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FEDERAL RESERVE BANK OF DALLAS
THIRD QUARTER 1998

Income Taxes as
Reciprocal Tariffs
W Micbael Cox, David M. Gould,
and Roy j. Ruffin

Seigniorage Revenue
and Monetary Policy:
Some Preliminary Evidence
josepb 11. Hasktg

The Economics of the
Private Equity Market
Slepben D. Prowse

This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org)

Economic Review
Federal Reserve Bank of Dallas
Robert D. McTeer, Jr.
Presidenl and Chief Execulive Officer

Helen E. Holcomb
Firsl Vice Presidenl and Chlel Operallng Oilicer

Harvey Rosenblum
Senior Vice Presldenl and Dlreclor of Research

W. Michael Cox
Vice Presldenl and Economic Advisor

Senior Economists and
Assistant Vice Presidents
Stephen P. A. Brown
John Duca
Robert W. Gilmer
Evan F. Koenig
Director, Center for Latin American
Economics, and Assistant Vice President
William C. Gruben
Senior Economist and
Research Officer
Mine K. YOcel
Economists
Robert Formaini
David M. Gould
Joseph H. Haslag
Keith R. Phillips
Stephen D. Prowse
Marci Rossell
Jason L. Saving
Fiona D. Sigalla
Lori L. Taylor
Lucinda Vargas
Mark A. Wynne
Carlos E. J. M. Zarazaga
Research Associates
Professor Nathan S. Balke
Southern Melhodlsl University

Professor Thomas B. Fomby
Soulhern Melhodlsl Unlversliy

Professor Gregory W. Huffman
Soulhern Melhodisl Unlverslly

Professor Finn E. Kydland
Carnegie Melion University

Professor Roy J. Ruffin
University 01 Houslon

Editors
Stephen P. A. Brown
Evan F. Koenig
Publications Director
Kay Champagne
Copy Editors
Anne L. Coursey
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Design & Production
Laura J. Bell

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Income Taxes as
Reciprocal Tariffs
W. Michael Cox, David M. Gould, and Roy J. Ruffin

Page 2

Seigniorage Revenue
and Monetary Policy:
Some Preliminary
Evidence
Joseph H. Haslag

Page 10

The Economics of the
Private Equity Market
Stephen D. Prowse

Page 21

This anicle shows dle eq uivalence between tariffs o n international trade and income taxation. Traditionally, income taxes have
been seen as lowering society's output through dle househo ld's
labor-leisure trade-off. Income taxes also red uce the degree to
which individuals specialize in market activity, which is similar to
dle way countries respond to tariffs in international trade. Income
taxes discourage individuals from specializing in activities dlat
refl ect dleir compa rative adva ntage. In so doing, income taxes may
have dleir most distorting effects, not by encouraging individu als to
work less but by ca using them to spend more time working at
endeavors for which dleir talent is limited .
Using a general model of interpersonal exchange, dle audlors
demonstrate parallels between incom taxes and tariffs. Over a
range of income taxes, raising taxes ca n benefit large groups of
similarly skilled individuals and hurt small groups. As in tariff
dleOty, the costs of inco me taxes are small only if they succeed in
raising revenue. Thus, it is vety costly for an economy to be on
dle downward portion of its tax revenue (Laffer) curve. The more
heterogeneous the society, the higher the income tax rate dlat will
maximize tax revenu es. By overlooking dle effects of heterogeneity
in the workforce and the potential for worker to flee to home production, policymakers may under- or overestimate dle effects of
income taxes on various sectors of the economy and tax widl unintended con equences.

Producing new money is inexpen ive, making seignio ragethe revenues earned from creating new money-a ttractive. However, the social costs of faster money crea tion most likely are
greater than dle production costs. These marginal social costs may
put limits on how mu ch rea l seigniorage revenu e the governme nt
ca n ea rn. In this articl e, Joseph Haslag looks across countries to
as ess the typica l reliance on se igniorage revenue. In add ition,
Haslag determines whedler countries with combinations of high
rates of mo ney growdl and high reserve req uirements tend to rely
especially heavily on seigniorage revenue.

The private eq uity market is an important source of funds for
sta rt-ups, private middle-market compani s, firms in fin ancial distress, and public firms seeking buyout financing . Over dle past
fifteen years , it has been the fastest growing corporate finance market, far surpass ing the public equ ity and public and private bond
markets. In this article, teph n Prowse exam ines dle economic
foundations of dle private eq uity market and describes its institutional structur . He also explores reasons for the market's explosive
growth and high light the main characteri tics of that growth,
including data on returns to private quity investors. He describes
the important inv stars, intermediaries, and issuers in the market
and th ir interactions with each other. In particu lar, he investigates
how the major intermediary in the market-dle limited partnership-addresses the evere information problems associated with
investing in small private firms.

Public finance experts have long explored
the issue of income taxes making the cost of
market transactions higher than nonmarket
ones. A 50 percent income tax, for example,
requires $20,000 in income to purchase $10,000
of market goods. The tax can be avoided, however, if the same goods can be produced at
home. The upshot is that income taxes encourage the home production of goods and services
that would otherwise be produced and traded
in the market. By restricting trade between individuals, income taxes reduce what Adam Smith
considered one of the primary benefits of the
marketplace—the gains to specialization.
Given that income taxes reduce specialization within an economy, it is easy to see
the similarities between the taxing of income
within a country and tariff barriers between
countries: income taxes encourage individuals
to trade less in the marketplace and produce
more goods at home; tariffs cause countries to
trade less internationally and produce more
domestically. Moreover, just as tariffs can redistribute income across countries, flat income tax
rates can redistribute income across skill
groups. Over a range of positive flat income
taxes (tit-for-tat tariffs), raising taxes may actually benefit large groups of similarly skilled
individuals (large countries) and hurt the small
groups (small countries). Other insights into the
effects of income taxation can also be elucidated from tariff theory. As in tariff theory, the
costs of income taxes are small only if they
succeed in raising revenue; thus, it seriously
harms an economy to be on the downward
portion of the tax revenue (Laffer) curve. The
larger the value of market income (trade) compared with total production (gross domestic
product) —that is, the more heterogeneous the
society—the higher the income tax rate that
maximizes revenue.
This article explores the parallel between
the standard theory of income taxation and the
theory of tariffs in international trade. Indeed,
there is no formal difference in economic theory
between a tariff war among countries and a flatrate personal income tax within an economy.
But although analysts generally consider tariff
wars extremely costly to economic activity, they
often look on income taxes with complacency.1
One possible reason for these different reactions is that tariff wars are explicitly used to
inflict damage on another country, whereas
income taxes are used primarily to finance public spending. This article looks at how insights
from the theory of tariffs can help us understand
the effects of income taxation.

Income Taxes as
Reciprocal Tariffs
W. Michael Cox
Vice President and Economic Advisor
Federal Reserve Bank of Dallas
David M. Gould
Senior Economist and Policy Advisor
Federal Reserve Bank of Dallas
Roy J. Ruffin
Professor
University of Houston
and
Research Associate
Federal Reserve Bank of Dallas

T

his article explores

the parallel between the
standard theory of income
taxation and the theory of tariffs
in international trade. Insights
from the theory of tariffs help us
understand how income taxes
undercut the very basis on
which people gain from
trade—specialization.

2

cycle theory. In McGrattan, Rogerson, and
Wright (1997), for example, private consumption goods come from market and nonmarket
production. Nonmarket goods are produced
from domestic capital and labor allocated to
home production. Because real-business-cycle
models typically assume a representative agent,
they cannot analyze how taxes affect individuals with different skills, which this article
examines.
In international trade theory, home production is not tied to any good or sector; it is
simply anything produced domestically. In tax
models, however, a separate household sector
typically produces only household goods distinct from those produced in the market sector. Consequently, in representative agent tax
models, putting high income taxes on market
transactions may reduce the market sector’s
size and change relative prices, but it will not
generate the contrasting experiences of different individuals and the autarkic tendencies of
tariff theory.
In the real world, nearly all households
produce cleaning, cooking, entertainment, transportation, repair, and many other services. While
relatively few goods may be produced at home,
households’ purchase of durable goods (refrigerators, computers, stoves, lawnmowers, and so
on) enables the production of many services.
Because of the tremendous diversity in skills
and behavior, households cannot be treated as
a single representative agent. Households will
respond differently to income taxes, just as
countries respond differently to tariffs. Thus,
departing from the approach of Sandmo (1990)
and McGrattan, Rogerson, and Wright (1997),
we do not set out a separate household sector
or identify a unique household good. All production can be consumed at home or “exported” to the market.
The results of this approach show effects
normally not associated with income taxes.
Over some range of positive flat income taxes,
raising tax rates may benefit a relatively large
sector of an economy at the expense of a
smaller sector. For example, if manufacturing is
the largest sector in an economy, it may benefit
from a flat income tax at the expense of agriculture. In a two-person economy, the highincome individual may benefit at the expense of
the low-income individual. This is similar to tariff theory, in which large countries may gain
from tariffs at the expense of small countries.
Flat income taxes, in essence, can boost some
economic sectors at the expense of others and
dramatically reduce specialization within an

HOME PRODUCTION AND INTERNATIONAL TRADE
As noted above, income taxes shift production from market work to home production.
Eisner (1989) estimates that the total value of
U.S. home production ranges from 20 percent to
50 percent of measured output (GDP). In
Sweden, a country with one of the highest
marginal income tax rates in the world, home
production accounts for an even larger part of
domestic output. Swedish men, for example,
averaged more than four hours per week on
home improvement activities in 1984. In contrast, U.S. men averaged 2.8 hours and Japanese
men less than one hour a week ( Juster and
Stafford 1991).2 Trade theorist Ivor Pearce succinctly sums up the effect of taxes on the division of labor:
The striking growth of do-it-yourself activity in recent years is neither an accident
nor a change in basic preferences. Tax is
avoided on work for self. Work for an
employer is heavily taxed. The cheapest
way to get something done is to do
it yourself, contrary to the principle of
the division of labor on which our high
present standards of living depend. The
whole structure of industry is deeply
affected (Pearce 1977, 105 – 6).

The effect of income taxes on home production and market specialization has not gone
unnoticed in economics. Boskin (1975) combines the household sector with a market sector to examine taxes in a general equilibrium
framework. His two-sector model includes capital and labor as factors of production, but
labor is untaxed in the household sector. Apps
(1981, 1982) uses the analogy of trade theory
to examine inequality issues that arise when
certain groups of individuals are excluded
from the market sector. Sandmo (1990) explicitly shows the similarities between income
taxes and tariffs in his examination of optimum
tax structures in a Becker-style model (Becker
1965) of household production. Sandmo notes
that when household production is included,
production efficiency is no longer feasible
because “taxes on households are in fact tariffs
on their trade with the rest of the economy”
(Sandmo 1990, 89). In his framework, however, it is assumed that households must make
market purchases, so the household equivalent
of international autarky is ruled out. Extensive
work on household production and taxation
can be found in the literature on real-business-

FEDERAL RESERVE BANK OF DALLAS

3

ECONOMIC REVIEW THIRD QUARTER 1998

taxes only on market transactions. These taxes
are essentially income (or, equivalently, sales)
taxes. We examine the effects of an income tax,
t, levied ad valorem on each household as a
proportion of its net dollar sales, or market
income. As a benchmark for the analysis, we
assume all income tax receipts, R i, are directly
rebated to each household in the amount paid
to the government, but each household treats
this as a lump-sum amount independent of any
decision the household might make. This device
allows us to investigate the distortionary effects
of taxation per se, exclusive of the effect of
resources absorbed by government.
Each household converts domestic production into domestic consumption through
market transactions. Each household’s lumpsum tax receipts plus net income (after taxes)
must equal market expenditures. Thus, the budget constraints of households are

economy. Representative agent models overlook this aspect because they treat everyone as
identical. In the real world, each household
activity competes with its counterpart in the
market economy. Taxes that shift activity away
from the market will have redistributional
effects outside the purview of representative
agent models.
As in tariff theory, the costs of income
taxes are small only if they succeed in raising
revenue; thus, it is very costly for an economy
to be on the downward side of the tax revenue
(Laffer) curve.
We also examine the effects of income
taxes on general welfare. Here we find that the
impact of income taxes depends in a complex
way on the heterogeneity of the society.
INCOME TAX THEORY
To consider the theory of income taxation
in a heterogeneous agent economy, suppose
there are two agents, households 1 and 2, producing two goods, 1 and 2. Each household can
produce and consume both goods, one of
which is “imported” and the other “exported.”
Comparative advantage determines which good
the household exports (sells) and which it
imports (buys). Household i produces and consumes amounts x ji and c ji of each good j.
Household i ’s utility function is
(1)

(tax receipts for household 1 + income
from selling good 1 = purchases of good 2)
and
R 2 + (x 22 – c 22 )p (1 – t) = (c 21 – x 21 ).

(4)

(tax receipts for household 2 + income
from selling good 2 = purchases of good 1)
Household 1 chooses (x 1j , c 1j ) to maximize the
Lagrangian

u i (c 1i , c i2 ),

and its production transformation function is
(2)

R 1 + (x 11 – c 11)(1 – t) = p (c 12 – x 12 ),

(3)

L

1

T i (x 1i , x i2 ) = k i .

= u 1(•) + lT 1(•) + m[R 1 + (x 11 – c 11)(1 – t)
– p (c 12 – x 12 )],

which yields the first-order conditions

This implicit function shows the maximum output of one good given the output of the other.
The function is set equal to the constant k i ,
reflecting household i ’s fixed endowments of
capital and labor. The subscript j on a function
denotes the partial derivative. Thus, u ji denotes
household i ’s marginal utility of good j.
Applying the implicit function rule to Equations
1 and 2, we let MRS i = u i2 /u 1i and MRT i =
–T i2 /T 1i denote the marginal rates of substitution
in consumption and transformation in production, with T ji denoting household i ’s marginal
resource cost of good j. Since only relative
prices matter, we let p denote the market price
of good 2 in terms of good 1. As a convention,
we suppose agent 1 (agent 2) always sells good
1 (good 2) and buys good 2 (good 1).
Because taxing household production or
consumption is not feasible (imagine trying to
tax home cooking or parents’ caring for their
children), we assume the government imposes

MRS 1 = MRT 1 = p/(1 – t).

(5)

Household 2 chooses production and consumption to maximize
L

2

= u 2(•) + lT 2 (•) + l[R 2 + (x 22 – c 22)p (1 – t)
– (c 21 – x 21)],

yielding
(6)

MRS 2 = MRT 2 = p (1 – t).

The remaining equations are the transformation function (Equation 2) and market clearing:
(7)

Si c i2 = Si x i2.

We rebate to each household the exact revenue
collected by the government. That is,
(8)

R 1 = t(x 11 – c 11);

(9)

R 2 = tp (x 22 – c 22 ).

Substituting Equations 8 and 9 into Equations 3

4

Table 1

Tariff Theory Versus Income Tax Theory
and 4, respectively, yields the tax-free budget
constraints

Tariff theory

x 1i + px i2 = c 1i + pc i2 .

(10)

MRS 1 = MRT 1 = p /(1 – t)

MRS 2 = MRT 2 = p /(1 + t 2 )

MRS 2 = MRT 2 = p (1 – t)

åi c 2i

Equations 2, 5, 6, 7, and 10 consist of nine
equations and nine variables for determining
the levels of household production, consumption, and p.

Income tax theory

MRS 1 = MRT 1 = p (1 + t 1)
=

åi x 2i

åi c 2i = åi x 2i

x 1i + px 2i = c 1i + pc 2i

x 1i + px 2i = c 1i + pc 2i

T i (x 1i , x 2i ) = 0

T i (x 1i , x 2i ) = 0

TARIFF THEORY
lates the supply constraints. There are nine
independent equations (two each for Equations
13, 14, 15, and 17) to solve for the nine variables. Table 1 compares the theory of income
taxation with the theory of tariffs. It is obvious
that they are formally equivalent provided

This section summarizes the traditional
theory of tariffs (see Jones 1969; Ruffin 1979) in
a form that is useful for comparison with income tax theory and in a way that parallels our
development of the theory of income taxation.
Countries 1 and 2 produce goods 1 and 2,
respectively. Country i exports good i. The
world price of good 2 in terms of good 1 is p.
The domestic relative price of good 2 is p i.
Country i imposes the ad valorem tariff rate t i
on the point-of-origin price (Lerner 1936). Since
country 1 imports good 2, the domestic price of
good 2 is higher than the foreign price:
(11)

The theory of tariffs can thus be interpreted as
the theory of sales taxation if countries are seen
as households.3
Income taxes work heavily against market
production because they act like reciprocal tariffs, which impose the same tariff rate on each
country. Table 2 uses Equation 18 to show the
reciprocal tariff equivalents for different income
tax rates. While a 10 percent income tax is the
same as an 11 percent reciprocal tariff (each
country imposes the same tariff), an income tax
of 33.33 percent is like a reciprocal tariff of 50
percent. A 50 percent income tax is equivalent
to a 100 percent tariff. In the parlance of tariff
theory, income taxation has potentially large
antispecialization effects. Income taxes are, in
effect, a government-sponsored tit-for-tat tariff
war between individuals.

p 1 = p (1 + t 1).

Since country 2 exports good 2, the domestic
relative price is lower than the world price:
(12)

p 2 = p /(1 + t 2).

Substituting households for countries, we can
use the same notation as before for describing
utility in country i and production possibilities.
We make the usual assumption in tariff
theory that all tax revenues are redistributed in
lump-sum form to consumers. We could proceed as before, but note that this assumption
is automatically captured if the rates of substitution and transformation are set equal to the
domestic price ratio and the value of exports
equals the value of imports at world prices, or,
equivalently, the value of production equals the
value of consumption at world prices. Thus, the
fundamental equations of tariff theory are:
(13)

x 1i + px i2 = c 1i + pc i2 ;

(14)

MRS 1 = MRT 1 = p (1 + t 1);

(15)

MRS 2 = MRT 2 = p/(1 + t 2);

(16)

Si c i2 = Si x i2 ;

(17)

T i (•) = 0.

Table 2

Reciprocal-Tariff Equivalents
to Income Taxes

Equation 13 describes the spending constraints, Equations 14 and 15 set out the private
optimization conditions, Equation 16 gives the
market-clearing conditions, and Equation 17 re-

FEDERAL RESERVE BANK OF DALLAS

(1 + t i ) = 1/(1 – t).

(18)

5

Income tax rate
(Percent)

Reciprocaltariff equivalent
(Percent)

10
20
25
33
50

11
25
33
50
100

ECONOMIC REVIEW THIRD QUARTER 1998

WELFARE

Substituting Equation 20 into Equation 21 yields

In this section we analyze the welfare
implications of income taxes in the same way
economists examine tariff theory (see Jones
1969). As a benchmark for the analysis, we continue to assume all income tax receipts are
directly rebated to each household in the
amount paid to the government. E ji = c ji – x ji is
household i ’s excess demand for good j. In
market equilibrium, one household’s excess
demand will just offset another household’s
excess supply. Use p i = MRS i = MRT i to denote
household i ’s opportunity cost in terms of good
2. Household i ’s change in real income is
defined as

(22)

Any increase in t will reduce the net price
of good 2 to household 2 when it sells the good
in the market, so dp 2 < 0. Because household 2
is a net seller of good 2, its excess demand for
the good is negative, so the second term in
Equation 22 is negative (the product of three
negatives). This shows that when there is any
change in income taxes and tax payments are
rebated in a lump sum, welfare can only
increase if the lump-sum payment increases. In
other words, increments in the income tax hurt
the most when the economy is on the downward side of the tax revenue function. If tax revenues are maximized at, say, t = 0.2, doubling
t from 0.05 to 0.1 will have a smaller impact on
welfare than increasing t from 0.2 to 0.25.
The most interesting implication of
Equation 20 is that an equal change in income
taxes across all households will not necessarily
affect everyone in the same manner. In our
model, taxation causes each individual to produce less of the good he or she sells. But taxation can also change the relative price of goods,
which benefits one household and hurts the
other. This differential impact arises from the
ambiguous effect a change in the income tax
rate, t, can have on the terms of trade, p. As
income taxes are raised, the terms-of-trade
effects are ambiguous because the offer curves
of both households shift inward. If households
are asymmetrical in terms of their production
possibilities and preferences, the terms of trade
will change as the offer curves shift inward at
different rates, and the relative price of one
good will most likely increase. For example, an
income tax may lower a plumber’s demand for
doctors’ services proportionately more or less
than it lowers a doctor’s demand for plumbers’
services.
Thus, when households are not symmetrically different, some will experience an
improvement in their terms of trade and find
their welfare increasing over a range of income
taxes. Just as a large country can gain at the
expense of a small one by imposing an optimal
tariff to improve its terms of trade, some households may gain at the expense of others when
income taxes are imposed. The proof of this
proposition is straightforward. Starting from
zero income taxes, ( p i – p) = 0, Equation 20
shows that a household experiencing an
improvement in the terms of trade from income
taxes (dp < 0 and E i2 > 0, or, dp > 0 and E i2 < 0)
will find its welfare enhanced:

dy i = dc i1 + p i dc i2.

(19)

Equation 19 is derived from the utility function
itself and is the total differential of utility measured in terms of the numeraire good, good 1.
We can convert the change in utility to market
variables by differentiating the budget constraint
(Equation 10) and using Equation 19, noting
that along the production transformation curve
dx i1 + p i dx i2 = 0. Thus,
(20)

dy i = ( p i – p)dE i2 – E i2dp.

This well-known equation in trade theory also
applies to households. If household i is a net
buyer of good 2 (that is, imports good 2
because p i > p), the change in welfare is the
household’s personal profit, ( p i – p)dE i2 , on
additional purchases minus the increase in the
cost of previous purchases, E i2dp.
We first use Equation 20 to show that sufficiently high taxes always reduce welfare.
Suppose taxes are so high that each household
is driven to autarky (E i2 = 0). Working backward
from autarky, we see that welfare increases as
taxes are reduced:
dy i ½E

i
2

=0

= ( p i – p)dE i2 > 0.

This inequality follows from Equation 20
because initially E i2 = 0 and dE i2 > 0 when taxes
are reduced. In other words, welfare falls as we
increase taxes and approach autarky.
Another result is that increases in income
taxes are the most costly when the economy
is on the downward side of the tax revenue
(Laffer) curve. Without loss of generality, we
can look at household 2, where (p 2 – p) =
–p t. Taxes paid (and rebated) to this household
are R 2 = (p 2 – p)E 22 . The change in revenue is
(21)

dy 2 = dR 2 – dp 2E 22 .

dR 2 = (p 2 – p)dE 22 + (dp 2 – dp)E 22 .

6

from no taxes, this benefits the high-income
person and hurts the low-income one. This
result of our model should not be interpreted as
meaning that in the real world income taxes
hurt low-income people more than high-income
people. This result applies to larger similarly
skilled groups versus smaller ones. Thus, if highincome individuals in the real world represent
a small share of total production and if their
comparative advantage overlaps little with that
of low-income individuals, flat income taxes
would affect them more adversely.
Figures 1, 2, and 3 show some illustrative
calculations for several hypothetical economies
(see the box entitled “Model Description” for a
characterization of the hypothetical economies).
It is assumed that the utility and product transformation functions display a constant elasticity
of substitution. Figure 1 shows a typical case in
which household 2’s income is roughly twice
that of household 1. As income taxes are increased, household 2’s utility rises while that of
household 1 falls. Indeed, household 2’s real
income is maximized when the tax rate is
approximately 13 percent, and its real income
does not fall below that associated with no
taxes until the tax rate is 25 percent. Thus, the
redistribution effects can be significant.
Figures 2 and 3 consider the case of equalincome households. In Figure 2 the households
are largely homogenous, with small differences
in their comparative advantages. In Figure 3 the
households are distinctly heterogeneous. In the
symmetrical cases the utility of each household
behaves in the same way. As the income tax
increases, nothing happens to the market price
because the increase in demand from one party

Figure 1

Unequal Household Incomes
Relative utility
1.04

.99

Large household

.94

.89

Small household

.84

.79

.74
0

5

10

15

20

25

30

35

40

45

50

55

Tax rate (percent)

(23)

dy i ½t = 0 = –E i2dp > 0.

Likewise, the household that experiences a
deterioration in its terms of trade will find its
welfare declines: dy i ½t = 0 < 0. Equation 23
shows that a small tax improves the welfare of
the party whose terms of trade improve. This is
because E 12 + E 22 = 0, so that facing the same
change in market price, dp, one household is
better off and the other worse off.4
Thus, we see that a sufficiently small
income tax of the sort being considered (tax
rebated in a lump sum) will usually help some
groups. Which groups will benefit? The answer
can be found by looking at income taxes as titfor-tat tariff wars. It is easy to see that large
countries will win a matching tariff war: they
can improve their terms of trade because they
have a larger impact on world prices. A similar
result obtains here. In the case of flat income
taxes, the consumer with the higher income will
benefit from higher taxes over a certain range.
Say the high-income person sells financial services to a low-income person in return for
painting. Starting from a zero flat income tax
rate, increasing tax rates will raise the market
price of both financial services and painting.
The high-income person will demand less painting, and the low-income person will demand
fewer financial services. However, because the
high-income person consumes relatively more
painting than the low-income person consumes
financial services, the relative demand for painting will fall more than that of financial services.
The high-income person’s demand falls by more
because a higher income essentially means
that demand curves are flatter (all else equal).
Therefore, the price of painting should fall relative to financial services. At the margin, starting

FEDERAL RESERVE BANK OF DALLAS

Figure 2

Small Differences in Comparative Advantage,
Equal Household Income
Revenue

Relative utility
1.01

.06

1

.05
Revenue

.99

.04

.98

.03
Utility
.02

.97

.01

.96

.95

0
0

5

10

15

20

25

30

35

Tax rate (percent)

7

ECONOMIC REVIEW THIRD QUARTER 1998

40

45

50

55

lose about 20 percent of the welfare they would
have with no income taxes.

Model Description
CONCLUSION

The model underlying the simulations in
Figures 1– 3 is as follows:

U 1 = (c

r
11

+c )

U 2 = (c

r
21

r 1/r
+ c 22
)

Traditionally, income taxes have been
seen as lowering society’s output through the
household’s labor – leisure trade-off. Income
taxes lower the after-tax wage rate and thus
encourage people to work less and enjoy more
leisure. However, income taxes also reduce the
degree to which individuals specialize in market activity, which is similar to the way countries respond to tariffs in international trade.
Income taxes discourage individuals from specializing in activities that reflect their comparative advantage. Instead, they encourage
everyone to become a jack-of-all-trades. In so
doing, income taxes may have their most distorting effects not by encouraging individuals to
work less but by causing them to spend more
time working at endeavors in which their talents do not lie.
As long as it is necessary to raise revenue,
the autarkic tendencies of income taxes, sales
taxes, and value-added taxes are unavoidable.
The only solution would be to minimize them
by imposing lump-sum supplements to these
antispecialization taxes. But, as the experience
of the Thatcher government in Britain illustrates,
even small poll taxes are highly unpopular.
Income taxes are thus likely to remain the primary source of government revenue.
Nevertheless, the ways in which income
taxes affect society’s welfare must be recognized. By focusing mostly on the labor–leisure
trade-off and ignoring heterogeneity in the
workforce and the potential for workers to flee
to home production, policymakers may underor overestimate the effect income taxes have on
various sectors of the economy and thereby tax
with unintended consequences. Just as in trade
among nations, where equal tariffs can wreak
more economic destruction in some nations
than in others, in the day-to-day commerce
within a nation even flat income taxes can have
differing deleterious effects. They affect the very
basis on which people gain from trade — the
ability to specialize.

r 1/r
12

x a11 + Bx a12 = k 1
Bx a21 + x a22 = k 2,
where r = 0.5, a = 1.5.
In Figure 1, B = 2 and k 1 = 1 and k 2 = 2.
In Figure 2, B = 2 and k 1 = k 2 = 1.
In Figure 3, B = 5 and k 1 = k 2 = 1.

equals the reduction in demand from the other.
Real income falls from the outset; the optimal
income tax for both households is zero, as
could be expected. The revenue, or Laffer,
curve is also shown. In Figure 2 the revenue
function reaches its maximum at an income tax
of 15 percent and revenue falls to zero when
both parties are reduced to autarky (no exchange) with an income tax rate of 29 percent.
In the autarky case, both parties lose about 5
percent of their welfare relative to the zero
income tax position. In Figure 3, with large
differences in comparative advantage (greater
heterogeneity), maximum revenue is achieved
at a tax rate of 30 percent, and autarky is
reached at a tax rate of 55 percent. In this case,
with taxes that choke off all trade, both parties

Figure 3

Large Differences in Comparative Advantage,
Equal Household Income
Revenue

Relative utility
1.01

.16

.99

.14

.97
.12
.95
.10

.93

Utility

.08

.91

Revenue

.89

.06

NOTES

.87
.04
.85
.02

.83

0

.81
0

5

10

15

20

25

30

35

40

45

50

1

55

Tax rate (percent)

8

We thank Avinash Dixit, Joseph Haslag, Peter Mieszkowski, and Jason Saving for helpful comments and
suggestions.
Indeed, the protectionist trade war triggered by the
Smoot– Hawley tariff may have contributed significantly

2

3

4

to the Great Depression. See, for example, Wanniski
(1978), Chapter 7, “The Stock Market and the Wedge,”
for a discussion of this topic.
Moreover, according to the same article, Swedish men
averaged 39.8 hours of market work and 18.1 of
housework (including home improvements) per week,
whereas U.S. men averaged 44 hours of market work
and 13.8 hours of housework.
Furthermore, we have shown that sales taxes are
equivalent to income taxes even in the presence of
household production. See Mieszkowski (1967, 251)
for a lucid statement of the equivalence of income taxes
and sales taxes in a world without home production.
Of course, the country as a whole is made worse off
because the terms-of-trade improvement for some
households is more than offset by the terms-of-trade
loss to the households that experience a fall in their
terms of trade. This can be demonstrated by Equation
20. Welfare is maximized when dy 1 + dy 2 = 0, which
implies that tax rates are zero.

Jones, Ronald W. (1969), “Tariffs and General Equilibrium: Comment,” American Economic Review 59 (June):
418 – 24.
Juster, F. Thomas, and Frank P. Stafford (1991), “The
Allocation of Time: Empirical Findings, Behavioral
Models, and Problems of Measurement,” Journal of
Economic Literature 29 (June): 471– 522.
Lerner, Abba P. (1936), “The Symmetry Between Import
and Export Taxes,” Economica 3 (August): 306 –13.
McGrattan, Ellen R., Richard Rogerson, and Randall
Wright (1997), “An Equilibrium Model of the Business
Cycle with Household Production and Fiscal Policy,”
International Economic Review 38 (May): 267– 90.
Mieszkowski, Peter M. (1967), “On the Theory of Tax
Incidence,” Journal of Political Economy 75 (June):
250 – 62.
Pearce, Ivor F. (1977), “Taxing the Dole,” in The State of
Taxation, ed. A. R. Prest et al. (London: Institute of
Economic Affairs), 91–107.

REFERENCES
Apps, Patricia (1981), A Theory of Inequality and
Taxation (Cambridge: Cambridge University Press).

Ruffin, Roy J. (1979), “Border Tax Adjustments and
Countervailing Duties,” Weltwirtschaftliches Archiv
115 (2): 351– 55.

——— (1982), “Institutional Inequality and Tax Incidence,”
Journal of Public Economics 18 (July): 217– 42.
Becker, Gary S. (1965), “A Theory of the Allocation of
Time,” Economic Journal 75 (September): 493 – 517.

Sandmo, Agnar (1990), “Tax Distortions and Household
Production,” Oxford Economic Papers 42 (January):
78 – 90.

Boskin, Michael J. (1975), “Efficiency Aspects of the
Differential Tax Treatment of Market and Household
Economic Activity,” Journal of Public Economics 4
(February): 1– 25.

Wanniski, Jude (1978), The Way the World Works (New
York: Simon and Schuster).

Eisner, Robert (1989), The Total Incomes System of
Accounts (Chicago: University of Chicago Press).

FEDERAL RESERVE BANK OF DALLAS

9

ECONOMIC REVIEW THIRD QUARTER 1998

Money creation is one potential source of
revenue for a government. Seigniorage—government revenue received through creating
money—is a relatively inexpensive means of
raising funds. Take the United States as an
example. It costs just a few pennies to print a
$100 bill. The resource costs to the U.S.
Treasury are more than offset by the value of
the goods that could be purchased with the
$100 bill. It is even less expensive for the
Federal Reserve to electronically purchase large
quantities of Treasury bonds, notes, and bills
from traders in New York. It is important to note
that the Federal Reserve returns the interest payments on its security holdings (less its expenses)
to the U.S. Treasury. Consequently, when the
Federal Reserve increases its bond holdings, for
example, the U.S. Treasury realizes an effective
reduction to its debt expenses.1 The present
value of the reduction in Treasury expenses is
equal to the amount of money injected by the
Federal Reserve’s open market purchase.
The problem is that although money may
be cheap to produce, the social costs of money
creation are almost certainly greater than what
the Federal Reserve pays to create it. Indeed, a
large body of empirical evidence suggests that
the rate of money creation is closely correlated
with inflation. Thus, faster money creation costs
society by eroding the purchasing power of
money already in circulation, which is the inflation tax. Though tempted by low production
costs, governments must balance the benefits
with social costs when deciding how much to
rely on seigniorage.
The article addresses two questions. First,
how much do countries rely on money creation
as a source of revenue? The answer to this question gives some idea of the size of the seigniorage revenue “problem.” For most of the
countries, money creation accounts for less than
2 percent of real GDP. The evidence indicates
that seigniorage revenue is not the primary
source of revenue for a government, but neither
is it quantitatively insignificant.
Second, are monetary policy settings systematically related to a government’s reliance
on real seigniorage revenue, and, if so, what is
the relationship? Such evidence should be a
useful guide for economic theories—that is, a
good theory should be able to account for a
government’s reliance on seigniorage revenue
versus, say, its reliance on income taxes.
Sargent (1986) presents some evidence
that very rapid money growth does not translate
into greater reliance on real seigniorage revenue. He studies monetary policy during four

Seigniorage
Revenue and
Monetary Policy
Joseph H. Haslag
Senior Economist and Policy Advisor
Federal Reserve Bank of Dallas

T

he resource costs to the

U.S. Treasury [to print a
$100 bill] are more than
offset by the value of the
goods that could be purchased
with the $100 bill.

10

hyperinflation episodes that occurred immediately following World War I. For two countries,
Austria and Hungary, Sargent reports data on
money growth and the fraction of government
spending earned through seigniorage revenue.
Austria raised about 67 percent of government
expenditures through money creation in the
first half of 1919. However, the ratio of money
creation to government expenditures fell to
about 40 percent of government expenditures
by 1922. Between 1919 and 1922, Austrian
crowns in circulation went from roughly 4.7
billion to nearly 4.1 trillion. For Hungary,
money creation accounted for more than 45
percent of its government expenditures in
1921–22, falling to about 33 percent in 1924 –25.
Between February 1921 and April 1925,
Hungary saw its notes in circulation rise from
15 billion kronen to 4.5 trillion kronen.2 For
these two case studies, the evidence suggests
that reliance on money creation decreases as
the rate of money growth increases.
Hyperinflations are rare and probably not good
laboratories for studying the relationship between monetary policy and seigniorage revenue. Still, the Austrian and Hungarian data show
that dramatic increases in the rate of money
growth do not necessarily translate into a
government’s increased reliance on seigniorage
revenue.
In this article, I use data from different
countries to identify whether a systematic relationship exists between monetary policy and a
country’s reliance on seigniorage revenue.
Rather than focus on year-to-year realizations,
the approach taken in this article is to study the
correlation between monetary policy and
seigniorage over a longer horizon; specifically,
the sample mean is computed from a 30-year
period. Both economic theory and problems
with statistical inference point to using a sufficient statistic to measure monetary policy. (A
sufficient statistic captures changes in the variable that the researcher is studying.) Here, the
monetary policy measure is a combination of
the money growth rate and the reserve ratio. As
such, the evidence bears on whether countries
with a high money growth rate–reserve ratio
combination also tend, on average, to rely more
heavily on seigniorage revenue over these
longer horizons than countries with a low
money growth rate–reserve ratio combination.
The cross-country evidence indicates a
positive association between the monetary
policy measure and a country’s reliance on
seigniorage revenue. Thus, countries with high
monetary policy settings tend to rely more on

FEDERAL RESERVE BANK OF DALLAS

seigniorage revenue than countries with low
monetary policy settings. An additional implication follows from the way in which the measure
of monetary policy is constructed; specifically,
one can infer that the relationship between the
reserve ratio, which holds the money growth
rate constant, and a country’s reliance on seigniorage revenue is concave. The concave relationship also holds between the money growth
rate and seigniorage reliance when the reserve
ratio is constant. The implied concavity complements Sargent’s findings for Austria and
Hungary.
It is useful to begin with a brief overview
of seigniorage revenue that shows how it fits
into a broader picture of government finance.
SEIGNIORAGE REVENUE—AN OVERVIEW
Suppose the government prints new
pieces of currency and uses these newly created
bills to buy goods and services, such as missiles
or computers, or pay workers’ salaries.3 For simplicity, I assume that the economy has a composite commodity (hereafter, the consumption
good). The government can buy units of this
consumption good with the newly printed
money, which is
(1)

(Mt – Mt –1)vt ,

where M denotes the total quantity of highpowered money in the economy (t denotes
time), and v denotes the money’s value in terms
of the units of the consumption good that can
be acquired with one unit of money (that is, the
inverse of the price level). Thus, Equation 1 represents the units of the consumption good that
can be purchased with newly printed money—
in other words, real seigniorage revenue.
Seigniorage revenue is just one part of a
larger picture. To see the complete picture, it is
necessary to give the government’s income
statement, or budget constraint. To keep things
simple, assume that the government issues only
one-period, fully indexed bonds.4 For this simple economy, the government’s budget constraint can be written as
(2)

gt + rt bt –1 = tt yt + bt + (Mt – Mt –1)vt .

In Equation 2, g is the total quantity of goods
purchased by the government; the product, rb,
is the principal and interest payments, measured
in units of the good, that the government owes
for one-period bonds issued at date t – 1; r is
the real gross return (principal plus net interest)
on government securities worth b goods. Thus,
the left-hand side of Equation 2 represents

11

ECONOMIC REVIEW THIRD QUARTER 1998

rate; that is, 1/p, where p = pt /pt –1.6 Other things
being equal, the rate of inflation is positively
related to the rate of money growth. Hence,
faster money growth means that the real return
on money falls. It follows that faster money
growth results in a smaller tax base for real
seigniorage revenue.
Overall, faster money growth can lead to
either more or less real seigniorage revenue,
depending on whether the change in the tax
rate or the change in the tax base is quantitatively larger.

the total expenditures by the government. The
right-hand side characterizes the government’s
total receipts. The product, ty, represents the
income tax revenue earned by the government
at rate t, and y is the aggregate level of real
income.
Note that in Equation 2 the government
has access to an income tax. Representing tax
revenue this way is not necessary. However,
there is a useful analogy between seigniorage
revenue and income tax revenue. The relationship between the income tax rate and tax revenue has been popularized in the Laffer curve.
Suppose that income, y, is negatively related to
the tax rate. With an increase in the tax rate, for
example, people would report less income.5
The basic supply-side question, therefore, is
whether higher tax rates are offset by a lower
tax base. Since tax revenues are the product of
these two factors, it is impossible to say, a priori, whether income tax revenues rise or fall in
response to an increase in tax rates.

Reserve Requirements and the Tax Base
There is another monetary policy tool that
could potentially influence real seigniorage revenue. The reserve requirement stipulates that
money balances cannot be less than g percent
of bank deposits, where g denotes the reserve
requirement ratio. Consequently, for a given
level of deposits, a higher reserve requirement
implies that the quantity of real money balances
increases; that is, a larger tax base. However,
holding the level of deposits constant is
unlikely. An increase in the reserve requirement
ratio may induce people to decrease their total
savings and hence their bank deposits. As a
result, people may avoid the inflation tax by
reducing their bank deposits.
To illustrate this point, people have two
means of saving: government bonds and money.
For simplicity, I assume that the real return on
the government bonds, r, is constant and that
these bonds dominate money in terms of offering a higher rate of return—that is, 1/p < r.
In this economy, banks serve a very simple function. I assume that government bonds
are issued in denominations that are too large
for any one saver to acquire. The bank costlessly pools the funds to acquire these government bonds. Because the bank maximizes
profits in a perfectly competitive market, the
rate of return on deposits will also be r. Each
person takes the rate of return on deposits as
given. The reserve requirement stipulates that
the person hold a fraction of these deposits as
money balances.7 Because money is rate of
return dominated by government bonds, the
person will not hold any fiat money in excess of
this reserve requirement. The equilibrium return
on a person’s savings is

Seigniorage Revenue and Money Growth
An increase in the money growth rate has
an effect on seigniorage that is analogous to the
effect that an increase in the tax rate has on
income tax revenue. To illustrate this point, I
modify the expression for seigniorage revenue
to identify a tax rate and tax base. The date t
quantity of money in circulation is equal to the
product of a growth rate and date t – 1 stock.
Thus,
(3)

Mt = qt Mt –1,

where q is the gross rate of money supply
expansion. With q > 0, the percentage change
in the money supply is q – 1. Use Equation 3
to substitute for Mt –1 in Equation 1. The resulting government budget constraint is given by
(2¢)

gt + rtbt –1 = tt yt + bt + vt Mt (1 – 1/qt ).

The analog to income tax revenue is now more
accessible. In Equation 2¢, the total revenue
from money creation is now the product of a
tax base, vt Mt , and a tax rate, (1 – 1/q), that is
positively related to the rate of money growth.
To complete the analogy to the tax revenue setting, linking the seigniorage tax base to
the seigniorage tax rate is necessary. One way
to do this is to assume that the real quantity of
money—which for seigniorage revenue is the
tax base—is a function of its real rate of return.
More specifically, let real money balances be
positively related to the real return on money. It
is straightforward to show that the real rate of
return on money is the inverse of the inflation

(4 )

q=

g
1+ g

•

1
r
+
,
p 1+ g

where q is the gross real return on savings. Note
that q is a weighted average of the rate of return
on real money balances and on government

12

Before reporting any statistics, it is important to note that the reserve requirement ratio
presents a measurement issue. In principal, the
average marginal reserve requirement ratio—
the ratio that applies to the next dollar
deposited—would be measured.10 In practice,
however, measuring this is not so simple. There
is a dizzying array of reserve requirements; U.S.
banks are currently required to hold reserves
equal to 3 percent of the first $49.3 million of
checkable deposits and 10 percent of all
deposits above the low-reserve tranche. Therefore, it matters whether the deposits are going
into small banks or large banks. In other countries, the reserve requirement structures are
even more convoluted.11
Equations 1 through 4 are built on the
notion that there is one reserve requirement
ratio that is the marginal reserve requirement.
To compute the marginal reserve requirement
ratio, one could use the distribution of deposits
across the different categories corresponding to
the reserve requirement structure. For example,
20 percent of the deposits are in small U.S.
banks (with less than $49.3 million in checkable
deposits) and 80 percent are in large banks.
The average marginal reserve requirement
ratio would be (0.2 •0.03) + (0.8•0.1) = 0.086.
Unfortunately, neither the United States nor any
other countries report the distribution across
deposit categories, which is necessary to construct such a measure. Consequently, I use the
reserve-to-deposit ratio, denoted R /D, (hereafter reserve ratio) as a proxy for the reserve
requirement ratio. Historically, reserve requirements have been applied against deposits
included in what is the U.S. counterpart to M2.
Accordingly, I use M2 less currency outside the
bank as my measure of bank deposits. As it is
measured, the reserve ratio ignores any extra
information contained in the distribution of
deposits across the alternative categories.
Instead, different deposit categories are treated
as if there is only one type.
Table 1 reports summary statistics for the
seigniorage ratio, S/Y ; as well as a monetary
policy measure, g; a tax rate measure, TAX; and
the growth rate of output, y ¢. On average,
seigniorage revenue accounts for a fairly small
fraction of total output—about 2 percent.12 Tax
receipts are, on average, about 22 percent of
aggregate output. As one would probably
expect, seigniorage revenue is not the primary
source of government revenue.
Generally, the government budget constraint links the variables in Table 1 together. As
such, the statistics describe the central tenden-

bonds. With 1/p < r, Equation 4 implies that
q < r. In other words, the reserve requirement
ratio drives a wedge between the return on
bonds and the return to savings.
Suppose there is an increase in the reserve
requirement ratio. The quantity of real money
balances held by people is gd, where d is the
quantity of goods deposited with banks. For a
given level of deposits, people will hold more
money and the tax base rises. Equation 4, however, implies that the real return on savings falls
as the reserve requirement ratio increases. It
seems reasonable to assume that people’s savings are positively related to the real return on
savings. Therefore, it follows that a higher
reserve requirement ratio will result in a decline
in a person’s savings. A decline in savings
implies a decline in the quantity of bank
deposits. As such, g is increasing and d is falling
so that the product —the seigniorage tax base—
could either increase or decrease.
The thrust of this section is twofold. First,
real seigniorage revenue is formally defined.
Second, economic theory offers an ambiguous
picture regarding the effects that monetary
policy settings have on the size of this revenue.
The gist of the economic argument is that
people try to avoid taxes, so with higher tax
rates, whether it be inflation or income, they
have an incentive to reduce the quantity of the
good being taxed. The remainder of this article
seeks to establish some preliminary observations on the correlation between a country’s
reliance on seigniorage revenue and its monetary policy settings.
THE DATA
I obtain the data in this article from
International Financial Statistics. I use annual
observations, spanning the period 1965–94. For
each of the variables I examine over this 30-year
period, I use the sample mean to measure each
country’s central tendency. Unfortunately, observations are not available for each country for
each year. Each country in the sample has at
least fifteen annual observations. The result is a
sample of sixty-seven countries.8
Following Fischer (1982), I compute the
ratio of seigniorage revenue to output, hereafter
S/Y, for each country.9 Here, I use high-powered
money as the measure of the money stock (M ).
One alternative to computing ratios is to convert
each country’s seigniorage to a dollar-equivalent
value. The chief advantage to using ratios is that
no assumptions are required regarding the exchange rate and purchasing power parity.

FEDERAL RESERVE BANK OF DALLAS

13

ECONOMIC REVIEW THIRD QUARTER 1998

Table 1

Summary Statistics
Variables

S/Y
R/D
g
TAX
y¢
S/Y
R/D
g
TAX
y¢

Sample
mean

Standard
deviation

Minimum

Maximum

.0211
.1712
.2085
.2254
.0407

.0201
.1303
.1667
.1008
.0181

.0025
.0068
.0332
.0537
–.0018

.0998
.6402
.8981
.5586
.0904

S/Y ratios tend to experience less variability in
the year-to-year reliance on seigniorage.
The correlation coefficient between a
country’s average reliance on seigniorage revenue and its sample standard deviation is 0.8462.
Thus, the high correlation coefficient suggests
that countries with high seigniorage rates have
the greatest volatility in year-over-year realizations. In other words, countries that rely, on
average, more heavily on money creation as a
source of revenue also tend to exhibit the
largest variability in reliance from year to year.
In contrast, countries that rely relatively little on
seigniorage revenue tend to receive about the
same fraction of GNP from year to year.13
Figure 1 focuses on the two monetary policy variables. Specifically, it plots combinations
of the average reserve ratio and the average
money growth rate for each country in this sample. The plot suggests that a country with a high
average reserve ratio has a high average money
growth rate. Formal statistics support the notion
that the reserve ratio and money growth are
positively related; the correlation coefficient
between the reserve ratio and the money
growth rate is 0.72.
Thus, three facts emerge from this preliminary review of the data. These facts serve to
answer the primary question of how much
countries rely on seigniorage revenue. First, for
most countries, seigniorage revenue accounts
for less than 2 percent of output. Second, countries with the highest average reliance on
seigniorage revenue also tend to have the
greater year-to-year volatility in the S/Y ratio.
Third, the evidence suggests that monetary
policy settings are not independent of one

Real seigniorage/real GDP
Bank reserves/deposits (M2 less currency)
Percentage change in high-powered money
Tax revenue/GDP
Percentage change in real GDP

cies and average dispersion of monetary policy,
fiscal policy, and some aggregate measure of
economic activity. The money growth rate, g, is
(Mt /Mt –1) – 1. TAX is the ratio of tax revenue to
GNP. Lastly, y ¢ = (Yt /Yt –1) – 1 is the growth rate
of output.
One rather interesting finding is how the
reliance on seigniorage revenue is distributed.
Approximately three-fourths of the countries
collect, on average, less than 2 percent of GNP
through money creation. Most of the variation,
therefore, occurs among those countries in the
top quartile of the distribution. In this sample,
Ghana relies most heavily on seigniorage, collecting revenues equal to 10 percent of output,
on average, through money creation. Overall,
the distribution of S/Y ratios is quite skewed
toward the low-seigniorage-reliance tail of the
distribution.
Table 1 also reports the range of reserve
ratios and average money growth rates. The difference between the minimum and maximum
values is substantial. Reserve ratios range from a
low of 0.6 percent to 64 percent. Money growth
rates range from 3.3 percent to nearly 90 percent. This evidence shows that banks hold a
substantial fraction of money against deposits in
some countries. It also shows that some countries create money at a rapid pace.
Do countries that rely heavily on seigniorage revenue also exhibit large year-to-year
volatility in their earnings from money creation?
The answer indicates whether countries tend to
rely on seigniorage revenue consistently or if
there are periods of heavy reliance on seigniorage interspersed with periods in which countries rely less on it. A positive correlation
between the seigniorage ratio and volatility
would show that countries with large values of
S/Y, for example, also tend to experience
greater year-over-year variability in the S/Y ratio.
Conversely, if the correlation coefficient is negative, then countries that have relatively high

Figure 1

Cross-Country Plots of Reserve Requirements
Versus Money Growth
Percentage change in high-powered money
1
.9
.8
.7
.6
.5
.4
.3
.2
.1
0
0

.1

.2

.3

.4

.5

Bank reserves/
deposits (M2 less currency)

14

.6

.7

Table 2

Regression Results for Seigniorage Ratios and
Monetary Policy Variable

another; countries with high money growth
rates also tend to have high reserve ratios.

Dependent variable: S/Y

MONETARY POLICY AND SEIGNIORAGE

Variable

To determine whether a relationship exists
between a country’s monetary policy settings
and its reliance on seigniorage revenue, I present results from a simple regression. Because
of this potentially nonlinear relationship, I use
a sufficient statistic, z, to measure monetary
policy settings. Specifically, let z = [R/D/(1 +
R/D)][g/(1 + g )]. The economics motivating this
decision is sketched out in the box entitled “A
Case for Combining the Money Growth Rate
with the Reserve Ratio.” Statistical issues also
arise, in part, because of the evidence presented
in Figure 1. Recall from Figure 1 (and the correlation coefficient) that countries with high
average reserve ratios tend to have high average
money growth rates. By studying the contribution of each of the monetary policy measures,
multicollinearity is a potential problem; that is,
if two independent variables are highly correlated, the standard errors of the coefficients are
inflated, creating inference problems. In measuring monetary policy settings with a single
variable, I am assuming that z is a sufficient
statistic for monetary policy. As a sufficient statistic, z is useful because changes in it capture
changes in each of the monetary policy variables being studied. As such, z is serving as a
measure of the overall thrust of monetary policy
as it relates to seigniorage revenue.
One additional property of z is noteworthy. It is straightforward to show that the
definition of z implies a concave relationship
between it and each of the two monetary policy
variables. To illustrate this, consider the effect of
a change in the reserve ratio, holding the
money growth rate constant. As the reserve
ratio increases, z increases also, but the change
in z will be smaller as the reserve ratio
increases. In other words, for a given increase
in the reserve ratio, z will increase at a diminishing rate. The same holds if, for example, the
money growth rate increases, holding the
reserve ratio constant. With a positive coefficient on z, the relationship between the
seigniorage rate and each of the monetary policy variables is concave.14
In the benchmark regression, I include the
squared value of z and a constant term as additional explanatory variables. In doing so, it is
possible to assess whether there are any additional nonlinearities that characterize the relationship between a country’s monetary policy

constant

FEDERAL RESERVE BANK OF DALLAS

z
z2

Benchmark
model

Financial
sophistication I

Financial
sophistication II

.011*
(.0032)
.3982†
(.1788)

.0094*
(.0034)
.4273†
(.1722)

.0113*
(.0032)
.3835†
(.1808)

–.1554
(1.1854)

–.0072
(1.1545)

–.0915
(1.157)

y 65 ‡

.—

OECD

.—

.—

–.006 §
(.0033)

OECD•z

.—

.—

–1.144*
(.3909)

OECD•z 2

.—

.—

adjusted R 2

.448

.504

.437

Standard error
of the estimate

.0148

.0135

.0149

–.338E-06
(.416E-06)

NOTE: Standard errors in parentheses.
* Significant at the 1 percent level.
† Significant at the 5 percent level.
‡ Per capita real GDP in 1965.
§ Significant at the 10 percent level.

settings and its reliance on seigniorage revenue. If the additional quadratic term in the
regression is significant, this relationship will
vary as z varies. For instance, if the coefficient
on z 2 is significantly less than zero, the evidence suggests that the relationship is concave.
Conversely, if the coefficient on the squared
term is significantly greater than zero, the evidence indicates that the relationship is convex.15
The results from the benchmark regression are reported in column 1 of Table 2.16 The
coefficient on z is significantly greater than zero,
while the coefficient on z 2 is not significantly
different from zero. Thus, the evidence is consistent with the notion that countries with high
monetary policy settings (high z values) tend to
rely more heavily on seigniorage revenue than
do countries with lower monetary policy settings (low z values). As discussed above, the
evidence suggests a positive, concave relationship between a country’s reserve ratio and
money growth rate and its reliance on seigniorage revenue. Further, the adjusted R 2 —a measure of the variation in seigniorage that is
accounted for by the regression variables—indicates the monetary policy measure accounts for
more than 40 percent of the variation in the S/Y
ratio, which is a reasonably good fit for a crosscountry sample.

15

ECONOMIC REVIEW THIRD QUARTER 1998

.—

165.817*
(37.035)

A Case for Combining the Money Growth Rate with the Reserve Ratio
In this box, I show that the S/Y ratio, in equilibrium, is a nonlinear function of the reserve requirement and money growth rate. This application is a
modified version of the economy developed in
Champ and Freeman (1994). The chief feature of
the model is that a person engages in market activity for two consecutive periods. In other words, N
people enter market activity at each date t, stay for
two periods, and then exit. It is equivalent to interpret this setup as one in which people are alive for
two periods. In this context for a particular date t,
those entering the market for the first time are “the
young,” and those entering the second period of
market activity are “the old.” Each person receives
labor income when young, but nothing when old.
Time is discrete and is indexed by t = 1, 2, 3, and
so on. I assume there are N people at date t = 1 who
have only one period in the economy; members of
this generation are the “initial old.” Preferences are
identical for all people born at date t and after.
For simplicity, I focus exclusively on a stationary version of the following economy. All people
born at date t = 1 and later have identical preferences. Thus, without loss of generality, one can
focus on the problem of the representative person,
which is characterized by the following equations:
(B.1)

maxc 1,c 2 ln (c 1t ) + bln (c 2t +1)

(B.2)

y ³ c 1t + at

(B.3)

c 2t +1 £ qt +1at

(B.4)

at = vt mt + dt

(B.5)

vt mt ³ gdt ,

bank deposits. Lastly, Equation B.5 is the reserve
requirement, dictating that real money balances
cannot be less than g percent of bank deposits.
I assume that deposits offer a greater return
than fiat money. Consequently, the typical person
will hold the minimum quantity of fiat money balances. Equations B.4 and B.5, therefore, imply that
at = (1 + g)d t . Substitute for a in Equations B.2 and
B.3, and solve Equation B.3 for (1 + g)d t , substituting the result into Equation B.2. After the algebra,
the expression is
(B.6)

y ³ c1t + c2t +1/qt +1,

which is the person’s lifetime budget.
To maximize lifetime utility, the typical person
will choose first- and second-period consumption
so that
(B.7)

1
bq
=
.
c1t c 2t +1

Equation B.7 is an efficiency condition. It says that
labor income will be allocated between first- and
second-period consumption so that the benefits
received from the last good consumed when young
(measured by 1/c1t ) are equal to the benefits
received from the last good consumed when old
(measured by bq /c2t +1). In this economy, the optimizing conditions imply that the typical person will
spend all of the labor income. Hence, Equation B.6
holds with equality.
In a stationary equilibrium, c1t = c1t +1 and
c 2t +1 = c 2t +2 at any date t, so that one can drop
the time subscripts. For a stationary equilibrium,
Equations B.6 and B.7 imply that c1 = y /(1 + b).
With 0 < b < 1, the typical person will spend a fixed
fraction of labor income on consumption when
young.
One might ask why the equilibrium expression
for c1 does not contain q. The answer is that a
change in the gross return on assets has two
opposing effects on consumption when young: substitution and wealth. With the substitution effect, an
increase in q, for example, makes consumption
when young more expensive relative to consumption when old. (Note that in the lifetime budget constraint [Equation B.6], 1/q can be interpreted as the
price of consumption when old.) Thus, an increase
in the gross return to assets would induce people
to consume less when young and more when old.
With the wealth effect, when c 2 becomes less
expensive, consuming more of both c 1 and c 2 is
possible. As such, an increase in q, for instance,
will induce people to consume more when young.
Clearly, the substitution and wealth effects have
opposing impacts on consumption when young.
With log utility, these effects exactly offset each
other. Consequently, in a stationary equilibrium the
value of c1 is independent of movements in the
gross return on assets.

where c1t is the young person’s consumption at
date t ; c 2t +1 is old-age consumption by the person
born at date t ; b is the person’s discount factor; y is
the person’s labor income; a is the total quantity of
goods saved by the young person; q is the gross
return on savings carried from date t to date t + 1;
and d is the quantity of goods stored as bank
deposits by the young person. A person can also
choose fiat money, which is m. Here, v stands for
the value of fiat money — that is, the quantity of the
consumption good that can be purchased with one
unit of money. The consumption good is perishable.
Equation B.1 is a function that describes the
welfare a representative person receives during a
market-active period. The person seeks to maximize
welfare by consuming as much of the consumption
good as possible. Equation B.2 represents the two
options — to save or to consume — that the typical
young person faces when young, while Equation
B.3 indicates that the typical old person can consume up to the value of principal and interest
earned on savings. Equation B.4 shows that savings
are in the form of either real money balances or

16

A Case for Combining the Money Growth Rate with the Reserve Ratio
(continued )
With c 1 = y /(1 + b), the level of bank deposits
can be represented as
(B.8)

d=

level of deposits is not affected even though q will
decline. Thus, the model economy predicts that the
equilibrium seigniorage ratio will rise in response to
an increase in the reserve requirement.
Next, consider a permanent, unanticipated
increase in the money growth rate. With faster
money growth, Equation B.10 indicates that an
economy’s reliance on real seigniorage revenue
will increase. With an increase in g, the tax rate on
real seigniorage revenue will rise and the gross
return on assets will decline. Because of the utility
function, the equilibrium quantity of real money balances is not affected by the decline in the gross
real return on assets. Thus, faster money growth
translates into an increase in the seigniorage ratio.
For this model economy, the s /y ratio
increases with respect to an increase in either the
reserve requirement ratio or money growth rate,
but at a declining rate. For different utility specifications, substitution and wealth effects would not
necessarily cancel each other out. Hence, the typical person could respond to an increase in q by
increasing consumption when young, thereby saving less. Accordingly, a young person could reduce
holdings of real money balances by enough to see
a decline in the s /y ratio for a given increase in
either the reserve requirement or the money growth
rate. The purpose of this box is to illustrate the
basic economic trade-offs. Hence, arguing the
appropriate utility specification is outside the scope
of this article.
Overall, Equation B.10 suggests a particular
sufficient statistic for assessing the relationship
between monetary policy and a country’s reliance
on seigniorage revenue. Throughout the statistical
analysis, I use the product z = [g/(1 + g)][g /(1 + g)]
as the measure of monetary policy.

g æ b ö
ç
÷.
1+ g è 1+ b ø

Next, substituting Equation B.8 into Equation B.5
yields the expression for the equilibrium value of
real money balances; formally,
(B.9)

v t mt =

b
g
•
y.
1+ b 1+ g

Here one can see the importance of the equilibrium expression for consumption when young.
Because of the substitution and wealth effects,
neither the quantity of deposits nor the quantity
of real money balances is affected by changes in
the gross return on assets. The implication is that
the tax base for real seigniorage revenue is not
affected by changes in real return on assets.
Expressing the equilibrium value of real
seigniorage revenue is now possible. Substituting
Equation B.9 into the expression for real seigniorage revenue yields vt mt (1 – 1/q). With g = q – 1,
I divide the expression by y so that the equilibrium reliance on seigniorage revenue per young
person is
(B.10)

b
g
s
g
=
•
•
.
y 1+ b 1+ g 1+ g

Equation B.10 indicates that the equilibrium s /y
ratio is a nonlinear function of the reserve ratio and
the money growth rate.1 Indeed, it is straightforward
to show that the equilibrium value of s /y is a concave function of both the reserve requirement ratio
and the money growth rate (see note 12).
To see how a change in monetary policy
affects the equilibrium seigniorage ratio, consider a
permanent, unanticipated increase in the reserve
requirement ratio. In this model economy, Equation
B.5 indicates that the holdings of real money balances will increase. Remember that the equilibrium

Note
1

Important differences across countries
could alter the relationship between monetary
policy and the reliance on seigniorage revenue.
For example, with only z as an explanatory
variable, the regression’s constant term captures
any differences between countries. Insofar as
differences across countries can be measured,
additional insight may be gained into the relationship between monetary policy and reliance
on seigniorage. Such measurements indicate
whether the results obtained in this analysis are
robust.
A particular concern is the ability of
people to avoid the inflation tax. Such avoid-

FEDERAL RESERVE BANK OF DALLAS

Here, the s /y ratio pertains to the ratio of per capita
levels, which accounts for the use of lowercase letters.

ance depends, in part, on a country’s financial
sophistication. Citizens in countries with more
sophisticated financial structure, for instance,
can avoid taxation by shifting to nonreservable
deposits. They can also dodge the tax by shifting from currency to, say, credit cards as the
means of payment. It would seem prudent,
therefore, to measure a country’s financial
sophistication to assess whether this omitted
variable affects the relationship between a
country’s monetary policy settings and its
reliance on seigniorage.
The measure of financial sophistication
should not depend on the monetary policy set-

17

ECONOMIC REVIEW THIRD QUARTER 1998

I report regression results in columns 2
and 3 of Table 2. Here, I use two proxies to
measure financial sophistication; one is the
OECD membership, and the other is per capita
real income in 1965. Two different sets of
results emerge. Specifically, with per capita real
income as the measure of financial sophistication, the evidence suggests a linear relationship between seigniorage reliance and z. As
such, the evidence suggests, as it did when
no financial sophistication measures were included, that countries that rely the most heavily
on seigniorage revenue have higher monetary
policy settings.
Consider, however, the results for a case in
which OECD membership is used as a proxy for
financial sophistication. These regression results
correspond to the evidence presented in Figure
2. The formal statistical analysis supports the
eyeball difference presented in the figure; that
is, the z –S/Y relationship is significantly different for OECD countries than for non-OECD
countries. The coefficient on OECD • z is negative and significant, and the coefficient on
OECD • z 2 is positive and significant. Thus, the
evidence suggests that the relationship between
seigniorage rates and monetary policy settings is
convex. Indeed, the evidence indicates that an
OECD country reaches a minimum reliance on
seigniorage revenue at a value of z = 0.0023.
To illustrate this result, suppose one is
looking at two OECD countries—country A and
country B. Each has a different monetary policy
setting, with country A always associated with
the lower value of z. According to the regression statistics, if z < 0.0023 for both countries,
then country B would rely less on seigniorage
revenue than would country A. In contrast, for
z > 0.0023, the regression predicts that country
B would rely more on seigniorage revenue than
would country A.18
The convex relationship exhibited by
OECD countries is puzzling. In the model economy described in the box, financial sophistication would seem to permit a country’s citizens
to avoid the inflation tax. Given an increase in
z, the equilibrium outcome for the S/Y ratio
would either decline or increase, but at a
decreasing rate as people avoid the inflation
tax. In other words, it is reasonable to expect
that increased tax-avoidance capabilities would
result in a more concave relationship between
a country’s monetary policy settings and its
reliance on seigniorage revenue, not a more
convex one.
Overall, the evidence suggests that there is
a systematic, positive relationship between a

Figure 2

Seigniorage–Income Ratio and
Monetary Policy Settings
Seigniorage ratio, S /Y
1
.9
.8
.7
.6
.5
.4
.3
.2
.1
0
0

.02

.04

.06

.08

.1

.12

.14

.16

.18

.2

Monetary policy settings, z
Non-OECD
OECD

Fitted line (non-OECD)
Fitted line (OECD)

tings to get an accurate estimate of the coefficient between monetary policy and seigniorage
reliance. In other words, movements in the
measure should not reflect behaviors related to
monetary policy settings, and yet the variable
should be reasonably well correlated with a
country’s level of financial sophistication. In
reality, finding such a measure is quite difficult.
Two variables are offered as proxies for financial sophistication: the level of real per capita
GDP in 1965 and a dummy variable indicating
whether the country is a member of the
Organization for Economic Cooperation and
Development (OECD).17 Certainly OECD membership and monetary policy settings are conceivably linked as part of a country’s policy
package. The more modest claim is that OECD
membership and per capita real GDP are less
likely to respond to movements in the monetary
policy settings than are financial-sophistication
measures such as bank deposits.
Figure 2 plots the combination of z and
S/Y as well as separate fitted lines for non-OECD
and OECD countries. Each line is fitted to a
regression of the form (S/Y )I = c0 + azi + bzi2.
These two fitted lines appear quite different.
Based on this preliminary look at the data, the
evidence suggests that the relationship between
a country’s monetary policy statistic and its
reliance on seigniorage revenue is different for
developed countries than it is for less developed
countries. Indeed, the fitted line for the nonOECD countries is upward sloping, whereas the
one for the OECD countries appears to have
some curvature.

18

country’s monetary policy settings and its reliance on seigniorage revenue. Thus, countries
with higher monetary policy settings tend to
rely more heavily on seigniorage. But compared
with less financially sophisticated countries, the
more financially sophisticated countries tend to
rely on seigniorage revenue at an increasing
rate. The findings with respect to financial
sophistication are difficult to explain and deserve more attention.

were to stand up to further scrutiny, economic
theory would need to address the puzzle. One
possible line of research would be to consider a
simple open economy in which two countries
differ in terms of financial sophistication and
monetary policy rules.
Another avenue for future research would
be to recognize that monetary policy variables
and seigniorage revenue are jointly determined.
While I have tried to describe the correlations
without referring to any monetary policy as
“causing” movements in seigniorage revenue,
the estimated regressions could be interpreted
as treating monetary policy as exogenous to the
determination of such revenue. Edwards and
Tabellini (1991) examine seigniorage revenue as
the outcome of various political forces that
influence, among other things, monetary policy
settings. Thus, future research could attempt
to disentangle the relative importance of political factors, controlling for monetary policy
explicitly.

CONCLUDING REMARKS
I present evidence in this article on the
importance of seigniorage revenue and its relationship to monetary policy. I use cross-country
observations to examine whether the average
money growth rate and average reserve ratio
are systematically related to a country’s reliance
on seigniorage revenue. Both economic and statistical considerations suggest that some combination of the money growth rate and the reserve
ratio should be used in the empirical analysis.
Consequently, a country’s monetary policy setting is measured using a combination variable
as opposed to investigating two separate relationships—one between seigniorage reliance
and the reserve ratio and the other between
seigniorage reliance and the money growth rate.
The main finding in this article is that there
is a systematic, positive relationship between a
country’s monetary policy settings and its reliance on seigniorage revenue. Thus, countries
that rely most heavily on seigniorage revenue
tend to have the highest values of the monetary
policy measure. There is some additional evidence that the relationship between the monetary policy variable and the seigniorage rate is
nonlinear for OECD countries. Here, OECD
membership is used as a proxy for financial
sophistication. The evidence suggests that OECD
countries rely on seigniorage revenue at an
increasing rate for given changes in the monetary policy variable.
The findings in this article constitute a
very preliminary investigation of the relationship between seigniorage revenue and monetary policy. There is always a risk of excluding
a key variable in a regression, and that risk
certainly holds here. One approach would be
to control for a host of other environmental
factors—for example, a more complete analysis
of the depth and structure of financial markets.
The most surprising and, in some ways,
the most interesting results are those differentiating between financially developed and less
financially developed countries. If these results

FEDERAL RESERVE BANK OF DALLAS

NOTES
1

2

3

4

5

6

19

See Cox (1992) for an excellent discussion of the
practical relationship between the Federal Reserve
and the U.S. Treasury. For an interesting description of
seigniorage in medieval times, see Rolnick, Velde, and
Weber (1994).
For reference, the United States raises, on average,
about 2 percent of federal government expenditures
through money creation.
After all the accounting is consolidated for the government and the central bank, the net change in the government’s income state is that money creation amounts
to a revenue source to cover various expenses.
Bryant and Wallace (1984) offer an explanation for the
coexistence of government bonds and money. They
argue that the two types of government paper effectively price discriminate between “rich” and “poor”
households.
As far as my assumption about one-period bonds
is concerned, I could examine a more complicated
maturity structure for government debt. Such generality would not alter the conclusions that I reach about
seigniorage revenue, but it would mean that I would
have to keep tabs on the entire distribution of government bonds and when each one matures.
The reduction in reported income can come either
from effective avoidance or from people working less
or acquiring less capital. Of course, the discussion
describes what happens to the steady-state level of
income.
There is no explicit interest on money. Consequently,
its one-period rate of return is calculated as the ratio
of the date t price (the potential selling price) to the

ECONOMIC REVIEW THIRD QUARTER 1998

7

8
9

10

11

12

13

14

15

date t – 1 price (the purchase price). Formally, this is
the ratio of vt /vt –1. With vt = 1/pt , then simple substitution yields the expression for the gross real return on
money.
Here, the reserve requirement pins down the fraction
of a person’s portfolio held in the form of money balances. This approach is qualitatively the same as one
in which the reserve requirement pins down the bank’s
portfolio.
The data set is available from the author upon request.
Fischer is primarily interested in describing why countries maintain national currencies. Computing the
seigniorage-to-GNP ratio demonstrates how important
seigniorage is. The ratio represents the command over
resources that a government obtains by creating money.
The income tax analog is the average marginal tax
rate. See, for example, Seater (1985).
Historically, the U.S. reserve requirement structure was
more convoluted. In the past, for example, it mattered
whether the commercial bank was located in a
Reserve Bank city or outside.
Interestingly, Fischer (1982) presents evidence that
several governments have made substantial use of
seigniorage. In Fischer’s sample, which generally
covers the period between 1960 and 1978, Argentina
collected, on average, 6.2 percent of GNP through
money creation.
This result does not bear directly on the relative importance of seigniorage revenue. Rather, it bears on the
issue of variability within a country across time. In
short, the reader gains a sense of how the countries in
the sample rely on seigniorage over time.
The effect of a change in the reserve ratio, holding
money growth constant, is given by the following derivative: ¶z /¶(R/D) = W/(1 + R/D)2, where W = g/(1 + g).
With W > 0, the expression says z is increasing the
reserve ratio. In addition, ¶ 2z /¶(R/D)2 = (–2•W )/(1 + R/D)3,
which is negative for W > 0.
To see this relationship, suppose the estimated regression is given by

18

REFERENCES
Bryant, John, and Neil Wallace (1984), “A Price Discrimination Analysis of Monetary Policy,” Review of Economic
Studies 51 (April): 279 – 88.
Champ, Bruce, and Scott Freeman (1994), Modelling
Monetary Economies (New York: John Wiley and Sons
Inc.).
Cox, W. Michael (1992), “Two Types of Paper: The Case
for Federal Reserve Independence,” Federal Reserve
Bank of Dallas Southwest Economy, Issue 6, November/
December, 3 – 8.
Edwards, Sebastian, and Guido Tabellini (1991),
“Explaining Fiscal Policies and Inflation in Developing
Countries,” Journal of International Money and Finance
10 (March): S16 – S48.
Fischer, Stanley (1982), “Seigniorage and the Case for a
National Money,” Journal of Political Economy 90 (April):
295 – 313.
Fomby, Thomas B., R. Carter Hill, and Stanley R. Johnson
(1984), Advanced Econometric Methods (New York:
Springer –Verlag Inc).

S /Y = c0 + az + bz 2.

16

17

native measures of financial sophistication in case the
1965 GDP value suffers from some time-specific factors. The regressions are qualitatively the same as
those reported in Table 2.
Three OECD countries in this sample — France, the
Netherlands, and Norway — have z values less than
0.0023. Using the method outlined in Fomby, Hill, and
Johnson (1984, 58), one can compute the standard
errors for the value of z at which seigniorage reliance
is minimized. With 90 percent confidence, the seigniorage-reliance minimizing value of z is between 0.0022
and 0.0024.

Rolnick, Arthur J., François R. Velde, and Warren E.
Weber (1994), “The Debasement Puzzle: An Essay on
Medieval Monetary Policy,” Federal Reserve Bank of
Minneapolis Working Paper no. 536 (October).

For a country with a 1-percentage-point higher average z, an estimate of the change in S/Y is a + 2bz.
Thus, a 1-percentage-point change in z depends on
the value of z.
In all regressions, the Newey–West procedure is
applied to correct any potential bias in standard
errors. In this particular application, heteroskedasticity
is the chief worry.
Per capita real GDP comes from the Summers –Heston
Penn World Tables. In addition, regressions are run
using per capita real GDP for 1980 and 1994 as alter-

Sargent, Thomas J. (1986), Rational Expectations and
Inflation (New York: Harper & Row).
Seater, John J. (1985), “On the Construction of Marginal
Federal Personal and Social Security Tax Rates in the
U.S.,” Journal of Monetary Economics 15 (January):
121– 35.

20

The private equity market is an important
source of funds for start-ups, private middlemarket companies, firms in financial distress,
and public firms seeking buyout financing.1
Over the past fifteen years, it has been the
fastest growing market for corporate finance, far
surpassing others such as the public equity and
bond markets and the market for private placement debt. Today the private equity market is
roughly one-quarter the size of both the market
for commercial and industrial bank loans and
the market for commercial paper in terms of
outstandings (Figure 1 ). In recent years, private
equity capital raised by partnerships has
matched, and sometimes exceeded, funds raised
through initial public offerings and gross
issuance of public high-yield corporate bonds.
Probably the most celebrated aspect of the private equity market is the investment in small,
often high-tech, start-up firms. These investments often fuel explosive growth in such firms.
For example, Microsoft, Dell Computer, and
Genentech all received private equity backing
in their early stages. In addition, the private
equity market supplied equity funds in the huge
leveraged buyouts of such large public companies as Safeway, RJR Nabisco, and Beatrice in
the 1980s.
Despite its dramatic growth and increased
significance for corporate finance, the private
equity market has received little attention in the
financial press or the academic literature.2 The
lack of attention is due partly to the nature of
the instrument itself. A private equity security is
exempt from registration with the Securities and
Exchange Commission by virtue of its being
issued in transactions “not involving any public
offering.” Thus, information about private transactions is often limited, and analyzing developments in this market is difficult.
This article examines the economic foundations of the private equity market and
describes its institutional structure. First, I briefly
discuss the growth of the limited partnership
as the major intermediary in the private equity
market over the last fifteen years. Next, I
explain the overall structure of the market,
focusing in turn on the major investors, intermediaries, and issuers. I then look at returns
to private equity over the last fifteen years.
Finally, I analyze the role of limited partnerships and why they are a particularly effective
form of intermediary in the private equity market. This entails a detailed examination of the
contracts these partnerships write with their
investors and the companies in which the partnerships invest.

The Economics
of the Private
Equity Market
Stephen D. Prowse
Senior Economist and Policy Advisor
Federal Reserve Bank of Dallas

T

his article examines

the economic foundations
of the private equity market
and describes its
institutional structure.

FEDERAL RESERVE BANK OF DALLAS

21

ECONOMIC REVIEW THIRD QUARTER 1998

Figure 1

Flows and Outstandings in Private Equity and Other Corporate Finance Markets
Amounts raised in 1996

Outstandings at year-end 1996

Billions of dollars

Billions of dollars

100

1,000

80

800

60

600

40

400

20

200

0

0

Private
equity

IPOs

Junk
bonds

Private
equity

Private
placements

C&I
loans

Commercial
paper

Private
placements

SOURCES: Federal Reserve Board flow of funds accounts; author’s estimates.

equity market. The specific advantages of limited partnerships are rooted in the way in which
they address these problems. The general partners specialize in finding, structuring, and managing equity investments in closely held private
companies. Limited partnerships are among the
largest and most active shareholders with significant means of both formal and informal control
and thus can direct companies to serve the
interests of their shareholders. At the same time,
limited partnerships employ organizational and
contractual mechanisms that align the interests
of the general and limited partners.
Limited partnership growth was also fostered by regulatory changes in the late 1970s
that permitted greater private equity investment

THE GROWTH OF LIMITED PARTNERSHIPS
IN THE PRIVATE EQUITY MARKET
The private equity market consists of professionally managed equity investments in the
unregistered securities of private and public companies.3 Professional management is provided
by specialized intermediaries called limited partnerships, which raise money from institutional
investors and invest it in both publicly and privately held corporations. Private equity managers acquire large ownership stakes and take
an active role in monitoring and advising companies in which they invest. They often exercise
as much or more control than company insiders.
The growth of private equity is a classic
example of how organizational innovation,
aided by regulatory and tax changes, can ignite
activity in a particular market. In this case, the
innovation was the widespread adoption of the
limited partnership as the means of organizing
private equity investments. Until the late 1970s,
private equity investments were undertaken
mainly by wealthy families, industrial corporations, and financial institutions investing directly
in issuing firms. By contrast, most investment
since 1980 has been undertaken by intermediaries on behalf of institutional investors. The
major intermediary is the limited partnership;
institutional investors are the limited partners,
and professional investment managers are the
general partners.
The emergence of the limited partnership
as the dominant form of intermediary is a result
of the extreme information asymmetries and
incentive problems that arise in the private

Figure 2

Private Equity Capital Outstanding,
by Source of Funds, 1980 and 1995
Billions of dollars
200
Other
160

Limited partnerships

120

80

40

0
1980

1995

SOURCES: Venture Economics; Fenn, Liang, and Prowse (1997).

22

Figure 3

Organized Private Equity Market
Investors

Intermediaries

Corporate pension funds

Dollars

Limited
partnership
interest

Public pension funds
Endowments
Foundations

Dollars

Bank holding companies

Equity
claim on
intermediary

Wealthy families and
individuals

Limited partnerships
• Managed by independent partnership
organizations
• Managed by affiliates
of financial institutions

Other intermediaries
• Small Business
Investment
Companies (SBICs)

Issuers

Dollars,
monitoring,
consulting

New ventures
• Early stage
• Later stage
Middle-market
private companies

Private
equity
securities

• Publicly traded
investment companies

• Expansion
– Capital expenditure
– Acquisitions
• Change in capital
structure
– Financial
restructuring
– Financial distress
• Change in ownership
– Retirement of owner
– Corporate spinoffs

Insurance companies
Direct investments

Investment banks
Nonfinancial corporations

(includes direct investments by both
BHC-affiliated SBICs and venture capital
subsidiaries of nonfinancial companies)
Dollars

Other investors

Public companies
• Management or
leveraged buyout
• Financial distress
• Special situations

Private equity securities

Investment advisers
to investors

• Evaluate limited partnerships
• Manage “funds of funds”

Placement agents for
partnerships

• Locate limited partners

• Advise issuers
• Locate equity investors

lists the major investors, the middle column lists
major intermediaries, and the right-hand column lists the major issuers in the private equity
market. Arrows pointing from left to right indicate the flow of dollars and other services;
arrows pointing from right to left indicate the
flow of private equity securities or other claims.
The bottom of Figure 3 lists an assortment of
agents and investment advisors that help issuers
or intermediaries raise money or advise investors on the best intermediaries in which to
invest. The role of each of these players in the
private equity market is discussed below.

by pension funds. The results of these changes
are telling: from 1980 to 1995, the amount of
capital under management in the organized private equity market increased from roughly $4.7
billion to over $175 billion. In addition, limited
partnerships went from managing less than 50
percent of private equity investments to managing more than 80 percent (Figure 2 ).4 Most of
the remaining private equity stock is held
directly by investors, but even much of this
direct investment activity is the result of knowledge that these investors have gained investing
in and alongside limited partnerships.

Investors
Figure 4 illustrates the total estimated private equity outstanding at year-end 1996 and
the portions held by the various investor
groups. Public and corporate pension funds are
the largest groups, together holding roughly 40
percent of capital outstanding and currently

THE STRUCTURE OF THE ORGANIZED
PRIVATE EQUITY MARKET
The organized private equity market has
three major players and an assortment of minor
ones. Figure 3 illustrates how these players
interact with each other. The left-hand column

FEDERAL RESERVE BANK OF DALLAS

Placement agents
for issuers

23

ECONOMIC REVIEW THIRD QUARTER 1998

firms typically invest in early-stage developmental ventures that may fit with their competitive and strategic objectives.

supplying close to 50 percent of all new funds
raised by partnerships.5 Public pension funds
are the fastest growing investor group and recently overtook private pension funds in terms
of the amount of total private equity held. Endowments and foundations, bank holding companies, and wealthy families and individuals each
hold about 10 percent of total private equity.
Insurance companies, investment banks, and
nonfinancial corporations are the remaining
major investor groups. Over the 1980s the
investor base within each investor group broadened dramatically, but still only a minority of
institutions within each group (primarily the
larger institutions) hold private equity.
Most institutional investors invest in private equity for strictly financial reasons, specifically because they expect the risk-adjusted
returns on private equity to be higher than
those on other investments and because of the
potential benefits of diversification.6 Bank holding companies, investment banks, and nonfinancial corporations may also invest in the
private equity market to take advantage of
economies of scope between private equity
investing and their other activities. Commercial
banks, for example, are large lenders to small
and medium-sized firms. As such, they have
contact with many potential candidates for private equity. Conversely, by investing in a private equity partnership, banks may be able to
generate lending opportunities to the firms in
which the partnership invests. Nonfinancial

Figure 4

Intermediaries
Intermediaries — mainly limited partnerships—manage an estimated 80 percent of private equity investments. Under the partnership
arrangement, institutional investors are the limited partners and a team of professional private
equity managers serves as the general partners.
Most often the general partners are associated
with a partnership management firm (such as
the venture capital firm Kleiner Perkins Caufield
& Byers or the buyout group Kohlberg Kravis
Roberts & Co.). Some management companies
are affiliates of a financial institution (an insurance company, bank holding company, or investment bank); the affiliated companies generally
are structured and managed no differently than
independent partnership management companies.
Investment companies not organized as
limited partnerships—Small Business Investment Companies (SBICs), publicly traded
investment companies, and other companies—
today play only a marginal role as intermediaries in the private equity market.7 SBICs,
established in 1958 to encourage investment in
private equity, can leverage their private capital
with loans from, or guaranteed by, the Small
Business Administration.8 In the 1970s they
accounted for as much as one-third of private
equity investment, but today they account for


,,






,,,

zz
yyy

{{{
||
,,







,,,





{{{
||




,,


Investors in the Private Equity Market, by Holdings of Outstandings at Year-End 1996
Billions of dollars

Other
$16

Corporate pension funds
$34.7

Investment banks
$8.6

Nonfinancial corporations
$7.5

Insurance companies
$12.7

Public pension funds
$39.5

Bank holding companies
$19.3

Wealthy families and individuals
$18.2

Endowments and foundations
$20

Total Private Equity Outstanding = $176.5 billion

24

Table 1

Characteristics of Major Issuers in the Private Equity Market

Characteristic

Early-stage
new ventures

Later stage
new ventures

Middle-market
private firms

Public and
private firms
in financial
distress

Public
buyouts

Other
public
firms

Size

Revenues
between
zero and
$15 million

Revenues
between
$15 million
and $50
million

Established,
with stable
cash flows
between
$25 million and
$500 million

Any size

Any size

Any size

Financial
attributes

High growth
potential

High growth
potential

Growth
prospects
vary widely

May be overleveraged or
have operating
problems

Underperforming

Depend on
reasons for
seeking private
equity

To effect a
turnaround

To finance a
change in
management or
in management
incentives

Reason(s) for
seeking private
equity

To start
operations

To expand plant
and operations
To cash out
early-stage
investors

Major source(s)
of private equity

“Angels”
Early-stage
venture
partnerships

Extent of access
to other financial
markets

For more
mature firms
with collateral,
limited access
to bank loans

To finance a
required change
in ownership or
capital structure

High levels of
free cash flow

To expand by
acquiring or
purchasing new
plant

Later stage
venture
partnerships

Later stage
venture
partnerships

To ensure
confidentiality
To issue a
small offering
For convenience
Because
industry is
temporarily out
of favor with
public equity
markets

“Turnaround”
partnerships

LBO and
mezzanine
debt
partnerships

Nonventure
partnerships

Very limited
access

Generally,
access to all
public and
private
markets

Generally,
access to all
public and
private
markets

Nonventure
partnerships
Access to bank
loans to finance
working capital

For more
mature, larger
firms, access to
private placement market

less than $1 billion of the $176.5 billion market.
The reduced role of SBICs has resulted in part
from their inability to make long-term equity
investments when they themselves are financed
with debt. Publicly traded investment companies also played a role in the past, but today
fewer than a dozen such companies are active,
and together they manage less than $300 million. Apparently the long-term nature of private
equity investing is not compatible with the
short-term investment horizons of stock analysts
and public investors.9
The dramatic growth of the limited partnership as the major intermediary in the private
equity market is a result of the limited partnership’s success in mitigating the severe information problems that exist in the market—both for

FEDERAL RESERVE BANK OF DALLAS

Access to bank
loans

institutional investors looking for appropriate
partnerships in which to invest and for partnerships looking for appropriate portfolio company investments. The mechanisms the limited
partnerships use to control these problems are
explored in detail in a following section.
Issuers
Issuers in the private equity market vary
widely in size and their motivation for raising
capital, as well as in other ways. They do share
a common trait, however: because private equity
is one of the most expensive forms of finance,
issuers generally are firms that cannot raise
financing from the debt or public equity markets.
Table 1 lists six major issuers of private
equity and their main characteristics. Issuers of

25

ECONOMIC REVIEW THIRD QUARTER 1998

Table 2

Average Internal Rates of Return for Venture and
Nonventure Private Equity Limited Partnerships
and for Public Small-Company Stocks

low-technology manufacturing, distribution, services, and retail industries. They use the private
equity market to finance expansion—through
new capital expenditures and acquisitions—
and to finance changes in capital structure and
in ownership (the latter increasingly the result
of private business owners reaching retirement
age).
Public companies also are issuers in the
nonventure sector of the private equity market.
Such companies often issue a combination of
debt and private equity to finance their management or leveraged buyout. Indeed, between
the mid- and late 1980s such transactions
absorbed most new nonventure private equity
capital. Public companies also issue private
equity to help them through periods of financial
distress, to avoid registration costs and public
disclosures, and to raise funds during periods
when their industry is out of favor with public
market investors.

Average annual return (percent)
Partnerships
formed in:
1969 – 79
1980 – 84
1985 – 89
1990 – 91
* Over
† Over
‡ Over
§ Over

the
the
the
the

period
period
period
period

1969
1980
1985
1990

to
to
to
to

Venture
capital

Nonventure
capital

Public smallcompany stocks

23.3
10.0
15.2
24.1

—
24.8
15.3
28.9

11.5*
15.3†
13.4‡
15.6§

1988.
1993.
1996.
1996.

SOURCE: Fenn, Liang, and Prowse (1997).

traditional venture capital are young firms, most
often those developing innovative technologies
that are predicted to show very high growth
rates in the future. They may be early-stage
companies, those still in the research and development stage or the earliest stages of commercialization, or later stage companies, those
with several years of sales but still trying to
grow rapidly.
Since 1980, nonventure private equity
investment—comprising investments in established public and private companies—has outpaced venture investment, as illustrated in
Figure 5. Nonventure investments include those
in middle-market companies (roughly, those
with annual sales of $25 million to $500 million), which have become increasingly attractive
to private equity investors. Many of these companies are stable, profitable businesses in

Agents and Advisors
Also important in the private equity market is a group of “information producers” whose
role has increased significantly in recent years.
These are the agents and advisors who place
private equity, raise funds for private equity
partnerships, and evaluate partnerships for
potential investors. They exist because they
reduce the costs associated with the information
problems that arise in private equity investing.
Agents facilitate private companies’ searches for
equity capital and limited partnerships’ searches
for institutional investors; they also advise on
the structure, timing, and pricing of private
equity issues and assist in negotiations. Advisors
facilitate institutional investors’ evaluations of
limited partnerships; they may be particularly
valuable to financial institutions unfamiliar with
the workings of the private equity market.

Figure 5

Private Equity Capital Outstanding,
by Type of Investment, 1980 and 1995

RETURNS IN THE PRIVATE EQUITY MARKET

Billions of dollars
200

A major reason for the explosive growth
of the private equity market since 1980 has been
the anticipation by institutional investors of
returns substantially higher than can be earned
in alternative markets. Of course, private equity
investments are regarded as considerably more
risky and more illiquid than other assets. For
those institutional investors that can bear such
risk and illiquidity, however, the high expected
returns are a major attraction.
Available data indicate that returns to private equity have at times far exceeded returns
in the public market. Table 2 shows internal

Nonventure
160

Venture

120

80

40

0
1980

1995

SOURCES: Venture Economics; Fenn, Liang, and Prowse (1997).

26

Table 3

Mechanisms Used to Align the Interests of Participants
in the Private Equity Market

rates of return on venture and nonventure
private equity partnerships during the period
in which the partnership was formed. These
returns are those experienced by the limited
partners; they are measured net of management
fees and other partnership expenses. Returns
to partnerships that have not yet been liquidated reflect the valuation of a residual component comprising investments whose market
values are unknown but are often reported at
cost. This may bias downward the returns reported for the funds formed from the mid-1980s
onward.
Overall, Table 2 suggests that returns to
private equity have generally been above those
experienced in the public equity market. The
fourth column of Table 2 shows the annual
average returns on a portfolio of public smallcompany stocks over various periods. These
periods are intended to be roughly comparable
with the ones during which the partnerships
listed were earning the bulk of their returns.10
Except for the early 1980s, returns to both venture and nonventure private equity are greater
than returns to public small-company stocks,
sometimes substantially so. Whether this is
enough to compensate investors for the increased risk of such investments is, of course,
another matter. However, as mentioned above,
returns for more recent partnerships may be
biased downward.
Table 2 also suggests that returns have
been higher for nonventure than for venture
partnerships. This pattern may partly explain
the faster growth of the later stage and, particu-

40

2

20

1

10

0

0
’69– ’76– ’80
’75 ’79

’81

’82

’83

’84

’85

’86

’87

’88

’89

’90

’91

Year partnership was formed
SOURCE: Fenn, Liang, and Prowse (1997).

FEDERAL RESERVE BANK OF DALLAS

Direct means of control
Partnership covenants
Advisory boards

Direct means of control
Voting rights
Board seats
Access to capital

Accompanying the rapid growth of the
private equity market in the 1980s was the rise
of professionally managed limited partnerships
as intermediaries, as illustrated in Figure 2. In
certain respects, the success of limited partnerships is paradoxical. Funds invested in such
partnerships are illiquid over the partnership’s
life, which in some cases runs more than ten
years. During this period, investors have little
control over the way their funds are managed.
Nevertheless, the increasing dominance of limited partnerships suggests that they benefit both
investors and issuers.
Table 3 provides an overview of the mechanisms that are used to align the interests of
(1) the limited and general partners and (2) the
partnerships and the management of the companies in which they invest. These mechanisms
can be categorized under the broad headings of
performance incentives and direct means of
control.
As shown on the left-hand side of Table 3,
performance incentives that align the interests
of the limited and general partners are twofold.
First, the general partners must establish a favorable track record to raise new partnerships.
Second, they operate under a pay-for-performance scheme in which most of their expected
compensation is a share of the profits earned on

Capital raised (dollars)
Internal rates of return (percent)
30

Performance incentives
Managerial ownership
Managerial compensation

THE ROLE OF LIMITED PARTNERSHIPS IN THE
PRIVATE EQUITY MARKET

Percent

3

Performance incentives
Reputation
General partner compensation

larly, nonventure sectors of the private equity
market over the past fifteen years.
To a certain extent, returns are driven by
capital availability. For venture investments, for
example, returns have been greatest on investments made during periods when relatively
small amounts of capital were available (Figure
6 ). Conversely, there is concern, if not a large
amount of evidence, that periods of greater
capital availability depress future returns.

Capital Raised by Venture Capital Partnerships
and Internal Rates of Return as of 1995
4

Partnership – portfolio companies

NOTE: Most important mechanisms are in bold type.

Figure 6

Billions of dollars

Limited partners – general partners

27

ECONOMIC REVIEW THIRD QUARTER 1998

intermediaries can be resolved.12 In the private
equity market, reputation plays a key role in
addressing these problems because the market
consists of a few actors that repeatedly interact
with each other. For example, partnership managers that fail to establish a favorable track
record may subsequently be unable to raise
funds or participate in investment syndicates
with other partnerships.13

investments. These provisions are the principal
means by which the interests of the general and
limited partners are harmonized. Of secondary
importance are direct control mechanisms such
as partnership agreements and advisory boards
composed of limited partners. Partnership
agreements give limited partners restricted
direct control over the general partners’ activities. These agreements consist mainly of restrictions on allowable investments and other
partnership covenants, which the advisory
board can waive by majority vote.
In contrast, the direct means of oversight
and control are the principal mechanisms for
aligning the interests of the partnership and
portfolio company management. The most
important of these mechanisms are a partnership’s voting rights, its seats on the company
board, and its ability to control companies’
access to additional capital. Performance
incentives for company management, including managerial ownership of stock, are also
important but are secondary to direct partnership control.

Overview of Private Equity Partnerships
Private equity partnerships are limited
partnerships in which the senior managers of a
partnership management firm serve as the general partners and institutional investors are the
limited partners. The general partners are
responsible for managing the partnership’s
investments and contributing a very small proportion of the partnership’s capital (most often,
1 percent); the limited partners provide the balance and bulk of the investment funds.
Each partnership has a contractually fixed
lifetime—generally ten years—with provisions
to extend the partnership, usually in one- or
two-year increments, up to a maximum of four
years. During the first three to five years, the
partnership’s capital is invested. Thereafter, the
investments are managed and gradually liquidated. As the investments are liquidated, distributions are made to the limited partners in the
form of cash or securities. The partnership managers typically raise a new partnership fund at
about the time the investment phase for an
existing partnership has been completed. Thus,
the managers are raising new partnership funds
approximately every three to five years and at
any one time may be managing several funds,
each in a different phase of its life. Each partnership is legally separate, however, and is
managed independently of the others.
A partnership typically invests in ten to
fifty portfolio companies (two to fifteen companies a year) during its three- to five-year investment phase. The number of limited partners is
not fixed: most private equity partnerships have
ten to thirty, though some have as few as one
and others more than fifty.14 The minimum commitment is typically $1 million, but partnerships
that cater to wealthy individuals may have a
lower minimum and larger partnerships may
have a $10 million to $20 million minimum.
Most partnership management firms have
six to twelve senior managers who serve as
general partners, although many new firms
are started by two or three general partners
and a few large firms have twenty or more.
Partnership management firms also employ

Information Problems in Private Equity Investing
Two types of problems frequently occur
when outsiders finance a firm’s investment
activity—sorting problems and incentive problems. Sorting (or adverse selection) problems
arise in the course of selecting investments.
Firm owners and managers typically know
much more about the condition of their business than do outsiders, and it is in their interest
to accent the positive while downplaying potential difficulties (see Leland and Pyle 1977; Ross
1977). Incentive (or moral hazard) problems
arise in the course of the firm’s operations.
Managers have many opportunities to take
actions that benefit themselves at the expense of
outside investors.
Private equity is used in financing situations in which the sorting and incentive problems are especially severe.11 Resolving these
problems requires that investors engage in intensive preinvestment due diligence and postinvestment monitoring. These activities are not
efficiently performed by large numbers of investors; there can either be too much of both
types of activities because investors duplicate
each others’ work, or too little of each owing
to the tendency for investors to free ride on the
efforts of others. Thus, delegating these activities to a single intermediary is potentially efficient.
The efficiency of intermediation depends
on how effectively the sorting and incentive
problems between the ultimate investors and

28

associates—general partners in training—usually in the ratio of one associate to every one or
two general partners. General partners often
have backgrounds as entrepreneurs and senior
managers in industries in which private equity
partnerships invest and, to a lesser extent, in
investment and commercial banking.

investigation varies with the type of investment.
With distressed companies, efforts are focused
on discussions with the company’s lenders; for
buyouts of family-owned businesses, management succession issues will warrant greater
attention; and for highly leveraged acquisitions,
efforts will focus on developing detailed cashflow projections.
Extensive due diligence in the private
equity market is needed because little, if any,
information about issuers is publicly available
and in most cases the partnership has had no
relationship with the issuer. Thus, the partnership must rely heavily on information that it can
produce de novo. Moreover, the management of
the issuing firm typically knows more than outsiders do about many aspects of its business.
This information asymmetry, combined with the
fact that issuing private equity is very expensive,
has the potential to create severe adverse selection problems for investors. In the private equity
market, this problem is mitigated by the extensive amount of due diligence and by the fact
that alternative sources of financing for private
equity issuers are limited.
Information asymmetries between investors and managers of the issuing firm give rise
to a potential moral hazard problem, whereby
management pursues its own interests at the
expense of investors. Private equity partnerships
rely on various mechanisms to align the interests of managers and investors. These mechanisms can be classified into two main
categories. The first category comprises mechanisms that relate to performance incentives,
including the level of managerial stock ownership, the type of private equity issued to
investors, and the terms of management
employment contracts. The second comprises
mechanisms that relate to direct means of control of the firm, including board representation,
allocation of voting rights, and control of access
to additional financing. These mechanisms are
examined in turn.

RELATIONSHIP BETWEEN A PARTNERSHIP
AND ITS PORTFOLIO COMPANIES
Partnership managers receive hundreds of
investment proposals each year. Of these proposals, only about 1 percent are chosen for
investment. The partnership managers’ success
depends upon their ability to select these proposals efficiently. Efficient selection is properly
regarded as more art than science and depends
on the acumen of the general partners acquired
through experience operating businesses as
well as experience in the private equity field.
Investment proposals are first screened to
eliminate those that are unpromising or that fail
to meet the partnership’s investment criteria.
Private equity partnerships typically specialize
by type of investment and by industry and
location of the investment. Specialization reduces the number of investment opportunities
considered and reflects the degree of specialized knowledge required to make successful
investment decisions.
This initial review consumes only a few
hours and results in the rejection of up to 90
percent of the proposals the partnership
receives. In many cases, the remaining proposals are subjected to a second review, which
may take several days. Critical information
included in the investment proposal is verified
and the major assumptions of the business plans
are scrutinized. As many as half the proposals
that survived the initial screening are rejected at
this stage.
Proposals that survive these preliminary
reviews become the subject of a more comprehensive due-diligence process that can last up
to six weeks. It includes visits to the firm; meetings and telephone discussions with key
employees, customers, suppliers, and creditors;
and the retention of outside lawyers, accountants, and industry consultants. For proposals
that involve new ventures, the main concerns
are the quality of the firm’s management and
the economic viability of the firm’s product or
service (Gladstone 1988). For proposals involving established firms, the general objective is to
gain a thorough understanding of the existing
business, although the precise focus of the

FEDERAL RESERVE BANK OF DALLAS

Performance Incentives
Managerial Stock Ownership. Private equity
managers usually insist that the portfolio firm’s
senior managers own a significant share of their
company’s stock, and stock ownership often
accounts for a large part of managers’ total compensation. In venture capital, management
stock ownership varies widely depending upon
the management’s financial resources and the
company’s financing needs and projected future
value. It also depends upon the number of
rounds of financing, as dilution typically occurs

29

ECONOMIC REVIEW THIRD QUARTER 1998

uating the firm’s performance, and contributing
significantly to the firm’s business and financial
planning process.
General partners can be extremely influential and effective outside directors. As large
stakeholders, they have an incentive to incur the
expense necessary to monitor the firm.
Moreover, they have the resources to be effective monitors—in the form of their own staff
members, information acquired during the duediligence process, and the expertise acquired
while monitoring similar companies.
Private equity partnerships in many cases
dominate the boards of their portfolio companies. Lerner (1994) reports that general partners
hold more than one-third of the seats on the
boards of venture-backed biotechnology firms,
which is more than the share held by management or other outside directors. Even if it is a
minority investor, a private equity partnership
usually has at least one board seat and is able to
participate actively in a company’s management.
Allocation of Voting Rights. For early-stage
new ventures, leveraged buyouts, and financially distressed firms, the investment is often
large enough to confer majority ownership. In
other situations, the partnership may obtain
voting control even if it is not a majority shareholder. Even if the partnership lacks voting
control, however, it is generally the largest nonmanagement shareholder. Thus, it has a disproportionate degree of influence on matters that
come to a shareholder vote.
In general, a partnership’s voting rights
do not depend on the type of stock issued.
For example, holders of convertible preferred
stock may be allowed to vote their shares on
an “as-converted” basis. Similarly, subordinated
debt can be designed so that investors have
voting rights should a vote take place. The issue
of voting control can also be addressed by
creating separate classes of voting and nonvoting stock.
Control of Access to Additional Financing.
Partnerships can also exercise control by providing a company with continued access to
funds. This is especially the case for new ventures. Venture capital is typically provided to
portfolio companies in several rounds at fairly
well-defined development stages, generally
with the amount provided just enough for the
firm to advance to the next stage of development. Even if diversification provisions in the
partnership agreement prevent the partnership
itself from providing further financing, the general partners have the power, through their
extensive contacts, to bring in other investors.

with each round. Even in later stage companies,
however, management ownership of 20 percent
is not unusual. For nonventure companies,
managerial share ownership usually ranges
between 10 percent and 20 percent.
A common provision in both venture and
nonventure financing is an equity “earn-out”
(Golder 1983). This arrangement allows management to increase its ownership share (at the
expense of investors) if certain performance
objectives are met.
Type of Private Equity Issued to Investors.
Convertible preferred stock is the private equity
security most frequently issued to investors. The
major difference between convertible preferred
stock and common stock is that holders of preferred stock are paid before holders of common
stock in the event of liquidation. From the partnership’s standpoint, this offers two advantages.
First, it reduces the partnership’s investment
risk. Second, and more important, it provides
strong performance incentives to the company’s
management because management typically
holds either common stock or warrants to purchase common stock. If the company is only
marginally successful, its common stock will be
worth relatively little. Thus, the use of convertible preferred stock mitigates moral hazard
problems. Subordinated debt with conversion
privileges or warrants is sometimes used as an
alternative way of financing the firm: it confers
the same liquidation preference to investors as
convertible preferred equity and, thus, the same
performance incentives to management.
Management Employment Contracts. In
principle, management’s equity position in the
firm could induce excessive risk taking.
However, management compensation can also
be structured to include provisions that penalize
poor performance, thereby offsetting incentives
for risk taking. Such provisions often take the
form of employment contracts that specify
conditions under which management can be
replaced and buyback provisions that allow the
firm to repurchase a manager’s shares in the
event that he or she is replaced.
Mechanisms of Direct Control
Although managerial incentives are a very
important means of aligning the interests of
management and investors, a private equity
partnership relies primarily on its ability to exercise control over the firm to protect its interests.
Board Representation. In principle, a firm’s
board of directors bears the ultimate responsibility for the management of the firm, including
hiring and firing the CEO, monitoring and eval-

30

Conversely, if the original partnership is unwilling to arrange for additional financing, it is
unlikely that any other partnership will choose
to do so; the reluctance of the original partnership is a strong signal that the company is a
poor investment.
Nonventure capital is also provided in
stages, though to a lesser extent. For example,
middle-market firms that embark on a strategy
of acquisitions periodically require capital infusions to finance growth; that capital is not provided all at once. Similarly, companies that
undergo leveraged buyouts are forced to service
debt out of free cash flow and subsequently
must justify the need for any new capital
(Palepu 1990).
Other Control Mechanisms. Other mechanisms by which partnerships control and monitor the activities of the companies in which they
invest include covenants that give the partnership the right to inspect the company’s facilities,
books, and records and to receive timely financial reports and operating statements. Other
covenants require that the company not sell
stock or securities, merge or sell the company,
or enter into large contracts without the
approval of the partnership.

tives can significantly curtail the general partners’ inclination to engage in behavior that does
not maximize value for investors. Direct control
mechanisms in the partnership agreement are
relatively less important means of controlling
the moral hazard problem between general and
limited partners.
Performance Incentives
Reputation. Partnerships have finite lives.
To remain in business, private equity managers
must regularly raise new funds, and fund raising
is less costly for more reputable firms. In fact, to
invest in portfolio companies on a continuous
basis, managers must raise new partnerships
once the funds from the existing partnership
are fully invested, or about once every three to
five years.
Raising partnership funds is time consuming and costly, involving presentations to institutional investors and their advisors that can
take from two months to well over a year,
depending on the general partners’ reputation
and experience. A favorable track record is
important because it conveys some information
about ability and suggests that general partners
will take extra care to protect their reputation.
Also, experience itself is regarded as an asset.
To minimize their expenses, partnership managers generally turn first to those who invested
in their previous partnerships—assuming, of
course, that their previous relationships were
satisfactory.
Certain features of a partnership enhance
the ability of the general partners to establish a
reputation. These features essentially make both
the partnership’s performance and the managers’ activities more transparent to investors
than might be the case for other financial intermediaries. One such feature is segregated
investment pools. By comparing one partnership’s investment returns with those of other
partnerships raised at the same time, it is easier
to account for factors that are beyond the control of the general partners, such as the stage of
the business cycle or the condition of the market for initial public offerings, mergers, and
acquisitions. By contrast, if private equity intermediaries did not maintain segregated investment pools, earnings would represent a blend
of investment returns that occur at different
stages of the business cycle or under different
market conditions.
Another feature is the separation of management expenses and investment funds. In a
limited partnership, management fees are specified in the partnership agreement (described

RELATIONSHIP BETWEEN THE LIMITED PARTNERS
AND THE GENERAL PARTNERS
By investing through a partnership rather
than directly in issuing firms, investors delegate
to the general partners the labor-intensive
responsibilities of selecting, structuring, managing, and eventually liquidating private equity
investments. However, limited partners must be
concerned with how effectively the general
partners safeguard their interests. Among the
more obvious ways in which general partners
can further their own interests at the expense of
the limited partners are spending too little effort
monitoring and advising portfolio firms, charging excessive management fees, taking undue
investment risks, and reserving the most attractive investment opportunities for themselves.
Private equity partnerships address these
problems in two basic ways: by using mechanisms that relate to performance incentives and
mechanisms that relate to direct means of control. Performance incentives are the more
important means of aligning general partners’
interests with those of the limited partners.
These incentives involve the general partners’
need to protect their reputations and the terms
of the general partners’ compensation structure,
such as their share of the profits. These incen-

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31

ECONOMIC REVIEW THIRD QUARTER 1998

below). Thus, the amount of investment capital
that can be consumed in the form of manager
salaries and other perquisites is capped. Moreover, because such expenses are transparent, it
is easier to compare expenses across partnerships. Other types of financial intermediaries
pay expenses and finance investments out of
the same funds raised from investors; although
expenses are reported, they are difficult to control before the fact and are not always transparent after the fact.
Compensation Structure. General partners
earn a management fee and a share of a partnership’s profits, the latter known as carried
interest. For a partnership that yields average
returns, carried interest may be several times
larger than the management fees (Sahlman
1990). This arrangement — providing limited
compensation for making and managing investments and significant compensation in the form
of profit sharing —lies at the heart of the partnership’s incentive structure.
Management fees are frequently set at a
fixed percentage of committed capital and
remain at that level over the partnership’s life.
Fee percentages range from 1 percent to 3 percent. Carried interest is most often set at 20
percent of the partnership’s net return.

Partnership covenants also limit deal fees
(by requiring that deal fees be offset against
management fees), restrict coinvestment with
the general partners’ earlier or later funds, and
restrict the ability of general partners and their
associates to coinvest selectively in the partnership’s deals.
Finally, partnership agreements allow limited partners some degree of oversight over the
partnership. Most partnerships have an advisory
board composed of the largest limited partners.
These boards help resolve conflicts involving
deal fees and conflict-of-interest transactions.
They do so by approving exemptions from partnership covenants. Special committees are also
created to help determine the value of the partnership’s investments. However, these two
types of bodies do not provide the kind of management oversight that a board of directors can
for a corporation; indeed, their power is limited
by the legal nature of the partnership, which
prohibits limited partners from taking an active
role in management.
CONCLUSION
This article has presented an economic
analysis of the private equity market. In particular, it has detailed how the contracts that
limited partnerships write with investors and
portfolio firms address many of the adverse
selection and moral hazard problems that face
investors considering investments in small and
medium-sized firms.
The private equity market’s success in
addressing these problems is evidenced by the
large number of successful firms that received
initial financing in this market. This success has
been much admired in the rest of the industrialized world, particularly in Japan and
Germany. In these countries, private equity markets of the U.S. kind do not exist, primarily due
to the heavily regulated nature of their securities
markets, and so firms rely much more on bank
financing. While such bank-centered systems
may have had advantages in the past, there is
an increasing feeling that such systems may
not adequately provide funds for small and
medium-sized firms that are the engine of future
economic growth and innovation. Both Japan
and Germany have recently taken steps to
deregulate their financial markets. By fostering
the growth of U.S. private equity market practices, these countries hope to solve the informational and governance problems of small firms
looking for capital.

Direct Control Mechanisms
Partnership agreements also protect limited partners’ interests through covenants that
place restrictions on a partnership’s investments
and on other activities of the general partners.
Restrictions on investments are especially important because a considerable portion of the
general partners’ compensation is in the form of
an option-like claim on the fund’s assets. This
form of compensation can lead to excessive risk
taking. In particular, it may be in the interest of
the general partners to maximize the partnership’s risk—and hence the expected value of
their carried interest—rather than the partnership’s risk-adjusted expected rate of return.
To address the problem of excessive risk
taking, partnership covenants usually set limits
on the percentage of the partnership’s capital
that may be invested in a single firm. Covenants
may also preclude investments in publicly
traded and foreign securities, derivatives, other
private equity funds, and private equity investments that deviate significantly from the partnership’s primary focus. Finally, covenants
usually restrict the fund’s use of debt and in
many cases require that cash from the sale of
portfolio assets be distributed to investors
immediately.

32

management may have little or no incentive to act in
equityholders’ best interests.

NOTES
1

2

3

4

5

6

7

8
9

10

11

This article draws selectively from a longer, more
comprehensive research paper on the private equity
market by Fenn, Liang, and Prowse (1997).
Some studies have been made of particular market
sectors, such as venture capital and leveraged buyouts (LBOs) of large public companies. On venture
capital, see Sahlman (1990) and special issues of
Financial Management (1994) and The Financier
(1994). For a summary of the LBO literature, see
Jensen (1994).
An equity investment is any form of security that has an
equity participation feature. The most common forms are
common stock, convertible preferred stock, and subordinated debt with conversion privileges or warrants.
The emergence of limited partnerships is actually
more dramatic than these figures indicate. As recently
as 1977, limited partnerships managed less than 20
percent of the private equity stock.
These and other figures in this section are my estimates based on information from a variety of sources.
See Fenn, Liang, and Prowse (1997) for details on how
these estimates are constructed.
Private equity is often included in a portfolio of “alternative assets” that also includes distressed debt,
emerging market stocks, real estate, oil and gas,
timber and farmland, and economically targeted
investments.
Two other types of private equity organizations are
SBICs owned by bank holding companies and venture
capital subsidiaries of nonfinancial corporations. Both
types were extremely important in the 1960s, and they
still manage significant amounts of private equity. However, these organizations invest only their corporate
parent’s capital. In this sense, neither is really an intermediary but rather a conduit for direct investments.
I treat the investments by these organizations as direct
investments, not as investments by intermediaries.
See the Venture Capital Journal, October 1983.
This, of course, raises the question of why private
equity investments haven’t proven to be ideal for
closed-end mutual funds, wherein the fund invests
money for the long term but investors can get out in
the short term.
For example, partnerships in the first row were formed
between the years 1969 and 1979. These funds would
have invested and earned returns on their capital
between the years 1969 and 1988. The first row/fourth
column thus shows the annual average return to public
small companies over this 20-year period. Returns for
small-company stocks for the other periods are similarly calculated. Returns for small-company stocks are
after transactions costs (Ibbotson 1997).
In venture investing, for example, the firm is often a
start-up with no track record. In a leveraged buyout,
while there may be ample information about the firm,

FEDERAL RESERVE BANK OF DALLAS

12

13

14

If, for example, investors must investigate the intermediary to the same extent that they would investigate
the investments that the intermediary makes on their
behalf, using one may be less efficient (Diamond 1984).
Intermediaries are also important because selecting,
structuring, and managing private equity investments
require considerable expertise. Gaining such expertise requires a critical mass of investment activity that
most institutional investors cannot attain on their own.
Managers of private equity intermediaries are able to
acquire such expertise through exposure to and
participation in a large number of investment opportunities. Although institutional investors could also
specialize in this way, they would lose the benefits of
diversification. Finally, intermediaries play an important
role in furnishing business expertise to the firms in
which they invest. Reputation, learning, and specialization all enhance an intermediary’s ability to provide
these services. For example, a reputation for investing
in well-managed firms is valuable in obtaining the services of underwriters. Likewise, specialization allows
an intermediary to more effectively assist its portfolio
companies in hiring personnel, dealing with suppliers,
and helping in other operations-related matters.
Many partnerships that have a single limited partner
have been initiated and organized by the limited partner rather than by the general partner. Such limited
partners are in many cases nonfinancial corporations
that want to invest for strategic as well as financial
reasons — for example, a corporation that wants exposure to emerging technologies in its field.

REFERENCES
Diamond, Douglas W. (1984), “Financial Intermediation
and Delegated Monitoring,” Review of Economic Studies
51 (July): 393 – 414.
Fenn, George, Nellie Liang, and Stephen D. Prowse
(1997), “The Private Equity Market: An Overview,” Financial Markets, Institutions and Instruments 6 (4): 1–105.

Financial Management 23 (1994), May.
The Financier 1 (1994), Autumn.
Gladstone, David (1988), Venture Capital Handbook
(Englewood Cliffs, N.J.: Prentice Hall).
Golder, Stanley (1983), “Structuring and Pricing the
Financing,” in Guide to Venture Capital, ed. Stanley Pratt
(Wellesley, Mass.: Capital Publishing Corp.).
Ibbotson, Roger (1997), Stocks, Bonds, Bills, and
Inflation 1997 Yearbook (Chicago: Ibbotson Associates).

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ECONOMIC REVIEW THIRD QUARTER 1998

Jensen, Michael C. (1994), “The Modern Industrial Revolution, Exit, and the Failure of Internal Control Systems,”
Journal of Applied Corporate Finance 6 (Winter): 4 – 23.

Ross, Stephen A. (1977), “The Determination of Financial
Structure: The Incentive-Signalling Approach,” Bell
Journal of Economics 8 (Spring): 23 – 40.

Leland, Hayne, and David Pyle (1977), “Information
Asymmetries, Financial Structure and Financial
Intermediation,” Journal of Finance 32 (May): 371– 87.

Sahlman, William A. (1990), “The Structure and Governance of Venture Capital Organizations,” Journal of
Financial Economics 27 (Spring): 473 – 521.

Lerner, Joshua (1994), “Venture Capitalists and the
Oversight of Private Firms” (unpublished working paper,
Harvard University).

Venture Capital Journal (1983), “SBICs After 25 Years:
Pioneers and Builders of Organized Venture Capital,”
October.

Palepu, Krishna (1990), “Consequences of Leveraged
Buyouts,” Journal of Financial Economics 27
(September): 247– 62.

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