. 1
( 2)


Interest and Prices

Michael Woodford
Princeton University

January 30, 2002


c Michael Woodford 2002

1 The Return of Monetary Rules 1
1 The Importance of Price Stability . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1 Toward a New “Neoclassical Synthesis” . . . . . . . . . . . . . . . . . 7
1.2 Microeconomic Foundations and Policy Analysis . . . . . . . . . . . . 13
2 The Importance of Policy Commitment . . . . . . . . . . . . . . . . . . . . . 17
2.1 Central Banking as Management of Expectations . . . . . . . . . . . 18
2.2 Pitfalls of Conventional Optimal Control . . . . . . . . . . . . . . . . 23
3 Monetary Policy without Control of a Monetary Aggregate . . . . . . . . . . 30
3.1 Implementing Interest-Rate Policy . . . . . . . . . . . . . . . . . . . 31
3.2 Monetary Policy in a Cashless Economy . . . . . . . . . . . . . . . . 37
4 Interest-Rate Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Contemporary Proposals . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 General Criticisms of Interest-Rate Rules . . . . . . . . . . . . . . . . 53
4.3 Neo-Wicksellian Monetary Theory . . . . . . . . . . . . . . . . . . . . 58
5 Plan of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Chapter 1

The Return of Monetary Rules

If it were in our power to regulate completely the price system of the future, the
ideal position ... would undoubtedly be one in which, without interfering with
the inevitable variations in the relative prices of commodities, the general average
level of money prices ... would be perfectly invariable and stable.
And why should not such regulation lie within the scope of practical politics?
... Attempts by means of tari¬s, state subsidies, export bounties, and the like,
to e¬ect a partial modi¬cation of the natural order of [relative prices] almost
inevitably involve some loss of utility to the community. Such attempts must so
far be regarded as opposed to all reason. Absolute prices on the other hand ”
money prices ” are a matter in the last analysis of pure convention, depending
on the choice of a standard of price which it lies within our own power to make.
” Knut Wicksell, Interest and Prices, 1898, p. 4.

The past century has been one of remarkable innovation in the world™s monetary systems.
At the turn of the twentieth century, it was taken for granted by practical men that the mean-
ing of a monetary unit should be guaranteed by its convertibility into a speci¬c quantity of
some precious metal; debates about monetary policy usually concerned the relative advan-
tages of gold and silver standards, or the possibility of a bimetallic standard. But through
¬ts and starts, the world™s currencies have come progressively to be more completely subject
to “management” by individual central banks. Since the collapse of the Bretton Woods
system of ¬xed exchange rates in the early 1970s, the last pretense of a connection of the


world™s currencies to any real commodity has been abandoned. We now live instead in a
world of pure “¬at” units of account, the value of each of which depends solely upon the
policies of the particular central bank with responsibility for it.

This has brought both opportunities and challenges. On the one hand, variations in
the purchasing power of money, with their disruptions of the pattern of economic activity,
need no longer result from the vagaries of the market for gold or some other precious metal.
The recognition that the purchasing power of money need not be dictated by any “natural”
market forces, and is instead a proper subject of government regulation, as proposed by the
monetary reformer Knut Wicksell a century ago, should in principle make possible greater
stability of the standard of value, facilitating contracting and market exchange. At the
same time, the responsibilities of the world™s central banks are more complex under a ¬at
system than they were when the banks™ tasks were simply to maintain convertibility of their
respective national currencies into gold, and it was not immediately apparent how the banks™
new freedom should best be used. Indeed, during the ¬rst decade of the new regime, the
policies of many industrial nations su¬ered from a tendency toward chronic in¬‚ation, lead
to calls from some quarters in the 1980s for a return to a commodity standard.

This has not proven to be necessary. Instead, since the 1980s the central banks of the
major industrial nations have been largely successful at bringing in¬‚ation down to low and
fairly stable levels. Nor does this seem to have involved any permanent sacri¬ce of other ob-
jectives; for example, real GDP growth has been if anything higher on average, and certainly
more stable, in the period since in¬‚ation has been stabilized in the U.S. Somewhat para-
doxically, this period of improved macroeconomic stability has coincided with a reduction,
in certain senses, in the ambition of central banks™ e¬orts at macroeconomic stabilization.
Banks around the world have committed themselves more explicitly to relatively straight-
forward objectives with regard to the control of in¬‚ation, and have found when they do so
not only that it is easier to control in¬‚ation than previous experience might have suggested,
but also that price stability creates a sound basis for real economic performance as well.

What appears to be developing, then, at the turn of another century, is a new consensus

in favor of a monetary policy that is disciplined by clear rules intended to ensure a stable
standard of value, rather than one that is determined on a purely discretionary basis to serve
whatever ends may seem most pressing at any given time. Yet the new monetary rules are not
so blindly mechanical as the rules of the gold standard, that de¬ned monetary orthodoxy a
century ago. They are instead principles of systematic conduct for institutions that are aware
of the consequences of their actions and take responsibility for them, and choose their policies
with careful attention to what they accomplish. Indeed, under the current approaches to
rule-based policymaking, more emphasis is given to explicit commitments regarding desired
economic outcomes, such as a target rate of in¬‚ation, than to particular technical indicators
that the central bank may ¬nd it useful to monitor in achieving that outcome.

The present study seeks to provide theoretical foundations for a rule-based approach
to monetary policy of this kind. The development of such a theory is an urgent task, for
rule-based monetary policy in the spirit that I have described is possible only in the case
that the central banks can develop a conscious and articulate account of what they are
doing. It is necessary in order for them to know how to systematically act in a way that
can serve their objectives, that are now de¬ned in terms of variables that are much farther
from being under the banks™ direct control. But it is also necessary in order for them to be
able to communicate the nature of their systematic commitments to the public, despite the
absence of such mechanical constraints as a commitment to exchange currency for some real
commodity. As we explain below, the advantages of a sound monetary policy are largely
dependent upon the policy™s being understood and relied upon by the private sector in
arranging its a¬airs.

And there can be little doubt that the past decade has seen a marked increase in the
self-consciousness of central banks about the way in which they conduct monetary policy,
and in the explicitness of their communication with the public about their actions and
the considerations upon which they are based. A particularly important development in
this regard has been the adoption of “in¬‚ation targeting” as an approach to the conduct

of monetary policy by many of the world™s central banks in the 1990s.1 As we discuss
in more detail below, this approach (best exempli¬ed by the practices of such innovators
as the Bank of England, the Bank of Canada, the Reserve Bank of New Zealand, and the
Swedish Riksbank) is characterized not only by public commitment to an explicit target, but
also by a commitment to explain the central bank™s policy actions in terms of a systematic
decision-making framework that is aimed at achieving this target. This has led to not only to
greatly increased communication with the public about the central bank™s interpretation of
current conditions and the outlook for the future, notably through the publication of detailed
In¬‚ation Reports; it has also involved fairly explicit discussion of the approach that they
follow in deliberating about policy actions, and in some cases even publication of the model
or models used in producing the forecasts that play a central role in these deliberations. As
a consequence, these banks in particular have found themselves in need of a clear theory of
how they can best achieve their objectives, and have played an important role in stimulating
re¬‚ection on this problem.
It is true that the conceptual frameworks proposed by central banks to deal with their
perceived need for a more systematic approach to policy were, until quite recently, largely
developed without much guidance from the academic literature on monetary economics.
Indeed, the central questions of practical interest for the conduct of policy ” how should
central banks decide about the appropriate level of overnight interest rates? how should
monetary policy respond to the various types of unexpected disturbances that occur? ”
had in recent decades ceased to be considered suitable topics for academic study. Reasons for
this included the trenchant critique of traditional methods of econometric policy evaluation
by Lucas (1976); the critique of the use of conventional methods of optimal control in the
conduct of economic policy by Kydland and Prescott (1977); and the develop of a new
generation of quantitative models of business ¬‚uctuations (“real business cycle theory”)
with more rigorous microeconomic foundations, but which implied no relevance of monetary
policy for economic welfare.

See, e.g., Bernanke et al. (19xx) for a thorough discussion of this development.

Nonetheless, recent developments, to be discussed in detail in this volume, have consid-
erably changed this picture. The present study will seek to show that it is possible to use the
tools of modern macroeconomic theory ” intertemporal equilibrium modeling, taking full
account of the endogeneity of private-sector expectations ” to analyze optimal interest-rate
setting in a way that takes seriously the concerns of central bankers, while simultaneously
taking account of the “New Classical” critique of traditional policy evaluation exercises. In
this way, the basic elements are presented of a theory that can provide a basis for the kind
of systematic approach to the conduct of monetary policy which many central banks are
currently seeking to develop. In the present chapter, we review some of the key features of
this theory, as preparation for the more systematic development that begins in chapter 2.

1 The Importance of Price Stability
A notable feature of the new rule-based approaches to monetary policy has been the increased
emphasis given to a particular policy objective: maintaining a low and stable rate of in¬‚ation.
This is most obvious in the case of the countries with explicit in¬‚ation targets. But it also
seems to characterize recent policy in the U.S. as well, where the past decade has seen unusual
stability of the in¬‚ation rate, and where many econometric studies have found evidence of a
stronger Fed reaction to in¬‚ation variations in recent years. (See further discussion of recent
U.S. policy in section 4.1 below.)
Yet the justi¬cation of such an emphasis from the standpoint of economic theory may
not be obvious. Standard general equilibrium models ” and the earliest generation of
quantitative equilibrium models of business ¬‚uctuations, the “real business cycle” models of
the 1980s ” imply that the absolute level of prices should be irrelevant for the allocation of
resources, which depends only on relative prices. Traditional Keynesian macroeconometric
models, of course, imply otherwise: variations in the growth rate of wages and prices are
found to be associated with substantial variations in economic activity and employment.
Yet the existence of such “Phillips curve” relations has typically been held to imply that
monetary policy should be used to achieve output or employment goals, rather than giving

priority to price stability.

The present study argues instead for a di¬erent view of the proper goals of monetary
policy. The use of monetary policy to stabilize an appropriately de¬ned price index is in fact
an important end to which policy should be directed ” at least to a ¬rst approximation, it
should be the primary aim of monetary policy. But this is not ” as proponents of in¬‚ation
targeting sometimes argue ” because variations in the rate of in¬‚ation have no real e¬ects.
Instead, it is exactly because instability of the general level of prices causes substantial real
distortions ” causing ine¬cient variation both in aggregate employment and output and in
the sectoral composition of economic activity ” that price stability is important.

Moreover, the existence of predictable real e¬ects of shifts in monetary policy need not
imply that policy should primarily be based on a calculation of its e¬ects on output or
employment. For the e¬cient aggregate level and sectoral composition of real activity is likely
to vary over time, as a result of real disturbances of variety of types. The market mechanism
performs a di¬cult computational task ” much of the time, fairly accurately ” in bringing
about a time-varying allocation of resources that responds to these changes in production
and consumption opportunities. Because of this, variation over time in employment and
output relative to some smooth trend cannot in itself be taken to indicate a failure of proper
market functioning. Instead, instability of the general level of prices is a good indicator of
ine¬ciency in the real allocation of resources ” at least when an appropriate price index
is used ” because a tendency of prices in general to move in the same direction (either all
rising relative to their past values, or all falling) is both a cause and a symptom of systematic
imbalances in resource allocation.

This general vision is in many respects an attempt to resurrect a view that was in¬‚u-
ential among monetary economists prior to the Keynesian revolution. It was perhaps best
articulated by the noted Swedish economic theorist Knut Wicksell at the turn of the previ-
ous century, along with his followers in the “Stockholm school” of the interwar period (such
as Erik Lindahl and Gunnar Myrdahl) and others in¬‚uenced by Wicksell™s work, such as
Friedrich Hayek. However, these authors developed their insights without the bene¬t of ei-

ther modern general equilibrium theory2 or macroeconometric modelling techniques, so that
it may be doubted whether Wicksellian theory can provide a basis for the kind of quantitative
policy analysis in which a modern central bank must engage ” and which has become only
more essential given current demands for public justi¬cation of policy decisions. This book
will seek to provide theoretical foundations for the view just sketched that meet modern
standards of conceptual rigor, and that are capable of elaboration in a form that can be ¬t
to economic time series.

1.1 Toward a New “Neoclassical Synthesis”

The approach to monetary policy proposed here builds upon advances in the analysis of
economic ¬‚uctuations, and of the monetary transmission mechanism in particular, over the
past few years.3 The models analyzed in this volume di¬er in crucial respects from the ¬rst
two generations of equilibrium business cycle models, namely the “New Classical” models
that took Lucas (1972) as their starting point, and the “real business cycle” models pioneered
by Kydland and Prescott (1982) and Plosser (1983). Neither of these early illustrations of
the possibility of rigorous intertemporal general-equilibrium analysis of short-run ¬‚uctuations
contained elements that would make them suitable for the analysis of monetary policy. While
the Lucas model allows for real e¬ects of unexpected variations in monetary policy (modeled
as stochastic variation in the growth rate of the money supply), it implies that any real
e¬ects of monetary policy must be purely transitory, and also that monetary disturbances
should have no real e¬ects to the extent that their e¬ects on aggregate nominal expenditure
can be forecast in advance. Yet, as shown chapter 3, VAR evidence on the e¬ects of identi¬ed
monetary policy shocks is quite inconsistent with these predictions; instead, the e¬ects of
monetary policy shocks on aggregate nominal expenditure are forecastable at least 6 months
Of course, Wicksell and his followers were quite familiar with Walrasian general equilibrium theory, and
used it as a starting point for their own thought. But at the time, general equilibrium theory meant a static
model of resource allocation, not obviously applicable to the problems of intertemporal resource allocation
with which they were primarily concerned. See, for example, Myrdahl (1931, chap. 2, sec. 4, and chap. 3,
sec. 5).
Useful surveys of recent developments include Goodfriend and King (1997) and Gali (2001).

in advance on the basis of federal-funds rate movements, while the (similarly delayed) e¬ects
on real activity are substantial and persist for many quarters. Nor is this empirical failure
of the model one of minor import for the analysis of monetary policy; the conclusion that
only unanticipated monetary policy can have real e¬ects leads fairly directly to the skeptical
conclusions of Sargent and Wallace (1975) about the necessary ine¬ectiveness of any attempt
to use monetary policy to stabilize real activity.

The real business cycle (RBC) models of the 1980s o¬ered a very di¬erent view of the
typical nature of short-run ¬‚uctuations in economic activity. But the classic models in this
vein similarly imply no scope at all for monetary stabilization policy, because real variables
are modeled as evolving in complete independence of any nominal variables; monetary policy
is thus (at least implicitly) assumed to be of no relevance as far as ¬‚uctuations in real activity
are concerned. Since neither the empirical evidence from VAR studies nor the practical
experience of central bankers supports this view, we should be reluctant to discuss the
nature of desirable monetary policy rules using models of this kind.

Chapters 3 and 4 review a more recent literature that has shown, instead, how models
with equally rigorous foundations in intertemporal optimizing behavior can be developed that
allow a more realistic account of the real e¬ects of monetary disturbances. These models
also imply that systematic monetary policy can make a substantial di¬erence for the way
that an economy responds to real disturbances of all sorts, and this is actually the prediction
of the models that is of greatest importance for our concerns. VAR models typically do not
imply that a large part of the variance of ¬‚uctuations in real activity should be attributed to
monetary policy shocks ” that is, to the purely random component of central-bank interest-
rate policy ” and in any event, one does not really need to understand exactly what the
e¬ects of such shocks are, since under almost any view it will be desirable to eliminate such
shocks (i.e., to render monetary policy predictable) to the extent possible. (Here, we discuss
the ability of our models to account for evidence with regard to the e¬ects of such shocks only
because this is the aspect of the e¬ects of monetary policy which can be empirically identi¬ed
under relatively weak, and hence more convincing, identifying assumptions.) On the other

hand, we are very interested in what a model implies about the way in which alternative
systematic monetary policies determine the e¬ects of real disturbances. The question of
practical importance in central banking is never “should we create some random noise this
month?”, but rather “does this month™s news justify a change in the level of interest rates?”
To think about this, we need to understand the consequences of di¬erent types of possible
monetary responses to exogenous disturbances.

The key to obtaining less trivial consequences of systematic monetary policy in the models
proposed here is the assumption that prices and/or wages are not continually adjusted, but
instead remain ¬xed for at least short periods (a few months, or even a year) at a level that
was judged desirable at an earlier time. However, this postulate does not mean accepting
the need for mechanical models of wage and price adjustment of the kind that were at the
heart of the Keynesian macroeconometric models of the 1960s. Rather than postulating that
prices or wages respond mechanically to some measure of market disequilibrium, they are set
optimally, i.e., so as to best serve the interests of the parties assumed to set them, according
to the information available at the time that they are set. The delays involved before the
next time that prices are reconsidered (or perhaps, before a newly chosen price takes e¬ect)
are here taken to be an institutional fact, just like the available production technology. But
the resulting constraints are taken account of by the decisionmakers who set them; thus
the assumed “stickiness” of prices implies that when they are reconsidered, they are set in
a forward-looking manner, on the basis of expectations regarding future demand and cost
conditions, and not simply in response to current conditions. As a result, expectations turn
out to be a crucial factor in the equilibrium relation between in¬‚ation and real activity (as
argued by Phelps and Friedman in the 1960s). Under certain special assumptions, described
in chapter 3, the relation is of exactly the form assumed in the “New Classical” literature:
deviations of output from its “natural rate” are proportional to the unexpected component
of in¬‚ation. However, this is not true more generally; other models, that I would judge to
be more realistic, also lead to “expectations-augmented Phillips curve” relations of a sort,
but not of the precise sort that implies that anticipated monetary policy cannot have real


It is also important to note that our emphasis upon nominal rigidities does not in any
way mean ignoring the real factors in business ¬‚uctuations stressed by RBC theory. One
important achievement of the RBC literature has been to show that the equilibrium level of
output can easily be disturbed by real disturbances of many sorts ” variations in the rate
of technical progress, variations in government purchases, changes in tax rates, or shifts in
tastes of various sorts. We shall not want to abstract from the existence of such disturbances
in our models; after all, it is only the existence of real disturbances (i.e., disturbances other
than those originating from randomness in monetary policy itself) that gives rise to non-
trivial questions about monetary policy, and we shall strive to obtain results that remain
valid for as broad a class of possible disturbances as possible. Of course, the predicted e¬ects
of real disturbances will not necessarily be the same in the models presented here as in RBC
theory, which, in its classic form, assumes complete ¬‚exibility of both wages and prices.
Instead, in our models, the predicted e¬ects of real disturbances will depend on the nature
of monetary policy.

Nonetheless, the predicted evolution of real variables under complete wage and price
¬‚exibility ” the topic studied in RBC theory ” represents an important benchmark in the
theory developed here. The level of output that would occur in an equilibrium with ¬‚exible
wages and prices, given current real factors (tastes, technology, government purchases) ”
what we call the “natural rate” of output, following Friedman (1968) ” turns out to be a
highly useful concept, even if our theory does not imply that this is what the actual level of
output will be, regardless of monetary policy. It is the gap between actual output and this
natural rate, rather than the level of output as such (or output relative to trend), that is
related to in¬‚ation dynamics in a properly speci¬ed Phillips-curve relation, as we show in
chapter 3. It is also this concept of the output gap to which interest rates should respond
if a “Taylor rule” is to be a successful approach to in¬‚ation stabilization, as we discuss in
chapter 4; it is this concept of the output gap that monetary policy should aim to stabilize
in order to maximize household welfare, as shown in chapter 6; and it is this concept of

the output gap to which optimal interest-rate rules and/or optimal in¬‚ation targets should
respond, as shown in chapter 8. From the point of view of any of these applications, the
fact that the natural rate of output may vary at business-cycle frequencies, as argued in
the RBC literature, is of tremendous practical importance. As will be seen, we are also
quite interested in the consequences of time variation in what Wicksell (1898) called the
“natural rate of interest” ” the equilibrium real rate of interest in the case of ¬‚exible wages
and prices, given current real factors.4 Once again, RBC theory has a great deal to tell us
about the kind of factors that should cause the natural rate of interest to vary. Hence RBC
theory, when correctly interpreted, constitutes an important building block of the theory to
be developed here.
It is for this reason that Goodfriend and King (1997) speak of models of this kind as
representing a “new neoclassical synthesis”, in the spirit of the synthesis between Keynesian
short-run analysis and neoclassical long-run analysis proposed by Hicks and Samuelson. In
the modern, more explicitly dynamic version of such a synthesis, the neoclassical theory
(i.e., RBC theory) de¬nes not a static “long-run equilibrium” but rather a dynamic path
which represents a sort of virtual equilibrium for the economy at each point in time ” the
equilibrium that one would have if wages and prices were not in fact sticky. The evolution of
the virtual equilibrium matters because the gaps between actual quantities and their virtual
equilibrium values are important measures of the incentives for wage and price adjustment,
and hence determinants of wage and price dynamics.
At the same time, the stickiness of prices and/or wages implies that short-run output
determination can be understood in a manner reminiscent of Keynesian theory. Indeed, our
basic analytical framework in this study will have the structure of a simple model consisting
of an “IS equation”, a monetary policy rule, and an “AS equation”. (The monetary policy
rule ” which we shall often suppose is something similar to a “Taylor rule” ” replaces
This is of course the origin of the “natural rate” terminology ” Friedman™s concept of a “natural rate of
unemployment” appealed to an analogy with Wicksell™s “natural rate of interest,” a concept with which his
readers were presumed already to be familiar. Nowadays, many readers will be more familiar with Friedman™s
concept, and will ¬nd the natural rate of interest most easy to understand as an analogy with Friedman™s
natural rate.

the “LM equation” of Hicksian pedagogy, since for the most part we are not here interested
in the consequences of monetary targeting.) Nonetheless, even for purposes of “short-run”
analysis, our model will be less static than an old-fashioned Keynesian model; in particular,
expectations will be crucial elements in our structural relations (e.g., our “intertemporal IS
relation”), so that anything that causes a change in expectations should shift them.

The inclusion of signi¬cant forward-looking terms in our key structural relations will have
substantial consequences for our analysis of the character of optimal policy, just as Lucas
(1976) argued, even if the consequences are not necessarily the ones suggested in the “New
Classical” literature. For example, estimated “IS equations” in traditional macroeconometric
models often indicate an e¬ect of lagged rather than current interest rates on aggregate
demand, since the coe¬cients on lagged rates are found to be more signi¬cant than those
on a current interest rate, in the case of a regression seeking to explain aggregate real
expenditure in terms of observable variables. In the optimization-based model estimated by
Rotemberg and Woodford (1997), instead, the observed delay in the e¬ects of an interest-rate
innovation on real GDP is explained by an assumption that the interest-sensitive component
of private spending is predetermined, though chosen in a forward-looking way. Thus current
aggregate demand is assumed to depend on past expectations of current and future interest
rates, rather than past interest rates.

Econometrically, the two hypotheses are not easily distinguished, given the substantial
serial correlation of observed interest rates; yet the second hypothesis, I would argue, has
a much simpler logic in terms of the optimal timing of expenditure, once one grants the
hypothesis of predetermination of spending decisions (just as with pricing decisions). And
the speci¬cation assumed matters greatly for one™s conclusions about the conduct of policy.
If expenditure is really a¬ected by lagged interest rates only, it becomes important for the
central bank to adjust interest rates in response to its forecast of how it would like to a¬ect
aggregate demand at a later date; “pre-emptive” actions will be essential. If instead only
past expectations of current and future interest rates matter, then unforecastable interest
rate movements will not a¬ect demand, so that immediate responses to news will serve no

purpose; it will instead be important for interest rates to continue to respond to the outlook
that had been perceived in the past, even if more recent news has substantially modi¬ed the
bank™s forecasts. This inertial character of optimal interest-rate policy is discussed further
in chapters 7 and 8.

1.2 Microeconomic Foundations and Policy Analysis

The development of a model of the monetary transmission mechanism with clear foundations
in individual optimization is important, in our view, for two reasons. One is that it allows us
to evaluate alternative monetary policies in a way that avoids the ¬‚aw in policy evaluation
exercises using traditional Keynesian macroeconometric models stressed by Lucas (1976).
Another is that the outcomes resulting from alternative policies can be evaluated in terms
of the preferences of private individuals that are re¬‚ected in the structural relations of one™s
Lucas (1976) argued that traditional policy evaluation exercises using macroeconometric
models were ¬‚awed by a failure to recognize that the relations typically estimated ” a
“consumption equation,” a ”price equation,” and so on ” were actually (at least under the
hypothesis of optimizing behavior by households and ¬rms) reduced-form rather than truly
structural relations. In particular, in the estimated equations, expectations regarding future
conditions (future income in the case of consumers, future costs and future demand in the
case of price-setters) were proxied for by current and lagged observable state variables; but
the correlation of expectations with those observables ought to be expected to change in the
case of a change in the government™s policy rule, as contemplated in the policy evaluation
This problem can be addressed by making use of structural relations that explicitly rep-
resent the dependence of economic decisions upon expectations regarding future endogenous
variables. The present study illustrates how this can be done, deriving the structural re-
lations that are to be used in the calculation of optimal policy rules from the ¬rst-order
conditions (Euler equations) that characterize optimal private-sector behavior. These condi-

tions explicitly involve private-sector expectations about the future evolution of endogenous
variables, and often they only implicitly de¬ne private-sector behavior, rather than giving a
“consumption equation” or “price equation” in closed form. Our preference for this form of
structural relations is precisely that they are ones that should remain invariant (insofar as
our theory is correct) under changes in policy that change the stochastic laws of motion of
the endogenous variables.

Of course, the mere fact that the structural relations derived here follow from explicit
optimization problems for households and ¬rms is no guarantee that they are correctly
speci¬ed; the (fairly simple) optimization problems that we consider here may or may not
be empirically realistic. (Indeed, insofar as we illustrate the principles of our approach
in the context of very simple examples, one can be certain that they are not very precise
representations of reality.) But this is not an objection to the method that we advocate here;
it simply means that there is no substitute for careful empirical research to ¬‚esh out the
details of a quantitatively realistic account of the monetary transmission mechanism. While
the present study does include some discussion of the extent to which the simple models
presented here are consistent with empirical evidence, in order to motivate the introduction
of certain model elements, no attempt is made here to set out a model that is su¬ciently
realistic to be used for actual policy analysis in a central bank. Nonetheless, the basic
elements of an optimizing model of the monetary transmission mechanism, developed in
chapters 3 and 4 of this book, are ones that we believe are representative of crucial elements
of a realistic model; and indeed, the illustrative models discussed here have many elements
in common with rational-expectations models of the monetary transmission mechanism that
are already being used for quantitative policy evaluation at a number of central banks.

A second advantage of proceeding from explicit microeconomic foundations is that in
this case, the welfare of private agents ” as indicated by the utility functions that underly
the structural relations of one™s model of the transmission mechanism ” provides a natural
objective in terms of which alternative policies should be evaluated. In taking this approach,
the present study seeks to treat questions of monetary policy in a way that is already standard

in other branches of public economics, such as the analysis of optimal tax policy. Nonetheless,
the approach has not been common in the literature on monetary policy evaluation, which
instead typically evaluates alternative policies in terms of ad hoc stabilization objectives for
various macroeconomic indicators.
Until recently, welfare-theoretic analyses of monetary policy have been associated exclu-
sively with the problem of reducing the transactions frictions (sometimes called “shoe-leather
costs”) that account for the use of money in purchases.5 This is because this was for a long
time the only sort of ine¬ciency present in general-equilibrium monetary models, which typ-
ically assumed perfectly ¬‚exible wages and prices and perfect competition. Here we show
how welfare analysis of monetary policy is also possible in settings that incorporate nominal
rigidities. Allowing for these additional frictions ” crucial to understanding the real e¬ects
of alternative monetary policies ” provides a welfare-theoretic justi¬cation for additional
policy goals.
As shown in chapter 6, taking account of delays in the adjustment of wages and prices
provides a clear justi¬cation for an approach to monetary policy that aims at price stabil-
ity. It might seem more obvious that allowing for real e¬ects of monetary policy provides
a justi¬cation for concern with output stabilization. The stickiness of prices explains why
actual output may di¬er from the “natural rate”, and so justi¬es a concern for the stabi-
lization of the “output gap”, i.e., the discrepancy between the actual and natural levels of
output. But price stickiness also justi¬es a concern with price stability. For when prices
are not constantly adjusted, instability of the general level of prices creates discrepancies
between relative prices owing to the absence of perfect synchronization in the adjustment of
the prices of di¬erent goods. These relative-price distortions lead in turn to an ine¬cient
sectoral allocation of resources, even when the aggregate level of output is correct.
Moreover, our theory implies not only that price stability should matter in addition to
stability of the output gap, but also that, at least under certain circumstances, in¬‚ation
stabilization eliminates any need for further concern with the level of real activity. This is
For reviews of that traditional literature, see Woodford (1990) and Chari and Kehoe (1999).

because, at least under the conditions described more precisely in chapter 6, the time-varying
e¬cient level of output is the same (up to a constant, which does not a¬ect the basic point)
as the level of output that eliminates any incentive for ¬rms on average to either raise or
lower their prices. It then follows that there is no con¬‚ict between the goal of in¬‚ation
stabilization and output-gap stabilization, once the welfare-relevant concept of the output
gap is properly understood. Furthermore, because of the di¬culty involved in measuring the
e¬cient level of economic activity in real time ” depending as this does on variations in
production costs, consumption needs, and investment opportunities ” it may well be more
convenient for a central bank to simply concern itself with monitoring the stability of prices.
The development of an explicit welfare analysis of the distortions resulting from in¬‚ation
variations has advantages beyond the mere provision of a justi¬cation for central bankers™
current concern with in¬‚ation stabilization. For the theory presented here also provides
guidance as to which price index it is most desirable to stabilize. This is a question of
no small practical interest. For example, the stock-market booms and crashes in many
industrial nations in the late 1990s led to discussion of whether central banks ought not
target an in¬‚ation measure that took account of “asset price in¬‚ation” as well as goods
The answer provided by the theory developed here is no. The prices that monetary policy
should aim to stabilize are the ones that are infrequently adjusted, and that consequently
can be expected to become misaligned in an environment that requires these prices to move
in either direction. Large movements in frequently adjusted prices ” and stock prices are
among the most ¬‚exible of prices ” can instead be allowed without raising such concerns,
and if allowing them to move makes possible greater stability of the sticky prices, such
instability of the ¬‚exible prices is desirable.7 In chapter 6, we show how such a conclusion
For examples of scholarly attention to the question, see Goodhart (20xx) and Cecchetti (2002).
The basic point was already evident to authors of the Stockholm school: “If one desires the greatest
possible diminution of the business cycle, ... then one must try to stabilize an index of those prices which
are sticky in themselves... Stability of the level of the sticky prices permits a certain freedom for all other
price levels, including capital values.... It is evident that [the price of capital goods] is the last price that
one should try to stabilize in a capitalist society.... The same is naturally true for all indices of ¬‚exible
commodity prices” (Myrdal, 1931, pp. 192-193).

can be justi¬ed from the point of view of welfare economics. We further show how to develop
a quantitative measure of the deadweight loss resulting from stabilization of alternative price
indices, so that more subtle distinctions between the relative stickiness of di¬erent prices can
be dealt with.
In addition to implying that an appropriate in¬‚ation target ought not involve asset prices,
our theory suggests that not all goods prices are equally relevant. Instead, central banks
should target a measure of “core” in¬‚ation that places greater weight on those prices that
are stickier. Furthermore, insofar as wages are also sticky, a desirable in¬‚ation target should
take account of wage in¬‚ation as well as goods prices. The empirical results discussed in
chapter 3 suggest that wages and prices are sticky to a similar extent, suggesting (as we
show in chapter 8) that a desirable in¬‚ation target should put roughly equal weight on wage
and price in¬‚ation.

2 The Importance of Policy Commitment
Thus far, we have summarized a theoretical justi¬cation for the concern of the in¬‚ation-
targeting central banks with price stability. But why should it follow that there is a need
for public commitment to a target in¬‚ation rate, let alone for commitment to a systematic
procedure for determining appropriate instrument settings? Why is it not enough to appoint
central bankers with a sound understanding of the way the economy works, and then grant
them complete discretion to pursue the public interest in the way that they judge best?
Should it not follow from our analysis that this would result in price stability, to the extent
that this is possible given the instruments available to the central bank and the information
available at the time that policy decisions must be made?
We shall argue instead that there is good reason for a central bank to commit itself to
a systematic approach to policy, that not only provides an explicit framework for decision-
making within the bank, but that is also used to explain the bank™s decisions to the public.
There are two important advantages of commitment to an appropriately chosen policy rule
of this kind. One is that the e¬ectiveness of monetary policy depends as much on the public™s

expectations about future policy as upon the bank™s actual actions. Hence a bank must not
only manage to make the right decision as often as possible; it is also important that its
actions be predictable.
The second, and subtler, reason is that even if the public has no di¬culty in correctly
perceiving the pattern in the central bank™s actions ” as assumed under the hypothesis of
rational expectations ” if a bank acts at each date under the assumption that it cannot
commit itself to any future behavior (and is not bound by any past commitments), it will
choose a systematic pattern of behavior that is suboptimal. We take up each of these
arguments in turn.

2.1 Central Banking as Management of Expectations

The ¬rst advantage of commitment to a policy rule is that it facilitates public understanding
of policy. It is important for the public to understand the central bank™s actions, to the
greatest extent possible, not only for reasons of democratic legitimacy ” though this is an
excellent reason itself, given that central bankers are granted substantial autonomy in the
execution of their task ” but also in order for monetary policy to be most e¬ective.
For successful monetary policy is not so much a matter of e¬ective control of overnight
interest rates as it is one of shaping market expectations of the way in which interest rates,
in¬‚ation and income are likely to evolve over the coming year and later. On the one hand,
optimizing models imply that private sector behavior should be forward-looking; hence ex-
pectations about future market conditions should be important determinants of current
behavior. It follows that, insofar as it is possible for the central bank to a¬ect expectations,
this should be an important tool of stabilization policy. And given the increasing sophistica-
tion of market participants about central banking over the past two decades, it is plausible
to suppose that a central bank™s commitment to a systematic policy will be factored into
private sector forecasts ” at least insofar as the bank™s actions are observed to match its
professed commitments.
Not only do expectations about policy matter, but, at least under current conditions,

very little else matters. Few central banks of major industrial nations still make much use
of credit controls or other attempts to directly regulate the ¬‚ow of funds through ¬nancial
markets and institutions. Increases in the sophistication of the ¬nancial system have made
it more di¬cult for such controls to be e¬ective, and in any event the goal of improvement
of the e¬ciency of the sectoral allocation of resources stressed above would hardly be served
by such controls, which (if successful) inevitably create ine¬cient distortions in the relative
cost of funds to di¬erent parts of the economy.

Instead, banks restrict themselves to interventions that seek to control the overnight
interest rate in an interbank market for central-bank balances (for example, the federal funds
rate in the U.S.). But the current level of overnight interest rates as such is of negligible
importance for economic decisionmaking; if a change in the overnight rate were thought
to imply only a change in the cost of overnight borrowing for that one night, then even a
large change (say, a full percentage point increase) would make little di¬erence to anyone™s
spending decisions. The e¬ectiveness of changes in central-bank targets for overnight rates
in a¬ecting spending decisions (and hence ultimately pricing and employment decisions) is
wholly dependent upon the impact of such actions upon other ¬nancial-market prices, such
as longer-term interest rates, equity prices and exchange rates. These are plausibly linked,
through arbitrage relations, to the short-term interest rates most directly a¬ected by central-
bank actions; but it is the expected future path of short-term rates over coming months and
even years that should matter for the determination of these other asset prices, rather than
the current level of short-term rates by itself.8

Thus the ability of central banks to in¬‚uence expenditure, and hence pricing, decisions is
critically dependent upon their ability to in¬‚uence market expectations regarding the future
path of overnight interest rates, and not merely their current level. Better information on

An e¬ect of the same kind is obtained in the basic “neo-Wicksellian” model developed in chapter 4,
insofar as the short-run real rate of interest determines not the absolute level of desired private-sector
expenditure, but rather the current level relative to the expected future level of expenditure, as a result of
an Euler equation for the optimal timing of expenditure. Expected future expenditure, relative to expected
expenditure even farther in the future, similarly depends upon expected future short rates, and so on for
expectations regarding the still farther future.

the part of market participants about central-bank actions and intentions should increase
the degree to which central-bank policy decisions can actually a¬ect these expectations, and
so increase the e¬ectiveness of monetary stabilization policy. Insofar as the signi¬cance of
current developments for future policy are clear to the private sector, markets can to a
large extent “do the central bank™s work for it,” in that the actual changes in overnight
rates required to achieve the desired changes in incentives can be much more modest when
expected future rates move as well.9
An obvious consequence of the importance of managing expectations is that a transpar-
ent central-bank decisionmaking process is highly desirable. This has come to be widely
accepted by central bankers over the past decade. (See Blinder et al., 2001, for a detailed
and authoritative discussion.) But it is sometimes supposed that the most crucial issues are
ones such as the frequency of press releases or the promptness and detail with which the
minutes of policy deliberations are published. Instead, from the perspective suggested here,
what is important is not so much that the central bank™s deliberations themselves be public,
as that the bank give clear signals about what the public should expect it to do in the future.
The public needs to have as clear as possible an understanding of the rule that the central
bank follows in deciding what it does. Inevitably, the best way to communicate about this
will be by o¬ering the public an explanation of the decisions that have already been made;
the bank itself would probably not be able to describe how it might act in all conceivable
circumstances, most of which will never arise.
Some good practical examples of communication with the public about the central bank™s
policy commitments are provided by the In¬‚ation Reports of the leading in¬‚ation-targeting
banks. These reports do not pretend to give a blow-by-blow account of the deliberations by
There is evidence that this is already happening, as a result both of greater sophistication on the part
of ¬nancial markets and greater transparency on the part of central banks, the two developing in a sort of
symbiosis with one another. Blinder et al. (2001, p. 8) argue that in the period from early 1996 through the
middle of 1999, one could observe the U.S. bond market moving in response to macroeconomic developments
that helped to stabilize the economy, despite relatively little change in the level of the federal funds rate, and
suggest that this re¬‚ected an improvement in the bond market™s ability to forecast Fed actions before they
occur. Statistical evidence of increased forecastability of Fed policy by the markets is provided by Lange et
al. (2001), who show that the ability of Treasury bill yields to predict changes in the federal funds rate some
months in advance has increased since the late 1980s.

which the central bank reached the position that it has determined to announce; but they do
explain the analysis that justi¬es the position that has been reached. This analysis provides
information about the bank™s systematic approach to policy by illustrating its application
to the concrete circumstances that have arisen since the last report; and it provides infor-
mation about how conditions are likely to develop in the future through explicit discussion
of the bank™s own projections. Because the analysis is made public, it can be expected to
shape future deliberations; the bank knows that it should be expected to explain why views
expressed in the past are not later being followed. Thus a commitment to transparency
of this sort helps to make policy more fully rule-based, as well as increasing the public™s
understanding of the rule.

It is perhaps worth clarifying further what we intend by “rule-based” policy. We do
not mean that a bank should commit itself to an explicit state-contingent plan for the entire
foreseeable future, specifying what it would do under every circumstance that might possibly
arise. That would obviously be impractical, even under complete unanimity about the correct
model of the economy and the objectives of policy, simply because of the vast number of
possible futures. But it is not necessary, in order to obtain the bene¬ts of commitment to
a systematic policy. It su¬ces that a central bank commit itself to a systematic way of
determining an appropriate response to future developments, without having to list all of
the implications of the rule for possible future developments.10

Nor is it necessary to imagine that commitment to a systematic rule means that once
a rule is adopted it must be followed forever, regardless of subsequent improvements in
understanding of the e¬ects of monetary policy on the economy, including experience with
the consequences of implementing the rule. If the private sector is forward-looking, and it
is possible for the central bank to make the private sector aware of its policy commitments,
then there are important advantages of commitment to a policy other than discretionary

We show in chapter 8 how policy rules can be designed that can be speci¬ed without any reference to
particular economic disturbances, but that nonetheless imply an optimal equilibrium response to additive
disturbances of an arbitrary type. The targeting rules advocated by Svensson (2001) are examples of rules
of this kind.

optimization ” i.e., simply doing what seems best at each point in time, with no commitment
regarding what may be done later. This is because there are advantages to having the private
sector be able to anticipate delayed responses to a disturbance, that may not be optimal ex
post if one re-optimizes taking the private sector™s past reaction as given. But one can create
the desired anticipations of subsequent behavior ” and justify them ” without committing
to follow a ¬xed rule in the future no matter what may happen in the meantime.
It su¬ces that the private sector have no ground to forecast that the bank™s behavior will
be systematically di¬erent from the rule that it pretends to follow. This will be the case if
the bank is committed to choosing a rule of conduct that is justi¬able on certain principles,
given its model of the economy. (An example of the sort of principles that I have in mind is
given in chapter 8.) The bank can then properly be expected to continue to follow its current
rule, as long as its understanding of the economy does not change; and as long as there is
no predictable direction in which its future model of the economy should be di¬erent from
its current one, private-sector expectations should not be di¬erent from those in the case
of an inde¬nite commitment to the current rule. Yet changing to a better rule will remain
possible in the case of improved knowledge (which is inevitable); and insofar as the change
is justi¬ed both in terms of established principles and in terms of a change in the bank™s
model of the economy that can itself be defended, this need not impair the credibility of the
bank™s professed commitments.
It follows that rule-based policymaking will necessarily mean a decision process in which
an explicit model of the economy (albeit one augmented by judgmental elements) plays a
central role, both in the deliberations of the policy committee and in explanation of those
deliberations to the public. This too has been a prominent feature of recent innovations in
the conduct of monetary by the in¬‚ation-targeting central banks. While there is undoubtedly
much room for improvement both in current models and current approaches to the use of
models in policy deliberations, one can only expect the importance of models to policy
deliberations to increase in a world of increasingly sophisticated ¬nancial markets.

2.2 Pitfalls of Conventional Optimal Control

But it is not enough that a central bank have sound objectives (re¬‚ecting a correct analysis
of social welfare), that it make policy in a systematic way, using a correct model of the econ-
omy and a sta¬ that is well-trained in numerical optimization, and that all this be explained
thoroughly to the public. A bank that approaches its problem as one of optimization under
discretion ” deciding afresh on the best action in each decision cycle, with no commitment
regarding future actions except that they will be the ones that seem best in whatever cir-
cumstances may arise ” may obtain a substantially worse outcome, from the point of view
of its own objectives, than one that commits itself to follow a properly chosen policy rule.
As Kydland and Prescott (1977) ¬rst showed, this can occur even when the central bank as
a correct quantitative model of the policy tradeo¬s that it faces at each point in time, and
the private sector has correct expectations about the way that policy will be conducted.
At ¬rst thought, discretionary optimization might seem exactly what one would want
an enlightened central bank to do. All sorts of unexpected events constantly occur that
a¬ect the determination of in¬‚ation and real activity, and it is not hard to see that, in
general, the optimal level of interest rates at any point in time should depend on precisely
what has occurred. It is plainly easiest, as a practical matter, to arrange for such complex
state-dependence of policy by having the instrument setting at a given point in time be
determined only after the unexpected shocks have already been observed. Furthermore,
it might seem that the dynamic programming approach to the solution of intertemporal
optimization problems provides justi¬cation for an approach in which a planning problem is
reduced to a series of independent choices at each of a succession of decision dates.
But standard dynamic programming methods are valid only for the optimal control of
a system that evolves mechanically in response to the current action of the controller, as
in the kind of industrial problems of typical interest in engineering control theory. The
problem of monetary stabilization policy is of a di¬erent sort, in that the consequences of
the central bank™s actions depend not only upon the sequence of instrument settings up until
the present time, but also upon private-sector expectations regarding future policy. In such

a case, sequential (discretionary) optimization leads to a sub-optimal outcome because at
each decision point, prior expectations are taken as given, rather than as something that can
be a¬ected by policy. Nonetheless, the predictable character of the central bank™s decisions,
taken from this point of view, do determine the (endogenous) expectations of the private
sector at earlier dates, under the hypothesis of rational expectations; a commitment to behave
di¬erently, that is made credible to the private sector, could shape those expectations in a
di¬erent way, and because expectations matter for the determination of the variables that
the central bank cares about, in general outcomes can be improved through shrewd use of
this opportunity.

The best-known example of a distortion created by discretionary optimization is the
“in¬‚ation bias” analyzed by Kydland and Prescott (1977) and Barro and Gordon (1983). In
the presence of a short-run “Phillips curve” tradeo¬ between in¬‚ation and real activity (given
in¬‚ation expectations), and a target level of real activity higher than the one associated
with an optimal in¬‚ation rate (in the case of in¬‚ation expectations also consistent with
that optimal rate), these authors showed that discretionary optimization leads to a rate of
in¬‚ation that is ine¬ciently high on average, owing to neglect of the way that pursuit of
such a policy raises in¬‚ation expectations (causing an adverse shift of the short-run Phillips
curve). A variety of solutions to the problem of in¬‚ation bias have been proposed. One
in¬‚uential idea is that this bias can be eliminated by assigning the central bank targets for
in¬‚ation and output that di¬er from those re¬‚ected in the true social welfare function (i.e.,
the central-bank objective assumed by Kydland and Prescott or Barro and Gordon), without
otherwise constraining the central bank™s discretion in the selection of policies to achieve its
objective. This is one of the primary reasons for the popularity of “in¬‚ation targeting”,
which involves commitment of a central bank to the pursuit of an assigned target rather
than being left to simply act as seems best for society at any point in time, while leaving
the bank a great deal of ¬‚exibility as to the way in which the assigned goal is to be pursued.

However, the distortions resulting from discretionary optimization go beyond simple bias
in the average levels of in¬‚ation or other endogenous variables; this approach to the conduct

of policy generally results in suboptimal responses to shocks as well, as shown in chapter 7.
For example, various types of real disturbances can create temporary ¬‚uctuations in what
Wicksell called the “natural rate of interest”, meaning (as shown in chapter 4) that the level
of nominal interest rates required to stabilize both in¬‚ation and the output gap varies over
time. However, the amplitude of the adjustment of short-term interest rates can be more
moderate ” and still have the desired size of e¬ect on spending and hence on both output
and in¬‚ation ” if it is made more persistent, so that when interest rates are increased, they
will not be expected to quickly return to their normal level, even if the real disturbance
that originally justi¬ed the adjustment has dissipated. Because aggregate demand depends
upon expected future short rates as well as current short rates, a more persistent increase
of smaller amplitude can have an equal a¬ect on spending. If one also cares about reducing
the volatility of short-term interest rates, a more inertial interest-rate policy of this kind will
be preferable; that is, the anticipation that the central bank will follow such a policy leads
to a preferable rational-expectations equilibrium. But a central bank that optimizes under
discretion has no incentive to continue to maintain interest rates high once the initial shock
has dissipated; at this point, prior demand has already responded to whatever interest-rate
expectations were held then, and the bank has no reason to take into account any e¬ect
upon demand at an earlier date in setting its current interest-rate target.

This distortion in the dynamic response of interest-rate policy to disturbances cannot be
cured by any adjustment of the targets that the bank is directed to aim for regardless of what
disturbances may occur; instead, policy must be made history-dependent, i.e., dependent
upon past conditions even when they are no longer relevant to the determination of the
current and future evolution of the variables that the bank cares about. Indeed, in general
no purely forward-looking decision procedure ” one that makes the bank™s action at each
decision point a function solely of the set of possible paths for its target variables from that
time onward ” can bring about optimal equilibrium responses to disturbances. Discretionary
optimization is an example of such a procedure, and it continues to be when the bank™s
objective is modi¬ed, if the modi¬cation does not introduce any history-dependence. But

other popular proposals are often purely forward-looking as well. Thus the classic “Taylor
rule” (Taylor, 1993) prescribes setting an interest-rate operating target at each decision point
as a function of current estimates of in¬‚ation and the output gap only (see below), and Taylor
(1999) expresses skepticism about the desirability of partial-adjustment dynamics of the kind
that characterize most estimated central-bank reaction functions. Popular descriptions of
in¬‚ation-forecast targeting are typically purely forward-looking as well; the interest-rate
setting at each decision point is to be determined purely as a function of the forecast from
that date forward for in¬‚ation (and possibly other target variables). Thus the intuition that
optimal policy should be purely forward-looking seems to be fairly commonplace; but when
the private sector is forward-looking, any purely forward-looking criterion for policy is almost
invariably sub-optimal.

Obtaining a more desirable pattern of responses to random disturbances therefore requires
commitment to a systematic policy rule, and not just a (one-time) adjustment of the bank™s
targets. The primary task of this study is to provide principles that can be used in the design
of such rules. By saying that a policy rule is necessary, we mean to draw a distinction with
two other conceptions of optimal policy. One is discretionary optimization, as just discussed;
specifying a rule means a more detailed description of the way in which a decision is to be
reached than is involved in a simple commitment to a particular objective. But we also
mean to distinguish the approach advocated here from the usual understanding of what an
optimal commitment involves.

In the literature that contrasts policy commitment with discretionary policymaking, fol-
lowing Kydland and Prescott, “commitment” is generally taken to mean a speci¬cation,
once and for all, of the state-contingent action to be taken at each subsequent date. An
optimal commitment is then a choice of such a state-contingent plan so as to maximize the
ex-ante expected value of the policymaker™s objective, as evaluated at the initial date t0 at
which the commitment is chosen. This leads to a description of optimal policy in terms of a
speci¬cation of the instrument setting as a function of the history of exogenous shocks since
date t0 .

But the solution to such an optimization problem is not an appealing policy recommen-
dation in practice. For it is generally not time consistent ” solving the same optimization
problem at a later date t1 , to determine the optimal commitment from that date onward,
will not result in a state-contingent plan from date t1 onward that continues the plan judged
to be optimal at date t0 . This is because the commitment chosen at date t0 will take ac-
count of the consequences of the commitments made for dates t1 and later for expectations
between dates t0 and t1 , while at date t1 these expectations will be taken as historical facts
that cannot be changed by the policy chosen from then on. (This is just the reason why
discretionary optimization does not lead to the same policy as an optimal commitment.)
Hence this policy proposal cannot be regarded as proposing a decision procedure that can be
used at each date to determine the best action at that date; instead, a state-contingent plan
must be determined once and for all, for the rest of time, and thereafter simply implemented,
whether it continues to appear desirable or not.

Such a proposal is not a practical one, for two reasons. First, enumeration in advance of
all of the possible subsequent histories of shocks will not be feasible ” the kinds of situations
that the central bank may face at a given date cannot are too various to possibly be listed
in advance. And second, the arbitrariness of continuing to stick to a particular speci¬ed
policy simply because it looked good at a particular past date ” the date t0 at which one
happened to make the commitment ” is su¬ciently unappealing that one cannot imagine a
central bank binding itself to behave in this way, or the private sector believing that it had.
Here my argument is not that central bankers are incapable of commitment to a systematic
rule of conduct, so that they are inevitably discretionary optimizers; it is rather that their
commitment must be based upon an understanding of the rational justi¬cation of the rule,
rather than the mere fact that it happens to been chosen (even by themselves) on a past

Both problems can be avoided by commitment to a systematic rule for determining their
policy action at each decision point, that does not reduce to a once-and-for-all speci¬cation
of the instrument setting as a function of the history of shocks. In chapter 8, it is shown

that one can design rules for setting the central bank™s interest-rate operating target that
lead to optimal dynamic responses to shocks, without the rule speci¬cation having to refer
to the various disturbances that may have occurred. The disturbances a¬ect the instrument
setting, of course; but they a¬ect it either as a result of having a¬ected endogenous variables,
such as in¬‚ation and output, to which the instrument setting responds, or as a result of
being factored into the central bank™s projections of the future evolution of the economy
under alternative possible instrument settings. Such a rule can result in optimal equilibrium
responses to disturbances of any of a vast number of possible types, so that the potential
disturbances need not even be listed in advance in order to describe the rule and evaluate
its desirability.

The optimal rules derived in accordance with the principles set out in chapter 8 are also
time-invariant in form. This means that the optimal rule that would be derived at date t0 ,
on the basis of a particular structural model of the monetary transmission mechanism and
a particular understanding of the central bank™s stabilization objectives, will also be derived
at date t1 , assuming that the bank™s model and objectives remain the same. A commitment
to conduct policy in accordance with a rule that is judged optimal on this criterion is thus
time consistent, in the sense that reconsideration of the matter at a later date on the basis
of the same principle will lead to a decision to continue the same course of action as had
been intended earlier.11

Because of this, adherence to a policy rule need not be taken to mean adoption of a rule
at some initial date, after which the rule is followed blindly, without ever again considering
its desirability. Instead, rule-based policymaking as the term is intended here means that
at each decision point an action is taken which conforms to a policy rule, which rule is
itself one that is judged to be optimal (from a “timeless perspective” that is made precise in
chapter 8) given the central bank™s understanding of the monetary transmission mechanism

Note that “time consistency” in the sense that we use the term here does not mean that the policymaker
does not believe at any time that it is possible to achieve a higher expected value for its objective by deviating
from its intended rule. Time consistency does not require this, because this is not the criterion according to
which the central bank™s action is judged to be optimal at any time, including the initial date t0 .

at the time that the decision is made. The desire to follow a rule (and so to avoid the trap
of discretionary optimization) does not mean that the bank must refrain from asking itself
whether adherence to the rule is consistent with its stabilization objectives. It simply means
that whenever this question is taken up, the bank should consider what an optimal rule of
conduct would be, rather than asking what an optimal action is on the individual occasion,
and that it should consider the desirability of alternative rules from an impartial perspective
that does not amount to simply ¬nding a rationalization for the action that it would like to
take on this particular occasion.12 A central bank might reconsider this question as often
as it likes, without this leading it into the kind of sub-optimal behavior that results from
discretionary optimization. And when considering the desirability of a policy rule, it is correct
for the bank to consider the e¬ects of its being expected to follow the rule inde¬nitely, even
though it does not contemplate binding itself to do so; for as long as its view of the policy
problem does not change (which it has no reason to expect), a commitment to rule-based
policymaking should guarantee that it will continue to act according to the rule judged to
be optimal.

Rule-based policymaking in this sense avoids the sorts of rigidity that are often associated
with commitment to a “rule”, and that probably account for much of the resistance that
central bankers often display toward the concept of a policy rule. A commitment to rule-
based policymaking does not preclude taking account of all of the information, from whatever
sources, that the central bank may have about current economic conditions, including the
recognition that disturbances may have occurred that would not have been thought possible
a few months earlier. For a policy rule need not specify the instrument setting as a function
of a speci¬ed list of exogenous states, and indeed it is argued in chapter 8 that an optimal
rule should in general not take this form. Nor does it preclude changing the form of the

The distinction between these two perspectives is similar to the distinction that is made in ethical theory
between “rule utilitarianism” and “act utilitarianism” (Brandt, 1959; Harsanyi, 1982). Act utilitarianism is
the view that the right act on any occasion is the one that will maximize social utility in the situation that
the actor is in at that time. Rule utilitarianism instead maintains that a right act is one that conforms to
the correct rule for this sort of situation, where a correct rule is one that would maximize social utility if
always followed in all situations of this type.

policy rule when the bank™s view of the monetary transmission changes, as it surely will,
owing both to institutional change in economies themselves and to the progress of knowledge
in economics. Hence it allows the sort of ¬‚exibility that is often associated with the term
“discretion”, while at the same time eliminating the systematic biases that follow from policy
analysis that naively applies dynamic-programming principles.

3 Monetary Policy without Control of a Monetary Ag-

Thus far we have discussed the desirability of a monetary policy rule without saying much
about the precise form of rule that is intended. To be more concrete, the present study
considers the design of a rule to be used in determining a central bank™s operating target
for a short-term nominal interest rate. This target will ordinarily be revised at intervals of
perhaps once a month (as at the ECB) or eight times a year (as in the U.S.).13
Our focus on the choice of an interest-rate rule should not surprise readers familiar with
the current practice of central banks. Monetary policy decisionmaking almost everywhere
means a decision about the operating target for an overnight interest rate, and the increased
transparency about policy in recent years has almost meant greater explicitness about the
central bank™s interest-rate target and about the way in which its interest-rate decisions are
made. In such a context, it is natural that adoption of a policy rule should mean commitment
to a speci¬c procedure for deciding what interest-rate target is appropriate.
Nonetheless, theoretical analyses of monetary policy have until recently almost invariably
characterized policy in terms of a path for the money supply, and discussions of policy rules in
the theoretical literature have mainly considered money-growth rules of one type or another.
This curious disjunction between theory and practice predates the enthusiasm of the 1970s
for monetary targets. Goodhart (1989) complains of “an unhelpful dichotomy, between the
The question of the optimal frequency of reconsideration of the interest-rate target is one of obvious
practical interest. But we shall not take it up in this study, as we consider optimal policy in the context
of a discrete-time model of the transmission mechanism with “periods” corresponding to the length of the
central bank™s decision cycle.

theory and the reality of Central Bank operations” that equally characterized the work of
John Maynard Keynes and Milton Friedman.

When either of these two great economists would discuss practical policy matters
concerning the level of short-term interest rates, they had no doubts that these
were normally determined by the authorities, and could be changed by them, and
were not freely determined in the market.... But when they came to their more
theoretical papers, they often reverted to the assumption that the Central Bank
sets the nominal money stock, or alternatively ¬xes the level of the monetary base,
[with] the demand and supply of money ... equilibrated in the short run ... by
market-led developments in nominal interest rates (pp. 330-331).

The present study instead seeks to revive the earlier approach of Knut Wicksell, and
considers the advantages of systematic monetary policies that are described in terms of rules
for setting a nominal interest rate. While the implied evolution of the money supply is
sometimes discussed, the question is often ignored; some of the time, we shall not bother
to specify policy (or our economic model) in su¬cient detail to determine the associated
path of the money supply, or even to tell if one can be uniquely determined in principle.
Some readers may fear as a result that we consider an ill-posed question ” that the “policy
rules” that we study may not represent su¬ciently complete descriptions of policy to allow
its consequences to be determined, or may not represent states of a¬airs that the central
bank is able to bring about. Hence some general remarks may be appropriate about why
it is possible to conceive of the problem of monetary policy as a problem of interest-rate
policy, before turning to examples of the speci¬c types of interest-rate rules that we wish to

3.1 Implementing Interest-Rate Policy

An argument that is sometimes made for specifying monetary policy in terms of a rule for
base-money growth rather than an interest-rate rule is that central banks do not actually ¬x
overnight interest rates. Even when banks have an operating target for the overnight rate,
they typically seek to implement it through open-market operations in Treasury securities or
their equivalent ” that is, by adjusting the supply of central-bank liabilities to a level that

is expected to cause the market for overnight cash to clear near the target rate. Thus it may
be argued that the action that the central bank actually takes each day is an adjustment
of the nominal magnitude of the monetary base, so that a complete speci¬cation of policy
should describe the size of this adjustment each day.
But even when banks implement their interest-rate targets entirely through quantity ad-
justments, as is largely correct as a description of current U.S. arrangements, this conclusion
hardly follows. Central banks like the U.S. Federal Reserve determine their quantity ad-
justments through a two-step procedure: ¬rst the interest-rate target is determined by a
monetary policy committee (the Federal Open Market Committee in the U.S.) without con-
sideration of the size of the implied open-market operations, and then the appropriate daily
open-market operations required to maintain the funds rate near the target are determined
by people closer to the ¬nancial markets (mainly the Trading Desk at the New York Fed).
The higher-level policy decision about the interest-rate target is the more complicated one,
made much less frequently because of the complexity of the deliberations involved,14 and it
is accordingly this decision with which the present study is concerned.
Nor is it the case that a central bank™s interest-rate target must be implemented through
choice of an appropriate supply of central-bank liabilities. A central bank can also in¬‚uence
the interest rate at which banks will lend overnight cash to one another through adjustment
of the interest rate paid on overnight balances held at the central bank and/or the interest
rate at which the central bank is willing to lend overnight cash to banks that run overdrafts
on their clearing accounts at the central bank. These are important policy tools outside
the U.S., and in some countries are the primary means through which the central bank
implements its interest-rate targets.
As is discussed in more detail in Woodford (2001xx), countries like Canada, Australia
The comparative simplicity of the decision about each day™s open-market operation is not so much
because each day™s demand for Fed balances is highly predictable as because the Fed learns immediately how
much it has misjudged market demand each day, and can act the following day in response to the previous
day™s gap between the actual funds rate and the target rate. Owing to intertemporal substitution in the
demand for reserves under U.S. regulations, a credible commitment by the Fed to respond the following day
is enough to keep the funds rate from deviating too much from the target most of the time. See Taylor
(2000) for further discussion of the Trading Desk™s reaction function.

and New Zealand now implement monetary policy through a “channel system”. In a system
of this kind, the overnight interest rate is kept near the central bank™s target rate through
the provision of standing facilities by the central bank, with interest rates determined by the
central bank™s current target interest rate ¯t . In addition to supplying a certain aggregate
quantity of clearing balances (adjusted through open-market operations), the central bank
o¬ers a lending facility, through which it stands ready to supply an arbitrary amount of
additional overnight balances at an interest rate determined by a ¬xed spread over the
target rate (i.e., il = ¯t + δ). In the countries just mentioned, the spread δ is generally equal

to 25 basis points, regardless of the level of the target rate. Finally, depository institutions
that settle payments through the central bank also have the right to maintain excess clearing
balances overnight with the central bank at a deposit rate id = ¯t ’ δ, where δ is the same

¬xed spread.

The lending rate on the one hand and the deposit rate on the other then de¬ne a channel
within which overnight interest rates should be contained.15 Because these are both standing
facilities (unlike the Fed™s discount window in the U.S.), no bank has any reason to pay
another bank a higher rate for overnight cash than the rate at which it could borrow from
the central bank; similarly, no bank has any reason to lend overnight cash at a rate lower
than the rate at which it can deposit with the central bank. The result is that the central
bank can control overnight interest rates within a fairly tight range regardless of what the
aggregate supply of clearing balances may be; frequent quantity adjustments accordingly
become less important.

Woodford (2001xx) describes a simple model of overnight interest-rate determination
under such a system. In this model, the daily demand for clearing balances by depository
institutions depends only on the location of the interbank market rate relative to the channel

It is arguable that the actual lower bound is somewhat above the deposit rate, because of the convenience
and lack of credit risk associated with the deposit facility, and similarly that the actual upper bound is slightly
above the lending rate, because of the collateral requirements and possible stigma associated with the lending
facility. Nonetheless, market rates are observed to stay within the channel established by these rates (except
for occasional slight breaches of the upper bound during the early months of operation of Canada™s system
” see Figure 1.1), and typically near its center.

established by the two standing facilities, rather than on the absolute level of this interest
rate. The interbank market then clears at an interest rate

it = id + F ’ (il ’ id ), (3.1)
t t t

where St is the aggregate supply of clearing balances (determined by the central bank™s open-
market operations), σt is a factor measuring the degree of uncertainty about payment ¬‚ows
on a given day, and F is a cumulative distribution function that increases monotonically
from 0 (when its argument is ’∞) to 1 (as the argument approaches +∞).
As noted, the market overnight rate is necessarily within the channel: id ¤ it ¤ il . Its
t t

exact position within the channel should be a decreasing function of the supply of central-
bank balances. The model predicts an equilibrium overnight rate at exactly the target rate
(the midpoint of the channel) when the supply of clearing balances is equal to

St = ’F ’1 (1/2) σt . (3.2)

If the probability distribution of unexpected payment ¬‚ows faced by each institution is
roughly symmetric, so that F (0) is near one-half, then the aggregate supply of clearing
balances required to maintain the overnight rate near the target rate should not vary much
with changes in σt . Even if this is not quite true, the adjustments of the supply of clearing
balances required by (3.2) are unrelated to changes in the target level of interest rates.
Thus achievement of the central bank™s operating target does not require any quantity
adjustments through open-market operations in response to deviations of the market rate
from the target rate; nor are any changes in the supply of central-bank balances required when
the bank wishes to change the level of overnight interest rates. The target level of clearing
balances in the system (3.2) need be adjusted only in response to “technical” factors (e.g.,
changes in the volume of payments on certain days that can be expected to a¬ect the σi ),
but not on occasions when it is desired to “tighten” or “loosen” monetary policy. Instead,
changes in the level of overnight rates, when desired, are brought about through the shifts in
the deposit rate and lending rate that automatically follow from a change in the target rate


overnight rate




Feb99 Jun99 Oct99 Feb99 Jun00 Oct00 Feb01 Jun01

Figure 1.1: The “channel” or operating band and the market overnight rate, since
introduction of the LVTS system in Canada. Source: Bank of Canada.

(and constitute the operational meaning of such a change), without any need for quantity
This type of system has proven highly e¬ective in Canada, Australia and New Zealand in
controlling the level of overnight interest rates. For example, Figure 1.1 plots the overnight
rate in Canada since the adoption of the Large-Value Transfer System for payments in
February 1999, at which time the standing facilities described above were adopted.16 One
observes that the channel system has been quite e¬ective, at least since early in 2000, at
keeping the overnight interest rate not only within the Bank™s 50-basis-point “operating
band” or channel, but usually within about one basis point of the target rate. Australia and
New Zealand similarly now achieve achieve considerably tighter control of overnight interest
A system of the kind described here has been used in Australia since June 1998, and in New Zealand
since March 1999.


ff rate







Jan99 May99 Sep99 Jan00 May00 Sep00 Jan01 May01 Aug01

Figure 1.2: The U.S. fed funds rate and the Fed™s operating target. Source: Federal Reserve

rates than is achieved under the current operating procedures employed in the U.S.17 (For
purposes of comparison, Figure 1.2 plots the federal funds rate together with the Fed™s
operating target over the same time period.)
Thus the quantity adjustments of the supply of central-bank balances18 that are involved
in implementation of interest-rate policy are quite di¬erent under a channel system as op-
Since March 2000, the standard deviation of it ’¯t has been only 1.5 basis points for Australia, 1.1 basis
points for Canada, and less than 0.4 basis points for New Zealand, but 13.4 basis points for the U.S. See
Woodford (2001xx) for corresponding plots for the other two countries, and for discussion of the di¬erences
in the four countries™ ability to respond to the “Y2K” panic without loss of control of short-term interest
We refer here to adjustments of the supply of central-bank balances rather than adjustments of the
monetary base because in all of the countries under discussion, changes in the public™s demand for currency
are automatically accommodated by open-market operations that change the monetary base while seeking to
insulate the supply of central-bank balances from the e¬ects of such developments. Thus despite the emphasis
of the academic literature on monetary-base rules, in practice a quantity-targeting rule that is intended to
directly specify the central bank™s daily open-market open-market operation would have to specify a target
supply of central-bank balances rather than a target value for the monetary base.

posed to the system used in the U.S. In the U.S., policy can be “tightened” only by restricting
the supply of Fed balances, so that the equilibrium spread between the return available on
interbank lending and that available on Fed balances increases; in Canada, instead, there
need be no change in supply, as there is no desire to change the spreads il ’ it or it ’ id .
t t

Yet there is no reason to believe that these institutional details have any important conse-
quences for the e¬ects of interest-rate policy on these economies, and hence for the way in
which it makes sense for these di¬erent central banks to determine their interest-rate oper-
ating targets. It follows that our conclusions would be of less universal validity if we were
to formulate them in terms of a rule for determining the appropriate size of open-market
operations, assuming American institutional arrangements.
Furthermore, for a country with a channel system, it would not be possible to formulate
our advice in terms of a quantity-targeting rule. On the occasions upon which it is appro-
priate for the central bank to tighten or loosen policy, this does not imply any change in the
appropriate target for the supply of central-bank balances; yet this does not at all mean that
the central bank should not act! Because the crucial policy instruments in these countries
are in fact the interest rates associated with the two standing facilities, that are in turn
directly based on the time-varying interest-rate target, a policy rule for such countries must
necessarily be formulated as an interest-rate rule. In fact, this way of specifying monetary
policy is equally convenient for a country like the U.S., and is the one that we shall use in
this study.

3.2 Monetary Policy in a Cashless Economy

Another case in which a monetary policy prescription would have to be speci¬ed in terms of
an interest-rate rule would be if our advice were to be applicable to a “cashless” economy,
by which we mean an economy in which there are no monetary frictions whatsoever. In a
hypothetical economy of this kind, no central-bank liabilities have any special role to play
in the payments system that results in a willingness to hold them despite yielding a lower
return than other, equally riskless short-term claims. Consideration of this extreme case is

of interest for two reasons.

First, it is possible to imagine that in the coming century the development of electronic
payments systems could not only substitute for the use of currency in transactions, but
also eliminate any advantage of clearing payments through accounts held at the central
bank, as discussed by King (1999). This prospect is highly speculative at present; most
current proposals for variants of “electronic money” still depend upon the ¬nal settlement
of transactions through the central bank, even if payments are made using electronic signals
rather than old-fashioned instruments such as paper checks.19 Yet it is possible that in the
future central banks will face the problem of what their role should be in such a world.
And the question of how the development of electronic money should be regulated will face
them much sooner. If one takes the view that monetary policy can be implemented only by
rationing the supply of something that ful¬lls an essential function in the payments system,
it is likely to be judged important to prevent the development of alternatives to payments
using central-bank money, in order to head o¬ a future in which the central bank is unable
to do anything at all on behalf of macroeconomic stabilization ” in which it becomes “an
army with only a signal corps,” in the evocative phrase of Benjamin Friedman (1999).

A second reason why it is useful to consider policy implementation in this hypothetical
case is that if we can show that e¬ective interest-rate control is possible even in the complete
absence of monetary frictions, it may well simplify our analysis of basic issues in the theory
of monetary policy to start from an analysis of the frictionless case, just as a physicist does
when analyzing the motion of a pendulum or the trajectory of a cannonball. The appeal
of this analytical approach was clear already to Wicksell (1898), who famously began his
analysis (though writing at the end of the nineteenth century!) by considering the case of a
“pure credit economy”, de¬ned as

Charles Freedman (2000), for one, argues that the special role of central banks in providing for ¬nal
settlement is unlikely ever to be replaced, owing to the unimpeachable solvency of these institutions, as
government entities that can create money at will. Some, such as Goodhart (2000), equally doubt that
electronic media can ever fully substitute for the use of currency.

a state of a¬airs in which money does not actually circulate at all, neither in the
form of coin (except perhaps as small change) nor in the form of notes, but where
all domestic payments are e¬ected by means of ... bookkeeping transfers (p. 70).

This is the approach that will be taken in the chapters to follow. Our basic model (developed
beginning in chapter 2) will be one that abstracts from monetary frictions, in order to direct
more attention to more essential aspects of the monetary transmission mechanism, such as
the way that spending decisions depend on expected future interest rates as well as current
ones, or the way in which ¬‚uctuations in nominal expenditure a¬ect real activity. We then
pause to consider at various points the modi¬cations of our analysis that are required in
order to take account of the monetary frictions that evidently exist, given the observation
that non-interest-earning currency continues to be held; it is shown that, as a quantitative
matter, these modi¬cations are of relatively minor importance.
In our discussion of interest-rate determination under a present-day channel system, we
have supposed that there is a demand for at least a small quantity of central-bank balances
for clearing purposes, and these are held despite the existence of a small opportunity cost
(25 basis points on average). But once the idea has been accepted that the central bank can
vary the overnight interest rate without ever having to vary the size of this return spread,
the functioning of the system no longer depends on the existence of a clearing demand. Let
us suppose instead that balances held with the central bank cease to be any more useful
to commercial banks than any other equally riskless overnight investment. In this case, the
demand for central-bank balances will be zero for all interest rates higher than the deposit
rate id . But banks should still be willing to hold arbitrary balances at the central bank as

long as the market overnight rate is no higher than the rate paid by the central bank. In
this case, it would no longer be possible to induce the overnight cash market to clear at a
target rate higher than the rate paid on overnight balances at the central bank; for equation
(3.1) reduces to it = id in the case of any positive supply of central-bank balances.

But the central bank could still control the equilibrium overnight rate, by using the
deposit rate as its policy instrument.20 Such a system would di¬er from current channel

systems in that an overnight lending facility would no longer be necessary, so that there
would no longer be a “channel”.21 And the rate paid on central-bank balances would no
longer be set at a ¬xed spread δ below the target overnight rate; instead, it would be set at
exactly the target rate.

Yet perfect control of overnight rates should still be possible through adjustments of
the rate paid on overnight central-bank balances, and changes in the target overnight rate
would not have to involve any change in the target supply of central-bank balances, just as
is true under current channel systems. Indeed, in this extreme case, any variations that did
occur in the supply of central-bank balances would cease to have any e¬ect at all upon the
equilibrium overnight rate.

But how can interest-rate variation be achieved without any adjustment at all of the
supply of central-bank balances? Informal discussions often treat interest-rate control by
the central bank like a species of price control. Certainly, if a government decides to peg
the price of some commodity, it may be able to do so, but only by holding stocks of the
commodity that are su¬ciently large relative to the world market for that commodity, and
by standing ready to vary its holdings of the commodity by large amounts as necessary. In

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