after tax rates of return on corporate bonds
--(l-T)RC—-, or RNA = (l-T)RC, then the investor is indif—
ferent between tax-exempts and corporate bonds. Thus the
tax rate which makes the investor indifferent between the
two assets is where T = l - (RNA/RC).

When T rises, TYBIL falls and fewer investors benefit
by having their wealth in tax-exempts, i.e. there is less
taxable income seeking municipal bonds as a tax shelter. T
changes when l - (RNA/RC) changes; RNA thus affects tax-
exempt demand through the TYBIL channel. In order to cap-
ture this influence, T = l - RNA/RC is regressed on TYBIL.
Using ordinary least squares, the Durbin—Watson statistic
strongly indicated the presence of serial—correlation. The
relationship between T and TYBIL was then reestimated using
the Cochrane—Orcutt procedure. The statistical results
show a constant of 1041.91, a regression coefficient on T
of -2797.7, a rho value of .9054133, and an R2 of .8879.

l - (RNA/RC) is then substituted into the T in the
estimated TYBIL function. This estimated TYBIL function is
then substituted into TYBIL in the original non-bank demand
equation. With these substitutions, non-bank demand has
RNA/RC as one of its arguments, where RNA = RRNA plus the
eXpected inflation rate. With these adjustments, the effect

of RRNA on non-bank demand caused by a change in RRNA

172

relative to the corporate bond rate is considered when
solving the whole system for equilibrium RRNA. Lines 1 - 4
of Chart 1 show the non-bank demand equation consequent to
these substitutions and reduction of variables.

Bank demand as mentioned is also specified using the
Cochrane-Orcutt procedure. The equation shown in Chart 1
is a slightly altered reexpression of equation 19 from
Table 3-2 in Chapter 3. In Chart 1 the variables X25 and
X35M of equation 19 are broken into their component parts.
X25 is set equal to (RRNA + WTU - RLU) - CALCI, and X35M is
set equal to (RRNA + WTU - RSMU) - CALCII. These substi-
tutions with simplification result in lines 5 - 10.

The supply equations are exactly as they appear in
previous chapters.

Upon simplification, an equilibrium solution for RRNA
can be determined. The supply equation can be simplified

to:

(C1 * RRNA + C2) * (3.85 + RRNA) ** -.0375442

- 2311.92 * RRNA + PS

Demand can be simplified to:

DN = PTDA + (-.00146863 * RDEPMR + .009568134

* W5X3R/RC + .00269436 * W5X3R) * RRNA.

‘With supply equal to demand, the following implicit function

results:

173

F = (C1 * RRNA + C2) * (3.85 + RRNA) ** - .0375442
+ C3 * RRNA + C4; Where (1)
C1 = - .00977768 * NMlS * PQl;
C2 = PQ1 * PQ2;
C3 = - 2311.92 - .099568134 * W5X3R/RC - .00269436
* W5X3R + .00146863 * RDEPMR;

C4 = ps - PDTA;

PQl (lines 13 and 14) * (3.85 + RRNA) ** .0375442;

PQ2 (line 15) + .00977768 * RRNA * NMlS;
PS = (line 12) + 2311.92 * RRNA;
PTDA = (lines 1 - 11) - (.00146863 * RDEPMR
+ .009568134 * W5X3R/RC + .00269436 * W5X3R)

* RRNA.

Since equation 1 cannot be solved for RRNA by hand, a
numerical approximation is necessary. An easy scheme for
finding roots is the Newton-Raphson method (Flanders, 1970,
pp. 207-215). To compute equilibrium RRNA, the equation
of the tangent line from some initial guess of RRNA -—RRNA0--
must be written. The initial guess used here is RRNAO =
- (C4 + C2)/(Cl + C3) —-the solution for RRNA that would
result if the exponent of RRNA, -.0375442, is set at zero.
The equation of the tangent line is: F'(RRNAO) = F(RRNA) -

F(RRNA0)/RRNA - RRNA The root of the tangent line is

0.
(RRNA

1, 0), where

RRNAl = RRNAO - (F(RRNAO)/F'(RRNAO)).

174

Using RRNAl as an initial guess, the procedure is then

1 - RRNAi is less than .000001, the

process stops and RRNA1+1 is used as the equilibrium value

repeated. Once RRNAi+

of RRNA.

Given values for the exogenous variables in any selec—
ted year, the equilibrium rate of return (RRNAE) for that
year can be determined. The results for the years 1964 to
1976 are shown in Table 5-1.

With the equilibrium RRNA solved the equilibrium
levels of NDH, NDB, NS0, and NSR can be found simply by put-
ting the equilibrium RRNA into the appropriate equation.

At the same time, for any given year the equilibrium
quantity of total municipal bonds outstanding can be deter-
mined. The equilibrium quantities for the years 1964 to
1976 are also shown in Table 5-1. The predicted or equi-
librium rates of return are always less than a percent away
from the actual rate and are sometimes less than a tenth of
a percent. When considering that RRNA depends on inflation-
ary expectations which vary widely between individuals and
create considerable uncertainty concerning what the real
rate should be, the closeness of the predicted values to the
actual values lends strong support to the validity of the

model.

The Multipliers

 

To find the changes in the equilibrium value of RRNA

(denoted RRNAE) with respect to a unit change in an

175

 

 

 

 

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176

exogenous variable requires the application of the implicit-
function rule to equation 1. More specifically: BRRNAE/
Bexogenous variable = — aF/aexogenous variable/BF/BRRNAE.
The mathematical solutions to these multipliers are shown

in Chart 3, where the BF/BRRNAE is denoted by DERIV. The
corresponding solutions for the years 1964 to 1976 are
shown in Table 5-2.

A change in the equilibrium quantity of tax-exempt
bonds with respect to a unit change in an exogenous variable
can also be easily determined with the use of previously
formulated aprtial derivatives. The multiplier can be
calculated with the use of the equilibrium demand function
(ND*) or the equilibrium supply function (NS*) since they
are equal in equilibrium. For instance, if an exogenous

variable (denoted ev) appears only on the demand side, so

that ND* ND(RRNAE(ev), ev) and NS* = NS(RRNAE(ev)), then

3ND*/3ev BDN/aRRNAE * aRRNAE/aev + END/aev, and 3NS*/3ev

= BNS/aRRNAE * BRRNAE/aev.

Applying the above methodology, the quantity multipliers are
shown in Chart 4. In Table 5-3 the arithmetically computed

values of the quantity multipliers are shown again for the

years 1964-1976.
Examination of the Multipliers

A brief examination of the multipliers shown in Tables

5-2 and 5-3 demonstrates how the model can be used to

 

177

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189

SYMBOL GLOSSARY TO MULTIPLIERS

Rate of Return Multipliers

DRDEX: expected inflation rate

DRDRC: rate of return on corporate bonds

DRDTRD: income to wealth ratio

DRDRST: after-tax rate of return on short-term Federal
securities

DRDW: wealth

DRDRL: after-tax rate of return on bank loans

DRDRSM: after-tax rate of return on medium-term Federal
securities

DRDYB: bank income

DRDDD: second difference of the unemployment rate

DRDDE: bank deposits

DRDDB: other demand

DRDUS: user fees

DRDDUS: change in user fees

DRDMl: one minus the matching rate on Federal grants
DRDLI: state and local income
DRDOS: age-distribution population factor

DRDDUM: density dummy

DRDXI: local spending to local income ratio

Equilibrium Supply Multipliers

 

DNEDEX: expected inflation rate
DNEDRC: rate of return on corporate bonds

DNEDTRP: income to wealth ratio

DNEDRT:

DNEDW:
DNEDRL:

DNEDRSM:

DNEDYB:
DNEDDD:
DNEDDE:
DNEDD3:
DNDRU:
DNDDU:
DNDMl:
DNDLI:
DNDOS:
DNDUM:
DNDXI:

DNSDR:

DNDDR:

190

after-tax rate of return on short-term Federal
securities

wealth
after-tax rate of return on bank loans

after-tax rate of return on mediumrterm Federal
securities

bank income

second difference of the unemployment rate
bank deposits

other demand

user fees

change in user fees

one minus the matching rate on Federal grants
state and local income

age-distribution population factor

density dummy

local spending to local income ratio

Supply and Demand Multipliers

 

change in supply with respect to a change in the
rate of return on tax-exempts

change in demand with respect to a change in the
rate of return on tax-exempts

191

observe occurrences in the municipal bond market in reaction
to changes in its environment.

The external forces which most influence the demand
side of the tax-exempt market probably come from the markets
of substitute assets. The non—bank private sector, recall,
perceives corporate bonds and long-term government
securities as such substitutes. When the rates on these
assets change, there are appropriate reactions which occur
in the tax-exempt market. The tables show that a 1%
increase in RC will bring an increase in RRNAE between .06%
and .14% and a decrease in equilibrium supply (NS*) between
$400 and $800 million. Similarly, an increase in RST of 1%
causes an increase in RRNAE between .21 and .31% and about
a $1700 million decrease in NS*. In the banking sector, a
similar result occurs when the rate on bank loans (RLU)
rises --a 1% increase causes an increase in RRNAE between
.12% and .18% and about a $1000 million decrease in NS*.

A dissimilar result occurs in the bank sector when the
rate on medium length treasury securities (RMS) rises.
Thinking back to the banking model and the variable X35M,
we found that a rise in RSM may indicate to loan officers
that they should move into tax-exempts since commercial
loan demand may soon be drying up. Hence we find a 1% rise
in RSM causes a drop in RRNA of about .20% and typically a
$1200 million increase in NS*. The interaction between

sectors is clearly in evidence here. The rates on long and

192

mid-term Treasury securities generally move in tandem.
Thus as the Treasury security rates change, demand picks up
in one sector and demand diminishes in the other sector.

RC and RLU tend to move in tandem also. Hence two
leftward shifts in demand will occur if both of these
variables rise. The magnitude of these shifts is given by
the multipliers. The shift caused by the RLU increase
represents a loss of bank demand only. The movement back
along the demand curve to equilibrium will come primarily
from household demand as RRNA rises relative to the origi-
nal RC increase. Thus some of the household demand lost
through the rise in RC is reclaimed because of forces occur-
ring in the banking sector.

Of course, these effects are only short run, as this
is a partial equilibrium model. A change in RRNA will also
be felt in the other asset markets, causing further changes
in other asset rates and again influencing the municipal
bond market. The final settling point depends on the
structure of all the asset markets. Specifically determin-
ing such a structure, although the general structure is
discussed in the demand chapter of this thesis, is beyond
the scope of this study.

Two other demand-side variables are also interesting
to look at. A .01 rise in TRSD5 (the ratio of income to
wealth) lowers RRNAE about .05% and raises NS* by $30 to

$36 million. An increase in bank income of $1 million

193

lowers RRNA about .00024%, but note the effect on NS*. Its
increase rises monotonically through the years from 1.06
million to 2.11 million. This trend is probably partly a
reflection of increasingly aggressive investment policy by
banks in recent years. The trend shows a reversal in 1975,
suggesting a return to less aggressive policy.

Finally, on the demand side, the wealth constraint and
the bank deposit constraint multipliers support the earlier
hypothesis that over time a larger and larger fraction of
wealth will be placed in tax-exempts as more and more inves-
tors are pushed into higher tax brackets. 3ND*/8W5X3R
rises from .023 in 1964 to .049 in 1975. This fraction is
its highest in those years with the greatest inflation rate.

On the supply-side several multipliers also show
interesting results. An increase in user fees of $1 million
is seen to generally decrease revenue bond supply by about
$.2 million; i.e. more current income reduces debt needs.

A $1 million increase in the change in user fees (DRUSR)
evokes a large increase in NS* --about $.85 million in the
early years and about $.50 million in the later years.

This result strongly suggests that officials are quick to
borrow and spend in the present if they see indications of
future income rising. This outcome is of course consistent
with the original hypothesis that officials tend to favor

current over future state and local good consumption.

194

A drop in the matching rate on Federal grants of .01
raises M1 by .01, decreases RRNA about .06%, and generally
lowers NS* by about $200 million. The trend in recent
years has been for the matching rate to rise --i.e. fiscal
federalism policies. ‘The multipliers indicate that the
overall effect of these policies is to raise state and
local debt. The lower price of state and local goods
induces additional expenditures requiring debt needs in
excess of the additional funds supplied by Federal grants.

The dummy variable (EDUM 12) indicating diminishing
municipal density and the purchase of capital services via
leasing, as expected has had a strong impact on the tax-
exempt market. The reduction in density from the 1960's
to the 1970's has lowered RRNAE by at least .06% and NS*
by about $150 million.

The other demographic variable, OSPOPF, also affects
the market, but not as importantly. A .01 increase in
OSPOPF raises NS* by about $17 or $18 million.

Changes in state-and local income to some degree
reflect demographics also. More income is often the result
of more people. Subsuming this population effect on income,
the multipliers indicate that a .01 increase in state and
local income raises RRNAE by about .001 and NS* by about
$3 million.

The expenditure to permanent income ratio (AEXLI) has

a strong influence on H (the fraction of non-Federally

195

funded capital financed with debt). An increase of .001 in
this ratio raises RRNAE generally between .018 and .029%,
and NS* about $70 to $90 million.

The only exogenous variable which appears in both
supply and demand is the expected rate of inflation --EXPA.
Chart 1 indicates a rightward shift in demand and leftward
shift in supply consequent to a rise in EXPA. Both of
these events tend to reduce RRNAE. In fact, the multiplier
suggests that a decrease of about .50% generally results
from a 1% increase in EXPA.

Although supply and demand shift in opposite direc-
tions, it is observed that in the time span shown, the
shift in supply always exceeds the shift in demand.
Throughout the period, a rise in EXPA has caused a fall in
NS*. This result is consistent with the discussion of
inflation within the section "Institutional Constraints" in
Chapter 4.

This brief examination of the supply—demand determined
multipliers thus demonstrates how all of the equations fit
together as a neoclassical model of the municipal bond
market.

In conclusion, the above review of the model's implica-
tions shows that a behavioral approach to the analysis of
tax-exempt bonds allows for more inferences and economic
insights than the simpler ad 223 or empirically convenient

approaches employed previously.

CHAPTER VI

CONCLUSION

In the final chapter, conclusions drawn from each
section will be summarized, and extensions of the model
beyond previous works will be reviewed. The model will then
be utilized to help weigh the political and economic ramifi—
cations resulting from legal changes or policy changes
associated with state and local government debt. This dis-
cussion is followed by a general appraisal of the complete
model.

It was found that the proposed bank-demand model, based
on bank officers' expectations of future economic conditions
and rates of return, tested statistically strong. Of
further importance, the model offers more economic content
than prior models. It is a dynamic behavioral model
involving variables easy to measure and easy for the
economic actors (the bank officers) to respond to. It is
also easy to modify to institutional changes in its environ-
ment while retaining its essential theoretical composition.

One such major institutional change occurred with the
1970 amendments to the Bank Holding Company Act which made
it easier for banking organizations to enter the equipment
leasing business by making leasing a permissible activity
of nonbanking affiliates of bank holding companies. Since

196

197

1970, the leasing activities of large banks has risen

dramatically. (Comptroller of the Currency, Annual Reports).

 

This change in the banking environment can be accounted for
by inserting the rate of return on leasing operations
relative to other substitutes in the bank demand equation.
As discussed earlier, a dummy variable was not an appro-
priate modification to allow for leasing operations. The
above modification, however, is superior, as it provides a
variable which the economic actors can respond to. This
alteration has not been made in the current model, but an
updated model should incorproate these changes.

The institutional environment has also been altered in
recent years by the tax treatment of thrift institutions
(saving and loan associations and mutual savings banks), in
particular the 1962 Revenue Act and the Tax Reform Act of
1969 which revoked a large percentage of one of the thrifts
major tax shelters. These tax changes in conjunction with
other market conditions, such as the leasing activities of
bank holding companies, have made the rate of return on
tax—exempts competitive with the rates on other assets held
by thrifts. Thrifts of course behave very similarly to
banks and a model incorporating thrifts could be a necessary
emendation in the future.

Similarly, institutional changes may occur elsewhere
which bring the need to more closely model other groups,

such as insurance companies. These modifications can be

198

made simply and with only a minor restyling of the original
rate of return --profit approach model. In short, this
model presents a general organizational approach to analyze
financial intermediaries which requires only minor modifica-
tions to environmental conditions.

The non-bank demand empirical specification permitted
measurement of the effects of inflation on the fraction of
net assets held in tax-exempts. It was shown that with the
recent inflationary experience, the progressive tax struc-
ture has induced a systematic rise in the fraction of
wealth held in tax-exempts. This empirical conclusion
verifies the theoretical contention put forth in the
theoretical model that the progressive tax structure lowers
the after tax rates of return on assets and brings about
substitution into tax-exempt assets.

Presently, there is a movement to place a price index
on the income tax. If successful, inflation would no
longer raise tax-exempt demand. The nominal income variable
in the empirical specification would have to be replaced by
real income. In this event it is expected, analogously to
inflationary effects, that the progressive tax system with
real income growth would systematically raise tax-exempt
demand.

Either with or without indexation a systematic rise in
tax-exempt demand accompanies the progressive tax system, as

more individuals move into higher tax rate classifications.

199

This trend strengthens a political block which opposes
elimination of the tax-exemption. As more middle income
individuals enter the tax-exempt market, they will favor
any tax advantage they can get, with very little interest
in the inefficient and inequitable aspects of the exemption

which some smart-ass economist might point to.

‘V‘”

In the 1980's other revisions in the Federal tax
structure have been advocated. Some of these proposals, if
enacted, would have a dramatic impact on the tax-exempt bond
market. One such proposal is the replacement of the pro-
gressive tax system with a proportional income tax rate.

Adoption of a proportional income tax rate would
require a relatively minor reformulation of the model devel-
oped here. Specifically, in the non-bank private demand
sector the tax rate applied to taxable bonds would become
the proportional tax rate rather than the tax rate of the
"marginal investor."

In the empirical specification, the variable TYBIL
would no longer be relevant. There would no longer be a
group of investors with a special need for sheltering; all
tax-payers would have equal sheltering needs. If the rate
of return on tax-exempts is greater than one minus the pro-
portional tax rate times the rate of return on equal quality
taxable bonds, then all investors would find it in their
interest to shift their assets into tax-exempts. Conversely,

if the rate on tax-exempts is less than one minus the

200

pr0portional tax rate times the rate on taxable bonds, then
all investors would gain by moving their assets into

taxable bonds. With the progressive system, only marginal
groups of investors find it beneficial to shift between
taxables and tax-exempts. Given a proportional tax rate, a
more appropriate specification for non-bank private demand
would replace TYBIL with the ratio of the rate of return on
tax-exempts to the rate of return on equal quality corporate
bonds.

The key implication of this revision is that the
effect of the progressive tax system on the fraction of
wealth held in tax-exempts as wealth rises is eliminated.
As the level of wealth rises over time, there will no
longer be a systematic increase in the fraction of this
wealth held in tax-exempts. As far as municipalities are
concerned this loss of potential future demand would, other
things being equal, increase future borrowing costs.

Another alternative to the progressive tax system has
also been advanced recently. This is the consumption tax.
The adoption of a consumption tax in place of an income tax
would render the tax-exemption on municipal bonds meaning-
less. All bonds would be tax-exempt. Municipalities would
have to borrow at the same higher rates as corporations,
the Federal government, or any other borrower.

The effects of such a change on this model are signifi-

cant, but not severely ruinous. On the supply side of the

201

model, the only effect is a higher price of capital
services. On the demand side, most of the demand-determin-
ing variables are still relevant. The main revision would
be to delete the tax rates from the rates of return on
assets. The minor revision would be to change the title
from a "tax-exempt bond model" to a "municipal bond model." i

In keeping with the demand model, the supply model was
developed in the neoclassical tradition, where the welfare
of the individual is revered. The general obligation model fl
places the welfare of the median voter at its foundation.
The median voter voluntarily pays for a flow of state and
local capital services which maximizes his/her welfare.
Paying for these services may involve debt, but interest
and amortization of the debt are covered each period so
that on a current account no deficit is run. Businesses
operate this way and many government units by legal decree
must operate this way. This may appear to be deficit spend-
ing when observing a balance sheet statement of total
expenditures and revenues, where expenditures less revenues
equals the deficit. But the model of this study reveals
the error in this logic and sterility of prior models which
used the balance-sheet method to determine tax-exempt bond
supply.

Recall Ott and Ott (1975) acknowledged the need to
place capital costs on a current account, but deferred

doing so because the price of capital services which the

202

median voter is willing to pay might not be equal to debt
retirement plus interest. They consequently opted to use
the ad hog balance-sheet approach to tax-exempt bond deter-
mination. The model herein rejected this methodology. The
price of the capital services for local capital was defined
and became integral to the theoretically derived desired
capital stock and amount of state and local debt. The
empirical work strongly supported this theoretical approach
despite possible disparities in the actual and expected
price of capital services from period to period.

It is this price of local capital services which in-
voked Peckman's statement, "It (the tax-exemption) reduces
investment in productive enterprises by diverting risk or
venture capital from the private sector. It distorts the
allocation of resources within the private sector, and
between the public and public and private sectors when
state and local governments issue tax-exempt securities to
finance such 'business' enterprises." (Peckman, 1966,

p. 93). In other words the exemption allows the rate on
tax-exempts --a component of the price of local capital
services-- to be less than the rates for other borrowers.
With a lower price of capital services on the flow of state
and local goods, citizens will choose more state and local
goods than is socially optimal.

The above argument was used for some time to advocate

the elimination of the exemption. Finally: "The 1969

203

conflict again proved that the state and local governments
have enough power to protect the exemption and that the
change can now come only through a compromise." (Huefner,
1972, p. 7). From this time forward, the Peckman argument
was no longer a primary issue in the debate. The double
payment inefficiencies and inequities as articulated by
Fortune became a greater issue. Once the ultimate need to
compromise was recognized, then it was also recognized that
elimination of the exemption would mean some other kind of
subsidy must be forthcoming to induce municipalities to
relinquish their tax-exempt financial instrument. These
other subsidies of course distort resource allocations in
much the same way as the tax-exemption. Thus the resource
allocation argument is lost in the compromise debate; it has
been replaced by the double payment argument.

The model of this study could be useful in estimating
the allocative effects of grants. Prior models were
unequipped to do this. They could only measure reductions
in the double payments. Recall the model estimated desired
capital needs where the price of capital services included
the rate of return on tax-exempt bonds. These capital
desires were also related to the matching grant rate. Any
number of experiments could be run using various trade-offs
between the grant rate and price of capital services. The
resulting desired capital stock could then be compared to

what Peckman might consider a socially optimal level of

204

state and local capital. At the same time, any trade-off
of the tax-exemption for a subsidy must be acceptable to
both Federal and local governments. If not politically
feasible, any economic justification for a specific action
would remain barren.

Returning again to the revenue bond model, it should
be mentioned that this was a difficult pioneer effort. The
model did succeed in three important ways. First, it
introduced a new decision-maker (the politician) and allowed
the voter model to operate on its own without contamination
from a separate decision-making body. Second, an empirical
model was finally achieved with the desired properties:
the budget constraint was highly flexible, allowing for
biased political estimates of future user fees; and the
equation showed some relation to the general obligation
model in that as borrowing rates rose and voters rejected
further general obligation bond issues, revenue bond issues
picked up the desired borrowing needs of officials. And
third, the estimated equation was statistically significant.

The model in its entirety also has useful prognostic
capabilities. For instance, the impact of reducing Federal
grants while simultaneously reducing marginal tax rates can
be estimated. The earlier multiplier analysis reveals that
decreasing Federal grants decreases tax-exempt bond supply.
Lowering the tax rates raises the after-tax rate of return

of substitute assets, thus demand also decreases. The

205

magnitude of these shifts can be determined through close
investigation of the appropriate multipliers. Qualitatively,
it is clear that the level of tax-exempt bond supply will
fall, while the change in the tax-exempt rate of return is
indeterminant.

In closing, it is appropriate to relate this study's
model to the current "problems” facing state and local
governments. Concern has been expressed in recent years by
many individuals that state and local governments are often
having difficulty marketing their debt. Furthermore, there
is a constant fear that demand for tax-exempts may be insuf-
ficient to keep the interest rate on tax-exempts low enough
for state and local governments to issue debt at levels
they feel are necessary. In short state and local govern—
ment administrators need to know how much the supply of
state and local debt will shift in the future, and they
need to know how much demand will shift in the future.

This knowledge should give them some indication of future
borrowing costs. With estimates of the future values for
the independent variables, this study's model can be used
to estimate future supply and demand curves. With this
accomplished, future tax-exempt rates of return can be
estimated.

This model thus offers no solution to state and local
governments, but given the institutional environment and the

competitive nature of financial markets and political

206

battles, it can provide a reliable estimate of future con-
ditions. It is a neoclassical model which accepts the
market as it is and is flexible enough to change when
environmental parameters change. It is also an optimistic
model. It indicates that if the present turn against state
and local expenditures is creating consternation among
local government officials, this is not too serious because
it merely indicates the individual voter is expressing the
current desire to spend elsewhere. If tax-exempt rates are
presently high or revenue bonds can't be marketed, then
this should be taken as an indicator that resources should
be used outside the local government sector, or that capital
funds are scarce everywhere and bids must be determined
where resources are needed most. In the final judgment,
this model in the neoclassical tradition emphasizes the
desires of individuals, not groups, such as local govern-
ments. Thus any rise or fall in the strength of the tax-
exempt bond market reflects individual desires and choices
either in a thriving economy with fewer constraints or a

faltering economy with greater constraints.

APPENDIX

APPENDIX

Data Sources

The various sectoral demands for tax-exempts can be

found in the Flow of Funds Accounts, Federal Reserve Board

 

of Governors.

Taxable income by income tax rate bracket is in
Statistics of Income: Individual Income Tax Returns,
Internal Revenue Service.

The rates of return are in the Survey of Current

 

Business, Department of Commerce; the Federal Reserve

 

Bulletin, Board of Governors; and An Analytical Record of
Yields and Yield Spreads, Solomon Brothers.
Saving, National Product, and stockholder's equity are

in the Economic Report of the President, Council of Economic

 

Advisors.

Bank deposit, bank reserves, currency Federal debt,
reserve requirements, regulation Q, bank lending rates,
the earning to price ratio on equity, the discount rate,

and unemployment rate are all found in the Federal Reserve

 

Bulletin, Board of Governors.
Bank income is in Federal Deposit Insurance Corporation

Bulletin.

207

208

Density measures come from the Statistical Abstract of

 

the U.S.
Population and local income measures are found in the

Economic Report of the President, the Council of Economic

 

Advisors.
All other supply-side data is taken from Governmental

Finances: Vol. 3, No. 5, Compendium of Government Finance,

 

and Vol. 6, No. 4, Historical Statistics on Governmental

Finances and Employment, U.S. Department of Commerce, Bureau

 

of the Census.

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