The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Economic
Review
Federal Reserve Bank
of San Francisco
Fall 1990
NUlIlber 4
Frederick T. Furlong
Tax Incentives for Corporate Leverage
in the 1980s
Sawaichiro Kamata
Managing Risk in Japanese Interbank
Payment Systems
Thomas 1. Sargent and
Francois R. Velde
The Analytics of German Monetary Unification
Ih b le o f Contents
Tax Incentives for Corporate Leverage in the 1980s „„09009e8, 0s 0„0<00*0*»„ 00„. 3
»
Frederick T. Furlong
Managing R isk in Japanese Interbank Payment Systems . . , e.. „ . . . . . . . . . . . . » . . 18
Sawaichiro Kamata
The Analytics of German Monetary Unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Thomas J. Sargent and Francois R. Velde
Federal Reserve Bank of San Francisco
1
Opinions expressed in the Economic Review do not neces
sarily reflect the views of the management of the Federal
Reserve Bank of San Francisco, or of the Board of Governors
of the Federal Reserve System.
The Federal Reserve Bank of San Francisco’s Economic Review is
published quarterly by the Bank’s Research Department under the
supervision of Jack H. Beebe, Senior Vice President and Director of
Research. The publication is edited by Barbara A. Bennett. Design,
production, and distribution are handled by the Public Information
Department, with the assistance of Karen Rusk and William Rosenthal.
For free copies of this and other Federal Reserve publicatons, write or
phone the Public Information Department, Federal Reserve Bank of San
Francisco, PO. Box 7702, San Francisco, California 94120. Phone
(415) 974-2163.
2
E conom ic R eview / Fall 1990
Tax Incentives for Corporate Leverage in the 1980s
Frederick T. Furlong
This paper shows that the rise in nominal interest rates
boosted the income-tax related incentives for corporate
leverage in the 1980s, but market-value leverage among
nonfinancial corporations in the latter half of the 1980sstill
was higher than would be expected given the estimated tax
incentives.
Research Officer, Federal Reserve Bank of San Francisco. The author thanks the editorial committee, Reuven
Glick, BharatTrehan, andMark Levonianfor their helpful
comments, and Michael Weiss for his valuable research
assistance.
Federal Reserve Bank of San Francisco
The 1980s were marked by a greater emphasis on debt
financing by corporations. This shift away from equity
financing is apparent in the rise in the aggregate, bookvalue, debt-to-equity ratio of nonfinancial corporations.
As shown in Chart 1, aggregate, book-value leverage
began rising in 1984, corresponding with an unprecedented surge in the net retirement of equities that many
attribute to the increase in corporate restructuring in
the 1980s.
The decade also was punctuated by two key tax reform
laws that brought about major changes in marginal income
tax rates. The 1981 tax reform act, for example, reduced the
maximum marginal tax rate on ordinary, personal income
from 70 percent to 50 percent. The 1986 tax reform act further reduced the maximum rate on ordinary, personal income, lowered the maximum tax rate on corporate profits,
and raised the maximum marginal tax rate capital gains.'
With this combination of developments, it is only natural to look for a link between the income-tax rate changes
and the shift away from equity and toward debt financing
by nonfinancial corporations during the 1980s. This paper
examines this connection. It differs from previous studies
in two ways. First, it considers the effects on corporate
leverage of changes in nominal interest rates working
through tax incentives as well as the direct effects of
changes in income-tax rates. The analysis in this paper
suggests that tax-related incentives toward leverage increase with nominal interest rates, and that this interest
rate link had a pronounced influence on income-tax incentives for corporate leverage in the 1980s. Moreover,
changes in income-tax rates, in theory, cause the nominal
interest rate to change, thereby partly offsetting the direct
effects of income-tax rate changes.
This paper also differs from previous studies in that
it evaluates the relationship between income-tax incentives and aggregate, market-value leverage among nonfinancial corporations. The empirical evidence indicates
that market-value leverage among nonfinancial corporations in the latter part of the 1980s was greater than can be
accounted for by income-tax incentives alone. This finding
is consistent with the predominant view in the literature
that factors such as financial innovation and deregulation,
3
Chart 1
Book-Value Leverage
and Net Issuance of Equity
Billions of
Dollars
50
o
-50
Ratio
.55
-1-----.. . . . ,. .". " " " . ,-" -
.50
''''¥v
Net Issuance .,
of Equity
(quarterly) *
-
-100
.45
.40
.,
.35
Book-Value
Debt-to-Equity **
(annual)
-150
-
-h-".-,.."--,-,-,.,..,-,-,--,-,-,.,....,--,-,-.,.....,-,....,...-r...,.-,-,,.-r-rr-,-,-""";+
52
56
60
64
68
72
76
80
84
.30
• 25
89
*Basedon seasonally-adjusted quarterly data at annualrates for
nonfinancial corporations.
**Based on annual data for nonfinancial corporations.
relaxed antitrust standards, improvements in "takeover
technology, " and higherlevels offree cashflow, ratherthan
income-tax incentives, contributed to higher leverage in
the 1980s. 2
This latter result is of particular interest in that the
supposed boost to corporate leverage in 1980s is not
apparentin the level of market-value leverage among nonfinancial corporations. This point is illustrated in Chart 2,
which traces the market-value debt-to-equity ratio (D/E)
for nonfinancial corporations. Theestimates of leverage in
the chart are based on Flowof Funds and National Income
Accounts data." Thechart shows that market-value corporate leverage has tended to increase since the early 1950s.
The most apparent run-up in leverage, however, occurred
in the early 1970s, notthe 1980s. In fact, the average level
of market-value leverage for the 1980s was aboutthe same
as that for the second half of the 1970s. 4
Thepaperpresents a model relatingthemarginal benefit
of corporate leverage to income tax rates and the nominal
interestrate. Thetheoretical framework is used to examine
how and why income-tax incentives for leverage changed
over time. The estimated empirical relationship between
income-tax incentives and corporate leverage then is used
to determine the contribution of income-tax incentives to
higher market-value, nonfinancial corporate leverage in
the 1980s.
Chart 2
Market-Value Debt-to-Equity Ratio
Percent
80
70
60
50
40
30
20
--!-r,......,.-,...,...,e-r-rr-.,....,..-r-r-.-.--r.......-r-,......,.-,...,...,..............,....,..-r-r-,....,...,.--,-,-..,...."..............
52
56
60
64
68
72
76
80
84
89
Based on seasonally-adjusted quarterly data for nonfinancial corporations.
4
Economic Review I Fall 1990
I. The Model
Income Taxes and Leverage
To illustratehow income taxconsiderations can affect a
firm'schoiceregarding market-value leverage, thevalue of
a firm(project) financed onlywithequity is compared with
the value of the same firm financed also with some debt.
Assuming two timeperiods, let I be the initial investment,
Y be the net nominal return from the projectin the second
period, andp be theinflation rate from Period 1 to Period 2.
For simplicity, it is assumed that all investors have perfect
foresight.
All investors are assumed to face flat tax rates on
ordinary, personal income (tp), corporate profits (tJ, and
personal, equity income (ts)' Furthermore, profits are paid
both in the form of dividends and capital gains in proportions wand (1 - w), respectively, where 0 S w :; 1. The
marginal tax rate on personal, equityincome is defined as
the weighted average of an individual's marginal tax rate
on ordinary, personal income and the marginal tax rate on
capital gains, such that ts = wtp + (1- w)tk , where tk is
the tax rate on capital gains. 5
With 100 percent equityfinancing, the value of the firm
in Period 1 is the discounted value of the gross, after-tax,
real return in Period 2:
_ 1+ {(l- tJ [w(1
VE
-
tp ) + (1- w)(11+ r
un- pI
' (1)
where r is the real after-tax required return. The required real after-tax return is exogenous and applies to all
investors.
Toincorporate theeffects ofleverage, theinitialinvestor
is assumed to issue debt to other (outside) investors in
Period 1 in some proportion, a, of the initial investment,
where0 < a < 1.6 Thenominal rate-of-return on the debt,
R, is the sum of the real required rate-of-return andthe rate
of inflation adjusted for taxes on interest income, so that
R = r+p
(2)
1- tp
This expression is the Darby (1975) respecification of the
Fisherequation, and it implies that an increase (decrease)
in the marginal tax rate on ordinary, personal income will
raise (lower) thebefore-tax, nominal interestrateondebt.7
Given these assumptions, the value of debt in Period 1
can be expressed as
_ _ aI+aI[R(1-tp ) - p ]
D-aIl+r
'
(3)
The value of the firm with debt financing, then, can
be derived from (1) and (3). This is accomplished by
adjusting the before-tax claims of the equity holderin (1)
by the before-tax claimsof the debtholders and adding the
after-tax value of debt. The value of the firm with debt
financing is:
!-D+(Y-DR){(l U[w(1+(1 w)(l-tk)J)
VD = ------...:-----=---.!.:.------...:::......:...-'=-----l+r
D+D[R(1
-p]
+ -----------:.1+r
or
l+r
From (4), it can be seen that the initial investor would
have an incentive to use debt financing as long as the tax
rate on interest income is less than the effective rate on
equityincome-that is, as long as tp < [tc+ t/1- tc )] ' The
tax rate on equity income reflects the double taxation of
corporate profits-first whenthe corporation pays taxes on
earnings and again when personal taxes are paid on dividends or capitalgains. Intereston debt, on theotherhand,
is tax-deductible for corporations, and, thus, is taxed only
once, as ordinary, personal income.
When interestincome is taxed at a lower ratethanequity
income, then, the value of the firm is positively related to
the amount of debt financing. For the case in which the
initial investor issues debt to finance the project, the
marginal benefit of debt versus equity financing is
g= aVD
aD
= R{(1-
-(1
tc)[w(l1+r
+(1
w)(1-tk ) ]} >0. (5)
For an existing corporation, (5) is the marginal tax
benefit fromusingdebt (ratherthan equity) to finance new
investment. 9 The expression shows that the income-tax
incentives for leveraging are a function of the marginal tax
rates as well as the nominal interest rate.
The reason the nominal interestrate has an effectis the
presence of theinflation premium. 10 From(5), theeffectof
inflation, and, thus, of the nominal interest rate, on the
incentives for leveraging, holding taxes constant, is:
(1-U[w(1+(1 w)(l-tk ) ]
1 - --'----"-------'-
1- - - - - - - - - ' - - - - - >0.
1+r
(6)
where D is both market-value and book-value of debt."
Federal Reserve Bank of San Francisco
5
An increase in inflation (rise in the nominal rate of return)
reinforces the positive effect on the value of the firm from
issuing debt, assuming that the tax rate on interestincome
is less than the effective rate on equity income." The
reason for this is that the higher nominal income due to
higher inflation is taxed at a lower rate when it is taken as
interest income rather than as equity income.
The unambiguous sign in (6) in part stems from the
absence of "bracket creep," which is assumed away by
having flat tax rates. With a progressive tax rate structure
and no inflation indexation, tp would risewithinflation due
to bracket creep. If the marginal tax rate on ordinary
income rises due to inflation, the theoretical effects of
inflationon the incentives forleveraging are ambiguous. 12
In the U.S., the 1981 tax reform act introduced inflation
indexation (effective in 1985), but in prioryears the marginal taxratesforindividuals increased withinflation. In any
case, the empirical evidence in the next section indicates
that the bracket creep effecthas not dominated.
The effect of a change in the tax rate on ordinary,
personalincome on the incentives fora firm to leverage can
be shown formally by differentiating (5) withrespectto tp '
This yields
ag
aR {(1-
atp
atp
+(l-w)(l-tk )])
g=
+--'--l+r
+(l-W)(l-t
)] }
R { 1 - - - - - - ' - - - - - - ' -k1-
l+r
R[(1-t
l+r
= 0 when w
1
{ <Owhenw< 1 .
(7)
As background to the discussion in theempirical section
on the effects of interestrates and tax rates on income-tax
incentives for leveraging, it is useful to consider the two
sets of termson theright-hand sideof (7). Thesecond setof
terms on the right-hand-side of (7) represents the direct
effect of a change in tp on the marginal benefit from an
increasein leverage. This termis negative forall allowable
values of w-that is, 0 S w S 1. Thisdirecteffectgenerally
is what analysts have in mind when arguing that lower
marginal tax rates on ordinary, personal income favor
greater corporate leverage. 13
When debt is issued to outside investors, the overall
6
(r+ p )te
1+r .
Fora given after-tax rate of return, the marginal benefit of
leverage depends on the corporate tax rate, but not on the
other tax rates, when w = 1.
From (5), it also follows that the incentives for issuing
debt versus equityto finance newinvestment are positively
related to the tax rates on corporate profits and capital
gains-that is,
or
c)w-1]
+----
_ R(I- tp)te
1 +r
g-
or, in the more familiar form,
R[(l- tJw -1]
(l-tc)[w(l-
effect of a change in tp on the incentives for leveraging,
however, will be less negative than that suggested by the
directeffect. Thisis true sincea changein the personal tax
rate alters the before-tax, nominal rate of retum.P The
effect of the change in the nominal interest rate is representedby thefirst setof termson theright-hand-side of (7).
This set of terms is positive for allowable values of w, and
increases with w. Ignoring the feedback of tax rates on the
nominal interestrate, then, would lead to an overstatement
of the effect of a change in tpo
Thus, the sign of thederivative in (7) is negative as long
as somecorporate profits are realizedin the formof capital
gains (W<1).15 A higher marginal tax rate on ordinary
income, then, would lead to less debt and lowerleverage.
Likewise, a lower tax rate would lead to more debt and
higher leverage.
However, if profits are paid out only in dividends
(w= 1), then, changes in a flat marginal tax rate on
ordinary, personal income would not affect the marginal
benefit form leveraging. From (5), the marginal benefit
from leveraging would be
dg
dte
= R{w(1- tp )
+ (1- w)(1- tk ) } >0
1+ r
(8)
and
dg
:.l
utk
=
R(1- te )(1 - w)
I +r
>0.
(9)
A higher corporate tax rate or higher personal tax rate on
capital gains would lead to an increase in debt and leverage. 16 The reason is the highertax rateslowerthe returnon
equity income relative to that on interest income.
Determination of Corporate Leverage
When financing new investment an investor would
choose all debtwhenthetaxrateonequityincome is higher
Economic Review / Fall1990
thanthaton interestincome, if thetaxtreatment of interest
and equityincomewere the onlyconsideration. Pure debt
(or pure equity) is not the observed pattern of corporate
financing, however, so otherfactors mustaffect the choice
of equity financing versus debt financing. Corporate leveragedecisions, forexample, can be affected by non-debt tax
shields associated with depreciation deductions and investment tax credits. DeAngelo and Masulis (1980) point
out that non-debt tax shields offset the income-tax advantage ofleverage and could be influential enough to determine DIE ratios for individual firms. 17
Non-tax considerations also can affect leverage; many
of these make leverage more costly, and work to offset
income-tax incentives favoring debt financing. An oftencited non-tax impediment to debt financing is the cost of
bankruptcy. The argument is that dead weight losses are
associated with a firm becoming insolvent and notmeeting
its debt obligations.P Everything else equal, at some
degreeof leverage, furtherincreases in debt financing will
raisetheprobability of bankruptcy andtheexpected costof
bankruptcy. Hence, bankruptcy costs would bias a firm
toward equity financing, and changes in expected bankruptcy cost would be negatively related to changes in
DIE ratios.
Costs associated with information asymmetries and
agency problems alsocan be affected by, and in tumaffect,
the degree of corporate leverage. 19 In thecase of anownermanaged firm, the manager (agent), who has more information about the firm than do outside investors, has
incentives to increase the firm's risk to the detriment of
the debtholders (principals). Ex post, such incentives for
risk-taking will increase with leverage.P In Jensen and
Meckling (1976), the monitoring and other agency costs
associated with outside financing will be borne by the
ownerand reduce the value of the firm relative to its value
with 100 percentinsidefinancing. To theextentthatinside
financing is identified with equity and outside financing
with debt, information asymmetries and agency costs
would serve to offset the tax shield advantages of debt,
and, thus, limit DIE ratios.
For many corporations, of course, agency problems
exist between managers and non-manager stockholders.
Forsuch firms, much of the equity as well as the debt can
be viewed as outside financing. With agency costs associated both with outside equity and debt, such costs would
notnecessarily increase monotonically withleverage. Jensen and Meckling argue that, for a given volume of inside
financing and firm size, total agency costs should fall and
then rise as the fraction financed through outside equity
rises.>' In this context, a firm's DIE mix, in principle,
could be determined uniquely without tax effects.
Even so, the income tax effects discussed above can be
important influences on firms' debt and equity choices. 22
Theoptimal DIE ratiofora corporation should balance the
marginal effects from leveraging related to income-tax
factors and othertax andnon-tax factors. With uncertainty,
therewould be an expected marginal benefit from leveraging associated withincome tax considerations comparable
to (5). Given that the expected marginal benefit from
leverage is positive, in equilibrium the expected net marginal effect of all other factors on leverage must just offset
that benefit.
Assuming that the expected net marginal cost of other
factors is some function fO of the level of leverage,
represented by the DIE ratio, and a vector of other variables, X, the long-run level of leverage would satisfy the
condition,
(10)
g - f(DIE, X) = 0,
where g in thiscontext is theexpected marginal income-tax
benefit from leveraging. If this equality does not hold at a
given point in time, a corporation could be expected to
adjust its leverage over time to eliminate the difference
between the expected marginal benefit and the marginal
cost.
II. Empirical Results
In this section the theoretical constructs developed
above are used to evaluate empirically how income-tax
considerations for corporate leverage have behaved and
how these incentives have affected aggregate leverage
among nonfinancial corporations in the 1980s. The analysis proceeds first by evaluating howincome-tax incentives
per se changedovertime and thenby relating thechanges
in aggregate, corporate leverage to the estimated incometax incentives.
Federal Reserve Bank of San Francisco
Estimated Income-Tax Incentives
To evaluate quantitatively how and why income-tax
incentives have changed overtime, estimates of the marginal value of issuing corporate debt can be derived by using
(5). Usingthe undiscounted value, the marginal gain from
leveraging is defined as:
G=R {(l- tp ) - (1- U[w(1- tp )
+ (1- w )(1- tk ) u
(11)
7
Using (11) requires choosing an appropriate before-tax
interestrateandestimating therelevant taxrates.Thenominal interestrateselected is the 10-yearTreasury bondrate.
Usinga Treasury security rate, ratherthana corporate bond
rate, tendsto understate the taxeffectsinceexpected ratesof-returns should be positively relatedto risk. On the other
hand, using acorporateinterest rate would overstate the
tax effectsinceit would be thepromised ratherthantheexpectedrate-of-return. In any case, theempirical results are
notverysensitive tothe useof eitheran interestrate oncorporatebondsor one on a longer-termTreasury instrument.
The estimated tax rates should reflect the marginal tax
rates of theinvestors that would holdthe additional debtor
equity issued. With regard to the stock of outstanding
securities, weobserved that individual investors hold both
equity and debt (apparently for diversification motives),
which means that, for estimating the average value of the
income-tax incentive, theappropriate tax-ratesforpersonal
income(bothinterest andequity) are weighted averages of
the tax rates forthe investors holding corporate securities.
If it is furtherassumed thatnew debtandequity is acquired
by investors in different tax brackets in the same proportion as the outstanding stocks, the average marginal tax
rates also are appropriate forevaluating the effects of taxes
on the marginal value ofleverage. In this section, then, (11)
is evaluated using estimates of the weighted average marginal tax rates for personal income-interest, dividends,
and capital gains, along with the maximum tax rate on
corporate profits.
For ordinary, personal income, separate estimates were
made for tax rates on interest income and for those on
dividend income.P This is necessary because debt and
equity instruments are not held in the same proportions
among investors subject to different marginal income-tax
rates. Equities tend to be held by investors with higher
incomes. The weighted-average marginal tax rates were
derived through 1986 based on data from Individual Income Tax Returns for the appropriate years. The average
marginal rate on interest income is based on the distribution of interestincome across adjustedgross income categories. Thisassumes thatthedistribution of corporate debt
holdings is proportional to the distribution of all debt. The
average marginal tax rate on dividends •. is •. based on.ehe
distribution of dividend income across adjusted gross
income categories.>' The estimates after 1986 were derived by applying the weights based on 1986 income data
to the marginal taxratesforthedifferent income categories
for each year.
Thetax rateon capital gains is basedon estimates oHhe
average marginal rate from the Congressional Budget
Office (CBO).25 TheCBOestimates represent taxrates on
realized capitalgains. Thecommon assumption is thatthe
effective tax rate is considerably lower than the rate on
realized gains because of the general deferral of taxes, the
selective realization of losses and gains, and the increase
of basis at death. The usual convention is to set the
effective capital gains tax rate equal to one-fourth the rate
on realized capital gains. 26
In estimating the average marginal personal tax rateon
equity income, w usually is set equal to one-halfbasedon
the observation that, historically, corporate profits have
been distributed about equally through dividends and
capital gains.27 Over the period from 1950 through 1988,
for example, the ratio of dividends to after-tax profits
among nonfinancial corporations averaged just about 50
percent.
Chart 3
Dividends to After-Tax Profits
Ratio
1.0
Avg. = 0.72
0.8
"
0.6
0.4
52
56
60
64
68
72
76
80
84
89
Based on seasonally-adjusted quarterly data for nonfinancial corporations.
8
Economic Review / Fall 1990
Chart3, however, indicates thatusinga fixedvalue for w
may not be appropriate. The dividend to profits ratio
jumped in the 1980s, averaging 72 percent after 1981 and
44 percent from 1950 through 1981. The significance of
this change depends on whether the higherratio is permanent or temporary. The higherratio could reflect a permanent endogenous response to the shift in tax rates in the
1980s, which narrowed the spread between the rate on
ordinary income and that on capital gains.
Alternatively, thechange in theratiocouldbe temporary.
First, corporations may have increased dividends as a way
of adjusting leverage in response to developments in the
1980s that are argued to have encouraged debt financing.
Second, the rapid appreciation in stockprices in the 1980s
are indicative of higher expected profits. If dividends are
relatedto long-run profits, the higherratios of dividends to
current income observed in the 1980s could decline as
higher levels of profits are realized in the future.
Based on these considerations, two sets of weights are
considered, one with a value of w fixed at 0.44 and the
second with a value of w set equal to 0.44 for the period
through 1981 and equal to 0.58 after 1981. The choice of
0.58 for the morerecentyears assumes that the increase in
the shareof long-run profits paid out in dividends is equal
to half of the observed rise in the aggregate, dividends-toprofits ratio.
Chart 4 shows the estimates of G, whichare affected by
income tax rates as wen as by interestrates. Thedark line
traces the estimated values of G when w is allowed to
change, while the light line traces the estimateswhen w is
held constant. The chart shows that the tax advantage of
debt overequity financing increased, on balance, overthe
Percent
last three decades. The incentives were greatest in 1982
andremained relatively highthrough1984. Afterdeclining
markedly through 1986, they rebounded some through
1989. The estimates of the tax incentives for leveraging in
1989 were a bit lower than at the start of the decade and
about equal to the level prevailing in the mid-1970s.
Toidentify the relative importance income-tax rates and
the nominal interestratein determining movements in G, it
is useful to separate the twoeffects. To isolate the tax rate
effects, the term in braces in (11) commonly is used. This
approach amounts to measuring the effectof income taxes
holding the before-tax nominal interest rate constant.
Doingthis, however, ignores the theoretical feedback from
tax rates to the before-tax nominal interest rate.
The discussion in the previous section suggests that, in
theory, the moreappropriate approach would be to evaluate
the tax rate effects holding the after-tax nominal interest
rate constant. This says that the marginal effect of debt
financing should be expressed in terms of the taxrates and
the after-tax nominal interest rate. 28 Using (2) and (11),
the undiscounted marginal value of leveraging can be
expressed as:
G == (r+ p) {I _ (1- tc H w(1 - tp ) + (1- w)(1- tk ) ]
1-tp
(12)
where (r +p) is the after-tax nominal interest rate on
debt.29 In this expression for G, the term in braces, in
principle, captures theeffects of changes in tax rateson the
incentives for leveraging, including those due to changes
in the before-tax nominal interest rate that are related to
income-tax rate changes.
Chart 4
Income-Tax Advantage
of Debt vs. Equity
4.0
3.5
3.0
2.5
2.0
Change
weight
*
I
Fixed weight'*
1.5
1.0
O. 5
}
-h--,--,-...,...,-.,..-,-,..,-,,--,;-r-r...,.,......-,--,-...,...,-.,..-,-,..,-,,--,;-r-r.,..,-,
56
60
64
68
72
76
80
84
89
*Weight = 0.44 (1954-1981), weight = 0.58 (1982-1989).
**Weight = 0.44
Federal Reserve Bank of San Francisco
9
Chart 5 shows thataccounting fortheeffects of taxes on
the nominal •. interest rate alters the perspective on how
recenttax law changes have affected incentives for corporations to leverage. Theblacklineis thevalue ofthetermin
bracesfrom (B), multipliedby theaverage value ofthetenyearTreasury bondrateforJ978 and 1979. Thegreen line
is the value, ofthe termin braces from (12), multiplied by
the average oftheafter-taxten-year Treasury rate for 1978
and1979.
BothseriesinChartS, however, show thatthebiasinthe
income tax ratestowarddebt financing has declined since
aboutthe mid-l960s.Theupward trendin G, shown in the
previous chart,then, is dueto the rise in nominal interest
rates. Thatis, based-on these estimates, higher interest
rates,ratherthan. tax.policy,per se, have increased the
relative attractiveness of debtfinancing.
With respect to therecent tax law changes, the series in
Chart 5 indicate that the changes in income-tax rates
following the1981 taxreform actboosted theincentives for
leveraging. This would be expected, given that the major
income-tax changes in the 1981 act lowered marginal tax
rates on ordinary income, with the maximum rate reduced
from 70 percent to 50 percent. The increase in the bias
toward debt financing from this act, however, did not do
much more than offset the decline in the bias inherent
in U.S. income tax policy during the second half of
the 1970s. 3o
The relatively strong incentives for leveraging in the
early 1980s primarily reflect the higher nominal interest
rates that prevailed in that period rather than changes in
marginal tax rates. Moreover, the subsequent decline in
these incentives from 1984 through 1986 was due to the
Percent
drop in nominal interest rates,which essentially offset the
effects of the 1981 tax act. By 1986, the tax advantage of
debt versus equity financing was only.a'Iittleabovethe
levels prevailing in the 1970s(seeChart 4).
The income taxrate changesfoUowingthe 1986 tax act
reduced thebiastoward debtfinancing, asindicated by the
decline in the series plotted in ChartS. Although the 1986
taxact lowered marginal taxrateson ordinary income and
raised them on 'capital gains, which, accordingto<the
discussion above, should 'have Javol'ed debt financing,· it
also lowered the marginal tax rate on corporate profits,
which should have reduced thetaxbiastowarddebtfinancing. Theestimates in Chart5,showinganetdeclineafter
1986, suggest that the changeintheicorporate tax rate
simply dominated. However, the. effectofthe•lawis more
complicated. Thereduction in themaximummarginal tax
rate on ordinary, personal income from 50 percentto 33
percent (28 percent for the highest tax brackets) lowered
the average marginal tax rate' for individuals earning
dividend income by much more thanthe average marginal
tax rate for individuals earning interest income. Asa
result, the estimated taxincentives for leveraging were not
boosted much by the lower taxrateson ordinary, personal
income. In fact, in the case of the green line in Chart 5,
which takes intoaccount theeffects of taxratesonnominal
interest rates, the net effect of the changes in personal-tax
rates was to reduce the incentives for leveraging, and to
reinforce the effect of the lower corporate tax-rate. This is
not a resultthat would have been anticipated based on the
model presented above, in which marginal tax rates on
interest anddividend income areequal andmove together.
Chart 5
Income-Tax Advantage of
Debt vs. Equity Holding Interest
Rates Constant
3.00
Constant before-tax
nominal interest rate
2.75
2.50
'"
/
2.25
Constant after-tax
nominal interest rate
2.00
1.75
1.50 -t-r,..,..,..,-,..,.-"..,,....,.,..,..,..,..,..,-,....,.,,....,.,..,..,..,..,..,-,..,.-,,..,
56
10
60
64
68
72
76
80
84
89
Economic Review /Fall1990
Tax Incentives and Leverage
The discussion in this section turns to the empirical
evidence on the relationship between income-tax incentives and the aggregate, market-value, debt-to-equity ratio
fornonfinancial corporations. Theanalysis startswith(10),
and the assumption that expected values are based on
lagged observations, except for the marginal tax rates.31
For the empirical analysis, the marginal benefit from
leveraging due to income taxes is represented by G. It is
further assumedthat10 takes the form B I (D IE )f2 I' with
the marginal cost of leveraging hypothesized to be positively related to the level of leverage. The leverage ratio
(DIE) is the market-value, debt-to-equity ratio plotted in
Chart 2.
Whentheequality in (10) doesnothold, corporations are
assumed to adjust (at a cost) to the difference. Using the
log-linear change in leverage, the adjustment process can
be expressed as:
IlI0g(DIE)t = bo{1ogGt- 1
-
[bl +b210g(DIE)t_l]}
+ e,
or
IlI0g(DI Ev, = bologGt- 1 + CI + c210g(DI E)t-I + e., (13)
Allowing for stock price shocks, the leverage adjustment equation can be rewritten as:
1l10g(DIE)t
= bologGt- 1 + ci + c210g(DIE)t_l
+ b41l10gSPt + u.;
(14)
where thechangein stockpricesis thelogdifference of the
S&P500 index.P The coefficient, b4 , is expected to be
negative and of the same magnitude as b3 •
Toallow for more flexibility in the short-run dynamics
ofthe adjustment in corporate leverage, lagged values for
thelog changes in G 'and in DIE were included in (14).
Lagged changes in leverage were significant, but lagged
values of the change in tax incentives were not. The
regression results in the table were derived by including
the first and second lagged values for the change in
leverage.
Theresultsin the first columnof that table show thatthe
coefficients have the expected signs. The coefficient for G
is positive and statistically significant, while the one for
lagged leverage is negative and significant. The positive
sign on the constantterm indicates that BI is estimated to
be less than one. The coefficient on the change in stock
where Gt - I is basedon the ten-yearTreasury bond rate at
t-1 and the tax rates prevailing at t. In the expressions, bo
is expected to have a positive sign. That coefficient should
reflect the average cost of adjusting leverage, which is
assumed to be constant over time. The coefficient b, is
equal to 10g(BI), so the sign of b, depends on whether
O<B I <l, BI. = lor BI <l. This means that the sign of the
constantterm in (13), ci = bob l , couldbe positive, negative
or zero. The expected sign of the coefficient on lagged
leverage, C2 = bob2 , is negative. The term e, is a random
disturbance term.
One problem estimating (13) is that ex post changes in
aggregate corporate leverage reflect not only decisions
regarding debt and equity financing, but also exogenous
shocks to equity prices. If corporations take their share
prices to be random walks and do not react to contemporaneous changes in these prices, the change in corporate
leverage in period t that would be related to income-tax
incentives and the marginal cost of leverage could be
expressed as:
IlI0g(DIE)t + b3£llogSPt,
where SP represents aggregate stock prices, and b3 would
be expected to be equal to 1.32 On the other hand, if
changes in stock prices were exogenous and there were
offsetting adjustments to the effects of changes in stock
prices on leverage, b3 could be greater than 1.
Federal Reserve Bank of San Francisco
n
prices is significantly different from zero, and its absolute
value is greater than one, which suggests that corporations
may attempt to offset some of the the effect of stock price
changes that occur during a quarter.>' The empirical
results are very similar whether G is defined using the fixed
value of w or allowing w to change after 1981. The statistics
in the table are derived assuming the weight, w, changes.
These results, then, are consistent with the hypothesis
that market-value leverage among non-financial corporations is affected by the difference between the leverage
gains related to income taxes and the net cost of other
factors. Of central interest to this paper is whether that
relationship shifted during the 1980s. Such a shift should
be reflected in the values of the coefficients in (14). For
example, a larger estimated constant term for more recent
years would be consistent with developments not directly
related to income-tax factors in the 1980s, on balance,
favoring more debt financing relative to equity financing
than was the case in earlier years.
Data on the net issuance of equity by nonfinancial
corporations in Chart I suggests that a shift in the relationship might have occurred around 1984. The Quandt (1958)
likelihood method also was employed to help identify the
most likely date for a shift in the leverage relationship. The
test indicates that a likely break in the 1980soccurred in the
latter part of 1985.
To evaluate the statistical significance of the break in the
relationship, the results from the Quandt test were used.
Accordingly, a bivariate dummy variable was used to test
for a change in the constant term after the third quarter of
1985. The coefficient on the dummy variable, d85, in
Column 2 of the table is statistically significant. The
estimated increase in the constant term indicates that, even
on a market-value basis, changes in corporate leverage
have been larger in recent years than would be expected
given stock price movements and income tax incentives for
leveraging.
To evaluate the extent to which controlling for the effects
of income-tax incentives for leveraging makes a difference
to this results, the leverage equation was estimated without
G and lagged leverage. A comparison of the statistics for
the dummy variable in Columns 2 and 3 shows that the
estimated shift is smaller and only marginally significant
when only changes in stock prices are taken into account.
At the same time, the results in Column 4 indicate that
controlling for the effects of changes in stock prices is
12
important. When the change in stock prices is not included, the estimated coefficient for d85 is not statistically
significant. 35 As also can be seen from the results in
Column 4, income-tax incentives explain a fairly small
portion of the quarterly change. in aggregated, marketvalue leverage among nonfinancial corporations.
The regression results, then, suggest that changes in
market-value corporate leverage did increase significantly
in the latter part of the 1980s, and that influences beyond
income-tax incentives contributed to the increase. This
result combined with the data on the estimated income-tax
advantage of debt shown in Chart 4 suggest that changes in
income-tax incentives for leveraging were not the impetus
for the rise in corporate restructuring in the second half of
the 1980s.Asshown in Chart 4, in the latter part of the
1980s the estimated income-tax incentives for corporate
leveraging were low relative to the first part of the decade
and a bit lower on average than in the latter part of the
1970s.. The other influences that contributed to the higher
leverage could be those discussed in the introduction and
identified in other studies as contributing to the surge in
corporate restructuring in the second part of the 1980s.
While changes in income-tax incentives may not have
spurred the much discussed rise in corporate restructuring
in the second part of the 1980s, the relatively high estimated income-tax advantage of debt over equity financing
in the first half of the 1980s may have contributed to a
higher average level of leverage over the decade. The
strong tax-incentives in the first part of the decade should
have resulted in higher leverage than if the incentives had
remained at the levels prevailing in 1978 and 1979.
To estimate how much the tax incentives might have
affected corporate leverage during the 1980s, two dynamic
simulations were conducted using the historical relationship of the change in aggregate, market-value, nonfinancial
corporate leverage to income-tax incentives and lagged
leverage. The simulations were run beginning in 1980. For
one simulation G took on its historical values and in the
other G was set equal to its average value over the 1978-79
period. The simulation results show an average level of
market-value leverage for the 1980s that is about five
percentage points higher with the historical movement in
income-tax incentives than is the case when the income-tax
incentives are held at the levels prevailing in the latter part
of the 1970s.
EconomicReview / Fall 1990
III. Conclusion
Income-tax incentives forcorporate leverage are a function of nominal interest rates as well as income-tax rates.
The estimates of income-tax incentives for leveraging
indicate that nominal interest rates have been important.
Over the past 25 years, the rise in interest rates has
accounted for theestimated net increase in the income-tax
bias favoring debt over equity financing.
Even during the1980s, which were punctuated bymajor
changes in income-tax rates,theswings in nominal interest
rates had a significant impact on the estimated income-tax
advantage of debt financing. In the first half of the 1980s,
high nominal interest rates raised the income-tax advantage of debt versus equity financing for corporations
relative to the levels prevailing in the second part of the
1970s. The subsequent net drop in interest rates reduced
theincome-tax advantage in thesecond halfof the 1980s to
levels thatgenerally were notmuch different from those in
the latter part of the 1970s. This pattern suggests that
income-tax incentives per se were notthe catalysts for the
sizeable net reductions in equity associated with corporate
restructuring beginning in 1984. Nevertheless, the relatively high.income-tax incentives for leveraging in thefirst
part of the decade should have encouraged more debt
financing relative to equity financing and should have
contributed to a measurably higher average level of lever-
Federal Reserve Bank of San Francisco
ageoverthedecade thanwould have beenthe caseif those
incentives had remained at their lower pre-1980s level.
While income-tax incentives may not have provided the
impetus for corporate restructuring in the second part of
the1980s, accounting fortheireffectdoes helptoreconcile
to some extent the difference between the pictures presented by the data on book-value and market-value leverage It is somewhat surprising that a marked shift toward
debtfinancing in the 1980s is not obvious whenlooking at
aggregate, market-value leverage for nonfinancial corporations. However, evidence forsucha shift is found when the
change in market-value corporate leverage is weighed
against the changes in the benefits and costs of leverage.
When the effects of income-tax incentives are taken into
account, along withthe effects of changes in stock prices,
changes in market-value corporate leverage are significantly largerin the second halfofthe 1980s. This result is
consistent with a shift to debt financing that is related to
developments otherthanchanges inincome-tax incentives.
While the regression analysis does not identify the factors
that have boosted leverage, other studies suggest that
financial innovation and deregulation, an easing of antitruststandards, as well as an increase in free cash flow may
have been important influences.
s
.
13
NOTES
1. The 1986 act provided for a reduction in the maximum
marginal tax rate on ordinary, personal income from 50
percentto 33 percent, a reduction inthe maximum corporate tax rate from 46 percent to 34 percent, and an
increase in themaximum tax rate oncapital gainsfrom 20
percent to 33 percent.
Provisions ofthe1981 and1986 taxactsalso affected nondebt tax shields. For example, the 1981 act increased
investment incentives like accelerated depreciation and
taxcredits on equipment, while the 198? act reduced an~
eveneliminated certain non-debt taxshields. These provisions of the 1981 act tended to reduce incentives for
leveraging andthose of the1986 act tended to make debt
financing more attractive.
2. Gertler and Hubbard (1989) and Summers (1989), .for
example, argue that financial innovations like the :Ise
in junk bonds, which facilitated corporate restructuring,
probably were more important than tax rate changes .to
the rise in corporate debt. Auerb~ch (1989a,b) als~ dl?countstheimportance of changes In tax rates to the rise In
corporate borrowing. Jensen (1987) discuss.es the other
factors mentioned in thetext, with anemphasis onthe role
of freecash flow. Also seeJensen (1988). Free cashflow is
defined asthat portion of cash flow(profits plusdepreciation) that cannot be reinvested in the firm profitably.
3. The estimate of the market value of nonfinancial corporate equity is taken from the Flow of Funds Accounts.
Market-value corporate debt is the sum of the face value
of short-term debt from theFlow of Funds and anestimate
of the market value of long-term debt. The market value of
long-term debt is estimated by capitalizing the difference
between gross nonfinancial corporate interest expenses
and interest expenses on short-term debt by the average
corporate bond rate. The estimates of leverage represent
end-of-quarter figures.
4. Bernanke and Campbell (1988) and Strong (1988),
using different measures of aggregated corporate leve~
age, also find that market-value leverage among non~l
nancial corporations did not increase much on balance In
the 1980s.
5. In a two period model, distinguishing bet.ween dividends and capital gains is somewhat contrived. Also,
unless t = tk other considerations not explicitly in the
model afe ne~ded to explain whyprofits would notbe paid
out in the form subject to the lower tax rate.
6. With VE>I, it is possible for the initial investor to issue
debt such that a>1. In that case, the initial investor presumably would have to pay taxes on the proceeds in
excess of the book-value of equity in Period 1.
7. This differs from the assumption in Hochman and
Palmon (1985) in which theinterest rate on debt is fixed for
a given expected interest rate.
8. This would not necessarily be the case if the initial
investors financed the entire project and merely designated a portion of I as debt since it must be the casethat
14
(YIl)?:.Rfor a!1 equity financin~ t.o. b~ feasible. Iftheoriginal
investordesignated alloftheinitial Investment asdebt, the
market-value of the debt (as well as that of the firm) in
Period 1 would be
0'
1+Y(1-tp)-pl >0
1 +r
The nominal before-tax rate-of-return on 0' alsowould be
R.The measured rate-of-return on I, which would representthe book-value of debt, would be (YII)?..R.
The assumption that the debt is held by individuals other
than the original investor als? altersthetax ef!ects of debt
financing and the comparative s~atlcs Involving cha~ges
in the inflation rate and the marginal tax rates. The differencesarisebecause, with outside debt holders, a portion
of the gross income from the project cannot be sheltered
from double taxation and because the rate-of-return on
the debt varies.
9. The expression for themarginal tax effect w~en debt is
used to replace existing equity is somewhat dlf.ferent. ~n
thatcase the initial investor can be assumed to Invest lin
the project before issuing debt. If VE>I, then, replacing
the initial funds (the equity) with debt will involve capital
gains realized in Period 1. The tax on the capital gains
would reduce the marginal benefit from using debt when
replacing existing equity relative to the effect in (5). Using
Ea to represent thebook-value of equity, which isequal to I
with all equity financing, and EM to represent the mark~t
value of equity, which is equal to VE with all equity
financing, the marginal effect from replacing equity with
debt is
, _ R{(1-tp)-(1-tcHw(1-tp)+(1-w)(1-tk )]}
1 +r
g -
-
(EM - Ea )tk
EM
<g.
(5')
Strictly speaking, (5') represents the marginal effectfrom
leveraging on the value of the firm plus the wealth of the
initial investor. The lastterm in(5') represents theeffect on
thewealth of the initial investor from the taxation of capital
gains in Period 1.
A similar comolication arises in Hochman and Palmon
(1985). In a model with more than two periods a~~ no
growth in real assets, a firm would have to Issue additional
debt and pay the proceeds to equity holders in order to
maintain a constant capital structure. In that case, these
payments to equity holders would be taxed at the personal tax rate on equity income. A higher tax rate on
personal equity income would work to discourage such
restructuring.
10. In the two-period model, with inflation equal to zero,
the marginal value of leveraging is:
r
g = 1+ r
{1
_ (1-tcHw(1-tp)+(1-w)(1-tk ) ]
1- i;
}
.
Economic Review I Fall 1990
However, when the analysis is extended to an infinite
period model with perpetual debt the interest rate terms
no lonqer ~nter the expression for g. In that case, the
expression IS:
1
g =
-
(1-tc)[w(1-tp)+(1-w)(1-tk)]
1-t
'
p
which is the Miller (1977) expression for the gains from
leverage pe~ dollar of debt. ~ith an inflation premium in
the nominal Interest rate, the Interest rate terms remain in
the expression for g.
11. In a Miller (1977) type world, tax rates on interest and
~quit.Y income for the marginal investor are equal and
Inflation doesnot affectleverage for an individual firm. On
the other hand, Modigliani (1982), allows for benefits from
diversification, and argues that the incentive for leveraging are positively related to inflation. Rangazas and Abdullah (1987) also show that tax incentives for leveraging
are positively related to nominal interest rates under the
assumption that firms minimize costs. That study, however, assumes that the before-tax nominal interest rate is
constant for a given expected rate of inflation.
12. Hochman and Palmon (1985) also argue that the
theoretical effectsof inflation on leverage areambiguous.
H?wever, theyassume a Miller (1977) typeworld, soto get
this result they have to introduce into their model other
leverage-related costs. Without suchcosts in their model
the effects of inflation (without inflation indexation) ar~
unambiguously negative because onlythe bracket creep
effect comes into play.
13. See, for example, Auerbach (1989b) and Gertler and
Hubbard (1989).
14. From (2) in the text,
aR
atp
r+p
(1-t)2
p
R
="'1=t
p
>0.
15. Another complication in assessing the sign of (7) is
that theproportions of profits distributed asdividends and
capital gains likely are related to the tax rates on the two
types of incomes. In practice, a decrease in tp , for example, should leadto a larger portion of profits distributed as
dividends-that is, the weight on tp should be negatively
related to tp ' In this case, as long as the marginal tax rate
on capital gains, tk , is less than the marginal tax rate on
ordinary income,. tp , an. increa~e i~ the weight on tp increases the marginal gainfrom ISSUing debt. Thus, even if
the proportion of profits paid out as dividends changes
with tp , (7) remains negative for values of w less than one.
!6. Inthecasewhere debt isusedto retire existing equity,
It can be seen from the expression in Note 9 thattheeffect
of a change in tk on the marginal benefit from leveraging
will involve another term.
17. DeAngelo and Masulis (1980) areresponding to Miller
(1977), who argues thattax considerations can determine
leverage at the aggregate level, without doing so at the
firm level. DeAngelo and Masulis argue that, as leverage
Federal Reserve Bankof San Francisco
increases, the earnings thatcan be sheltered by non-debt
shields decline. A~ lev.erage increases, then, themarginal
tax advantage of Issuing debt (net of the loss in value of
the non-debt shields) should eventually decrease and
can go to zero. This means thatfactors affecting thevalue
of non-debt shields can affect the marginal tax benefit of
debt financing .
DeAngelo and Masulis also point out that inflation can
reduce the value of certain non-debt shields. They note
thatfor depletion anddepreciation allowances thedeductions. are fixed at the time of the relevant investment.
Therefore a rise in inflation and the nominal income of a
firm would diminish the effects of non-debt shields and
enhance the effect of the debt shield. This effect would
reinforce the positive effects that inflation has on the
incentives for leveraging in (7).
18. Bernanke and Campbell (1988) argue that "nearbankruptcy" ~osts, such as curtailment of projects dueto
a lack of funding, alsocan serve to reduce the attractiveness of debt financing.
19. Information asymmetries exist because a firm insider
like an owner-manager, knows more about the ex ante
investment opportunities, as in Meyer and Mujlud (1984),
or abo.ut the ~x post retur~s, as in Williamson (1986).
These Information asymmetries affect the cost of outside
funds ~e~ause.the interests ofthe insider (agent) often do
not coincide With those of the outsiders (principals).
20. See Furlong and Keeley (1989).
21. Financing by insiders still would be preferred, all else
equal. The amount of internal funds presumably would be
related to the net worth of insiders.
22. The tax effects relate strictly to the firms choice between debt and equity and not necessarily to the choice
between inside and outside financing.
23. The expression for the taxincentive for debtfinancing
becomes:
G=R{(1-tp;)-(1-tc)[w(1-tpe)+(1-w)(1-tk)]},
where tp ; isthe personal tax rate on interest income and tp
IS the personal tax rate on dividends.
e
24. This approach is used inWright (1969) and Rangazas
and Abdullah (1987), though the latter use the average
rate based on dividend income for both interest and
dividend income.
By using gross adjusted income categories, rather than
income actually taxed, thisapproach should overstate the
marqinal tax rates. Also, using only data on personal
Income tax rates could overstate the average rate given
thatcertain holders of debt and equity are argued to face
verylowor even zero marginal tax rates (see, forexample,
Summers (1989), Auerbach (1989b), King and Fullerton
(1984)). Nevertheless, the estimates of tax rates on interest and dividend income should be useful for examining
the m~vements in the income-tax incentive for leveraging
over time.
15
25. See How Capital Gains Tax Rates Affect Revenues:
The Historical Evidence.
26. SeeKing andFulierton (1984), page 222.
27. See, for example, Rangazas and Abdullah (1987).
28. Gandolfi.(1982) and Rose (1986) show that, with
taxes on capital gains(and tk<tp ) and depreciation allowances based on historical costs, the tax-amended
Fisher equation is more complicated than. the Darby
(1975) respecification.
29. Asareminder,theavere.ge tax rates on interest and
dividends are estimated separately. Following the notation in Note 23, (12) is
G=(r+p){1- (1-tc)[w(1-tp e)+(1-w)(1-tk ) ]
1-tpi
}.
30. This decline for the most part reflects the impact of
bracket creep on income tax rates and some rise in the
average marginal tax rate on capital gains.
31. Changes inthestatutory taxrates areknown ahead of
time, though exact income distributions are not.
32. In this case, firms would make decisions regarding
debt and equity based on the level of stock prices at the
16
beginning of the period. The change in leverage can be
rewritten as
(OIE)t
o,
NtSPt- 1
log[ (0IE)t-1 ] = log( 0t-1 ) - log( Nt - 1SPt - 1
SP t
- log( SP - ),
t
1
whereN isthenumber of shares. Ina givenperiod, thefirst
tworight-hand-side terms are the ones that would reflect
the decisions of firms.
33. The specification in (14) raises the issue of simultaneity bias, since changes in leverage can affect stock
prices. However, it seems reasonable that the dominant
channel of causationis from exogenous shocks toprices
affecting the market value of equity, and, thus, marketvalue leverage.
34. The magnitude of the coefficient alsocould be due to
the use of the S&P500 index to measure the change in
stock prices for all nonfinancial corporations.
35. Lagged values of the change in leverage were not
significant, so the regression for Column 4 wasestimated
without those variables.
Economic Review / Fall 1990
REFERENCES
Auerbach, Alan J. Leveraged Buyouts and Corporate
Debt. Hearing before the Committee on Finance,
January 25, 1.989a.
_ _.............~ •. "Tax Policy and Corporate Borrowing, " Processed. Paper delivered at a conference entitled, "Are
the Distinctions between Equity and Debt Disappearing?" sponsored by the Federal Reserve Bank of
Boston, October5-6, 1989b.
Bernanke, Ben andJohn Y. Campbell. "Is There aCorporate Debt Crisis?," Brookings Papers on Economic
Activity, 11988.
Congressional Budget Office. How Capital Gains Tax
Rates Affect Revenues: The Historical Evidence.
March 1988.
Darby, Michael R. "The Financial andTax Effects ofMonetary Policy on Interest Rates," Economic Inquiry, June
1975.
DeAngelo, Harry andRonald W. Masulis. "Optimal Capital
Structure Under Corporate and Personal Taxation,"
Journal of Financial Economics, 8 March 1980.
Department of theTreasury. Statistics of Income: Individual Returns. Various years.
Furlong, Frederick 1. and Michael C. Keeley. "Capital
Regulation andBank Risk-Taking: A Note,"Journal of
Banking and Finance, 13(December) 1989.
Gandolfi, Arthur E. "Inflation, Taxation, and Interest
Rates," The Journal of Finance, June 1982.
Gertler, Mark and R. Glenn Hubbard. "Taxation, Corporate Capital Structure, and Financial Stress," NBER,
Working Paper Series No. 3202, December 1989.
Hochman, Shalom and Oded Palmon. "The Impact of
Inflation on the Aggregate Debt-Asset Ratio," The
Journal of Finance, September 1985.
Jensen, Michael C. "The Free Cash Flow Theory of Takeovers: A Financial Perspective onMergers and Acquisitions and theEconomy," in eds. Lynn E. Browne and
Eric S. Rosengren, Merger Boom. Federal Reserve
Bank of Boston, 1987.
____ . "Takeovers: The Causes and Consequences,"
The Journal of Economic Perspectives, Winter 1988.
FederalReserve Bank of San Francisco
____ . and William Meckling. "The Theory of the
Firm: Managerial Behavior, Agency Costs and Ownership Structure," Journal of Financial Economics,
October1976.
King, Mervyn A. and Don Fullerton (eds.). The Taxation of
Income from Capital. NBER Monograph, The University of Chicago Press, Chicago London, 1984.
Meyers, Stewart C. and N. S. Majluf. "Corporate Financing
and Investment Decisions when Firms Have Information that Investors Do Not Have," Journal of Financial
Economics, June1984.
Miller, Merton H. "Debt and Taxes," The Journal of Finance, May1977.
Modigliani, Franco. "Debt, Dividend Policy, Taxes, Inflation and Market Valuation," The Journal of Finance,
May 1982.
Quandt, Richard E. "TheEstimation of theParameters of a
Linear Regression System Obeying Two Separate
Regimes," Journal of the American Statistical Association, vol. 53, 1958.
Rangazas, Peter and Dewan Abdullah. "Taxes and the
Corporate Sector Debt Ratio: Some Time Series Evidence," The Review of Economics and Statistics,
September 1985.
Rose, Louis A. "The Respecified Tax-Adjusted Fisher
Relation," Economic Inquiry, 24 April 1986.
Strong, John S. "The Market Valuation of Credit Market
Debt,"Journal of Money, Credit, and Banking, August
1989.
Summers, Lawrence H. Leveraged Buyouts and Corporate Debt. Hearing before the Committee on Finance,
January 25, 1989.
Williamson, Stephen D. "Costly Monitoring, Financial Intermediation, andEquilibrium Credit Rationing," Journal of Monetary Economics, September 1986.
Wright, Colin. "Savings and the Rate of Interest," in A
Harberger and M. J. Bailey (eds.), The Taxation of
Income from Capital, Washington D.C.: The Brookings Institution, 1969.
17
Managing Risk in Japanese
Interbank Payments Systems
Sawaichiro Kamata
The author, currently at the Information and Computer
System department of the Bank of Japan, was a visiting
scholar at the Federal Reserve Bank of San Francisco
from January to June 1990. He appreciates many helpful
and constructive comments from the editorial committee
and seminar participants at the Federal Reserve Bank of
San Francisco. Members of the editorial committee were
Reuven Glick, Elizabeth Laderman, and Ramon Moreno.
Opinions expressed in this article do not necessarily reflect
the views of the Bank of Japan.
As a result of differences in the approach to managing
payments systems, Japanese payments systems may differ
in their risk and efficiency characteristics from U.S. pay
ments systems. The existence of a facility for real-time
transfers, prohibitions on daylight overdrafts, certain
collateral requirements, loss-sharing among banks, and
the pricing of credit in half-day markets are arrangements
in Japanese payment systems that have historically not
been present in U.S. payment systems. Three possible
measures could further reduce risk in Japanese payments
systems: (i) improve the balance between real-time trans
fers and designated-time transfers; (ii) expedite payment
transactions; and (iii) introduce delivery-versus-payment.
18
Over the past fifteen years, the financial markets of the
major industrial economies have become larger and more
integrated as a result of deregulation and advances in
telecommunications and electronics technology. The ac
companying growth of national and international financial
transactions has spurred a rapid expansion in payment vol
ume and linked national payments systems more closely. In
Japan, for example, the payments value of the major private
payments systems increased five-fold over the past 15 years
to a level of about 25 times nominal GNP. In the United
States, the total payment value for CHIPS and Fedwire rose
from about 20 times nominal GNP in the mid-1970s to over
50 times nominal GNP in 1986.1
The enormous growth and globalization of payments
systems have generated increasing concern about the pos
sibility of default within those systems. Risk of default
arises when financial institutions extend credit to each
other by making payment before receipt. “Systemic” risk
of default arises when default by an individual payments
system participant adversely affects the position of a large
number of other participants and thereby produces a chain
of additional defaults.
While some degree of systemic risk is inherent in all
financial transactions, many policy makers are concerned
that this risk has increased significantly in recent years,
due to the large increases in payment volumes and closer
international integration of payments systems. In particu
lar, closer integration of payments systems may have
increased systemic risk because default on the part of one
participant can now spread more widely beyond national
borders, and national authorities can neither monitor nor
control the riskiness of activities of participants in foreign
payments networks.
The perception that systemic risk in payments system
may have increased has prompted policy makers and
financial institutions to focus attention on the operation
and risk characteristics of different payments systems. In
E conom ic R eview / Fall 1990
the United States, a privately formed committee, called the
Large-Dollar Payments Systems Advisory Group, and a
group formed by the Federal Reserve, called the Task Force
on Controlling Payments Systems Risk, published reports
on the daylight overdrafts of Fedwire in August 1988. In
Japan, as well, efforts are being made to make payments
system safer and more efficient.
This paper describes Japanese payments systems, dis
cusses how risk is managed in these systems, and reviews
possible measures for further reducing risk. This paper is
meant to provide not only an understanding of Japanese
payments system themselves, but also of the Japanese
financial system as a whole, since a payments system is
closely related to the market practices and historical back
ground of the country concerned. Reference is made to the
payments systems of other countries as well.
The paper is organized as follows: Section I briefly
discusses general features of different types of payments
systems. In Section II, the four Japanese payments systems
are described in detail. Section III discusses how payment
system risk in Japan may be reduced and Section IV
presents several conclusions.
I. Paym ents Systems and Risk
Interbank payments arise from the transfer of funds
between the account holders of different banks. Interbank
payments systems can be categorized into two types ac
cording to whether funds are transferred among banks on a
net or a gross basis.
A clearing system is a payments system that transfers
funds among banks on a n et basis. In such a system, all
payment instructions (information which causes a re
ceiver’s account to be credited) are cleared through a single
location where differences between the total amount due to
be received and the total amount due to be paid by each
bank, i.e. the n et credit/debit positions, are calculated.
Typically, these net positions are then settled at a predeter
mined time through the transfer of funds between reserve
accounts at the central bank. The check clearing systems of
most countries generally are clearing systems. The Zengin
System and the Gaitame-Yen System in Japan, and CHIPS
and ACH in the U.S. can be classified in this category.
A settlement system is a payments system that transfers
funds among participants’ reserve accounts with a central
bank on a g ro ss basis; i.e. on a payment instruction by
payment instruction basis. Net positions from a clearing
system usually are settled through a settlement system.
BOJ-NET, managed by the Bank of Japan, Fedwire, man
aged by the Federal Reserve System in the U.S., and Swiss
Interbank Clearing (SIC), managed by the Swiss National
Bank in Switzerland, are examples of settlement systems.
Clearing systems and settlement systems differ from
each other in terms of operational efficiency. A clearing
system, in which only participants’ net positions are set
tled, is operationally more efficient than a settlement
system, in which every payment instruction generates an
interbank settlement. Hence, the workload for a given
number of payments is considerably less in a clearing
system.
However, this difference in terms of efficiency is not as
significant as in the past, when payment instructions were
Federal Reserve Bank o f San F rancisco
exchanged on a paper basis. Now that payment instruc
tions are exchanged electronically, the cost associated with
processing each payment instruction in a settlement sys
tem has decreased dramatically. As a result, the relative
advantage of a clearing system in terms of operational
efficiency is disappearing.
The two types of systems differ more importantly with
respect to the degree of systemic risk. In general, settle
ment systems entail less systemic risk than do clearing
systems. The reason is that in a settlement system payment
instructions and interbank settlements through the central
bank are processed at the same time. This is important
because once reserve funds with a central bank are trans
ferred, the transfer is said to be “final,” meaning that the
central bank guarantees that the receiving bank will never
lose the amount received, even as a result of the sending
bank’s default or legal proceedings stemming from its
insolvency. (A payments system in which settlement is
guaranteed at the same time that the payment instruction is
received is often said to have “finality.”) Therefore, in a
settlement system, no chain of credit is generated among
participants and systemic risk is minimized.
In contrast, in a clearing system the processing of
payment instructions (including calculation of each par
ticipant’s net position and transmission of payment in
structions among banks) and interbank settlement are
conducted separately. Typically, settlement does not take
place, and therefore payments are not final until the end of
the day or on the next day. Therefore, before the interbank
settlement takes place, the receiving bank gets an instruc
tion that it should credit funds to a receiving customer’s ac
count. By crediting the funds, the receiving bank in effect
grants credit to the sending bank until the interbank settle
ment occurs. Whether or not the receiving bank credits
funds to a customer before settlement is left to its dis
cretion, but it often does so for the customer’s convenience.
19
It is the buildup of such a chain of credit within a
clearing system that creates systemic risk. Since default by
one member can lead to default by others, even those which
have no direct transaction with it, the risk of a series of
defaults within a clearing system exists. This arises espe
cially in a clearing system with “unwinding, ” a procedure
under which participants’ net positions are recalculated
with payment instructions of the defaulting participant
put aside.2
Both types of payments systems involve some form of
credit risk. In clearing systems, credit flows between
banks whenever receiving customers are credited before
settlement of net debit and credit positions occurs. The
time lag between the initiation of a payment instruction and
the settlement of reserve accounts influences the amount of
credit that is generated, and hence the level of risk. A
payments system in which settlement occurs within the
same day that a sender instructs payment is called a “ sameday settlement” system. A payments system in which
settlement occurs on the day after a sender instructs
payment is called a “next-day settlement” system. Be
cause unsettled time in a next-day system is longer than in a
same-day system, more credit is accumulated in the former
and risk is correspondingly greater.
In settlement systems credit risk arises from the intraday
credit markets which become sometimes necessary for
providing banks with needed reserve funds. In the U.S.,
for example, the Federal Reserve Banks grant free intraday
credit to sending banks on Fedwire. They do this by
crediting receiving banks reserve accounts as soon as they
receive the payment message, but debiting sending banks’
reserve accounts only at the end of the day. The resulting
“daylight overdrafts” on Fedwire represent credit risk to
the Federal Reserve.
Daylight overdrafts are not permitted on Japan’s BOJNET, nor on Switzerland’s SIC. In BOJ-NET, however,
there is a designated-time transfer facility by which par
ticipants can send payment instructions in advance for
settlement at a designated time of a business day. With this,
they can input instructions for any amount even if the
payment exceeds the current reserve account at the input
time, therefore, it can be said that implicit free credits flow
among private banks. Furthermore, there are private half
day interbank credit markets called Asa-han (morning
session) and Go-han (afternoon session), where banks lend
reserve funds to one another.3 It is these private bank
lenders of reserve funds in Japan that bear the credit risk.
The presence of credit risk raises potential problems for
both settlement systems and clearing systems concerning
the appropriate amount of credit. In an economically
20
efficient payments system, the equilibrium amount of
interbank credit4 accurately reflects both the private and
social marginal costs, and benefits, of credit creation. In
either a settlement or a clearing system, if interbank credit
is mispriced, economic inefficiency is generated. For
instance, it can be argued that unpriced daylight overdrafts,
as on Fedwire, create too much credit risk exposure for the
Federal Reserve.5 Free credit associated with interbank
payments is not restricted to the United States, and it is
likely that its prevalence is one of the reasons for the recent
expansion of worldwide payment volume.
One solution to the problem of too much credit risk is to
set a positive price for interbank credit. However, choosing
the proper price may be difficult. In some situations, the
private market can be relied upon to arrive at an eco
nomically efficient price. In Japan, in the half-day inter
bank private credit markets, credit is priced at about 3.65
basis points for lending and about 14.6 basis points for
borrowing. Because of the presence of the negative exter
nality related to systemic risk, however, private market
pricing might underprice credit to the extent it does not
take into account the costs associated with systemic risk.
As a result, some countries have made attempts to adminis
ter the pricing of interbank credit, with the goal of balanc
ing the social benefits of credit against the social costs,
including systemic risk. On the basis of an assessment of
this type, the Federal Reserve is scheduled to charge 25
basis points annually for daylight overdrafts on Fedwire
beginning in mid-1991.
Another option is to attempt to control the quantity of
interbank credit directly. Quantity controls typically are
not administered by a government financial system au
thority, but are exercised at the option of payments system
participants.6 The idea here is that the inability of pay
ments system participants to control their own positions in
clearing systems is one factor that may contribute to credit
quantities exceeding their efficient levels. Bilateral credit
limits and sender net debit caps are typical quantity
controls.
Bilateral credit limits constitute upper limits that par
ticipants set on net positive positions (net amount received)
vis-a-vis other individual participants. A participant can
refuse to accept payment instructions from another partici
pant if doing so would cause its credit limit vis-a-vis that
participant to be exceeded. A sender net debit cap is a
participant’s upper limit on its aggregated negative posi
tion (total amount sent).
Although such direct restrictions may be very effective
in reducing the credit associated with interbank payments,
and the corresponding credit risk, they likely have a
E conom ic R eview / Fall 1990
negative effect on operational efficiency by raising the
processing costs in clearing systems. In addition, they may
introduce the risk that customers may claim damages
against their bank if the bank misses making time-critical
payments due to the existence of these restrictions.
There may be other means whereby systemic risk can be
reduced. One is to set entrance requirements for payments
system participants that assure that only relatively finan
cially strong institutions have access. Another is to design
loss-sharing rules and/or collateral requirements that re
duce the probability of a chain reaction when one partici
pant defaults in a clearing system.
II. Japanese Paym ents System
There are four major interbank yen payments systems in
Japan—BOJ-NET, the Zengin System,7 the Gaitame-Yen
System,8 and the check clearing system. Except for the
check clearing system, these systems are all generated
electronically. BOJ-NET is a settlem en t system , and is
similar to Fedwire and SIC. The other three systems are
clearing system s. As in other countries, the settlement
system, BOJ-NET, is managed by the central bank, the
Bank of Japan. The three clearing systems in Japan all are
managed privately.
BOJ-NET, the Zengin System, and the check clearing
system handle mostly domestic payments. BOJ-NET han
dles high value institutional transactions for the money and
security markets; the number of transactions handled is
Table 1
Features of Large-Value Interbank Yen Payments Systems in Japan
BOJ-NET
Features
• Settlement system
for domestic wholesale
transactions
• Funds transfer and
Japanese Government
Bond transfer system
• Electronic basis
Zengin System
• Clearing system
for domestic retail
transactions
• Electronic basis
Gaitame-Yen System
Check Clearing System
• Clearing system for
• Clearing system for
domestic commercial
cross border transactions
trades.
• Electronic basis
• Paper basis except
for Tokyo.
Established
1988
1973
1980
1879
Managed by
BOJ
TBA1
TBA1
Check clearing houses
No. of Participants2
(of which foreign
banks)
351
(82)
4,870
(3)
151
(61)
5993
(87)
Risk Structure
• Same-day transfer for
both customers and
banks
• Same-day transfer for
customers, next-day
transfer for banks
• Overnight credit risk
• Same-day transfer for
both customers and
banks
• Daylight credit risk
• Next-day transfer for
both customers and
banks. 3
• Overnight credit risk.
• Unwinding risk.
Risk Management
• No daylight overdraft
• Real-time and
designated-time transfer
• Third party transfer
• BOJ’s guarantee
• Collateral
• Loss sharing among all
the participants
• Sender net debit cap
• Bilateral net credit limit • Suspension of
• Liquidity sharing among
transaction system
banks with positive
• Collateral
balance against the
defaulting bank
'TBA: Tokyo Bankers Association
2As of the end of December 1989
3Tokyo Clearing House only
Federal Reserve B ank o f San Francisco
21
relatively small. The Zengin System handles lower value
individual transactions in large volume. The check clear
ing system handles comparatively small value bills or
checks originating from commercial trade in local areas.
The Gaitame-Yen System, which is similar to CHIPS in
the U.S., handles international payments, such as yen
payments arising from foreign exchange, Euro-Yen trading
and other cross-border transactions. Table 1 provides a
summary of the important features of the various payments
systems, while Tables 2 through 4 provide some indicators
of size and use.
The operation of these payments systems is supple
mented by an intraday interbank credit market, which
provides funds for clearing at designated times. Funds for
the morning session are borrowed at opening (9:00 a.m.)
and repaid at check-clearing time (1:00 p.m.). Funds for the
afternoon session are borrowed at check-clearing time and
repaid at the day’s closing (3:00 p.m.).9 As mentioned
earlier, credit in this intraday market is priced (about
3.65 basis points for lending, about 14.6 basis points for
borrowing).
BOJ-NET
BOJ-NET is composed of two systems—the funds
transfer system, which began operations in October 19881
0
and the security (Japanese Government Bond) transfer
system, initiated in May 1990. The funds transfer system is
a same-day gross settlement system, similar to Fedwire in
the United States. Most of the transfers are executed for the
settlement of wholesale transactions, such as in the money
market or the securities market. Payment orders on BOJNET are processed through an on-line computer network
among account holders and the BOJ. A payment order
instructs the user’s reserve account at the BOJ to be debited
and another account holder’s reserve account to be cred
ited. Though non-on-line users continue to rely on paper-
Table 2
Recent Trends in Use
a. Volume of transactions (thousand)
Transfer through BOJ
current accounts
(Market Operations Dept.)
Zengin
System
GaitameYen System
Check Clearing
System
Total
1,719
2,281
2,523
n. a.
n. a.
242,880
410,379
454,089
508,195
574,692
n. a.
n. a.
n. a.
n. a.
n. a.
432,685
403,989
396,263
394,511
381,534
675,565
814,368
850,352
972,706
956,226
(1980-87)%
5.6
1 0 .0
n. a.
-1.4
3.9
Transfer through
BOJ current accounts
(all offices)
Zengin
System
GaitameYen System
Check Clearing
System
Total Value
Share of
nominal GNP
1980
3,231
318
1,425
1,789
7.5
1986
1987
1988
1989
10,714
18,860
22,205
29,653
799
1,023
1,276
1,600
43
1981: 430
2,227
3,184
3,757
5,105
2,882
4,173
3,992
4,469
5,908
8,380
9,025
11,174
17.8
24.5
24.6
28.6
19.7
(1981-1989)
36.2
13.5
1980
1986
1987
1988
1989
Annual growth
rate (1980-89)
b. Value of transactions (¥ trillion)
Annual growth
rate (1980-89)
%
27.9
2 2 .6
’Transactions among BOJ accounts are on a one-way basis.
2The use of BOJ reserve accounts is excluded in the total.
22
E conom ic R eview / F all 1990
based orders, even in this case all data are input at
terminals in the BOJ’s head office and branches by the
BOJ’s operators. Out of 651 account holders with the Bank
of Japan, 351 currently are participants of the funds
transfer network (as of the end of August 1990). Parti
cipants mainly are banking institutions, but securities
houses and money market dealers (ta n sh i ) also are in
cluded. All 82 foreign banks that have offices in Japan hold
accounts at the Bank of Japan, and 80 of them are partici
pants in BOJ-NET.
BOJ-NET allows both real-time instantaneous transfers
and transfers at designated times of the day, specifically at
9:00 a.m., 1:00 p.m. and 3:00 p.m. Funds transfer orders
for designated times can be revoked until the designated
times, unlike real-time transfers.1 Users also can send
1
post-dated instructions, for settlement at one of the desig
nated times on the following business day.
The Bank of Japan offers finality on BOJ-NET transfers.
However, unlike many other central banks, the Bank of
Japan does not permit daylight overdrafts in reserve ac
counts.12 This limits the amount of transfer to the insti
tution’s reserve balance at the time of the transfer, whether
it be a real-time transfer or a transfer taking place at a
predetermined designated time. If a participant has insuffi
cient funds in its reserve account at the time of the transfer,
the payment instruction automatically is rejected. This
implies that the Bank of Japan bears relatively little risk.
1.0
33
( 6.7)
2.5
35
( 5.6)
1PM
BOJ-Net
funds
transfers
Value per one
transaction
(¥ million)
Zengin Gaitame-Yen1
System
System
118,6132
6,396
21,257
2,288
21
3
1 ,0 1 2
15,3003
(Sam ple survey co n d u cte d on 9 /2 8 /8 9 )
32
( 4.4)
76.9
651
(27.2)
50.2
Check
clearing
System4
2,484
(12.9)
3,135
(15.9)
3 PM
684
(18.9)
538
(1 1 .6 )
41.4
17,876
(15,020)
RealTime
31
( 1-4)
76
( 2 .0 )
5.9
1,526
(564)
Total
3,231
(14.0)
(per day in 1989)
11
Share of Transaction Volume
at Posting Time
9 AM
Settlement value and volume
Volume (in
thousands)
Table 4
Non-Tanshi
Posting ^anshi Companies Companies
Total
Time Volume Share % Volume Share % Volume Share %
Table 3
Value
(¥ billion)
In the case of designated-time transfers, BOJ-NET
participants extend payment instructions to another bank
in expectation of an incoming transfer at a future desig
nated time. It can be argued that this facility is very similar
to a clearing system in terms of the interdependent credit
that it generates, and thus in terms of its systemic risk.
In addition to funds transfers among account holders
with the Bank of Japan, BOJ-NET provides the facility for
large value funds transfers for the customers of account
holders (so-called “third-parties”). This facility provides
the convenience of same day funds transfer with payment
finality for large payments. The services provided here are
similar to those offered by other central banks’ systems,
such as Fedwire or SIC. The minimum transfer amount on
BOJ-NET is set at a relatively high 300 million yen for
third-party transfers.
There are other restrictions in connection with thirdparty transfers that are initiated by security firms and other
non-bank participants in BOJ-NET. Specifically, if the
11.7
(26.6)
lFigures for March to December 1989.
transactions among BOJ accounts
(including those of non-financial institutions).
3Sample survey conducted on 9/28/89. The sample consists of 18
accounts at the head office of the Bank of Japan, whose activity
in June 1989 accounted for 28.8% of the total transactions.
4Figures in parentheses indicate transactions through the Tokyo
Clearing House.
F ederal Reserve B ank o f San F rancisco
2 1 .2
1.0
1 0 0 .0
1,298
(18.7)
1 ,2 2 2
0 .8
69.2
27.0
(15.6)
1 00 .0
107
( 1-9)
4,529
(15.3)
2.4
1 00 .0
notes 1. The sample consists of 18 accounts of major brokers
and banks at the head office of the Bank of Japan,
whose activity in June 1989 accounted for 28.8%
of the total transactions.
2. The figures represent actual transfer orders originating
from the accounts of sample institutions to other ac
counts at BOJ. The figures differ from those in other
charts in this respect.
3. The figures given in parentheses in the volume column
are the average amount of transfer orders in billions
of yen.
23
transferring entity is a non-bank institution, it cannot
specify its paying customer’s name on the payment instruc
tion. Likewise, if the transferee is a non-bank institution,
the transferring institution cannot specify the payee’s name
on the payment instruction. The rationale for these restric
tions is that a full third-party transfers are considered to be
part of the funds transfer business, which may not legally
be conducted by non-bank institutions due to the separa
tion between the banking and securities businesses in
Japan.13 Due to such restrictions, the use of third-party
transfers is not as large as that of funds transfers among
account holders with the Bank of Japan.
The input hours of funds transfer are from 9:00 a.m. to
4:30 p.m.. However, transfer instructions for the same day
are accepted only until 3:00 p.m. (in the case of third-party
transfer instructions, until 2:00 p.m.). Post-dated instruc
tions are accepted until 4:30 p.m. The operational cycle of
funds transfers on BOJ-NET is shown in Table 5.
The number of transfers of reserve accounts, almost all
of which stem from the use of BOJ-NET, is approximately
eleven thousand a day. This is very small compared with
the private payments system in Japan and also is smaller
than that of major central banks abroad.14 The average
value per transfer is 15.3 billion yen.
To sum up, BOJ-NET is a large-value settlement sys
tem. BOJ-NET does offer finality, but because of the
prohibition on daylight overdrafts, this entails relatively
little risk for the Bank of Japan. The real-time transfer
portion of BOJ-NET has relatively little systemic risk, but
its operational efficiency is likely to be relatively low. The
designated-time transfer system may help to improve oper
ational efficiency, but may introduce significant systemic
risk (See Section IV).
Table 5
BOJ-NET Operations
Day
Funds transfers
T-3
T-1
Gaitame-Yen System
• (Advance input of
transfer orders
possible for T-day
• Advance input for
next day’s transfers
possible
(settlement day)
9:00—Opening • Funds for the day’s • Input of transfer
opening available
orders starts
• Receive data on
1 0 :0 0 —
check clearings and
Zengin System
• Input for the day’s
1 1 :0 0 —
and next day’s
transfers possible at
any time during the
1 2 :0 0 —
business hour
13:00—Check- • Settlement at check- • End of input for the
clearing clearing time
day’s transfers and
time
collective calculation
(13:45)
14:00—
• End of input for the
day’s transfers for
third parties
15:00—Closing • Settlement at the
• Settlement at the
day’s closing
day’s closing
16:00—
• End of input for
post-dated transfers
The Zengin System
The Zengin System, which is managed by the Tokyo
Bankers Association,15 processes nationwide domestic
funds transfers by translating each bank’s position against
that of other banks into a bilateral position against the
Bank of Japan. These positions are then settled through
adjustment of BOJ reserve accounts.16The Zengin System
thus is a clearing system.17
The Zengin System is used mainly for relatively small
value transfers such as private funds transfers, direct
deposits, pension payments, stock dividend payments,
etc.1 It started its operation in 1973 as a nationwide
8
electronic clearing system, and now has grown to a large
network system of nearly five thousand banks and other
deposit-taking institutions as participants. Its original
members were nationwide banks (city banks, long-term
24
16:30—
• End of input for
post-dated transfers
• Processing of the
next day’s opening
credit banks, trust banks, regional banks) and the Shokochukin Bank (a financial institution for small businesses),
but other institutions joined later.19 In addition, three
foreign banks are members.20 At the end of December
1989, the system included 4,870 institutions with 43,684
places of business.
Central financial institutions such as the Z en sh in ren
Bank, the National Federation of Credit Co-operatives,
and the N o rin ch u kin Bank act on behalf of small financial
E conom ic R eview / Fall 1990
institutions in their respective sectors (respectively the
small business shinkin banks (454), credit co-operatives
(414), and agricultural cooperatives (3,685)).21 The ex
change balances of these central institutions with the Bank
of Japan therefore include their own exchange balances
plus those of the related financial institutions. This system
is called a proxy settlement system and was initiated in
February 1979.
The Zengin system processes as many as two million
transactions per day. However, it is mainly used for bulk
payments, and as a result, the average value per transaction
is comparatively small, about 3 million yen.
The processing of domestic funds transfers in the Zengin
System is depicted in Chart 1. Assume at time T a sender a
asks a participant bank (Bank A) to send his money to a
beneficiary b who has an account at another participant
bank (Bank B ). The sender bank debits a 's account and
instructs the beneficiary bank to credit b ’s account through
the Zengin System Center.
This process is virtually real-time, in the sense that the
transferred amount becomes almost immediately available
to the beneficiary b. Thus, the Zengin System is a sameday settlement system from the customer’s viewpoint.
However, this system is a next-day settlement system for
the participant banks. The balance between the sending
and receiving banks, which is calculated at the Zengin
System Center, is settled on the following day (T +1 day) at
the check clearing time of 1:00 p.m. by BOJ-NET. Under
the Zengin System, the beneficiary bank bears an over
night credit risk since funds become available to the
beneficiary on the transaction day while interbank funds
settlement is conducted on the following day.
To cope with this risk and secure the clearing process,
the Bank of Japan stands ready to provide provisional
liquidity if a transferor becomes insolvent at the time of
final settlement on the following day. Under this agree
ment, every participating bank is required to deposit
collateral with the Bank of Japan,22 and all participants
assume joint responsibility when unsettled liabilities ex
ceed the collateral value of the failed bank. To further
control the risk exposure, a sender net debit cap was
introduced in July 1990.23
The BOJ’s provisional liquidity guarantee and the par
ticipants’ joint loss sharing agreement contribute to the
avoidance of unwinding. Moreover, the loss sharing agree
ment and the required collateral reduce the credit exposure
from receiving banks to sending banks. Although the
system is thus very well organized to provide liquidity and
limit credit risk, the Bank of Japan’s deep involvement
might encourage the misconception that it is willing to
bear unlimited losses.
The Zengin System, being a clearing system, does entail
some systemic risk, but the BOJ’s provisional liquidity
guarantee, the collateral requirements and the joint loss
sharing agreement reduce this risk somewhat. The netting
of debits and credits in the Zengin System is operationally
efficient, but the involvement of the BOJ in the System
Chart 1
Zengin System Flow of Funds
Federal Reserve B ank o f San F rancisco
25
may lead participants to underprice risk and therefore
overextend credit beyond economically efficient levels.
The Gaitame-Yen System
The Gaitame-Yen System, similar to CHIPS in the
United States, is a same-day, net settlement facility that
settles yen payments arising from foreign exchange and
other cross-border transactions.24 It began operations in
October 1980. Like the Zengin System, the Gaitame-Yen
System is managed by the Tokyo Bankers Association.
Since March 1989, the Bank of Japan has operated the
Gaitame-Yen System as a part of the BOJ-NET. All
procedures are currently conducted electronically.
The number of transactions conducted through the
Gaitame-Yen System is about 21 thousand per day and the
average value of transactions is approximately one billion
yen. Foreign banks are the big players in the Gaitame-Yen
System; 61 out of 151 participants are foreign banks as of
the end of December 1989, and they handle one fourth of
the total volume of transactions.
Banks sending or receiving a large volume of settlement
orders connect their computers directly with the BOJ’s
host computer. When a bank receives transfer orders via
SWIFT,25 the data are automatically input into its com
puter and finally processed by BOJ’s host computer.
Payment instructions on the Gaitame-Yen System are
netted out among participants, and the net position of each
is settled through reserve accounts with the Bank of Japan.
Transfer orders for the same day are input at the sending
bank’s terminal by 1:45 p.m. (for post-dated transfer by
4:00 p.m.) and output at the receiving bank’s terminal
immediately.26 How soon the payee has funds available for
use depends on when the receiving bank credits his ac
count after it receives a payment instruction. Usually, it
credits the payee’s account immediately after receiving
payment instructions.
While the Gaitame-Yen system is similar to the Zengin
System (see Chart 1), it differs in that net debit and credit
positions of Gaitame-Yen System participants are settled
at the sa m e- day’s closing (3:00 p.m.) while those of Zengin
System participants are settled at check clearing time (1:00
p.m.) on the next- day. Therefore, a receiving bank can
obtain final funds on the same business day as they were
sent in the Gaitame-Yen System. Even in this case, though,
the receiving bank bears a credit risk to the sending bank if
the receiving bank credits its beneficiary’s account before
settlement.27
To cope with this credit risk, a bilateral net credit limit
26
facility is offered at the receiver’s option. With this option,
each bank can set an upper limit on the net credit position it
will accept from any other bank. Such a limit can be
changed at the bank’s discretion through its terminals.
When the BOJ receives an on-line funds transfer order, it
checks to see that it does not exceed the limit placed by the
receiving bank. If the amount exceeds the given limit, the
BOJ notifies the remitting bank of the error. Another rule,
introduced in March 1989, states that when a bank de
faults, all banks with bilateral net credit balance against
the former will jointly bear the shortage of liquidity so that
there will be no need for unwinding.
Unlike in the Zengin System, settlement of net positions
of participating banks in the Gaitame-Yen System is not
insured by the BOJ. However, it is not necessary to unwind
in the event of a participant’s default because of the
existence of the liquidity sharing rule. Nevertheless, since
there are no clear agreements on how to share the loss
among participants,28 this rule does not give clear incen
tives to participants to reduce risk.
The Gaitame-Yen System has some systemic risk, but it
is reduced by the bilateral net credit limits and the liquidity
sharing rules. To the degree that unsettled amount accumu
lates with the time lag between transfer instructions and
settlement, risk in the Gaitame-Yen System is reduced by
its being a same-day system. The netting of transactions
makes the Gaitame-Yen System relatively efficient, in an
operational sense.
The Check Clearing System
The check clearing system is a paper-based payment
system under which financial institutions of a specified
area come together at a clearing house at a specified time
every day in order to exchange checks payable at other
institutions as well as bills, receipts, bond coupons, and
other such instruments. Checks and bills are the most
popular means of payment between corporations and indi
vidual participants in financial markets.29
Checks and bills usually are passed through clearing
houses by banks, and are not processed by the Bank of
Japan. As of March 1989, there were 183 clearing houses
legally designated by the Minister of Justice as well as 595
other private clearing houses managed either as associate
institutions of the Bankers’ Associations of the various
regions or as independent corporations.30 The exchanges
and settlements at the clearing houses include not only city
banks, regional banks, trust banks, and long-term credit
banks, but also the second tier regional banks, sh inkin
E conom ic R eview / F all 1990
banks, credit co-operatives, and other institutions either as
direct participants or as participants through correspon
dents with which they have dealings. The clearing balances
of individual banks normally are settled through transfers
among reserve accounts at the Bank of Japan. For locations
where the Bank of Japan does not have branches, settle
ments are carried out through interbank deposits at spec
ified banks. The number of transactions through clearing
houses is about 1.5 million per day, and the average value of
transactions is about 12 million yen.
The rules and procedures in Japanese check clearing
systems basically are similar to those in other countries. A
typical transaction in the Tokyo Clearing House, for exam
ple, is processed as follows: the beneficiary presents a
check to his bank (the transferee bank), and this is passed
on to the Clearing House in the evening, where net
balances are calculated and the transferor bank receives the
check (the T day). Settlement between reserve accounts at
the BOJ is then carried out at 1:00 p.m. (“check clearing
time”) on the following business day ( T + 1 day).
In the case of a failure to pay, the transferor bank returns
the dishonored check to the transferee bank and requests
that its reserve account be credited the previously debited
amount on the next day (the T + 2 day). This means that a
series of transactions are not final but provisional on
confirmation on the T + 2 day that the check has not been
dishonored. Thus, this check clearing system can be
described as a next-day settlement system, since benefici
aries have to wait at least another day (until the T +1 day)
for the fund to be credited to them, and since interbank
settlement cannot be finalized until the day after the
clearing (the T + 2 day).
The transferee bank bears short-term insolvency risk if it
credits funds to the beneficiary’s account before confirma
tion on the T + 2 day, since the transferor bank can claim
refund of reserve funds in case of a default. In this system,
therefore, transferee banks have to be particularly careful
in determining when to credit funds to the beneficiary’s
accounts.
Collateral usually is used to control risk in the check
clearing system. In the case of the Tokyo Clearing House,
participants must deposit bonds (namely public and corpo
rate bonds, with total face value of 3 million yen) as
collateral with the Clearing House. However, this amount
of collateral is too small to cover participating banks’
default, should it occur. Therefore, the possibility of un
winding, and hence systemic risk, still remains in the
check clearing system.3
1
III. Reducing Risk in Japanese Payments Systems
It is apparent from the discussion in Section II that the
approach to managing payments systems in Japan differs
in some respects from that in the U.S. This implies some
differences in risk and efficiency characteristics. In partic
ular, the existence of a facility for real-time transfers and
the prohibition on daylight overdrafts (BOJ-NET); collat
eral requirements, loss sharing among banks (Zengin
system); and the pricing of credit by participants in
half-day credit markets are all arrangements that tend to
reduce risk, and that have historically not been present in
U.S. payments systems.32 Although the risk-management
measures adopted in Japanese payments systems have
proved to be adequate, continuing developments in finan
cial markets and technological innovations suggest that
efforts to reduce risk even further may be desirable.
There are three ways in which the risk in Japanese
payments systems may further be reduced: (i) improving
the balance between real-time and designated-time trans
fers; (ii) expediting payment transactions; (iii) introducing
delivery versus payment. In all three cases, a major
concern in attempting to manage payments system risk
entails a loss of efficiency in payments. While it can be
argued that less risk in payments systems is generally
F ederal Reserve B ank o f Sam Francisco
desirable, risk reduction measures may lead to less credit
than is socially optimal.
Improving the balance between
real-time and designated-time transfers
Though there are two facilities in BOJ-NET, namely the
real-time instantaneous transfer and the designated-time
transfer, the use of the real-time transfer is very small.
Only 2.4 percent of all transactions are in real-time,33
while 97.6 percent are delayed to designated times, with
69.2 percent at the check clearing time (1:00 p.m.) and
27.0 percent at the business closing time (3:00 p.m.).34
(see Table 4.)
Real-time transfers are more desirable than designatedtime transfers from the point of view of risk. First, with
real-time transfers, payment instructions are indepen
dently executed, transaction by transaction, on a final
basis. This limits any chain reaction to a single partici
pant’s default. On the other hand, with designated-time
transfers, payment instructions are concentrated at a spe
cific time, and therefore are interdependent. This generates
greater systemic risk of a chain response to individual
defaults. Second, with real-time transfers, users cannot
27
input instructions for payments which exceed their current
account balance at the input time. In contrast, with designated-time transfers, they can input instructions for any
amount of payment in advance, even if the payment ex
ceeds the current account balance at the input time. This
potentially allows implicit interest-free credit and hence
greater default risk to be generated among private financial
institutions. Third, since in Japan most interbank settle
ments are processed at two designated times, increases in
daylight overdrafts in customers’ accounts with banks are
likely to arise with designated-time transfers because
customers are not fully aware of the settlement times.
However, designated-time transfers have certain advan
tages. First, users of BOJ-NET are less constrained by the
prohibition on daylight overdrafts when they use the desig
nated-time facility rather than the real-time facility. One of
the reasons is that they can resort to credit in the half-day
markets to obtain funds to settle at the designated times.
This is much more difficult when using the real-time
facility. Second, participants tend to prefer the designatedtime transfer to the real-time transfer because the fixed
settlement times of the former enable banks to enjoy the
advantages of concentrating their transactions. In particu
lar, banks can synchronize funds transfers arising from the
inflow and outflow of funds at the designated times.35
Given this trade-off between risk and efficiency, it is not
entirely clear whether measures to encourage greater use
of the real-time facility in order to reduce risk in the
Japanese payments system are called for. Further research
on this issue may shed light on appropriate ways to weight
risk and efficiency in payments systems, and the relative
merits of designated-time and real-time transfers from a
social point of view.
settlement systems. With a next-day settlement system,
unsettled balances remain until settlement is finally com
pleted on the next day, while with a same-day settlement
system, they disappear within the same day that a sender
instructs payment.
Both same-day and next-day settlement systems are
employed in Japanese financial markets. For example,
transactions in the call and bill markets are mostly settled
through BOJ-NET and Euro-yen transactions are settled
through the Gaitame-Yen System (both are same-day set
tlement systems). Other short-term money markets trans
actions, such as those involving CDs and commercial
paper, large value financial transactions involving govern
ment bonds, and foreign exchange, utilize BOJ-NET, a
same-day settlement system, as well as the Zengin System
and the check clearing system, both of which are next-day
settlement systems.
In contrast, most trading in overseas financial markets
now is settled through same-day settlement systems. In the
United States, transactions in the short-term money mar
kets (federal funds, CDs, commercial paper and bankers
acceptances), government bond markets (T-Bills, T-Notes,
T-Bonds), financial futures, and options markets all are
settled through Fedwire, which is a same-day settlement
system. A large portion of Euro-dollar and foreign ex
change transactions are settled through CHIPS, a sameday settlement system.37
From the standpoint of minimizing settlement risk as
well as enhancing global interdependence, it may be
desirable for Japan to move to a system where the settle
ment of large value transactions in major financial markets
are processed through same-day settlement systems. Given
developments in technology, such a change would seem to
impose no significant operational or economic costs.
Expediting Payment Transactions
The credit risk in payment systems can be viewed as
proportional to the amount of unsettled payments bal
ances. This amount depends in turn on the time lag
between contract and settlement. The longer the lag, the
larger the accumulated unsettled balances.36 This suggests
that measures that shorten the lag may reduce the risk in
payments systems. In the Japanese stock market the time
lag between contract and settlement is shorter than the
international standard. For government bonds, however,
the lag runs up to ten business days (see also note 34),
making it one of the longest among the major industrial
countries. Hence, expediting settlement in the government
bond market in Japan is very important.
With regard to the unsettled balances, it is important to
recognize a difference between same-day and next-day
28
Delivery-Versus-Payment
Delivery-versus-payment is a mechanism under which a
fund transfer and a security transfer are conducted simul
taneously. When delivery-versus-payment is not available,
the possibility arises that a party to a transaction might fail
to receive the funds expected in return for the completed
delivery of a security, or, conversely might fail to receive
the security expected in return for a completed payment,
owing to the counterparty’s default.
The development of electronic funds transfer technology
has increased the feasibility of delivery-versus-payment
system. Electronic delivery-versus-payment systems al
ready are operating in government bond markets in the
United Kingdom (CGO System), the United States (Fed
wire), and in the Euro-market (Euroclear, CEDEL). In
E conom ic R eview / Fall 1990
Japan, however, although individual participants have
some devices for ensuring delivery-versus-payment,38 an
electronic deli very-versus payment system does not exist.
The introduction of electronic delivery-versus-payment
in Japan would reduce risk in payment systems without any
cost in efficiency, and thus appears to be desirable. Since
the establishment of the Japanese government securities
system in BOJ-NET in May 1990, it has become feasible to
introduce delivery-versus-payment by integrating the cash
and securities delivery systems of BOJ-NET.
IV. Concluding R em arks
The discussion in this paper has highlighted two impor
tant features of Japanese payments systems. First, the risks
associated with payments systems in Japan are common to
those of payments systems in other countries. Delivery
lags and the interdependence of transactions produce
credit and systemic risk in Japanese payments systems,, as
they do elsewhere. Second, the approach to managing
payments systems in Japan in some respects differs from
the U.S. approach. As a result, Japanese payments systems
may differ in their risk and efficiency characteristics from
U.S. payments systems. In particular, the existence of a
facility for real-time transfers and the prohibition on day
light overdrafts (BOJ-NET), collateral requirements, loss
sharing among banks (Zengin system), and the pricing of
credit in half-day credit markets are all arrangements that
tend to reduce risk, and that have historically not been
present in U.S. payments systems.
Three possible measures for further reducing risk in
Federal Reserve Bank o f San Francisco
Japanese payments systems also have been discussed: (i)
improving the balance between real-time transfers and
designated-time transfers, (ii) expediting payment transac
tions (iii) introducing delivery-versus-payment. Further
research is required to determine the advisability of the
first measure, but it is apparent that the second and third
measures could reduce risks without introducing signifi
cant operational or economic costs.
Further research also is required to identify other meas
ures that may reduce payments systems risk in the face of
the growing integration of world financial markets. As a
result of such integration, payments systems in one coun
try are now easily influenced by incidents in other coun
tries. Various kinds of international cooperation as well as
a better understanding of foreign systems will become
increasingly important components of efforts to manage
payments systems risks.
29
NOTES
1. CHIPS stands for Clearinghouse Interbank Payments
System, and is a clearing system for dollar payments
arising from international transactions. It is owned and
operated by the New York Clearinghouse banks. Fedwire
is managed by the Federal Reserve System, and is used
for transferring reserve account balances of depository
institutions, as well as governm ent securities.
2. Unwinding, which is characteristic of clearing systems,
is a procedure under which participants’ net positions are
recalculated with payment instructions of the defaulting
participant put aside and the recalculated new positions
are settled. The risk in unwinding arises because settling
the new positions may be difficult because the net posi
tions of all participants will have changed. In order to
settle, participants may need to make arrangem ents for
raising additional funds or cancel certain prior com m it
ments. Such rearrangements or contract cancellations
may cause other participants to default.
3. There are also longer-term private interbank credit
markets in Japan.
4. “ Interbank cre d it” here includes both credit among
private banks and credit from a central bank to private
banks.
5. Since the Federal Reserve has unlimited financial
strength com pared with private banks, the problem is not
that the Federal Reserve bears too much risk by itself, but
that private banks have an incentive to use daylight over
drafts excessively.
6. In some countries, it may be politically infeasible for a
central bank or other authority to limit the credit exposure
of individual payments system participants due to pos
sible charges of discrimination.
7. "Z engin” means “ nationwide banks” in Japanese.
8. “ G aitam e” means “ foreign exchange” in Japanese.
9. Funds for the morning session are utilized either for the
large withdrawal of cash from BOJ windows or large funds
transfer from Tokyo to cities nationwide in the early morn
ing. Funds for the afternoon session are mostly in demand
by institutions who need to cover a shortage of funds in
BOJ accounts arising from bill/check clearings, Zengin
System transfers, etc., at check-clearing time (1:00 p.m.).
10. Before the introduction of BOJ-NET, BOJ-checks had
been mainly used for transfers among account holders
with the BOJ. A payee who gets a B O J-checkfrom a payer
(drawer) presents it at a BOJ window for funds transfer
within the Bank. Though BOJ-checks were largely re
placed by com puter transactions, they still are used for
several purposes, for example, settlements by relatively
small, non-BOJ-NET-participant account holders with the
Bank of Japan. The Bank of Japan does not accept
payment orders by telephone, so BOJ-checks remain one
of the im portant large-scale means of payment in Japan
despite the Bank’s effort to enhance the convenience and
applicability of BOJ-NET.
30
11. A real-time transfer cannot be revoked because it is
final. However, if both parties agree to it, a reverse trans
action can be used to undo a transfer.
12. The Federal Reserve Banks and the Bundesbank
allow daylight overdrafts up to a limit and the Bank of
England and the Bank of France allow them without any
limit. Like the Bank of Japan, the Swiss National Bank
does not allow daylight overdrafts.
13. Major securities firms hold accounts with BOJ, so that
they can also be users of BOJ-NET. However, they are not
allowed to engage in traditional com m ercial banking op
erations, such as taking deposits or providing funds trans
fer services to customers. They can, therefore, only effect
funds transfer orders with custom er information through
BOJ-NET if they themselves are either the ultimate bene
ficiary or the originator. This ensures that securities firms
them selves do not engage in the business of funds trans
fer for customers. In the U.S., such an issue would not
arise because securities firms are not participants in
Fedwire.
14. Transaction volumes using Fedwire and SIC are
approxim ately 200,000 (1986) and 170,000 (Novem ber
1988) per day, respectively.
15. Founded in 1945, the Tokyo Bankers Association com
prises 131 banks (city banks, long-term credit banks, trust
banks, regional banks and second-tier regional banks).
Its main functions are to study the financial system,
rationalize banking activities, and manage the Zengin
System, the Gaitame-Yen System, and the Tokyo Clear
inghouse.
16. Actually, this scheme is called the “ dom estic ex
change settlement system .” The Zengin System is used
only for the electronic exchange of payment instructions.
Payment instructions are exchanged on a paper basis,
too; however, the use of such paper exchange is very
small. For simplicity, the paper transactions are ignored in
the text.
17. For one participant, aggregated receiving and send
ing amounts are debited from and credited to his reserve
account, respectively. In this sense, this procedure is a lit
tle different from that of an ordinary clearing system which
transfers one net position for one participant through a
shadow account (or nominal account) with a central bank.
18. The Zengin System is a retail funds transfer system
with no exact equivalent in the U.S. Although the Auto
mated Clearing House is used by many private firms in the
United States to make recurring payments, such as pay
roll payments, electronically, it is not used nearly as exten
sively by the private sector as the Zengin System is used
in Japan.
19. The second-tier regional banks (formerly sogo banks),
shinkin banks, and the Norinchukln Bank joined in Febru
ary 1979. Credit co-operatives, labor credit associations,
and agricultural co-operatives joined in August 1984.
E conom ic R eview / Fall 1990
20. Foreign bank participation in the Zengin small-valuetransaction system is limited because foreign banks in
Japan generally do not do much retail business.
21. Figures in parentheses indicate the number of institu
tions as of the end of March 1990.
22. The collateral required of a participant is its average
daily net debit position over the previous year.
23. The sender net debit cap was introduced as an
informal guideline in 1987 at 15 times the required collat
eral level. It was strengthened to a formal restriction at 10
tim es as much as the required collateral level (“ warning
line” at 5 times) in July 1990.
24. For example, the Gaitame-Yen System handles yen
transfers based on correspondent agreements, yen remit
tances, payments resulting from export/im port trade, yen
settlement of foreign exchange, etc. As far as foreign
exchange transactions are concerned, though almost all
the transactions outside the Tokyo market and transac
tions between dom estic banks and offshore banks use
the Gaitame-Yen System, transactions between dom estic
units are settled through the check clearing system.
25. SWIFT (Society for W orldwide Interbank Financial
Telecomm unications) is a nonprofit, cooperative organi
zation that facilitates the exchange of payment instruc
tions between financial institutions around the world.
SWIFT is considered to be a mere message transfer
system, not a payments system per se. Used worldwide,
the SWIFT format is the most popular world standard. As
of August 1989, 1,487 banks from 65 countries were
participating in SWIFT.
26. A transfer order can be input up to three business
days prior to the settlement date. This helps to reduce the
peak workload of each participant bank.
27. In this case, if the beneficiary withdraws from his
account, the receiving bank bears a liquidity risk in addi
tion to the credit risk.
28. Participants are required to discuss how to share the
loss later, but there is no clear agreem ent on how this is to
be done.
29. Flowever, very few personal checks are used in
Japan.
30. The clearing houses designated by the Minister of
Justice are exem pt from antitrust laws. Moreover, the
presentation of bills or checks to the designated clearing
houses as opposed to private clearing houses is more
effective from a legal viewpoint.
31. The issuer of a bill or check that is dishonored be
cause of insufficient funds or for other reasons is subject
to the posting of a notice of failure to collect. Those who
issue dishonored bills again within six months are subject
to a two-year prohibition from current account transac
tions and lending transactions with mem ber financial in
stitutions of the clearing house. This suspension from the
transaction system is designed to deter default by cus
tomers, not by banks.
F ederal Reserve B ank o f San Francisco
32. Note that pricing of credit does exist in the Federal
funds market, but since it is not an intraday market, it
cannot meet liquidity needs for intraday transactions.
Instead, participants in U.S. payment systems incur un
priced daylight overdrafts in the course of their daily
transactions subject to limits that have been introduced in
recent years. Also note that in 1986, the Federal Reserve
adopted a policy under which banks are encouraged to
voluntarily establish limits on the net amount they can owe
at any one time across all large-dollar networks. Although
the program is voluntary, only those institutions that set a
cap are permitted to incur daylight overdrafts on Fedwire.
33. Alm ost all users of real-time transfers are regional
banks and second-tier regional banks (former sogo
banks), which have relatively large intraday reserve bal
ances. City banks usually use the designated-tim e trans
fer facility.
34. There also are business customs in Japan that con
centrate funds transfers on specific days of the month,
particularly on the 10th, 20th and the end of the month.
These customs also apply in settling maturity dates of
corporate financial investment in large-scale-tim e depos
its, CDs and other instruments as well as those Japanese
governm ent bonds. The settlement dates for Japanese
governm ent bonds, however, have been changed to 5,10,
15, 20, 25 and the end of the month since August 1987
(so-called 5/10 days settlement).
35. There is a custom of designated-tim e transfer in the
BO J-checks system too. The drawer of a BOJ check
stamps either “ check clearing” or “the day’s closing” on it
to show when the settlement should be executed. When
the payee presents the check at a BOJ window, BOJ
debits/credits the account of the payer/payee at the time
duly designated on the check (the designated time should
come after the check presentation, and on the same
business day). Checks without stamps of time designa
tion are processed im mediately after their presentation
(immediate processing).
36. The shortening of the time lag between contract and
settlement will lessen settlement risk. At the same time,
however, the probability of settlement failures due to
operational mistakes may rise.
37. With the bankruptcy of the Herstatt Bank in 1974,
CHI PS, initially a next-day settlement system, shifted to a
sam e-day settlement system. In the United Kingdom,
funds transfers in the short-term money, foreign exchange
and futures markets are handled by CFIAPS or Town
Clearing, which is a same-day settlement system, and
gilts are settled through CGO (Central Gilts Office), which
is a sam e-day settlement system operated by the Bank of
England. In Switzerland, most funds transfers in financial
markets are settled through SIC (Swiss Interbank Clear
ing), which is a same-day settlement system.
38. A BO J-check is one of the devices for ensuring delivery-versus-payment. For example, an overseas institu
tional investor sells Japanese stocks through a securities
house in Japan. The securities house presents a BOJ-
31
check, which may be received from a bank where it has an
account if the securities house does not have an account
with the Bank of Japan, to the proxy bank where the
overseas investor holds an account. The proxy bank
presents stocks to the securities house. In this way, the
BO J-check and the stock are physically exchanged at the
same time. This is a delivery-versus-paym ent system
because a BO J-check is regarded as cash by financial
institutions in Japan. This is one of the reasons why the
BO J-checks system remains in use despite the introduc
tion of the electronic BOJ-NET system.
REFERENCES
Bank of Japan, “ Japanese Transfer Systems in the Era of
Financial Deregulation and G lobalization,” the Bank
of Japan Report (No. 1), July 1989.
Group of Experts on Payment Systems of the Central
Banks of the Group of Ten Countries, “ Report on
Netting Schem es,” February 1989.
32
Federal Reserve Bank of New York, “ Large-Dollar Pay
ment Flows from New York,” Ouarterly Review, Winter
1987-88 pp. 6-13.
Suzuki, Yoshio (editor), “ The Japanese Financial System,”
Oxford: Clarendon Press, 1987.
E conom ic R eview / Fall 1990
The Analytics of German Monetary Unification
Thomas 1. Sargent and
Francois R. Velde
Visiting Scholar, Federal Reserve Bank of San Fran
cisco, and Senior Fellow, Hoover Institution; and Stanford
University. Support for Mr. Velde's research was provided
by a grant from the Center for Economic Policy Research
Stanford University. The authors would like to thank
Darrell Duffie and the members of theeditorial committee,
Bharat Trehan and Chan Huh, for their comments.
This paper studies a situation in which two previously
isolated countries decide to unite their currencies and
their fiscal policies. We assume that initially there is a
"so currency" country and a "hard currency" country.
ft
Given fiscal policy, we study the range ofexchange ratesof
"sof t" for "hard" currency that are feasible set. The
inflation rate under the new consolidated government
depends on thefiscal policy itfollows, but does not depend
on the exchange rate selected.
Federal Reserve Bank of San Francisco
OnJuly 2,1990, EastandWest Germany became united
through a common currency. The West German Deutsche
Mark (DM) became the only legal tender on both sides of
the border, and debts and payments denominated in the
East German Ostmark (OM) were converted to DM at
rates stipulated in an agreement signed by both govern
ments on May 2.
The monetary union of East and West Germany raises a
variety of issues , including the consequences of choosing
one conversion rate over other possible rates, the price
level implications of the conversion , and the welfare
implications of the conversion for citizens of the two
countries. To shed light on some the issues involved, this
paper provides a theoretical analysis of German monetary
unification .
Our analysis relies on a standard model of money,
specifically, the overlapping generations model of Sam
uelson (1958). Although othermodels , suchas thecash-in
advance model , are available, our key conclusions depend
on aspects of the model that would appearin virtually any
model of money, namely, the budget constraints of the two
governments and the demand for fiat currency in each of
the two countries being a function of the rate of return on
currency. Thus, very similar results would emerge from
these other models.
We analyze two countries which initially manage to
isolate themselves , so that neither country trades with or
borrows from the other, nordo theresidents of one country
hold the currency of the other. One country balances its
budget and thereby supports a zero-inflation monetary
system . There is also a country that runs a persistent
government deficit and finances the deficit by a combina
tion of inflation tax and repressed inflation. We model re
pressed inflation as a legal restriction or rationing scheme
that forces citizens to hold more currency thanthey volun
tarily would . This produces a "currency overhang" and
repressed inflation. These legal restrictions are to be
interpreted in the mannerof Bryant and Wallace (1984) as
devices to increase the base of the inflation tax.
We refer to the first country as the " hard currency
country " because the value of its currency is stable over
33
time (there is zero or low inflation), and people hold and
exchange its currency voluntarily. We refer to the other
country as the "soft currency country" because its currency lacks one or both of those attributes: the value of
its currency is deteriorating over time, and/or particular
classes of people (typically, citizens of the soft currency
country) are required to hold some of its currency involuntarily, eitherthrough explicit savings requirements or as a
consequence of a commodity rationing scheme.
We compare the initial situation with.a second one
whichwecall monetary union: in the former softcurrency
country, the controls that forced residents to hold the soft
currency are dismantled. Thecurrency andcreditmarkets
are united with those of the hard currency country. In the
process, the new, consolidated government chooses a rate
at which the old, soft currency will be exchanged for the
new, single currency. We study howtheinflation ratein the
unified monetary system depends on thefiscal policy ofthe
new government. We show thatthereis a rangeofratesthat
can be sustained as equilibrium exchange rates, and we
study the welfare consequences of a choice in this range.
I. Overview
In this section, we provide a brief overview of our
arguments and results. Our reasoning exploits properties
of two basic relationships: a demand function for government-issued currency, and the government's budget constraint.
In themodel weuse, money is heldvoluntarily by agents
to an extent determined by the return on currency. Since
currency does not pay explicit interest, the real rate of
return on currency is the change in its purchasing power.
Sinceweprefer to work with gross rates ofreturn (one plus
the net change), we denote the rate of return on currency
from t to t+ I as Rt =p(t)/p(t+ 1), where p(t) is the price
level at t. We assume thattherealdemand for currency in a
country is anincreasing function of Rt , which wedenote by
f(R t ) ; the nominal supply, or stock of currency at t isH (t),
and f(R t ) = H(t)/p(t).
A government can raise real revenues by generating
inflation, thereby imposing an inflation taxon people who
hold currency from t to t +1. The basefor thetax is f(R t ) ,
the realamount of currency held,while therate ofthetaxis
1- R; The government's budget constraint at t can be
written as
H(t) - H(t-l)
p(t)
=D
In a steady statesituation, Rt equation becomes
f (R) x
base of
inflation
tax
(1- R)
= R, = R, sotheabove
=D
rate of
inflation
tax
which decomposes the amount of inflation tax collected
into the product of the base for the tax and the tax rate.
When the demand forcurrency is an increasing function
of R, the inflation tax revenue function f(R) (1- R) is as
depicted in Figure 1. As R rises from some low value,
f(R ) (1- R) initially risesbecause the baseof the taxf(R)
risesfaster thantherate 1- R falls. Eventually, however, as
R risestoward 1, thatis, as inflation falls to O,f(R) (1- R)
begins to fall toward O. Notice that, as a result of the
curve's shape, if there exists one tax rate that finances a
Figure 1
fIR)
f(R)(1-R)
feR}
H(1)
(1)
,
1
f(R)
II
H(O)
--11--+0
p(1)
p(1)
where D is the real value, assumed constant over time, of
that portion of the deficit financed by currency creation.
This budget constraint can be written as
H(t) _ H(t-l) p(t-l)
p(t)
p(t-l) p(t)
=D
0l--
----::;~~----~---
or
O;---~---------+___,
R
34
Economic Review / Fall 1990
steady state deficit D, then there are in general two such
rates. Forreasons indicated below, wewill assume that we
are always in the "good" equilibrium (with a higher R or,
equivalently, a lowerinflation rate).
For a single closed economy, Figure 1 can be used to
determine the steady state equilibrium value of R, and an
initial price level p(l) at some time t= 1. First, the equilibrium R is determined by the intersection of f(R) (1- R)
withthedeficitD. Then, giventhatvalue of R, equation (1)
writtenat t = 1 canbe manipulated to yieldan equation that
determines p(1) as a function of some initial inherited
currency stock H (0):
H(1) - H(O)
p(l)
=D
or
H(1)
H(O)
f(R) = p(l) = p(l)
+ D.
Thisequation can be solved for p (1) as a function ofD and
H(O). We can use Figure 1 to pick off the value of f(R)
associated with the equilibrium R.
Our model of EastandWest Germany before unification
describes the two separate economies using two versions
of Figure 1, one witha very lowD, theotherwitha highD.
The country that runs a low deficit D attains a highreturn
on moneyR and a low inflation rate. The country with a
higherD attains a lowerR, assuming it is willing to allow
the pricelevel to be determined freely by the supply of and
demand for its currency. Later in this paper, we describe
some measures that a government can take to enhance
artificially the demand for its currency. Usinga version of
Figure1, weshallshowhow suchmeasures can beused to
raise the base of the inflation tax and reduce the tax rate
needed to finance a given deficit. We represent East
Germany as having resorted to such measures.
Our approach to studying currency unification can be
summarized by constructing a figure as the vertical summationof thetwo versions of Figure 1. At some time t = 1,
we suppose that the two countries open their borders and
consolidate both their currencies and their government
budgets. The stock of the new currency is the sumof the
old western currency and the old eastern currency multiplied by an exchange rate e: the old easterncurrency is, in
effect, exchanged for the new currency at a rate of e DM
per OM. This means that the currency stock inherited at
time t= 1from the old regime is Hw(O) + eHE(O), where
the subscripts Wand E referto West andEast, respectively.
We want to studythe consequences of alternative values of
e. The unified monetary-fiscal authority assumes the old
Federal Reserve Bank of San Francisco
deficits, so that the deficit of the unified government is
simplyD = DE + Dw. Thedemand for the new currency
isf(R) = fE(R) + fw(R), so that the inflation tax revenue
is (1- R) [fE(R) + fw(R)).
Figure 2 depicts the equilibrium values for R andp(1) in
the new regime. Inspection of that figure shows that
whether an equilibrium exists in the new regime does not
depend on the value of the exchange rate e. Indeed, if an
equilibrium exists, there are many values of e compatible
with that equilibrium.' A stationary equilibrium depends
only on the size of DE + Dw relative to the maximum
height attained by the inflation tax revenue function
(1- R) (fE (R) + f w (R) ). When a stationary equilibrium
exists, the value of e influences the value of the pricelevel
p(l): the higher is e, the higher p(1) will be. Thus, our
apparatus distinguishes sharply between the "level" and
"rate of change" effects. The setting of e is irrelevant for
the steady state inflation rate under the new regime, but e
does influence the "one-time" inflation at the start of the
new regime.
In the remainder of this paper we use this model to
elaborate on the consequences of the move to monetary
unification. We study what difference the choice of e
makes, and to whom. We find that the choice of e matters
to easterners and westerners who enter unification with
either assets or debts denominated in either former currency, but that it doesn't affect the welfare of others.
Although the exact detail of who wins and loses in the
process of unification maydependon our particularmodel
(which is the overlapping generations model of Samuelson, as notedabove), the generalmacroeconomic features
Figure 2
fIR)
f(R)(1-R)
H(1)
feR)
De + Ow
= --=
He(O) + eH w (0)
p(1)
p(1)
+
D
I-------~~~--~----
O+---~---------'------.:~__,
(fe(R) + f
=
w
f(R)(1-R)
(R»(1-R) ~
R
35
of our results, are muchmore robust, because they depend
only on features of the demand formoney and the government budget constraint that are embodied in Figures 1
and 2.
The remainder of this paper is organized as follows.
Section II presents the basic economic model we use to
describe a closed monetary economy, and some of the
policy options open to the monetary-fiscal authorities. In
Section III weindicate which options are assumed to have
been chosen by the authorities of the two countries. Section IV describes the consequences of a monetary unification hitherto unforeseen and suddenly implemented.
Section V examines the effects of an anticipated monetary
unification. Section VI examines anticipated unification
when there is uncertainty about the exact terms of unification. Finally, Section VII discusses some qualifications.
II. TheModel
We willbe usingan overlapping generations model of a
simple kind. Models of the type used in this paper were
used by Wallace (1980), Sargent and Wallace (1981,1982),
Bryant andWallace (1984) andSargent (1987). Thepresentation in this paper most closely follows Sargent (1987).
Time is discrete and starts at t = 1. Each period, a
generation is born, which is destined to live two periods,
and is indexed by thesubscript t; also,inperiod 1, there are
agents called the initial old, who live only one period.
There is a single consumption good in each period. The
agents'identical preferences aredefined overconsumption
in each period of their lives; these preferences are representedby u(c/t), c/t+ 1»; theinitial oldhave preferences
uo(co(1» . The vector of endowments in both periods is
represented by thepair (6)7 (t), w7 (t+ 1», where h indexes
the agent. We allow the possibility that some agents have
different endowments from others. There is no production
in this model, nor is there any uncertainty.
Therearetwo countries, calledEastandWest. Variables
that arespecific to eithercountry carry an E or W subscript.
Each country has a constant population of size 2Ni for
i E {E, W}. Before themonetary reform, eachcountry hasa
government which can collect lump-sum taxes on agent h
of generation t. After-tax endowments will be called
(w1 (t), w7 (t+ 1». Ourintention is to focus onthechanges
in fiscal policy that will be feasible after unification; for
this reason, weconsider the taxschedule prevailing before
unification as given, andsubsume it in the after-tax endowments. Later, we will analyze departures from this initial
state.
A government can alsoissue intrinsically useless pieces
of paper called East or West Marks (and denoted EM or
WM). The total amount of currency outstanding at theend
of period t is written Hi(r). Theinitial oldin bothcountries
are endowed with an aggregate amount H/O) of their
currency. Governments purchase the consumption good in
36
the amounts G/t), and dispose of it in ways that procure
utility for no one.
Eachperiod, there is a market fortheconsumption good
in each country, and the price of the good in Marks is
written p /t). There is alsoa market forloans among young
agents. We willassume thatthese loansaredenominated in
Marks, and carry a nominal interest rate denoted rt. 2 The
real interest rate on these loans, by definition, is R, =
rtp(t)/p(t+ 1).
We assume that an impermeable separation stands between the two countries (a Wall), so that no interaction
takes place between East andWest. This Wall was erected
before period 1, and is initially expected to stand indefinitely.
We begin the analysis with a study of some of the
policies that the two governments can conduct. For simplicity, we represent a government's task as the financing
of a constant deficit of taxes with respect to expenditures,
denoted D=:::'O. A government can require the young in
each generation to holda minimum amount A =:::.0 of the
currency in real terms. The parameter A is a policy
instrument that is designed to influence the base of the
inflation tax. 3
We willstudy two possible regimes; in the first one, A is
set equal to 0, so that constraint (2), below, is only the
traditional one which forbids agents to issue currency. In
the second regime, A is positive, and the corresponding
constraint is binding. These options are available in either
country, and this section sets forth the analytics in the
context of a single, closed economy with general endowment patterns. We will later specify which regime will
prevail in each country.
All young agents solve the following problem:
max
u(ct(t), ct(t+ 1»
c/t), ct(t+ 1), let)
(P)
Economic Review / Fall1990
(3). Writing d=DIN, we express condition (3) as
subject to the constraints
ct(t) +
m(t)+l(t)
pet)
~ wt(t)
Rt =
met) + rtl(t)
Ct(t+l)~wt(t+1) + p(t+1)
A. < met)
- pet)
= <p(R t -
(2)
where l(t) denotes the. amount lent (or borrowed, if negative) by the young agent, and met) the agent's choice of
money holdings.
Theequilibrium is the solution to the agents' maximizationproblem, the goverment's budgetconstraint, as wellas
an equilibriumcondition in the credit market.
Regime 1: Either A. = 0 or thecurrency constraint is never
binding
A classic arbitrage argument shows that equilibrium
requires
rt = lorRt~
pet)
p(t+1)
Agents' decisions can be represented by a saving function,
which is thesolution to the maximization problem above.
Lettingf7(Rt) be the saving of agent h of generation t, we
have
f7(R t) = w7(t) - C7(t),
where R, = p(t)/p(t+ 1) is the rate of return on money
holdings. The functionf7 will be strictly increasing in Rt ,
underthe assumption of gross substitutability of consumption in the two periods. It should be kept in mind that this
function depends on the after-tax endowment of each
agent.
The government's budget constraint is
(5)
l )·
An equilibrium sequence {R t } ";'= 1 will solve thisfirst-order
non-linear difference equation.
The function <p can take many forms, depending on the
utility function u. In the case where u takes the form
u(cf'Ct + l ) = In(ct)
f is found to be
feR) =
ill
2 -
where il j =
t
+ In(ct+ l )
n,
2R
(6)
w7 for i E {1,2}, and (5) becomes
il
2
If + 2d-il l-il2+il l Rt - l =0
t
which is shown in Figure 3. If ill > il2 holds, then for
values 0 ~ d ~ d * = (~ - v'TI;)2 there are two
stationary solutions for R (andfor h), found by intersecting
the graph of d + Rf(R) with that of f(R). Figure 4 shows
the function (1- R)f(R), and the two stationary solutions
=
can be found for any deficit d < d*. In the case d 0 0, the
two solutions are 13 and 1, where we define 13 = 0 21 < 1.
Under rational expectations dynamics, the lower gross
rate of return on currency, B., is stable, whilethe higher R,
is unstable. Anypath startingat h (1) E [0, hl (respectively
s, E [ ~2 R]) will converge to b:. (respectively B.). Paths
starting at'h(1) > Ii (respectively R, > R) are not feasible
because they eventually drive h (t) to +00, which would
Figure 3
H(t)-H(t-1)
D=
()
,t>l
pt
-
fIR)
H(t-1)
H(t)
=-()-Rt- l P ( l 1),t>2
Pt
r:
+d
t:' (Rt-t!(R t- l ) + d)
f(R t) = Rt-t!(R t- l )
(3)
-
d + Rf(R)
Rf(R)
~~JI'I'-- feR)
and the equilibrium condition in the credit market is
h
=
_ H(t)
~ ft(R t) -Nf(R t) - p(t) .
(4)
This equation states that the net saving of generation t
equals the net dissaving of generation t - 1 and of the
government.
Equation (3) defines a one-to-one mapping between R,
and h(t) = H (t) INp(t). We use it to replace H(t) Ipet) in
Federal Reserve Bank of San Francisco
Or=-J~~~-----_:"'-_----,
R
1
R
37
eventually meannegative consumption. HenceR,is necessarily in [ ~ , Ii].
Figure 5
[
Notice that the comparative dynamics associated with
the "stable" stationary values 8. are in some sense perverse: an increase in the deficit raises 8., and lowers
inflation.Thus,we cannotrelyontherationalexpectations
dynamics of this model to focus attention on government
deficits as a causeof inflation. However, it hasbeen shown
in severalcontexts, boththeoretical and experimental, that
learning reverses the stability of the stationary points
CR, Ii) relative to the rational expectations dynamics. 4
Such learning schemes suggest that we select the higher
stationarypointIi as ourequilibrium. PointIi is associated
with "classical" comparative dynamics: a higher deficit
lowers Ii, and thus raises the inflation rate. We appeal to
these learning dynamics as ourjustification forfocusing on
the R stationary equilibrium.
A young agent'sbudgetset is depictedin Figure5: point
C is attained when an interest rate of 1 prevails (in other
words whenthe price level is constant) whereas point B is
attained for R < 1. The seigniorage function f(R)(1 - R)
can be read as the distance Aw, when the line AB has a
slope of -1.
C(t+1)
00 -f(R)
1
CIt)
inflation rate. Note also that the nominal amountof forced
savings per capita grows with time, since it is A- pet).
Chart 1 shows the actual data for East Germany> For the
constraintto be binding, we must verify that
A- ~f7(Rt) for all hand t ~ 1,
which translates into the condition
d~
(7)
(l-R)f(R).
Regime 2: A- > 0, and the currency constraintis always
binding
Another condition must also hold, namely, that consumption remainpositive. This imposes on A- the condition that
We now consider a regime in which A- is positive and
binding.
Evidently, ifthe currencyconstraint is binding, h (t) = Afor all t ~ 1, and
A-
d
< mln (wf) = ~I'
which translates into the following condition on R:
R<1
_.!!-
=
R*
!QI
d=A-(l-R t ) or Rt=R=l-""5:.
Thus, the inflation rate is unique, constant, and positive.
Note that increasing A- raises R, thereby lowering the
Figure 4
Chart 1
Nominal Savings Per Capita
in East Germany (1949 - 1989)
Thousand
Marks
10
f(R)(1-R)
8
6
4
2
d
O+-~t...--'-----------'~...3or-----,
R
38
1950
1960
1970
1980
1990
Economic Review /Fa1l1990
Thus R is bounded above, away from 1; furthermore, R
must lie in the regions of (0, 7?*) where condition (7) is
satisfied.
In the case of the logarithm utility function, (7) is
satisfied if: a) d > d * , and then it is true for all 7? E ( 0 , R * y ,
or b) 0 < d < d * , and then it is true for R € (0,7?) u {R,
R *). Note that a) corresponds to values of the deficit that
cannot be financed in regime 1. Moreover, in b) the return
on money R can be chosen to be higher than in regime 1.
Figure 6 illustrates this: the seigniorage function
(1 —R ) f { R ) is represented and the region below that curve
is shaded. When the deficit is d2, it cannot be financed by
voluntary holdings of money. A solution with forced sav
ings can be found as the intersection of the d 2 line with the
graph of \(1 —R ) , with the resulting rate R 2. If the deficit
is d x, it can be financed with or without the currency
constraint; with the constraint^ a rate such as R x can be
achieved, which is higher than R. With a lower value of A
.,
lower rates of return are achieved, such as 7?3.6
It is possible, depending on the utility function and
endowments, that every agent would prefer regime 2 to
regime 1. This situation is illustrated in Figure 7: point A is
that attained in regime 1, point B in regime 2: the utility
level is higher under the forced savings regime. Thus
regime 2 could be justified on two grounds, depending on
the level of deficit the government has chosen to finance via
inflation: that this deficit is too high to be financed with
voluntary holding of money by agents, or that the govern
ment can improve agents’ welfare by moving from regime
1 to regime 2.
Figure 7
can be made higher (and the inflation rate lower) in regime
2, as we saw. The other is that the initial price level p { 1) is
higher in regime 1.
To see this, we solve for p { 1). The government budget
constraint at t = 1 is
d =
77(1)-77(0)
'
In regime 1, the equilibrium condition yields
Npil)
a,
P ( 1)
T
There are two senses in which we can speak of repressed
inflation in regime 2: one is that the rate of return on money
N{iV
77(1)
N
+
H( 0)
2 - fl2/27?!-<7)
H{ 0)
N
H {
0)
N (m )- d )
In regime 2, it yields
N p (\)\
77(1)
H {
Figure 6
a
a
) = p m
27?j
a,
P(D(
P(l)
Repressed Inflation
P i 2)
p(l)
0)
= N (\-d) ■
Thus, as long as the legal constraint on money holdings is
binding, the initial price level is higher in regime 1.
This result can be reformulated in the following terms:
suppose that regime 2 has been in force from t = 1 on, and
that, at time t = t0, the legal restriction on money holdings
is removed unexpectedly, all other parameters of the prob
lem remaining unchanged. Then, either the deficit is too
high to be financed and money becomes worthless imme
diately, or else it can be financed, in which circumstance
the actual price level p ( t 0 ) is higher than was previously
expected, and the inflation rate is higher from t0 on than at
any time before. This is the content we give here to the
phrase “repressed inflation.”
Federal Reserve Bank o f San F rancisco
39
III. East and West before Unification
In countryEast, appropriate socialarrangements ensure
that all agents receive identical after-tax endowments ("Il'
.
"12 ) , "11 > "12' m all generations t ~ 1. Agents within a
generation are identical in preferences and endowments
which implies that there will be no intra-generational
lending: each agent chooses l ~(t) = O.
The government of East faces a constantpositive deficit
of tax revenues with respectto its expenditures, so that for
all t~.1
GE(t) -
t
~ 77(t) -
77-1 (t) =
DE
with D.E > O. It h~s chosen to resort to a currency
constraI~t, so that regime 2 as described above prevails in
East. ThIS meansthat the equilibrium pricelevel pathis of
the form:
PE(t) = PE(l)(
1
R
)t-I
E
with RE = 1 -
~E =
~
1-
~
NEA '
E
> <X 2 and f32 >
~I'
which makes the first type of agents (indexed by Wo)
"lenders" and the second type (indexed by Wf3) "bor:owers". A consequence of this assumption will be to
mtroduce some distributional effects of the events which
will happen in Sections V and VI. It is assumed that
N I <X 2
NI<X I
+ N2 f32 = - ~ <1
0
+ N2~I 0 tv '
which insures existence of equilibria with valued fiat
currency.
Agents solve the maximization problem (P) referredto
a?ove and ~hoose to hold private debt as well as money:
SInce we still assume that private debt is not indexed the
budget constraint of a young agent in the West endowed
40
+
m {\r(t) + l {\r(t)
< h
Pw (t )
- w1
c7(t+ 1) <
t
-
wh
+ m{\r(t) + l{\r(t)
Pw(t+ 1)
2
m{\r(t) ~ O.
Lenders are indifferent between holding money or private debt, while borrowers will set m{\r13 (t) = 0 and
l{\rl3(t)
:s o.
The government of country West is assumed to be
running a "tight" policy: the deficit is set to D = 0 in all
periods, and the money stockis constant, H (r) = H (0) for
all t. Taxes are set so as to achieve this goal.
.Thisis merely a particularcase of regime 1, with D = 0;
WIth the logarithmic utility functions, we know that there
may be two stationary solutions f3 and 1. Indeed, the
equilibrium condition is
l{\r(t)+m{\r(t) =
Pw(t)
h
) .
In countryWest, N I agents have the endowment (o <x )
while N 2 =Nw - N I agents have the endowment (f3I~~2).
We assume that
<Xl
ht )
c(\t
!
HE(O)
p(l) = NE(A-d
.
WIth (00 h h)·IS
1,00 2
!
h
h
_ Hw(O)
fw(t) - Pw(t)
,t~ 1
(8)
and with logarithmic utility functions (8) becomes
OF
2 -
Pw(t+ 1) O~
Hw(O)
Pw(t)
T = Pw(t) .
(9)
The general solution to this first-orderdifference equation
in P (t) is found to be
Pw(t) = Pw
+ (Pw(O)
- Pw) (
~
)t
(10)
s
where we defined
_
_
Pw -
2Hw(0)
OW_f'lW
1 H2
> 0 and R s
ow
=
0 ~ < 1.
1
Th~
constantPw is the unique non-inflationary solution, in
WhICh R, = 1. For all other solutions, R, = R, < 1 is a
constant, and limt_>oop(t) = 00. The sameargument about
stabilityunder learning, as described above, will serveto
select the non-inflationary equilibrium, in other words the
one withthehighestreturnon money. We willconsiderthis
equilibrium to be prevailing in West.
Economic Review / Fall1990
IV. Monetary Unification
We consider the following situation. At some date,
whichwerenormalize to be t = 0, the Wall separating East
and West unexpectedly disappears. The two countries
unite, and become provinces of a single country. The two
governments merge to form a single government. Thisnew
government inherits the stream of expenditures and preunification taxes, and has the power to impose new taxes
on the citizens of both(former) countries. Wewill assume
that the new government enacts the following rule: residentsofeachhalfofthenewcountry maymove totheother
half, in which case they will receive an endowment of
(0,0). 7 This ensures that the distribution of population
remains the same after unification: agents will not move
between the two provinces, and they can be taxed at
different rates, depending on prior citizenship (that is, on
their current place of residence). The single government
also has the ability to issue a currency called the Mark
(denoted M). These arrangements prevail for t 2:. 1. At the
beginning of period 1, all West Marks are exchanged for
Marks oneforone, andall EastMarks areexchanged at the
rate ofone EM for e M. The government chooses e, and
sets A = 0, which means that in theEast the compulsion to
hold currency has been eliminated.
Our purpose in this section is to describe the class of
exchange rates, interest rates, price levels, and inflation
ratesthat are consistent with thesenewarrangements. We
establish the following:
1. If the consolidated government adopts the fiscal
policies of the two preexisting governments, so that the
deficit of theconsolidated government is simply thesumof
thedeficits of the two priorgovernments, it mayormay not
be feasible to effect monetary unification without fiscal
changes, depending onhowbig theconsolidated deficit is.
2. If it is feasible for the new government to effect
monetary unification under a fixed policy that simply
consolidates thedeficits of thetwo countries, then there is a
large number of admissible exchange rates. For young
people born at t 2:. 1, welfare is identical for any feasible
choice of an exchange rate. For the old at t = 1, who bring
theiroldEastandWest Marks intothe new unified system,
the choice of the exchange rate matters. Easterners are
better off, the higher the value chosen for e.
3. If the fiscal policy of the new government simply
consolidates and continues the deficits of the old governments, the move to monetary unification raises the inflation rate in the West and mayor may not reduce it in the
East, depending on the real value of the constraint previously imposed. All western lenders born at t ::::. 1 are
Federal Reserve Bank of San Francisco
madebetteroff by this change. Western borrowers bornat
t::::, 1 are made worse off by this change.
4. Theincreased inflation rate imposed onwesterners by
the monetary unification can be avoided by reducing the
deficit of the consolidated government. Theconsequences
for different citizens' welfare of this deficit reduction
depends on precisely which people's taxes are raised.
The new government has the possibility to depart from
prior taxing practices; any new taxes it decides upon will
be denoted 'T 7(i) (tax on agent h of generation t in period
i E {I,2} ofhislife). Theresulting after-tax endowment will
be denoted w7(i). The aggregate tax burdenon the young
(respectively old) in period t is denoted T1 (t) (respectively
T2 (t)). Our assumptions imply that the government may
forever tax young and old in each (former) country separately; therefore both T1 (t) and T2 (t) may carry E and W
superscripts.
Theoldgeneration at time t = 1,whoareindexed 0, have
the budget constraints
h
m~(O)_
easternborrowers: c E(l) -::; e p(l)
+ 'Y2
c{\r(l)-::;
m{\r(~(:)l{\r(O) + &2
western borrowers: c{\r(l)S
m{\r(~(:;{\r(O) + ~2
western lenders:
The young in all generations will henceforth face the
following problem:
max u(ct(t), ct(t+ 1))
subject to the constraints
ct(t)
+
m(t)+l(t)
p(t)
~ wt(t)
c/t+ 1)S w/t+ 1) +
m(t)+l(t)
p(t+ 1)
the solution to which is represented by the saving function
f7(R t ) = (mh(t)+lh(t))/p(t).
The government faces the budget constraint
H(t)
H(t-l)
D(t) = p(t) - Rt- 1 p(t-l) ,t > 1
(lIa)
D(I)= H(I) _ Hw(O)+eHE(O)
p(l)
p(l)
(lIb)
41
D(t) = Dw(t)+DE(t) = (-TF(t)-Tr(t-1)
+ (DE
-Tf(t)-T~(t-l».
The equilibrium condition is, for all t
Ft(R t) =N1f'fa.(Rt)
H(t)
pet) .
~
1:
+ N2f'f13(Rt) + NEff(R t)
(12)
The following proposition is a straightforward application of the Kareken and Wallace (1981) result on the
indeterminacy of exchange rates.
Proposition 1. Given an equilibrium {Rt, pet), H(t),
(1' 7-1 (t), l' 7(t) )h' C7-1 (r), C7(t), e} '7= 1
,foranyeE (0,00)
there existsanotherequilibrium satisfying Rt = k; l' 7-1 (t)
= f7-1(t), 1'7(t)= f7(t), c7(t)=c7(t), c7(t+1) =
C7(t+ 1) for all h; andp (t) =1= pet), B(t) =1= Ii (t),for all
t, c3(1) =1= c3(1).
Proof:
We take as given that a monetary equilibrium exists; the
macron-bearing equilibrium, {Rt, pet), B (t), 15 (t), e} '7= l'
solves (11) and (12). For any choice of eE (0,00), wecan
construct a caret-bearing equilibrium as follows. Given a
choice of e, combine (lIb) and (12) into
D(I)
= F (R)
1
1
_ Hw(O)+eHE(O)
p(1)
Solve this equation for p(l) to get
A(1) = Hw(O)+eHE(O).
p
F 1(R 1) - D (1 )
(13)
Since the macron-bearing equilibrium solves (11) and (12)
with positive money stocks, the denominator on the right
hand side of (13) is positive, and (13) can be solved for
P(1)· Then p(t+l)=p(t)/Rp and (12) gives fi(t) =
Ft(Rt)p(t). Sincefi(t)/p(t) = B(t)/p(t), (l1a) will be
satisfied. 8
One can interpret this proposition in the following
sense: fora given fiscal policy {(1'7-1 (t), 1'7(t) )h}'7= 1such
that money has value in equilibrium, there are corresponding sequences of "real" variables {Dt, Rt, (c7(t),
c7 (t + 1))h } '7= t- There is a continuum of price paths
{p (t) }'7= 1 (and corresponding paths {H (t)} '7= 1) consistent
with these sequences, indexed by p(1); the choice of e E
(0,00) is sufficient to select thepricepathvia equation (13)
(which gives p (1) as an affine? function of e), without
altering anyotheraspect of theequilibrium. Theexistence
itself of the equilibrium is a disjoint issue from the choice
42
ofthe exchange rate, andis amenable to the same analysis '
aswas conducted in Section II. Moreover, since thewelfare
of generations t ~ 1 depends only on R, and not on the
specific price level path, the choice of e affects only the
consumption of the old at t = 1. Forthe latter, eachchoice
of e corresponds to a particular distribution of consumption good.
When does a monetary equilibrium exist? Figure 8 will
be helpful in this context. The seigniorage functions of
bothprovinces f E(R) (1- R) and fW (R) (1- R) have been
represented, as well as the sum F (R) (1- R). Since the
unified country will not resort to the A constraint, a
monetary solution is found as the intersection of the y = d
linewiththegraphof F (R) (1 - R). If thenew government
simply consolidates East's deficit without raising taxes,
that is, D(t)=DE, then a monetary equilibrium mayor
may not exist. In Figure 8, the deficit d2 cannot be
financed, although it was financed by Eastunderregime 2.
On the otherhand, d 1 can be financed. The value d* is the
largestdeficit that can be financed.
If an equilibrium exists in the unified country, the
inflation rate will rise in West, simply because it was 0
previously (Rw = 1), and because R = 1 is incompatible
witha positive deficit. AsforEast,theinflation ratemay be
higher or lower, depending on the choice of A that was
made initially. For AI' the new rate of return R will be
higherthan R 1, and conversely for R2 . It is also apparent
that, should thedeficit belowered, theinflation ratemay be
made lower. How this affects agents' welfare, however,
will depend on who is taxed to finance this deficit reduction.
Thus, if we compare the welfare of generations t < 0
with that of generations t ~ 1 (and assume that taxes are
unchanged), weneedonly consider realrates ofreturn, and
Figure 8
f(R)(1-R)
EconomicReview / Fall 1990
we see that while western lenders will necessarily suffer
(and western borrowers benefit) from the unification and
the ensuing increase in inflation, easterners can be better
or worse off. Which way easterners' welfare goes does not
depend on the exchange rate chosen, but rather on the
extent to which they were constrained initially. We refer
again to Figure7 on this question.
Welfare implications for the t = 0 generation
We now consider the welfare implications of monetary
unification for the old at time t = 1. For all save the first
generation, welfare is identical under all the equilibria of
Proposition 1 above. Forthe old at time t = 1, on the other
hand, the reallocation effects of varying the exchange rate
are important, simply because they are exchanging their
old money for the new one, in bothprovinces. To see this,
rewrite the eastern old's consumption in period 1 as
h
_
CE(l) - 'Y2
+
PEel)
e pw(l)
Pw(l)
p(l)
REfE(RE)
where PEel) denotes the price level which would have
prevailed had the Wall not fallen. For the western old,
consumption is
With logarithmic preferences, the saving function for
each consumer is
W2-1'~
2R,
The equilibrium condition becomes
t
f7(R,) =
01 -T1
02-T2
H(t)
2
2R,
= pet) ,
(14)
and the government's budgetconstraint
D =H (t_)-_H~(t_-_1)
__
pet)
(15)
Equations (14) and (15) imply a second-order difference
equation inp(t)
(01- Tl)P(t+1) - (01-Tl+02-T2-2D)p(t)
+
(02 - T2 )p (t-1) = 0
(16)
which,undera boundedness condition on D, hassolutions
of the form
pet) = a(
;1 )'-1 + b( }2 )'-1 withR. > R2,
h
_
Pw(l)
_
Pwpel)
c w (1 ) - w2 + p(l) Rwfw(Rw)-W2+fw(l)
where a and b aresubject to thecondition thatp (t) remains
positive, as well as to the initial condition
Remembering thatfw(l) > 0 forlenders, it is clearthatthe
welfare oflenders worsens, thehigher theactual price level
is in period 1, and conversely for borrowers (inflation
benefits debtors). Whether they are better off than if the
Wall hadn't fallen depends on whether pw= Pw(1) > p(1).
The eastern old's welfare falls when elp(l) falls; whether
they are better off without the Wall depends on whether
ePE(l)Ip (1) > 1. Notethattheeastern old'sinterests donot
necessarily conflict with that of either class of western old.10
Thus, to evaluate the welfare consequences of the move
to monetary union, we need to specify what fiscal policy
the new government adopts. This fiscal policy will determine the new equilibrium returnon currency R, as well as
the the price level p(1) as a function of e. To compute
solutions for various fiscal policies, we return to the
assumption thatpreferences are identical in bothcountries
and of the logarithmic form studied above.
Let us consider the case where the new government
decides to tax the young of all generations and of both
provinces by an amount T1 = !h 1'1 in the aggregate, and
the oldby an aggregate amount T2 = ! h l' ~, for t ~ 1so as
to set a constant deficitD =DE - T1 - T2 ~ 0 forali t ~ 1
(recall that the previous deficit pathswere DE forEast and
ofor West).
Dp(1) =
Federal Reserve Bank of San Francisco
°
1 -T1 p(l)
2
-
°
2 -T2
2
p(2)
- Hw(O) - eHE(O).
(17)
A stationary or constant-inflation equilibrium corresponds
toa=p(l), b=O or to a=O, b=p(1). In both cases, the
path {p (t)} ';"= 1 is ofthe form
pet)
= p(1)( ~.
)'-1, i E {1,2}
I
and imposing (17) determines p(l) as
p(1) =
2(Hw(O)+eHE(O))
01-Tl + (02-T2)IRj - 2D
(18)
Thus, p(1) is an affine function of the exchange rate
chosen. From Section IV, we know that
2Hw (O
)
Pw(1) = Ow-Ow'
1
2
Hence
p(1) > Pw(1) if and onlyif
(1)
_ _ _ _ _ _ _ _2H--=..E(_O_)e_______
>Pw r
NE('YI ~'Y2/ Ri ) +°2(1-1/ Ri ) -2DE + T1 + (2+ 1/ Ri)T2
43
It appears that there exists a critical value
Hw(O)
e*= - HE (0)
X
NE("i1 - "i21 R;) +11 (1-1 IRi ) - 2DE + TI + (2 + 11R;)T2
2
11 1 -11 2
such that p(1) > Pw(1) if and only if e > e*.
Note that e * may possibly be negative. But if it is
positive, and if the government chooses e < e *, a relative
deflation in the West" will take place in period 1, western
lenders will be made better off and western borrowers
worse off than with the Wall. Conversely, for e > e *, a
relative inflation will occurin period 1. This critical value
of the exchange rate does not depend on the price level in
country East (which is determined by A) but rather on the
ratio of money stocks, on endowment and population
parameters, and on the fiscal policy chosen. In particular,
the value e: =Pw(1)/ PE(1) is irrelevant to theoccurrence of
inflation in the West in period 1, and to the welfare of the
western old. However, e: matters for the eastern old's
welfare, which willbehigher than with theWall if andonly
if el e: > p(1)/Pw(1). The value e: can be thought of as
representing a "black market exchange rate" at thetimeof
unification.
We canconsider a few examples: onepossibility open to
the government is simply to leave after-tax endowments
identical to what they were before unification. In other
words, the East's deficit is left intact and financed by
inflation, and T, = T2 = O. We then rewrite (18) as
P (1) = 2
+ eHE(O)
Hw(O)
ill - il 2 /R i
-
2DE
The critical value is
Hw(O) NE('Yl-'Y2/ Ri ) + il 2 (1 - lIRJ - 2DE
e t = - - -=----'-''---...:..::...----=:.-=---=-;,:------=----~
HE (0)
ill - il2
Another possibility is for the government to tax only the
young of each generation so that T2 = 0, in which case
*
_ Hw(O)
e (Tl) - HE(O)
x
NE'Yl- N E'Y2/ Ri (Tl) + il2 (1-1 /Ri (T l)) - 2DE+ T l
il l-il 2
We must keep in mind that R, will change with T l . If
T, = D, which corresponds to a balanced budget policy,
then R = 1 or R = il2 / ill'
These examples illustrate theway in which thegovernment
has the ability to choose an initial inflation or deflation
(i.e., p (1) > Pw (1) or P (1) < Pw (1)), onceit haschosen a
fiscal policy.
V. The Effects of an Anticipated Unification
We now examine the consequences of a delay between
the announcement of monetary unification and the time
at which it is implemented. We make the following assumptions.
All arrangements described in the first paragraph of
Section IV are announced at time 1 to be prevailing for
t> T. Inperiods t = 1, ... , T - 1, thesame arrangements as
before are maintained, that is, both countries remain
separate, government spending and taxes are unchanged,
East still imposes savings restrictions, and so on.
We assume that at t = 1 a fiscal policy is specified
for periods t:::::"'T, by which we mean that {('T7-l(t),
'T 7(t) )h} ":'= T are announced; a rate e, at which East Marks
will bereceived at t= Tin exchange fornew Marks, is also
announced at t = 1. Agents can therefore compute the
equilibrium allocations and pricepaths.
At time T, everything willproceed exactly as in Section
IV; E and W subscripts will disappear, the old of generation T - I will exchange theirmonies formint-fresh Marks,
markets will open, a price level P (T) (which can be
computed given the fiscal parameters) will prevail.
44
The young of generation T - 1 in the West willthusface
problem (P):
maxu(cT_ l (T - 1), CT-l(T))
subject to the constraints
m (T - 1) + l (T - 1)
TC l (T-l)+
_
CT- l
(T ).9i>2 +
Pw(T-l)
::;: WI
m (T - 1) + l (T - 1)
P (T)
,
the solution to which is again represented by the saving
function!}_l (Pw(T~ 1) / P (T)). The equilibrium condition can then be written
I jh
h
T-l
(Pw(T-1)) =
Hw(O)
peT)
Pw(T-I)
(19)
which is then solved forPw (T - 1) as a function of p (T).
Young agents of previous generations 1:; t :; T - 1 willbe
solving the same problem, and the path {Pw(1), ... ,
Economic Review / Fall1990
Figure 9
Pw(T -I)} can be computed through a backward re-
cursion.
Inthe caseof logarithmic utilityfunctions, (19) takesthe
form
fir _ fiw
2
2
Pw(T)
2pW(T - 1)
Pw(T-1) = Rs-1 P (T)
=
Hw(O)
Pw (T - I) or
+ 2Hn~0)
(20)
1
This is solved backward to give
Pw(t) = Pw+ (p (T) - Pw )(Rsy-tfor 1 S. t
< T-1
(21)
which is just another version of (10), with a specific
starting condition. Therefore, if P (T) > Pw (as in the
examples at the end of Section IV), there will be a
progressive increasein thepricelevel untilit reaches P (T);
andP (t) will increase at an accelerating rate as unification
approaches. Duringthatperiod, theinflation rateincreases
butremains bounded above by 1IRs. Thetimepathof P (t)
is shown in Figure 9. Theinitialboutofinflation atthetime
unification is announced is
Pw(l)
Pw(O)
=
1
+ (p(T)
Pw
- l)(R V-I
s'
whichis increasing in P (T), and, givenp (T), is decreasing in 1. It can be shown that R s > .5 is a sufficient
condition for inflation to be higher in period 1 than in
period 2, as illustrated by Figure 9.
o
1
T
Clearly, if p (T) = Pw, then the price level remains
constant, and if p (T) < Pw the price level will fall
increasingly rapidly as T approaches.
It should alsobe noted thatthevalue of p (T) determines
which path of price levels will prevail in the period
t = 1, ... , T, and therefore the interestrates whichagents
of generations 1to T face. Thismeansthatthe choice of the
exchange rate affects the real allocations of all agents in
generations 1to T, the sameway consumption ofthe old at
time of unification depended on the exchange rate in the
previous section.
VI. Anticipated Unification with Uncertainty
We now add a new wrinkle to the previous set-up, by
introducing someuncertainty overthe exchange rate to be
chosen at time T.
At time 1, the same announcements are made as in
Section V: the two countries will unite at time T, a
consolidated government will take charge of both streams
of government expenditures, and tax residents of both
provinces. A fiscal policy is announced, which supports
a monetary equilibrium. All parameters of the policy
are made known, except for the exchange rate e. It is
announced that the government will randomly choose
among n possible exchange rates (eI , ... , en), with
probabilities ('IT't> ..• , 'IT'n) where Ij'IT'j= 1. The choice
will be made at the beginning of period T. These induce n
states of the world in period T. There is no other uncertainty.
As Proposition 1 makes clear, the information available
to agents allows them to compute the equilibrium se-
Federal Reserve Bankof San Francisco
quences of consumptions and interest rates, for t ::::. T,
whichwill be identical in all statesof the world. The price
and money stock sequences, however, will depend on the
(random) exchange rate: in particular, n possible price
levels may prevail in period T, namely (PI (T), ... ,
Pn(T)), computed from e1 and e2 by using (13):
pj(T) =
Hw(T)+ejHE(T)
.
FT(RT)-D(T) for 1 = 1, ... ,
n.
The probabilities attached to the price levels are ('IT' l' ... ,
'IT' n). Itis morehelpful to thinkof this distribution in terms
of the value money may have in each state, that is, the
reciprocals of the price levels (lIP1(T), ... , lIPn(T)).
We will assume that agents maximize expected utility,
and that utility is additively separable, of the form
u(c(t), c(t+l)) = u(c(t))
+ u(c(t+l)).
We assume that financial markets available to agents of
45
generation T - 1 can be represented by n markets for
claims on one unit of consumption in state i. We denote qi
as the pricesof theseclaims, and s as the quantity of such
claims bought (or sold) by the agent. The price of a real
loan and the price of a nominal loan can be derived from
these n securities prices as
n
1
(22)
'~lqi = -R1T-1
r
=
1
p(T-l)
(23)
--:=-----:-:-
Money is therefore one of the assets available to the agent
for purposes of transfering wealth across timeand statesof
the world.
We will again proceed by backward recursion, starting
from the generation born right before unification, at time
T - 1. The problem solved by an agentof generation T-l
will be
maxE{u(ch(T-l»
+ u(ch(T))}
= u(ch(T-I»
Once p(T-l) and RT- 1 are solved for using these
equations, the next steps are identical to those taken in
Section V. An agent of generation T - 2 faces a pair
of prices (p (T - 2), P (T - 1) and an interest rate RT - 2
(which must equal p (T - 2) /P (T - 1) to preclude arbitrage). His saving function can be derived the sameway as
before, equilibrium will impose
h
p(T-2) _ H(D)
fT-2(p(T-l) ) - p(T-2)
~
which allows us to compute p (T - 2) givenp (T - 1), and
so forth to p(l). Theonlygeneration to face uncertainty is
generation T - 1.
In the case of the logarithmic utility function u (c) =
in (c), (27) becomes
cr(T)
'IT.
= -! ch(T-l).
(3D.O
qi
When these values are substituted into (26) we find
ch (T -
1)
wq
= -2 +
wh
Equation (29) becomes
subject to the constraints
n
I
ch (T - 1) +
clJ(T)<
1
-
i=l
q.slJ
1 1
< wh
1
2H(D)
(25)
Note that the agent now has n + 1 budget constraints,
which can be consolidated into a singlebudget constraint
i
wh
ch (T - 1) + i= 1 q.1 c IJ(T) < to h + R -2
I
(26)
1
1
T 1
'ITi
qi
u'(cr(T)=u'(ch(T-l».
Equations (26-27) describe each agent's behavior.
The market-clearing conditions on all financial markets
i
h=l
~
h
(ci(T)
_
(
h _
2) -
Ih (w1- ch(T -
H(D)
)=°1- p(T-l)
02
_
1
(32)
RT_ 1
or
Ih
ch(T-l) =!li.
'IT
i
(H(D)
Pi (T)
+
q.
c?(T)
n ) _ !l.L
2
-
'ITj
( H(D)
Pj(T)
q),
= _-:":_"..,,-
1
Pi (T)k i
p/T)kj
where we denote
=
H (D) +
n2fJ jeT)
(28)
and use (22) to solve for qi as functions of RT-1:
1
kiPi(T)
.
qi = - R I~ k. .(T) for i = 1, ... ,n
H(D)
pi(T)
H(D)
l » = --p(T-l )
(29)
p(T-1) and RT- 1:
T-1
)=
1 ']
p)
(33)
We then invoke (23) to obtain another relation between
Equation (29) is redundant but convenient. Equilibrium is
characterized by conditions (26-28).
46
Ih
k,
pJT)
can be written in the form
7:
°
RT~l
'IT.
slJ = H(D)
1
1
This equation relates p(T-1) and RT- 1•
We can use (28) and (3D) to obtain
'ITi
(27)
0
=
p(T-l)
qi
The first order conditions are (26) and
(01+
c
(24)
-
wh+s lJ
2
I
fori = 1,... ,n
1
h(T-l)="2
~
(31)
2
2RT -
p(T-1)
= pRT- 1
(34)
Economic Review / Fal1l990
with
n
j~l
n
p
= .I 1 ( -----;:::.----.::---:-- )Pi(T).
n
Equations (32) and (34) at last allow us to solve for
p(T-l):
+ il2
ill
(35)
p
ill
Note the formal analogy between (20) and (35). This will
allow an easy comparison with the case under certainty.
Since P(T - 1) is solved as a function of the distribution
of (PI (T), ... ,pn (T) ), the price sequence {p (1), ... ,
P(T - 2)} can be solved for recursively, using equation
(20):
for 1
~ t ~
T -1,
p(t)=p+(p(T-l)-p)(
n
_1
il2
)t-Y+l
(36)
withp being thezero-inflation pricelevel prevailing before
t=O.
We establish the following result:
Lemma. In the logarithmic utility case, for any distribution (Pl(T), 'IT l;··· ;Pn(T), 'IT n), thefollowing holds:
1
P > (E p(T))
-1
n
j~l (o.j-a)(j(o.) - i~l'ITJ(o.i))
1=
peT -1) = 2B(0)
(o.j-a)(j(o.) - f(a)) <0
.
Proof:
We wish to prove that
n
n
j~l o.J(o.j) - a( i~l 'IT i f(o.i))
<0
<0
We are now in a position to compare two possible
policies. First, the government may announce a nondegenerate distribution of possible exchange rates (el ,
'IT l; ... ; en' 'ITn). This distribution induces a distribution of
pricelevels (PI(T), 'ITl;" .; Pn(T), 'IT n), and a distribution
of values of money (1IPl(T), 'IT l;.·.; lIPn(T), 'ITn). We
call the mean value of money E (1IP (T) ) = Ir= 1
'ITi IPi (T). This results in the equilibrium sequence {p (1),
Rl' ... , P(T - 1), Ry ~ I} which we just computed, and
which we call the equilibrium under uncertainty.
Alternatively, the government, exactly as in Section V,
may announce that an exchange rate ewill be chosen with
certainty at time T: we denote {p(1), RI>'''' p(T-l),
Ry -1' P(T)} the corresponding equilibrium sequence,
which we call the equilibrium under certainty for short.
We consider the case where e is such that 1I P(T) =
E(l/p(T)).
The lemma implies:
Proposition 2. Assume logarithmic utility functions. In
the equilibrium under uncertainty, the price levels for
t = 1, ... , T - 1 are higher, and the rates of return lower,
than in the equilibrium under certainty with IIp(T) =
E(llp(T)).
Proof:
'IT.
n
n
n
(i~l p/n )(i~lkiPi(T)) > i~lki
1
n
pJT)
n
The lemma establishes that p > p (T). From (35), it is
apparentthatp (T-l) > P(T-l),andfrom(34) thatRY _ l
< R - l . Since equation (36) describes bothpaths of price
y
levels inbothequilibria, it must be thatP (t) > P(r) for1 '5:. t
::5 T - 2 as well. As for the rates of return,
(i~l'ITi pJT) )(i~l'ITi B(O) + il2Pi(T) )
i
>
i=l
'IT. _1_ =,.-:-::-:---=-P-:...i(~T-,--)---:-~
1 Pi(T)
B(O) + il2Pi(T)
if we denote o.i = Yl p, (T), a = Ir= 1 o.i and f(x)
II (B(0)+il 2 x ), we want to prove
n
n
n
c.I 'IT.1 o..)(.I 'IT.j(0..)) > C.I 'IT.1 0.. f(o.·));
1=1
1
1=1
1
1=1
1
1
I
Note thatfis strictly decreasing in x: therefore
o.j'.?: a ifff(o.) '5:.f(a)
(o.j- a) (j(o.j) - f(a)) < 0 for allj
Federal Reserve Bank of San Francisco
R,
Pt-l
P + (P(T-l)-p)(il l/il2Y-Y
= -p; = P + (P(T-l)-p)(il l/il2y-Y+l
and ill I il2 > 1ensures the result.
Theproposition confirms what intuition might suggest:
wecompare a world where money willhave a certain value
at time T, to one where the future value of money is
uncertain, but on average the same. In otherwords, in the
second situation we have introduced some randomness in
the value of money, around a given mean. Thesame way a
risk-averse agent will prefer to receive with certainty the
meanvalue of a lottery, rather thanthelottery itself, wefind
that in our model the demand for money (which is
47
H (0) /p (T -1), with H (0) identical in the two experiments) will fall when uncertainty is introduced. The price
level, and the inflation rates, will be higher in all periods
between the announcement and the implementation of
monetary union, because of the added uncertainty on the
future value of money.
The proposition is set forth in terms of distributions of
price levels at time T, andis notlinkedto theparticularway
in whichrandomness is introduced in thepricelevel at time
T. Other forms of randomness may be considered. Suppose, for example, that the exchange rate is determined
with certainty at time 1 (e = 1, say), but fiscal policy
remains indeterminate. Assuming that the aggregate deficit can be financed by inflation, and that the government
will choose to finance some constantfraction 8 E [0,1] of
that deficit, the price level at time T is given by equation
(13), where the denominator F (R T ) - 8D = RT F (RT ) is
positive by assumption, and decreasing in 8, as Figure 3
makes clear. Thus the uncertainty over 8, if the government does not commit to a specific value before time T,
will induce a distribution of possible values of money, the
lowest one associated witha 8 = and thehighestonewith
a balanced budget.
The sameresultthen applies: the addeduncertainty has
the effect of increasing the price levels and the inflation
ratesin allperiods priorto unification, when compared to a
choice of fiscal policywhich would set the value of money
1/ p (T) at the mean of the possible values of money.
°
VII. Final Comments
The model we usedin this paperhas, as any model must
have, a number of limitations. Some are the inevitable
drawbacks which characterize any overlapping generations model; they are wellknown, and this is notthe place
to discuss them. We might mention that they oftenplague
other workable models of money. We rather wish to point
out drawbacks that are specific to the model we used,
which should be borne in mind when trying to find
similarities between this model and actual persons or
events.
In our model, the country once unified remains closed,
in the samesensethetwocountries wereoriginally takento
be closed: there is norestoftheworld, andconsequently no
foreign trade. As a result, we lose the ability to discuss
consequences of monetary union on trade, and we miss an
important consideration in the determination of the initial
inflationary shock at unification. As some have pointed
out, the DM is convertible, whereas the OM is not. East
Germans endowed with hard Marks would presumably
buy goods from abroadas wellas fromWest Germany, and
this may have a mitigating effect on inflation.
In our model, thereareonlytwoperiods in agents' lives;
therefore, at thetimeofunification onlyoldpeoplecomein
from the Eastto exchange theirsoftMarks forhardMarks,
and these old people, by construction, only wish to spend
their balances. Although thedemographic structure ofEast
Germany isn't extremely different from that of West Germany,12 in actuality some East Germans may not want to
spend all theirfreshly mintedDM on bananas. Again, this
reduces the strength of inflationary forces.
Our model simply assumes that the new government
48
converts all OM instantaneously into freely expendable
Marks, and at a singleexchange rate. Theplan which will
. be implemented in Germany will not have this feature,
although any legal restriction on the expendability of East
German savings will have to be easily enforceable.P A
possible feature would have East Germans buy the State's
capital stockwith their savings; another would freeze part
of their holdings for a period of time left to the Bundesbank's discretion. It is also possible that a fraction of East
Germans' money holdings willbeconvertible at a rate, and
the remainder at another, less favorable rate.
We have assumed that the good with which Easterners
are endowed is of the samenature as the good available for
purchase in the West. One mightobject to such a ruthless
subsumption of BMWs and Trabants as identical commodities, and wantto allow for less than perfect substitution. To illustrate the argument, the results of Section IV
can be re-examined with "VI = "12 = 0, in other words
with the assumption that goods produced in country East
are considered worthless for consumption purposes, once
agents are given a choice. Taking this consideration into
account would reinforce the inflationary factors. We have
also assumed that the Easterners' endowments would not
change after unification. Incorporating such a feature
would change conclusions about inflationary forces, but
would also leave Proposition 1 unchanged.
On a theoretical level, one might object that we have
assumed perfect foresight on the part of our agents, before
as wellas after, unification. But wehave shown our agents
expecting the Wall to remain in place indefinitely in
Section III, andwehave thenbetrayed theirexpectations in
EconomicReview / Fall 1990
Section IV (the element of surprise was of course crucial
for the trick played on the old people at time 1). We would
answer that we in fact assumed a particular probability
distribution, namely that the status quo would remain with
probability l-: E, and that the Wall would come down with
probability E (the latter is understood to be as small as
usual). We would further argue that this representation is
but a stylized version of most observers' probability distributions until the early days of October 1989.
NOTES
1. As we remark later, this result is simply an application
andinterpretation ofthereasoning onwhich theexchange
rate indeterminacy result of Kareken andWallace (1981) is
based.
2. Models of this type usually specify that loans are
denominated in the consumption good (e.g. Sargent
(1987)). A departure from this usage does not matter in a
model with perfectforesight, such as ours, until such time
as an unanticipated change in policy occurs.
3. It is possible to interpret therestriction onreal balances
as the outcome of a commodity rationing scheme which
forces the young to hold more money than they would
want by limiting the goods available for purchase. Notice
that the scheme we use leaves old agents free to spend
their accumulated cash balances.
4. See Marcet and Sargent (1989) and Arifovic and
Sargent (1990) for some theoretical work on learning
schemes in the context of this model. See Marimon and
Sundar (1989) for some experimental evidence.
5. "The growth of the total balance of savings is the
expression of the people's trust in the socialist development of the German Democratic Republic, and in the
stability of its money" (DDR Handbuch (1979)).
6. The two regimes described here obviously do not
cover all possibilities. For a given value of the deficit
o, S d*, and when A. is set as low as A.2 in Figure 5, then
there are three stationary equilibria, one in which the
constraint is binding with R = R3 , and two in which it is not
binding, with R = Ri or R = R2 . Thus, when the deficitcan
be financed by inflation alone, imposing the constraint
doesnotnecessarily implythatit will be binding, because
multiple equilibria are possible.
7. This assumption is notexcessive, in view of the severe
restrictions recently placed on eligibility of East German
citizens for social benefits in West Germany.
Federal Reserve Bankof San Francisco
8. The allocations of the old at time 0 will be affected by
p(1): at an extreme, for low values of p(1) the deflation
could be so severe that Western borrowers would be
unable to honor their commitments. In a sense, this is
irrelevant because the only economic forces determining
the equilibrium values ofvariables arethedecisions of the
young of generations t ~ 1. However, a government wishing to spare the original old Western borrowers this predicament would choose e within a range (~, +C1J), where ~
verifies
Hw(O)+§ HE(O)Hw(O)+~HE(O) _ Ifo.,l3(R w)1
Fi(Ri)-D i
~2
so that old Western borrowers' consumption after repayment of loans remains positive.
9. A variable y is saidto be an affine function of variables
Xi, X2, ... .x; if there exist constants b o, b-, ... , b; such
that y=b o + b. Xi + ... + bnxn·
10. Had we followed the usual practice of denominating
private debt in real terms rather than nominal terms,
western borrowers would have been unaffected by the
unification, and western lenders would have been affected through their holdings of money only.
11. By relative deflation in the West we mean that
p(1) < Pw(1), that is, the price level actually prevailing at
time 1 is lower than it would have been, had the Wall
remained in place.
12. One East German out of four is over the age of 50,
compared to one West German out of three.
13. This paper was written before the details of the currency unification were worked out.
49
Data Appendix
The following summarizes some of the available data
on the German economies. All amounts (except population figures) are in billions of local currency. Sources
are Statistisches lahrbuch fur die BRD 1989, Deutsche
Bundesbank monthly report Apr. 1990, Encyclopedia
Britannica Yearbook 1989. 1
Federal Republic of Germany
population (88)
GNP (89)
govt spending (89)
monetary base (end 89)
Ml aggregate (end 89)
M2 aggregate (end 89)
M3 aggregate (end 89)
60.8m
2260.4
699.5
216.6
450.6
776.4
1255.5
German Democratic Republic
population (88)
TSP (87)
govt spending (88)
currency stock (end 87)
savings accounts (end 87)
-(end 89)
16.6m
789.5
291.0
15.0
141.9
151 to 157
black market exchange rate (OM/DM)
-(as of late March 1990)
4:1 to 6:1
4.40:1
1. TSP is Total Social Product (the socialist version of
GNP, which excludes services, etc.). The 1990 figures for
savings in East Germany and the black market exchange
rate are the ones commonly cited (e.g. New York Times
March 14, 1990; International Herald Tribune Feb.10-11,
1990; die Welt, March 6, 1990; Frankfurter Rundschau,
April 2, 1990).
REFERENCES
Arifovic, J. and T.J. Sargent. "Three Models of Learning
about Deficits." Manuscript. 1990.
Bryant, J. and N. Wallace. "A Price Discrimination Analysis of Monetary Policy," Review of Economic Studies
51(2),1984. pp. 279-288.
Handbuch der DDR. Leipzig: VEB Verlag Enzyklopadie.
1979.
Kareken, J.H. and N. Wallace. "On the Indeterminacy of
Equilibrium Exchange Rates," Quarterly Journal of
Economics 96(2),1981. pp. 207-222.
Marcet, A.andTJ. Sargent. "Least-Squares Learning and
the Dynamics of Hyperinflation," in W.A. Barnett, J.
Geweke, and K. Shell, eds., Economic Complexity:
Chaos, Sunspots, Bubbles and Nonlinearity. Cambridge: Cambridge University Press. 1989.
Marimon, R. andS.Sunder. "Rational Expectations versus
Adaptive Behavior in a Hyperinflationary World." Dis-
50
cussion paper 244. Center for Economic Research,
University of Minnesota, Minneapolis. 1988.
Samuelson, P.A. "An Exact Consumption-Loan Model of
Interest With or Without the Social Contrivance of
Money," Journal of Political Economy 66(6), 1958.
pp. 467-482.
Sargent, TJ. Dynamic Macroeconomic Theory. Cambridge, MA: Harvard University Press. 1987.
Sargent, TJ. and N. Wallace. "Some Unpleasant Monetarist Arithmetic," Federal Reserve Bank of Minneapolis
Quarterly Review 5(3),1981. pp. 1-17.
____ "The Real Bills Doctrine vs. the Quantity Theory: A Reconsideration," Journal of Political Economy
90(6), 1982. pp. 1212-1236.
Wallace, N. "The Overlapping-Generations Model of Fiat
Money," inJ.H. Kareken andN. Wallace, eds., Models
of Monetary Economics. Minneapolis: Federal Reserve Bankof Minneapolis. pp. 49-82.
Economic Review / Fall 1990
@FedFRASER