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Vol. 26, No. 4
ECONOMIC REVIEW
1990 Quarter 4
Bank Capital Requirements
and Leverage: A Review
of the Literature
2
by William P. Osterberg
Expectations and the Core
Rate of Inflation
13
by Richard H. Jefferis, Jr.
The Case of the Missing Interest
Deductions: Will Tax Reform
Increase U.S. Saving Rates?
by David Altig
FEDERAL RESERVE BANK
OF CLEVELAND
22
1990 Quarter IV
Vol. 26, No. 4
Bank Capital
Requirements and
Leverage: A Review
of the Literature
2
by William P. Osterberg
Requiring banks to increase their capital-asset ratios continues to
be viewed as a policy that would improve the safety of the com
mercial banking system. However, relatively little is known about
how banks adjust to increased capital requirements. This paper
reviews the existing literature on the subject and addresses a key
complication: the need to disentangle the influences of market and
regulatory forces on banks' capital decisions. In order to illustrate
the interaction between these forces, the author also presents a
model of a bank’s choice of optimal leverage.
Expectations and the
Core Rate of Inflation
13
by Richard H. Jefferis, Jr.
Inflation rates associated with different price series are both volatile
and weakly correlated, properties that make realized inflation an un
attractive guide for monetary policy. In contrast, the expected infla
tion series generated by a wide variety of econometric models are
less volatile than actual inflation and are highly correlated. This cor
relation suggests that the different series are tracking a common
trend, or core rate, and makes expected inflation a suitable bench
mark for monetary policy directed toward controlling inflation.
The Case of the
Missing Interest
Deductions: Will Tax
Reform Increase
U.S. Saving Rates?
22
by David Altig
As of the coming tax year, U.S. taxpayers may no longer deduct per
sonal interest expense when calculating taxable income. Will this
change, resulting from the Tax Reform Act of 1986, increase the
saving rate in the nation? This paper suggests that the answer is
yes: An examination of private saving rates among several OECD
countries shows that saving rates are, on average, higher in coun
tries that have not historically subsidized borrowing through interest
deductibility. The author also finds that the divergence of U.S. and
Canadian saving rates over the past several decades appears to be
significantly related to differential tax treatment of interest expense.
Economic Review is published
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ment of the Federal Reserve Bank
of Cleveland. Copies of the Review
are available through our Public
Affairs and Bank Relations Depart
ment, 216/579-2157.
Coordinating Economist:
Randall W. Eberts
Editors: Tess Ferg
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Design: Michael Galka
Typography: Liz Hanna
Opinions stated in Economic
Review are those of the authors
and not necessarily those of the
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Material may be reprinted
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ISSN 0013-0281
Bank Capital Requirements
and Leverage: A Review
of the Literature
by W illia m P. Osterberg
William P. Osterberg is an economist at
the Federal Reserve Bank of Cleveland.
The author would like to thank Randall
Eberts, James Thomson, and Haluk Unal
for helpful comments and suggestions,
and Kyle Fleming for valuable research
assistance.
Introduction
Recognition of the extensive losses inflicted on
the Federal Savings and Loan Insurance Corpo
ration (and thus indirectly on the taxpayers) by
the thrift industry crisis has led to increased scru
tiny of the safety and soundness of commercial
banks and other financial institutions. It has
become obvious that some of the factors respon
sible for excessive risk-taking by savings and
loans may also be relevant to commercial banks.
In particular, the current system of fixed-rate
deposit insurance and supervision and regula
tion interacts in complex ways with the market
forces that may ordinarily discipline banks. An
understanding of these interactions is crucial to
financial institution reform.
This article reviews the literature relevant to
assessing one proposed regulatory reform —
increased capital requirements for banks. The
arguments for higher capital requirements rely
primarily on the premise that they will strengthen
market discipline, and secondarily on the desire to
provide a greater cushion for the deposit insurance
agency. In theory, increased capital requirements
can at least partially compensate for the weaken
ing of market discipline that may result from the
continued presence of fixed-rate deposit insur
ance. However, the magnitude of the impact of
past changes in capital requirements on banks’
capital decisions is unclear, mainly because mar
ket forces also affect such decisions.
Any analysis of the impact of capital require
ments must take into account the current system
of fixed-rate deposit insurance. The presence of
non-risk-related insurance premiums and govern
ment guarantees influences the capital decision
by blunting the effect that increased capital-asset
ratios would otherwise have on banks’ cost of
funds. The current system complicates identifying
the impact of changes in required capital-asset
ratios, because the subsidy itself may be influ
enced by the ratios and other factors.
Fixed-rate insurance is also widely viewed
as subsidizing risk-taking, thus providing a ra
tionale for capital regulation. In the absence of
government guarantees, shareholders would
need higher levels of capital as a buffer against
losses in order to avoid risk-related increases in
their cost of funds. These guarantees thus lead
to a substitution of deposits for equity, thereby
lowering capital ratios.
Although this distortion has led to reform pro
posals that emphasize reductions in the scope of
government guarantees, proposals to increase
capital requirements continue to emerge despite
the introduction of risk-based requirements. This
has occurred in part because changes in capital
requirements are seen as relatively easy to imple
ment. In addition, as noted above, capital
3
requirements may induce shareholders to evaluate
risk more carefully and to submit to the market’s
evaluation when they attempt to raise capital.
O n the surface, capital requirements seem to
be effective, because almost all banks increase
their capital-asset ratios (book value) after the
requirements are increased. However, other fac
tors may influence the ratios, especially if they
are calculated in terms of book value. For exam
ple, suppose that the regulatory standards were
increased in response to a general market per
ception that capital is inadequate. In this case,
the subsequent adjustment may be partly due to
banks’ desire to avoid an increase in the risk
premium in their cost of funds. Clearly, in order
to disentangle such influences, investigators
must have a model of the factors that determine
bank capital-asset ratios.
The remainder of this paper is organized as
follows. Section I reviews the theoretical litera
ture on the determination of banks’ capital struc
ture. Section II covers a closely related topic, the
impact of capital requirements on portfolio risk.
Section III presents a model of a bank’s choice of
capital structure. Section IV analyzes the model’s
implications for the impact of market and regula
tory forces on bank leverage.1Section V reviews
the empirical findings on the effects of capital
requirements, contrasting various results in terms
of the implications presented in section IV. Sec
tion VI presents suggestions for future research
and concludes.
I. Optimal Capital
Structure Theory for
Financial Institutions
I first discuss the theoretical findings relevant to
nonfinancial corporations, since to some extent
these may extend to banks, and then review the
limited number of analyses of how and why the
capital structure decisions of banks may differ
from those of nonfinancial institutions.2 I then
focus on specific analyses of banks’ capital
■
1 Leverage is often defined as the ratio between debt and equity,
measured in book or market values. In the model presented here, the bank
chooses the level of promised payments to depositors, given an exoge
nous asset portfolio. This is equivalent to choosing the debt-to-equity
ratio directly. In Osterberg and Thomson's (1990) empirical study, the
measure of leverage is the ratio between the book value of debt and the
total of the book value of debt and the market value of equity. This is close
to another often-analyzed measure of leverage, the debt-to-asset ratio.
structure, most of which assign a prominent
role to deposit insurance.
The literature analyzing the capital structure
decisions of nonfinancial corporations is so
broad as to defy easy description.3 However,
one of the strongest conclusions to emerge from
the empirical studies is that optimal capital struc
ture is influenced by the tax code, possibly in
combination with leverage-related costs. For
example, the ability of corporations to deduct
interest on debt may encourage an increase in
leverage. O n the other hand, higher levels of non
debt tax shields, such as depreciation and tax
credits, may reduce optimal leverage by increas
ing the probability that not all interest expenses
will be deductible. Taxes on personal equity and
interest income may also decrease the net tax
advantage of debt and optimal leverage.
Leverage-related costs include the expected
costs of bankruptcy, and agency costs associated
with conflicts among creditors, stockholders, and
managers. The direct costs of bankruptcy are mini
mal (mainly involving administrative and legal
fees), but agency costs, which include any decrease
in firm value associated with contractual arrange
ments to protect one party from actions taken by
another party with conflicting interests, can be sig
nificant. Bond covenants that restrict cash-flow
usage may impose agency costs. However, such
covenants may be a part of optimal contracts recon
ciling bondholders with stockholders.
The theory of optimal financial structures for
financial intermediaries differs somewhat from
the theory for nonfinancial firms. First, in analyz
ing capital structure for either financial or non
financial firms, it is convenient to assume that
operating and financing decisions can be
separated. This assumption is harder to defend
for financial intermediaries. The existence of
complete markets, which makes separation
■
2 In this section, we review the theoretical analyses relevant to un
derstanding the impact of changes in bank capital requirements. Because
few analyses of bank capital structure are available (relative to the number
that deal with the capital structure of nonfinancial institutions), it is not
useful to attempt to categorize various approaches. In addition, the dis
sim ilarities in approach prevent the development of a general model to
which all others specialize.
■ 3 Among several useful surveys is one by Harris and Raviv (1990),
who categorize the forces that may influence capital structure into desires
to 1) ameliorate conflicts of interest, 2) convey private information to
markets, 3) influence product or input markets, and 4) affect corporate
control contests. The authors exclude tax-driven theories that they admit
are of great empirical importance. Although few analyses of the capital
structure of banks consider these four forces, several take into account
taxes and other considerations discussed here.
more likely, makes it difficult to explain the exis
tence of intermediaries: If markets were com
plete, lenders and borrowers could transact
without them. In addition, deposits seem to play
a role in both the real and financial decisions of
banks, because deposits are not only an input
into banks’ production, but a component of debt
in their capital structure. Another reason that
analyses of banks’ capital structure differ is that
regulatory forces aimed directly at capital struc
ture (for example, capital-asset ratios) must be
considered.
Although most studies of the impact of cap
ital requirements on banks do not view these
institutions as fundamentally different from non
financial entities, many others have examined
the role of informational asymmetries and con
tracts in explaining the existence of intermedi
aries. Early examples are Boyd and Prescott
(1986) and Diamond (1984). Sealey (1985) ana
lyzes a model of incomplete markets and inter
mediaries, showing the conditions under which
shareholder unanimity holds and under which
unanimity implies separation. Sealey (1983) ex
amines a model of incomplete markets in which
economies of scale in the provision of deposit
services influence bank leverage. Chen, Doher
ty, and Park (1988) utilize an option-pricing
framework to analyze the capital structure deci
sions of depository financial intermediaries in
the presence of deposit insurance, reserve
requirements, liquidity effects, and taxation.
They conclude that no clear separation exists
between operating and financial decisions, and
that this finding even applies to analyses of the
impact of taxation on leverage decisions.
As noted in Santomero (1984), most studies
of bank capital structure assume that real and
financial decisions can be separated, and try to
explain leverage choice conditional on a given
portfolio of assets. One example is Orgler and
Taggart (1983), who show how personal and cor
porate taxes, reserve requirements, and econ
omies of scale influence intermediaries’ optimal
leverage. Applications of the option-pricing
framework also assume that portfolio composi
tion is held constant. Pyle (1986) shows that the
use of book values in capital regulation is inap
propriate when combined with closure rules that
deviate from an economic solvency condition.
The conclusions of theoretical analyses of
the impact of capital requirements are closely
related to the treatment of deposit insurance and
government guarantees. If deposit insurance is
underpriced and unresponsive to risk, then stock
holders are being subsidized by the insurer, and
the size of the subsidy is a function of portfolio
risk and leverage. This subsidy has a direct im
pact on banks’ responses to changes in capital
requirements. Buser, Chen, and Kane (1981) ex
amine how the combination of capital regulation
and flat-rate deposit insurance jointly influences
bank leverage. They note that because capital
regulation encompasses more than just numerical
standards for capital-asset ratios, such regulation
can be seen as imposing an implicit risk-related
insurance premium that discourages banks from
exploiting the subsidy implied by flat-rate deposit
insurance.
II. The Impact
of Capital
Requirements
on Portfolio
Composition
Although most studies of bank capital structure
assume a given portfolio of assets, several
authors have examined the impact of capital re
quirements on portfolio risk, assuming that
leverage is at the regulatory maximum.4 An
overall assessment of the impact of capital re
quirements on bank capital structure would
have to allow for possible feedback from varia
tion in portfolio changes.
Koehn and Santomero (1980) conclude that
increased numerical capital requirements lead
banks that are risk-averse expected utility maxi
mizers to reshuffle their portfolios so as to in
crease the probability of bankruptcy. Lam and
Chen (1985) and Kim and Santomero (1988) use
similar approaches. Keeley and Furlong (1987),
who employ a value-maximization framework,
point out that Koehn and Santomero ignore the
impact of changes in leverage and portfolio risk
on the deposit insurance subsidy. Osterberg and
Thomson (1988) show how the impact of capi
tal requirements on portfolio shares is altered
by allowing the cost of funds to be influenced
by leverage.
■ 4
Flannery (1989) shows why insured banks may have a preference
for safe individual loans but still prefer risky overall portfolios. Capital ade
quacy standards and loan examination procedures are key elements of his
analysis. Lucas and McDonald (1987) study the impact of capital regula
tion on bank portfolio choice when banks have private information about
loan quality.
EQUATIONS
(1)
AN
A
A
= (X - - Y) (1 --tc) + cp
(l)
A
9+
1
H
1
= (1- A.)[(X
81-
if X > Y +
A
if Y + * < x ■
*c
A
A
= ( 1 - X) (X - Y)
if Y < X < Y +
= 0
if X < Y
A
5 - (p
A
A
= Y
if Y < X
= X (1 - k )
if 0 < X < Y
A
otherwise.
where
X = end-of-period value of bank assets,
Ys , Yb — gross end-of-period cash flows accruing to bank stockholders and depositors, respectively,
A
Y = total end-of-period promised payment to depositors,
cp = total end-of-period after-tax value of nondebt tax shields when fully utilized,
X = regulatory penalty,
8 = capital requirement,
k = cost of financial distress to depositors, and
d = proportion between 8 and Y (a capital requirement proxy).
III. A Model of
Market and
Regulatory Influence
on Bank Capital
Structure
To aid in this review, I present a model in which
market and regulatory influences on banks’ cap
ital structure are intertwined. The model also
provides a limited synthesis of the theoretical lit
erature. However, influences that could explain
the existence of intermediaries, such as the pres
ence of incomplete markets, are not incorporated.
The only factor included that distinguishes banks
is capital regulation. In addition, the model main
tains the separation of real and financial decisions
by holding constant the bank’s asset portfolio and
return variance. Although I initially assume that
there is no deposit insurance, such insurance is
easily introduced (see Osterberg and Thomson
[1990] and the following discussion).5
Equations (1) and (2) describe the uncertain
outcomes facing stockholders and depositors. I
view the bank as attempting to maximize the
total of the values of equity and deposits, each
of which depends on the uncertain outcomes
and their associated probabilities.
Pre-tax returns to stockholders depend on the
uncertain end-of-period value of bank assets, X.
The first line of equation (1) indicates the return
when income (asset values) is high enough that
the capital guideline is not violated. I assume in
this case that all nondebt tax shields can be util~
A
ized (X > Y+ (p/ic); however, the results are
not significantly affected by this assumption. In
the second case, when income is high enough
to use all the shields but the capital requirement
is not met {X[\- tc]+ cp - Y < 8 ), regulators
impose a tax of X on stockholder returns. In the
third case, income is positive but insufficient to
utilize nondebt tax shields, and the guidelines
are not met.
■
5 This model is a variant of the one developed by Bradley, Jarrell,
and Kim (1984), hereafter referred to as BJK. Detailed assumptions un
derlying the model are given in appendix 1.
Equation (2) indicates the end-of-period pre
tax flows to depositors. A crucial distinction
between stockholders and depositors is readily
apparent: Depositors only receive Y, even if
income greatly exceeds promised payments.
O n the other hand, if income is positive but in
sufficient to meet promised payments, the bank
is in financial distress and incurs real costs that
reduce the return to depositors by the fraction k.
The bank is assumed to know 1) the relevant
tax rates, 2) the amount of nondebt tax shields,
3) the required capital-asset ratio, d, 4) the regu
latory response, embodied in X, 5) the costs of
financial distress, 6) the average income, X, and
7) the standard deviation of income, (p. The bank
A
chooses Y to maximize the market value of its
debt plus equity (see appendix 1).
Equation (3) is the derivative of V with
respect to Y: V*(dV/dY).
(3)
1 - t.p b
A
A A
V£ = ----— [ l - F ( Y ) ~ k Y f ( Y ) ]
1 - tp s
A
r
CP A
[ - ( l - f c ) [ l - F ( y + Y)\
(P
[F(Y + j
A
)-/r(K)]-X{
,
A
Cp
[F(Y+ j )
<p
A Cp
d ( 8 - cp)
- f < r + 7 )]+ [8 + - 7 3 7 — )
A
8 - cp
,
where F ( ) is the cumulative probability density
function of X . If banks in fact choose Y so as to
satisfy equation (3), then this expression indi
cates how both market and regulatory forces
influence bank leverage.
If X = 0, the model’s implications are consis
tent with theories of optimal capital structure in
which the assumed tax advantage of debt bal
ances the expected cost of bankruptcy (see BJK).
These implications are as follows. First, an in
crease in f raises optimal leverage by increas
ing the cost of equity. Analogous reasoning
implies that an increase in tpb reduces optimal
leverage. Second, an increase in tc raises opti
mal leverage by increasing the tax advantage of
debt. For this reason, an increase in cp reduces op
timal leverage by increasing the probability that
not all interest expenses will be deductible. Third,
an increase in k reduces optimal leverage by
increasing the expected cost of a bank’s inability
to make all promised payments.
The model is also consistent with theoretical
approaches that assign deposit insurance a role
in distorting market discipline. The effect of fixedrate deposit insurance on optimal leverage can
be seen by comparing equation (3) with
under full insurance (see Osterberg and Thom
son [I99O]). Optimal leverage is higher with fixedrate deposit insurance by the amount (1 )
[F (Y) + kYf\Y)VrQ. Fixed-rate deposit insur
ance increases the optimal Y by insuring that
depositors are always paid in full and by shifting
the cost of financial distress from depositors to
the Federal Deposit Insurance Corporation. In
the context of the model presented above, these
two^influences are equivalent to assuming that
F ( Y ) = 0 and k = 0. Although this model does
not allow the higher leverage to influence bank
riskiness, the increase in leverage induced by
deposit insurance provides a rationale for capital
regulation.
The impact of capital regulation on leverage
can be seen by examining the last term in equa
tion (3), X (• ). The first two components of
X ( •) comprise the expected after-tax regulatory
penalty resulting from issuing the last dollar of
deposits. As equations (1) and (2) demonstrate,
the possibility of a regulatory penalty affects the
return to equity, which one would expect to be
reflected in the rate of return demanded by
stockholders and thus in the bank’s leverage
decision. In fact, the last component of X ( ■) is
the increase in the cost of equity capital that
results from issuing one more dollar of deposits,
[8 + ¿ ( 8 - c p ) / ( 1 - tc )] f [ K + ( 8 - c p ) / ( l - t c )]
Because all of the components are positive, the
possibility of a regulatory penalty reduces a
bank’s optimal leverage.
IV. The Impact of
Regulatory and
Market Forces on
Optimal Leverage
Although equation (3) clearly shows that both
market forces and regulatory variables influence
leverage with signs consistent with theory, it is
more important for our purposes to note that
this expression also implies that the impact of
an increase in X (the regulatory penalty) on
leverage depends on market forces entering
X ( •). Empirical studies of capital requirements
vary in their treatment of the influence of such
market forces ( cp, k, tc, tf)S, tph, and o, where
a is the standard deviation of X ) on Y.
To show how market influences affect the
impact of capital regulation on bank leverage,
one can differentiate the optimality condition
(equation 131) with respect to the regulatory vari
ables. The derivatives with respect to the marketforce variables are indicated in appendix 2.
Further details can be found in Osterberg and
Thomson (1990).
Equation (4) gives the impact of a change in
d on optimal leverage. The ratio d is closely
related to a required capital-asset ratio, because
it is the minim um level of the end-of-period
equity value and because 5 = Yd.
a
5-9
f ( Y + 1— “ )
{ 25 —cp —[ F5 +
(F+ —-
5(5-9)
1 - i.
— - X ) / o 2} ^ 0
The impact of d on leverage clearly depends
on market forces, implying that such forces in
fluence leverage even if a bank fails to meet the
guidelines. As discussed below, some studies
imply that such banks are influenced only by
regulation, while banks meeting the guidelines
are influenced only by market forces. No such
dichotomy emerges here.
Equation (4) implies that V$d is negative
whenever X > Y+ (5 - cp ) / ( l - tc); that is, an
increase in d reduces leverage when the bank
expects to meet the capital requirements. How
ever, if a bank does not expect to meet the re
quirements, an increase in d may induce it to
increase leverage and thus move even further
below the guidelines.
Equation (5) shows that an increase in the
regulatory penalty, A,, reduces bank leverage.
Here, as in the response of leverage to d, the
impact of capital regulation depends on market
factors. Equation (6) shows that an increase in
the costs of financial distress, k, also reduces
optimal leverage. Although k is referred to
above as a market factor, the cost of financial
distress can be influenced by regulatory policies
pertaining to bank closure.
(5)
Vfa =
1 - 1p s
-
A
Cp
F {Y + j)}
¿ /(5 -c p )
A
5 — cp
+ (8 +^ T ^ ) / ( V +-r r r )] < 0
1 - t.p b
(6)
Vpk = -
A
[y f{
A
y
)] < o
V. Evidence on the
Impact of Capital
Requirements on
Bank Leverage
Separating market forces from regulatory forces
has been a major difficulty in ascertaining the
effectiveness of capital guidelines. Dietrich and
James (1983) criticize earlier studies by Peltzman
(1970) and Mingo (1975) for ignoring depositrate ceilings in their analyses of the impact of
capital requirements. Under such ceilings, banks
can influence risk-adjusted returns on bank debt
by augmenting capital. However, only under
less-than-full deposit insurance would more
capital benefit stockholders, by inducing unin
sured depositors to accept lower interest rates.
Dietrich and James conclude that the guidelines
have no effect on bank capital changes.
Although the model presented here does not
directly consider the possibility of interest-rate ceil
ings, capital levels influence the returns to stock
holders and thus the rate of return required on
equity. The latter can be calculated as the ratio
between E ( Y ) , the expected returns to stock
holders, and S, the market value of equity (see
appendix 1 and BJK). Equation (1) indicates that
returns to stockholders are influenced by several
market forces that must be controlled for in any
analysis of the impact of capital requirements.
Marcus (1983), Wall and Peterson (1987), and
Keeley (1988a, 1988b) examine bank holding
companies rather than independent banks. Wall
and Peterson apply a switching regression tech
nique to movements of equity values in an attempt
to distinguish a regime in which capital ratios
exceed the requirements (and are thus influenced
by market forces) from a regime in which ratios
are at the regulatory limit. They conclude that
most banks are influenced by regulation.
The model presented here implies that 1)
banks may respond to market forces even if the
guidelines are not being met and 2) regulatory
forces may influence leverage even if the bank
exceeds the guidelines. In addition, equation (4)
indicates that banks below the guidelines may
actually respond to stiffer requirements perversely.
Keeley (1988a) examines the response of
bank holding companies to the increased capital
requirements of the 1980s. Although capitaldeficient banks increased their book-value ratios
more than capital-sufficient banks did, market
ratios increased for both classes. However, regu
latory subsidies or taxes can influence the
response of market-value ratios to increased capi
tal guidelines, because the value of the subsidy
may vary with leverage or risk. Keeley (1988b)
claims that increased competition erodes the
value of bank charters and thus raises incentives
to increase leverage or to reduce capital ratios.
Marcus (1983) utilizes a time series crosssectional approach, measuring regulatory pres
sure to increase capital by the holding company’s
capital ratio relative to the average (in terms of
book or market value). He finds that the incen
tive to decrease capital varies positively with the
level and variability of interest rates, as well as
with the tax disadvantage of equity finance.
Regulation seems to have no effect. However,
his regulatory measure does not incorporate risk.
In the model presented above, d is close to
a statutory capital-asset ratio. However, analyz
ing banks’ capital ratios relative to the average
may be a more useful way to isolate the impact
of capital regulation. There are at least two rea
sons for this. First, relatively few banks are
below the statutory guidelines. Second, evi
dence suggests that capital regulation is based
on a peer-group standard. In fact, a peer-group
capital standard may be a useful proxy for the
regulatory penalty variable, X.
The relevance of taxes to the capital struc
ture of banks is discussed in more detail by Wall
and Peterson (1988) and Gelfand and Hanweck
(1987). Wall and Peterson argue that taxes do
not influence the capital structure of banks affil
iated with holding companies, because the tax
consequences of the parent issuing debt to buy
subsidiary equity are similar to those ensuing
when the bank itself issues debt. Gelfand and
Hanweck examine the financial statements of
11,000 banks and find strong evidence for mar
ket influences (tax rates, risk, and municipal
securities [munis] as proxies for nondebt tax
shields) on leverage.
Osterberg and Thomson (1990) investigate
the influence of capital regulation on bank hold
ing company leverage empirically, drawing on
the implications of the model presented above.
The authors find that market forces influence
leverage through three channels: a direct chan
nel, a channel in which market forces interact
with risk ( a ), and a channel in which market
forces interact with capital regulation. In addi
tion, their analysis explicitly allows for the simul
taneous determination of leverage and muni
holdings. Although the latter may no longer be
an important channel through which banks
manage their tax liability, this may not have
been the case during the period examined
(1986-1987).6 The interactive capital regulation
measures, taken as a whole, are significant, as
are the interactive risk measures. In addition,
muni holdings appear to be significant deter
minants of leverage, as do market forces.
VI. Conclusions and
Suggestions for
Future Research
This article reviews the literature relevant to assess
ing the impact of increased bank capital require
ments. Although researchers have suggested
various proposals to correct the distorted incen
tives facing bankers, raising required capital ratios
continues to emerge as a possible means of
strengthening market discipline. However, pre
vious studies have failed to clarify the impact of
numerical guidelines on banks’ capital-asset ratios.
The primary difficulty in discerning the influ
ence of such guidelines lies in disentangling the
impacts of regulatory and market forces. In
order to illustrate the way in which these forces
interact, I present a model of a bank’s choice of
leverage ratio where, in the absence of capital
regulation, tax considerations and bankruptcy
costs imply an interior solution. W hen capital
regulation is introduced, it becomes clear that
the impact of such regulation depends on
market forces.
These results may provide useful insight for
regulators. For example, the response of bank
leverage to capital regulation may depend on
■
6 Scholes, Wilson, and Wolfson (1990) present evidence that
banks’ muni holdings responded to changes in the tax code between
1983 and 1987, and that capital regulation seemed to influence banks'
timing of capital loss realization. This seems to suggest that capital
regulation and the tax code interact in a manner sim ilar to that suggested
inthisoaner.
the market factors considered in this paper, such
as tax rates, nondebt tax shields, and muni hold
ings, not just on the capital position of the bank.
This implies that evaluations of banks’ leverage
and capital-asset ratios should take into account
market influences on the leverage decision.
The model may also explain previous empiri
cal findings regarding the impact of capital
requirements. Most studies do not control for
many of the market influences on banks’ capital
decisions. The analysis presented here thus
implies that theoretical examinations of bank
capital structure may further improve our under
standing of the influence of capital require
ments. In this regard, it may be particularly
useful to analyze capital requirements through
models that incorporate informational asymme
tries and market imperfections to explain the
existence of financial intermediaries.
Appendix 1
11.
The capital constraint, 5 , is not binding
unless X is such that the tax shields are being
fully utilized.
Assumption 10 allows us to separate the ef
fects of capital requirements from the effects of
deposit insurance. Thomson (1987) shows that
this is equivalent to assuming 100 percent deposit
insurance if the insurance is fairly priced. The
case in which all liabilities are covered by fixedrate, zero-premium deposit insurance is analyzed
in appendix A of Osterberg and Thomson (1990).
Assumption 11 is made for convenience only;
my results are not materially affected by the al
ternative assumption that 8 is binding for values
of X where (p > (X - Y) tc .
Under the assumption of risk neutrality, and
given the uncertain outcomes detailed in the
text, the after-tax market value of the banking
firm is the sum of the market values of deposits
and equity:
(ia )
v = j r [ ] i ( i - /„ ) [ ( £ - i b u - O
0
Detailed
Assumptions
and Structure
of the Model
m
t
+ <p]+ ( l - t pb) Y \ f ( X ) d X
izi
1 -/
The main assumptions of the model presented
in the text are as follows:
1. Investors are risk-neutral.
2. The personal tax rates on returns from
bank debt and bank equity are tph and tps,
respectively.
3. Bank income is taxed at the corporate
rate, tc .
4. All taxes are levied on end-of-period
wealth.
5. The firm’s end-of-period tax liability can
be reduced through nondebt tax shields, (p ,
such as investment tax credits and depreciation.
6. Unused tax credits cannot be transferred
across time or across firms.
7. If banks cannot meet their end-of-period
promised payments to depositors, Y, costs of
financial distress are incurred that reduce bank
equity value by a factor of k.
8. The end-of-period capital requirement is
8 = Yd.
9. If X - Y< (S - cp ) / l - tc), a regulatory
penalty reduces stockholders’ returns by a con
stant fraction X ( X is the end-of-period value of
assets).
10. All bank liabilities are uninsured
deposits.
-
J
£+s>
/
n o - o
+ q) ] f ( X ) d X
t
+
J
[(1 - $ » ) ( ! - X ) ( i - Y)
Y
+ ( 1 - f ^ ) Y if(X )d X
A
Y
+ \ ( l - t pb) { l - k ) x f ( x ) d x ] ,
0
where f ( X ) = the probability density of X ,
and rQ= one plus the rate of return on a risk
free tax-exempt bond.
The four integrals in equation (1A) are,
respectively, 1) the expected value of the bank
over the range of X where the bank fully utilizes
its nondebt tax shields, 2) the expected value of
the regulatory tax over the range of X where the
bank fully utilizes its nondebt tax shields but fails
to meet its capital guideline, 3) the expected
value of the bank over the range of X where
nondebt tax shields are no longer fully utilized,
and 4) the expected value of the bank when X
is not large enough to meet promised payments
to the depositors and k percent of the firm value
is lost to financial distress.
Appendix 2
The Impact of
Market Forces
on Optimal Bank
Leverage
The effect of an increase in nondebt tax shields,
q>, on optimal leverage is indicated by equation
(2A).
when X > Y + (8 - <p ) / ( l - tc ) arises be
cause the capital constraint is assumed to be
binding when the bank’s net tax bill is positive.
There are two offsetting effects. First, an in
crease in tc raises the value of the interest
deduction on debt, which induces the bank to
issue more deposits. This is the familiar effect
discussed in the finance literature on optimal
capital structure for nonfinancial entities. The
second effect is a reduction in the after-tax
value of equity and an associated increase in
the probability that the bank will violate the
capital constraint and reduce leverage.
(3A )
1 - t.
Vp,= — ^ { \ - F ( Y + j )
'o
(2A)
i/ a
Yip
l - ‘ps
=
lc
A 8 - cp
+ \[f ( y + j r y ) -
[(1+ X ) f ( y + S )
a
9
F(<Y + 7 > ]
, r a
8 9 ,
d
+ Xf(Y + - — r ) { 1 +
1 - tc
1 - tc
-[8 +
¿(5-q>)
r
d
X (S -
d ( 8 - cp )
erage increases if X > Y + ( 8 - cp )/( 1 - tc).
This possibility is created by the combination of
the capital requirement being based on the after
tax value of equity, which includes the value of
the shields, and the fact that the capital require
ment is binding when the tax shields are being
fully utilized. For high-enough values of X , an
additional dollar of tax shields reduces the prob
ability that the bank will violate the capital con
straint and incur the regulatory penalty.
The effects of changes in the various tax
rates on the optimal level of debt are shown in
equations (3A), (4A), and (5A). In equation
(3A), the response of bank leverage to an in
crease in the marginal corporate tax rate is posi
tive when X > Y + (8 - (p)/(l - tc ) . In other
words, if expected end-of-period income is
large enough to meet the capital requirements,
then an increase in tc reduces the optimal level
of debt. The ambiguous sign for equation (3A)
. 18 +
lc
If there were no regulatory penalty ( X = 0 ),
I would obtain the same results as BJK; that is, a
higher level of nondebt tax shields would
reduce leverage ( <
0). Here, however, lev
\
+ [<1 + i 3 T
1- h
1
<P)
1- L
8 - cp
_
U r+ j . , - * ) ]
a
5 — cp ,
■ A Y + T—
)} ^ 0
c
If there were no costs of financial distress
(k —0), equation (4A) would be unambiguously
negative at the optimal level of debt. In addition,
if all of the bank’s deposits were insured,
V<st would be clearly negative. However, more
ph
generally, equation (4A) is negative when the
probability that Y is less than X exceeds the
marginal expected leverage-related costs. This
result is similar to the findings of BJK. Note that
we have assumed that the costs of financial dis
tress facing the depositors (k ) are distinct from
the regulatory penalty. As in BJK, Vfa is unam
ps
biguously positive. However, here the response
depends on the regulatory penalty, X.
(4A)
Vfr = - — [1 - F ( Y ) - k Y f(Y ) ] < 0
pb
rn
(5A)
{ a -< c) t i - f ( 7 + ^ ) ]
= - 7
Ps
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(May 1983), pp. 212-21.
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Expectations and the
Core Rate of Inflation
by Richard H. Jefferis, Jr.
Richard H. Jefferis, Jr., is a profes
sor of finance in the School of
Business Administration at the
University of Colorado, Boulder,
and was formerly a visiting schol
ar at the Federal Reserve Bank of
Cleveland. The author would like
to thank Michael Bryan, William
Gavin, Jeffrey Hallman, and
James Hamilton for helpful dis
cussions and advice.
Introduction
Policymakers seeking to control inflation are
confronted by a bewildering array of price statis
tics that often provide conflicting signals about
the current inflation rate. The disparity among
different measures of inflation is illustrated by fig
ure 1, which depicts quarterly inflation rates im
plied by movements in several well-known price
series between 1954 and 1987, and by table 1,
which displays the correlation among inflation
rates associated with a broader group of indices
over the same period.1 Although the CPI , the
PCE deflator, and the PPI trend together, there is
a wide variation in the movements of these price
indices over periods as long as a quarter.
The discrepancy among inflation rates asso
ciated with different price indices has important
implications for the conduct of monetary policy
linked to inflation targets. If long-term increases
in the price level are masked by statistical noise
that is a consequence of changing circumstances
in individual markets, then monetary policy
linked to any index of current inflation will be
affected by transient shocks as well as by the
■
1 The price indices are the Consumer Price Index (CPI), the serv
ice component of the CPI (CPIS), the Producer Price Index (PPI), the PPI
without food and energy (PPIWF), and the Personal Consumption Expen
diture (PCE) deflator. Only the CPI, PPI, and PCE deflator appear in the
figure.
http://fraser.stlouisfed.org/
Federal Reserve Bank of St. Louis
secular trend in prices. Although shocks to the
price of individual commodities or groups of
commodities do affect the cost of living, they do
not necessarily reflect the impact of money
growth on the price level. Nor is the appropriate
policy response to these two types of inflation
necessarily the same. Overall, both the source
of noise and the amount of noise in individual
price indices make them a poor choice for infla
tion targets.
A related problem associated with using real
ized inflation as a guide for monetary policy is
the timing of inflation signals. The inflation rate
of last quarter or even last month is a poor guide
for policy that seeks to influence the future
course of the economy, yet this is the type of
information provided by direct examination of
any historical record. Forward-looking policies
linked to a measure of current inflation should
be based on what the past can tell us about the
present and the future. To make the historical
record useful, we need to extract from it infor
mation about current inflation and expected
future inflation.
Inflationary expectations address both of these
problems. Expectations are, by their nature,
linked to long-term trends in the price level rather
than to transient movements. They are forwardlooking. Moreover, there is a remarkable degree
of correlation among the inflation forecasts
ta
FIGURE
1
Different Measures of Inflation,
1954-1987
Percent, a n n u a l rate
25
1954
1959
1964
1969
1974
1979
1984
SOURCES: U.S. Department o f Commerce, Bureau o f Economic Analysis, and U.S. Department o f Labor, Bureau o f Labor Statistics.
generated by different price indices and forecast
methodologies. Realistic models of inflation dis
count current innovations in the inflation rate,
which are largely noise, and focus instead on
movements that tend to persist over time. As a
result, different models of expected inflation
agree on what is likely to occur in the immediate
future, even when individual price series give
conflicting signals about the current inflation rate.
The common trend in the different series is an
indicator of the pervasive price growth, or core
inflation, that is of interest to policymakers.
I. Expected Inflation
We usually think of expected inflation as the ex
pected rate of change in a particular price index,
and judge different models of expectations by
their ability to project movements in that index.
The two criteria most commonly used to judge
model performance are the mean squared error
and bias of the inflation forecast. Both statistics
are informative, since an unbiased forecast that
fails to identify large, predictable movements in
inflation will have a larger mean squared error
than a forecast that is, on average, less accurate
but better able to predict significant changes in
the inflation rate.
Two types of statistical models used to
forecast inflation have, in the past, performed
equally well in terms of both bias and mean
squared error.2 Time series models identify tem
poral patterns in the inflation rate and use those
patterns, combined with information about the
recent history of inflation, to predict future infla
tion. These models are capable of identifying
very complex relationships among inflation rates
at different points in time, but tend to ignore
other contemporaneous information that might
be useful in forecasting.
Econometric models that incorporate informa
tion about interest rates or money growth attempt
to remedy this shortcoming. Although the history
of money growth is correlated with inflation, in
terest rates often take the place of money in fore
casting models. The motivation for this choice is
the notion that, in an efficient capital market, the
■ 2 Fama and Gibbons (1984) compare pure time-series models and
interest-rate models, and find that the interest-rate models yield a smaller
root mean squared error in out-of-sample forecasts. The differences in
forecast performance increase with the forecast horizon.
TABLE
1
The Correlation among Quarterly
Inflation Rates Based on Different
Price Indices between 1954 and 1987
CPI
CPIS
PPI
PPIW F
PCED1
CPI
1.00
0.83
0.74
0.72
0.82
CPIS
0.83
1.00
0.48
0.56
0.56
PPI
0.74
0.48
1.00
0.79
0.76
PPIW F
0.72
0.56
0.79
1.00
0.78
PCEDEF
0.82
0.56
0.76
0.78
1.00
SOURCE: Author’s calculations.
In this model, 7 ( 0 is the inflation rate at time t
and e ( O is an impulse that affects that rate.3
Conceptually, the impulse comes either from
expansion of the money stock or from some
change in market conditions, such as a drought
or the threat of war in the Middle East. The cur
rent change in the inflation rate is determined
by current and past impulses, where the weight
assigned to the past is 0.
These models have an appealing interpretation
in terms of expected and unexpected inflation.4
From equation (1), we know that
(2)
A/(0 = e(0-8e(f-l).
This implies that
(3)
J(O = 7 ( f - l ) - 0 e ( f - l )
or that
inflation premium in nominal interest rates is a
sufficient statistic for expected inflation.
In practice, money may have some incremental
predictive power, because the decomposition of
nominal rates into an expected real return and an
inflation premium is not observable, but is imposed
on the data by the econometrician. To the extent
that this decomposition is imperfect, the economet
ric model will fail to uncover the market’s inflation
forecast, even if movements in the nominal interest
rate are completely determined by changes in the
expected real rate and expected inflation, as theory
would suggest. The merits of econometric models
that extract inflation forecasts from interest rates
and the empirical relevance of monetary growth
for predicting inflation are issues that may be
resolved only by examining the data.
II. Time Series
Models
Time series models express current inflation as
a weighted sum of past inflation and past
changes in the inflation rate. The manner in
which this history is translated into forecasts
depends on the properties of the inflation
process. W hen movements in the inflation rate
tend to be transient, current innovations play a
marginal role in the formation of expectations,
and the historical record receives more empha
sis in the inflation forecast. If, on the other hand,
increases in inflation tend to persist, the infla
tion forecast will be closely linked to the behav
ior of prices during the recent past.
A time series model of inflation that has been
found to forecast well is
http://fraser.stlouisfed.org/
(1 )
7 (f) - IQ-l) = e (t) Federal Reserve Bank of St. Louis
0 8 (t—1 ) .
(4)
A 7(i) = A / ( / - 1) - 0 A e ( i - 1).
Using the definition of A I ( t ) from equation
(2) and the fact that A [0 e (t- 1) ] = 0 [ e ( t —1)
- e (?- 2) ], we obtain
(5)
A 7 ( 0 = (1 - 0 ) e (t- 1).
Expression (5) states that expected inflation
follows a random walk, with an innovation var
iance that is (1 - 0)2 times the variance of 8 (t).
Values of 0 close to 1 imply that most of the
variance in inflation is accounted for by tran
sient shocks, so that current innovations are not
reflected in expected future inflation, while
values of 0 close to 0 imply that most of the
variance is accounted for by movements in infla
tion that are expected to persist.5
Estimation of equation (1) for the different
series described in table 1 and figure 1 yields val
ues of 0 that range from 0.45 for the PCE deflator
to 0.70 for the PPI. 6 The evidence from the econ
ometric model is therefore in accord with the in
tuition suggested by the data: A modest fraction
of the quarterly innovation in inflation is reflected
■ 3 The model described here is examined by Fama and Gibbons
(1982).
■
4 Jeffrey Hallman suggested this interpretation.
■ 5 Ansley (1980) provides an alternative interpretation that yields
the same inference.
■ 6 Maximum likelihood estimates are based on a sample of inflation
rates from the first quarter of 1954 to the fourth quarter of 1987. The
Breusch-Pagan Lagrange multiplier test for autoregressive conditional
heteroscedasticity (ARCH) effects reveals that the data are conditionally
heteroscedastic. All estimates involve an ARCH (2,0) model of the condi
tional variance, although this is found to have only a minimal impact on
estimated parameter values and forecasts.
TABLE
2
The Correlation among Expected
Quarterly Inflation Rates Generated
by a One-Parameter Time Series
Model. Inflation Is Assumed to
Follow an IMA (1,1) Process
PPI
PPIW F
0.92
0.93
0.90
0.90
1.00
0.82
0.81
0.71
0.93
0.82
1.00
0.93
0.89
PPIW F
0.90
0.81
0.93
1.00
0.87
PCEDEF
0.90
0.71
0.89
0.87
1.00
CPI
CPIS
CPI
1.00
CPIS
0.92
PPI
PCED1
SOURCE: Author’s calculations.
in expected future inflation. In the case of the
PCE deflator, a 1 percent increase in quarterly in
flation is associated with a 0.55 percent increase
in expected inflation. That fraction is 0.30 in the
case of the PPI. An alternative perspective on the
estimated value of 0 is provided by examining
the fraction of the variance of changes in quarter
ly inflation accounted for by changes in expected
inflation. This number ranges from 10 percent in
the case of the PPI to 30 percent in the case of
the PCE deflator.
The effect of filtering the inflation-rate series
with this model, and focusing on the expected
inflation series implied by equation (3), is illus
trated in table 2. The correlation among expected
inflation rates inferred from the different price
series is substantially greater than the correlation
in realized inflation rates, even when expecta
tions are generated by the parsimonious oneparameter time series model. For example, the
correlation between the expected inflation rate
inferred from the CPI and the expected inflation
rate inferred from the PPI over 35 years of quar
terly data is 0.93, while the correlation between
the realized rates of inflation implied by these
same indices is 0.74. Thus, the different price
series yield highly correlated inflation forecasts,
even though there is substantial disagreement
about the current inflation rate among these series.
III. Econometric
Models
Inflation forecasts based exclusively on the tem
poral pattern of past inflation ignore a great deal
of potentially useful data. Information about
money growth or interest rates will be without
value only in the event that the history of infla
tion is a sufficient statistic for its expected future
course. Both the tremendous amount of noise
in the various inflation series and common sense
suggest that this is unlikely.
Nominal interest rates are an especially appeal
ing source of information, since the yield on fixedrate debt instruments contains a premium that
compensates the investor for expected deprecia
tion in the purchasing power of money over the
life of the instrument. The advantage of using
interest rates to identify expected inflation, rather
than modeling the link between money and
prices directly, is that the inflation premium found
in bond yields represents a consensus forecast of
inflation over a fixed time interval known to the
observer. In contrast, the history of money growth
provides little information about when an increase
in money will be reflected in prices, or even
whether it will be reflected in prices rather than
output. Focusing on bond yields rather than on
money growth makes it unnecessary to consider
the complex lag structures typical of macroeco
nomic models that attempt to characterize directly
the link between money and prices.
Extracting inflationary expectations from
bond yields is not a trivial exercise: Variations in
nominal yields reflect changes in expected real
returns as well as changes in expected inflation.
(Yields may also contain a risk premium when
inflation is uncertain, but this feature of returns is
rarely modeled.) Neither component of nominal
yields is observed directly, and models that ex
ploit interest-rate data rely on auxiliary assump
tions to separate expected real rates from
expected inflation. The models discussed below
are distinguished by the assumptions about the
real rate process that are used to identify these
components of the nominal interest rate.
One method of identifying the model is to
assume that the expected real rate of return fol
lows a random walk. This implies that
(6)
R (t) = R ( t - l) + i( t ) .
Then, if the realized real return is equal to
the expected real return plus a noise term r\(t ),
the first difference of the observed real return
takes the form
(7)
A /? (0 = S ( 0 +Tl(0-Tl(f-1).
TABLE
3
The Correlation among Expected
Quarterly Inflation Rates when the
Expected Real Rate Follows a
Random Walk and the Nominal Yield
Is the Sum of the Expected Real Rate
and Expected Inflation
PCEDI
CPI
CPIS
PPI
PPIW F
CPI
1.00
0.95
0.96
0.93
0.92
CPIS
0.95
1.00
0.88
0.87
0.78
PPI
0.96
0.88
1.00
0.96
0.92
PPIW F
0.93
0.87
0.96
1.00
0.89
PCEDEF
0.92
0.78
0.92
0.89
1.00
(8)
SOURCE: Author’s calculations.
TABLE
4
The Correlation among Expected
Quarterly Inflation Rates Generated
by a Regression-Based Model. The
First Difference in Inflation Is
Projected onto the First Difference in
the 90-Day Treasury Yield
CPI
CPIS
PPI
PPIW F
CPI
1.00
0.95
0.94
0.93
0.91
CPIS
0.95
1.00
0.85
0.88
0.78
PCEDI
PPI
0.94
0.85
1.00
0.95
0.90
PPIW F
0.93
0.88
0.95
1.00
0.88
PCEDEF
0.91
0.78
0.90
0.88
1.00
SOURCE: Author’s calculations.
This has a first-order moving average repre
sentation identical to that of equation (1). Esti
mation of this model yields an expected real
return series.7 Quarterly inflation forecasts are
then constructed by subtracting the expected real
return series corresponding to a particular price
index from the yield on 90-day Treasury bills.
The correlation among the inflation forecasts
created in this manner is described in table 3The more sophisticated model of expecta
tions yields inflation forecasts that are both
more accurate and more highly correlated with
each other than those from the time series
model, even when the dynamics of the ex
pected real interest rate are extremely simple.8
The increased correlation is especially notice
able in situations where the correlation between
the time series forecasts is lowest; for example,
in the service component of the CPI and PPI.
The high correlation among the fitted values
from the interest-rate-based models suggests
that all of the forecasts are tracking some under
lying trend. The natural interpretation of that
trend is the core rate of inflation.
This interpretation is reinforced by estimates
from a closely related model. If expected real
rates are constant or nearly constant between
adjacent quarters, the main source of variation
in Treasury yields is the inflation premium. This
suggests a regression-based model of the form
A 7i ( 0 = (3 o + A i ( t ) Pi + e (t),
where A n (t) is the change in inflation from
one quarter to the next and A i ( t ) is the change
in Treasury yields from the beginning of quarter
t- 1 to the beginning of quarter t . Estimation of
this model indicates a statistically significant
relationship between the change in Treasury
yields and the change in inflation.9
The correlation among fitted values obtained
by estimating equation (8) is documented in
table 4. The strong resemblance between these
results and those presented in table 3 suggests
that whether interest rates are included in the
model is a more important consideration than
the manner in which they are incorporated. As
before, the expected inflation forecasts track
each other quite closely.
Adding lagged values of either the growth
rate of money or the change in the growth rate
of money to the regression equation has almost
no impact on the fitted values for expected infla
tion, even though the regression coefficients as
sociated with these variables are statistically
■
7 Application of the Breusch-Pagan test to the residuals from maxi
mum likelihood estimates reveals ARCH effects. The figures in table 3 are
based on fitted values from a maximum likelihood model where the condi
tional variance is ARCH (2,0). It is also worthwhile noting that the mag
nitude of the moving-average parameter is considerably less than in the
results reported by Fama and Gibbons for monthly data. In other words,
monthly data contain even more noise.
■
8 Fama and Gibbons (1984) document the superiority of this
model relative to the time series model, using monthly data.
■ 9 The model is estimated by maximum likelihood with an MA(1)
error structure and an ARCH correction for conditional heteroscedasticity.
The regresssion coefficient (ii is statistically significant at 1 percent for
all of the inflation series when the parameter covariance matrix is esti
mated from the information matrix, with or without the Newey-West cor
rection for heteroscedasticity.
1 TAB L E
5
V. Hamilton’s Model
The Correlation among Actual and
Predicted Series for the CPI
A potential shortcoming of the econometric
IMA
Actual
(1,1)
Real rate
is a
random
walk
Regres
sion
w/int.
rates
1.00
0.76
0.81
0.80
0.82
0.76
1.00
0.96
0.97
0.95
0.81
0.96
1.00
0.99
0.98
Regression
0.80
with interest
rates
0.97
0.99
1.00
0.98
Same with
0.82
interest rates
and money
0.95
0.98
0.98
1.00
Actual
IMA
(1,1)
Real rate is
a random
walk
Same
w/int.
rates and
money
methodologies that I have considered is the ex
tremely simple dynamics that are imposed on
expected real interest rates and expected infla
tion in order to identify these components of
the nominal rate process. Hamilton (1985) has
proposed and estimated a model that permits
richer dynamics in both components, and for
malizes the intuition that the observed rate is
equal to a signal (expected inflation) plus noise.
The model, which contains the random-walk
formulation (6) as a special case, assumes that
the following relations among inflation, ex
pected inflation, and real interest rates are
stable over time:
(9)
SOURCE: Author’s calculations.
IV. Correlation
among Forecasts
from Different
Methodologies
The results discussed above concern the correla
tion among the predicted values of different
inflation series obtained with a specific econo
metric methodology. Inspection of the predicted
values for a given series and different methodol
ogies suggests that three observations are in
order. First, the inflation forecasts from the dif
ferent models are highly correlated; they appear
to be tracking a common element. Second, the
forecasts track each other more closely than they
track actual inflation, consistent with my interpre
tation of the inflation series as signal plus noise.
Third, the forecasts that incorporate interest-rate
data are both more accurate than the forecasts
generated by the time series model and more
highly correlated with each other than with the
time series model. Although table 5 describes
the correlation among forecasts only for the CPI,
similar results obtain for the other price series.
A
A
r ( t ) = kr+ 0 ( L ) r ( t ) + ' ¥ ( L ) n ( t )
+ Ç ( Z ) 7 c ( f ) + er ( f ) >
(10)
significant in all of the models. Indeed, the cor
relation among fitted values cannot be distin
guished from the results presented in table 4.
This is consistent with results reported by Fama
(1982), who finds that interest rates contain
most of the information about expected infla
tion that may be extracted from the history of
money and output.
A
n (t) = k n + a (Z) r ( t ) + (3 (Z) n (t)
+ Y(Z)7t ( O + M O ,
(11)
71 ( t ) = n (t) + e(t).
Expected real rates and expected inflation are
described by linear projections of these variables
on their own past values and on the past values
of actual inflation. The difference between ex
pected inflation and actual inflation is a noise
term, as in the simpler models discussed above.
These assumptions, along with the assumption
that the nominal rate is equal to the real rate plus
the expected inflation rate, are sufficient to iden
tify expected real rates and expected inflation.
Note that equations (9) and (10), like equations
(7) and (8), are statistical models of the relation
ships among these variables; there is no presump
tion that the lag polynomials O (Z ), \
j/ (Z ), £, (Z ),
a (Z ), (3 (Z ), and y (Z ) represent the decision
rules that agents use to form expectations about
real rates and inflation.
Hamilton’s model enjoys a second advantage
relative to the simple models in addition to
encompassing a wider variety of time series be
havior. In equations (9), (10), and (11), the dis
tinction between errors in expectations and
errors that result from the econometrician’s ina
bility to observe expected real rates or expected
inflation is modeled explicitly. The error terms
£r and £k represent innovations in the expected
real rate and expected inflation rate that are not
captured by the linear projections of equations
(9) and (10). These innovations arise because
TABLE
6
The Correlation among Expected
Quarterly Inflation Rates Generated
by Hamilton’s Kalman Filter Model of
Expected Inflation and Interest Rates
CPI
CPI
CPIS
PPI
PPIW F
PCED1
0.57
0.60
1.00
0.57
0.40
CPIS
0.57
1.00
0.51
0.69
0.69
PPI
0.40
0.51
1.00
0.65
0.62
PPIW F
0.57
0.69
0.65
1.00
0.85
PCEDEF
0.60
0.69
0.62
0.85
1.00
SOURCE: Author’s calculations.
we are unable to observe expectations. The
error term e(t ) represents the difference be
tween what agents thought would occur and
what did in fact occur. Estimation of these para
meters allows us to evaluate explicitly the con
tribution of these different sources of noise to
the difference between expected inflation and
actual inflation, making it unnecessary to assign
an economic interpretation to the movingaverage parameter in a time series model.
The estimated series are consistent with those
produced by the other econometric models, in
that innovations in the inflation rates appear to
contain a substantial noise component.10 One
indicator of this phenomenon is the set of coeffi
cients that represents the projection of expected
inflation onto past values of inflation and ex
pected inflation. In general, the sum of the coef
ficients for the four lagged values of expected
inflation tends to be near one, while the sum of
the coefficients for the four lagged values of ac
tual inflation tends to be near zero. At the first
two lags, the effect is even stronger; estimated
parameter values imply that inflationary expec
tations tend to persist, while inflationary shocks
tend to be reversed. This pattern, which is con
sistent with the time series properties of the er
rors in the simpler econometric models, is
characteristic of all of the series except for the
PCE deflator.11 It suggests that expectations of
■
10 1estimate the state space version of the model described in Burmeister, Wall, and Hamilton (1986). By doing so, I avoid dealing with the
moving-average error terms that characterize the earlier formulation.
■ 11 My estimates for the deflator series are qualitatively similar to
those reported by Hamilton (1985) and Burmeister, Wall, and Hamilton
(1986).
inflation tend to persist, even in the face of sig
nificant changes in the current inflation rate.
A second indicator of the noise in the series
for realized inflation is the fraction of the varia
tion in the inflation rate accounted for by the
expectation error series e ( t ). This ranges from
20 percent in the case of the PCE deflator to 60
percent in the case of the PPI.
The expected inflation series from Hamilton’s
model differ from the estimates produced by the
simpler econometric models in one important
respect: The substantial increase in the number
of explanatory variables yields a significant im
provement in fit. As a result, the predicted
values bear a stronger resemblance to the actual
values and a weaker resemblance to each other.
This fact is evidenced by the correlation among
predicted values described in table 6.
VI. A Multiple
Indicator Model
A multiple indicator model based on Hamilton’s
methodology incorporates the flexible dynamics
of that model, but focuses on the common com
ponent of the different series rather than on the
expected component of a particular series. Inter
est rates and a set of realized inflation series are
driven by a single expected inflation series. This
series is distinguished from the expected inflation
series generated by Hamilton’s model in that it
provides information about pervasive price growth
rather than about the behavior of a particular
index.
I
estimate the model by projecting expected
inflation and the expected real interest rate onto
their own past values and onto past values of the
PPL The realized values of the PCE deflator and
the CPI both serve as indicators of the core rate.
The realized value of inflation for each index is
presumed to be equal to expected inflation plus
a noise term.
The expected inflation series for this model is
presented in figure 2, along with the actual series
for the CPI and the PCE deflator. Expected infla
tion exhibits the same time-series properties as do
the individual series described above. Innovations
in realized inflation are reflected only weakly in
current expected inflation, which nonetheless dis
plays a great deal of persistence.
F I GU R E
2
Expected and Realized Inflation,
1955 -1987
Percent, a n n u a l rate
SOURCES: U.S. Department o f Commerce, Bureau o f Economic Analysis, and U.S. Department o f Labor, Bureau o f Labor Statistics.
VII. Conclusion
Inflation targets may contribute significantly to
the credibility of a monetary policy that is
oriented toward controlling inflation. A potential
problem with inflation targets is that inflexible
mles would couple money growth to random
shocks in the price level; the substantial noise in
individual inflation series suggests that this con
cern is more than academic. Building flexibility
into policy rules is one means of dealing with
this problem, but flexibility tends to undermine
the credibility of the commitment to control infla
tion. An inflation target that filters out these tran
sient shocks, combined with a tight feedback
mle from the filtered inflation rate to money
growth, is an alternative that maintains
credibility while mitigating the problems as
sociated with noise in the policy targets.
Expected inflation is an indicator of the perva
sive price growth, or core inflation, that interests the
architects of monetary policy. The correlation
among expected inflation rates from different price
series and forecast methodologies suggests that
these series are tracking the core rate. Signal extrac
tion models formalize this intuition. Policy rules
linked to the expected inflation series from any of
the econometric models examined here are both
forward-looking and reasonably insulated from
index-specific shocks. Moreover, such broadly
based targets would be difficult to manipulate. All
of these properties suggest that expected inflation
may serve as an effective guide to monetary policy.
El
References
Ansley, Craig F. “Signal Extraction in Finite
Series and the Estimation of Stochastic Regres
sion Coefficients,” Washington, D.C.: Ameri
can Statistical Association, Proceedings of the
Business and Economic Statistics Section,
19 8 0 .
Burmeister, Edwin K., Kent D. Wall, and
James D. Hamilton. “Estimation of Unob
served Expected Monthly Inflation Using Kal
man Filtering,” Jo u rn a l o f Business a n d
Econom ic Statistics, vol. 4, no. 2 (April 1986),
pp. 147-60.
Fama, Eugene F. “Inflation, Output, and
Money,” Jo u rn a l o f Business, vol. 55, no. 2
(April 1982), pp. 201-31.
________ , and Michael R. Gibbons. “A Com
parison of Inflation Forecasts, "Jo u rn a l o f
M onetary Economics, vol. 13, no. 3 (May
1984), pp. 327-48.
________ , and________ . “Inflation, Real
Returns, and Capital Investment,” Jo u rn a l o f
M onetary Economics, vol. 9, no. 2 (May
1982), pp. 297-323.
Hamilton, James D. “Uncovering Financial
Market Expectations of Inflation,” Jo u rn a l o f
P o litical Economy, vol. 93, no. 6 (December
1985), pp. 1224-41.
The Case of the Missing
Interest Deductions: Will
Tax Reform Increase
U.S. Saving Rates?
by David A ltig
David Altig is an assistant profes
sor of business economics and
public policy at Indiana University
and is an economist at the Federal
Reserve Bank of Cleveland. The
author gratefully acknowledges
helpful comments from Michael
Bryan, Chris Carroll, Randall
Eberts, and Jagadeesh Gokhale
and excellent research assistance
from Sharon Parrott.
Introduction
this percentage increased steadily, from 0.85 per
cent in 1977 to 1.7 percent in 1986 (see figure 1).
The period subsequent to 1976 was also dis
tinguished by a downward trend in personal,
private, and national saving rates (see figure 2).
The coincidence of decreasing personal saving
rates and increasing personal interest deductions
can also be seen in figure 3, which plots per
sonal saving (as a percentage of GNP) against
nonhousing interest deductions (as a percent
age of GNP).
While the negative relationship that appears
in figure 3 does not necessarily imply that elim
inating the deductibility of nonhousing interest
Beginning in tax year 1991, U.S. taxpayers may
no longer deduct personal interest expense
when calculating taxable income, thus complet
ing the transition from the unlimited deductibil
ity provisions that existed prior to enactment of
the Tax Reform Act of 1986 (TRA86). In tax-speak,
personal interest expense comprises interest pay
ments not associated with mortgages on qualified
residences or certain income-generating ac
tivities. Generally speaking, personal interest ex
pense amounts to interest payments on
consumer loans not secured by real estate.
Although a large share of household interest
payments are associated with mortgage-related
interest payments, which remain deductible
under TRA86, disallowing deductions for per
sonal interest expense is likely to have a sub
stantial impact on consumer behavior.1 Indeed,
eliminating the deductibility of personal interest
expense may, in the final analysis, be one of the
more important legacies of TRA86.
It is certainly obvious that personal interest
deductions had been increasingly exploited in
the years preceding passage of TRA86. After
trending upward during the 1950s, the growth
of nonhousing interest deductions stabilized
through the mid-1970s, fluctuating between 0.8
and 1.1 percent of GNP. After 1976, however,
■
1 The ratio of housing to nonhousing interest deductions on per
sonal tax returns was 1.19 in 1966,1.78 in 1976, and 1.78 again in
1986. The largest value of this ratio over the 1964-1986 period was 1.94,
which was realized in 1983. Unfortunately, the Internal Revenue Service's
Statistics o f Income, from which these numbers are calculated, does not
generally distinguish among the categories of nonhousing interest deduc
tions. The nonhousing interest measures used in this paper therefore in
clude interest expense associated with personal investment. Fortunately,
available data suggest that investment interest expense claimed by indi
viduals is small relative to personal interest expense. In 1977, for exam
ple, 65 percent of total household interest deductions were associated
with home mortgages, 34 percent were associated with personal interest
expense, and only 1 percent was associated with interest expense from in
vestment activity.
23
FIGURE
1
Nonhousing Interest Deductions
Percent o f GNP
1950
I9 6 0
1970
1980
1990
SOURCES: U.S. Department o f Commerce, Bureau o f Economic
Analysis, and Internal Revenue Service.
F I G U R E
2
Saving Rates
Percent o f GNP
SOURCE: Carroll and Summers (1987).
F I G U R E
3
Personal Saving vs.
Nonhousing Interest Deductions
U nadjusted p e rso n al saving, p e rce n t o f GNP
N o n h o u sin g interest d e d uctio n s, pe rce n t o f GNP
SOURCES: U.S. Department o f Commerce, Bureau o f Economic
expense will cause an increase in the U.S. saving
rate, it is commonly believed that removing in
centives to dissave does indeed result in higher
savings relative to income. To a large extent,
this belief arises from the simple intuition that
increasing the price of an activity— in this case,
borrowing— will naturally lead to a decrease in
that activity. Economic theory thus leads us to
conclude that more restrictive tax treatment of
personal interest expense will lead to less con
sumption and more saving.
Although empirical evidence is limited, it ap
pears that the negative relationship between
household borrowing subsidies and saving be
havior suggested by economic theory can be
found in real-world economies. Tanzi (1987)
has shown that personal saving as a percentage
of disposable income has tended to be lower in
countries with the most generous tax treatment
of personal interest expense (this evidence is
also presented in Sheshinski [1990])- In a
provocative comparison of U.S. and Canadian
saving rates, Carroll and Summers (1987) argue
that part of the historical divergence between
observed saving rates in these two very similar
economies is likely because, unlike taxpayers in
the United States, Canadian taxpayers were un
able to deduct personal interest expense.2
In this paper, I consider further some of the
evidence presented by Tanzi and Carroll and
Summers. Specifically, I ask two simple ques
tions. First, do private saving rates tend to be
higher, on average, in countries that prohibit
the deductibility of personal interest expense?
Second, do tax subsidies to borrowing help ex
plain U.S.-Canadian saving rate differentials?
The empirical evidence I present gives affir
mative answers to both questions. With respect
to the first question, I examine private saving
rates from 1975 to 1986 in a sample of 15 mem
ber countries of the Organisation for Economic
Co-operation and Development (OECD). I find
that private saving rates were indeed higher on
average in countries without tax subsidies to
consumption loans. These results confirm for
private saving the observations made by Tanzi
with respect to personal saving.3
■
2 Limitations on interest deductions available to Canadian tax
payers also apply to interest expense from home mortgages. See the dis
cussions in Carroll and Summers (1987) and Tanzi (1984).
Analysis, Internal Revenue Service, and Carroll and Summers (1987).
■
3 Private saving is the sum of saving by households, or personal
saving, and saving by corporations.
Et
O f course, simply comparing aggregated
cross-country saving rates provides only casual
evidence. Like the relationship in figure 3, such
comparisons do not control for other causal fac
tors. A more detailed analysis, which builds on
the Carroll and Summers work, is provided in
section III. The empirical models in this section
add proxies for the U.S. subsidy rate on con
sumption loans to the Carroll and Summers
regression equations for U.S.-Canadian saving
differentials. The subsidy variables consistently
appear with statistically and economically sig
nificant negative effects on private saving, a
result that is remarkably robust across different
specifications of the empirical model.
Even the more sophisticated analysis of sec
tion III has serious limitations — the data include
only 24 annual observations, no attempt is made
to control for simultaneity bias, and the subsidy
proxies are admittedly crude, to name just a few.
Furthermore, the effect of the borrowing subsidy
variable is not consistently significant in regres
sion models of the U.S. saving rate alone. None
theless, the results reported here are generally
supportive of the assertion that consumptionloan subsidies may have important negative ef
fects on saving behavior, and hence important
implications for the long-mn performance of the
U.S. economy in the wake of TRA86.
Savers in the model have access to two types
of assets: physical capital, denoted by a {. for an
age i individual of generation j, and private
debt, which takes the form of consumption
loans between generations.4
To make the model interesting, it is necessary
that some generation chooses to borrow. I there
fore assume that each generation is endowed
with an identical, exogenous life-cycle labor
productivity profile given by (Ej, £2, 0), where £2
is sufficiently larger than £: to ensure that the
young always choose to borrow. Let borrowing
by a young household born at time t be given
by slr Abstracting from population growth, mar
ket clearing in the consumption loans market
requires that s1; = h2 t _x , where h71A is lending
by the generation that is middle-aged in time t. 5
With these definitions in hand, the budget
constraints for each generation are defined as
(2)
C u = E1wt+ s u ,
(3)
^ 2 / = £ 2tti + l _
[l +r+
d l{\-bt+l) ] s lt- a 2t- h 2t,
and
(4)
C^t = (1 + rt+2) a 2t
+ [1 + r f 2(1 - p f+2) ] h 2t,
I. A Simple
Analytical
Framework
Although the intuition for a negative relation
ship between favorable tax treatment of house
hold borrowing and personal saving is readily
apparent, introducing a simple analytical
framework will help to organize the issues.
The framework presented here is a simple,
perfect-certainty, overlapping generations model
in which each generation lives three periods.
Every generation consists of identical individuals
who inelastically supply one unit of labor in the
first two periods of life, retiring in the third. Utility
is assumed to be a logarithmic, time-separable
function of consumption given by
where r is the rate of return to physical capital,
r d is the return to private debt, 8 is the subsidy
rate on borrowing (or, alternatively, the marginal
tax rate on nonwage income for age 2 individ
uals), and p is the tax rate on interest income
earned from the purchase of private debt. Equa
tions (2), (3), and (4) embody the assumption
that the young choose to borrow, the condition
that all generations will consume their full life
time resources (so that only middle-aged individ
uals save), and the simplifying assumption that
the marginal tax rate on income from physical
capital is zero.
Assuming interior solutions for individual
saving and dissaving decisions, utility maximiza
tion implies the first-order conditions
3
(1)
M C„).
i= 1
The variable (3 is the individual subjective timediscount factor, and the subscript t indexes
each generation by date of birth.
■
4 Because the analysis here abstracts entirely from transaction
costs, nothing essential is lost by ignoring the role of intermediaries and
assuming that loan contracts are directly traded between generations.
■
5 The model abstracts from bequest motives and uncertainty, so all
generations choose to “die" with no assets. The old will therefore never
choose to accumulate capital or lend in the consumption loans market.
25
TABLE
1
Crowding-Out Effects of increasing
the Subsidy to Consumption Loans
Percentage R e d u c tio n in Steady-State C a p ital
8
B e n ch m ark
P o p u la tio n
g ro w th =
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.5
1.0
1.6
2.1
2.6
3.2
3.7
4.3
4.8
5.4
5.9
6.5
7.0
7.6
8.2
0.6
1.1
1.7
2.3
2.9
3.5
4.1
4.7
5.3
6.0
6.7
7.3
8.0
8.7
9.4
P ro d uctivity
p ro file =
(0, 10, 0)
0.8
1.6
2.4
3.3
4.2
5.0
6.0
6.9
7.8
8.8
9.8
10.8
11.9
12.9
14.0
NOTE: Each entry gives the percentage reduction in the steady-state capi
tal stock w hen the subsidy rate on borrowing, 8, is increased from zero.
The benchmark case assumes (3 = 0.778, 0 = 0.25, zero population growth,
(Ej, e2, e3) = (1.5,8.5, 0), and p = 0.11. The other cases maintain the
benchmark assumptions, w ith the exception o f the indicated parameters.
SOURCE: Author’s calculations.
(5)
C 2,= p[l + r f , ( l - 8 , + 1) ] C 1,,
(6 )
C 3, = p [ l + r f 2( l - p , + 1) ] C 2, ,
and
(7)
C 3,= p ( l + r,+ 2) C 2,.
Equations (6) and (7) imply that, in assetmarket equilibrium, r t = r dt( 1 - p t ).
The long-run effect of changes in the subsidy
variable 8 can be demonstrated by a few simple
simulation exercises. Table 1 reports the reduc
tion in the steady-state capital stock caused by
increasing the subsidy rate 8 for particular parameterizations of the model.6 In the benchmark
case, which is described in table 1, increasing 8
from 0 to 10 percent causes the steady-state capi-
■
tal stock to fall by 5.4 percent.7 By extension,
interest rates rise and per capita income falls.8
Table 1 also shows how factors that increase
the demand for consumption loans amplify the
crowding-out effects of allowing personal interest
expense to be deducted for tax purposes. Thus,
an increase in either the rate of population growth
or the steepness of the productivity profile be-,
tween young and middle ages results in larger
percentage decreases in steady-state capital for a
given change in 8. (See Bryan and Byrne [1990]
and the references therein for a general discus
sion of the effects of demographics on aggregate
saving in a life-cycle context.)
Because substantial disagreement persists
among economists concerning the appropriate
model of aggregate saving behavior, it is impor
tant to note that the qualitative results of the
model presented here are not dependent on life
cycle assumptions. Altig and Davis (1989) show
that changes in the subsidy rate on consumption
loans can also have significant long-run negative
effects on aggregate savings in models where
parents and children are altruistically linked, as in
Barro (1974). In fact, under the plausible assump
tion that the tax rate on interest income exceeds
the subsidy rate on borrowing, Barro-type models
predict that changes in subsidy rates can have
large long-run effects on the size of the capital
stock even when changes in the tax rate on inter
est income do not (see Altig and Davis [19891 for
a full treatment of this issue).
II. Do Private Saving
Rates Tend to Be
Higher in Countries
Without Borrowing
Subsidies?
Table 2 answers this question directly. The
answer is yes, at least for the subset of OECD
countries examined here.9 The results in table 2
■
7 In general, the direction of change in aggregate savings depends
on the nature of the assumed preference structure. Under “standard”
preferences, however, changes in the subsidy rate will have effects that
are qualitatively the same as the ones reported here. The seminal discus
sion of this issue in an overlapping generations framework can be found
in Diamond (1965).
■
8 The simulations reported in table 1 assume a Cobb-Douglas
production technology, expressed in effective labor units as y = k d.The
steady-state rate of return to capital is therefore given by 0 /re ‘ 1. Thus,
y is increasing in k, and r and r d (by the asset-market clearing condi
tion) are decreasing in k.
■
6 The simulations reported in table 1 assume that all revenues
raised (or lost) through distortionary taxation are rebated (or recovered)
via lump-sum subsidies (or tax levies) to the affected generations.
9 The countries are Australia, Austria, Belgium, Canada, Denmark,
France, Ireland, Japan, the Netherlands, Norway, Sweden, Switzerland,
the United Kingdom, the United States, and West Germany. The data are
from OECD National Accounts.
□
TABLE
2
Average Private Saving Rates,
1975-1985
G ro u p Averages
C onsum e r
interest
n o t de d uctible
C o n sum e r
interest
d eductible
Simple
average
10.68
8.65
Weighted
average
11.14
8.38
In d iv id u a l C o u n try Averages
C o n sum e r
interest
n o t de d uctible
Average
saving
rate
Australia
5.65
Austria
9.83
Belgium
12.73
Canada
11.81
France
9.74
Ireland
14.80
Japan
15.73
United Kingdom
7.33
West Germany
8.53
C o n sum e r
interest
d e d uctible
Denmark
Netherlands
Norway
Sweden
Switzerland
United States
Average
saving
rate
7.45
12.24
5.04
5.23
13.72
8.22
NOTE: Entries represent averages for subsets o f 15 OECD countries. C oun
tries are classified into deductible and nondeductible groups according to
the information provided by Tanzi (1984). Weighted averages are con
structed using within-group relative shares o f real GDP. Real GDP figures
are obtained from Summers and Heston (1988). Saving rates are expressed
as percentages o f GNP.
SOURCE: Organisation for Economic Co-operation and Development,
National Accounts o f OECD Countries, 1975-1987, Volum e II.
were obtained by first averaging private saving
as a percentage of gross domestic product
(GDP) over the sample period 1975 to 1985 for
each of the 15 countries considered.10 The
countries were then grouped according to
whether tax subsidies were provided to interest
expense from general (nonhousing) consumer
credit.11 Two sets of group-average measures
are reported in table 2— one based on simple
averaging and one obtained by weighting the
individual country averages by within-group
relative shares of real GDP.12
The average private saving rate for the
sample period was 10.68 percent in countries
without favorable tax treatment of personal inter
est expense and 8.65 percent in countries with
favorable tax treatment of personal interest ex
pense (11.14 percent and 8.38 percent, respec
tively, when country-specific saving rates are
weighted by GDP shares). To put the magnitude
of this difference in some perspective, the U.S.
current account deficit was 5 percent of GDP in
1988. A 2 percent increase in the private saving
rate for 1988 could therefore have financed
more than one-third of the U.S. current account
deficit, an amount equivalent to about $44 bil
lion in 1988 dollars.
Table 2 also clearly shows that, in the chosen
sample, average saving rates varied substantial
ly among countries with similar tax treatment of
personal interest expense.13 It is impossible to
know how much of the variation can be ac
counted for by economic, demographic, and
policy variables without a more detailed inves
tigation of the data. Unfortunately, the informa
tion that is necessary to conduct a more detailed
■
10 The savings measures used here are net of depreciation. See
Aghevli et al. (1990) for a general discussion of the OECD saving
measures.
■
11 Countries are classified into subsidy and nonsubsidy groups
according to information reported in appendix III of Tanzi (1984). Up
dated information in Tanzi (1987) indicates that these classifications were
still valid in 1985.
■ 12 Relative GDP shares are obtained using real GDP at internation
al prices calculated by Summers and Heston (1988).
■
13 There were also significant differences in the trend of saving
rates for countries within the two groups. In the subsidy group, for
instance, Norway, Sweden, and the United States experienced declining
saving rates over the sample period, while Denmark, the Netherlands, and
Switzerland all experienced fairly strong upward trends.
a
inquiry is difficult to come by.14 Because of this
difficulty, the balance of this paper focuses on a
comparison between two countries for which
data are more readily available: the United
States and Canada.
III. Has the Subsidy
Rate on Consumer
Loans Reduced U.S.
Saving Relative to
Canadian Saving?
Following Carroll and Summers (1987), the start
ing point of the analysis in this section is a
simple saving equation given by
(8)
St = a 0 + a 17i1+ a 2UNt + a 3SURPt +
a 4SHELTt + a 5NWt + a 6R f + r\t ,
where St is the time t differential between the
U.S. and Canadian private saving rate (as a per
cent of GNP), n t is the differential in inflation
rates for consumer prices, UN( is the differential
in unemployment rates (as a percent of the total
labor force), SURPt is the differential in net gov
ernment saving (as a percent of GNP), SHELTt is
the differential in the level of saving in taxsheltered assets (as a percent of personal dispos
able income), NWt is the differential in household
net worth (as a percent of GNP), and Rtat is the
differential in weighted averages of after-tax
returns to sheltered and nonsheltered saving.
Before proceeding to a discussion of my em
pirical work, it will be useful to introduce the ra
tionale for including the particular regressors
shown in equation (8). The inflation variable is
included to control for the tendency of national
income-account saving measures to overstate
actual saving when inflation increases. The idea
is that standard measures of income are dis
torted by changes in nominal interest rates that
arise solely from changes in the rate of inflation
or, more precisely, from the expected rate of in
flation. This issue is examined in detail by Jum p
■
14 I did examine many cross-sectional regressions with variations
ot the empirical specification employed by Feldstein (1980). In particular,
I attempted to find whether this type of cross-sectional empirical saving
model tends to underpredict the average private saving rate for countries
without borrowing subsidies and overpredict the saving rate for countries
with borrowing subsidies. For some of the models, I found regression
errors were uniformly positive for the no-subsidy countries and uniformly
negative for the countries with subsidies. However, the results were so
sensitive to sample size, choice of regressors, and sample period that it
was impossible to make a convincing case one way or the other. The
general nonrobustness of Feldstein-like empirical saving models is also
reported by Slemrod (1990) and Bosworth (1990).
(1980). The expected sign of a l is positive if
the type of measurement problem Jum p iden
tifies is the primary channel through which infla
tion rates help to explain aggregate savings.
The unemployment variable is a proxy for
differences in cyclical conditions across the two
countries. Assuming that changes in unemploy
ment primarily reflect deviations from the equi
librium rate of unemployment, an appeal to the
reasoning underlying the permanent-income
hypothesis implies that a 2 < 0. In other words,
we expect higher unemployment and more dis
saving when income is temporarily low.
The coefficient a 3 measures the relationship
between public saving and private saving. In
the simplest scenario, we expect to find a 3 = -1
if the conditions necessary for Ricardian equiva
lence are true and a 3 > -1 if those conditions
are not true.15 However, unambiguous predic
tions for the value of a 3 are complicated by the
fact that equation (8) does not control for inde
pendent effects associated with government ex
penditures (see Aschauer [1985D.
The significance of the sheltered saving vari
able is the key finding of Carroll and Summers.
SHELTt specifically measures the U.S.-Canadian
differential in total personal saving in tax-sheltered forms (as a percentage of disposable per
sonal income). In the United States, sheltered
saving is represented by contributions to indi
vidual retirement accounts (IRAs). The
Canadian equivalent of IRAs are registered
retirement savings plans.
Carroll and Summers estimate values of a 4
that range between 1 and 2, implying that in
creases in the amount of saving in tax-sheltered
assets are associated with greater than one-toone increases in total private saving. Although
this impact seems large, it is qualitatively consis
tent with microdata evidence presented by
Venti and Wise (1987), who estimate that 80 to
90 percent of IRA contributions represent net in
creases in personal saving.
The final two variables, NWt and Rtat, are
expected to enter equation (8) with negative
and positive coefficients, respectively. The networth variable is included to capture the possi
bility that private saving, as measured on a
national income accounts basis, changes as
households seek to maintain target wealth-toincome ratios. Thus, as net worth rises relative
to GNP, private saving tends to fall.
■
15 The literature on Ricardian equivalence is massive. Good
general discussions can be found in Bernheim (1987,1989) and Barro
(1989a, 1989b).
TABLE
3
Regression Results
M odel
C oefficient
V alues
CONST
INFL
1
4
-.027
.004
.004
.016
(.45)
(.43)
(2.3)b
.231
.197
-.017
.156
(.04)
(.43)
.430
.404
.290
(.62)
SURP
3
(3.3)a
(.95)
UN
2
-.837
(3.4)a
SHELT
(1.1)
.506
(1.4)
-.267
(1.1)
-.281
(1.3)
-.365
(1.2)
(1.2)
(1.8)c
1.74
1.98
-.665
(4.2)a
(3.2)a
(.64)
-.254
.228
(.55)
(.54)
R at
NW
.179
(2.9)a
Adj. R 2
.559
.760
.751
.824
P
.585
.408
.407
.226
from regression analysis on equation (8) cannot
be viewed as decisive indicators of the structural
relationships between U.S.-Canadian saving dif
ferentials and the explanatory variables.16 The
appropriate interpretation of the approach taken
here is that of an investigation into whether par
tial correlations of saving differentials and in
cluded regressors are consistent with structuraltheoretical predictions.
Table 3 presents the results of several regres
sions based on equation (8). The data are
annual and, with a few exceptions, are from
Carroll and Summers (1987).17 Model 1 in table
3 includes inflation, unemployment, and gov
ernment surplus differentials as regressors. The
coefficients on the inflation and government
surplus variables have the anticipated sign, but
only the government surplus variable is statisti
cally significant.18 The coefficient on the unem
ployment differential has the “wrong” sign, but
is not statistically different from zero.
Models 2-4 in table 3 all include the differen
tial in sheltered saving as a regressor. Models 2
and 3 essentially replicate the crucial Carroll and
Summers result — the coefficient on SHELT is
positive, large, and statistically significant. The
coefficient on SHELT does become statistically in
significant when the U.S.-Canadian net wealth
differential is added to the basic regression model.
a. The null hypothesis that the corresponding coefficient is zero can be
rejected at the 99 percent confidence level.
b. The null hypothesis that the corresponding coefficient is zero can be
rejected at the 95 percent confidence level.
c. The null hypothesis that the corresponding coefficient is zero can be
rejected at the 90 percent confidence level.
NOTE: The dependent variable is the U.S.-Canadian differential in private
saving relative to disposable income. All other variables are as defined in
equation (8). The variable p is the first-order autocorrelation coefficient of
the residual series. The numbers in parentheses are the absolute value of
the t statistics for the corresponding coefficient estimate.
SOURCE: Author’s calculations.
The after-tax real interest rate is included to
capture the effects of changes in the return to
saving. The expectation that a 6 > 0 assumes that
preferences cause substitution effects to domi
nate income effects and that ex post real rates
are reasonable proxies for ex ante real rates.
An important consideration in discussing the
expected signs of the coefficients in equation (8)
is that I have described the relationships that
would arise in an explicitly structural saving func
tion. Equation (8) is, of course, decidedly nonstructural. Thus, coefficient estimates derived
■ 16 The problems in interpreting coefficient estimates from equa
tion (8) are twofold. First, the coefficients in equation (8) are almost cer
tainly “mongrel parameters,” that is, unspecified functions of the under
lying structural parameters. Second, no attempt is made to control for
biases that may arise if the regressors are correlated with the error term
n i, a situation that seems likely. With respect to this latter problem, I did
some limited experimentation with instrumental variables (IV) estimation.
Unfortunately, the standard errors of the IV estimates were so large that
no interesting inferences were possible.
■ 17 Unemployment rates are taken from the OECD Labor Force
Statistics. The SHELT variable was constructed from data graciously
provided by Chris Carroll (for Canada) and from data reported in Carroll
and Summers (for the United States).
■ 18 The tables indicate coefficients that are statistically nonzero at
the 90 percent, 95 percent, and 99 percent confidence levels. In the Car
roll and Summers paper, reported t statistics are corrected for serial cor
relation. Although such corrections were made for all of the models
reported in this paper, I have chosen not to report corrected t statistics
for two reasons. First, almost all of the models estimated yield DurbinWatson statistics that fall within the “ inconclusive" range. Furthermore,
although many of the models estimated yield “ large” values of the firstorder correlation coefficient of the residual series (p), the null hypothesis
p = 0 is rarely rejected at the 95 percent confidence level. Second, work
by Mishkin (1990) indicates that the type of correction employed by Car
roll and Summers has undesirable properties in small samples. In most
cases, the basic message is independent of whether t statistics are cor
rected or uncorrected.
29
TABLE
4
Regression Results Including
Subsidy Variable
M odel
C o efficien t
V alu es
CONST
6
7
8
.100
.092
.093
.064
(4.7)a
(1.8)b
(6.1)a
INFL
UN
-.018
.004
.060
.108
(.14)
(.03)
(.21)
(.36)
-.077
.010
.025
.081
(.32)
(.04)
(.09)
(.29)
-.260
SURP
00
5
(1.8)b
SHELT
-.210
(1.4)
-.206
(1.3)
-.247
(1.5)
.353
.273
-.372
(.89)
(.50)
(.44)
.069
(.21)
.185
(.54)
R at
.062
NW
(1.0)
SUB
Adj. R 2
P
-4.25
-3.76
-3.80
-3.19
(8.0)a
(4.9)a
(4.7)a
(3.2)a
.893
.891
.885
.885
-.128
-.150
-.170
-.232
a. The null hypothesis that the corresponding coefficient is zero can be
rejected at the 99 percent confidence level.
b. The null hypothesis that the corresponding coefficient is zero can be
rejected at the 90 percent confidence level.
NOTE: SUB is measured as the ratio o f nonhousing personal interest
deductions to adjusted gross income reported on itemized returns. See
table 3 for other definitions.
SOURCE: Author’s calculations.
Note also that the sign on the net wealth coeffi
cient is positive and statistically significant.19
Table 4 presents results of regressions that add
to models 1-4 a variable measuring the average
borrowing subsidy. The subsidy variable is con
structed as the ratio of total nonhousing interest
deductions on personal tax returns to the adjusted
gross income of all taxpayers with itemized
deductions. This series on average subsidy rates
is constructed from various issues of the Statistics
■
19 Carroll and Summers do not find the same sensitivity of the
SHELT coefficient in their empirical analysis. The differences between
their results and mine apparently result from the data. As subsequent
results make clear, I find that no stable inference can be made about the
relationship
between U.S.-Canadian private saving differentials and dif
ferences in the amount of sheltered saving in the two countries.
http://fraser.stlouisfed.org/
Federal Reserve Bank of St. Louis
o fIncom e fo r Individuals (published by the In
ternal Revenue Service).20
The results in table 4 are striking. In every
case, the null hypothesis that the subsidy vari
able has zero effect on private saving is easily
rejected at the 99 percent confidence level. As
would be expected, the explanatory power of
the saving models also increases when the sub
sidy variable is included— in some cases, sub
stantially.
It is necessary to bear in mind, however, that
the average subsidy variable included in these
regressions is at best a crude proxy for the vari
able that is theoretically important — namely,
the m arginal subsidy rate on consumption
loans. In fact, it is difficult to distinguish move
ments in the subsidy variable that result from
changes in tax incentives for borrowing from
movements that result from shifts in the demand
for consumption loans that are not associated
with tax distortions.
For example, suppose that an individual,
facing no change in borrowing subsidies, simply
decides to borrow an extra $10 at the margin.
Suppose further that the rate of interest on this
loan is 10 percent. Then the individual’s saving
falls by $10 while his or her interest expense rises
by $1. This single episode would suggest that the
coefficient on the subsidy variable constructed
from reported interest expense is -10, even
though the borrowing behavior had nothing to
do with tax-related borrowing subsidies.21
The regressions reported in table 5 replicate
the regressions reported in table 4, with the sub
sidy variable calculated as 20 percent of the
average nominal annualized return on threemonth Treasury bills. Because personal interest
deductibility provisions did not change during
the sample period, exogenous changes in bor
rowing subsidies arose through two channels—
changes in structural marginal tax rates and
changes associated with variation in the rate of
inflation in the context of a tax code that allowed
for the deductibility of nom inal interest expense.
The subsidy variable used for the regressions in
table 5 is designed to capture the effects of the lat
ter channel.22
■ 20 Values for personal interest deductions are interpolated for the
odd years from 1961-1971 and for 1974 by assuming that total interest
deductions and mortgage-related interest deductions increase from the
previous tax years at the same rate as total itemized deductions.
■ 21 I am grateful to Chris Carroll for suggesting this example, as
well as the alternative subsidy variable discussed in the subsequent para
graphs.
■ 22 Twenty percent is chosen as a rough approximation to the
average marginal subsidy rate on borrowing in accordance with the num
bers reported in table 1 of Altig and Davis (1989).
TABLE
5
Regression Results with
Alternative Subsidy Variable
M odel
C oe fficie n t
V alues
CONST
INFL
9
10
11
.016
.017
.017
-.012
(2.1)a
(2.2)a
(2.1)a
(.72)
.227
(1.7)
UN
SURP
.221
(1.6)
12
.142
.214
(.43)
(.70)
.072
.138
.113
.167
(.28)
(.49)
(.37)
(.59)
-.506
-.438
-.441
-.458
(3.5)b
(2.5)a
(2.4)c
(2.7)a
.326
.428
-.873
SHELT
(.69)
R at
(.69)
(1.0)
-.094
.171
(.26)
(.48)
NW
.111
(2.0)c
SUB
Adj. R 2
P
-2.94
-2.60
-2.58
-2.00
(6.9)b
(3.9)b
(3.8)b
(2.9)a
.867
.864
.856
.877
-.074
-.068
-.064
-.232
a. The null hypothesis that the corresponding coefficient is zero can be
rejected at the 95 percent confidence level.
b. The null hypothesis that the corresponding coefficient is zero can be
rejected at the 99 percent confidence level.
c. The null hypothesis that the corresponding coefficient is zero can be
rejected at the 90 percent confidence level.
NOTE: SUB is measured as 20 percent of the average annualized return
on three-month Treasury bills. See table 3 for other definitions.
SOURCE: Author’s calculations.
The results in table 5 do not differ appreciably
from those reported in table 4. Although the coef
ficients on the subsidy variables decrease in mag
nitude, they remain large in absolute value and
are always statistically different from zero. Fur
thermore, as in the regressions reported in table
4, inclusion of the subsidy variable renders the
SHELT variable insignificant in all cases.23
Table 6 presents the results of regressions based
on other variations of the model given in equation
(8) for each of the two subsidy variables used in
tables 4 and 5. Models 13-16 report the results of
estimated models in which demographic and
income-growth variables are included as explana
tory variables, extensions suggested by the theoreti-
cal model in section I. Models 13 and 14 include
the U.S.-Canadian differential in the percentage
of the population aged 15-65. Models 15 and 16
report results in which the real GNP growth-rate
differential is included as a regressor. 24
Models 17 and 18 of table 6 report results
with personal saving taken as the dependent
variable and corporate saving introduced
separately as a regressor. Analogous to the ob
servations made about the government surplus
variable in equation (8), corporate saving, after
controlling for total wealth, should have a onefor-one negative effect on personal saving if in
dividuals “pierce the corporate veil.” 25
In every case, including numerous regres
sions not reported in the tables, the result is the
same. With the arguable exception of the
government surplus variable, the borrowing
subsidy, however measured, is the only explan
atory variable that consistently shows up with a
statistically significant effect on the U.S.Canadian saving differential. Furthermore, the
effect is always negative, and strongly so.
One further set of tests is reported in table 7.
Because borrowing subsidies are zero for
Canada, all variation in the subsidy variable
arises from the U.S. data. The regressions in
table 7 are therefore based on U.S. data alone.26
Although the models with the subsidy variable
constructed from Treasury bill rates yield results
that are consistent with regressions based on
U.S.-Canadian saving differentials, it is apparent
■ 23 The subsidy proxy included in the table 5 regressions is, of
course, subject to some of the same potential endogeneity problems as
the subsidy variable employed in the table 4 regressions. For example,
suppose that individuals in the economy anticipate better times ahead
(and that these expectations are not closely related to effects that are con
trolled for by the inclusion of unemployment or GNP growth differen
tials). Permanent-income theory then tells us that the response w ill be an
average increase in the desire to borrow. The resulting shift in the ag
gregate saving curve will drive up both real and nominal interest rates
(holding expected inflation fixed).
■ 24 If faster GNP growth means steeper life-cycle productivity
profiles, the results of the simulations in section I suggest that coeffi
cients on the GNP growth differential should be negative. However, the
growth-rate differential may also pick up changes in cyclical conditions
not captured by the unemployment-rate differential. This latter interpreta
tion seems more likely in light of the significant positive coefficient es
timates reported in table 6.
■ 25 The necessity of controlling for total wealth is emphasized in
the empirical studies by Auerbach and Hassett (1989) and Poterba
(1989). The results in these papers suggest to me that individuals do in
deed internalize corporate saving when making personal consumption
decisions. However, the evidence is, as usual, ambiguous.
■ 26
I am grateful to Randall Eberts for suggesting these regressions.
31
TABLE
6
Regression Results with
Alternative Models
M odel
C oefficient
Values
14
15
16
I7 a
18a
.065
-.056
.082
-.057
.071
.015
(1.8)b
(2.0)b
(2.3)c
(.30)
(3.9)d
(2.5)c
.293
(.88)
.271
.289
.263
.380
(.90)
(.87)
(.99)
.294
.285
.102
(.98)
(.84)
(.45)
13
CONST
INFL
.111
(.36)
UN
SURP
.078
-.822
(.27)
(1.4)
-.242
-1.26
(1.4)
(2.9)c
-.306
-.481
(1.9)b
(2.7)c
CORP
SHELT
-.193
(.74)
-.439
(2.6)c
-.075
(.28)
.64
.442
(1.3)
(.70)
-2.4
.144
-.617
(.42)
(2.0)b
(.16)
(.64)
.186
.401
.283
.222
(.52)
(.98)
(.85)
(.60)
(.14)
.131
(.47)
.059
.104
-.005
.084
-.014
.002
(.34)
(.05)
NW
(.87)
POPRAT
(1.6)
.031
-.011
(.13)
(.05)
YGROW
(.07)
.204
(1.6)
-3.19
-3.24
(3.1)d
(3.4)d
SUB 2
-1.88
(1.2)
.034
.097
(.65)
-2.65
(3.4)d
-1.82
-1.89
(2.6)c
(2.8)c
(2.6)c
.878
.871
.924
-.221
-.383
-.276
Adj. R 2
P
.193
(.80)
-.364
R al
SUB I
-.192
(1.4)
(1.3)
.873
.910
.896
-.193
-.122
-.009
a. The dependent variable is the personal saving rate differential.
b. The null hypothesis that the corresponding coefficient is zero can be rejected at the 90 percent confidence level.
c. The null hypothesis that the corresponding coefficient is zero can be rejected at the 95 percent confidence level.
d. The null hypothesis that the corresponding coefficient is zero can be rejected at the 99 percent confidence level.
NOTE: POPRAT is the differential in the percentage o f the population aged 15-65; YGROW'is the differential in real GNP growth rates;
CORP is the differential in private minus personal saving rates; SUB 1 is the subsidy variable as defined in table 4; and SUB 2 is the subsidy
variable as defined in table 5. See previous tables for other definitions.
SOURCES: Author’s calculations and OECD National Accounts, various issues.
TABLE
7
Regression Results for
U.S. Personal Saving
M odel
C oefficient
V alues
19
CONST
UN
SIM P
SHELT
Rdt
22
.107
.085
.066
23
(3.5)c
(2.8)a
.499
(2.4)a
(.36)
.103
(2.1)b
-.489
(2.2)a
-.515
.086
-.071
.007
-.472
-.024
(1.8)h
(.52)
(.24)
(.04)
(1.9)b
(.13)
-.271
-.643
(3.2)c
-.106
-.373
-.444
-.636
(1.3)
(.42)
(2.3)a
(2.3)a
(3.2)c
-1.21
-1.19
-.194
-1.52
(1.5)
(2.3)a
(.21)
-1.31
(2.6)a
-.675
.028
00
(5.9)c
-.466
(1.2)
(2.1)a
-.771
.463
-.492
(3.0)c
(2.0)b
(2.0)b
.002
.009
(3.2)c
NW
(.54)
.006
(1.4)
.008
(2.7)a
YGROW
.175
.090
(1.8)b
(1.2)
(1.2)
Adj. R 2
P
.655
.791
-.195
-.012
.310
.756
-0.18
(1.2)
-2.60
-1.91
(4.6)c
.490
.322
(1.2)
(.25)
1.68
(4.0)c
(1.3)
.007
-1.18
-3.44
.325
(2.1)a
2.80
SUB 2
.079
(8.2)c
.001
(2.6)a
SUB I
24
.079
(8.1)c
(2.8)a
INFL
21
o
.060
20
(2.4)a
.745
.797
.040
.052
a. The null hypothesis that the corresponding coefficient is zero can be rejected at the 95 percent confidence level.
b. The null hypothesis that the corresponding coefficient is zero can be rejected at the 90 percent confidence level.
c. The null hypothesis that the corresponding coefficient is zero can be rejected at the 99 percent confidence level.
NOTE: All variables refer to the U.S. values o f the variables defined in earlier tables. The dependent variable is U.S. personal saving as a
percentage of disposable income. See table 6 for other definitions.
SOURCE: Author’s calculations.
33
that the effects of borrowing subsidies are far
less consistent when included as regressors in
the U.S. private saving-rate models. Note also
that the sheltered saving variables are in some
cases negative, large, and statistically significant.
Explaining these anomalies is an important
topic for future investigations.
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