. 2
( 2)

the market in question is a large one (more to the point, if either supply or demand in the
market is relatively price-elastic) relative to the size of the balance sheet of the government
entity seeking to control the price, one doubts that such e¬orts will be e¬ective. What is
di¬erent about controlling short-term nominal interest rates?

Grimes (1992) makes a related point, showing that variation of the interest rate paid on central-bank
balances would be e¬ective in an environment in which central-bank reserves are no more useful for carrying
out transactions than other liquid government securities, so that open-market purchases or sales of such
securities are completely ine¬ective. Hall (1983, 1999) has also proposed this as a method of price-level
control in the complete absence of monetary frictions. Hall speaks of control of the interest yield on a
government “security”, without any need for a central bank at all. But because of the special features that
this instrument would need to possess, that are not possessed by privately issued securities ” it is a claim
only to future delivery of more units of the same instrument, and society™s unit of account is de¬ned in terms
of this instrument ” it seems best to think of it as still taking the same institutional form that it does today,
namely, balances in an account with the central bank.
This presumes a world in which no payments are cleared using central-bank balances. Of course, there
would be no harm in continuing to o¬er such a facility as long as the central-bank clearing system were still
used for at least some payments.

The di¬erence is that there is no inherent “equilibrium” level of interest rates to which
the market would tend in the absence of central-bank intervention, and against which the
central bank must therefore exert a signi¬cant countervailing force in order to achieve a
given operating target.22 This is because there is no inherent value (in terms of real goods
and services) for a ¬at unit of account such as the “dollar”, except insofar as a particular
exchange value results from the monetary policy commitments of the central bank. The
basic point was clear to Wicksell (1898, pp. 100-101), who compares relative prices to a
pendulum that returns always to the same equilibrium position when perturbed, while the
money prices of goods in general are compared to a cylinder resting on a horizontal plane,
that can remain equally well in any location on the plane to which it may happen to be
moved.23 Alternative price-level paths are thus equally consistent with market equilibrium
in the absence of any intervention that would vary the supply of any real goods or services
to the private sector. And associated with these alternative paths for the general level of
prices are alternative paths for short-term nominal interest rates.

Of course, this analysis might suggest that while central banks can bring about an ar-
bitrary level of nominal interest rates (by creating expectations of the appropriate rate of
in¬‚ation), they should not be able to signi¬cantly a¬ect real interest rates, except through
trades that are large relative to the economy that they seek to a¬ect. It may also suggest
that banks should be able to move nominal rates only by altering in¬‚ation expectations; yet
banks generally do not feel that they can easily alter expectations of in¬‚ation over the near
term, so that one might doubt that banks should be able to a¬ect short-term nominal rates
through such a mechanism.

However, once one recognizes that many prices (and wages) are fairly sticky over short

This does not mean that Wicksell™s notion of a “natural” rate of interest determined by real factors is
of no relevance to the consideration of the policy options facing a central bank. It is indeed, as argued in
chapter 4. But the natural rate of interest is the rate of interest required for an equilibrium with stable
prices; the central bank nonetheless can arbitrarily choose the level of interest rates (within limits), because
it can choose the degree to which prices shall increase or decrease.
This is the ground for his argument ” in the quotation from the introduction to his book that begins
this chapter ” that control of the general level of prices involves no interference with the market mechanism
of the kind that is required if some relative price is to be controlled.

time intervals, the arbitrariness of the path of nominal prices (in the sense of their underde-
termination by real factors alone) implies that the path of real activity, and the associated
path of equilibrium real interest rates, are equally arbitrary. It is equally possible, from a
logical standpoint, to imagine allowing the central bank to determine, by arbitrary ¬at, the
path of aggregate real activity, or the path of real interest rates, or the path of nominal in-
terest rates, as it is to imagine allowing it to determine the path of nominal interest rates.24
In practice, it is easiest for central banks to exert relatively direct control over overnight
nominal interest rates, and so banks generally formulate their short-run objectives (their
operating target) in terms of the e¬ect that they seek to bring about in this variable rather
than one of the others.
Even recognizing the existence of a very large set of rational expectations equilibria ”
equally consistent with optimizing private-sector behavior and with market clearing, in the
absence of any speci¬cation of monetary policy ” one might nonetheless suppose, as Fischer
Black (1970) once did, that in a fully deregulated system the central bank should have
no way of using monetary policy to select among these alternative equilibria. The path
of money prices (and similarly nominal interest rates, nominal exchange rates, and so on)
would then be determined solely by the self-ful¬lling expectations of market participants.
Why should the central bank play any special role in determining which of these outcomes
should actually occur, if it does not possess any monopoly power as the unique supplier of
some crucial service?
The answer is that the unit of account in a purely ¬at system is de¬ned in terms of the
liabilities of the central bank.25 A ¬nancial contract that promises to deliver a certain number

This does not mean, of course, that absolutely any paths for these variables can be achieved through
monetary policy; the chosen paths must be consistent with certain constraints implied by the conditions for
a rational-expectations equilibrium, for example those presented in chapter 4. But this is true even in the
case of the central bank™s choice of a path for the price level. Even in a world with fully ¬‚exible wages and
prices, for example, it would not be possible to bring about a rate of de¬‚ation so fast as to imply a negative
nominal interest rate.
See Hall (1999) and White (2001) for expressions of similar views. White emphasizes the role of legal
tender statutes in de¬ning the meaning of a national currency unit. But such statutes do not represent a
restriction upon the means of payment that can be used within a given geographical region ” or at any
rate, there need be no such restrictions upon private agreements for the point to be valid. What matters is

of U.S. dollars at a speci¬ed future date is promising payment in terms of Federal Reserve
notes or clearing balances at the Fed (which are treated as freely convertible into one another
by Fed). Even in the technological utopia imagined by the enthusiasts of electronic money ”
where ¬nancial market participants are willing to accept as ¬nal settlement transfers made
over electronic networks in which the central bank is not involved ” if debts are contracted
in units of a national currency, then clearing balances at the central bank will still de¬ne the
thing to which these other claims are accepted as equivalent.

This explains why the nominal interest yield on clearing balances at the central bank
can determine overnight rates in the market as a whole. The central bank can obviously
de¬ne the nominal yield on overnight deposits in its clearing accounts as it chooses; it is
simply promising to increase the nominal amount credited to a given account, after all. It
can also determine this independently of its determination of the quantity of such balances
that it supplies. Commercial banks may exchange claims to such deposits among themselves
on whatever terms they like. But the market value of a dollar deposit in such an account
cannot be anything other than a dollar ” because this de¬nes the meaning of a “dollar”!

This places the Fed in a di¬erent situation than any other issuer of dollar-denominated
liabilities.26 Citibank can determine the number of dollars that one of its jumbo CDs will be
worth at maturity, but must then allow the market to determine the current dollar value of
such a claim; it cannot determine both the quantity that it wishes to issue of such claims and

simply what contracts written in terms of a particular unit of account are taken to mean, and the role of
law in stabilizing such meanings is essentially no di¬erent than, say, in the case of trademarks.
Costa and De Grauwe (2001) instead argue that “in a cashless society ... the central bank cannot ˜force
the banks to swallow™ the reserves it creates” (p. 11), and speak of the central bank being forced to “liquidate
... assets” in order the redeem the central-bank liabilities that commercial banks are “unwilling to hold”
in their portfolios. This neglects the fact that the de¬nition of the U.S. dollar allows the Fed to honor a
commitment to pay a certain number of dollars to account-holders the next day by simply crediting them
with an account of that size at the Fed ” there is no possibility of demanding payment in terms of some
other asset valued more highly by the market. Similarly, Costa and De Grauwe argue that “the problem of
the central bank in a cashless society is comparable to [that of a] central bank pegging a ¬xed exchange rate”
(footnote 15). But the problem of a bank seeking to maintain an exchange-rate peg is that it promises to
deliver a foreign currency in exchange for its liabilities, not liabilities of its own that it freely creates. Costa
and De Grauwe say that they imagine a world in which “the unit of account remains a national a¬air ...
and is provided by the state” (p. 1), but seem not to realize that this means de¬ning that unit of account
in terms of central-bank liabilities.

the interest yield on them. Yet the Fed can, and does so daily ” though at present it chooses
to ¬x the interest yield on Fed balances at zero and only to vary the supply. The Fed™s current
position as monopoly supplier of an instrument that serves a special function is necessary
in order for variations in the quantity supplied to a¬ect the equilibrium spread between this
interest rate and other market rates, but not in order to allow separate determination of the
interest rate on central-bank balances and the quantity of them in existence.

Yes, some may respond, a central bank would still be able to determine the interest rate
on overnight deposits at the central bank, and thus the interest rate in the interbank market
for such claims, even in a world of completely frictionless ¬nancial markets. But would
control of this interest rate necessarily have consequences for other market rates, the ones
that matter for critical intertemporal decisions such as investment spending? The answer
is that it must ” and all the more so in a world in which ¬nancial markets have become
highly e¬cient, so that arbitrage opportunities created by discrepancies among the yields
on di¬erent market instruments are immediately eliminated. Equally riskless short-term
claims issued by the private sector (say, shares in a money-market mutual fund holding very
short-term Treasury bills) would not be able to promise a di¬erent interest rate than the one
available on deposits at the central bank; otherwise, there would excess supply or demand
for the private-sector instruments. And determination of the overnight interest rate would
also have to imply determination of the equilibrium overnight holding return on longer-lived
securities, up to a correction for risk; and so determination of the expected future path of
overnight interest rates would essentially determine longer-term interest rates.

The special feature of central banks, then, is simply that they are entities the liabilities of
which happen to be used to de¬ne the unit of account in a wide range of contracts that other
people exchange with one another. There is perhaps no deep, universal reason why this need
be so; it is certainly not essential that there be one such entity per national political unit.
Nonetheless, the provision of a well-managed unit of account ” one in terms of which the
equilibrium prices of many goods and services will be relatively stable ” clearly facilitates
economic life. And given the evident convenience of having a single unit of account be used by

most of the parties with whom one wishes to trade, one may well suppose that this function
should properly continue to be taken on by the government, even in a world of highly e¬cient
information processing. We here assume a world in which central banks (whether national
or supra-national, as in the case of the ECB) continue to ful¬ll this function, and in which
they are interested in managing their ¬at currency in the public interest. The present study
aims to supply a theory that can help them to do so.

4 Interest-Rate Rules

We have argued that the central problem of the theory of monetary policy is to provide
principles that can be used in selecting a desirable rule for setting a central bank™s interest-
rate operating target. It is perhaps worth saying a bit more at this point about exactly what
form of rules we have in mind, and what sort of questions we would like to answer about
them. This will provide a more concrete background for the analysis to be developed in the
chapters to come.

Probably the earliest example of a prescription for monetary policy in terms of an interest-
rate rule is due to Wicksell (1898, 1907). Although writing at a time when the leading indus-
trial nations remained committed to the gold standard, and even most scholars assumed the
necessity of a commodity standard of one sort or another, Wicksell foresaw the possibility of
a pure ¬at standard, and indeed argued that it was essential for the development of “a ratio-
nal monetary system.” He furthermore advocated an interest-rate rule for the management
of such a system. His original (1898) statement of the proposed rule was as follows:

So long as prices remain unaltered the [central] banks™ rate of interest27 is to
remain unaltered. If prices rise, the rate of interest is to be raised; and if prices
fall, the rate of interest is to be lowered; and the rate of interest is henceforth
to be maintained at its new level until a further movement of prices calls for a
further change in one direction or the other (p. 189, italicized in original).

Wicksell™s proposal can be represented mathematically as a commitment to set the central

bank™s interest-rate operating target it according to a relation of the form28

it = ¯ + φ p t ,
± (4.1)

where pt is the log of some general price index (the one that the policy aims to stabilize)
and φ is a positive response coe¬cient, or alternatively by a rule of the form

∆it = φ πt (4.2)

where πt ≡ ∆pt is the in¬‚ation rate.29 We study price-level determination under policy rules
of this kind in chapter 2, and argue that such a rule should indeed succeed in stabilizing the
price index around a constant level; the principles that determine the equilibrium price level
under such a regime are brie¬‚y sketched in section xx.
A simple “Wicksellian” rule of this kind has other advantages as well, at least in compari-
son to other equally simple rules, as discussed in chapter 7. Nonetheless, we shall not con¬ne
our attention to rules of this kind. Our primary interest in this study is in the analysis of
proposals that are closer in form to the policies currently followed by many central banks.
These rules involve an (explicit or implicit) target for the in¬‚ation rate, rather than for the
price level; nor are they expressible solely in terms of interest-rate changes, so that they
are equivalent to a rule that responds to the price level, as in the case of (4.2). The rules
typically allow for “base drift” in the price level as a result ” even if the in¬‚ation rate is
kept within a narrow interval at all times, there is no long-run mean reversion in the price
level, or even in the price level de¬‚ated by some deterministic target path. And as we shall
eventually conclude in chapter 8, optimal interest-rate rules are likely to have this property.
Wicksell proposes nothing so speci¬c as a log-linear relation of this kind, of course; he only describes a
monotonic relationship. The log-linear speci¬cation is useful for the simple calculations of the next section.
In chapter 2, we discuss the usefulness of this sort of log-linear approximation of what is necessarily not a
globally log-linear rule. The speci¬cation (4.1) cannot be maintained for all possible price levels, owing to
the requirement that the nominal interest rate be non-negative.
Note that a commitment to set the interest rate according to (4.2) from some date t0 forward is equivalent
to a commitment to set it according to a rule of the form (4.1), where the intercept ¯ corresponds to
it0 ’1 ’φ pt0 ’1 . Fuhrer and Moore (1995xx) propose a more complicated interpretation of Wicksell™s proposal,
in which the interest change is instead a function of the price level. While their rule is slightly more di¬cult
to analyze, it does not lead to substantially di¬erent conclusions about the consequences of commitment to
a Wicksellian rule.

4.1 Contemporary Proposals

The best-known example of a proposed rule for setting interest rates is probably the one
proposed by John Taylor (1993), both as a rough description of the way that policy had
actually been made by the U.S. Federal Reserve under Alan Greenspan™s chairmanship,
and as a normative prescription (on the basis of stochastic simulations using a number of
econometric models). According to the “Taylor rule,” as it has come to be known, the Fed™s
funds-rate operating target it is set as a linear function of measures of the current in¬‚ation
rate and the current gap between real output and potential:

it = .04 + 1.5 (¯t ’ .02) + 0.5 (yt ’ yt ),
π (4.3)

where πt is the rate of in¬‚ation (the change in the log GDP de¬‚ator over the previous four
quarters, in Taylor™s illustration of the rule™s empirical ¬t), yt is log output (log real GDP
in Taylor™s plot), and yt is log “potential” output (log real GDP minus a linear trend, in
Taylor™s plot). The constants in Taylor™s numerical speci¬cation indicate an implicit in¬‚ation
target of two percent per annum, and an estimate of the long-run real federal funds rate of
two percent per annum as well, so that a long-run average in¬‚ation rate at the target requires
a long-run average funds rate of four percent. A slightly simpler rule in the same vein was
proposed for the U.K. by Charles Goodhart (1992), according to which “there should be a
presumption” that the nominal interest rate would satisfy an equation of the form

it = .03 + 1.5 πt ,

and “the Governor should be asked, say twice a year, to account for any divergence from
that ˜rule™ ”(p. 324).
The coe¬cients 1.5 and 0.5 in the Taylor rule are round ¬gures argued to approximately
characterize U.S. policy between 1987 and 1992, and that were found to result in desirable
outcomes (in terms of in¬‚ation and output stability) in simulations.30 In Taylor™s discussions
A similar form of policy rule was advocated, also on the basis of simulation studies, at around the same
time by Henderson and McKibbin (1993).

of the rule, he places particular stress upon the importance of responding to in¬‚ation above
the target rate by raising the nominal interest-rate operating target by more than the amount
by which in¬‚ation exceeds the target; the importance of this “Taylor Principle” is considered
in detail in chapters 2 and 4. Taylor (1999xx) argues that the Fed did not adhere to this
principle before 1979 (at which time Fed chairman Paul Volcker instituted a radical shift in
policy), and this failure may well have been responsible for the greater U.S. macroeconomic
instability during the 1960s and 1970s. Taylor illustrates the change in policy by estimating
simple Fed reaction functions of the form

it = ¯ + φπ (¯t ’ π ) + φx xt
± π ¯ (4.4)

for two di¬erent sample periods, using ordinary least squares; his coe¬cient estimates are
shown in Table 1.1. (Here we introduce the notation xt for the output gap, again equated
with deviations of log real GDP from trend in Taylor™s empirical work.) Nelson (2001) ¬nds
that estimates of Taylor-type rules for the U.K. tell a similar story; prior to the adoption of
in¬‚ation targeting in 1992, U.K. interest rates rose less than one-for-one with increases in
in¬‚ation (and in the mid-1970s, responded little at all), but since 1992, the long-run in¬‚ation
response coe¬cient is estimated to have been nearly 1.3.
Estimates of empirical central-bank reaction functions typically ¬nd that a dynamic
speci¬cation ¬ts the data better, whatever the validity may be of Taylor™s (1999xx) preference
for a purely contemporaneous speci¬cation on normative grounds.31 For example, Judd
and Rudebusch (1998) estimate Fed reaction functions according to which the funds-rate
operating target adjusts in response to changes in an implicit desired level of the funds rate
¯t according to partial-adjustment dynamics of the form32

it = (1 ’ ρ1 ) ¯t + ρ1 it’1 + ρ2 (it’1 ’ it’2 ).
± (4.5)

This is also true of the estimates for the U.K. reported in Nelson (2001). This is why we refer to Nel-
son™s “long-run in¬‚ation response coe¬cient” in the previous paragraph, rather than to a contemporaneous
response coe¬cient of the kind estimated by Taylor (1999xx).
Here as in all other regressions reported in this section, periods are assumed to be quarters, and quarterly
data are used in the estimation.

φπ (s.e.) φx (s.e.) γ ρ1 (s.e.) ρ2 (s.e)

Taylor (1999)
1960-79 0.81 (.06) 0.25 (.05)
1987-97 1.53 (.16) 0.77 (.09)

Judd-Rudebusch (1998)
1979-87 1.46 (.26) 1.53 (.80) 1 0.56 (.12)
1987-97 1.54 (.18) 0.99 (.13) 0 0.72 (.05) 0.43 (.10)

Clarida et al. (2000)
1960-79 0.83 (.07) 0.27 (.08) 0.68 (.05)
1979-96 2.15 (.40) 0.93 (.42) 0.79 (.04)

Orphanides (2001)
1966-79 1.64 (.38) 0.57 (.12) 0.70 (.07)
1979-95 1.80 (.48) 0.27 (.30) 0.79 (.11)

Table 1.1. Alternative estimates of Fed reaction functions.

The desired level of the funds rate in turn depends upon in¬‚ation and the output gap in a
manner similar to that postulated by Taylor,

¯t = ¯ + φπ (¯t ’ π ) + φx (xt ’ γxt’1 ),
± ± π ¯ (4.6)

except that the allowance for nonzero γ means that the desired funds rate may respond
to the rate of change of the output gap as well as (or instead of) its level. The Judd-
Rudebusch estimated coe¬cients for two di¬erent sample periods, corresponding to the Fed
chairmanships of Paul Volcker and Alan Greenspan respectively, are also reported in Table
1.1.33 Taylor™s view of the nature of policy in the Greenspan period is largely con¬rmed,
with the exception that Judd and Rudebusch estimate partial-adjustment dynamics implying
substantial persistence. They give a similar characterization of policy in the Volcker period,
In their preferred estimates, the value of γ is imposed rather than estimated. The extreme values
assumed for the separate periods, however, are suggested by preliminary regressions in which the value of γ
is unconstrained.

except that in this period the desired funds rate is found to depend on the rate of change of
the output gap, rather than its level.34
Many recent discussions of central bank behavior, both positive and normative, argue
instead for speci¬cations in which a bank™s operating target depends on forecasts. For
example, Clarida et al. (2000xx) estimate Fed reaction functions of the form35

¯t = ¯ + φπ E[πt+1 ’ π |„¦t ] + φx E[xt |„¦t ],
± ± ¯ (4.7)

where „¦t is the information set assumed to be available to the Fed when setting it , and
the actual operating target is again related to the desired funds rate ¯t through partial-
adjustment dynamics. Like Taylor, these authors ¬nd an important increase in the degree
to which the Fed™s desired level for the funds rate responds to in¬‚ation variations since 1979,
though in their speci¬cation the Fed responds to an in¬‚ation forecast rather than in¬‚ation
that has already occurred.36
Finally, it should be noted that the view that the Fed has responded more vigorously to
in¬‚ation variations since 1979 has not gone unchallenged. Attanasio (2001) argues instead
that the ¬ndings of Taylor and the other authors just cited are distorted by the use of in¬‚ation
and output-gap data (especially the output-gap estimates) that were not available to the
Fed at the time that its interest-rate decisions were made. When he instead estimates Fed
reaction functions of the kind assumed by Clarida et al. using the forecasts actually produced
by Fed sta¬ at the time rather than econometric projections using the data available now, he
obtains much more similar estimates for the pre-Volcker and post-Volcker periods, as shown
in the table. The in¬‚ation-response coe¬cient φπ is well above one in both periods, according
Judd and Rudebusch also estimate a reaction function for the period (1970-78) corresponding to the
chairmanship of Arthur Burns. Like Taylor, in this period they estimate an in¬‚ation-response coe¬cient φπ
less than one, though not signi¬cantly so in their case.
Clarida et al. also estimate variants of the rule in which the forecast horizon is assumed to be more than
one quarter in the future. The policies of in¬‚ation-targeting central banks have often been represented by
rules in which the interest-rate operating target responds to a forecast of in¬‚ation as many as 8 quarters in
the future. See, e.g., Black et al., (19xx), Batini and Haldane (1999).
Like Taylor, they also suggest that this change has led to greater macroeconomic stability in the later
period. They provide a theoretical analysis of why this could have been so, in terms of the vulnerability of
an economy to instability due to self-ful¬lling expectations in the case of a policy rule of the kind that they
estimate for the period 1960-79. Reasons for this are discussed in chapter 4.

to Orphanides™ estimates; he instead emphasizes the reduction in the size of φx as the crucial
policy change after 1979, and the key to U.S. macroeconomic stability since the mid-1980s.
We shall not seek here to resolve this debate about historical Fed policy, but simply note
that much current debate both about the explanation of recent U.S. policy successes and
about the reason for past policy failures turns upon claims about the desirability of particular
coe¬cients in Taylor-type rules.

These alternative characterizations suggest a number of questions about the form of a
desirable interest-rate rule. One obvious question is whether the variables to which the
Fed is described as responding in the Taylor rule and the estimated reaction functions just
discussed ” some measures of in¬‚ation and the output gap ” are ones that make sense. Is
it desirable for interest rates to be adjusted in response to variations in these variables, and
with the signs proposed by Taylor? Is there any ground for thinking it more important to
respond to variations in these variables than in others? Is responding to variations in these
variables an adequate substitute for attempting to respond to the underlying disturbances
that are perceived to be currently a¬ecting the economy?

If it does make sense to respond to these variables, how exactly should they be de¬ned?
Which sort of price index is most appropriately used in the in¬‚ation measure? Relative to
what concept of “potential output” should the “output gap” measure be de¬ned? And how
strongly is it desirable to respond to variations in these variables? Is a value of φπ greater
than one essential, as argued by Taylor? Is a large value of φx dangerous, as argued by

We shall also be interested in the most desirable dynamic speci¬cation of such an interest-
rate rule. Are purely contemporaneous responses, as prescribed by Taylor, preferable? Is
there any justi¬cation for the more inertial interest-rate dynamics indicated by the estimated
reaction functions? If so, how inertial is it desirable for interest-rate policy to be? Is it
preferable to respond to forecasts rather than to current or past values of in¬‚ation and the
output gap? If so, how far in the future should the forecasts look?

Another type of policy rule that has ¬gured prominently both in recent descriptions of

actual central-bank behavior and in normative prescriptions is an in¬‚ation-forecast targeting
rule. A classic example is the sort of rule that is often used to explain the current procedures
of the Bank of England (e.g., Vickers, 1998). According to the formula, the Bank should be
willing to adopt a given operating target it for the overnight interest rate at date t if and
only if the Bank™s forecast of the evolution of in¬‚ation over the next two years, conditional
upon the interest rate remaining at the level it , implies an in¬‚ation rate of 2.5 percent per
annum (the Bank™s current in¬‚ation target) two years after date t. This is an example of
what Svensson (1999, 2001) calls a “targeting rule” as opposed to an instrument rule. No
formula is speci¬ed for the central bank™s interest-rate operating target; instead, it is to be
set at whatever level may turn out to be required in order for the bank™s projections to
satisfy a certain target criterion. The target criterion need not involve only future in¬‚ation;
for example, Svensson (1999) advocates a “¬‚exible in¬‚ation targeting” rule in which the
interest rate is adjusted at date t so as to ensure that

Et πt+j + » Et xt+k = π ,
¯ (4.8)

where π is the average in¬‚ation target, the coe¬cient » > 0 depends on the relative im-
portance of output-gap stabilization, and the horizons j and k are not necessarily the same
distance in the future.
We shall also wish to consider the desirable speci¬cation of a target criterion in the case
of a policy rule of this sort. Again, a basic question is whether it makes sense to de¬ne
the target criterion in terms of projections for these particular variables, in¬‚ation and the
output gap, rather than others, such as monetary aggregates. If so, what should determine
the relative weight, if any, to be placed on the output-gap forecast? How far in the future
should the forecasts in the target criterion look? And is a desirable criterion purely forward-
looking, as in the case of the two examples just mentioned, or should the in¬‚ation target be
history-dependent, in addition to (possibly) depending on projected future output gaps?
This study will seek to elaborate a methodology that can be used to give quantitative
answers to questions of this sort about optimal policy rules. Of the course, the answers

obtained will depend on the details of what one assumes about the nature of the monetary
transmission mechanism, and I do not propose to argue for a speci¬c quantitative rule.
The aim of the present study is more to suggest a way of approaching the problem than
to announce the details of its solution. However, certain model elements recur in many of
the models currently used in studies of the e¬ects of monetary policy, both in the academic
literature and in central banks; and given the likelihood that a reasonable model will be
judged to include these features, we may obtain some tentative conclusions as to the likely
form of reasonable policy rules.

4.2 General Criticisms of Interest-Rate Rules

Before taking up speci¬c questions of these kinds about the form of desirable interest-rate
rules, it is ¬rst necessary to address some more basic issues. Would any form of interest-rate
rule represent a sensible approach to monetary policy? Proponents of monetary targeting
have often argued against interest-rate control as such ” asserting not that skill is required
in the choice of an interest-rate operating target, but that it is a serious mistake to have one
at all.
One famous argument, mentioned above, is that of Sargent and Wallace (1975). Sar-
gent and Wallace consider a general class of money-supply rules on the one hand, and a
general class of interest-rate rules on the other, and argue that while any of the money-
supply rules leads to a determinate rational expectations equilibrium (in the context of a
particular rational-expectations IS-LM model), none of the interest-rate rules do. By de-
terminacy of the equilibrium I mean that there is a unique equilibrium satisfying certain
bounds, made precise in chapter 2. Sargent and Wallace argue that interest-rate rules lead
to indeterminacy, meaning that even if one restricts one™s attention to bounded solutions to
the equilibrium relations (as we shall largely do in this study), there is an extremely large set
of equally possible equilibria. These include equilibria in which endogenous variables such
as in¬‚ation and output respond to random events that are completely unrelated to economic
“fundamentals” (i.e., to the exogenous disturbances that a¬ect the structural relations that

determine in¬‚ation and output), and also equilibria in which “fundamental” disturbances
cause ¬‚uctuations in equilibrium in¬‚ation and output that are arbitrarily large relative to the
degree to which the structural relations are perturbed. Thus in such a case, macroeconomic
instability can occur due purely to self-ful¬lling expectations. This is plainly undesirable, if
one™s objective is to stabilize in¬‚ation and/or output.37 Hence Sargent and Wallace argue
that interest-rate rules can be excluded from consideration as a class; the problem of optimal
monetary policy is then properly framed as a question of what the best money-supply rule
would be.
However, as McCallum (1981) notes, the Sargent-Wallace indeterminacy result applies,
even in the context of their own model, only in the case of interest-rate rules that specify an
exogenous evolution for the nominal interest rate; this includes the possibility of rules that
specify the nominal interest rate as a function of the history of exogenous disturbances, but
not rules that make the nominal interest rate a function of endogenous variables, such as
in¬‚ation or output. Yet the Taylor rule, and the other interest-rate rules discussed above,
are all rules of the latter sort, so that the Sargent-Wallace result need not apply. The same
is shown to be true, in chapters 2 and 4, in the case of the optimizing models of in¬‚ation and
output determination considered here. Indeed, we ¬nd that, at least in the case of the simple
model of the monetary transmission mechanism that is most extensively analyzed here, either
the type of feedback from the general price level to the interest rate (or from changes in the
price level to changes in the interest rate) advocated by Wicksell, or the type of feedback
from in¬‚ation and output to the central bank™s interest-rate operating target prescribed by
Taylor, would su¬ce to imply a determinate rational expectations equilibrium. In the case
of a level-to-level (or change-to-change) Wicksellian speci¬cation, it is only necessary that
the sign of the response be the one advocated by Wicksell. In the case of a change-to-level
speci¬cation like that proposed by Taylor, the “Taylor principle” mentioned above ” the
requirement that a sustained increase in in¬‚ation eventually result in an increase in nominal
The point remains valid if one™s objective is, as we shall argue that it should be, to stabilize output
relative to its natural rate, rather than output stabilization as such. For the ¬‚uctuations in output due
purely to self-ful¬lling expectations just mentioned will imply ¬‚uctuations in the output gap as well.

interest rates that is even larger in percentage points ” turns out to be the critical condition
that determines whether equilibrium should be determinate or not.38
A related criticism of interest-rate targeting also maintains that such a policy is dangerous
because it allows instability to be generated by self-ful¬lling expectations, but is not based
on the possibility of multiple rational-expectations equilibria. Friedman (1968) argues that
attempting to control nominal interest rates is dangerous on the basis of Wicksell™s (1898,
1907) famous analysis of the “cumulative process”. With a nominal interest rate that is ¬xed
at a level below the “natural rate”, in¬‚ation is generated that increases in¬‚ation expectations,
which then stimulates demand even further due to the reduction in the real rate, generating
even faster in¬‚ation, further increasing in¬‚ation expectations, and so on without bound.39
The same process should occur with the opposite sign if the interest rate happens to be set
above the natural rate; thus any attempt to ¬x the nominal interest rate would seem almost
inevitably to generate severe instability of the in¬‚ation rate. (In Friedman™s analysis, there
is no indeterminacy of the path of in¬‚ation, as in¬‚ation expectations are assumed to be a
speci¬c function of previously observed in¬‚ation.)
As is discussed in chapter 4, this analysis can be formalized in the context of an optimizing
model in which in¬‚ation and income forecasts are based on extrapolation from past data (e.g.,
using empirical time-series models). But once again, the classic analysis applies only in the
case of a policy that exogenously speci¬es the path of nominal interest rates. If instead a
surge in in¬‚ation and output leads to increases in nominal interest rates large enough to
raise real rates, then demand should be damped, tending to lower in¬‚ation as well ” so that
there should be no explosive instability of either in¬‚ation or output dynamics under adaptive
learning. Indeed, the analyses of Bullard and Mitra (2000, 2002) and Preston (2002) ¬nd
that conformity to the Taylor principle is both a necessary and su¬cient condition (at least
Clarida et al. (2000xx) argue on this basis that the macroeconomic instability of the 1970s in the U.S.
may have been increased by self-ful¬lling expectations, given that their estimates (see Table 1.1) imply that
the Taylor principle has been satis¬ed by post-1979 policy but not by previous policy.
This summarizes Friedman™s account, rather than Wicksell™s original discussion; Wicksell does not discuss
endogenous in¬‚ation expectations, and so concludes that the price level should rise without bound, rather
than the in¬‚ation rate. Lindahl (1939) was the ¬rst to introduce endogenous in¬‚ation expectations into the
analysis, and so to conclude that the in¬‚ation rate could rise without bound.

within certain simple classes of policy rules) for adaptive learning dynamics to converge to
a stationary rational-expectations equilibrium, in which in¬‚ation and output ¬‚uctuate only
in response to “fundamentals”.

Thus it is important to realize that these well-known criticisms of interest-rate targeting
assume that under such a policy the interest-rate target would remain ¬xed, regardless of
the path of in¬‚ation. The analyses are quite inapplicable in the case of policy rules such
as Wicksell™s rule, the Taylor rule or typical in¬‚ation-forecast targeting rules, which require
that interest rates be raised sharply if in¬‚ation is either observed or forecasted to exceed
the target rate consistently for a substantial period of time. In fact, in these conventional
arguments for monetary targeting, the reason for control of money growth is precisely that
this is a policy commitment that ensures that an excessive rate of in¬‚ation will lead to
interest-rate increases su¬cient to curb the growth of nominal expenditure. A ¬xed target
path for the money supply (or more generally, a path that is contingent only upon exogenous
state variables, not upon the path of the price level) implies that if the price level grows more
rapidly, the private sector will be forced to operate with a lower level of real money balances;
this will require interest-rate increases and/or a reduction in real activity su¬cient to reduce
desired real money balances to the level of the real money supply.

But the same kind of automatic increase in interest rates, curbing expenditure, can
be arranged through a simple commitment of the central bank to raise interest rates in
response to deviations of the general level of prices from its desired path, as ¬rst proposed
by Wicksell. And once one recognizes that quantity control is not necessary for such a
system to work, it is hard to see why one should wish to encumbered by it. Over the course
of the twentieth century, it came to be accepted that no convertibility of national currencies
into a real commodity such as gold was necessary in order for central banks to act in a
way that controlled the value of their currencies; and once this was accepted, it quickly
became evident that nations were better o¬ not relying upon such a crude mechanism as a
gold standard, which left the value of the national unit of account vulnerable to ¬‚uctuations
in the market for gold. Similarly, once one accepts that the adjustment of interest rates

to head o¬ undesired price-level variation can be managed by central banks without any
need for so mechanical a discipline as is provided by a money-growth target, it should be
clear that a properly chosen interest-rate rule can be more e¬cient than monetary targeting,
which has the unwanted side e¬ect of making interest rates (and hence the pace of aggregate
expenditure) vulnerable to variations in the relation between desired money balances and
the volume of transactions.
A more subtle criticism of interest-rate rules as an approach to systematic monetary
policy would argue that even if such rules lead to well-de¬ned, well-behaved equilibria, the
description of policy in this way may still not be useful to a central bank that wishes to
understand, and thus to accurately calibrate, the consequences of its actions. It is often
supposed that the key to understanding the e¬ects of monetary policy on in¬‚ation must
always be the quantity theory of money, according to which the price level is determined
by the relation between the nominal money supply on the one hand and the demand for
real money balances on the other. It may then be concluded that what matters about
any monetary policy is the implied path of the money supply, whether this is determined
through straightforward monetary targeting or in some more indirect manner.40 From such
a perspective, it might seem that a clearer understanding of the consequences of a central
bank™s actions would be facilitated by an explicit focus on what evolution of the money
supply the bank intends to bring about ” that is, by monetary targeting ” rather than
by talk about interest rate policy that, even if it does imply a speci¬c path for the money
supply, does not make the intended path entirely transparent.
The present study aims to show that the basic premise of such a criticism is incorrect.
One of the primary goals of Part I of this book is the development of a theoretical framework
in which the consequences of alternative interest-rate rules can be analyzed, which does not
require that they ¬rst be translated into equivalent rules for the evolution of the money
supply. Indeed, much of the time we shall analyze the consequences of interest-rate rules
without having to solve for the implied path of the money supply, or even having to specify
This is for example the perspective taken in the Monetary History of Friedman and Schwartz (1963).

the coe¬cients of a “money demand” relation. In the case of an economy without monetary
frictions ” a case that I shall argue is an analytically convenient approximation for many
purposes, and that may well represent the future, as discussed above ” there will not even
be any meaningful money supply or demand to be de¬ned. If instead we take account
of the sort of frictions that evidently still exist in an economy like the U.S. at present,
then our models will imply an equilibrium path for the money supply along with other
endogenous variables. But the factors determining the equilibrium paths of both in¬‚ation
and output will continue to be nearly the same as in the frictionless economy, so that it
does not seem at all natural or useful to try to explain the predicted paths of in¬‚ation and
output as consequences of the implied path of the money supply. Instead, it proves to be
possible to discuss the determinants of in¬‚ation and output in a fairly straightforward way in
terms of the coe¬cients of an interest-rate rule. Thus the characterizations of central-bank
policy o¬ered above are found to be quite convenient for analysis of the consequences of one
quantitative speci¬cation or another. We further show, in chapter 8, that optimal policy can
be conveniently represented in terms of speci¬cations of exactly this sort, leading to answers
to the very speci¬c questions about interest-rate policy posed in the previous section.

4.3 Neo-Wicksellian Monetary Theory

The non-quantity-theoretic analytical framework developed here develops several important
themes from the monetary writings of Knut Wicksell (1898, 1906, 1907). Wicksell argued
that even the variations in the price level observed in his own time, under the international
gold standard, were not primarily due to variations in the world gold supply, but rather to
two other factors ” the policies followed by central banks, adjusting the “bank rate” at
which they were willing to discount short-term bills, on the one hand, and real disturbances,
a¬ecting the “natural rate of interest” on the other. In Wicksell™s view, price stability
depended on keeping the interest rate controlled by the central bank in line with the “natural
rate” determined by real factors (such as the marginal product of capital). In¬‚ation occurred
whenever the central banks lowered interest rates, without any decline in the natural rate

having occurred to justify this, or whenever the natural rate of interest increased (due,
for example, to an increase in the productivity of investment opportunities), without any
adjustment of the interest rates controlled by central banks in response. De¬‚ation occurred
whenever a disparity was created of the opposite sign.
Whatever the validity of such a non-quantity-theoretic approach for the analysis of price-
level determination under the gold standard, Wicksell™s approach is a particularly congenial
one for thinking about our present circumstances ” a world of purely ¬at currencies in which
central banks adjust their operating targets for nominal interest rates in response to perceived
risks of in¬‚ation, but pay little if any attention to the evolution of monetary aggregates ”
to say nothing of the one to which we may be headed, in which monetary frictions become
negligible.41 In such a world, where the concepts of money supply and demand become
inapplicable, what is there to determine an equilibrium value for the general level of money
prices? One possible answer is the role of past prices in determining current equilibrium
prices, due either to wage or price stickiness, or to the e¬ect of past prices on expectations
regarding future prices (the critical factor in Wicksell™s own analysis). Thus once prices have
been at a certain level (for whatever arbitrary reason), this historical initial condition ties
down their subsequent evolution, though they may subsequently drift arbitrarily far from
that level. But probably the most important factor, in general, is the interest-rate policy of
the central bank, insofar as this responds to the evolution of some price index. A state of
a¬airs in which all wages and prices were 10 percent higher than they presently are would
not be equally possible as an equilibrium, if the observation of such a jump in the price level
would trigger an increase in interest rates, as called for under either a Wicksellian rule or
the Taylor rule.
The way in which the equilibrium price level can be determined by the central bank™s
interest-rate response to price-level variations, without any reference to the associated ¬‚uc-
tuations in any monetary aggregate, can be illustrated very simply. Let us suppose that
the equilibrium real rate of interest is determined by real factors (such as time preference
As noted earlier, Wicksell™s basic exposition of his theory is for the case of a “pure credit economy.”

and the productivity of capital), in complete independence of how nominal quantities may
evolve,42 and let {rt } be an exogenous stochastic process for this real rate. It then follows
that the short-term nominal interest rate it and the log price level pt must at all times satisfy
the Fisherian relation

pt = Et pt+1 + rt ’ it , (4.9)

assuming rational expectations on the part of the private sector. Because rt is a certain
function of exogenous real factors, rather than the measured real rate of return, this is an
equilibrium relation ” the condition required for equality between aggregate saving and
investment ” rather than an identity. This “¬‚exible-price IS equation” indicates how the
price level that clears the goods market ” or equivalently, that equates saving and investment
” depends on the expected future price level, real factors a¬ecting saving and investment,
and the nominal interest rate controlled by the central bank.
Now suppose that the central bank sets the short-term nominal interest rate according
to the Wicksellian rule

it = ¯t + φ pt ,
± (4.10)

which generalizes (4.1) in allowing for a time-varying intercept, indicating possible shifts
over time in monetary policy. Suppose furthermore that {¯t } is another exogenous stochastic
process (that is, determined independently of the evolution of prices), that may or may not
be correlated with the exogenous ¬‚uctuations in the equilibrium real rate of interest. Then
substituting (??) into (4.9) to eliminate it , we obtain a relation of the form

pt = ±Et pt+1 + ±(rt ’ ¯t )
± (4.11)

to determine the equilibrium evolution of the price level, given the exogenous processes
{rt , ¯t }, where ± ≡ 1/(1 + φ) is a coe¬cient satisfying 0 < ± < 1.
In the case that {rt , ¯t } are bounded processes, equation (4.11) has a unique bounded
In chapter 2, we present assumptions under which this is true in an explicit intertemporal equilibrium
model with ¬‚exible prices.

solution, obtained by “solving forward,” namely

±j+1 Et (rt+j ’ ¯t+j ).
pt = ± (4.12)

Thus the equilibrium price level ¬‚uctuates in a bounded interval around the long-run average
p ≡ φ’1 (¯ ’ ¯),
¯ r±

where r, ¯ are the long-run average values of rt and ¯t respectively. This analysis shows how
¯± ±
a policy rule that involves no targets for any monetary aggregate can nonetheless control
the long-run price level. It also shows how the determinants of equilibrium in¬‚ation can
be understood without any reference to the determinants of either the money supply or of
money demand ” indeed, it does not matter for the analysis just presented whether there
is any well-de¬ned demand function for the monetary base.
The account of price-level determination implied by this theory has a strongly Wicksellian
¬‚avor. We observe from (4.12) that the equilibrium price level at any date t is increased
by either a “loosening” of monetary policy ” represented by a reduction of the intercept
term ¯t ” not justi¬ed by any decline in the equilibrium real rate, or by an increase in
the equilibrium real rate rt that is not matched by a tightening of policy. Our forward-
looking model also implies that any news that allows the private sector to forecast the future
occurrence of either of these things should stimulate in¬‚ation immediately.
In the simple model sketched here, there is no distinction of the sort that Wicksell
makes between the actual real rate of return and the “natural rate” that would occur in an
intertemporal equilibrium with ¬‚exible prices. In chapter 4, however, we show how one can
usefully introduce such a distinction, in the context of a model with sticky prices. When
prices are temporarily sticky, the real rate of return at which borrowing and lending occurs
can di¬er from the natural rate of interest, just as the level of output can di¬er from its
natural rate; and the degree to which both occur depends on the degree of instability of the
overall price level, as it is only when the general level of prices is changing that price rigidity
creates distortions. Equilibrium condition (4.9) must then be replaced by a more general

one, of the form
it ’ Et πt+1 = rt + δ(πt , . . .), (4.13)

where rt is the natural rate of interest (here still assumed to depend only on exogenous
real factors), and the discrepancy δ(·) is a function of both current and expected future
in¬‚ation.43 The system consisting of conditions (4.10) and (4.13) can again be solved for a
unique bounded process for the price level, and the solution is of the form

pt = ψj Et (rt+j ’ ¯t+j )

for certain coe¬cients {ψj }. Thus in the more general case, it is variation in the natural rate
of interest due to real disturbances of various sorts, to the extent that such variation is not
matched by corresponding adjustment of the central bank™s reaction function, that causes
in¬‚ation variation. Just as in Wicksell™s theory, real disturbances a¬ecting desired saving
and investment are predicted to be important sources of price-level variations; and as in that
theory, the implied variation in the natural rate of interest is a useful summary statistic for
the way in which a variety of real disturbances should a¬ect the rate of in¬‚ation.
In chapters 2 and 4, we show how a similar analysis of equilibrium in¬‚ation determination
is possible in the case of a rule like the Taylor rule. In this case a positive response of the
interest rate to ¬‚uctuations in the in¬‚ation rate is not su¬cient to guarantee a determinate
equilibrium (a unique non-explosive equilibrium path for the in¬‚ation rate, rather than the
price level); it is instead necessary that the response coe¬cient be greater than one, in
accordance with the “Taylor principle” mentioned earlier. But in that case similar results
are obtained; equilibrium in¬‚ation is a function of current and expected future gaps between
the natural rate of interest and the intercept term in the Taylor rule.
We ¬nd, then, that it is possible to determine the consequences for in¬‚ation dynamics of
a given monetary policy rule when it is expressed in terms of an interest-rate rule, without
any need to ¬rst translate the rule into an implied state-contingent path for the money
In the case of the basic neo-Wicksellian model developed in chapter 4, δ is a function of πt , Et πt+1 , and
Et πt+2. .

supply. Hence the terms used to describe both actual central-bank policies and simple
policy prescriptions in the literature summarized above are not inappropriate ones; we can
conveniently analyze the consequences of systematic policies of these types as functions of
exactly the coe¬cients appearing in Table 1.1.

While the usefulness of the neo-Wicksellian framework sketched here is perhaps most
evident in the case of an economy without monetary frictions, so that the familiar quantity-
theoretic apparatus is plainly inapplicable, it is also equally useful in the case of an economy
in which monetary frictions still exist, at least of the modest sort that are indicated by the
observed willingness to hold non-interest-earning currency in an advanced economies like
that of the U.S. today. In what we have written above, we have not actually relied upon any
assumed absence of monetary frictions, except in assuming that the equilibrium real rate of
interest (or more generally, the natural rate of interest) is independent of the evolution of
nominal variables. But even in the presence of transactions frictions resulting in a demand
for base money despite its below-market rate of return, it is unlikely that the natural rate of
interest is much a¬ected, as a quantitative matter, by variations in the rate of in¬‚ation. (The
accuracy of the approximation involved in neglecting such e¬ects is considered numerically
in chapters 2 and 4.) Hence the approach proposed here is also appropriate for analysis
of the e¬ects of a Taylor rule in an economy like that of the U.S., where changes in the
Fed™s interest-rate operating target are implemented through adjustments in the supply of
(non-interest-earning) Fed balances. The monetary frictions that create a demand for such
balances are important for the size of quantity adjustment required to achieve a given change
in the funds rate, but of little importance for the e¬ects upon output and in¬‚ation of any
given change in the path of the funds rate.

Nor are the predictions of the neo-Wicksellian theory really any di¬erent from those of
a standard quantity-theoretic analysis, despite the apparent dissimilarity of approach. In
a quantity-theoretic analysis of in¬‚ation determination, central importance is given to the
money-demand relation that describes desired real money balances as a function of interest
rates and other variables. However, in the case of an interest-rate rule like any of those

described above, the money supply varies passively so as to satisfy this relation; hence the
relation places no restrictions upon the equilibrium evolution of interest rates and goods
prices. Thus in such a system, the equilibrium paths of interest and prices are determined
by solving equations (4.9) and (4.10), or equations (4.10) and (4.13) in the case of sticky
prices, just as above. Once one knows the equilibrium paths of interest and prices, the money-
demand relation can then be used to determined the implied evolution of the money supply
as well. But this last relation plays no important role in determining equilibrium in¬‚ation
under such an analysis. And an insistence upon ¬rst solving for the state-contingent path
of the money supply implied by the policy rule, and then deriving the equilibrium path
of in¬‚ation from this along quantity-theoretic lines, would be an unnecessarily roundabout
procedure, given that one must ¬rst solve for the path of prices and interest rates in order
to determine the path of the money supply.

The neo-Wicksellian approach is thus clearly preferable, even granting the existence of
a well-de¬ned, econometrically stable money-demand relation, if one wishes to analyze the
consequences of interest-rate rules such as the Taylor rule. But, it might be asked, is it clear
that desirable policy rules should belong to this class, regardless of the current popularity
of such prescriptions? Might not a money-growth rule be preferable, in which case a more
traditional quantity-theoretic approach would also be necessary in order to explain its e¬ects?

The results of this study suggest that the answer is no. As is shown in chapter 8, it
is possible to derive optimal policy rules that indicate how a short-term nominal interest-
rate operating target should be set, as a function of the projected evolution of in¬‚ation and
the output gap, without any reference to the paths of monetary aggregates. It is argued
furthermore that this form of prescription has the advantage, relative to other possible char-
acterizations of optimal policy, of being invariant under a larger class of possible exogenous
disturbances. For example, in the case of an economy with a well-de¬ned demand for base
money, it is possible to compute both the state-contingent evolution of overnight interest
rates and the state-contingent evolution of the monetary base in an optimal equilibrium.
However, the desired evolution of the monetary base, even when well-de¬ned, will depend

upon factors that are of little or no relevance to the desired evolution of interest rates, and
this makes it simpler to characterize optimal policy in terms of an interest-rate operating

One such factor is the dependence of the optimal path of the monetary base on changes in
the transactions technology ” for example, available opportunities for substitution among
alternative means of payment ” that have signi¬cant e¬ects on money demand in the pres-
ence of a given interest di¬erential between base money and other riskless assets, but have
little e¬ect on the relations between interest rates and the incentives for intertemporal substi-
tution of expenditure that determine the desired evolution of interest rates. (In an economy
where the ¬nancial system is already highly e¬cient, one expects further innovations to rep-
resent movements from one highly e¬cient system to another, so that the relations between
interest rates and the real allocation of resources will remain near that predicted by a model
with no ¬nancial frictions; but money demand may be greatly a¬ected in percentage terms,
as it ceases to be de¬ned in the frictionless limit.) Another is the dependence of the opti-
mal evolution of the monetary base on the details of monetary policy implementation. The
desired path of money-market interest rates is largely independent of the rate of interest
paid on the monetary base; this instead depends on the intertemporal marginal rates of
substitution and marginal products of real investment implied by the desired allocation of
resources, and on the desired path for in¬‚ation. But the desired path of the monetary base
depends greatly on whether it is assumed for institutional reasons that zero interest is paid
on base money, or whether instead the interest paid on money varies when other short-term
interest rates vary; for the demand for base money depends not on the absolute level of
nominal interest rates, but on the spread between the interest rate paid on base money and
that available on other assets.

Thus even when the desired evolution of the monetary base is well-de¬ned, it is more
dependent on special “technical” factors than is the desired evolution of short-term nominal
interest rates; this makes a description of optimal monetary policy in terms of a state-
contingent money growth rate less convenient. And if, as some forecast, monetary frictions

are largely eliminated in the coming century owing to the development of electronic pay-
ments media, a description of optimal policy in terms of the desired evolution of a monetary
aggregate is likely to become awkward if not altogether impossible. Yet a description of op-
timal policy in terms of the principles that should regulate the adjustment of an interest-rate
operating target should still be possible. Indeed, increasing e¬ciency of the ¬nancial system
should only simplify the description of optimal policy in these terms, insofar as the arbitrage
relations that connect the overnight interest rate directly targeted by the central bank to
other interest rates and asset prices should become simpler and more reliable. Hence the
neo-Wicksellian framework proposed here directs attention to precisely those elements of the
monetary transmission mechanism that are likely to remain of fundamental importance for
the design of e¬ective monetary policies in a world of increasingly e¬cient ¬nancial markets
and institutions.

5 Plan of the Book
Part I of this book develops a theoretical framework that can be used to analyze the conse-
quences of alternative monetary policy rules, in a way that takes full account of the conse-
quences of forward-looking private sector behavior. Chapter 2 begins by considering price-
level determination when monetary policy is speci¬ed by an interest-rate rule, in the case
of a model where, for simplicity, prices are completely ¬‚exible and the supply of goods is
given by an exogenous endowment. This chapter demonstrates the possibility of a coherent
theory of price-level determination even in the complete absence of monetary frictions ” a
special case that is considered repeatedly in what follows, in order to direct attention more
closely to the economic relations that are considered to be of more fundamental importance
for the characterization of optimal policy. But it also considers price-level determination
under an interest-rate rule in a standard optimization-based monetarist framework, allowing
a comparison between the consequences of monetary targeting and those of commitment
to an interest-rate rule, and an analysis of the extent to which the presence of monetary
frictions changes one™s conclusions about the e¬ects of an interest-rate rule.

Chapter 3 then introduces endogenous goods supply and nominal price and wage rigidi-
ties, so that monetary policy can a¬ect the level of real activity as well as the in¬‚ation rate.
Considerable attention is given to the microeconomic foundations of the aggregate-supply
relations that result from delays in the adjustment of prices or wages, in order to select
speci¬cations (from among those that might appear similarly consistent with econometric
evidence) with clear behavioral interpretations, that thereby allow one to take account of
the “Lucas critique”. At the same time, attention is also paid to the need to ¬nd a speci-
¬cation of the dynamic relations between real activity and in¬‚ation that is consistent with
econometric evidence regarding the e¬ects of identi¬ed monetary disturbances. A series of
modi¬cations of a basic sticky-price model are introduced that can improve the model™s ¬t
with estimated responses on various dimensions.

Chapter 4 then integrates the analysis in chapters 2 and 3, considering the e¬ects of
interest-rate rules in a framework where monetary policy can a¬ect real activity, and where
feedback from measures of real activity to the central bank™s interest-rate operating target
matter for the predicted e¬ects of such rules. In the neo-Wicksellian framework developed
here, in¬‚ation dynamics result from the interaction between real disturbances on the one
hand and the central bank™s interest-rate rule on the other. Wicksell™s “natural rate of inter-
est” is shown to play a central role, summarizing the e¬ects of a variety of real disturbances
that are relevant for in¬‚ation and output-gap determination, in the case of a class of policy
rules that may be thought of as generalized Taylor rules. The chapter also includes a ¬rst
analysis of the consequences of such a framework for the design of desirable policy rules, by
considering the conditions under which a Taylor-like rule should be able to stabilize in¬‚ation
and the output gap.

Chapter 5 completes the theoretical framework by considering the consequences for in-
¬‚ation determination of alternative ¬scal policy rules. The analyses of interest-rate rules in
chapters 2 and 4 are conducted under a particular assumption about ¬scal policy ” that it
is at least “locally Ricardian” ” that is arguably realistic given current ¬scal policy com-
mitments in countries like the U.S., but that need not hold, and that may not have held even

in the U.S. at all times. Chapter 5 shows that the in¬‚ation dynamics implied by a given
interest-rate rule may be di¬erent in the case of alternative ¬scal rules, and uses this analysis
to explain the consequences of the bond-price support regime in the U.S. during the 1940s.
In fact, the analysis o¬ered later in the book implies that an optimal regime should involve
a locally Ricardian ¬scal policy, so that the case emphasized in chapters 2 and 4 is argued to
be the relevant one for the choice of an optimal monetary policy rule. But it is important to
recognize that an optimal policy regime must include the proper sort of ¬scal commitment
as well, and that a commitment to an “optimal” interest-rate rule need not imply desirable
in¬‚ation dynamics in the absence of a suitable ¬scal commitment.

Part II of the book then considers the optimal conduct of monetary policy in the light of
the theoretical framework introduced in the earlier chapters. Chapter 6 begins by considering
appropriate stabilization goals for monetary policy. An advantage of the derivation of our
model™s structural relations from explicit microeconomic foundations in Part I is that it is
possible to ask what sort of monetary policy should best serve economic welfare, given the
objectives and constraints of the agents whose decisions account for the observed e¬ects
of monetary policy. Chapter 6 considers the connection between the obvious measure of
economic welfare in such a model ” the expected utility of the representative household ”
and the stabilization of macroeconomic aggregates such as in¬‚ation and the output gap.

It is shown that a quadratic approximation to expected utility, which su¬ces (under
certain conditions) for the derivation of a linear approximation to an optimal policy rule,
can be expressed in terms of the expected value of squared deviations of certain aggregate
variables from target values for those variables; the variables that are relevant, and the
details of the quadratic loss function that can be justi¬ed on welfare-theoretic grounds,
depend on the microeconomic foundations of one™s model of the monetary transmission
mechanism. In particular, it is shown that di¬erent assumptions regarding price and/or wage
stickiness imply that price and/or wage in¬‚ation should enter the central bank™s loss function
in di¬erent ways. Nonetheless, it is argued that price stability, suitably interpreted ” e.g.,
quite possibly in terms of an index that includes wages as well as the prices of ¬nal goods

and services ” should be an important consideration, though not necessarily the only one,
in the selection of a monetary policy rule. Grounds for inclusion of output-gap stabilization
and interest-rate stabilization objectives in the loss function as well are considered; but it is
argued that in practice, these additional concerns are not likely to justify either an average
rate of in¬‚ation much greater than zero or substantial variability in the rate of in¬‚ation in
response to shocks.

Chapter 7 then considers the optimal state-contingent evolution of in¬‚ation, output and
interest rates in response to real disturbances of various sorts, from the point of view of the
sort of loss function argued for in chapter 6 and in the context of a forward-looking model
of the monetary transmission mechanism of the kind developed in Part I. An important
general issue treated in this chapter is the way in which optimal control techniques must be
adapted in the case of control of a forward-looking system. The responses to shocks under an
optimal commitment are distinguished from the equilibrium responses under discretionary
optimization by the central bank. Particular attention is given to the fact that in general,
optimal responses will be history-dependent in a way that is inconsistent with any purely
forward-looking decision procedure for monetary policy. Alternative approaches to introduc-
ing the desired sort of history-dependence into the conduct of policy are surveyed; the one
that is emphasized in this study is the possibility of commitment to a policy rule that is
history-dependent in the desired way.

Finally, chapter 8 considers the problem of choice of a policy rule to implement the desired
state-contingent evolution of in¬‚ation, output and interest rates, as derived in chapter 7.
From the standpoint taken here, this problem of implementation of the desired equilibrium
is a non-trivial part of the characterization of optimal policy; for the mapping from the
history of exogenous disturbances to the desired overnight interest rate at any point in time
is not a suitable description of an optimal policy rule, for reasons taken up in this chapter.
Instead, it is argued that a more suitable policy prescription should relate the instrument
setting to the evolution (observed or projected) of endogenous variables such as in¬‚ation and
the output gap, as in the proposals mentioned above. A general method is presented for

constructing optimal policy rules of this form in the case of a fairly general class of log-linear
structural models and quadratic loss functions; the method is then applied to several of the
simple optimizing models of the monetary transmission mechanism developed in previous
It is shown that optimal rules can easily take the form of generalized Taylor rules, or
the form of target criteria for a forecast-targeting procedure like that used at the Bank of
England. However, even in the case of fairly simple models of the transmission mechanism,
the optimal rules are somewhat di¬erent from the proposals described above. While there is a
fairly clear logic for rules that respond to (and perhaps only to) variations in in¬‚ation and in
the output gap, the theoretically appropriate measures of in¬‚ation and of the output gap may
not be the ones used in the characterizations above of current central-bank behavior. And
the optimal rules that we obtain are typically di¬erent in their dynamic speci¬cations as well.
Optimal rules are history-dependent in ways that neither the classic Taylor rule nor familiar
descriptions of in¬‚ation-forecast targeting are; and while they may well be more forward-
looking than the classic Taylor rule, in all of our calibrated examples they are considerably
less forward-looking than the procedures currently used at the in¬‚ation-targeting central
Conclusions about the precise content of an optimal policy rule, of course, depend on the
details of one™s model of the transmission mechanism, and we do not attempt here to reach
¬nal conclusions in that regard. The answer is likely to be somewhat di¬erent for di¬erent
countries in any event. Our more important goal is to provide a method that individual
central banks can use in order to choose sensible systematic policies on the basis of their
own research on the nature of the transmission mechanism in their respective economies. It
is hoped that the present essay can provide useful guidelines for such an inquiry.


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