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Economic Quarterly—Volume 94, Number 3—Summer 2008—Pages 197–218

New Keynesian Economics:
A Monetary Perspective
Stephen D. Williamson

ince John Maynard Keynes wrote the General Theory of Employment,
Interest, and Money in 1936, Keynesian economics has been highly inﬂuential among academics and policymakers. Keynes has certainly had
his detractors, though, with the most inﬂuential being Milton Friedman, Robert
Lucas, and Edward C. Prescott. Monetarist thought, the desire for stronger
theoretical foundations in macroeconomics, and real business cycle theory
have at times been at odds with Keynesian economics. However, Keynesianism has remained a strong force, in part because its practitioners periodically
adapt by absorbing the views of its detractors into the latest “synthesis.”
John Hicks’s IS-LM interpretation of Keynes (Hicks 1937) and the popularization of this approach, particularly in Samuelson’s textbook (Samuelson
1997), gave birth to the “neoclassical synthesis.” Later, the menu cost models
developed in the 1980s were a response to a drive for a more serious theory of
sticky prices (Mankiw 1985, Caplin and Spulber 1987). More recently, New
Keynesian economists have attempted to absorb real business cycle analysis and other ideas from post-1972 macroeconomics into a “new neoclassical
synthesis” (Goodfriend and King 1997).
The important New Keynesian ideas, as summarized, for example in
Clarida, Gal´, and Gertler (1999) and Woodford (2003), are the following:
ı
1. The key friction that gives rise to short-run nonneutralities of money
and the primary concern of monetary policy is sticky prices. Because
some prices are not fully ﬂexible, inﬂation or deﬂation induces relative
price distortions and welfare losses.
Williamson is afﬁliated with Washington University in St. Louis, the Federal Reserve Bank
of Richmond, and the Federal Reserve Bank of St. Louis. He thanks Huberto Ennis, Robert
Hetzel, John Weinberg, and Alex Wolman for helpful comments and suggestions. Any opinions
expressed in this article are the author’s and do not necessarily reﬂect those of the Federal
Reserve Bank of Richmond, the Federal Reserve Bank of St. Louis, or the Federal Reserve
System. E-mail: swilliam@artsci.wustl.edu.

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Federal Reserve Bank of Richmond Economic Quarterly
2. Modern monetary economics is not part of the New Keynesian synthesis. New Keynesians typically regard the frictions that we encounter
in deep (e.g., Lagos and Wright 2005) and not-so-deep (e.g., Lucas
and Stokey 1987) monetary economics as being second-order importance. These frictions are absence-of-double-coincidence problems
and information frictions that give rise to a fundamental role for monetary exchange, and typically lead to intertemporal distortions that can
be corrected by monetary policy (for example, a ubiquitous result in
monetary economics is Friedman’s zero-nominal-interest-rate rule for
correcting intertemporal monetary distortions). The Friedman rule is
certainly not ubiquitous in New Keynesian economics.
3. The central bank is viewed as being able to set a short-term nominal
interest rate, and the monetary policy problem is presented as the choice
over alternative rules for how this nominal interest rate should be set
in response to endogenous and exogenous variables.
4. There is a short-run Phillips curve tradeoff. A monetary policy that
produces an increase in unanticipated inﬂation will tend to increase
real aggregate output.

The goal of this paper is to construct a simple sticky-price New Keynesian
model and then use it to understand and evaluate the ideas above. In this model
there are some important departures from the typical New Keynesian models
studied by Clarida, Gal´, and Gertler; Woodford; and others. However, these
ı
departures will highlight where the central ideas and results in New Keynesian
analysis are coming from.
For monetary economists, key aspects of New Keynesian economics can
be puzzling. For example in Woodford (2003), the apparently preferred framework for analysis is a “cashless model” in which no outside money is held in
equilibrium. Prices are denominated in terms of some object called money,
and these prices are assumed to be sticky. The interest rate on a nominal bond
can be determined in the cashless model, and the central bank is assumed capable of setting this nominal interest rate. Then, the monetary policy problem is
formulated as the choice over rules for setting this nominal interest rate. This
approach can be contrasted with the common practice in monetary economics,
where we start with a framework in which money overcomes some friction,
serves as a medium of exchange, and is held in equilibrium in spite of being
dominated in rate of return by other assets. Then, studying the effects of monetary policy amounts to examining the consequences of changing the stock
of outside money through various means: open market operations, central
bank lending, or outright “helicopter drops.” It is usually possible to consider
monetary policy rules that dictate the contingent behavior of a nominal interest rate, but in most monetary models we can see what underlying actions
the central bank must take concerning monetary quantities to support such a

S. D. Williamson: New Keynesian Economics

199

policy. What is going on here? Is the New Keynesian approach inconsistent
with the principles of monetary economics? Is it misleading?
The ﬁrst task in this article is to construct a cashless model with sticky
prices. This model departs from the usual New Keynesian construct in that
there are competitive markets rather than Dixit-Stiglitz (1977) monopolistic
competition. This departure helps to make the model simple, and yields information on the importance of the noncompetitive behavior of ﬁrms for New
Keynesian economics. In general, given the emphasis on the sticky-price friction in New Keynesian economics, we would hope that it is something inherent
in the functioning of a sticky-price economy, rather than simply strategic behavior, that is at the heart of the New Keynesian mechanism.
Our cashless model is consistent with most of the predictions of standard
Keynesian models, new and old. The sticky-price friction leads to a relative
price distortion in that with inﬂation (deﬂation), too large (too small) a quantity of sticky-price goods is produced and consumed relative to ﬂexible-price
goods. Optimally, the inﬂation rate is zero, which eliminates the relative price
distortion. One aspect in which this model differs from standard New Keynesian models is that it does not exhibit Phillips curve correlations. If the
substitution effect dominates in the labor supply response to a wage increase
(which we consider the standard case), then output is decreasing (increasing) in
the inﬂation rate when the inﬂation rate is positive (negative). This is because
the distortion caused by sticky prices rises with the deviation from a constant
price level, and the representative consumer supplies less labor in response
to a larger sticky-price distortion. Thus, under these circumstances output
is maximized when the inﬂation rate is zero and there is no output/inﬂation
tradeoff. In the case where the income effect dominates in the labor supply
response to a change in wages, output increases (decreases) for positive (negative) inﬂation rates. Here there is a Phillips curve tradeoff if the inﬂation rate
is positive, but a zero inﬂation rate is optimal.
In most New Keynesian models, Phillips curve correlations are generated
because of the strategic forward-looking behavior of price-setting ﬁrms. A
ﬁrm, given the opportunity to set the price in units of money for its product,
knows it will not have this opportunity again until some time in the future.
Roughly, what matters to the ﬁrm is its expectation of the path for the price
level during the period of time until its next price-setting opportunity. If the
inﬂation rate is unusually high in the future, then the ﬁrm’s relative price will
be unexpectedly low, and then, by assumption, it will be satisfying higherthan-expected demand for its product. Given that all ﬁrms behave in the same
way, unanticipated inﬂation will tend to be associated with high real output.
One message from our model is that Phillips curve behavior can disappear in
the absence of strategic behavior by ﬁrms, even with sticky prices.
We live in a world where outside money is held by consumers, ﬁrms, and
ﬁnancial institutions in the form of currency and reserve balances, and this

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outside money is supplied by the central bank and used in various transactions
at the retail level and among ﬁnancial institutions. In using a cashless model
to analyze monetary policy, we should feel conﬁdent that we are not being led
astray by a quest for simplicity. To evaluate what we might lose in focusing on
a cashless model, we develop a monetary model that is a straightforward cashin-advance extension of the cashless model. Then, in the spirit of Woodford
(2003), we explore how the behavior of this model compares to that of the
cashless model and study the “cashless limit” of the more elaborate model. As
it turns out, it requires very special assumptions for the limiting economy to
behave in the same way as the monetary economy, and, in any case, quantity
theory principles hold in equilibrium in the monetary economy. It is useful to
know how monetary quantities should be manipulated to produce particular
time paths of nominal interest rates, prices, and quantities in the economy, as
the key instruments that a central bank has available to it are the quantities
on its balance sheet. Thus, it would seem preferable to analyze monetary
economies rather than cashless economies.
This article is organized as follows. In Section 1 we construct the basic
cashless model, work through examples, and uncover the general properties of
this model. Section 2 contains a monetary model, extending the cashless model
as a cash-in-advance construct with money and credit. Section 3 is a detailed
discussion of the importance of the results, and Section 4 is a conclusion.

CASHLESS MODEL

The goal of this section of the paper is to construct a simple sticky-price
model that will capture the key aspects of New Keynesian economics, while
also taking a somewhat different approach to price determination, in order
to simplify and illuminate the important principles at work. The model we
construct shares features with typical New Keynesian “cashless” models (see
Woodford 2003), which are the following:
1. Money is not useful for overcoming frictions, it does not enter a cashin-advance constraint or a utility function, nor does it economize on
transactions costs.
2. Money is a numeraire in which all prices are denominated.
3. The money prices of goods are sticky in that, during any period, some
goods prices are predetermined and do not respond to current aggregate
shocks.
This model captures the essential friction that New Keynesians argue
should be the focus of monetary policy—a sticky-price friction. New
Keynesians argue that the other frictions that we typically encounter in monetary models—absence-of-double-coincidence problems and intertemporal

S. D. Williamson: New Keynesian Economics

201

price distortions, for example—are of second order for the problem at hand.
Further, New Keynesians feel that it is important to model the monetary policy problem in terms of the choice of nominal interest rate rules and that this
framework is a very convenient vehicle in that respect.
The model we will work with here has an inﬁnite-lived representative
consumer who maximizes
∞

β t u(ct1 ) + u(ct2 ) − v(nt ) ,

(1)

t=0

denotes consumption of the i th good, i = 1, 2, and nt is labor
where
supply. Assume that u(·) is strictly increasing, strictly concave, twice continuously differentiable, and has the property u (0) = ∞. As well, v(·) is
strictly increasing, strictly convex, and twice differentiable with v (0) = 0
and v (h) = ∞ for some h > 0. We have assumed a separable period utility
function for convenience, and a two-good model is sufﬁcient to exposit the
ideas of interest. Goods are perishable. There are linear technologies for
producing goods from labor input, i.e.,
cti

yti = γ t ni ,
t

(2)

where yti is output of good i, γ t is aggregate productivity, and ni is the quantity
t
of labor input applied to production of good i. Assume that γ t follows an
exogenous stochastic process.
This model is very simple. There is no investment or capital, and an
optimal allocation is a sequence {n1 , n2 , ct1 , ct2 }∞ satisfying n1 = n2 = nt
˜ t ˜ t ˜ ˜ t=0
˜t
˜t
˜
and ct1 = ct2 = ct , with ct = γ t nt , where nt solves
˜
˜
˜
˜
˜
˜
v (2nt )
˜
= γ t.
u (γ t nt )
˜

(3)

Therefore, at the optimum, consumption of the two goods should be equal
in each period with the same quantity of labor allocated to production of each
good, given symmetry. As well, from (3) the ratio of the marginal disutility
of labor to the marginal utility of consumption should be equal to aggregate
productivity for each good in each period.
There is another object, which we will call money, that plays only the role
of numeraire. We will assume a form of price stickiness reminiscent of what
obtains in the staggered wage-setting models of Fischer (1977) and Taylor
(1979). That is, assume that prices are sticky, in the sense that, if the price of
a good is ﬂexible in period t, then it remains ﬁxed at its period t value through
period t + 1, and is subsequently ﬂexible in period t + 2, etc. In any given
period, one good is ﬂexible and the other is sticky. Now, since in (1) and (2)
the two goods are treated symmetrically in preferences and technology, we
can let good 1 be the ﬂexible-price good in each period. Then, let Pt denote
the price in units of money of the ﬂexible-price good in period t, and then Pt−1

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is the price of the sticky-price good. As well, let Wt denote the nominal wage
rate.
The Keynesian modeler must always deal with the problem of how ﬁrms
and consumers behave in the face of price and/or wage stickiness, as well as
how quantities are determined. In typical textbook sticky-wage approaches,
the nominal wage is exogenous, and the quantity of labor traded is determined
by what is optimal for the representative ﬁrm. Standard textbook sticky-price
models have a single good sold at an exogenous nominal price, and the quantity
of output is demand-determined.1
In New Keynesian economics, the emphasis is on price stickiness (as opposed to wage stickiness), the distribution of prices across goods, and relative
price distortions. Clearly, if there is a homogeneous good, constant returns
to scale, competitive equilibrium, and perfect information, we cannot have
anything other than a degenerate distribution of prices in equilibrium, where
all ﬁrms producing positive output charge the same price. The New Keynesian
approach at least requires heterogeneous goods, and the standard model in the
literature is currently one with monopolistically competitive ﬁrms. For example, a typical approach is to assume monopolistic competition with Calvo
(1983) price setting (or “time-dependent pricing”). In such a model, each ﬁrm
randomly obtains the opportunity to change its nominal price each period,
so that with a continuum of ﬁrms, some constant fraction of ﬁrms changes
their prices optimally, while the remaining fraction is constrained to setting
prices at the previous period’s values. Alternatively, it could be assumed that
each of the monopolistically competitive ﬁrms must set their prices one period in advance, before observing aggregate (or possibly idiosyncratic) shocks.
Woodford (2003), for example, takes both approaches.
Neither Calvo pricing nor price setting one period in advance in monopolistic competition models is without problems. In a Calvo pricing model, each
monopolistically competitive ﬁrm is constrained to producing one product.
There may be states of the world where some ﬁrms will earn negative proﬁts,
but they are somehow required to produce strictly positive output anyway, and
ﬁrms cannot reallocate productive factors to the production of ﬂexible-price
goods that will yield higher proﬁts. With prices set one period in advance,
ﬁrms are constrained to produce, even in the face of negative ex post proﬁts.
Here, we have assumed differentiated products, but we will maintain competitive pricing. This model is certainly not typical, so it requires some explanation. First, the consumer’s budget constraint will imply that all wage
income will be spent on the two consumption goods, so
Pt γ t n1 + Pt−1 γ t n2 − Wt (n1 + n2 ) = 0.
t
t
t
t

(4)

1 See Williamson (2008) for examples of standard Keynesian sticky-wage and sticky-price
models.

S. D. Williamson: New Keynesian Economics

203

However, this would then seem to imply that, unless Pt = Pt−1 , the production
and sale of one good will earn strictly positive proﬁts and production and sale
of the other good will yield strictly negative proﬁts. Thus, it seems that it
cannot be proﬁt-maximizing for both goods to be produced in equilibrium.
However, suppose that we take for granted, as is typical in much of the New
Keynesian literature, that there will be some ﬁrms that are constrained to
producing the sticky-price good, and that the ﬁrms who produce this good
will satisfy whatever demand arises at the price Pt−1 . How then should we
determine which ﬁrms produce which good? For this purpose, assume that
there is a lottery, which works as follows. Before a ﬁrm produces, it enters a
lottery where the outcome of the lottery determines whether the ﬁrm produces
the ﬂexible-price good or the sticky-price good. If it is determined through the
lottery that a particular ﬁrm produces the ﬂexible-price good, then that ﬁrm
receives a subsidy of st1 in nominal terms, per unit of output. If it is determined
that a particular ﬁrm produces the ﬁxed-price good, that ﬁrm receives st2 per
unit of output. The agent that offers the lottery will set st1 and st2 so that any
ﬁrm is indifferent between producing the ﬁxed-price and ﬂexible-price goods,
i.e.,
Pt − st1 = Pt−1 − st2 .

(5)

Further, the agent offering the lottery breaks even, so that
st1 n1 + st2 n2 = 0,
t
t

(6)

so solving for the subsidy rates, we obtain
st1 =

n2 (Pt − Pt−1 )
t
and
(n1 + n2 )
t
t

st2 =

n1 (Pt−1 − Pt )
t
.
(n1 + n2 )
t
t

Given these subsidy rates, the agent offering the lottery breaks even and each
ﬁrm is willing to enter the lottery as proﬁts per unit produced are zero in
equilibrium, whether the ﬁrm ultimately produces the ﬂexible-price or stickyprice good. Though this cross-subsidization setup may seem unrealistic, it
does not seem less palatable than what occurs in typical Keynesian stickyprice models. In fact, the randomness in determining which ﬁrms produce
which good is reminiscent of the randomness in Calvo (1983) pricing, but our
approach is much more tractable.
Now, let π t denote the relative price of ﬂexible-price and sticky-price
goods, which is also the gross rate of increase in the price of the ﬂexibleprice good. Under some special circumstances, π t will also be the measured
inﬂation rate, but in general that is not the case. However, π t is the relative
price that captures the extent of the effects of the sticky-price friction. Letting

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Federal Reserve Bank of Richmond Economic Quarterly

wt denote the relative price of labor and ﬂexible-price goods, we can rewrite
equation (4) as
γ t n2
t
− wt (n1 + n2 ) = 0.
(7)
t
t
πt
Optimization by the consumer is summarized by the following two marginal
conditions:
γ t n1 +
t

u (ct1 ) − π t u (ct2 ) = 0 and

(8)

wt u (ct1 ) − v (n1 + n2 ) = 0.
t
t
In equilibrium all output must be consumed, so
cti = γ t ni
t

(9)
(10)

for i = 1, 2. Further, letting qt denote the price at time t of a claim to one unit
of money in period t + 1, we can determine qt in the usual fashion by
qt = βEt

1
u (ct+1 )
.
π t+1 u (ct1 )

(11)

An equilibrium is deﬁned to be a stochastic process {π t , wt , qt , n1 , n2 , ct1 ,
t
t
ct2 }∞ given an exogenous stochastic process for γ t , that satisﬁes (7)–(11) and
t=0
qt ≤ 1, so that the nominal interest rate is nonnegative in each state of the
world. There is clearly indeterminacy here, as there appears to be nothing
that will pin down prices. In equilibrium there is an object called money
that is in zero supply, and which, for some unspeciﬁed reason, serves as a
unit of account in which prices are denominated. The path that π t follows in
equilibrium clearly matters, because prices are sticky, but the possibilities for
equilibrium paths for π t are limitless.

Examples
One equilibrium is π t = 1 for all t, which from (7)–(11) gives the optimal
allocation with n1 = n2 = nt and ct1 = ct2 = ct , where ct = γ t nt , and where
˜t
˜t
˜
˜
˜
˜
˜
˜
nt solves (3). Solving for qt from equation (11), we get
˜
˜
u (γ t+1 nt+1 )
qt = βEt
,
(12)
u (γ t nt )
˜
and so long as the variability in productivity is not too large, we will have
qt ≤ 1 for all t, so that the nominal interest rate is always nonnegative, and
this is indeed an equilibrium.
Alternatively (for example, see Woodford 2003), we could argue that the
1
central bank can set the nominal interest rate it = qt − 1. In this instance, if
the central bank sets the nominal interest rate from equation (12) according to
it = βEt

˜
u (γ t+1 nt+1 )
u (γ t nt )
˜

−1

− 1,

(13)

S. D. Williamson: New Keynesian Economics

205

an equilibrium with π t = 1 for all t can be achieved, which is optimal.
There is nothing in the model that tells us why the central bank can control
it , and why it cannot control π t , for example. In New Keynesian models, the
justiﬁcation for treating the market nominal interest rate as a direct instrument
of the central bank comes from outside the model, along the lines of “this is
what most central banks do.” In any case, an optimal policy implies that, since
π t = 1, the price level is constant and the inﬂation rate is zero. This optimal
policy could then be characterized as an inﬂation rate peg, or as a policy that
requires, from (13), that the nominal interest rate target for the central bank
ﬂuctuate with the aggregate technology shock. More simply, from (13), the
nominal interest rate at the optimum should equal the “Wicksellian natural
rate of interest” (see Woodford 2003).
There are, of course, many suboptimal equilibria in this model. For example, consider the special case where u(c) = ln c and v(n) = δn, for δ > 0.
Though v(·) does not satisfy some of our initial restrictions, this example
proves particularly convenient. We will ﬁrst construct an equilibrium with a
constant inﬂation rate, which has the property that π t = α, where α is a positive constant (recall that π t is not the gross inﬂation rate, but if π t is constant
then the inﬂation rate is constant). From (7)–(11), the equilibrium solution
we obtain is
2γ t
,
(14)
wt =
1+α
qt =

βγ t
Et
α

1
γ t+1

(15)

n1 =
t

1
,
δ(1 + α)

(16)

n2 =
t

α
,
δ(1 + α)

(17)

γt
, and
δ(1 + α)

(18)

αγ t
.
δ(1 + α)

(19)

ct1 =

In this equilibrium, the rate of inﬂation is α − 1. Note, from (14)–(19),
that higher inﬂation causes a reallocation of consumption and labor supply
from ﬂexible-price to sticky-price goods. From equation (15) for qt ≤ 1,
it is sufﬁcient that α not be too small and that γ t not be too variable. This
equilibrium is of particular interest because it involves an inﬂation rate peg.
Of course, as we showed previously, α = 1 is optimal.

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Federal Reserve Bank of Richmond Economic Quarterly

Alternatively, consider the same example as above, with log utility from
consumption and linear disutility to supplying labor, but now suppose that π t
is governed by a rule that responds to productivity shocks, for example,
γ
π t = t−1 .
γt
Then, from (7)–(11), we obtain the equilibrium solution
wt =

2γ 2
t
,
γ t−1 + γ t

(20)

γ t (γ t + γ t+1 )
,
γ t+1 (γ t−1 + γ t )

(21)

n1 =
t

2γ t
,
δ(γ t−1 + γ t )

(22)

n2 =
t

2γ t−1
,
δ(γ t−1 + γ t )

(23)

2γ 2
t
, and
δ(γ t−1 + γ t )

(24)

2γ t γ t−1
.
δ(γ t−1 + γ t )

(25)

qt = βEt

ct1 =

From (21) it is sufﬁcient for the existence of equilibrium that γ t not be too
variable. Note in the solution, (20)–(25), that equilibrium quantities and prices
all exhibit persistence because of the contingent path that prices follow. Complicated dynamics can be induced through the nominal interest rate rule, of
which (25) is an example in this case. Indeed, it is possible (see Woodford
2003), given some nominal interest rate rules, to obtain equilibrium solutions
where current endogenous variables depend on anticipated future aggregate
shocks. Typical New Keynesian models also obtain equilibrium solutions with
such properties through the forward-looking price-setting behavior of monopolistically competitive producers. This latter mechanism is not present in our
model.

General Properties of the Model
To further analyze our model, we ﬁnd it useful to consider how we would
solve for an equilibrium in this model in the absence of sticky prices. The
model is purely static, so we can solve period-by-period. An equilibrium for
period t consists of relative prices π t and wt , and quantities n1 , n2 , ct1 , and
t
t

S. D. Williamson: New Keynesian Economics

207

ct2 that solve the marginal conditions (8) and (9), the equilibrium conditions
(10), and two zero-proﬁt conditions:
γ t n1 − wt n1 = 0 and
t
t

(26)

γ t n2
t
− wt n2 = 0.
(27)
t
πt
Of course, the solution we get is the optimum, with wt = γ t , π t = 1,
n1 = n2 = nt , and ct1 = ct2 = ct = γ t nt , with nt determined as the solution
˜
˜
˜
˜
t
t
to (3).
Now, how should we think about solving the system (7)–(11) under sticky
prices? It seems most useful to think of this system in the traditional Keynesian
sense, as a model where one price, π t , is ﬁxed exogenously. Given any
exogenous π t = 1, it cannot be the case that all agents optimize and all
markets clear in equilibrium. The solution we have chosen here, which is in
line with standard New Keynesian economics, is to allow for the fact that (26)
and (27) do not both hold. Instead, we allow for cross-subsidization with zero
net subsidies across production units and zero proﬁts in equilibrium net of
subsidies for production of each good, which gives us equation (7).
Given this interpretation of the model, how should we interpret qt , as
determined by equation (11)? Since π t is simply the relative price of good 2
in terms of good 1 in period t, qt is the price, in units of good 1 in period t, that
a consumer would pay for delivery of one unit of good 2 in period t + 1. Why,
then, should we require an arbitrage condition that qt ≤ 1, or why should
1
u (ct+1 )
≤1
(28)
π t+1 u (ct1 )
hold? Such a condition requires the existence of a monetary object. Then
we can interpret (11) as determining the price in units of money in period
t of a claim to one unit of money delivered in period t + 1, and inequality
(28) is required so that zero money balances are held in equilibrium. Thus, in
equilibrium the model is purely atemporal. There is no intertemporal trade,
nevertheless there exist equilibrium prices for money in terms of goods and
for the nominal bond in each period.
Thus far, this may be somewhat puzzling for most monetary economists,
who are accustomed to thinking about situations in which money is not held
in equilibrium as ones in which the value of money in units of goods is zero
in each period. This does not happen here, but no fundamental principles of
economic analysis appear to have been violated.
The key question, then, is what we can learn from this model. First, we
will get some idea of the operating characteristics of the model through linear
approximation. If we treat π t as exogenous, following our interpretation
above, then the exogenous variables are γ t and π t . Substitute using equation
(10) in (7)–(9), and then linearize around the solution we get with γ t = γ and
¯

βEt

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Federal Reserve Bank of Richmond Economic Quarterly

¯
π t = 1, where γ is a positive constant. The equilibrium solution we get in
this benchmark case is wt = γ , n1 = n2 = n, and ct1 = ct2 = γ n, where n
¯ t
¯
¯¯
¯
t
solves
¯
γ u (γ n) − v (2n) = 0.
¯ ¯¯
The solution to the linearized model is (leaving out the solution for the wage,
wt ) :
¯
n1 = n +
t

u (−2v + γ 2 u )
u + γ nu
¯
¯¯
(π t − 1) − 2
(γ t − γ ),
¯
2
2γ u (γ u − 2v )
¯
¯
γ u − 2v
¯

(29)

n2 = n +
¯
t

u (2v − γ 2 u )
u + γ nu
¯
¯¯
(π t − 1) − 2
(γ t − γ ),
¯
2
2γ u (γ u − 2v )
¯
¯
γ u − 2v
¯

(30)

¯¯
ct1 = γ n +

u (−2v + γ 2 u )
2nv + γ u
¯
¯
¯
(π t − 1) − 2
(γ t − γ ), and (31)
¯
2
2u (γ u − 2v )
¯
γ u − 2v
¯

¯¯
ct2 = γ n +

¯
¯
u (2v − γ 2 u )
2nv + γ u
¯
(π t − 1) − 2
(γ t − γ ),
¯
2
¯
2u (γ u − 2v )
γ u − 2v
¯

(32)

and aggregate labor supply and output are given, respectively, by
n1 + n2 = 2n −
¯
t
t

¯¯
2(u + γ nu )
(γ t − γ ) and
¯
2
γ u − 2v
¯

(33)

¯
2(2nv + γ u )
¯
(γ t − γ ).
¯
2
γ u − 2v
¯

(34)

¯¯
ct1 + ct2 = 2γ n −

Therefore, from (29)–(34), in the neighborhood of an equilibrium with constant prices, an increase in π t , which corresponds to an increase in the inﬂation
rate, results in a decrease in the production and consumption of the ﬂexibleprice good, an increase in production and consumption of the ﬁxed-price good,
and no effect on aggregate labor supply and output. Thus, this model does
not produce a Phillips curve correlation, at least locally, and increases in the
inﬂation rate serve only to misallocate production and consumption across
goods.
As well, from (29)–(34), a positive shock to aggregate productivity has
the same effect on production and consumption of both goods. If
u + γ nu > 0,
¯¯

(35)

then the substitution effect of the productivity increase offsets the income
effect on labor supply so that aggregate labor supply increases. In what follows, we assume that the substitution effect dominates, i.e., (35) holds. From
(34), aggregate output increases with an increase in productivity, regardless
of whether the substitution effect dominates.

S. D. Williamson: New Keynesian Economics

209

The absence of a Phillips curve effect here might seem puzzling, as a positive relationship between inﬂation and output often appears as a cornerstone
of new and old Keynesian economics. Thus, we should explore this further to
see how π t affects output outside of the neighborhood of our baseline equilibrium. Consider an example that will yield closed-form solutions, in particular
1−α −1
u(c) = c 1−α and v (n) = δn, with α > 0 and δ > 0. Solving (7)–(10), we
obtain
1
⎛
⎞α
1
α −1
1
1 + πt ⎠
1
−1
n1 = γ tα δ − α ⎝
,
(36)
t
1
1 + π tα
⎛
1
α −1

n2 = γ t
t

1
α

2
α −1

π + πt
1
δ− α ⎝ t
1
1 + π tα
⎛

1
α −1

1
⎞α

⎠ ,

(37)

1
⎞α

1 + πt ⎠
1
,
ct1 = γ t δ − α ⎝
1
1 + π tα
1
α

⎛

1
α

2
α −1

π + πt
1
ct2 = γ t δ − α ⎝ t
1
1 + π tα
1
α

⎛
wt = γ t ⎝

1
α −1

1 + πt

1
α

(38)

1
⎞α

⎠ , and

(39)

⎞
⎠.

(40)

1 + πt

Then, aggregate labor supply and aggregate output are given by
1
α −1

n2
t

= γt

ct1

n1
t

ct2

1
α

1
−α

= γt δ

1
−α

1
α −1

1 + πt

1
α −1

1 + πt

1
α

1
1− α

1
α

1 + πt

and

(41)

(42)

1
1− α

1
α

1 + πt

Now, in the solution (36)–(42), the condition (35) is equivalent to α < 1.
Given this, labor supply in both sectors is increasing in productivity, as, of
course, is consumption of each good and total output.
Our primary interest in this example is what it tells us about the relationship between π t and aggregate output. Note from equation (42) that this
relationship is determined by the properties of the function
1

G(π ) = 1 + π α −1

1
α

1+πα

1
1− α

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Federal Reserve Bank of Richmond Economic Quarterly

Differentiating, we obtain
1

G (π ) = π α −2 1 + π α −1

1
α −1

1+πα

1
−α

1
α

1
− 1 (1 − π ).
α

Therefore, for the case α < 1, we have G (1) = 0, G (π ) > 0 for π < 1, and
G (π ) < 0 for π > 1. Thus, output is maximized for π = 1 and the Phillips
curve has a negative slope when inﬂation is positive and a positive slope when
inﬂation is negative. The key to the Phillips curve relationship is how labor
supply responds to the distortion created by inﬂation or deﬂation due to the
the sticky-price friction. When the substitution effect on labor supply of an
increase in productivity dominates the income effect, an increase or decrease
in the inﬂation rate from zero implies that the marginal payoff from supplying
labor falls, and the consumer therefore reduces labor supply.
The interesting aspect of these results is that they point to a nonrobust link
between price stickiness and Phillips curve correlations. In spite of the fact
that ﬁrms do not set prices strategically in a forward-looking manner, intuition
might tell us that there should still be a Phillips curve correlation. That is,
with higher inﬂation, it might seem that the additional quantity of output
produced by sticky-price ﬁrms should be greater than the reduction in output
by ﬂexible-price ﬁrms, and aggregate output should increase. However, our
analysis shows that this need not be the case and that the key to understanding
the mechanism at work is labor supply behavior.
In our model, since not all prices are sticky, the key effect of inﬂation
on output comes from the relative price distortion, and labor supply may
increase or decrease in response to higher inﬂation, with a decrease occurring
when the elasticity of substitution of labor supply is sufﬁciently high. As we
commented earlier, the assumptions on price stickiness and ﬁrm behavior in
our model seem no less palatable than what is typically assumed. Thus, the
nonrobustness of the Phillips curve we ﬁnd here deserves attention.

2. A MONETARY MODEL AND THE “CASHLESS LIMIT”
In New Keynesian economics (e.g., Woodford 2003), baseline “cashless” models are taken seriously as frameworks for monetary policy analysis. As we
have seen, the cashless model focuses attention on the sticky-price friction
as the key source of short-run nonneutralities of money. New Keynesian arguments for using a cashless model appear to be as follows: (i) the standard
intertemporal monetary distortions—for example, labor supply distortions and
the tendency for real cash balances to be suboptimally low when the nominal interest rate is greater than zero—are quantitatively unimportant; (ii) in
models where there is some motive for holding money, if we take the limit
as the motive for holding money goes to zero, then this limiting economy has
essentially the same properties as does the cashless economy. The purpose

S. D. Williamson: New Keynesian Economics

211

of this section is to evaluate these arguments in the context of a particular
monetary model.
For our purposes, a convenient expository vehicle is a cash-in-advance
model of money and credit where we can parameterize the friction that makes
money useful in transactions. There are other types of approaches we could
take here; for example, we could use a monetary search and matching framework along the lines of Lagos and Wright (2005),2 but the model we use here
allows us to append monetary exchange to the cashless model in Section 2 with
the least fuss. Our framework is much like that in Alvarez, Lucas, and Weber
(2001), absent limited participation frictions, but including the labor supply
decision and the sticky-price friction we have been maintaining throughout.
The structure of preferences, technology, and price determination is identical
to that which we assumed in the cashless model.
Here, suppose that the representative consumer trades on asset markets at
the beginning of each period and then takes the remaining money to the goods
market, where goods can be purchased with money and credit. The consumer
faces the cash-in-advance constraint
Pt ct1 + Pt−1 ct2 + qt bt+1 ≤ θ Wt (n1 + n2 ) + mt + τ t + st lt + bt ,
t
t

(43)

where bt denotes one-period nominal bonds purchased by the consumer in
period t − 1, each of which pays off one unit of money in period t; mt denotes
nominal money balances carried over from the previous period; τ t is a nominal
lump-sum transfer from the government; and st lt is a within-period money loan
from the central bank, where lt is the nominal amount that must be returned
to the central bank at the end of the period. Also, θ denotes the fraction of
current-period wage income that can be accessed in the form of within-period
credit when the consumer trades in the goods market. Note that s1t − 1 is the
1
within-period nominal interest rate on central bank loans, and, as above, qt −1
is the one-period nominal interest rate. Here 0 ≤ θ ≤ 1, and θ is the critical
parameter that captures the usefulness of money in transactions. With θ = 0,
this is a pure monetary economy, and with θ = 1, money is irrelevant.
The consumer must also satisfy his or her budget constraint, given by
Pt ct1 +Pt−1 ct2 +mt+1 +qt bt+1 = Wt (n1 +n2 )+mt +τ t +(st − 1) lt +bt . (44)
t
t
Let Mt denote the supply of money and Lt denote the supply of central
bank loans. Then the asset market equilibrium conditions are
mt = Mt ; bt = 0; lt = Lt ,

(45)

or, money demand equals money supply, the demand for bonds equals the
supply, and the demand for central bank loans equals the supply.
2 See, for example, Aruoba and Schorfheide (2008), where a monetary search model with
nominal rigidities is constructed for use in quantitative work.

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Federal Reserve Bank of Richmond Economic Quarterly

Eliminating Intertemporal Distortions with Central
Bank Lending
In general, an equilibrium in this model is difﬁcult to characterize, as price
stickiness complicates the dynamics. In part, our goal will be to determine
the features of a “cashless limit” in this economy, along the lines of Woodford
(2003). To that end, given the New Keynesian view that intertemporal distortions are unimportant, suppose that the regime of central bank lending is set up
so that those distortions are eliminated. That is, suppose that the central bank
supplies no money, except through central bank loans made at the beginning
of the period at a zero nominal interest rate.
Let st = 1, and suppose that the central bank accommodates whatever
demand for central bank loans arises at a zero nominal interest rate. We then
have Mt = τ t = 0 for all t and Lt = (1−θ )Wt (n1 +n2 ). Then, given (43)–(45),
t
t
optimization, and goods market equilibrium, we can deﬁne an equilibrium in
terms of relative prices and quantities, just as in the cashless economy.
This monetary regime is then one where all economic agents have access
to a daylight overdraft facility, much like the Federal Reserve System uses
each day to accommodate payments among ﬁnancial institutions. Given a
zero nominal interest rate on daylight overdrafts, money will not be held
between periods, which we can interpret as a system in which holdings of
outside money are zero overnight (interpreting a period as a day). This setup
is extreme, as it allows universal access to central bank lending facilities and
does not admit anything resembling currency-holding in equilibrium.
In equilibrium, (7)–(11) must be satisﬁed, just as in the cashless economy.
The key difference in this monetary economy will be in the determination of
π t . Supposing for convenience that (43) always holds with equality in each
period, then, given (7), we can determine π t by
πt =

Lt wt−1 (n1 + n2 )
t−1
t−1
,
1
2
Lt−1 wt (nt + nt )

(46)

for t = 1, 2, 3, ..., with π 0 given. An equilibrium is a stochastic process
{n1 , n2 , ct1 , ct2 , wt , π t , qt }∞ , with π 0 given, solving (7)–(11) and (46). The
t
t
t=0
solution must satisfy qt ≤ 1 for all t, which assures that an equilibrium
exists where (43) holds with equality. In general, it is not straightforward to
characterize a solution, but it is clear from (46) that the solution is consistent
with the quantity theory of money. That is, Lt is the nominal quantity of money
γ t n2
available to spend in period t, and wt (n1 + n2 ) = γ t n1 + π t t is total GDP.
t
t
t
Therefore, (46) states that the rate of increase in the price of the ﬂexible-price
good is roughly equal to the rate of money growth minus the rate of growth
in real GDP. Note that the parameter θ does not appear anywhere in (7)–(11)
and (46). That is, we can treat the equilibrium solution as the cashless limit,
as we will obtain the same solution for any θ > 0. Note here that the cashless
limit of this monetary economy is not the cashless economy, and the quantity

S. D. Williamson: New Keynesian Economics

213

of money is important for the solution, along quantity theory lines, in spite of
the fact that no money is held between periods. Thus, we have followed the
logic of Woodford (2003) here, but we do not get Woodford’s results.
What is an optimal monetary policy here, given that the within-period
nominal interest rate is zero? The key choice for the central bank is Lt , the
nominal loan quantity in each period. If Lt can be set so that π t = 1 for all
t, then clearly this would be an optimal policy, since from (7)–(11) we will
obtain ni = nt for all t and i = 1, 2. From equation (46), this requires that
˜
t
˜
γ t nt
Lt
=
.
Lt−1
γ t−1 nt−1
˜

(47)

This optimal policy then implies a nominal bond price
u (γ t+1 nt+1 )
˜
,
(48)
u (γ t nt )
˜
and for this optimal policy to support an equilibrium, we require that qt ≤ 1
for all t, which is satisﬁed provided the variability in γ t is sufﬁciently small.
Thus, we can deﬁne the optimal monetary policy as a rule for monetary growth,
which accommodates GDP growth according to (47) or as a nominal interest
rate rule governed by (48), i.e., the money growth rule and nominal interest
rate rule are ﬂip sides of the same monetary policy. On the one hand, the
money growth rule in (47) states that the money supply should always grow at
the same rate as optimal GDP. On the other hand, the nominal interest rate rule
states that the nominal interest rate should move in response to productivity
shocks in such a way that it is equal to the optimal real interest rate.
Part of the New Keynesian justiﬁcation for use of a cashless model (see
Woodford 2003) is that if intertemporal frictions are insigniﬁcant, even if
there is a monetary friction in the model, then the prescription for the optimal
nominal interest rate rule is the same as in the cashless economy. This is
certainly true here, as the nominal interest rate rule implicit in (48) is the same
as (12). For our purposes, though, the monetary economy is more informative
about policy, as it says something about the monetary policy regime that is
necessary to get this result, and gives us a prescription for how the central
bank should manipulate the quantities that it has under its control.
qt = βEt

DISCUSSION

In this section we will discuss our results, organized in terms of monetary
policy instruments, Phillips curves, and monetary frictions.

Monetary Policy Instruments
What can a central bank control? Ultimately, if we ignore the central bank’s
regulatory powers, a central bank can control two sets of things. First, it

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Federal Reserve Bank of Richmond Economic Quarterly

can determine the quantities on its balance sheet, including lending to private
sector economic agents. Second, it can determine the interest rates on deposits
(reserves) held with the central bank and the interest rates on the loans it makes,
in particular the interest rates on daylight overdrafts associated with payments
made using outside money and the interest rates on overnight central bank
lending or lending at longer maturities. The key power a central bank holds
is its monopoly on the issue of ﬁat money. Essentially, a central bank is much
like any other bank in that its liabilities serve as a means of payment, and it
performs a type of liquidity transformation in intermediating assets that are
difﬁcult to use as means of payment. Central bankers, and many economists,
hold the view that the quantity of intermediation that the central bank carries
out, reﬂected in the quantity of ﬁat money outstanding, has consequences for
real economic activity in the short run and for prices.
Central banks cannot set market interest rates, though they might like to.
New Keynesians typically model central bank behavior as the determination
of a market nominal interest rate as a function of endogenous and exogenous
variables. There are good reasons to think that a central bank operating procedure consisting of periodic revision of an overnight nominal interest rate
target or inﬂation rate targeting is preferable to the money growth targeting
that Friedman (1968) had in mind. That is, the predominant shocks that are of
concern to the central bank in the very short run, say between Federal Open
Market Committee meetings, are ﬁnancial market shocks that cause ﬂuctuations in the demand for outside money. Given that these shocks are difﬁcult to
observe, a sensible procedure may be to smooth the overnight nominal interest
rate, which may serve to optimally accommodate ﬁnancial market shocks.
Though it may be possible in the short run for a central bank to use the
instruments at its disposal to keep a market nominal interest rate within a
tight prespeciﬁed corridor, it is inappropriate to use this as a justiﬁcation for
a mode of analysis that eliminates monetary considerations. A model that is
used to analyze and evaluate monetary policy should tell us how the economy
functions under one central bank operating procedure (e.g., monetary targeting) versus another (e.g., nominal interest rate targeting), how the instruments
available to the central bank (i.e., monetary quantities) need to be manipulated
to implement a particular policy rule, and how using alternative instruments
(e.g., central bank lending versus open market operations) makes a difference.

Phillips Curves
Some type of Phillips curve relationship, i.e., a positive relationship between
the “output gap,” on the one hand, and the rate of inﬂation or the unanticipated
component of inﬂation, on the other hand, is typically found in New Keynesian
macroeconomic models. The Phillips curve was an important example in
1970s policy debates of how policy could go wrong in treating an empirical

S. D. Williamson: New Keynesian Economics

215

correlation as structural (Lucas 1972). In New Keynesian economics, the
Phillips curve has made a comeback as a structural relationship and plays a
central role in reduced-form New Keynesian models (e.g., Clarida, Gal´, and
ı
Gertler 1999).
As we have shown here, in a sticky-price model that seems as reasonable
as typical monopolistically competitive New Keynesian setups, there is no
tradeoff between output and inﬂation in the standard case where substitution
effects dominate in the response of labor supply to a wage increase. With a
zero inﬂation rate, output is maximized. Even in the case where income effects
are large, more output can be obtained if the inﬂation rate deviates from zero,
but this is inefﬁcient. Further, in this case, more output can be obtained not
only with inﬂation, but with deﬂation.

Monetary Frictions
We know that what makes a modern central bank unique is the power granted to
it as the monopoly issuer of outside money, which takes the form of deposits
with the central bank and circulating currency. We also know that central
banking is not a necessity. Indeed, there are examples of economies that grew
and thrived without a central bank. The United States did not have a central
bank until 1914, and the private currency systems in place in Scotland from
1716–1845 and in Canada before 1935 are generally regarded as successes.
Before asking how a central bank should behave, we might want to ask what
justiﬁes its existence in the ﬁrst place.
From the viewpoint of a monetary economist, a theory of central banking
should not only tell us what the role of the central bank is in a modern economy,
but also why we should grant the central bank a monopoly in supplying key
media of exchange. Such a central banking theory must necessarily come
to grips with the principal frictions that make money useful as a medium of
exchange and the frictions that may make private provision of some types of
media of exchange inefﬁcient.
New Keynesians argue that we can do a better job of understanding how
monetary policy works and how it should be conducted by ignoring these
frictions. By using a very simple cash-in-advance construct, we have shown
these arguments require some very special assumptions. For our cashless
sticky-price economy to work in the same way as does a comparable monetary economy requires that: (i) a monetary regime be in place that corrects
intertemporal inefﬁciencies; (ii) all economic agents be on the receiving end of
the central bank’s actions; and (iii) currency holding be unimportant. While
some countries, such as Canada and New Zealand, have moved to monetary systems without reserve requirements and with interest on reserves, thus
correcting some distortions, most countries are far from the elimination of intertemporal monetary frictions. Thus, in practice it is likely that intertemporal

216

Federal Reserve Bank of Richmond Economic Quarterly

distortions play an important role, and arguably the important role if we are
considering the effects of long-run anticipated inﬂation. Also, the fact that
not all economic agents are on the receiving end of monetary policy actions,
which gives rise to distributional effects of monetary policy, is regarded as
important in the segmented markets literature. Market segmentation (in both
goods and ﬁnancial markets) is perhaps of greater signiﬁcance than stickyprice frictions in generating short-run nonneutralities of money (see Alvarez
and Atkeson 1997; Alvarez, Atkeson, and Kehoe 2003; Williamson [ForthcomingA, ForthcomingB]). Finally, currency is still widely used in the world
economy (Alvarez and Lippi 2007). In spite of technological improvements in
transactions technologies, currency is a wonderfully simple transactions technology that permits exchange in the many circumstances where anonymous
individuals need to transact with each other.

CONCLUSION

Recent events involving turmoil in credit markets and heretofore unheard-of
interventions by the Federal Reserve System make it abundantly clear that the
monetary policy problem is far from solved. Further, for the key questions that
need to be answered in the midst of this crisis, New Keynesian economics appears to be unhelpful. How is central bank lending different from open market
operations in terms of the effects on ﬁnancial markets and goods markets? To
which institutions should a central bank be lending and under what conditions?
What regulatory power should the Federal Reserve System exercise over the
institutions to which it lends? Should the Fed’s direct intervention be limited
to conventional banks, or should this intervention be extended to investment
banks and government-sponsored ﬁnancial institutions? Unfortunately, typical New Keynesian models ignore credit markets, monetary frictions, and
banking and are, therefore, of little or no use in addressing these pressing
questions.
What hope do we have of developing a theory of money and central banking that can satisfy monetary economists and also be of practical use to central
bankers? Monetary economics and banking theory have come a long way in
the last 30 years or more, and perhaps the economics profession needs to be
educated as to why modern monetary and banking theory is useful and can be
applied to policy problems. We now understand that recordkeeping and the
ﬂow of information over space and time is critical to the role of currency as
a medium of exchange (Kocherlakota 1998). We know that decentralized
exchange with currency can lead to holdup problems that accentuate the
welfare losses from inﬂation (Lagos and Wright 2005). We understand how
banks act to insure private agents against liquidity risk (Diamond and
Dybvig 1983) and to economize on monitoring costs (Diamond 1984,
Williamson 1986). We know that ﬁnancial market segmentation and goods

S. D. Williamson: New Keynesian Economics

217

market segmentation are important for monetary policy (Alvarez and
Atkeson 1997; Alvarez, Atkeson, and Kehoe 2003; Williamson
[Forthcoming A; Forthcoming B]). Putting together elements of these ideas in
a comprehensive theory of central banking is certainly within our grasp, and
I very much look forward to future developments.

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Economic Quarterly—Volume 94, Number 3—Summer 2008—Pages 219–233

Nominal Frictions, Relative
Price Adjustment, and the
Limits to Monetary Policy
Alexander L. Wolman

here are two broad classes of sticky-price models that have become
popular in recent years. In the ﬁrst class, prices adjust infrequently by
assumption (so-called time-dependent models) and in the second class
prices adjust infrequently because there is assumed to be a ﬁxed cost of price
adjustment (so-called state-dependent models). In both types of models it is
common to assume that there are many goods, each produced with identical
technologies. Consumers have a preference for variety, but their preferences
treat all goods symmetrically. These assumptions mean that it is efﬁcient
for all goods to be produced in the same quantities. For that to happen, all
goods must sell for the same price at any point in time. Assuming that price
adjustment is staggered (as opposed to synchronized), the prices of all goods
must be constant over time in order for all goods to be produced in the same
quantities. If the aggregate price level were changing over time—even at a
constant rate—then with staggered price adjustment prices would necessarily
differ across goods.
If there are multiple sectors that possess changing relative technologies
or that face changing relative demand conditions (because consumers’ preferences are changing across goods), then in general it will no longer be efﬁcient
to produce all the goods in the same quantities. Equating marginal rates of
transformation to marginal rates of substitution may require relative prices to
change over time. These efﬁcient changes in relative prices across sectors
require nominal prices to change within sectors. With frictions in nominal
The views here are the author’s and should not be attributed to the Federal Reserve Bank of
Richmond, the Federal Reserve System, or the Board of Governors of the Federal Reserve
System. For helpful comments, the author would like to thank Juan Carlos Hatchondo, Andreas
Hornstein, Yash Mehra, and Anne Stilwell. E-mail: alexander.wolman@rich.frb.org.

220

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price adjustment, nominal price changes bring with them costly misallocations within (and perhaps across) sectors.1
In the circumstances just described, where efﬁciency across sectors requires nominal price changes within a sector or sectors, a zero inﬂation rate
for the consumption price index may no longer be the optimal prescription for
monetary policy in the presence of sticky prices. Which inﬂation rate results
in the smallest distortions from price stickiness depends on the details of the
environment: chieﬂy, the rates of relative price change across sectors and the
degree of price stickiness in each sector. To cite an extreme example, suppose
there are two sectors with different average rates of productivity growth. Suppose further that the sector with low productivity growth (increasing relative
price) has sticky prices, whereas the sector with high productivity growth has
ﬂexible prices. Then it would be optimal to have deﬂation overall. Deﬂation
would allow the desired relative price increase to occur with zero nominal
price changes for the sticky-price goods and, thus, with no misallocation from
the nominal frictions.
The principles for optimal monetary policy I have discussed thus far involve only frictions associated with nominal price adjustment. In reality,
monetary policy must balance other frictions as well. As the literature on the
Friedman rule emphasizes, the fact that money is nearly costless to produce
means that it is socially optimal for individuals to face nearly zero private
costs of holding money. This requires a near-zero nominal interest rate, which
corresponds to moderate deﬂation. Other frictions are less well understood,
but may be just as important. Many central banks have mandates to achieve
price stability, and the fact that my models do not necessarily support this
objective does not mean it is misguided; that is, my models may still be lacking. The message of this paper is not that monetary policy should deviate
from zero inﬂation in order to minimize distortions associated with nominal
price adjustment. Rather, it is that in the presence of fundamental relative
price changes and nominal price adjustment frictions, there is no monetary
policy—zero inﬂation or otherwise—that can render those frictions costless.
Section 1 works through the optimality of price stability in a benchmark
one-sector model. Section 2 describes a two-sector model where a trend in
relative productivities means that all prices cannot be stabilized. In Section 2
I also display U.S. data for broad categories of consumption, which display
trends in relative prices. The data show that even on average, it is not possible
to stabilize all nominal prices; trends in relative prices mean that if the price
of one category of consumption goods is stabilized then prices for the other
categories must have a trend. Furthermore, relative price trends in the United
1 These statements are qualitative ones. Unless monetary policy is extremely volatile or generates very large inﬂation or deﬂation, most current models attribute relatively small welfare costs
to nominal frictions.

A. L. Wolman: Relative Prices and Monetary Policy

221

States have been rather large; since 1947, the price of the services component
of personal consumption expenditures has risen by a factor of ﬁve relative to
the price of the durable goods component. Sections 3 and 4 provide a brief
review of existing literature on relative price variation and monetary policy.
In contrast to the material in Section 2, the existing literature has concentrated
on random ﬂuctuations in relative prices around a steady state where relative
prices are constant. Section 3 reviews the literature on cyclical variation in
relative prices, and Section 4 summarizes related work on wages (a form of
relative price) and prices across locations. Section 5 concludes.

OPTIMALITY OF PRICE STABILITY IN A ONE-SECTOR
MODEL

Here I formalize the explanation for how price stability eliminates the distortions associated with price stickiness in a one-sector model. Suppose there
are a large number of goods, speciﬁcally a continuum of goods indexed by
z ∈ [0, 1], and suppose that consumers’ utility from consuming ct (z) of each
good is given by ct , where that utility is determined by the following aggregator function:
ε/(ε−1)

ct =

ct (z)(ε−1)/ε dz

(1)

where ε is the elasticity of substitution in consumption between different
goods. Suppose that each good is produced with a technology that uses only
labor input, and that one unit of the consumption good can be produced with
1/at units of labor input:
ct (z) = at nt (z) , for z ∈ [0, 1].

(2)

Thus, at is a productivity factor common to all goods. I assume that at is
exogenous. In particular, monetary policy has no effect on at . Finally, there
is a constraint on the total quantity of labor input:2
1

nt (z) ≤ Nt .

(3)

Without specifying anything about the structure of markets or price-setting
behavior, I can discuss efﬁcient production of consumption goods in this
model. Efﬁciency dictates that the marginal rate of substitution in consumption be equated to the marginal rate of transformation in production. That
is, the rate at which consumers trade off goods according to their preferences
2 In models with inelastic labor supply, N would be a constant equal to the time endowment.
t

Otherwise, Nt would be equal to the difference between the time endowment and the endogenous
quantity of leisure.

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(represented by [1]) should be equal to the rate at which the technology (represented by [2]) allows goods to be traded off against one another in production.
For the aggregator function in (1), consumers’marginal rate of substitution
between any two goods, ct (z0 ) and ct (z1 ), is given by
ct (z0 ) −1/ε
∂ct /∂ct (z0 )
.
(4)
=
∂ct /∂ct (z1 )
ct (z1 )
For the simple linear technology in (2), the marginal rate of transformation
between any two goods indexed by z0 and z1 is unity: Reducing the labor
used in the production of z0 by one unit yields a 1/at unit reduction in ct (z0 ) ,
and transferring that labor to the production of z1 yields an identical 1/at unit
increase in ct (z1 ). Given my assumptions about consumers’ preferences and
the technology for producing goods, equating the marginal rate of substitution
to the marginal rate of transformation requires that each good, z, be produced
in the same quantity. Only then can it be the case that
mrs (ct (z0 ) , ct (z1 )) =

(ct (z0 ) /ct (z1 ))−1/ε = 1

(5)

for all z0 , z1 ∈ [0, 1] .
At this point I know that efﬁciency requires all goods be produced in the
same quantity. Under what conditions are the allocations in sticky-price models efﬁcient? A standard assumption in sticky-price models, and an assumption
I will make here, is that each individual good is produced by a separate monopolist. Because the Dixit-Stiglitz aggregator function (1) means that each
good has many close substitutes, monopoly production of each good leads to
an overall market structure known as monopolistic competition.
The demand curve faced by the monopoly producer of any good, z, is
Pt (z) −ε
ct ,
Pt
where Pt is the price index for the consumption basket and is given by
ct (z) =

1/(1−ε)

Pt =

(6)

Pt (z)1−ε dz

(7)

The demand curve and the price index can be derived from the consumer’s
problem of choosing consumption of individual goods in order to minimize
the cost of one unit of the consumption basket (see, for example, Wolman
1999).
From the demand functions and the efﬁciency condition, it is clear that
efﬁciency requires all goods to have the same price. If price adjustment is
infrequent (i.e., if prices are sticky) and if price adjustment is staggered across
ﬁrms, then all goods can have the same price only if the aggregate price
level is constant. If the price level varied over time, then changes in the
price level would occur with only some ﬁrms adjusting their price, which
would be inconsistent with all ﬁrms charging the same price. In somewhat

A. L. Wolman: Relative Prices and Monetary Policy

223

simpliﬁed form, this is the reasoning behind optimality of price stability in
sticky-price models (see, for example, Goodfriend and King 1997, Rotemberg
and Woodford 1997, and King and Wolman 1999).

2. TREND VARIATION IN RELATIVE PRICES
The model sketched in the previous section is a useful benchmark, but it is
obviously unrealistic to suppose that the consumption goods valued by households are all “identical” in the sense of entering preferences symmetrically
(1) and being produced with identical technologies (2). Departing from that
benchmark, research on monetary policy in multisector sticky-price models
has concentrated on the extent to which cyclical ﬂuctuations in the determinants of relative prices interfere with the ability of monetary policy to eliminate
sticky-price distortions on a period-by-period basis, and the related question
of whether overall price stability remains optimal in such environments. However, more fundamental is the question of whether a trend in relative prices
affects the ability of monetary policy to eliminate distortions even in steady
state, and the related question of whether price stability is optimal on average,
i.e., whether the optimal rate of inﬂation is zero. I consider these questions in
Wolman (2008) and I draw on that analysis in what follows, emphasizing the
former question (Can distortions be eliminated in a steady state?).

Theory
In contrast to the one-sector framework, suppose that consumers have CobbDouglas preferences over two composite goods, and that each of those
composites has the characteristics of the single consumption aggregate (ct )
in the previous section. Here, ct will denote the overall consumption basket
comprised of the two types of goods, and c1,t and c2,t will denote the sectoral baskets each comprised of a continuum of individual goods. The overall
basket is now
ν 1−ν
ct = c1,t c2,t ,

(8)

and the sectoral baskets are
ε/(ε−1)

ck,t =

ck,t (z)(ε−1)/ε dz

, for k = 1, 2.

(9)

As before, ε is the elasticity of substitution between individual goods within
a sector. The elasticity of substitution across sectors is unity, and the sectoral
expenditure shares for the two sectors are ν and 1 − ν. The constraint on labor
input is
1
0

n1,t (z) +
0

n2,t (z) ≤ Nt .

(10)

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Technology for producing individual goods is the same as above,
ck,t (z) = ak,t nk,t (z) , for k = 1, 2,

(11)

except that now I allow for different levels of productivity (ak,t ) in the two
sectors. Again, productivity is exogenous, or unaffected by monetary policy.
Quantities and efﬁciency

I can analyze efﬁciency just as I did in the one-sector model. However, here
there are two dimensions of efﬁciency to be concerned with: efﬁciency within
sectors and efﬁciency across sectors. Within either sector, the analysis is
identical to that in the one-sector model. Efﬁciency within a sector requires
equal production of each good,
ck,t (z0 ) /ck,t (z1 )

−1/ε

= 1 for z0 , z1 ∈ [0, 1] , for k = 1, 2,

(12)

because of symmetry in preferences and identical technologies. Across sectors, the marginal rate of substitution is
mrs c1,t (z0 ) , c2,t (z1 )
for z0 , z1

ν
=
1−ν
∈ [0, 1] ,

c2,t
c1,t

c1,t (z0 ) /c1,t
c2,t (z1 ) /c2,t

−1
ε

, (13)

and the marginal rate of transformation is
mrt c1,t (z0 ) , c2,t (z1 ) =

a2,t
a1,t

, for z0 , z1 ∈ [0, 1] .

(14)

Note that in order for efﬁciency to hold across sectors, it must hold within
sectors; if within-sector efﬁciency does not hold, then from (12) the marginal
rate of substitution varies across combinations of z0 , z1 . With the marginal
rate of transformation independent of z (from [14]), it is not possible for the
marginal rate of substitution to be equated to the marginal rate of transformation for all combinations of z0 , z1 unless there is efﬁciency within each sector.
Efﬁciency within and across sectors then holds if and only if
ck,t (z0 ) = ck,t (z1 ) for z0 , z1 ∈ [0, 1] , for k = 1, 2,

(15)

and
a1,t
=
a2,t

1−ν
ν

c1,t
c2,t

(16)

The former condition states that quantities must be identical for all goods
within a sector. The latter condition states that the ratio of sectoral consumptions should be proportional to the ratio of sectoral productivities; thus, if the
ratio of sectoral productivities changes over time, then the ratio of sectoral
consumptions must change in order to maintain efﬁciency.

A. L. Wolman: Relative Prices and Monetary Policy

225

Prices and efﬁciency

As in the one-sector model, in order to determine the conditions under which
efﬁciency holds I need to specify market structure and pricing behavior. I
make analogous assumptions to the one-sector model, namely that individual
goods are produced by monopolists, which implies monopolistic competition
among producers.
The demand curve faced by the monopoly producer of a good z in sector
k is
Pk,t (z)
Pk,t

ck,t (z) =

−ε

ck,t , k = 1, 2,

(17)

where Pk,t is the price index for the sector k consumption basket,
1/(1−ε)

Pk,t =

Pk,t (z)1−ε dz

(18)

The index of sector k consumption in (17) can be replaced by the appropriate
demand function,
P1,t
Pt

c1,t

= ν

c2,t

= (1 − ν)

−1

ct , or
P2,t
Pt

(19)

−1

ct .

(20)

These demand functions, as well as the overall price index in the two-sector
model (Pt ), are derived from the consumer’s problem of choosing sectoral
consumption in order to minimize the cost of one unit of the consumption
basket. The price index is given by
Pt =

P1,t
ν

P2,t
1−ν

1−ν

(21)

Note from (19) and (20) that the share of consumption spending (expenditure
share) going to sector one (sector two) is constant and equal to ν (equal to
1 − ν).
From the demand curves for individual goods (17) and the within-sector
efﬁciency condition (15), it is again clear that efﬁciency requires all goods
within a sector to have the same price:
Pk,t (z0 ) = Pk,t (z1 ) for z0 , z1 ∈ [0, 1] , for k = 1, 2.

(22)

Across sectors, because efﬁciency requires relative consumptions to move
with relative productivities, sectoral relative prices must vary with relative
productivities. Combining (16) with (19) and (20) yields
P2,t
a1,t
=
.
a2,t
P1,t

(23)

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Federal Reserve Bank of Richmond Economic Quarterly

Working now in terms of prices instead of quantities, conditions (22) and (23)
are necessary and sufﬁcient for efﬁciency.
Earlier I stated that productivity in each sector was exogenous. Now I will
make the further assumption that there is a trend in the growth rate of sector
one’s productivity relative to sector two’s productivity:
a1,t
= (1 + γ )t , t = 0, 1, 2, ..., γ > 1,
(24)
a2,t
where γ is an exogenous parameter representing relative productivity growth
in sector one. Substituting this relationship into the second efﬁciency condition
(23) implies
P2,t
= (1 + γ )t ;
P1,t

(25)

efﬁciency requires the price of sector two’s composite good to rise over time
relative to the price of sector one’s composite good. The requirement that
there be a trend in the relative price P2,t /P1,t could be satisﬁed with a variety
of different combinations of nominal price behavior for P2,t and P1,t , but each
of those combinations involves at least one nominal price having a nonzero
rate of change. In other words, when there is a trend in relative productivity
growth across the two sectors, some nominal prices must change in order
for efﬁciency to hold. But now there is a contradiction, because from the
requirement that prices be identical for all goods within a sector (22), I can
use the same reasoning as in the one-sector model of Section 1 to conclude
that efﬁciency with price stickiness requires zero price changes within each
sector. It is not possible to have both zero price changes within each sector
and a nonzero rate of price change in at least one sector.
Wolman (2008) shows how one can determine the optimal rate of inﬂation
in a sticky-price model that has the features described here. For my purpose, it
is enough to conclude that when there are different trend productivity growth
rates across sectors, price stickiness inevitably leads to some real distortions
that cannot be undone by monetary policy.

Measurement: Price Stickiness and Relative Price
Trends
It is one thing to make a theoretical argument showing that, given certain
assumptions, monetary policy cannot overcome the frictions associated with
price stickiness. Here I take the next step and argue that those conditions seem
to exist in the United States. The conditions I discuss are, ﬁrst, that there is
some price stickiness (infrequent price adjustment), and second, that there are
trends in the relative prices of different categories of consumption goods.
Concerning infrequent price adjustment, a vast literature has arisen in recent years reporting on the behavior of the prices of large numbers of individual

A. L. Wolman: Relative Prices and Monetary Policy

227

Figure 1 Sectoral Prices Indexes

Services
10

Overall PCE
Price Index

Nondurables
4

Durables

0
1947 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007
Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1

goods. The seminal paper in this literature is by Bils and Klenow (2004), who
study individual prices that serve as inputs into the United States Bureau of
Labor Statistics (BLS) Consumer Price Index computations. Although their
headline result is about price adjustment being more frequent than previous
studies had estimated, they show that there is substantial heterogeneity in the
frequency of price adjustment. The median price duration in their sample is
4.3 months, but one-third of consumption expenditure is on goods and services
with price durations greater than 6.8 months, and one-quarter is on goods and
services with price durations greater than 9 months.
In the model in Section 2, there were two sectors, and thus only one independent sectoral relative price. In contrast, the BLS compiles price indexes
for hundreds of categories of consumption goods. Thus, there are hundreds of
sectoral relative prices one could study. Here I will report on relative prices
from highly aggregated categories of consumption: durable goods, nondurable
goods, and services. Price indexes for these categories are reported by the
United States Commerce Department’s Bureau of Economic Analysis. Figure
1 plots the price indexes for durables, nondurables, and services from 1947 to
2008. There are clear positive trends in the prices of services and nondurables
relative to durables. Since 1947, the price of nondurables relative to durables

228

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 “Zero-Inﬂation” Price Indexes

1.6
1.4

Services
1.2
1.0
0.8

Nondurables

0.6
0.4

Durables
0.2
0.0

1947 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007
Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1

has risen by a factor of more than two, and the price of services relative to
durables has risen by a factor of more than ﬁve. With these trends in relative prices, it would not have been possible to stabilize the individual prices
of each consumption category. Figure 2 displays the counterfactual paths of
the price indexes from Figure 1 that are consistent with zero inﬂation in each
quarter, given the historical values for relative prices and expenditure shares;
stabilizing the overall price level would have required the nominal price of
durables to fall by almost 80 percent and the nominal price of services to rise
by almost 40 percent.3
Together, the presence of infrequent individual price adjustment and trends
in the relative prices of different consumption categories makes clear that
monetary policy cannot eliminate the frictions associated with nominal price
3 Figure 2 is constructed as follows: First, I normalize the levels of the sectoral price indexes
at one in the ﬁrst quarter of 1947. Then, for each subsequent quarter, I divide the gross rate of
sectoral price change for each sector by the expenditure share weighted average of the gross rates
of sectoral price changes (that is, I divide by the overall inﬂation rate). The resulting quotient for
each sector is the rate of change of the zero-inﬂation price indexes in Figure 2. By construction,
the expenditure share weighted average of the rates of price change for the zero-inﬂation sectoral
price indexes is zero.

A. L. Wolman: Relative Prices and Monetary Policy

229

adjustment. In other words, while monetary policy can stabilize an overall
price index, it cannot stabilize all individual prices. To the extent that individual price adjustment is costly, either directly (state-dependent pricing) or
indirectly (time-dependent pricing), stability of individual prices is required
if nominal frictions are to be eliminated.

CYCLICAL VARIATION IN RELATIVE PRICES

Thus far I have concentrated on the limits to monetary policy when there is a
trend in the relative prices of goods with sticky nominal prices. In this setting
monetary policy cannot stabilize all nominal prices, even in the absence of
shocks. In contrast, most of the growing literature on relative prices and
monetary policy has focused on optimal stabilization. That is, the literature
has assumed that the optimal average inﬂation rate (the inﬂation target) is
zero—price stability—and then gone on to study how monetary policy should
make inﬂation behave in response to various shocks. A number of papers in
this literature have used multisector models to study cyclical analogues of the
kind of issues discussed in the previous section. I review some of them here.
The most inﬂuential early paper in this line of research is by Aoki (2001).
In Aoki’s paper there are sector-speciﬁc productivity shocks that make it infeasible to stabilize all nominal prices. However, one of the two sectors in
Aoki’s model has ﬂexible prices. Thus, inability to stabilize all prices does
not prevent monetary policy from neutralizing nominal frictions. Optimal
monetary policy involves stabilizing prices in the sticky-price sector, allowing
prices in the other sector to ﬂuctuate with relative productivity.
Subsequently, other authors have extended Aoki’s analysis to environments where price stickiness in both (or all) sectors means that monetary
policy cannot neutralize the nominal frictions. Huang and Liu (2005) study a
model with both intermediate and ﬁnal goods sectors, with price stickiness in
both sectors. As in Aoki’s paper, productivity shocks are sector-speciﬁc, but
they inevitably lead to distortions because of price stickiness in both sectors.
Huang and Liu emphasize that stabilizing consumer prices at the expense of
highly volatile producer prices can be quite costly; optimal monetary policy
should place nonnegligible weight on producer price inﬂation.
Like Huang and Liu, Erceg and Levin (2006) study a model with two
sticky-price sectors. Instead of intermediate and ﬁnal goods, the sectors produce durable and nondurable ﬁnal goods.4 As in Huang and Liu’s paper,
sector-speciﬁc productivity shocks ought to involve relative price changes,
and with price stickiness these relative price changes necessarily involve distortions. However, the presence of durable goods gives the model some
4 Erceg and Levin’s paper also includes wage stickiness, which I will discuss in the next
section.

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additional interesting properties. A shock to government spending—an aggregate shock—now also should involve relative price changes, because it raises
the real interest rate, making durable goods less attractive. With sticky prices
in both sectors, stabilizing prices in both sectors is infeasible in response to
a government spending shock. Thus, even an aggregate shock can inevitably
lead to nominal distortions in a multisector model.5

4. WAGES AND PRICES ACROSS LOCATIONS
By now it should be clear that when individual goods prices are sticky, shocks
that optimally change the relative price across sectors inevitably restrict the
monetary authority’s ability to achieve efﬁcient allocations. Elements of this
reasoning also apply to wage stickiness and to prices across regions in a currency union.6
The labor market can be thought of as a sector, and if nominal prices in
that sector are sticky (i.e., if nominal wages are sticky) then aggregate shocks
that require real wage adjustment will lead to inefﬁciencies, even under optimal monetary policy. Erceg, Henderson, and Levin (2000) work through the
details in a model with sticky wages and prices. Wage stickiness is introduced
in a similar manner to price stickiness: Firms must assemble a range of different types of labor inputs, and the supplier of each input has monopoly power
and sets her wage only occasionally. In this framework, it is not optimal to
completely stabilize prices or wages, but in general higher welfare is achieved
by stabilizing wage inﬂation than by stabilizing price inﬂation. Wage dispersion has two costs in the model: it makes production less efﬁcient, and it is
disliked by households, who would prefer to spread their labor input evenly
over all ﬁrms. Price dispersion has only the analogue to the ﬁrst cost (that is,
it makes consumption of the aggregate good less efﬁcient), and this helps to
explain why wage inﬂation takes priority over price inﬂation. Another factor
that works toward stabilizing wage inﬂation is that the productive inefﬁciency
from wage dispersion affects each intermediate good and feeds through into
inefﬁcient production of ﬁnal goods. In contrast, price dispersion leads only
to inefﬁcient production of ﬁnal goods.7
Amano et al. (2007) use a model similar to that of Erceg, Henderson, and
Levin to address trend instead of cyclical issues. They assume there is trend
productivity growth so that the real wage should rise over time. In a steady
state (balanced growth path), a rising real wage means that the nominal wage
5 There are many other recent papers that study multisector models with nominal rigidities.
They include Mankiw and Reis (2003, to be discussed in the next section), Carlstrom et al. (2006),
Carvalho (2006), and Nakamura and Steinsson (2008).
6 Erceg, Henderson, and Levin (2000) recognized the generality of this point.
7 Similar reasoning may help to explain Huang and Liu’s (2005) quantitative ﬁndings regarding producer price inﬂation, mentioned previously.

A. L. Wolman: Relative Prices and Monetary Policy

231

must be rising or nominal prices must be falling. With infrequent adjustment
for both wages and prices, any such scenario involves distortions. Amano et al.
show that optimal monetary policy involves slight deﬂation so that nominal
wages are rising at a rate lower than real wages—a compromise between
constant wages and constant prices.
Mankiw and Reis (2003) provide a general framework for thinking about
optimal monetary policy in the presence of wage and price stickiness as well as
sectoral considerations. They frame the monetary policy problem as choosing
the appropriate index of prices and wages to stabilize. Consistent with Erceg,
Henderson, and Levin (2000), Mankiw and Reis ﬁnd that nominal wages carry
large weight in the “price index” that should be stabilized.
Benigno (2004) studies optimal monetary policy in a two-region currency
area. If nominal prices are sticky in both regions and real factors lead to efﬁcient relative price variation across regions, then once again monetary policy
cannot eliminate the real effects of price stickiness. The optimal monetary
policy problem involves trading off price distortions in the two regions.

CONCLUSION

If prices or wages are sticky in only one sector of an economy, and if there is
no heterogeneity across regions, then monetary policy can undo the effects of
price stickiness. However, if there is more than one sector with sticky prices,
or if wages and prices are sticky, or if there are heterogeneous regions, then
nominal rigidities cause distortions under any monetary policy.8 I described
several examples of these distortions, emphasizing an underappreciated one,
trending relative prices across sectors.
Macroeconomists are acutely aware of the limited ability of monetary
policy to counteract real distortions that may be present in the economy (for
example, search frictions in labor markets or monopoly power in goods markets). However, we have been perhaps less modest about the ability of monetary policy to counteract nominal distortions—in particular price adjustment
frictions. A recent literature on monetary policy in multisector models with
price stickiness has served to make us more modest, and this paper aims to
draw attention to that literature.

8 Loyo (2002) points out that if different sectors have different currencies, then nominal rigidities can be undone. That possibility is intriguing but not currently relevant.

232

Federal Reserve Bank of Richmond Economic Quarterly

REFERENCES
Amano, Robert, Kevin Moran, Stephen Murchison, and Andrew Rennison.
2007. “Trend Inﬂation, Wage and Price Rigidities, and Welfare.” Bank of
Canada Working Paper 07-42.
Aoki, Kosuke. 2001. “Optimal Monetary Policy Response to Relative Price
Changes.” Journal of Monetary Economics 48: 55–80.
Benigno, Pierpaolo. 2004. “Optimal Monetary Policy in a Currency Area.”
Journal of International Economics 63 (July): 293–320.
Bils, Mark, and Peter Klenow. 2004. “Some Evidence on the Importance of
Sticky Prices.” Journal of Political Economy 112 (October): 947–85.
Carlstrom, Charles T., Timothy S. Fuerst, Fabio Ghironi, and K´ lver
o
Hern´ ndez. 2006. “Relative Price Dynamics and the Aggregate
a
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with Durable Consumption Goods.” Journal of Monetary Economics 53:
1341–59.
Erceg, Christopher, Dale Henderson, and Andrew Levin. 2000. “Optimal
Monetary Policy with Staggered Wage and Price Contracts.” Journal of
Monetary Economics 46 (October): 281–313.
Goodfriend, Marvin, and Robert King. 1997. “The New Neoclassical
Synthesis and the Role of Monetary Policy.” In NBER Macroeconomics
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Economic Quarterly—Volume 94, Number 3—Summer 2008—Pages 235–263

Understanding Monetary
Policy Implementation
Huberto M. Ennis and Todd Keister

ver the last two decades, central banks around the world have adopted
a common approach to monetary policy that involves targeting the
value of a short-term interest rate. In the United States, for example,
the Federal Open Market Committee (FOMC) announces a rate that it wishes
to prevail in the federal funds market, where commercial banks lend balances
held at the Federal Reserve to each other overnight. Changes in this shortterm interest rate eventually translate into changes in other interest rates in the
economy and thereby inﬂuence the overall level of prices and of real economic
activity.
Once a target interest rate is announced, the problem of implementation
arises: How can a central bank ensure that the relevant market interest rate
stays at or near the chosen target? The Federal Reserve has a variety of tools
available to inﬂuence the behavior of the interest rate in the federal funds
market (called the fed funds rate). In general, the Fed aims to adjust the total
supply of reserve balances so that it equals demand at exactly the target rate
of interest. This process necessarily involves some estimation, since the Fed
does not know the exact demand for reserve balances, nor does it completely
control the supply in the market.
A critical issue in the implementation process, therefore, is the sensitivity
of the market interest rate to unanticipated changes in supply and/or demand.
Some of the material in this article resulted from our participation in the Federal Reserve
System task force created to study paying interest on reserves. We are very grateful to the
other members of this group, who patiently taught us many of the things that we discuss here.
We also would like to thank Kevin Bryan, Yash Mehra, Rafael Repullo, John Walter, John
Weinberg, and the participants at the 2008 Columbia Business School/New York Fed conference on “The Role of Money Markets” for useful comments on a previous draft. All remaining errors are, of course, our own. The views expressed here do not necessarily represent
those of the Federal Reserve Bank of New York, the Federal Reserve Bank of Richmond,
or the Federal Reserve System. Ennis is on leave from the Richmond Fed at University
Carlos III of Madrid and Keister is at the Federal Reserve Bank of New York. E-mails:
hennis@eco.uc3m.es, Todd.Keister@ny.frb.org.

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If small estimation errors lead to large swings in the interest rate, a central
bank will ﬁnd it difﬁcult to effectively implement monetary policy, that is, to
consistently hit the target rate. The degree of sensitivity depends on a variety
of factors related to the design of the implementation process, such as the time
period over which banks are required to hold reserves and the interest rate, if
any, that a central bank pays on reserve balances.
The ability to hit a target interest rate consistently plays a critical role in a
central bank’s communication policy. The overall effectiveness of monetary
policy depends, in part, on individuals’ perceptions of the central bank’s actions and objectives. If the market interest rate were to deviate consistently
from the central bank’s announced target, individuals might question whether
these deviations simply represent glitches in the implementation process or
whether they instead represent an unannounced change in the stance of monetary policy. Sustained deviations of the average fed funds rate from the
FOMC’s target in August 2007, for example, led some media commentators
to claim that the Fed had engaged in a “stealth easing,” taking actions that
lowered the market interest rate without announcing a change in the ofﬁcial
target.1 In such times, the ability to hit a target interest rate consistently allows
the central bank to clearly (and credibly) communicate its policy to market
participants.
Under most circumstances, the Fed changes the total supply of reserve
balances available to commercial banks by exchanging government bonds
or other securities for reserves in an open market operation. Occasionally,
the Fed also provides reserves directly to certain banks through its discount
window. In some situations, the Fed has developed other, ad hoc methods
of inﬂuencing the supply and distribution of reserves in the market. For
example, during the recent period of ﬁnancial turmoil, the market’s ability to
smoothly distribute reserves across banks became partially impaired, which
led to signiﬁcant ﬂuctuations in the average fed funds rate both during the day
and across days. In December 2007, partly to address these problems, the Fed
introduced the Term Auction Facility (TAF), a bimonthly auction of a ﬁxed
quantity of reserve balances to all banks eligible to borrow at the discount
window. In principle, the TAF has increased these banks’ ability to access
reserves directly and, in this way, has helped ease the pressure on the market
to redistribute reserves and avoid abnormal ﬂuctuations in the market rate.
Such operations, of course, need to be managed so as to achieve the ultimate
goal of implementing the chosen target interest rate. Balancing the demand
and supply of reserves is at the very core of this problem.
This article presents a simple analytical framework for understanding the
process of monetary policy implementation and the factors that inﬂuence a
1 See, for example, “A ‘Stealth Easing’ by the Fed?” (Coy 2007).

H. M. Ennis and T. Keister: Monetary Policy Implementation

237

central bank’s ability to keep the market interest rate close to a target level.
We present this framework graphically, focusing on how various features of
the implementation process affect the sensitivity of the market interest rate to
unanticipated changes in supply or demand. We discuss the current approach
used by the Fed, including the use of reserve maintenance periods to decrease
this sensitivity. We also show how this framework can be used to study a wide
range of issues related to monetary policy implementation.
In 2006, the U.S. Congress enacted legislation that will give the Fed the
authority to pay interest on reserve balances beginning in October 2011.2
We use our simple framework to illustrate how the ability to pay interest on
reserves can be a useful policy tool for a central bank. In particular, we show
how paying interest on reserves can decrease the sensitivity of the market
interest rate to estimation errors and, thus, enable a central bank to better
achieve its desired interest rate.
The model we present uses the basic approach to reserve management
introduced by Poole (1968) and subsequently advanced by many others (see,
for example, Dotsey 1991; Guthrie and Wright 2000; Bartolini, Bertola, and
Prati 2002; and Clouse and Dow 2002). The speciﬁc details of our formalization closely follow those in Ennis and Weinberg (2007), after some additional
simpliﬁcations that allow us to conduct all of our analysis graphically. Ennis
and Weinberg (2007) focused on the interplay between daylight credit and
the Fed’s overnight treatment of bank reserves. In this article, we take a more
comprehensive view of the process of monetary policy implementation and we
investigate several important topics, such as the role of reserve maintenance
periods, which were left unexplored by Ennis and Weinberg (2007).

U.S. MONETARY POLICY IMPLEMENTATION

Banks hold reserve balances in accounts at the Federal Reserve in order to
satisfy reserve requirements and to be able to make interbank payments. During the day, banks can also access funds by obtaining an overdraft from their
reserve accounts at the Fed. The terms by which the Fed provides daylight
credit are one of the factors determining the demand for reserves by banks.
To adjust their reserve holdings, banks can borrow and lend balances in
the fed funds market, which operates weekdays from 9:30 a.m. to 6:30 p.m.
A bank wanting to decrease its reserve holdings, for example, can do so in this
market by making unsecured, overnight loans to other banks.
The fed funds market plays a crucial role in monetary policy implementation because this is where the Federal Reserve intervenes to pursue its policy
objectives. The stance of monetary policy is decided by the FOMC, which
2 After this article was written, the effective date for the authority to pay interest on reserves
was moved to October 1, 2008, by the Emergency Economic Stabilization Act of 2008.

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selects a target for the overnight interest rate prevailing in this market. The
Committee then instructs the Open Market Desk to adjust, via open market
operations, the supply of reserve balances so as to steer the market interest
rate toward the selected target.3
The Desk conducts open market operations largely by arranging repurchase agreements (repos) with primary securities dealers in a sealed-bid,
discriminatory price auction. Repos involve using reserve balances to purchase securities with the explicit agreement that the transaction will be
reversed at maturity. Repos usually have overnight maturity, but the Desk
also employs other maturities (for example, two-day and two-week repos are
commonly used). Open market operations are typically conducted early in
the morning when the market for repos is most active.
The new reserves created in an open market operation are deposited in the
participating securities dealers’ bank accounts and, hence, increase the total
supply of reserves in the banking system. In this way, each day the Desk
tries to move the supply of reserve balances as close as possible to the level
that would leave the market-clearing interest rate equal to the target rate. An
essential step in this process is accurately forecasting both aggregate reserve
demand and those changes in the existing supply of reserve balances that are
due to autonomous factors beyond the Fed’s control, such as payments into
and out of the Treasury’s account and changes in the quantity of currency in
circulation. Forecasting errors will lead the actual supply of reserve balances
to deviate from the intended level and, hence, will cause the market rate to
diverge from the target rate, even if reserve demand is perfectly anticipated.
Reserve requirements in the United States are calculated as a proportion
of the quantity of transaction deposits on a bank’s balance sheet during a twoweek computation period prior to the start of the maintenance period. These
requirements can be met through a combination of vault cash and reserve
balances held at the Fed. During the two-week reserve maintenance period,
a bank’s end-of-day reserve balances must, on average, equal the reserve
requirement minus the quantity of vault cash held during the computation
period. Reserve requirements make a large portion of the demand for reserve
balances fairly predictable, which simpliﬁes monetary policy implementation.
Reserve maintenance periods allow banks to spread out their reserve holdings over time without having to scramble for funds to meet a requirement at
the end of each day. However, near the end of the maintenance period, this
averaging effect tends to lose force. On the last day of the period, a bank has
some level of remaining requirement that must be met on that day. This generates a fairly inelastic demand for reserve balances and makes implementing
a target interest rate more challenging. For this reason, the Fed allows banks
3 See Hilton and Hrung (2007) for a more detailed overview of the Fed’s monetary policy
implementation procedures.

H. M. Ennis and T. Keister: Monetary Policy Implementation

239

holding excess or deﬁcient balances at the end of a maintenance period to carry
over those balances and use them to satisfy up to 4 percent of their requirement
in the following period.
If a bank ﬁnds itself short of reserves at the end of the maintenance period,
even after taking into account the carryover possibilities, it has several options.
It can try to ﬁnd a counterparty late in the day offering an acceptable interest
rate. However, this may not be feasible because of an aggregate shortage of
reserve balances or because of the existence of trading frictions in this market.
A second alternative is to borrow at the discount window of its corresponding
Federal Reserve Bank.4 The discount window offers collateralized overnight
loans of reserves to banks that have previously pledged appropriate collateral.
Discount window loans are typically charged an interest rate that is 100 basis
points above the target fed funds rate, although changing the size of this gap
is possible and has been used, at times, as a policy instrument. Finally, if
the bank does not have the appropriate collateral or chooses not to borrow
at the discount window for other reasons, it will be charged a penalty fee
proportional to the amount of the shortage.
Currently, banks earn no interest on the reserve balances they hold in
their accounts at the Federal Reserve.5 This situation may soon change: The
Financial Services Regulatory Relief Act of 2006 allows the Fed to begin
paying interest on reserve balances in October 2011. The Act also includes
provisions that give the Fed more ﬂexibility in determining reserve requirements, including the ability to eliminate the requirements altogether. Thus,
this legislation opens the door to potentially substantial changes in the way
the Fed implements monetary policy. To evaluate the best approach within the
new, broader set of alternatives, it seems useful to develop a simple analytical
framework that is able to address many of the relevant aspects of the problem.
We introduce and discuss such a framework in the sections that follow.

2. THE DEMAND FOR RESERVES
In this section, we present a simple framework that is useful for understanding
banks’demand for reserves. In this framework, a bank holds reserves primarily
to satisfy reserve requirements, although other factors, such as the desire to
make interbank payments, may also play a role. Since banks cannot fully
predict the timing of payments, they face uncertainty about the net outﬂows
from their reserve accounts and, therefore, are typically unable to exactly
satisfy their reserve requirements. Instead, they must balance the possibility
4 There are 12 regions and corresponding Reserve Banks in the Federal Reserve System. For
each commercial bank, the corresponding Reserve Bank is determined by the region where the
commercial bank is headquartered.
5 See footnote 2.

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Federal Reserve Bank of Richmond Economic Quarterly

of holding excess reserve balances—and the associated opportunity cost—
against the possibility of being penalized for a reserve deﬁciency. A bank’s
demand for reserves results from optimally balancing these two concerns.

The Basic Framework
We assume banks are risk-neutral and maximize expected proﬁts. At the
beginning of the day, banks can borrow and lend reserves in a competitive
interbank market. Let R be the quantity of reserves chosen by a bank in
the interbank market. The central bank affects the supply of reserves in this
market by conducting open market operations. Total reserve supply is equal
to the quantity set by the central bank through its operations, adjusted by a
potentially random amount to reﬂect unpredictable changes in autonomous
factors.
During the day, each bank makes payments to and receives payments from
other banks. To keep things as simple as possible, suppose that each bank
will make exactly one payment and receive exactly one payment during the
“middle” part of the day. Furthermore, suppose that these two payment ﬂows
are of exactly the same size, PD > 0, and that this size is nonstochastic. However, the order in which these payments occur during the day is random; some
banks will receive the incoming payment before making the outgoing one,
while others will make the outgoing payment before receiving the incoming
one.
At the end of the day, after the interbank market has closed, each bank
experiences another payment shock, P , that affects its end-of-day reserve
balance. The value of P can be either positive, indicating a net outﬂow of
funds, or negative, indicating a net inﬂow of funds. We assume that the
payment shock, P , is uniformly distributed on the interval −P , P . The
value of this shock is not yet known when the interbank market is open; hence,
a bank’s demand for reserves in this market is affected by the distribution of
the payment shock and not the realization.
We assume, as a starting point, that a bank must meet a given reserve
requirement, K, at the end of each day.6 If the bank ﬁnds itself holding fewer
than K reserves at the end of the day, after the payment shock P has been
realized, it must borrow funds at a “penalty” rate of interest, rP , to satisfy the
requirement. This rate can be thought of as the rate charged by the central
bank on discount window loans, adjusted to take into account any “stigma”
associated with using this facility. In reality, a bank may pay a deﬁciency
fee instead of borrowing from the discount window or it may borrow funds
6 We discuss more complicated systems of reserve requirements later, including multiple-day

maintenance periods. For the logic in the derivations that follow, the particular value of K does
not matter. The case of K = 0 corresponds to a system without reserve requirements.

H. M. Ennis and T. Keister: Monetary Policy Implementation

241

in the interbank market very late in the day when this market is illiquid. In
the model, the rate rP simply represents the cost associated with a late-day
reserve deﬁciency, whatever the source of that cost may be.
The speciﬁc assumptions we make about the number and size of payments
that a bank sends are not important; they only serve to keep the analysis free
of unnecessary complications. Two basic features of the model are important.
First, the bank cannot perfectly anticipate its end-of-day reserve position.
This uncertainty creates a “precautionary” demand for reserves that smoothly
responds to changes in the interest rate. Second, a bank makes payments
during the day as a part of its normal operations and the pattern of these
payments can potentially lead to an overdraft in the bank’s reserve account.
We initially assume that the central bank offers daylight credit to banks to cover
such overdrafts at no charge. We study the case where daylight overdrafts are
costly later in this section.

The Benchmark Case
We begin by analyzing a simple benchmark case; we show later in this section
how the framework can be extended to include a variety of features that are
important in reality. In the benchmark case, banks must meet their reserve
requirement at the end of each day, and the central bank pays no interest
on reserves held by banks overnight. Furthermore, the central bank offers
daylight credit free of charge.
Figure 1 depicts an individual bank’s demand for reserves in the interbank
market under this benchmark scenario. On the horizontal axis we measure the
bank’s choice of reserve holdings before the late-day payment is realized. On
the vertical axis we measure the market interest rate for overnight loans. To
draw the demand curve, we ask: Given a particular value for the interest rate,
what quantity of reserves would the bank demand to hold if that rate prevailed
in the market?
A bank would be unwilling to hold any reserves if the market interest rate
were higher than rP . If the market rate were higher than the penalty rate,
the bank would choose to meet its requirement entirely by borrowing from
the discount window. It would actually like to borrow even more than its
requirement and lend the rest out at the higher market rate, but this fact is not
important for the analysis. The important point is simply that there will be no
demand for (nonborrowed) reserves for any interest rate larger than rP .
When the market interest rate exactly equals the penalty rate, rP , a bank
would be indifferent between holding any amount of reserves between zero
and K − P and, hence, the demand curve is horizontal at rP . As long as
the bank’s reserve holdings, R, are smaller than K − P , the bank will need
to borrow at the discount window to satisfy its reserve requirement, K, even
if the late-day inﬂow of funds into the bank’s reserve account is the largest

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Figure 1 Benchmark Demand for Reserves
r

Demand for
Reserves

K-P

K+P

possible value, P .7 The alternative would be to borrow more reserves in the
market to reduce this potential need for discount window lending. Since the
market rate is equal to the penalty rate, both strategies deliver the same level
of proﬁt and the bank is indifferent between them.
For market interest rates below the penalty rate, however, a bank will
choose to hold at least K − P reserves. As discussed above, if the bank held
fewer than K − P reserves it would be certain to need to borrow from the
discount window, which would not be an optimal choice when the market
rate is lower than the discount rate. The bank’s demand for reserves in this
situation can be described as “precautionary” in the sense that the bank chooses
its reserve holdings to balance the possibility of falling short of the requirement
against the possibility of ending up with extra reserves in its account at the
end of the day.
7 To see this, note that even in the best case scenario the bank will ﬁnd itself holding R + P
reserves after the arrival of the late-day payment ﬂow. When R < K − P , the bank’s end-of-day
holdings of reserves is insufﬁcient to satisfy its reserve requirement, K, unless it takes a loan at
the discount window.

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243

If the market interest rate were very low—close to zero—the opportunity
cost of holding reserves would be very small. In this case, the bank would
hold enough precautionary reserves so that it is virtually certain that unforeseen movements on its balance sheet will not decrease its reserves below the
required level. In other words, the bank will hold K + P reserves in this
case. If the market interest rate were exactly zero, there would be no opportunity cost of holding reserves. The demand curve is, therefore, ﬂat along the
horizontal axis after K + P .
In between the two extremes, K − P and K + P , the demand for reserves
will vary inversely with the market interest rate measured on the vertical axis;
this portion of the demand curve is represented by the downward-sloping
line in Figure 1. The curve is downward-sloping for two reasons. First,
the market interest rate represents the opportunity cost of holding reserves
overnight. When this rate is lower, ﬁnding itself with excess balances is less
costly for the bank and, hence, the bank is more willing to hold precautionary
balances. Second, when the market rate is lower, the relative cost of having to
access the discount window is larger, which also tends to increase the bank’s
precautionary demand for reserves.
The linearity of the downward-sloping part of the demand curve results
from the assumption that the late-day payment shock is uniformly distributed.
With other probability distributions, the demand curve will be nonlinear, but
its basic shape will remain unchanged. In particular, the points where the
demand curve intersects the penalty rate, rP , and the horizontal axis will be
the same for any distribution with support −P , P .8

The Equilibrium Interest Rate
Suppose, for the moment, that there is a single bank in the economy. Then
the demand curve in Figure 1 also represents the total demand for reserves.
Let S denote the total supply of reserves in the interbank market, as jointly
determined by the central bank’s open market operations and autonomous
factors. Then the equilibrium interest rate is determined by the height of the
demand curve at point S. As shown in the diagram, there is a unique level of
reserve supply, ST , that will generate a given target interest rate, rT .
Now suppose there are many banks in the economy, but they are all identical in that they have the same level of required reserves, face the same payment
shock, etc. When there are many banks, the total demand for reserves can be
found by simply “adding up” the individual demand curves. For any interest
8 The support of the probability distribution is the set of values of the payment shock that
is assigned positive probability. An explicit formula for the demand curve in the uniform case is
derived in Ennis and Weinberg (2007). If the shock instead had an unbounded distribution, such
as the normal distribution used by Whitesell (2006) and others, the demand curve would asymptote
to the penalty rate and the horizontal axis but never intersect them.

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rate r, total demand is simply the sum of the quantity of reserves demanded
by each individual bank.
For presentation purposes, it is useful to look at the average demand for
reserves, that is, the total demand divided by the number of banks. When
all banks are identical, the average demand is exactly equal to the demand
of each individual bank. In other words, in the benchmark case where banks
are identical, the demand curve in Figure 1 also represents the aggregate
demand for reserves, expressed in per-bank terms. The determination of the
equilibrium interest rate then proceeds exactly as in the single-bank case. In
particular, the market-clearing interest rate will be equal to the target rate, rT ,
if and only if reserve supply (expressed in per-bank terms) is equal to ST .
Note that the central bank has two distinct ways in which it can potentially
affect the market interest rate: changing the supply of reserves available in the
market and changing (either directly or indirectly) the penalty rate. Suppose,
for example, that the central bank wishes to decrease the market interest rate.
It could either increase the supply of reserves through open market operations,
leading to a movement down the demand curve, or it could decrease the penalty
rate, which would rotate the demand curve downward while leaving the supply
of reserves unchanged. Both policies would cause the market interest rate
to fall.

Heterogeneity
While the assumption that all banks are identical was useful for simplifying
the presentation above, it is clearly a poor representation of reality in most
economies. The United States, for example, has thousands of banks and other
depository institutions that differ dramatically in size, range of activities, etc.
We now show how the analysis above changes when there is heterogeneity
among banks and, in particular, how the size distribution of banks might affect
the aggregate demand for reserves.
Each bank still has a demand curve of the form depicted in Figure 1, but
now these curves can be different from each other because banks may have
different levels of required reserves, face different distributions of the payment
shock, and/or face different penalty rates. These individual demand curves
can be aggregated exactly as before: For any interest rate r, the total demand
for reserves is simply the sum of the quantity of reserves demanded by each
individual bank. The aggregate demand curve, expressed in per-bank terms,
will again be similar to that presented in Figure 1, with the exact shape being
determined by the properties of the various individual demands. If different
banks have different levels of required reserves, for example, the requirement
K in the aggregate demand curve will be equal to the average of the individual
banks’ requirements.

H. M. Ennis and T. Keister: Monetary Policy Implementation

245

Our interest here is in studying how bank heterogeneity affects the properties of this demand curve. We focus on heterogeneity in bank size, which
is particularly relevant in the United States, where there are some very large
banks and thousands of smaller banks. We ask how large banks may differ
from small banks in the context of the simple framework and how the presence of both large and small banks might affect the properties of the aggregate
demand curve. To simplify the presentation, we study the three possible
dimensions of heterogeneity addressed by the model one at a time. In reality,
of course, the three cases are closely intertwined.

Size of Requirements

Perhaps the most natural way of capturing differences in bank size is by
allowing for heterogeneity in reserve requirements. When requirements are
calculated as a percentage of the deposit base, larger banks will tend to have a
larger level of required reserves in absolute terms. Suppose, then, that banks
have different levels of K, but they face the same late-day payment shock and
the same penalty rate for a reserve deﬁciency. How would the size distribution
of banks affect the aggregate demand for reserves in this case?
To begin, note that in Figure 1 the slope of the demand curve is independent
of the size of the bank’s reserve requirement, K. To see why this is the case,
consider an increase in the value of K. Since both K − P and K + P become
larger numbers, the demand curve in Figure 1 shifts to the right. Notice
that these two points shift exactly the same distance, leaving the slope of the
downward-sloping segment of the demand curve unchanged.
Simple aggregation then shows that the slope of the aggregate demand
curve will be independent of the size distribution of banks. In other words, for
the case of heterogeneity in K, the sensitivity of reserve demand to changes in
the interest rate does not depend at all on whether the economy is comprised
of only large banks or, as in the United States, has a few large banks and very
many small ones.
Adding heterogeneity in reserve requirements does generate an interesting
implication for the distribution of excess reserve holdings across banks. If
large and small banks face similar (effective) penalty rates and are not too
different in their exposure to late-day payment uncertainty, then the framework
suggests that all banks should hold similar quantities of precautionary reserves.
In other words, for a given level of the interest rate, the difference between
the chosen reserve balances, R, and the requirement, K, should be similar for
all banks. After the payment shocks are realized, of course, some banks will
end up holding excess reserves and others will end up needing to borrow. On
average, however, a large bank and a small one should ﬁnish the period with
comparable levels of excess reserves. If the banking system is composed of
a relatively small number of large banks and a much larger number of small

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Heterogeneity
Panel A
r

Small Banks

r s
P

L
P

Large Banks

sL s s

K-P

K+P

Panel B
r

Low-Variance
Demand
r

HighVariance
Demand
r

K-P

K+P L

K+P H

banks, then the majority of the excess reserves in the banking system will be
held by small banks, simply because there are so many more of them. Even if
large banks hold the majority of total reserve balances because of their larger
requirements, most of the excess reserve balances will be held by small banks.
This implication is broadly in line with the data for the United States.
The Penalty Rate

Another way in which small banks might differ from large ones is the penalty
rate they face if they need to borrow to avoid a reserve deﬁciency. To be

H. M. Ennis and T. Keister: Monetary Policy Implementation

247

eligible to borrow at the discount window, for example, a bank must establish
an agreement with its Reserve Bank and post collateral. This ﬁxed cost may
lead some smaller banks to forgo accessing the discount window and instead
borrow at a very high rate in the market (or pay the reserve deﬁciency fee)
when necessary. Smaller banks may also have fewer established relationships
with counterparties in the fed funds market and, as a consequence, may ﬁnd it
more difﬁcult to borrow at a favorable interest rate late in the day (see Ashcraft,
McAndrews, and Skeie 2007).
S
Suppose small banks do face a higher penalty rate, such as the value rP
L
depicted in Figure 2, Panel A, while larger banks face a lower rate, rP . The
ﬁgure is drawn as if the two banks have the same level of requirements, but
this is done only to make the comparison between the curves clear. The ﬁgure
shows two immediate implications of this type of heterogeneity. First, at
any given interest rate, small banks will hold a higher level of precautionary
reserves, that is, they will choose a larger reserve balance relative to their
level of required reserves. In the ﬁgure, the smaller bank will hold a quantity
SS while the larger bank holds only SL , even though—in this example—both
face the same requirement and the same uncertainty about their end-of-day
balance. As a result, the distribution of excess reserves in the economy will
tend to be skewed even more heavily toward small banks than the earlier
discussion would suggest.
The second implication shown in Figure 2, Panel A is that the demand
curve for small banks has a steeper slope. In an economy with a large number
of small banks, therefore, the aggregate demand curve will tend to be steeper,
meaning that average reserve balances will be less sensitive to changes in the
market interest rate. Notice that this result obtains even though there are no
costs of reserve management in the model.

Support of the Payment Shock

A third way in which banks potentially differ from each other is in the distribution of the late-day payment shock they face. Figure 2, Panel B depicts two
demand curves, one for a bank facing a higher variance of this distribution and
one for a bank facing a lower variance. The ﬁgure shows that having more
uncertainty about the end-of-day reserve position leads to a ﬂatter demand
curve and, hence, a reserve balance that is more responsive to changes in the
interest rate.
In this case, it is not completely clear which curve corresponds better to
large banks and which to small banks. Banks with larger and more complex
operations might be expected to face much larger day-to-day variations in
their payment ﬂows. However, such banks also tend to have sophisticated
reserve management systems in place. As a result, it is not clear whether the
end-of-day uncertainty faced by a large bank is higher or lower than that faced

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by a small bank.9 The effect of the size distribution of banks on the shape of
the aggregate demand curve is, therefore, ambiguous in this case.

Daylight Credit Fees
So far, we have proceeded under the assumption that banks are free to hold
negative balances in their reserve accounts during the day and that no fees
are associated with such daylight overdrafts. Most central banks, however,
place some restriction on banks’ access to overdrafts. In many cases, banks
must post collateral at the central bank in order to be allowed to overdraft their
account. The Federal Reserve currently charges an explicit fee for daylight
overdrafts to compensate for credit risk. We now investigate how reserve
demand changes in the basic framework when access to daylight credit is
costly.
Suppose a bank sends its daytime payment, PD , before receiving the incoming payment. If PD is larger than R (the bank’s reserve holdings), the
bank’s account will be overdrawn until the offsetting payment arrives. Let
re denote the interest rate the central bank charges on daylight credit, δ denote the time period between the two payment ﬂows during the day, and π
denote the probability that a bank sends the outgoing payment before receiving the incoming one. Then the bank’s expected cost of daylight credit is
π re δ (PD − R). This expression shows that an additional dollar of reserve
holdings will decrease the bank’s expected cost of daylight credit by π re δ.
In this way, the terms at which the central bank offers daylight credit can
inﬂuence the bank’s choice of reserve position.10
Figure 3 depicts a bank’s demand for reserves when daylight credit is
costly (that is, when re > 0). The case studied in Figure 1 (that is, when
re = 0) is included in the ﬁgure for reference. It is still true that there will be
no demand for reserves if the market rate is above the penalty rate rP . The
interest rate measured on the vertical axis is (as in all of our ﬁgures) the rate
for a 24-hour loan. If the market rate were above the penalty rate, a bank
would prefer to lend out all of its reserves at the (high) market rate and satisfy
its requirements by borrowing at the penalty rate. By arranging these loans to
settle at approximately the same time on both days, this plan would have no
9 One possibility is that large banks face a wider support of the shock because of their larger
operations, but face a smaller variance because of economies of scale in reserve management. This
distinction cannot be captured in the ﬁgures here, which are drawn under the assumption that the
distribution of the payment shock is uniform. For other distributions, the variance generally plays
a more important role in the analysis than the support.
10 The treatment of overnight reserves can, in turn, inﬂuence the level of daylight credit usage.
See Ennis and Weinberg (2007) for an investigation of this effect in a closely-related framework.
See, also, the discussion in Keister, Martin, and McAndrews (2008).

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249

Figure 3 Daylight Credit Fees
r

No Fee
Positive Fee

rT
re

K-P

K+P

effect on the bank’s daylight credit usage and, hence, would generate a pure
proﬁt.
It is also still true that whenever the market rate is below the penalty
rate, the bank will choose to hold at least K − P reserves, since otherwise
it would be certain to need a discount window loan to meet its requirement.
As the ﬁgure shows, the downward-sloping part of the demand curve is ﬂatter
when daylight credit is costly. For any market interest rate below the discount
rate, the bank will choose to hold a higher quantity of reserves because these
reserves now have the added beneﬁt of reducing daylight credit fees.
Rather than decreasing all the way to the horizontal axis as in Figure 1,
the demand curve now becomes ﬂat at the bank’s expected marginal cost of
intraday funds, π re δ. As long as R is smaller than PD , the bank would not be
willing to lend out funds at an interest rate below π re δ, because the expected
increase in daylight credit fees would be more than the interest earned on the
loan. For values of R larger than PD , the bank is holding sufﬁcient reserves to
cover all of its intraday payments and the demand curve drops to the horizontal
axis.11
11 The analysis here assumes a particular form of daylight credit usage; if an overdraft occurs,
the size of the overdraft is constant over time. Alternative assumptions about the process of daytime
payments would lead to minor changes in the ﬁgure, but the qualitative properties would be largely

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As the ﬁgure shows, when daylight credit is costly, the level of reserves
required to implement a given target rate is higher (S2 rather than S1 in the
diagram). In other words, costly daylight credit tends to increase banks’
reserve holdings. The demand curve is also ﬂatter, meaning that reserve
holdings are more sensitive to changes in the interest rate.

INTEREST RATE VOLATILITY

One of the key determinants of a central bank’s ability to consistently achieve
its target interest rate is the slope of the aggregate demand curve for reserves. In
this section, we describe the relationship between this slope and the volatility
of the market interest rate in the basic framework. The next two sections then
discuss policy tools that can be used to limit this volatility.
While the central bank can use open market operations to affect the supply
of reserves available in the market, it typically cannot completely control this
supply. Payments into and out of the Treasury account, as well as changes in
the amount of cash in circulation, also affect the total supply of reserves. The
central bank can anticipate much of the change in such autonomous factors,
but there will often be signiﬁcant unanticipated changes that cause the total
supply of reserves to be different from what the central bank intended. As
is clear from Figure 1, if the supply of reserves ends up being different from
the intended amount, ST , the market interest rate will deviate from the target
rate, rT .
Figure 4 illustrates the fact that a ﬂatter demand curve for reserves is
associated with less volatility in the market interest rate, given a particular level
of uncertainty associated with autonomous factors. Suppose this uncertainty
implies that, after a given open market operation, the total supply of reserves
will be equal to either S or S in the ﬁgure. With the steeper (thick) demand
curve, this uncertainty about the supply of reserves leads to a relatively wide
range of uncertainty about the market rate. With the ﬂatter (thin) demand
curve, in contrast, the variation in the market rate is smaller. For this reason,
the slope of the demand curve, and those policies that affect the slope, are
important determinants of the observed degree of volatility of the market
interest rate around the target.
As discussed in the previous section, a variety of factors affect the slope
of the aggregate demand for reserves. Figure 4 can be viewed, for example, as
comparing a situation where all banks face relatively little late-day uncertainty
with one where all banks face more uncertainty; the latter case corresponds
unaffected. The analysis also takes the size and timing of payments as given. Several papers have
studied the interesting question of how banks respond to incentives in choosing the timing of their
outgoing payments and, hence, their daylight credit usage. See, for example, McAndrews and
Rajan (2000) and Bech and Garratt (2003).

H. M. Ennis and T. Keister: Monetary Policy Implementation

251

Figure 4 Interest Rate Volatility
r

rH
High
Volatility

Low Volatility

rL
rL

to the thin line in the ﬁgure. However, it should be clear that the reasoning
presented above does not depend on this particular interpretation. The exact
same results about interest rate volatility would obtain if the demand curves had
different slopes because banks face different penalty rates in the two scenarios
or because of some other factor(s). What the ﬁgure shows is that there is a
direct relationship between the slope of the demand curve and the amount of
interest rate volatility caused by forecast errors or other unanticipated changes
in the supply of reserves.
Central banks generally aim to limit the volatility of the interest rate around
their target level to the extent possible. For this reason, a variety of policy
arrangements have been designed in an attempt to decrease the slope of the
demand curve, at least in the region that is considered “relevant.” In the
remainder of the article, we show how some of these tools can be analyzed
in the context of our simple framework. In Section 4 we discuss reserve
maintenance periods, while in Section 5 we discuss approaches that become
feasible when the central bank pays interest on reserves.

RESERVE MAINTENANCE PERIODS

Perhaps the most signiﬁcant arrangement designed to ﬂatten the demand curve
for reserves is the introduction of reserve maintenance periods. In a system

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Federal Reserve Bank of Richmond Economic Quarterly

with a reserve maintenance period, banks are not required to hold a particular
quantity of reserves each day. Rather, each bank is required to hold a certain
average level of reserves over the maintenance period. In the United States,
the length of the maintenance period is currently two weeks.
The presence of a reserve maintenance period gives banks some ﬂexibility
in determining when they hold reserves to meet their requirement. In general,
banks will try to hold more reserves on days in which they expect the market
interest rate to be lower and fewer reserves on days when they expect the rate
to be higher. This ﬂexibility implies that a bank’s reserve holdings will tend to
be more responsive to changes in the interest rate on any given day. In other
words, having a reserve maintenance period tends to make the demand curve
ﬂatter, at least on days prior to the last day of the maintenance period. We
illustrate this effect by studying a two-day maintenance period in the context
of the simple framework. We then brieﬂy explain how the same logic applies
to longer periods.

A Two-Day Maintenance Period
Let K denote the average daily requirement so that the total requirement for
the two-day maintenance period is 2K. The derivation of the demand curve
for reserves on the second (and ﬁnal) day of the maintenance period follows
exactly the same logic as in our benchmark case. The only difference with
Figure 1 is that the reserve requirement will be given by the amount of reserves
that the bank has left to hold in order to satisfy the requirement for the period.
In other words, the reserve requirement on the second day is equal to 2K
minus the quantity of reserves the bank held at the end of the ﬁrst day.
On the ﬁrst day of the maintenance period, a bank’s demand for reserves
depends crucially on its belief about what the market interest rate will be on the
second day. Suppose the bank expects the market interest rate on the second
day to equal the target rate, rT . Figure 5 depicts the demand for reserves on the
ﬁrst day under this assumption.12 As in the basic case presented in Figure 1,
there would be no demand for reserves if the market interest rate were greater
than rP . Suppose instead that the market interest rate on the ﬁrst day is close
to, but smaller than, the penalty rate, rP . Then the bank will want to satisfy as
much of its reserve requirement as possible on the second day, when it expects
the rate to be substantially lower. However, if the bank’s reserve balance after
the late-day payment shock is negative, it will be forced to borrow funds at the
penalty rate to avoid incurring an overnight overdraft. As long as the market
rate is below the penalty rate, the bank will choose a reserve position of at least
−P . Note that this reserve position represents the amount of reserves held by
12 For simplicity, Figure 5 is drawn with no discounting on the part of the bank. The effect
of discounting is very small and inessential for understanding the basic logic described here.

H. M. Ennis and T. Keister: Monetary Policy Implementation

253

Figure 5 A Two-Day Maintenance Period
r

2K-P

2K+P

the bank before the late-day payment shock is realized. Even if this position is
negative, as would be the case when the market rate is close to rP in Figure 5,
it is still possible that the bank will receive a late-day inﬂow of reserves such
that it does not need to borrow funds at the penalty rate to avoid an overnight
overdraft. However, if the bank were to choose a position smaller than −P ,
it would be certain to need to borrow at the penalty rate, which cannot be an
optimal choice as long as the market rate is lower.
For interest rates below rP , but still larger than the target rate, the bank will
choose to hold some “precautionary” reserves to decrease the probability that
it will need to borrow at the penalty rate. This precautionary motive generates
the ﬁrst downward-sloping part of the demand curve in the ﬁgure. As long
as the day-one interest rate is above the target rate, however, the bank will
not hold more than P in reserves on the ﬁrst day. By holding P , the bank is
assured that it will have a positive reserve balance after the late-day payment
shock. If the bank were holding more than P on the ﬁrst day, it could lend
those reserves out at the (relatively high) market rate and meet its requirement
by borrowing reserves on the second day in the event that the interest rate is
expected to be at the (lower) target rate, yielding a positive proﬁt. Hence, the
ﬁrst downward-sloping part of the demand curve must end at P .
Now suppose the ﬁrst-day interest rate is exactly equal to the target rate,
rT . In this case, the bank expects the rate to be the same on both days and is,

254

Federal Reserve Bank of Richmond Economic Quarterly

therefore, indifferent between holding reserves on either day for the purpose
of meeting reserve requirements. In choosing its ﬁrst-day reserve position, the
bank will consider the following issues. It will choose to hold at least enough
reserves to ensure that it will not need to borrow at the penalty rate at the end
of the ﬁrst day. In other words, reserve holdings will be at least as large as the
largest possible payment P .
The bank is willing to hold more reserves than P for the purpose of
satisfying some of its requirement. However, it wants to avoid the possibility of over-satisfying the requirement on the ﬁrst day (that is, becoming
“locked-in”), since it must hold a non-negative quantity of reserves on the
second day to avoid an overnight overdraft. This implies that the bank will
not be willing to hold more than the total requirement, 2K, minus the largest
possible payment inﬂow, P , on the ﬁrst day. The demand curve is ﬂat between
these two points (that is, P and 2K −P ), indicating that the bank is indifferent
between the various levels of reserves in this interval.
Finally, suppose the market interest rate on the ﬁrst day is smaller than the
target rate. Then the bank wants to satisfy most of the requirement on the ﬁrst
day, since it expects the market rate to be higher on the second day. In this case,
the bank will hold at least 2K − P reserves on the ﬁrst day. If it held any less
than this amount, it would be certain to have some requirement remaining on
the second day, which would not be an optimal choice given that the rate will
be higher on the second day. As the interest rate moves farther below the target
rate, the bank will hold more reserves for the usual precautionary reasons. In
this case, the bank is balancing the possibility of being locked-in after the
ﬁrst day against the possibility of needing to meet some of its requirement on
the more-expensive second day. The larger the difference between the rates
on the two days, the larger the quantity the bank will choose to hold on the
ﬁrst day. This trade-off generates the second downward-sloping part of the
demand curve.
The intermediate ﬂat portion of the demand curve in Figure 5 can help
to reduce the volatility of the interest rate on days prior to the settlement
day. As long as movements in autonomous factors are small enough such that
the supply of reserves stays in this portion of the demand curve, interest rate
ﬂuctuations will be minimal. For a central bank that is interested in minimizing
volatility around its target rate, this represents a substantial improvement over
the situation depicted in Figure 1.13
13 It should be noted that Figure 5 is drawn under the assumption that the reserve requirement
is relatively large. Speciﬁcally, K > P is assumed to hold, so that the total reserve requirement for
the period, 2K, is larger than the width of the support of the late-day payment shock, 2P . If this
inequality were reserved, the ﬂat portion of the demand curve would not exist. In general, reserve
maintenance periods are most useful as a policy tool when the underlying reserve requirements
are sufﬁciently large relative to the end-of-day balance uncertainty.

H. M. Ennis and T. Keister: Monetary Policy Implementation

255

There are, however, some issues that make implementing the target rate
through reserve maintenance periods more difﬁcult than a simple interpretation of Figure 5 might suggest. First, the position of the ﬂat portion of the
demand curve at the exact level of the target rate depends on the central bank’s
ability to hit the target rate (on average) on settlement day. If banks expected
the settlement-day interest rate to be lower than the current target, for example,
the ﬂat portion of the ﬁrst-day demand curve would also lie below the target.
This issue is particularly problematic when market participants expect the central bank’s target rate to change during the course of a reserve maintenance
period. A second difﬁculty is that the ﬂat portion of the demand curve disappears on the settlement day and the curve reverts to that in Figure 1.14 This
feature of the model indicates why market interest rates are likely to be more
volatile on settlement days.

Multiple-Day Maintenance Periods
Maintenance periods with three or more days can be easily analyzed in a
similar way. Consider, for example, the case of a three-day maintenance
period with an average daily requirement equal to K. As before, suppose that
the central bank is expected to hit the target rate on the subsequent days of the
maintenance period and consider the demand for reserves on the ﬁrst day. This
demand will be ﬂat between the points P and 3K − P . That is, the demand
curve will be similar to that plotted in Figure 5, but the ﬂat portion will be
wider.
To determine the shape of the demand curve for reserves on the second
day we need to know how many reserves the bank held on the ﬁrst day of
the maintenance period. Suppose the bank held R1 reserves with R1 < 3K.
Then on the second day of the maintenance period, the demand curve for
reserves would be ﬂat between the points P and 3K − R1 − P . Hence, we see
that as the bank approaches the ﬁnal day of the maintenance period, the ﬂat
portion of its demand curve is likely to become smaller, potentially opening the
door to increases in interest rate volatility. For the interested reader, Bartolini,
Bertola, and Prati (2002) provide a more thorough analysis of the implications
of multiple-day maintenance periods on the behavior of the overnight market
interest rate using a model similar to, but more general than, ours.
14 In practice, central banks often use carryover provisions in an attempt to generate a small
ﬂat region in the demand curve on a settlement day. Another alternative would be to stagger the
reserve maintenance periods for different groups of banks. This idea goes back to as early as the
1960s (see, for example, the discussion between Sternlight 1964 and Cox and Leach 1964 in the
Journal of Finance). One common argument against staggering the periods is that it could make
the task of predicting reserve demand more difﬁcult. Whether the beneﬁts of reducing settlement
day variability outweigh the potential costs of staggering is difﬁcult to determine.

256
5.

Federal Reserve Bank of Richmond Economic Quarterly

PAYING INTEREST ON RESERVES

We now introduce the possibility that the central bank pays interest on the
reserve balances held overnight by banks in their accounts at the central bank.
As discussed in Section 1, most central banks currently pay interest on reserves
in some form, and Congress has authorized the Federal Reserve to begin doing
so in October 2011. The ability to pay interest on reserves gives a central bank
an additional policy tool that can be used to help minimize the volatility of
the market interest rate and steer this rate to the target level. This tool can be
especially useful during periods of ﬁnancial distress. For example, during the
recent ﬁnancial turmoil, the fed funds rate has experienced increased volatility
during the day and has, in many cases, collapsed to values near zero late in
the day. As we will see below, the ability to pay interest on reserves allows
the central bank to effectively put a ﬂoor on the values of the interest rate that
can be observed in the market. Such a ﬂoor reduces volatility and potentially
increases the ability of the central bank to achieve its target rate.
In this section, we describe two approaches to monetary policy implementation that rely on paying interest on reserves: an interest rate corridor
and a system with clearing bands. We explain the basic components of each
approach and how each tends to ﬂatten the demand curve for reserves.

Interest Rate Corridors
One simple policy a central bank could follow would be to pay a ﬁxed interest
rate, rD , on all reserve balances that a bank holds in its account at the central
bank.15 This policy places a ﬂoor on the market interest rate: No bank would
be willing to lend reserves at an interest rate lower than rD , since they could
instead earn rD by simply holding the reserves on deposit at the central bank.
Together, the penalty rate, rP , and the deposit rate, rD , form a “corridor” in
which the market interest rate will remain.16
Figure 6 depicts the demand for reserves under a corridor system. As in
the earlier ﬁgures, there is no demand for reserves if the market interest rate is
higher than the penalty rate, rP . For values of the market interest rate below
rP , a bank will choose to hold at least K − P reserves for exactly the same
15 In practice, reserve balances held to meet requirements are often compensated at a different
rate than those that are held in excess of a bank’s requirement. For the daily process of targeting
the overnight market interest rate, the rate paid on excess reserves is what matters; this is the rate
we denote rD in our analysis.
16 A central bank may prefer to use a lending facility that is distinct from its discount window
to form the upper bound of the corridor. Banks may be reluctant to borrow from the discount
window, which serves as a lender of last resort, because they fear that others would interpret this
borrowing as a sign of poor ﬁnancial health. The terms associated with the lending facility could
be designed to minimize this type of stigma effect and, thus, create a more reliable upper bound
on the market interest rate.

H. M. Ennis and T. Keister: Monetary Policy Implementation

257

Figure 6 A Conventional Corridor
r

P
Demand for
Reserves

K-P

K+P

reason as in Figure 1: if it held a lower level of reserves, it would be certain to
need to borrow at the penalty rate, rP . Also as before, the demand for reserves
is downward-sloping in this region. The big change from Figure 1 is that the
demand curve now becomes ﬂat at the deposit rate. If the market rate were
lower than the deposit rate, a bank’s demand for reserves would be essentially
inﬁnite, as it would try to borrow at the market rate and earn a proﬁt by simply
holding the reserves overnight.
The ﬁgure shows that, regardless of the level of reserve supply, S, the
market interest rate will always stay in the corridor formed by the rates rP
and rD . The width of the corridor, rP − rD , is then a policy choice. Choosing
a relatively narrow corridor will clearly limit the range and volatility of the
market interest rate. Note that narrowing the corridor also implies that the
downward-sloping part of the demand curve becomes ﬂatter (to see this, notice
that the boundary points K − P and K + P do not depend on rP or rD ).
Hence, the size of the interest rate movement associated with a given shock
to an autonomous factor is smaller, even when the shock is small enough to
keep the rate within the corridor.
An interesting case to consider is one in which the lending and deposit
rates are set the same distance on either side of the target rate (x basis points
above and below the target, respectively). This system is called a symmetric

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Federal Reserve Bank of Richmond Economic Quarterly

corridor. A change in policy stance that involves increasing the target rate,
then, effectively amounts to changing the levels of the lending and deposit
rates, which shifts the demand curve along with them. The supply of reserves
needed to maintain a higher target rate, for example, may not be lower. In
fact— perhaps surprisingly—in the simple model studied here, the target level
of the supply of reserves would not change at all when the policy rate changes.
If the demand curve in Figure 6 is too steep to allow the central bank to
effectively achieve its goal of keeping the market rate close to the target, a
corridor system could be combined with a reserve maintenance period of the
type described in Section 4. The presence of a reserve maintenance period
would generate a ﬂat region in the demand curve as in Figure 5. The features of
the corridor would make the two downward-sloping parts of the demand curve
in Figure 5 less steep, which would limit the interest rate volatility associated
with events where reserve supply exits the ﬂat region of the demand curve, as
well as on the last day of the maintenance period when the ﬂat region is not
present.
Another way to limit interest rate volatility is for the central bank to set the
deposit rate equal to the target rate and then provide enough reserves to make
the supply, ST , intersect the demand curve well into the ﬂat portion of the
demand curve at rate rD . This “ﬂoor system” has been recently advocated as a
way to simplify monetary policy implementation (see, for example, Woodford
2000, Goodfriend 2002, and Lacker 2006). Note that such a system does
not rely on a reserve maintenance period to generate the ﬂat region of the
demand curve, nor does it rely on reserve requirements to induce banks to
hold reserves. To the extent that reserve requirements, and the associated
reporting procedures, place signiﬁcant administrative burdens on both banks
and the central bank, setting the ﬂoor of the corridor at the target rate and
simplifying, or even eliminating, reserve requirements could potentially be an
attractive system for monetary policy implementation.
It should be noted, however, that the market interest rate will always
remain some distance above the ﬂoor in such a system, since lenders in the
market must be compensated for transactions costs and for assuming some
counterparty credit risk. In other words, in a ﬂoor system the central bank is
able to fully control the risk-free interest rate, but not necessarily the market
rate. In normal times, the gap between the market rate and the rate paid on
reserves would likely be stable and small. In periods of ﬁnancial distress,
however, elevated credit risk premia may drive the average market interest
rate signiﬁcantly above the interest rate paid on reserves. Our simple model
abstracts from these important considerations.17
17 The central bank could also set an upper limit for the quantity of reserves on which it
would pay the target rate of interest to a bank; reserves above this limit would earn a lower
rate (possibly zero). Whitesell (2006) proposed that banks be allowed to choose their own upper

H. M. Ennis and T. Keister: Monetary Policy Implementation

259

Clearing Bands
Another approach to generating a ﬂat region in the demand curve for reserves is the use of daily clearing bands. This approach does not rely on a
reserve maintenance period. Instead, the central bank pays interest on a bank’s
reserve holdings at the target rate, rT , as long as those holdings fall within a
pre-speciﬁed band. Let K and K denote the lower and upper bounds of this
band, respectively. If the bank’s reserve balance falls below K, it must borrow
at the penalty rate, rP , to bring its balance up to at least K. If, on the other
hand, the bank’s reserve balance is higher than K, it will earn the target rate,
rT , on all balances up to K but will earn a lower rate, rE , beyond that bound.
The demand curve for reserves under such a system is depicted in Figure
7. The ﬁgure is drawn under the assumption that the clearing band is fairly
wide relative to the support of the late-day payment shock. In particular, we
assume that K + P < K − P . Let us call the interval K + P , K − P the
“intermediate region” for reserves. By choosing any level of reserves in this
intermediate region, a bank can ensure that its end-of-day reserve balance will
fall within the clearing band. The bank would then be sure that it will earn the
target rate of interest on all of the reserves it ends up holding overnight.
When the market interest rate is equal to the target rate, rT , a bank is
indifferent between choosing any level of reserves in the intermediate region.
For example, if the bank borrows in the market to slightly increase its reserve
holdings, the cost it would pay in the market for those reserves would be exactly
offset by the extra interest it would earn from the central bank. Similarly,
lending out reserves to slightly decrease the bank’s holdings would also leave
proﬁt unchanged. This reasoning shows that the demand curve for reserves
will be ﬂat in the intermediate region between K + P and K − P . As long as
the central bank is able to keep the supply of reserves within this region, the
market interest rate will equal the target rate, rT , regardless of the exact level
of reserve supply.
Outside the intermediate region, the logic behind the shape of the demand
curve is very similar to that explained in our benchmark case. When the market
interest rate is higher than rT , a bank can earn more by lending reserves in
the market than by holding them on deposit at the central bank. It would,
therefore, prefer not to hold more than the minimum level of reserves needed
to avoid being penalized, K. Of course, the bank would be willing to hold
some precautionary reserves to guard against the possibility that the lateday payment shock will drive their reserve balance below K. The quantity of
precautionary reserves it would choose to hold is, as before, an inverse function
of the market interest rate; this reasoning generates the ﬁrst downward-sloping
part of the demand curve in Figure 7.
limits by paying a facility fee per unit of capacity. Such an approach leads to a demand curve
for reserves that is ﬂat at the target rate over a wide region.

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Figure 7 A Clearing Band
r

K-P

K+P

K-P

K+P

When the market rate is below rT , on the other hand, the bank would like
to take full advantage of its ability to earn the target interest rate by holding
reserves at the central bank. It would, however, take into consideration the
possibility that a late-day inﬂow of funds will leave it with a ﬁnal balance
higher than K, in which case it would earn the lower interest rate, rE , on the
excess funds. The resulting decision process generates a downward-sloping
region of the demand curve between the rates rT and rE . As in Figure 6, the
demand curve never falls below the interest rate paid on excess reserves (now
labeled rE ); thus, this rate creates a ﬂoor for the market interest rate.
The demand curve in Figure 7 has the same basic shape as the one generated by a reserve maintenance period, which was depicted in Figure 5. It is
important to keep in mind, however, that the forces generating the ﬂat portion
of the demand curve in the intermediate region are fundamentally different in
the two cases. The reserve maintenance period approach relies on intertemporal arbitrage: banks will want to hold more reserves on days when the
market interest rate is low and fewer reserves when the market rate is high.
This activity will tend to equate the current market interest rate to the expected
future rate (as long as the supply of reserves is in the intermediate region).
The clearing band system relies instead on intraday arbitrage to generate the
ﬂat portion of the demand curve: banks will want to hold more reserves when

H. M. Ennis and T. Keister: Monetary Policy Implementation

261

the market interest rate is low, for example, simply to earn the higher interest
rate paid by the central bank.
The intertemporal aspect of reserve maintenance periods has two clear
drawbacks. First, if—for whatever reason—the expected future rate differs
from the target rate, rT , it becomes difﬁcult for the central bank to achieve the
target rate in the current period. Second, large shocks to the supply of reserves
on one day can have spillover effects on subsequent days in the maintenance
period. If, for example, the supply of reserves is unusually high one day, banks
will satisfy an unusually large portion of their reserve requirements and, as a
result, the ﬂat portion of the demand curve will be smaller on all subsequent
days, increasing the potential for rate volatility on those days.
The clearing band approach, in contrast, generates a ﬂat portion in the
demand curve that always lies at the current target interest rate, even if market
participants expect the target rate to change in the near future. Moreover,
the width of the ﬂat portion is “reset” every day; it does not depend on past
events. These features are important potential advantages of the clearing band
approach. We should again point out, however, that our simple model has
abstracted from transaction costs and credit risk. As with the ﬂoor system discussed above, these considerations could result in the average market interest
rate being higher than the rate rT , as the latter represents a risk-free rate.

CONCLUSION

A recent change in legislation that allows the Federal Reserve to pay interest on
reserves has renewed interest in the debate over the most effective way to implement monetary policy. In this article, we have provided a basic framework
that can be useful for analyzing the main properties of the various alternatives. While we have conducted all our analysis graphically, our simplifying
assumptions permit a fairly precise description of the alternatives and their
effectiveness at implementing a target interest rate.
Many extensions of our basic framework are possible and we have analyzed several of them in this article. However, some important issues remain
unexplored. For example, we only brieﬂy mentioned the difﬁculties that ﬂuctuations in aggregate credit risk can introduce in the implementation process.
Also, as the debate continues, new questions will arise. We believe that the
framework introduced in this article can be a useful ﬁrst step in the search for
much-needed answers.

262

Federal Reserve Bank of Richmond Economic Quarterly

REFERENCES
Ashcraft, Adam, James McAndrews, and David Skeie. 2007. “Precautionary
Reserves and the Interbank Market.” Mimeo, Federal Reserve Bank of
New York (July).
Bartolini, Leonardo, Giuseppe Bertola, and Alessandro Prati. 2002.
“Day-To-Day Monetary Policy and the Volatility of the Federal Funds
Interest Rate.” Journal of Money, Credit, and Banking 34 (February):
137–59.
Bech, M. L., and Rod Garratt. 2003. “The Intraday Liquidity Management
Game.” Journal of Economic Theory 109 (April): 198–219.
Clouse, James A., and James P. Dow, Jr. 2002. “A Computational Model of
Banks’ Optimal Reserve Management Policy.” Journal of Economic
Dynamics and Control 26 (September): 1787–814.
Cox, Albert H., Jr., and Ralph F. Leach. 1964. “Open Market Operations and
Reserve Settlement Periods: A Proposed Experiment.” Journal of
Finance 19 (September): 534–9.
Coy, Peter. 2007. “A ‘Stealth Easing’ by the Fed?” BusinessWeek.
http://www.businessweek.com/investor/content/aug2007/
pi20070817 445336.htm [17 August].
Dotsey, Michael. 1991. “Monetary Policy and Operating Procedures in New
Zealand.” Federal Reserve Bank of Richmond Economic Review
(September/October): 13–9.
Ennis, Huberto M., and John A. Weinberg. 2007. “Interest on Reserves and
Daylight Credit.” Federal Reserve Bank of Richmond Economic
Quarterly 93 (Spring): 111–42.
Goodfriend, Marvin. 2002. “Interest on Reserves and Monetary Policy.”
Federal Reserve Bank of New York Economic Policy Review 8 (May):
77–84.
Guthrie, Graeme, and Julian Wright. 2000. “Open Mouth Operations.”
Journal of Monetary Economics 46 (October): 489–516.
Hilton, Spence, and Warren B. Hrung. 2007. “Reserve Levels and Intraday
Federal Funds Rate Behavior.” Federal Reserve Bank of New York Staff
Report 284 (May).
Keister, Todd, Antoine Martin, and James McAndrews. 2008. “Divorcing
Money from Monetary Policy.” Federal Reserve Bank of New York
Economic Policy Review 14 (September): 41–56.

H. M. Ennis and T. Keister: Monetary Policy Implementation

263

Lacker, Jeffrey M. 2006. “Central Bank Credit in the Theory of Money and
Payments.” Speech. http://www.richmondfed.org/news and speeches/
presidents speeches/index.cfm/2006/id=88/pdf=true.
McAndrews, James, and Samira Rajan. 2000. “The Timing and Funding of
Fedwire Funds Transfers.” Federal Reserve Bank of New York
Economic Policy Review 6 (July): 17–32.
Poole, William. 1968. “Commercial Bank Reserve Management in a
Stochastic Model: Implications for Monetary Policy.” Journal of
Finance 23 (December): 769–91.
Sternlight, Peter D. 1964. “Reserve Settlement Periods of Member Banks:
Comment.” Journal of Finance 19 (March): 94–8.
Whitesell, William. 2006. “Interest Rate Corridors and Reserves.” Journal of
Monetary Economics 53 (September): 1177–95.
Woodford, Michael. 2000. “Monetary Policy in a World Without Money.”
International Finance 3 (July): 229–60.

Economic Quarterly—Volume 94, Number 3—Summer 2008—Pages 265–300

CEO Compensation:
Trends, Market Changes,
and Regulation
Arantxa Jarque

ompensation ﬁgures for the top managers of large ﬁrms are on the
news frequently. Newspapers report the salaries, the bonuses, and the
proﬁts from selling stock options of the highest paid executives, often
under headlines suggesting excessive levels of pay or a very weak relation of
pay to the performance of the ﬁrms.1 Especially after the fraud scandals at
Enron and other important corporations around the world, executive performance and pay have been carefully scrutinized by the public.
Academic economists, however, have long ago recognized the importance
of understanding the issues involved in determining executive pay and have
been studying them for decades. In short, the main economic problem behind
executive compensation design is that ﬁrm owners need to align the incentives
of the executives to their own interests—typically to maximize ﬁrm value.
To achieve this alignment, the compensation of the manager is usually made
contingent on the performance of the ﬁrm. While in the largest ﬁrms executive
compensation typically represents a small fraction of the total ﬁrm value, the
decisions that a top executive makes can be potentially important for ﬁrm
performance. Therefore, the way in which the dependence of compensation
on ﬁrm performance is structured can have a signiﬁcant impact on the added
value that the executive brings to the ﬁrm. There is by now a large body
of academic studies that document practices in executive pay and study the
The author would like to thank Brian Gaines, Borys Grochulski, Leornardo Martinez, and John
Weinberg for helpful comments. Jarque is an assistant professor at the Universidad Carlos III
de Madrid. This article was written while the author was a visiting economist at the Federal
Reserve Bank of Richmond. The views expressed in this article do not necessarily represent
the views of the Federal Reserve Bank of Richmond or the Federal Reserve System. E-mail:
ajarque@eco.uc3m.es.
1 Some recent examples, following the release of an Associated Press study for 2007, include
Beck and Fordahl (2008a, 2008b) and Associated Press (2008).

266

Federal Reserve Bank of Richmond Economic Quarterly

optimal design of compensation contracts. Some of the most important and
recent ﬁndings in the literature are summarized in this article.
In Section 1, I present the various instruments commonly used to compensate executives and the main empirical regularities about executive pay. Over
the last two decades, the average pay of a chief executive ofﬁcer (CEO) working in one of the 500 largest ﬁrms in the United States has increased six-fold.
This increase has occurred simultaneously with a change in the composition
of pay of these CEOs, moving away from salary and increasingly toward
performance-based compensation in the form of stock grants and stock option
grants. This shift has resulted in a clear increase in the sensitivity of the total
pay of CEOs to the performance of their ﬁrms. Although the increase in the
level and the sensitivity are most likely related, I separate the discussion into
two sections for a more detailed exposition of the evidence and a discussion
of possible explanations.
In Section 2, I summarize how the level of pay has evolved since 1936.
Then I brieﬂy review some of the explanations in the academic literature for
the sharp increase in the last two decades. I focus on a recent strand of the
literature that has built on ideas from the classic papers of Lucas (1978) and
Rosen (1981, 1982) that model ﬁrms’ competition for the scarce talent of
managers. These studies argue that the sharp increase in ﬁrm size and value
of the last decades could be important to explain the six-fold increase in the
level of CEO pay over the same period.
In Section 3, I focus on how the pay of CEOs depends on their performance. I introduce several measures of sensitivity of the CEO’s pay to the
results of the ﬁrm that are widely used in the literature. The empirical studies
provide a wide range of estimates for sensitivity, but there is consensus about
two facts: an increase in sensitivity over the last two decades and a negative
relation of sensitivity with ﬁrm size (as measured by market capitalization
value). I discuss some of the recent explanations for these regularities. Many
of the explanations are based on studying the interaction between the manager and the owners of the ﬁrm as a moral hazard problem. In the model,
shareholders minimize the cost of bringing the (risk averse) CEO to exert
an unobservable effort that improves the results of the ﬁrm. This analysis is
typically performed in partial equilibrium and aims to describe the form of
optimal compensation contracts, i.e., the optimal sensitivity of pay to ﬁrm
performance. Some recent studies suggest that a seemingly low sensitivity
of pay to performance, as well as the negative relation between sensitivity
of pay and ﬁrm size, could be features of dynamic optimal contracts that are
used to solve the moral hazard problem. Also in this moral hazard framework,
several recent articles demonstrate the efﬁciency of some seemingly unintuitive pay practices that are often discussed by the media, such as bonuses
in bad earning years or repricing of out-of-the-money options. The level of
market competition across ﬁrms, as well as the relative demand of general

A. Jarque: CEO Compensation

267

versus ﬁrm-speciﬁc skills, has also been shown to be empirically signiﬁcant
in explaining pay trends.
In Section 4, I describe the main regulatory changes affecting executive
compensation in the last 15 years: changes in personal, corporate, and capital
gains taxes; new limits on the deductibility of CEO pay expenses that favor
performance-based compensation; an increase in the disclosure requirements
about CEO pay; a standardization of the expensing of option grants; and
several initiatives fostering shareholders’ activism and independence of the
board of directors. Amidst the headlines on excessive pay, the popular press
has been debating these changes in regulation, their potential role in the recent
rise in pay, and the need for new government intervention.2
To shed some light on the role of regulation, I review the ﬁndings of
academic studies that have rigorously tried to quantify the effect of several
speciﬁc measures on the level and sensitivity of compensation. As it turns out,
these studies ﬁnd little evidence of a sizable effect on pay practices coming
from tax advantages or salary caps. Following the main regulatory changes,
some studies ﬁnd evidence of a small shift of compensation from salaries
and bonuses toward performance-based compensation (stocks and options),
which translates into a slight increase in the sensitivity of pay to performance.
Better corporate governance and the increase in the proportion of institutional
shareholders appear to be associated with higher company returns and higher
incentives for CEOs. This suggests that regulation efforts to improve corporate
governance and transparency have been moving in the right direction, although
it is difﬁcult to evaluate the relative importance of regulation versus the marketinduced changes in governance practices.
Designing executive compensation packages is, no doubt, complicated.
Judging the appropriateness of those packages is, consequently, a very difﬁcult task in which models and sophisticated econometric tools are a necessity. I now proceed to review the most recent attempts at this task and their
conclusions.

UNDERSTANDING AND MEASURING CEO
COMPENSATION

Today companies pay their top executives through some or all of the following
instruments: a salary, a bonus program, stock grants (usually with restrictions
2 On one hand, in the most recent special report on CEO compensation published by the
Wall Street Journal (2008), one of the articles is dedicated to the unintended consequences of
regulation changes. On the other hand, the “say on pay” proposals, which seek to force boards
of directors to have a (nonbinding) vote on the compensation plan that they design for a CEO,
have been receiving particular attention in the press—see The Economist (2008b, “Pay Attention”)
on the recent trend of pay in Europe and the regulation responses of some European governments,
and The Economist (2008a, “Fair or Foul”) on the “say on pay” proposals both in Europe and
the United States, which cites both U.S. presidential candidates as being in favor of forcing the
shareholders’ vote.

268

Federal Reserve Bank of Richmond Economic Quarterly

on the ability to sell them), grants of options on the stock of the ﬁrm, and
long-term incentive plans that specify retirement and severance payments, as
well as pension plans and deferred beneﬁts. The most accepted explanation
for these variable compensation instruments is the existence of a moral hazard
problem: The separation of ownership and control of the ﬁrm implies the need
to provide incentives to the CEO that align his interests with those of the ﬁrm
owners. In the presence of moral hazard, the optimal contract prescribes that
the pay of the executive should vary with the results of the ﬁrm. However,
in spite of the need for incentives, limited funds on the part of CEOs or
risk aversion considerations imply that exposing the CEO to the same risk as
shareholders is typically either an unfeasible or inefﬁcient arrangement. The
optimal contract should balance incentives and insurance. Therefore, part of
the compensation should be variable and could be provided through stock
or stock options, while part of the compensation, such as the annual salary,
should not be subject to risk, providing some insurance to the CEO against
bad ﬁrm performance due to factors that he cannot control.
Data on the level of annual compensation of workers classiﬁed as CEOs
are available from the Bureau of Labor Statistics (BLS). These are wages
representative of the whole economy. However, details are not available on
the speciﬁc forms of the contract (i.e., the compensation instruments that
were used in providing that compensation). Data from the BLS show that
the average CEO earns an annual wage of $151,370 (May 2007)—less than
the average doctor (internist) and about $25,000 more per year than a lawyer.
The annual wage of the average CEO today is about 3.5 times that of the
average worker in the economy, and the evolution of this comparison over
the last seven years has followed a similar pattern as that of other white-collar
professions. However, the distribution of wages of CEOs is extremely skewed.
Figure 1 shows the evolution of the total level of pay for the CEOs of the 500
largest ﬁrms in the economy, according to the ﬁgures in Forbes, a magazine
that publishes surveys of top CEO pay annually. The average annual wage of
this sample of executives in 2007 was about $15 million, approximately 300
times that of the average worker in the U.S. economy.
For the top 500 ﬁrms, information about CEO pay is readily available.
Since these companies are public, they ﬁle their proxy statements with the
Securities and Exchange Commission (SEC), making their reports on their top
executives’compensation public. Most academic studies restrict themselves to
studying the compensation of the CEOs in this subsample of ﬁrms. Therefore,
I too concentrate on this subsample in the rest of the article. From this point
on, the acronym “CEO” refers to the chief executive ofﬁcer of one of the top
500 ﬁrms in the United States.
Figure 1 also shows the evolution of the three main components of CEO
pay from 1989 to 2007. Stock gains refers to the value realized during the
given ﬁscal year by exercising vested options granted in previous years. The

A. Jarque: CEO Compensation

269

Figure 1 Compensation Data Based on Forbes Magazine’s Annual
Survey (2007 Constant Dollars)
16
Salary and Bonus
Stock Gains

4.4

Other Compensation
12

$ Millions

4.1 3.2

3.2
1.3

1.9

2.2

1.3

1.3
1.1
0.6 0.7

4
0.2 0.2

0.5 0.4

0.7
0.6

2.2

7.5
6.3 7.4 1.3

1.7

5.9

6.3

6.3
5

3.2

3.1

1.2

1.8 1.7

0.6
3.3
3.3 3.5 3.6 3.3
2.6 2.6 2.9
2.2 2.1 2.1 2.6
1.6 1.8 1.9
1.5 1.5 1.5 1.4 1.5

2 0.6 0.6 0.6 0.8
0
1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

gain is the difference between the stock price on the date of exercise and the
exercise price of the option. Other compensation includes long-term incentive
payouts and the value realized from vesting of restricted stock and performance
shares, and other perks such as premiums for supplemental life insurance,
annual medical examinations, tax preparation and ﬁnancial counseling fees,
club memberships, security services, and the use of corporate aircraft. The
main trend that we observe in this ﬁgure is that, although annual salaries have
been increasing, the proportion of total pay that they represent has decreased
in the last 20 years, while compensation through options has become the most
important component, increasing from a low of 35 percent to 77 percent. The
total levels of pay have risen six-fold.3
The shift of compensation practices toward options and restricted stocks
has one immediate implication: the total compensation of the CEO is now
3 The data is from Forbes magazine’s annual survey. Prior to 1992, the data on options is
a record of the gains from exercise. After 1992, Forbes records the value of the option grants at
the date of granting, using the valuation method that the ﬁrm uses in its proxy statement. This
method is mostly the Black and Scholes formula, for which the company reports the parameters
as established in the SEC disclosure rules of 1993. See Section 4 of this article on regulation.
Also, note that good data on pensions is not available and most studies leave it out of their
analysis.

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 2 Annual Compensation (Forbes Magazine) and Dow Jones
Industrial Average During the Previous Year
16

Total Compensation
Dow Jones Industrial Average (Monthly)

14,000

12,000

$ Millions

10,000
10
8,000
8
6,000
6
4,000
4
2,000

2007

2005

2006

2004

2003

2001

2002

2000

1999

1998

1996

1997

1995

1993

1994

1991

1990

1989

1988

1992

more closely tied to the performance of the ﬁrm than it was in the 1980s.
In Figure 2, I plot the Forbes measure of total compensation from Figure 1,
together with the Dow Jones Industrial Average during the previous year, as
an approximation for the average performance of the ﬁrms managed by the
CEOs included in the compensation surveys. Apparently, on average, the
compensation of top CEOs is closely correlated with the performance of the
top ﬁrms that they manage. A more detailed analysis is needed to determine
this relation at the individual ﬁrm level. In the next two sections, I review the
empirical literature that has performed a detailed analysis, documenting the
trends in the level and sensitivity of pay. In a widely cited paper, Jensen and
Murphy (1990a) studied changes in compensation facts from 1974 to 1986.
Following this paper, many studies on pay have been published. Rosen (1992)
provided a ﬁrst survey of the empirical ﬁndings on CEO compensation and
Murphy (1999) is a very complete survey of the literature in the 1990s. The
general picture, according to the most recent studies, is that the rates of growth
in the level of CEO pay have increased dramatically since the 1980s, but pay
has become, over the same period, more closely linked to ﬁrm performance.
I present the evidence in two separate sections, one focusing on the level
of pay and one on the sensitivity of pay—although, as will become clear

A. Jarque: CEO Compensation

271

Table 1 Median CEO Pay

Period
1936–1939
1940–1945
1946–1949
1950–1959
1960–1969
1970–1979
1980–1989
1990–1999
2000–2005

Median CEO Pay
(Million $)
1.11
1.07
0.90
0.97
0.99
1.17
1.81
4.09
9.20

Avg. Annual
Growth Rate
−0.01
−0.04
0.01
0.00
0.02
0.04
0.08
0.14

Source: Frydman and Saks (2007). CEO pay is in constant year 2000 dollars.

from the discussion, the two features are related through risk and incentive
considerations.

2. THE LEVEL OF PAY
The bulk of the literature on CEO compensation (see Jensen, Murphy, and
Wruck 2004; Frydman and Saks 2007; Gabaix and Landier 2008) has documented that, after moderate rates of growth in the 1970s, CEO pay rose much
faster in the most recent decades. Total compensation reached a median value
of $9.20 million (in 2000 constant dollars) in 2005. Frydman and Saks (2007)
present previously unavailable historical evidence starting in the 1930s. They
ﬁnd that compensation decreased sharply after World War II and it had a modest rate of growth of about 0.8 percent for the following 30 years. Hence,
the recent growth in pay (see Table 1 and Figure 1), with annual growth rates
above 10 percent in the period 1998–2007, represents a remarkable change
from previous trends.
In the ﬁrst subsection, I review some estimations of the relevance and
appropriateness of the levels of CEO pay that we observe today. I follow with
a subsection on the proposed explanations for the time trends of the level of
pay in the last century, which are divided into two groups: theories based on
competitive markets and optimal contracts and theories based on inefﬁcient
practices.

Are Today’s Levels of Pay Justiﬁed?
According to some recent studies, the cost of CEO compensation for ﬁrms may
not be so economically signiﬁcant. However, the economic consequences of
not providing the right incentives appear to be potentially large. Gabaix and

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Federal Reserve Bank of Richmond Economic Quarterly

Landier (2008), for example, report an average value of CEO pay over ﬁrm
earnings of 0.5 percent during the period 1992–2003. Margiotta and Miller
(2000), relying on a moral hazard model and historical data on compensation
contracts of 34 ﬁrms from 1948 to 1977, ﬁnd that companies beneﬁt highly
from providing the right level of incentives (ranging from $83 million to $263
million in 1977 dollars, depending on the industry). The observed contracts in
their sample, however, imply a modest cost of providing incentives to induce
high effort (about $0.5 million in 1967 dollars).4 More recently, Bennedsen,
P´ rez-Gonz´ lez, and Wolfenzon (2007) use data from Danish ﬁrms from 1992
e
a
to 2003 to estimate the effect of the CEO’s death on ﬁrm performance. They
ﬁnd that the industry-adjusted operating returns on assets decrease by 1.7
percent following the absence of the CEO. They also report a decrease of 0.7
percent after a close family member of the CEO passes away. Both measures
indicate the importance of CEO input into the performance of the ﬁrm, either
through effort, talent, or both. Using a competitive model, Tervi¨ (2008)
o
estimates the talent distribution for CEOs and ﬁnds that if the managers of
the 1,000 largest U.S. companies in 2004 had been substituted by a CEO of
the same talent as that of the 1,000th company, the combined value of those
companies would have been between $21.3 billion and $25 billion lower. His
calculations imply that the contribution of the talented CEOs (net of pay) was
between $16.9 billion and $20.6 billion (approximately 15 percent of the total
market capitalization of the largest 1,000 ﬁrms), while the combined payments
to the 1,000 CEOs that year were $7.1 billion.

Explanations for the Increase in the Level of Pay
The widely documented increase in the level and sensitivity of pay in the past
two decades has motivated research efforts to construct robust explanations
for these trends. Gabaix and Landier (2008) argue in a recent inﬂuential article
that the six-fold increase in pay since the 1980s can be explained by the six-fold
increase in the market value of U.S. ﬁrms in the same period. Building on work
by Lucas (1978) and Rosen (1981, 1982), Gabaix and Landier’s model presents
a competitive economy in which ﬁrms compete for a manager’s talent.5 In
their characterization of the equilibrium, they show that the wage of the CEO
increases both with the size of the ﬁrm and the average size of the ﬁrm in
the economy. Using extreme value theory, they calibrate the distribution for
a manager’s talent and combine this with a calibration of the size distribution
of ﬁrms. Their results are consistent with the ﬁndings of Tervi¨ (2008), who
o
4 Margiotta and Miller (2000) use exponential utility speciﬁcations in their empirical estimations, for which incentive considerations are independent of the level of wealth.
5 See Prescott (2003) for a related model.

A. Jarque: CEO Compensation

273

independently used a competitive model to estimate the distribution of CEO
talent that does not rely on extreme value theory.
Although the model in Gabaix and Landier (2008) can explain trends in
CEO compensation since the 1980s, recent evidence in Frydman and Saks
(2007) challenges their hypothesis for earlier periods. Frydman and Saks
provide a comprehensive empirical account of the evolution of CEO pay in
the last century. Their database includes previously unavailable data for the
period 1936–1992, hand-collected from the 10-K ﬁlings of ﬁrms with the SEC.
They study an unbalanced panel of 101 ﬁrms, selected for being the largest
according to market value at three different dates. They ﬁnd, consistent with
previous work, that the increase in CEO pay was moderate in the 1970s and
picked up in the last three decades. However, their new historical evidence
starting in the 1930s shows that prior to the mid-1970s, while the level of
pay was positively correlated with the relative size ranking of the ﬁrm in the
economy, the correlation between changes in the market value of ﬁrms and the
changes in the level of compensation was very weak. In particular, their data
shows that CEO pay was stagnant from the 1940s until the 1970s, a period
during which there was considerable growth of ﬁrms—particularly during the
1950s and 1960s.
Some authors in the literature have departed from the usual modeling
approach by proposing that the observed contracts are in fact suboptimal. The
following are three representative proposals of this sort.
Misperception of the Cost of Options

Murphy (1999) and Jensen, Murphy, and Wruck (2004) have argued that the
signiﬁcant increase in the use of option grants in recent years can be explained
in part by the fact that compensation boards do not correctly valuate the cost
of granting options. They argue that the tax and accounting advantages of
options make it an attractive method of compensation.6 They claim that, in
fact, options are an expensive way of compensating the CEO: risk aversion,
combined with the impossibility of hedging, as well as the high percentages
of human and monetary wealth that CEOs invest in their own ﬁrm, and the
positive probability of being unable to exercise the options if they are ﬁred
before the options become vested, all imply that managers ought to demand a
high risk premium for the options. Thus, while ﬁrms are experiencing a cost
that is well approximated by the Black-Scholes value of the grants disclosed in
the proxy statements and listed in the executive compensation databases, CEOs
highly discount their value. Hall and Murphy (2002) explicitly model these
issues and provide calculations on how the CEO’s risk aversion inﬂuences the
6 Recent changes in regulation extend the expensing requirements to grants that have an
exercise price equal to or above the market price at the time of granting.

274

Federal Reserve Bank of Richmond Economic Quarterly

valuation of the stock grants. They ﬁnd that the increase of “risk-adjusted”
pay from 1992 to 1999 has not been nearly as dramatic as that of total pay
ﬁgures taken at face value.
Ratchet Effect

Murphy (1999) provides a description of how ﬁrms decide on the annual option
grant to be awarded to executives. He points to the fact that ﬁrms typically use
a measure of the average compensation given to executives in a peer group for
reference. His data also indicates that 40 percent of ﬁrms have compensation
plans that specify the number of options to be granted, ﬁxed for several years,
as opposed to the value of the options. In times of a growing stock market,
such as the late 1990s, these two compensation practices together would result
in a “rachet effect”—an escalation in total pay based on mutual benchmarking,
as opposed to rewarding exceptional performance of the individual CEOs.
Entrenchment

Bebchuck and several coauthors (see, for example, Bebchuck and Fried [2003,
2004] and references therein) have argued that there is ample evidence suggesting that executives control the boards of directors and effectively determine
their own pay. Kuhnen and Zwiebel (2008) provide a formal model of this
hypothesis, which presents the problem of the manager maximizing his own
pay subject to an “acceptable” outrage level of the shareholders. The mainstream literature accepts that some incentive problems remain unsolved given
the current compensation and corporate practices in effect (see Holmstr¨ m and
o
Kaplan 2003 or Jensen, Murphy, and Wruck 2004). Yet, there is no consensus
on whether the entrenchment model is a better description of real life than the
classic moral hazard model, which has shareholders maximizing their value
subject to the incentive constraints of CEOs (see Grossman and Hart 1983). It
is also worth noticing that the entrenchment explanation per se does not help
in understanding the upward trend in the level of pay observed in the last 15
years, since corporate governance practices have been improving during this
period (see Holmstr¨ m and Kaplan 2003).
o

3. THE SENSITIVITY OF PAY TO PERFORMANCE
The literature on CEO compensation uses the term “sensitivity of pay to performance” to refer to the changes in the total pay of a CEO that are implied by
a given measure of the performance of the ﬁrm. The most common measure
of ﬁrm performance used in the empirical estimations of the sensitivity of pay
is the change in the value to shareholders, i.e., stock price change. Theoretical
studies based on moral hazard models have shown that the design of the optimal compensation scheme is a complicated task. The way in which the level

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of risk aversion of undiversiﬁed CEOs decreases with their wealth (which may
originate both from their ﬁrm pay and from outside sources), for example, has
not been well established empirically (Haubrich 1994). Also, ﬁnding empirical evidence on the parameters of the model is difﬁcult: How does the hidden
action of the CEO affect the results of the ﬁrm and how costly is this action
to the CEO? These considerations make it difﬁcult to assess quantitatively the
optimal sensitivity of direct pay. Moreover, the sensitivity itself is difﬁcult to
estimate empirically, since the pay of the CEO changes with ﬁrm performance
both through direct and indirect channels: The competition for talented CEOs
in the market, for example, implies that career concerns and the risk of being
ﬁred impose some incentives on the executives that are not captured by their
compensation contracts.
In the ﬁrst subsection, I review the academic work that attempts to quantify
the incentives provided through direct pay. In the second subsection, I review
the work that quantiﬁes incentives through indirect pay, consisting mainly
of studies that document historical trends of the probability of employment
termination for CEOs. Although there is no agreement in the literature about
the right measure of sensitivity, two stylized facts are widely accepted: total
(direct plus indirect) sensitivity of pay has been increasing in the last two
decades and sensitivity is negatively correlated with ﬁrm size. In the third
subsection, I review some of the proposed explanations for these stylized
facts, as well as several models that justify the diversity of instruments in real
life compensation packages.

Sensitivity of Direct Pay
In an inﬂuential paper, Jensen and Murphy (1990a) point out the seemingly
low sensitivity of executive pay to performance: an increase in total wealth of
$3.25 for each $1,000 of increase in the ﬁrm value. This measure of sensitivity
is, in the data, highly negatively correlated with the size of the ﬁrm. As an
alternative that allows for variation of the Jensen and Murphy (1990a) measure
across ﬁrm size, other studies have estimated the elasticity of pay to ﬁrm
performance. For both measures, a sharp increase in the sensitivity of pay
over the last two decades has been widely documented: estimations suggest
an increase in sensitivity of more than ﬁve times over that period.
I now describe in detail each of the two measures and the main ﬁndings,
including a discussion of the regularities with respect to ﬁrm size.
The Jensen-Murphy Statistic

Jensen and Murphy (1990a) use data on compensation of approximately 2,000
CEOs of large corporations collected by Forbes magazine from 1974 to 1986.
In their paper, they focus on a particular measure of pay sensitivity to

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performance: They estimate how a $1,000 change in the value of a ﬁrm translates into dollar changes in the wealth of its CEO. This measure of sensitivity
is often reported in the literature as the Jensen-Murphy statistic.
In their paper, they run regressions of the form
w = α + β ( V ) + θ (CON T ROLS) ,

(1)

where V includes lagged as well as contemporaneous measures of changes
in the dollar value of the ﬁrm. They report that the median CEO in their
sample experiences an increase in his total wealth of $3.25 for each $1,000
of increase in the value of the ﬁrm he manages. Of this change in wealth, 2
cents correspond to year-to-year changes in salary and bonus, while the rest is
because of changes in the value of the stock and option holdings of the CEO,
the effect of performance on future wages and bonus payments, and the wealth
losses associated with variations in the probability of dismissal. The authors
qualify this sensitivity of pay as “low” and inconsistent with the predictions of
any agency model. Murphy (1999) updates these estimates using Execucomp
data up to 1996 and reports an increase in the sensitivity of pay to $6 per
$1,000 by that year.
Garen (1994) and Haubrich (1994) point out that the seemingly low estimates of Jensen and Murphy are consistent with optimal incentives in the
presence of moral hazard if the right parameters of risk aversion are chosen
for the speciﬁc functional forms. Garen (1994) presents a static moral hazard
model with closed forms solutions and, as an alternative test for the theory,
derives comparative static predictions, which do not rely on the particular
values of parameters and are more robust to functional form speciﬁcations.
He concludes that most implications of moral hazard are consistent with the
data. In the same spirit, Wang (1997) provides a computed solution to a dynamic agency (repeated moral hazard) model that, under a reasonable range
of parameters, is able to replicate the low sensitivity of pay results in Jensen
and Murphy (1990a). The model shows that deferred compensation is sometimes a more efﬁcient way of providing incentives than current pay because
of incentive-smoothing over time.
Changes in Sensitivities with Firm Size

The Jensen-Murphy statistic has been documented to be very different across
different ﬁrm size subsamples: Jensen and Murphy (1990a) divide their sample according to market value and ﬁnd a total pay sensitivity value of $1.85
for the subsample of larger ﬁrms versus $8.05 for that of smaller ﬁrms.7 Updates of this measure provided in Murphy (1999) suggest that the increase in
median pay sensitivity from 1992 to 1996 was a lot higher for large ﬁrms than
7 See, also, Jensen and Murphy (1990b).

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for smaller ones (64 percent [from $2.65 to $4.36] for the largest half of the
S&P 500, 5 percent [from $7.33 to $7.69] for the smallest half of the S&P
500, 28 percent [from $12.04 to $15.38] for the S&P Mid-Cap corporations,
and 24 percent [from $22.84 to $28.23] for the S&P Small-Cap corporations).
Garen (1994) also ﬁnds a negative relationship between sensitivity of pay and
ﬁrm size. Schaefer (1998) ﬁnds that the Jensen and Murphy (1990a) measure
is approximately inversely proportional to the square root of ﬁrm size. Recent
estimations of this measure use quantile regressions to prevent estimations
from being driven by big ﬁrms in the samples.8
The literature agrees that the Jensen-Murphy measure is adequate for ﬁrms
in which the marginal effect of effort is independent of ﬁrm size. However,
it has been repeatedly pointed out that it does not correctly capture incentives
when the marginal product increases with ﬁrm size. Baker and Hall (2004)
propose a model that relates compensation to the marginal product of the CEO.
They conﬁrm the previous estimates of decreasing sensitivity of pay to ﬁrm
size and they identify higher marginal products of CEOs working in bigger
ﬁrms as the main cause.9 Their model implies that, although the Jensen and
Murphy (1990a) measure of sensitivity falls sharply with ﬁrm size, the total
incentives of CEOs remain constant or fall only slightly since the effect of
CEOs’ actions increases with ﬁrm size. A similar assumption is used in the
competitive market model of Edmans, Gabaix, and Landier (forthcoming), in
which the effort cost for the CEO is bounded above, but his marginal impact
depends on the size of the ﬁrm he manages.
Elasticity of Pay to Firm Value

An alternative measure of sensitivity of pay is the elasticity of compensation
to performance: the percent increase in executive wealth for a 1 percent improvement in the performance of the ﬁrm. Note that assuming a constant
elasticity across ﬁrms implies variation in the Jensen-Murphy statistic across
ﬁrm sizes.
A convenient way of estimating the elasticity of pay to ﬁrm performance
is to regress the logarithm of earnings on the return of the ﬁrm’s stock:
ln wt = a + b × rt .

(2)

Then b = d(ln w)/dr measures the semi-elasticity of earnings to ﬁrm value
and the elasticity is recovered for each particular return value as approximately b = r b. Initial estimates of the semi-elasticity of cash compensation
(salary and bonus) to stock returns, surveyed in Rosen (1992), had reported
8 See, for example, Murphy (1999) and Frydman and Saks (2007).
9 This is consistent with the hypothesis that more talented CEOs work for bigger ﬁrms, as

mentioned in Rosen (1992). See, also, the competitive market for talent models of Gabaix and
Landier (2008) and Tervi¨ (2008) reviewed later in this article.
o

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a median value for b of about 0.10—an increase in a ﬁrm’s return of 10
percent ( r = 0.1) implies a 1 percent increase in pay.10 Using average values for w and r, Rosen (1992) reports that these semi-elasticity values imply a
Jensen-Murphy statistic for cash compensation (salary plus bonus) of 10 cents,
compared with their ﬁnding of 2 cents.11 He concludes that lower sensitivities of pay at bigger ﬁrms probably inﬂuence the Jensen-Murphy estimation,
especially since they do not log the compensation ﬁgures.
Hall and Liebman (1998) provide estimates of the elasticity of compensation using detailed data on CEO pay from 1980 to 1994. To correctly estimate
the elasticity and several other measures of sensitivity of pay (including the
Jensen-Murphy statistic), they collect data on stock and options grants from
the proxy statements of ﬁrms. They construct the portfolio of stock and options for each CEO in their databases in 1994: This way they can include
in their measure of total pay the variation in the wealth of the CEO because
of the changes in the price of the ﬁrm’s stock.12 Also, they can evaluate the
potential changes in wealth for different realizations of the stock price (the ex
ante sensitivity of pay). Since changes in the wealth of the CEO are sometimes negative because of the decrease in the value of their stock holdings,
Hall and Liebman cannot directly run the regression in (2) to calculate the
semi-elasticity. Instead, with information both on current total compensation
as a function of the ﬁrm’s return in 1994, w (rt ) , and on the distribution of
annual stock returns, they predict changes in compensation for a given change
in ﬁrm return, a hypothetical w (rt+1 ). With this predicted total compensation
measure, they calculate the semi-elasticity directly from the formula
w (rt+1 ) − w (rt )
= b × (rt+1 − rt ) .
w (rt )
In their data for 1994, Hall and Liebman evaluate the effects of a typical
change in ﬁrm return: from a median performance (r = 5.9 percent) to a 70th
percentile performance (r = 20.5 percent), which implies a 14.6 increase in
r.13 For this typical change, they calculate the semi-elasticity for each CEO
10 Rosen (1992) points out the discrepancy of the ﬁndings in the literature with those of
Jensen and Murphy. The sensitivity of salary and bonus in Jensen and Murphy (1990a) is 1.35
cents for $1,000. This number implies an elasticity at the mean ﬁrm size of 0.0325; equivalently,
an elasticity of 0.1 translates into a change of 10 cents per $1,000 increase in ﬁrm value. Rosen
attributes these differences to functional forms and to the sensitivity measure, which is dominated
by the large ﬁrms’ observations, with signiﬁcantly lower sensitivities.
11 Rosen (1992) uses an average value for w/V of 10−3 . Following his calculations, the
w
Jensen-Murphy statistic from equation (1) is β ≈ b V .
12 Jensen and Murphy (1990a) also include in their total compensation measures the changes
in the wealth of the CEO attributable to his holdings of stocks and options. Their sample, however,
ends in 1983, before the signiﬁcant increase in option grants that is captured in the Hall and
Liebman (1998) sample up to 1994. Moreover, the sample in Jensen and Murphy (1990a) is from
Forbes 800 and includes the value of exercised options as opposed to the value of options at the
time of granting. After 1992, Execucomp started collecting this information.
13 The median standard deviation of r is about 32 percent in their data.

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279

in their data set:
b=

w(0.205)−w(0.059)
w(0.059)

.
0.146
The implied mean elasticity is 4.9 and the median is 3.9. Hall and Liebman
also compute the Jensen-Murphy median sensitivity based on variation in
stock and options only: they ﬁnd a value of $6, compared to $3.25 reported
in Jensen and Murphy (1990a) for the period 1974–1986.14 They conﬁrm the
ﬁnding in Jensen and Murphy (1990a) that incentives are provided mainly
through the granting of stocks and stock options. The sensitivity of salary
and bonuses to ﬁrm performance is very low, while the changes in the wealth
of the CEO that originate from his stock and option holdings are very big.
They ﬁnd a large increase in the use of option grants in the period covered by
their sample, which translates into a signiﬁcant increase in the sensitivity of
various pay to performance measures: Between 1980 and 1994, the median
elasticity went from 1.2 to 3.9, while the median wealth change per $1,000
(the Jensen-Murphy statistic) went from $2.5 to $5.3.

Indirect Sensitivity: Provision of Incentives through
Career Concerns or Threat of Dismissal
Even if the total pay of a CEO was independent from the performance of his
ﬁrm, the manager still would have some incentives to exert effort if the threat of
dismissal was high enough or career concerns were present. Career concerns
is the term used to summarize the fact that workers expect to receive offers for
better paying jobs after an above-average performance. Several studies have
tried to quantify the importance of these two implicit incentive channels.
Jensen and Murphy (1990a) recognize the existence of indirect provision
of incentives that is implicit in the threat of dismissal of the CEO following
poor performance. To account for those indirect incentives in their sensitivity
measure, Jensen and Murphy provide an approximation of the wealth variations for the CEO that would follow if he were ﬁred from his job. To estimate
this wealth loss, they ﬁrst estimate the probability of CEO turnover as a function of ﬁrm performance (net-of-market return in the current and previous
year). They ﬁnd that a CEO in a ﬁrm with average market returns in the past
two years has a .111 dismissal probability, while a performance 50 percent
below market returns for two years increases the dismissal probability to .175.
Since they do not have information on whether the separation was voluntary
14 Hall and Liebman also report the mean sensitivity of pay in their sample, equal to $25
without evaluating potential changes in wealth due to the threat of dismissal. They claim that the
large differences between the mean and the median values are due to the high skewness of stock
and option holdings in the sample of CEOs. Jensen and Murphy (1990a) do not report mean
values.

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or because of retirement, these estimated values represent a rough measure of
the real probability of dismissal. They also ﬁnd evidence of greater effects of
performance on turnover for younger CEOs and for smaller ﬁrms. They use
these estimated probabilities and a simplifying assumption that a ﬁred executive will earn a salary of $1 million elsewhere until retirement to calculate
the dismissal-related wealth loss of CEOs of various ages and as a function
of their net-of-market return. For example, a 62-year-old CEO would suffer a
loss of 26.4 cents for every $1,000 lost by shareholders if his ﬁrm performed 75
percent below the market, as opposed to performing the same as the market.15
The highest sensitivity they ﬁnd is for younger CEOs, who would experience
a loss of 89 cents per $1,000.
Subsequent studies have found an increase in job turnover probabilities in
recent years, as well as evidence of the importance of relative performance as a
determinant of ﬁring decisions. Kaplan and Minton (2006) extend the analysis
for the period 1992–2005, and they ﬁnd an increase in the probability of
turnover with respect to previous periods. They report a decrease of the average
tenure of a CEO from over ten years, as reported in Jensen and Murphy (1990a),
to less than seven years for the period 1992–2003 (which corresponds to a
probability of turnover of 0.149). The average for 1998–2003 is signiﬁcantly
lower, at just over six years (a probability of 0.165), and this subperiod shows
higher sensitivity to current measures of performance than in previous periods.
Kaplan and Minton include in their analysis three measures of performance:
ﬁrm performance relative to industry, industry performance relative to the
overall market, and the performance of the overall stock market. They ﬁnd that
turnover initiated by boards is sensitive not only to ﬁrm performance measures
but also to bad industry or economy-wide performance. They interpret this fact
as indicative of a change in corporate governance since the 1970s and 1980s,
when bad industry or economy-wide performance inﬂuenced CEO turnover
in the form of hostile takeovers.
In a related study, Jenter and Kanaan (2006), using a new sample
including both voluntary and involuntary turnovers during 1993 to 2001,
conﬁrm the results in Kaplan and Minton (2006). They ﬁnd that both poor
industry-wide performance and poor market-wide performance signiﬁcantly
increase the probability of a CEO being ﬁred. A decline in the industry performance from the 75th to the 25th percentile, for example, increases the
probability of a forced CEO turnover by approximately 50 percent, controlling for ﬁrm-speciﬁc performance. The ﬁrm-speciﬁc performance measures
are also weighted by boards more heavily when the overall market and industry
performance is worse.
15 1986 constant dollars.

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281

Gibbons and Murphy (1992) derive a model with explicit contracts and
career concerns that builds on Holmstr¨ m (1999). Career concerns represent
o
the expectation over future wages based on the market beliefs about the quality
of the CEO. They present empirical evidence that explicit incentives increase
as the CEO gets closer to retirement age: for one, two, or three years left in
ofﬁce, respectively, they ﬁnd elasticities of pay to performance of .178, .203,
and .183, compared with elasticities of .119 and .116 when they have ﬁve
or six years left. They interpret this evidence as support for their theoretical
ﬁndings that career concerns complement the explicit incentives provided by
the ties of current wealth to performance in their current employment.
Overall, the available measures of indirect sensitivity of pay to performance appear to have been increasing in the last three decades, in accord with
the increase in the direct sensitivity of pay.

Explanations of Sensitivity Facts
Two main empirical regularities emerge from the studies reviewed previously.
First, the sensitivity of pay is smaller for CEOs of larger ﬁrms. Second, the
sensitivity of pay across all ﬁrm sizes has increased in the last two decades. In
the following subsections, I review the main theoretical explanations proposed
for these two facts. Finally, I include a subsection that presents justiﬁcations
for a set of characteristics of real life compensation contracts. These characteristics may, to the uninformed eye, seem unappealing for the provision of
incentives. The theoretical models show, however, that they may just be the
optimal instruments to implement sensitivity of pay to performance.
Fact 1: The Sensitivity of Pay Decreases with Firm Size

Baker and Hall (2004) show that, in the presence of moral hazard, the
sensitivity of pay optimally decreases with the size of the ﬁrm. They rely
on a partial equilibrium model with multitasking and heterogeneity in the
marginal productivity of the CEO as a function of the ﬁrm size. In recent work,
Edmans, Gabaix, and Landier (forthcoming) extend Gabaix and Landier (2008)
and present an agency model embedded in a competitive market model for talent. They propose a measure of sensitivity of pay that their theory predicts as
independent of ﬁrm size: the dollar change in wealth for a percentage change
in ﬁrm value, scaled by annual pay.
Fact 2: There has been an Increase in Sensitivity of Pay in
the Last Two Decades

The explanations for the increase in sensitivity of pay to performance fall
mostly into two categories: those that maintain that the increase has been
driven by changes in ﬁrm characteristics and increased market competition

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Federal Reserve Bank of Richmond Economic Quarterly

and those that maintain that the increase has been driven by an improvement
in corporate governance practices.
A good example of the ﬁrst category of explanations is the work of Cu˜ at
n
and Guadalupe who, in a series of three papers (2004, 2005, 2006), evaluate
the changes in CEO compensation following several changes in market conditions:16 Cu˜ at and Guadalupe (2004) study two episodes of deregulation of
n
the U.S. banking system and ﬁnd that the increase in competition is correlated
with an increase in sensitivity of pay; Cu˜ at and Guadalupe (2005) ﬁnd that in
n
the period following the sudden appreciation of the pound in 1996, which implied different levels of competition for tradables and nontradables, we observe
an increase in sensitivity of pay for executives in the tradables sector; Cu˜ at
n
and Guadalupe (2006) ﬁnd, for a sample of U.S. executives, that industries
more exposed to globalization (higher foreign competition as instrumented by
tariffs and exchange rates) exhibit higher sensitivity of pay, higher dispersion
of wages across different levels of executives, and higher demand for talent
at the top, which drives up the salary of the CEO. This evidence supports the
conclusions of some theoretical papers that analyze the effects of increased
competition for talented CEOs. Frydman (2005), for example, presents a dynamic model of executive compensation and promotions in which the superior
information of ﬁrms about their incumbent workers implies that an increase in
the relative importance of general skills versus ﬁrm-speciﬁc skills triggers an
increase in manager turnover, increased differences in pay among executives
of different ranks of the same ﬁrm, and higher levels of pay. Frydman contrasts these implications with historical data on compensation, careers, and
education of top U.S. executives from 1936 to 2003. She concludes that facts
are consistent with the predictions of her model under the hypothesis of an
increase in the relative demand of general skills after the 1970s.
The work of Holmstr¨ m and Kaplan (2003) falls under the second
o
(possibly complementary) category of explanations. They argue that the
changes in corporate governance of U.S. ﬁrms in the last two decades have
had a net positive impact, translating into higher sensitivity of pay to performance. Although they recognize that the increase in options compensation
has probably led to new incentive problems that may be behind the corporate
scandals of recent years, they argue that the evidence is still in favor of an
improvement in the management of ﬁrms. They identify three main positive
signs: the good comparative performance of the U.S. stock market with respect
to the rest of the world, the undisputable increase in the link between CEO
compensation and ﬁrm performance, and the use of compensation schemes
by buyout investors and venture capital investors that resemble those of the
average public ﬁrm. They review the trends in corporate governance since the
16 See, also, references in Gabaix and Landier (2008).

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1980s and they identify, as a sign of success, the increasing convergence of
international governance practices to those of the United States, which were
drastically different from those of, for example, Germany and Japan during
the 1980s. They also point to an increase in shareholder activism, which may
be due to an increased institutional shareholders’ stake in public companies:
their overall share in the total stock market went from 30 percent in 1980 to
more than 50 percent in 1994. Gompers and Metrick (2001) report evidence
supporting the hypothesis in Holmstr¨ m and Kaplan (2003) that institutional
o
investors improve corporate governance. They ﬁnd that over the period 1980–
1996, ﬁrms with higher shares of institutional shareholders had signiﬁcantly
higher stock returns. Gompers, Ishii, and Metrick (2003) construct an index to
proxy for the level of good governance of ﬁrms based on data on completion of
a number of governance provisions aimed at protecting shareholder’s rights.
They collect data on four dates between 1990 and 1998 and include a very
high proportion of the largest U.S. ﬁrms according to market capitalization.
They ﬁnd strong correlation between good governance and good ﬁrm performance in terms of Tobin’s Q (market value over book value), proﬁts, and sales
growth. Holmstr¨ m and Kaplan (2003) also identify signs of improved board
o
of directors’ independence: an increase in CEO turnover, a decrease in the
size of boards, and an increase in the proportion of the compensation of board
members that is in the form of stock and options of the ﬁrm.17 An earlier
theoretical paper, Hermalin and Weisback (1998), provides support for the
importance of board independence on sensitivity of pay and, in general, CEO
performance. This paper models explicitly the determination of independence
levels of the board of directors. The CEO uses his perceived higher ability
with respect to any alternative hire to bargain with the board and inﬂuence its
composition. Their model has implications consistent with empirical facts for
the 1980s and 1990s, such as CEO turnover being negatively related to prior
performance, with greater effect for ﬁrms with more independent boards and
with accounting measures being better predictors of turnover than stock price
performance. Also, the independence of the board is likely to increase after
poor ﬁrm performance and decrease over a CEO’s career.
Diversity of Compensation Practices

In spite of the existence of some stylized facts on sensitivity of pay, real
life compensation packages are highly complex and diverse. It is easy to
ﬁnd examples of features of compensation instruments and practices that
may seem counterintuitive to the uneducated eye, such as the lack of relative
17 Compensation boards are independent committees that design the compensation of the top

managers of the ﬁrm. See Section 4 on regulation for details on the legal requirements for deﬁning
this board and the board of directors as “independent.”

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performance evaluation, or the repricing of options gone out-of-the-money.
However, changing environments and dynamic considerations sometimes imply that such features are part of an efﬁcient provision of incentives. What
follows is a brief (nonexhaustive) list of recent theoretical articles that provide
justiﬁcation for some controversial compensation practices.
Commitment. Clementi, Cooley, and Wang (2006) show in a dynamic
model of CEO compensation that implementing optimal incentives for executives in the presence of moral hazard and limited commitment through
the issue of securities dominates deferred cash compensation arrangements;
granting securities improves commitment and helps retain CEOs.
Dynamic Incentives. Wang (1997), as discussed previously, provides a
model of repeated moral hazard that can explain very small (or even negative)
sensitivities of CEO pay based on the optimal smoothing of incentives over
time.
Learning. Celentani and Loveira (2006) show how learning about common shocks in the economy can explain the apparent absence of relative
performance evaluation documented in the literature.18 In the presence of
moral hazard, if the productivity of the CEO’s effort depends on aggregate
conditions, the optimal compensation contract is not necessarily decreasing
in poor relative performance.
Short-term Stock Price Performance. Current compensation plans are
often criticized for providing incentives for CEOs to engage in actions that
increase stock prices in the short term as opposed to creating long-term value
for the shareholders.19 Bolton, Scheinkman, and Xiong (2006) present a
model that explicitly accounts for liquidity needs as a reason to participate in
the stock market. They show that shareholders may in some circumstances
beneﬁt from artiﬁcial increases in today’s stock prices, which inﬂuence the
belief of speculators and allow the ﬁrm to sell its stock at higher prices in
the future. This implies that compensation packages are sometimes optimally
designed to make CEOs take actions that make short-term proﬁts higher.
Targeting Efforts of the CEO. Kadan and Swinkels (2008) present a
model in which the choice between restricted stock grants or option grants
is linked to the potential effect of a manager’s actions on ﬁrm survival. In
ﬁnancially distressed ﬁrms or startups where this effect is higher, stock is
more efﬁcient than options. The choice of compensation instruments helps
the ﬁrm tailor the sensitivity of pay to the ﬁrm’s idiosyncratic position. They
ﬁnd empirical evidence of stock being more widely used than options in ﬁrms
with a higher probability of bankruptcy.
Repricing. The public perception of the practice of decreasing the exercise price of options that are out-of-the-money is that it “undoes” incentives
18 See, for example, Gibbons and Murphy (1990).
19 See, for example, Jensen, Murphy, and Wruck (2004).

A. Jarque: CEO Compensation

285

and is thus interpreted as a sign of management entrenchment. This practice of
repricing is fairly uncommon: Brenner, Sundaram, andYermack (2000) report
that 1.3 percent of the executives in their sample (top ﬁve ofﬁcers in a sample
of 1,500 ﬁrms between 1992 and 1995) had options repriced in a given year.
However, it has received academic attention, perhaps motivated by its reputation as a bad compensation practice. Chance, Kumar, and Todd (2000) identify
size as the main predictor for ﬁrm reprices, with smaller ﬁrms repricing more
often. Brenner, Sundaram, and Yermack (2000) ﬁnd that higher volatility also
signiﬁcantly raises the probability of repricing. Carter and Lynch (2001) ﬁnd
that young high technology ﬁrms and those whose outstanding options are
more out-of-the-money are more likely to reprice. Chen (2004) ﬁnds that
ﬁrms that restrict repricing have a higher probability of losing their CEO after
a decline in their stock price and that they typically grant new options in those
circumstances, possibly in an effort to retain the CEO. Acharya, John, and
Sundaram (2000) present a theoretical model that implies that the practice
of repricing can be optimal in a wide range of circumstances. The intuition
is that there are beneﬁts to adjusting incentives to information that becomes
available after the initial granting and before the expiration of the options;
in many cases, these beneﬁts offset any loss in ex ante incentive provisions
because of the lack of credibility from possible repricings.

REGULATION

The current levels of CEO compensation are viewed by many as excessive
and unjustiﬁed. It is not uncommon to see demands in the popular press
for government regulation of CEO pay.20 However, the effects of regulation in a complicated matter such as the design of compensation packages
for top executives are not always clear. An example of this is the change
in regulation that was introduced in 1993 that limits tax deductions for any
compensation above $1 million. This limit was introduced partly as a response to the popular rejection of the big increases in CEO pay that took
place in the early 1990s. The law, however, established an exception to the
limit: “performance-based” compensation (such as, for example, bonuses and
options granted at the money).21 Empirical studies cited below have found
that ﬁrms have shifted compensation away from salary and toward stocks and
options in response to the limit. A popular view today is that the inclusion
20 As a recent example, the Emergency Economic Stabilization Act of 2008 passed by
Congress on October 3, 2008, explicitly includes some limits on CEO compensation for ﬁrms
in which the Treasury acquires assets or is given a meaningful equity or debt position. The
compensation practices of such ﬁrms “must observe standards limiting incentives, allowing clawback and prohibiting golden parachutes.” Restrictions also apply to ﬁrms that sell more than $300
million in assets to the Treasury through auction.
21 For references, see United States Senate (2006).

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of stocks and options in the compensation packages, together with the stock
market boom, is partly responsible for the recent increase in CEO pay. Did
the $1 million limit contribute sizably to the increase in pay by encouraging
the use of performance-based compensation? In this section, I review the
academic studies that have studied this question, as well as the effect of other
changes in the tax treatment of CEO compensation.
Regulation has also been introduced in recent years to improve corporate
governance in the United States.22 Mainly, the measures have targeted improved coordination and power of shareholders, as well as the transparency
of compensation practices. As a recent example, in the aftermath of corporate
accounting scandals at Enron, WorldCom, and other important U.S. ﬁrms,
the Sarbanes-Oxley Act of 2002 (SOX) increased the legal responsibilities
of CEOs and of compensation committees. There are academic studies on
the effect of regulation on corporate governance and I summarize their main
conclusions in the second part of this section.

Tax Advantages
Tax exemptions for deferred compensation have been in place since the early
1980s. These tax exemptions apply to the capital gains tax owed by a CEO,
which is levied for capital gains that are part of his compensation. We may
wonder whether the savings on capital gains tax for stock option grants could
have played a role in explaining the spectacular increase in the use of options
in compensation packages. Also, some of the regulatory efforts that have
stated speciﬁc limits for tax deductions have triggered criticisms since ﬁrms
that were paying less to their executives may now raise their salaries to the
limit, which is rendered by the regulation as acceptable. For example, with the
passing of the Deﬁcit Reduction Act of 1984, the U.S. government imposed
a tax on excessive (three times the executive’s recent average remuneration)
“golden parachutes,” i.e., payments to incumbent managers who were being
ﬁred in relation to a change in control. Jensen, Murphy, and Wruck (2004)
argue that these types of agreements were fairly uncommon before the law was
passed and that the regulation had the effect of endorsing the practice, which
became a standard in the following years. A similar argument has been made
for the Omnibus Budget Reconciliation Act resolution 162(m) of 1992, which
imposed a $1 million cap on the amount of the CEO’s nonperformance-based
compensation that qualiﬁes for a tax deduction.
In this section, I review a few of the academic studies that have tried to
quantify the effect of tax advantages on CEO compensation. The main conclusion is that there exists a tax advantage of deferred compensation, although
22 See Weinberg (2003) for a discussion of the ﬁnancial reporting issues in corporate governance and of the Sarbanes-Oxley Act of 2002.

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287

a modest one. Also, studies of the effect of resolution 162(m) have found
evidence of a certain increase in salaries of companies that were paying less
than $1 million before the new law was enacted, as well as some shifting of
compensation toward performance-based instruments and away from salaries.
There is evidence that this shift translated into a slight increase in total compensation. The studies, however, do not ﬁnd evidence that the majority of the
spectacular rises in the level of compensation and the increases in the use of
options can be attributed to tax reasons.
Quantifying the Effect of the Special Tax Treatment for
Compensation in the Form of Options

Currently, pay in the form of options has a tax advantage for CEOs when
compared to payments in salary: There are no capital gains tax charges on the
increase in value of a stock from the grant date to the exercise date. If, after
exercise, the executive holds the stock and there is further increase in its value,
capital gains tax is owed only on the appreciation from the date of exercise to
the date of sale.
Motivated by different tax treatments of various instruments of compensation, Miller and Scholes (2002) explicitly compare the after-tax value (together
for the ﬁrm and the CEO) of compensation in wages and several deferred
compensation instruments (deferred salary schemes, stock purchase plans,
deferred stock plans, nonqualiﬁed option plans, and insurance plans). Miller
and Scholes document that by 1980 there had been already a rapid increase
in the usage of deferred compensation versus bonus and salary. The use of
these instruments is usually interpreted as a sign of incentive provision: With
the granting of stock options, the compensation board attempts to align the
incentives of the CEO with those of the shareholders, which helps increase
the long-term value of the company. However, they ﬁnd that none of the
instruments they analyze have clear tax disadvantages with respect to wage
payments: they are all either beneﬁcial or tax-neutral. They argue that the tax
savings makes it difﬁcult to identify incentive provision as the only reason for
deferred compensation.
The advantage of options versus pay is also analyzed in Hall and Liebman
(2000) with data for 1980–1994.23 A simpliﬁed version of their analysis is
presented here. We must compare two alternative ways of compensating the
CEO, both with net present value of P for the ﬁrm. On one hand, the ﬁrm
could grant options to the CEO for a present value of P , which would vest
in N years. The return of this compensation to the CEO, assuming an annual
return of r for his ﬁrm, is
P [1 + r (1 − Tc )]N 1 − Tp ,
23 For details on current tax treatment of CEO compensation, see United States Senate (2006).

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Figure 3 Evolution of Tax Advantage Compared with the Proportion of
Pay Given in the Form of Stock and Options

20
10

0
2006

2004

2002

2000

1998

1996

1994

1992

1990

1988

1986

1984

1980

1982

Percent

Tax Advantage (A) (Percent of Total Pay) Left Axis
Percent of Stock and Options (Percent of Total Pay [Source: Forbes]) Right Axis

Source: IRS and Forbes magazine.

where Tp , Tc , and Tcg are, respectively, the personal, corporate, and capital
gains tax rates. On the other hand, the ﬁrm could schedule a cash payment of
P today. Assuming the CEO invests the whole after-income tax amount in a
nondividend-paying security with the same return, r, for the same number of
years, N, the return of the cash payment to the CEO is
P 1 − Tp [1 + r (1 − Tc )]N − Tcg P 1 − Tp

(1 + r (1 − Tc ))N − 1

Therefore, the options advantage, A, depends on the three tax rates:
A Tp , Tc , Tcg = Tcg P 1 − Tp

(1 + r (1 − Tc ))N − 1

Hall and Liebman (2000) report the value of A for the period 1980–
1998 by substituting the corresponding rates, keeping everything else equal.
They ﬁnd that the advantage of options versus cash compensation reached a
maximum of $7 per $100 of compensation P in 1988–1990 and was down
to $4 per $100 in 1998. Figure 3 plots the value of the advantage reported
in the paper, plus the value for the period 1980–2007 using recent tax rates.
The Bush tax breaks have decreased the advantage of options in recent years;

A. Jarque: CEO Compensation

289

after they expire, and with no further changes, the advantage should go back
to the $4 calculated for 1998. In the same ﬁgure, on the right axis, I have
plotted the ratio of option grants over total compensation from 1992 to 2007
from the Forbes data previously shown. Comparing the two series, we can
see that, although tax advantages were decreasing in the later period, options
were being used relatively more intensively than salaries. Hall and Liebman
(2000) complement their analysis with regressions of the use of options on
the several tax rates and their calculation of the tax advantage and ﬁnd no
evidence of a sizable effect.
Quantifying the Effect of Caps on Deductibility of CEO
Salaries

When ﬁrms calculate their corporate tax liability, under the Internal Revenue
Code, they are allowed to subtract from their revenues the compensation of
their workers. Prior to 1993, this deduction included all compensation given
to the top executives of the ﬁrm.24 In 1993, new regulation took effect that
limited the deductions of the compensation of each of the ﬁve highest ranked
executives of a ﬁrm to $1 million (section 162(m) of the Internal Revenue
Code). The regulation speciﬁes an exception to the $1 million limit: Compensation that is performance-based can be deducted regardless of being worth
more than $1 million.
The requirements to qualify as performance-based for each form of compensation can be summarized as follows:
• Salaries are, by nature, nonperformance-based. Any company paying
its CEO a salary higher than $1 million would face higher tax costs
after the change in regulation.
• A bonus program qualiﬁes if it speciﬁes payments contingent on objective performance measures and is approved in advance by the vote
of the shareholders.25
• Stock options are considered entirely performance-based compensation. In order to qualify for tax deduction, ﬁrms have to detail in an
option grant plan the maximum number of options that can be awarded
24 The accounting of compensation expenses is brieﬂy discussed later in relation to regulation
of disclosure of information to shareholders and the valuation of options.
25 Murphy (1999) documents that companies do include subjective measures of the
performance of the CEO in their bonus plans, usually labeled “individual performance.” In the
typical bonus plan in his data source, this subjective component rarely exceeds 25 percent of the
executive’s bonus.

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to a given executive in the speciﬁed time frame. The plan needs to be
approved by the shareholders.26
• Stock grants and other types of deferred compensation (pensions, severance payments, etc.) are only considered performance-based if they are
granted or their selling restrictions vest based on performance targets.

I now review the three main academic studies of the effect of this change
in regulation.
A simple strategy of testing for the effect of section 162(m) on pay practices is to regress changes in compensation on changes in ﬁrm value:
ln (wit ) = β 0 rit + δ t + ε it ,
where δ t captures the annual growth rates.27 Lower values of δ after the reform
would imply the regulation succeeded in slowing the growth of executive
compensation. However, the trends in CEO compensation may be responding
to changes in the environment other than regulation. To identify the effect of
the reform, the empirical studies have exploited the cross-sectional variation
in the population of ﬁrms. By separating the ﬁrms in which compensation
practices were not affected by the cap on deductions, they can use those as a
control group and isolate the effect of the regulation:
ln (wit ) = β 0 rit + α t AF F ECT ED + δ t + ε it ,
where the difference in α t before and after the change in regulation captures
the effect of deduction limits on the growth of pay in the affected ﬁrms.28
Deciding which ﬁrms should be classiﬁed as affected is not such a simple
task, however. Hall and Liebman (2000), for this purpose, use data on the
compensation in 1992, the only observation available in the Execucomp data
set before the change in the law. They construct a variable equal to 1 if the
salary observation in 1992 is above $1 million, and equal to $1 million divided
by the salary for ﬁrms below that level. They ﬁnd that a CEO with a $1 million
salary in 1992 saw, after the new regulation, his salary grow at an annual rate
of approximately 0.6 percent less than an executive earning $500,000.
Perry and Zenner (2001) propose three alternatives for identifying the set
of ﬁrms affected by the regulation. One is the same indicator constructed in
26 These plans are usually speciﬁed for several years. If, after approval, the compensation
board ﬁnds it necessary to exceed the total number of options speciﬁed in the plan for a given
CEO, the excess amount of options does not qualify for a deduction.
27 In the empirical studies, several measures of performance (sometimes logged, sometimes

in differences) and lagged performance are included as explanatory variables, as well as other
controls like CEO tenure and other relevant available information. In this section, I use a simpliﬁed
statement of the regression equations meant only for illustration.
28 It has also been argued that setting the deduction cap at $1 million encouraged ﬁrms
that were far below this level of compensation to increase their manager’s pay, since $1 million
became “acceptable” (see Wall Street Journal 2008). If this effect really existed, it would bias the
estimates in the above regression.

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291

Hall and Liebman (2000), a second one is an indicator that takes a value of 1
if the salary in 1992 is above $900,000, and a third is an indicator that takes a
value of 1 if the executive had a combined salary and bonus payment above
$1 million in any year before the change in regulation. They ﬁnd similar
results in the three speciﬁcations. Consistent with Hall and Liebman (2000),
Perry and Zenner estimate lower growth of salaries for affected ﬁrms and
evidence of an increase in the sensitivity of bonus and total compensation to
stock performance after 1993.
Rose and Wolfram (2002) point out that using 1992 levels of pay to classify ﬁrms creates statistical correlation between compensation and the variable
that indicates whether ﬁrms are affected by the regulation that does not correspond to an effect of the change in the law: Firms that had higher compensation
levels in 1992 had different characteristics than low compensation ﬁrms and
these characteristics likely inﬂuence their pay growth rate. They propose an
alternative estimation using differences in differences that circumvents this
problem.29 To correct for potential bias, Rose and Wolfram construct their
indicator for affected ﬁrms using predicted instead of observed compensation for years after 1993: They use data in 1992 to construct what the level
of compensation of each ﬁrm in the sample would have been had there not
been a change in regulation. They construct the indicator based on combined
salary and bonus payments, since they ﬁnd that using only salary or broader
measures of compensation constitutes a less precise predictor. Based on their
classiﬁcation methodology, the sample mean growth rates of compensation
after 1993 were higher for affected ﬁrms than for those that were unaffected.
An important feature in Rose and Wolfram’s analysis is that they include data
on the decisions of qualiﬁcation of salary, bonus, and stock plans (although
this is limited to a small sample of ﬁrms, based on a consultant ﬁrm survey).
Stock option plan qualiﬁcation is the most common choice; in their sample,
this implies a tax savings of about 25 percent of ex ante total compensation.
About two-thirds of the sample of ﬁrms had qualiﬁed their stock plans by 1997.
Rose and Wolfram ﬁnd that affected ﬁrms were more likely than unaffected
ﬁrms to qualify their long-term incentive plans (more than twice as likely) and
bonus plans (three times more likely), but both groups qualify their option
plans in the same proportion. They ﬁnd evidence of salary compression at the
$1 million level after 1993 and a ﬂattening of the distribution of cash payments
(salary plus bonus) for ﬁrms that choose to qualify bonus plans. However, they
do not ﬁnd strong statistical evidence for an overall compression effect for all
ﬁrms. Hence, they ﬁnd no evidence of a perverse consequence of the law
suggested in the ﬁnancial press, whereby the argument was that nonaffected
ﬁrms raised their salaries to $1 million because the limit was in fact made into
29 See, also, Rose and Wolfram (2000) for a detailed explanation.

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an “acceptable” standard by the new law. Interestingly, Rose and Wolfram
ﬁnd that ﬁrms that choose to qualify their option plan have higher growth of
salary, bonus, and total compensation after 1993 than both unaffected ﬁrms
and affected ﬁrms that do not qualify. Their estimates are, in general, very
noisy, but their evidence is consistent with the hypothesis that qualiﬁcation
and limiting the compensation growth are alternative means of responding to
political pressures on executive compensation.

Regulating Corporate Governance
Several regulations passed in the last 15 years have focused on improving
corporate governance in U.S. ﬁrms. I now summarize the most important
initiatives.
In 1992 the SEC increased the disclosure requirements in proxy statements, asking ﬁrms to include detailed information about the compensation
of the CEO, chief ﬁnancial ofﬁcer, and the three other highest-paid executives.
Along with those details, the statements had to include an explanation of the
compensation policies of the ﬁrm, as well as performance measures of the
ﬁrm in the past ﬁve years. In particular, ﬁrms were required to report the
value of option grants given to the executives. Options could be valued at the
time of grant using several alternatives. If Black-Scholes valuation was used,
companies were not required to specify the value of the parameters used in
the formula, such as the risk-free interest rate, expected volatility, and dividend yield, or any adjustment to the valuation made to take into account the
nontransferability of the options and the risk of forfeiture. Alternatively, ﬁrms
could choose any other accepted pricing methodology, even simply the value
of the options under the assumption that stock prices would grow at 5 percent
or 10 percent annually during the term of the option (the “potential” or “intrinsic” value of options). In November 1993, the SEC amended its rules and
required the disclosure of the parameters used for the valuation and details of
any discount.30 The reforms of 1992 also expanded the set of allowable topics
for shareholder proposals to include executive compensation and decreased
the minimum share or capital stake necessary to initiate a proxy vote.
Following the accounting fraud scandals at Enron, Tyco, WorldCom, and
a number of other ﬁrms, the government passed the Sarbanes-Oxley Act in
July 2002.31 The Act had several consequences for corporate governance
practices, mainly the requirement of independent accounting auditing, mandatory executive certiﬁcation of ﬁnancial reports (accompanied by an increase
in penalties for corporate fraud), forfeiture of certain bonuses to executives
30 Murphy (1996) ﬁnds evidence that, in the year in which they had a choice, managers
chose the valuation method that minimized the value of their pay.
31 In November 2001, after weeks of SEC investigations, Enron ﬁled a restatement of its
ﬁnancial results that revealed that the company had underreported its debt exposure.

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after a ﬁnancial restatement resulting from malpractice, or the prohibition of
personal loans extended by the ﬁrm to the executives. In November 2003,
the SEC approved proposals by the NYSE and NASDAQ to guarantee the
independence of directors, compensation committees, and auditors.
In 2004, the Financial Accounting Standards Board (FASB) modiﬁed their
recommendations for the valuation of stock grants: Reporting the fair value
of options became the norm, eliminating the previous alternative of reporting
their intrinsic value, and expensing requirements were extended to options
granted with an exercise price equal to or higher than the market price at the
time of granting (FAS 123[R]). In 2006, the SEC made these recommendations compulsory. At the same time, it increased the disclosure requirements
of compensation of the executives (salary and bonus payments for the past
three years, a detailed separate account of stock and option grants, as well
as holdings that originated in previous year’s grants, including their vesting
status, and retirement and post-employment compensation details). The SEC
also demanded an explanation of compensation objectives and implementation in “plain English.” It required a classiﬁcation of the members of the
board of directors and of the compensation committees as independent or not
independent, with an explicit statement of the arguments used for this classiﬁcation. Finally, it asked for the disclosure of compensation of directors
following rules similar to those for the top executives.
Recently, the proposal of making mandatory a “say on pay” nonbinding
vote of shareholders on the compensation of the CEO has received attention
both from the media and politicians, and has been voluntarily adopted by a few
U.S. corporations.32 This proposal is in line with the above described efforts
of making compensation practices as transparent as possible to shareholders.
Quantifying Effects of Regulation on Corporate Governance

Most of the above described changes in regulation could directly or indirectly
inﬂuence compensation contracts, as well as ﬁrm performance. A few studies
have tried to quantify these potential effects.
Johnson, Nelson, and Shackell (2001) document that the 1992 SEC reforms related to shareholder participation translated into an increase in the
number of shareholder-initiated proposals on CEO pay. However, they do not
conclude that the probability of a proposal is higher for ﬁrms with poor incentive alignment.33 Instead, this probability of proposal is higher for ﬁrms with
higher levels (or lower sensitivity) of CEO compensation. They attribute this
correlation to the higher “exposure” of the compensation practices of ﬁrms
32 The “say on pay” practice is already in place in the United Kingdom, the Netherlands,
and Australia. See, for example, the article “Fair or Foul” (The Economist 2008a).
33 Poor incentive alignment is approximated by the proportion of compensation that is not
predictable by observable variables, following Core, Holthausen, and Larcker (1999).

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with higher salaries. They ﬁnd, however, a positive effect on corporate governance when they look at the probability of acceptance of the proposals: it
is higher in ﬁrms with poor incentive alignment and higher for institutional
investor proposals.
Chhaochharia and Grinstein (2007) provide some evidence on the effects
of SOX and of the changes in the stock exchange independence requirements,
as evaluated by investors in the stock market. They analyze the effects of the
announcements of those regulatory changes on the stock prices of ﬁrms with
different compliance levels. They construct portfolios of ﬁrms based on their
degrees of compliance and ﬁnd that less compliant ﬁrms (for example, ﬁrms
that restated their ﬁnancial statements or that do not have independent boards)
earn abnormal returns of about 6 to 20 percent around the announcement of
the new rules. They also report evidence that the market believes that small
ﬁrms ﬁnd it more difﬁcult to comply with requirements for internal control
and independence of directors: Their portfolios have small negative abnormal
returns after the announcements, in contrast with positive abnormal returns of
larger noncompliant ﬁrms.
The imposition of the $1 million limit with the passing of section 162(m)
discussed earlier arguably could have consequences for corporate
governance—on top of any direct effect on executive compensation. The
evidence discussed in the previous subsection points to an increase in sensitivity of pay, which may have translated to better alignment of the incentives
of the CEO with those of shareholders. This hypothesis is consistent with the
evidence in Maisondieu-Laforge, Kim, and Kim (2007): They ﬁnd that stock
returns and operating returns improve for ﬁrms affected by the cap. However, one may argue that compensation committees may have been compelled
to forego some of the subjective components in the granting of bonuses and
options in order to qualify compensation plans for tax exemptions. These
committees may have been compelled to qualify their compensation plans
solely for tax savings purposes, or to comply with what may have been
viewed as the “correct” practice after section 162(m) was approved. Hayes and
Schaefer (2000) ﬁnd that the part of CEO compensation that is unexplained by
observable performance measures is a good predictor for future performance.
This suggests that discretion of the compensation board may in fact be rewarding good executive performance, and the requirements for qualiﬁcation
of bonus schemes may be distorting good compensation practices.

CONCLUSION

Real life compensation contracts are complicated. Even in the absence of
illegal actions on the part of CEOs, it is easy to ﬁnd examples in which the
incentives of managers are not perfectly aligned with those of the shareholders. The recent cases of fraudulent behavior, such as the accounting scandals

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at Enron, the backdating of options, or insider trading, obviously demand
government intervention, as does any other breach of the law. However,
a close look at the problem of CEO pay design demonstrates that providing incentives is a complicated matter and that many seemingly unintuitive
features of compensation packages may, in fact, be helpful in solving incentive
problems. There is ample evidence that, despite rising levels of CEO pay in
the last two decades, improved corporate governance practices have translated
into stronger ties between pay and performance over the same period. Recent
regulation of corporate governance seems to have been aiding market-driven
changes in internal control. However, it is also easy to ﬁnd indications that
some of the compensation regulation may impose unnecessary burdens and
distortions on ﬁrms.

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