Long-Run Monetary Neutrality
and Contemporary Policy Analysis
Keynote Speech by Bennett T. McCallum

Arguments are developed concerning a number of topics including longrun monetary neutrality, superneutrality, the natural-rate hypothesis, thequantity theory of money, the equation of exchange, the Fisher equation,and purchasing power parity. These are basic, fundamental topics that all
students of monetary economics refer to frequently, but there is evidently
considerable disagreement concerning their exact nature. Some of thedisagreement has likely been generated by the recent practice by monetary
economists of conducting monetary policy analysis in models that include
no mention of any monetary variable such as M1 or the monetary base—
thereby reflecting the actual policy practice of most central banks. It isargued that these models are consistent in most important ways withhighly traditional monetary analysis. More generally, relationships among
the various topics are developed and the validity of empirical tests (e.g.,
cointegration tests) relating to several of the topics are reconsidered.
Keywords: Superneutrality; Natural-rate hypothesis; Quantity theory ofmoney; Cointegration
JEL Classification: E0, E4, E5Carnegie Mellon University (E-mail: bmccallum@cmu.edu)
I am grateful to David Laidler and Edward Nelson for helpful comments.
MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004
DO NOT REPRINT OR REPRODUCE WITHOUT PERMISSION.

15

I. Introduction
At a conference on “sustained economic growth” held by a central bank, it seems
appropriate for me, a monetary economist, to discuss the long-run relationship between
monetary policy and real economic growth. One could make this a very short talkwithout being entirely wrong by just saying that there is no long-run relationship andstopping with that, but presumably it would be better for me to go on a bit longer byadding some elaborations and qualifications to that basic proposition.
Accordingly, I would like to discuss a number of interrelated topics including
long-run monetary neutrality, superneutrality, the natural-rate hypothesis, the quantity
theory of money, the Fisher equation, purchasing power parity (PPP), and empiricaltests relating to some of the above. These are basic, fundamental topics that all students
of monetary economics refer to frequently, but there is evidently considerable
disagreement concerning their exact nature, a matter that is certainly worthy of
discussion. Some of this disagreement, moreover, has perhaps been generated by the
recent tendency by leading monetary economists to conduct monetary policy analysis
in models that include no mention of any monetary variable such as M1 or themonetary base. This tendency by analysts reflects, of course, the actual policy practiceof most central banks in industrial nations, so several of the issues that come up could
be of practical importance.

II. What Is the Quantity Theory of Money?
There is hardly a more basic topic in monetary economics than the quantity theoryof money (QTM), yet there exists substantial disagreement over the meaning of theterm. Some writers identify the QTM with the equation of exchange, MV = PY,
where M, Y, and P are measures of money, real transactions, and the price levelwith V the implied “velocity.” Such an identification is highly undesirable, however,
because the equation of exchange is an identity—I think of it as the definition ofvelocity. Accordingly, the equation of exchange is consistent with any proposition
concerning monetary economics and therefore cannot play any essential role indistinguishing different views. To identify the QTM with the equation of exchange
would, therefore, rob it of any empirical or theoretical content.
That somewhat different meanings are assigned to the QTM can be seen by
consulting the writings of Hume (1752), Wicksell (1906/1935), Fisher (1911),
Keynes (1936), Friedman (1956), Patinkin (1956), Friedman and Schwartz (1963),
Samuelson (1968), and Lucas (1980). Nevertheless, there is one basic proposition
characterizing the QTM, one common thread that unites various definitions andapplications. This proposition is that if a change in the quantity of money were
exogenously engineered by the monetary authority, then the long-run effect would
be a change in the price level (and other nominal variables) of the same proportion
as the money stock, with no change resulting in the value of any real variable.1
1. The statement is ceteris paribus in the sense that it concerns effects of the single postulated change.

16 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004

Long-Run Monetary Neutrality and Contemporary Policy Analysis

This proposition pertains to “long-run” effects, i.e., effects that would occur hypothetically after all adjustments are completed. In real time, there will always bechanges occurring in tastes or technology before full adjustment can be effected, so
no experiment of this kind can literally be carried out in actual economies.
Furthermore, in most actual economies the monetary authority does not conductmonetary policy so as to generate exogenous changes in the stock of money, so
nothing even approximating the hypothetical experiment is ever attempted in reality.
Does that imply that we cannot say anything with empirical content about
the QTM? Of course not; it is the ultimate task of economics to make predictions
about hypothetical policy experiments, on the basis of models designed to reflect theproperties of actual economies, so that knowledge about the models’ behavior underalternative policies can be obtained without having to undertake massive real-worldsocial experiments. In the case of the QTM, the essential point is that the basic QTM
proposition mentioned above will hold in an economy if and only if it possesses theproperty known as long-run “neutrality of money.” Indeed, the latter concept isdefined so as to satisfy the stated proposition. Accordingly, I would argue that the
QTM is a claim that actual economies possess the properties that imply long-run
monetary neutrality.2 What are these properties? Basically, they are that private
agents’ objective functions and technology constraints are formulated entirely interms of real variables—there is no concern for nominal magnitudes per se.3 Then
implied supply and demand equations will also include only real variables—will behomogenous of degree zero in nominal variables.4 Since supply and demand relations
can be estimated econometrically, the QTM has empirical content—it requires thatall supply and demand equations have the stated homogeneity property. These equations, if properly formulated, are structural relations that do not depend upon thepolicy rule in effect.5 Their validity or invalidity therefore has nothing to do with theoperating procedures of the monetary authority. The QTM does not, consequently,
have anything to do with “the exogeneity of money” in actual practice. In particular,
it does not matter whether the central bank is using an interest rate or a monetary
aggregate (or, say, the price of foreign exchange) as its instrument variable.6
One of the relations in any complete macro/monetary model is a demand function
for real money balances.7 For long-run neutrality to hold, this function must relate thedemand for real balances only to real variables (usually including a real rate of return
differential that is the opportunity cost of holding money8 and a real transactions
quantity). This equation implies then that the steady-state inflation rate will equal
2. This position is closer to that of Patinkin (1972) than that of Friedman (1972), in their famous dispute.
3. It is possible that tax rules imposed by the government might be such that budget constraints are, nevertheless, notentirely in real terms. For simplicity, I am ignoring this case.
4. Note that in this (standard) case the monetary authority must conduct policy in a manner that depends uponsome nominal variable; otherwise, nominal indeterminacy will prevail—i.e., the model will fail to determine thevalue of any nominal variable. This is very different from the type of “indeterminacy” featured in recent writingsby, e.g., Woodford (2003).
5. Here I have in mind behavioral relations—e.g., Euler equations—rather than supply and demand functions undersome terminologies.
6. For insightful discussion of related issues, see Nelson (2003).
7. It does not have to be known by the central bank in order for it to conduct monetary policy, of course.
8. This differential is the difference between the real (and nominal!) rates of return on money and interest-bearing
assets. Here, for simplicity we assume that money is, like actual currency, non-interest-bearing.

17

the steady-state rate of growth of the money stock minus a term pertaining to therate of growth of real transactions. An exogenous change (if it somehow occurred) in
the rate of growth of the money stock would, therefore, induce a change of the same
magnitude in the inflation rate unless it induced a change in the rate of growth ofreal transactions or the real interest differential. Neither of these possibilities seems
at all plausible, so the QTM essentially implies that steady-state inflation rates move
one-for-one with steady-state money growth rates.

III. Cointegration Tests
Various empirical procedures have been utilized to test variants of the QTM
hypothesis. One that was popular a few years ago concerns possible cointegration ofthe (log of the) price level, pt , with other variables including mt , the (log of the)money stock. In particular, a frequently expressed contention is that if two or moredifference stationary (DS) variables are not cointegrated, then there exists no longrun relationship between (or among) them.9 Cuthbertson and Taylor (1990, p. 295)
have, for instance, stated the notion as follows: “If the concept of a stable, long-run
money demand function is to have any empirical content whatsoever, then mt must
be cointegrated” with pt , yt (the log of real income), and R t (the relevant nominalinterest rate). Cointegration requires that all linear distributed-lag relationships
among these variables have residual disturbance terms that are covariance stationary.
But is it true that this cointegration concept accurately expresses the relevant
notion of a long-run relationship? There is a definitional sense in which it does, inwhich the suggestions are correct: if z t and xt are both DS but not cointegrated, thenthe disturbance term in any linear relationship between them must by definition
be nonstationary, implying that z t and xt can drift apart as time passes. I wish toargue, however, that it would be wrong to conclude that in practical terms long-run
relationships are therefore nonexistent—or that long-run monetary neutrality (i.e.,
the QTM) does not hold.
To develop the argument, consider the example of an economy that includes a
traditional money demand function of the form
mt − pt = 0 + 1yt + 2R t + t .

(1)

Suppose for the purpose of the present argument that mt , pt , yt , and R t are allDS(1) variables that have been processed by the removal of deterministic trends.10
Then the cointegration status of the four variables depends upon the propertiesof the disturbance t ; if its process is of the DS type, the variables in (1) will not
be cointegrated.

9. A time-series variable is said to be DS of order d ≥ 1 if it has to be differenced d times in order to be covariancestationary.
10. This step should not be at issue; the existence of technological change in the payments industry is generally
accepted by monetary analysts.

18 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004

Long-Run Monetary Neutrality and Contemporary Policy Analysis

It is my contention, however, that traditional money demand theory—as describedby McCallum and Goodfriend (1987), for example—suggests that the variables in(1) are actually unlikely to be cointegrated. The reason is that the theoretical rationale
for relationship (1) depends upon the transaction-facilitating function of money,
but an economy’s technology for conducting transactions is continually changing.
Since technical progress cannot be well represented by measurable variables, furthermore, the effects of technical change that are not captured by the deterministic trend
show up in the disturbance term, t . And the nature of technological progress is suchthat changes (shocks) are typically not reversed. Thus one would expect there to bea significant permanent (i.e., unit root) component to the t process, making it oneof the DS type.
In such a case, however, the “long-run” messages of traditional monetary theory
continue to apply. Most importantly, the zero-degree homogeneity of the money
demand function is not altered, so long-run neutrality could continue to hold. Also,from an informal perspective, inflation rates pt would continue to be dominated bymt values, provided that the variability of the latter is large relative to the variabilityof the innovation component of t . In short, the failure of pt to be cointegrated with
mt , yt , and R t does not necessarily imply any violation of the messages of traditionalmonetary theory.
Similar conclusions apply in the field of exchange rate analysis concerning
the concept of PPP. In that context, various researchers have concluded, on the basisof cointegration tests, that PPP fails to hold even as a long-run tendency. These tests
involve the relationshipst = pt − p*t + qt ,where st is the log of the price of foreign exchange while pt and p*t are logs of the homecountry and foreign-country price levels. Then, st will be cointegrated with pt − p*t if
and only if qt is trend-stationary.11 Several studies have found qt to be nonstationary,
however, and have then concluded that PPP fails even as a long-run matter.
I would argue, nevertheless, that one should not be surprised to find a DS component in the process generating qt , the real exchange rate, for the latter will be affectedby preference and technology shocks that would be likely to include permanent
components, implying that qt is not covariance stationary. That situation would
imply that st and pt − p*t are not cointegrated, but it would not necessarily invalidate
the practical messages of the PPP doctrine.12 Furthermore, if one expresses PPP as along-run neutrality proposition, then it is clearly not invalidated by the presence of apermanent real component in the qt process. It is my opinion that this is the way that
PPP should be stated in the first place, i.e., as a long-run neutrality proposition.

11. Trend stationary means covariance stationary after removal of any deterministic trend.
12. I refer to long-run messages, of course. On a quarter-to-quarter or year-to-year basis, PPP fails in all respects.

19IV. Superneutrality
The QTM proposition ending Section II, that steady-state inflation rates move
one-for-one with steady-state money growth rates, does not imply that different
maintained money growth (and inflation) rates do not have sustained effects onreal variables. In particular, it does not rule out permanent effects on levels of output,
consumption, real interest rates, etc. In fact, an increased (for example) inflation
rate will normally imply an increased nominal interest rate and therefore an increased
differential between the rates of interest on money and “bonds.” This change amounts
to an increased cost of holding real money balances so rational agents will choose tohold a smaller fraction of their assets in the form of money. Unless agents are holding
so much money that they are satiated with its transaction-facilitating services, therefore, they will utilize smaller amounts of these services. In many cases, the implied typeof portfolio readjustment will lead to changes in the steady-state levels of capital/laborand capital/output ratios, which are important real variables. If no such changes in realvariables occur with altered steady-state inflation rates, the economy is said to possess
the property of “superneutrality.” The latter is thus another concept to consider in thecontext of long-run relationships between monetary and real variables. From what has
been said, however, it should be clear that superneutrality should not be expected tohold in economies in which money provides transaction-facilitating services, as it
does normally in most actual economies. Departures from superneutrality are likely tobe small, however, for reasons discussed in McCallum (1990). Thus, for example, anincrease in the steady-state inflation rate from zero percent (per annum) to 5 percent
would perhaps result in a fall in the steady-state real rate of interest of only about
0.04 percent.13
One of the variables that is unaffected by alternative ongoing inflation rates whensuperneutrality holds is the (e.g., one-period) real rate of interest. The absence ofsuperneutrality, on the other hand, implies that a change in the steady-state inflation
rate may change the steady-state real rate of interest. It should be noted that thistype of change does not imply any violation of the famous Fisher equation, rt =R t − Et pt +1. The latter should be thought of, I would suggest, as a definition of rt .14
There is arguably some confusion in the literature on this matter, with some writers
incorrectly suggesting that the Fisher equation is incompatible with an alteredinflation rate having a (steady-state) effect on the real interest rate. In the SidrauskiBrock model, the steady-state real rate of interest is invariant to the steady-state rateof inflation, but such is not the case in a typical overlapping-generations model, eventhough the Fisher equation holds in both of them (McCallum [1990]).

13. For this calculation, involving specific assumptions about functional forms and quantitative magnitudes, see
McCallum (2000, pp. 876–879).
14. Actually, the exact discrete-time expression is (1 + R t ) = (1 + rt )(1 + Et pt +1). In these expressions, Et z t +j reflects
the expectation formed in period t of z t + j .

20 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004

Long-Run Monetary Neutrality and Contemporary Policy Analysis

V. The Natural-Rate Hypothesis
There is another concept involving long-run relationships, frequently mentioned in
the literature, that differs from both neutrality and superneutrality—but is sometimes confused with the latter. This is the “natural-rate hypothesis,” introduced byFriedman (1966, 1968) and refined by Lucas (1972). Friedman’s version of thishypothesis is that differing steady-state inflation rates will not keep output (oremployment) permanently high or low relative to the “natural-rate” levels that would
prevail in the absence of nominal price stickiness in the relevant economies. Lucas’s
version is stronger; it is that there is no monetary policy that can permanently keep
output (or employment) above its natural-rate value, not even an ever-increasing(or ever-decreasing) inflation rate. Note the distinction between these concepts andsuperneutrality: an economy could be one in which superneutrality does not obtain,in the sense that different permanent inflation rates lead to different steady-statelevels of capital and thus the natural rate of output, without any implied failure of
the natural-rate hypothesis (NRH).
The validity of the NRH, or Friedman’s weaker version called the “accelerationist”
hypothesis, was a matter of much analysis and debate in the late 1970s and early 1980s.
Initial empirical tests were not supportive of the NRH, but the arguments of Lucas(1972) and Sargent (1971) that the utilized test procedures presumed expectational
irrationality led to a reversal of typical findings and by 1980 even self-styled Keynesian
economists were agreeing to the proposition that the NRH was basically valid. In
recent years, however, this agreement has seemingly been implicitly overturned, notby argument but merely by example, via the widespread adoption of the famous Calvo(1983) model of nominal price stickiness. In its basic discrete-time form, the Calvomodel posits that price adjustments can be made during any period by only a fractionof all sellers, with all others holding their nominal prices fixed at their previous-period
values. This assumption leads to the following aggregate (average) relationship, in
which t represents inflation, yt is the log of output, and y–t is the natural rate (i.e.,
flexible price) level of output:

t = Et t +1 +  (yt − y–t ).

(2)Here,  is a discount factor satisfying 0 <  < 1 so, in a steady state, we have an implied
relationship between inflation and the (constant) output gap, i.e., the constant value ofyt − y–t . Therefore, the Calvo model does not satisfy even the accelerationist hypothesis,much less the stronger NRH. It is surprising to me that relationships similar to(2) would be used so frequently in today’s analysis.15 I would think that analysts would,
at a minimum, replace (2) with something like the following:t −  =  (Et t +1 −  ) +  (yt − y–t ).

(2′)

15. I have used them several times myself, but mainly for illustrative purposes (as below).

21

Here,  represents the steady-state inflation rate under an existing policy rule,assumed to be one that permits a steady-state inflation rate.16 Such a relationshipwould result if it is assumed that those sellers that do not have an opportunity (in agiven period) to reset their prices optimally have their prices rise at the ongoing inflation rate (rather than held constant). From a steady-state perspective, (2′) would
imply yt − y–t = 0, thereby satisfying the accelerationist hypothesis, Friedman’s weakerversion of the NRH. (Even so, specification (2′) does not imply the stronger Lucas
version, which pertains to inflation paths more general than steady states.)
In what way would this change affect current reasoning regarding monetary
policy? Basically, it would imply that different steady-state inflation rates would not
induce different steady-state output gaps. In the influential analysis of Woodford(2003, chapter 6), the optimal steady-state inflation rate is zero, in the absence oftraditional shoe-leather costs of inflation (due to transaction frictions that givemoney its medium-of-exchange role).17 Thus, with these frictions included, as inFriedman (1969), the optimal rate will lie between zero and the negative value
implied by Friedman’s analysis. But with our suggested change to price adjustment
specification (2′), the Friedman rate (which reduces the opportunity cost of holding
money to zero) would seem to be implied from the steady-state perspective.
This last bit of reasoning does not, it should be added, take account of the zero lower
bound on short-term interest rates—a complication that we have come to appreciate
in recent years. That topic too is treated in detail by Woodford (2003). I hope that you
will be relieved to hear that I have nothing to say about that subject today.

VI. Contemporary Monetary Policy Analysis
I have observed elsewhere (McCallum [2001]) that recent years have seen a notable
convergence, among academic and central bank researchers, on a general approach for
conducting analysis of monetary policy. While there are some aspects of this approachthat I find slightly disquieting, by and large the convergence and the general approachboth seem predominantly fruitful and encouraging. Let me briefly describe theapproach and discuss a few issues that it raises. The method or approach on which
there is substantial agreement can be outlined as follows: the researcher specifies aquantitative macro model that is intended to be structural (invariant to policy changes)
and consistent with both theory and data. Then, by stochastic simulation or analyticalmeans, he determines how crucial endogenous variables (such as inflation and theoutput gap) behave on average under various alternative policy rules. Usually, rational
expectations (RE) is assumed to hold and frequently the model is based on optimizing
analysis but with some form of nominal price or wage stickiness included. Evaluationof the different outcomes can be accomplished by means of an optimal control
exercise, or by reference to an explicit objective function, or left to the judgment (i.e.,
objective function) of the implied policymaker. This approach is not entirely new,
16. Other reference values for inflation yield similar results.
17. Also see King and Wolman (1999).

22 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004

Long-Run Monetary Neutrality and Contemporary Policy Analysis

of course, but major advances have been made in the last 10–12 years in terms oftechniques, models, and extent of agreement.18
There is also considerable agreement about the general, broad structure—not
details—of the macroeconomic model to be used.19 It can be outlined in terms of asimplified three-sector representation in which R t is a one-period interest rate while
pt and y t are logs of the price level and output, with y–t the natural-rate value of yt :yt = b 0 + b1(R t − Et pt +1) + Et yt +1 + vt b1 < 0(3)

pt = Et pt +1 +  (yt − y–t ) + u t  > 0(4)

R t = (1 − 3)[0 + pt + 1(pt −  *) + 2( yt − y–t )]+ 3R t−1 + et .

(5)Here, (3) represents an optimizing IS-type relation or set of relations, (4) a priceadjustment relation or set of relations such as (2) above, and (5) a Taylor-style monetary policy rule for period-by-period (e.g., quarters) setting of the policy instrument
R t . Also, Et zt +j is the expectation of zt +j conditional on information available in t,
while vt , ut , and et are exogenous shocks, vt reflecting tastes and fiscal policy. If capitaland therefore y–t are treated as exogenous, as in the simplest versions, then (3)–(5)determine time paths for yt , pt , and R t .20 If investment is treated endogenously, thencapital and y–t become endogenous and additional relations must be included in the
sector here represented by (3). With no money stock terms in (3) or (4), it is notnecessary to include a money demand equation even though one may be implied by
the optimizing analysis.
The policy rule may or may not reflect optimizing behavior by the central bank,depending on the purpose of the analysis. If the object is to find the optimal policy
for the particular model under consideration, then (5) will be replaced by the implied
rule for R t that results from optimization with respect to the central bank’s objectivefunction—which itself may or may not be explicitly based on the utility function ofprivate agents.21 But it seems to me untrue that all worthwhile analysis presumes optimization by the central bank; analysis of the differing effects of different hypotheticalrules represents an alternative approach that may be useful for certain problems.

VII. Some Issues
One issue that has been raised by various economists concerns the absence of monetary
variables from the system (3)–(5). Does this absence imply that the model represents
18. The development has been due to many researchers. Outstanding contributions include Taylor (1993), King and
Wolman (1996), Clarida, Gali, and Gertler (1999), Rotemberg and Woodford (1997), and Woodford (1999a,
2003), among others.
19. See, e.g., Clarida, Gali, and Gertler (1999) and papers in the volume edited by Taylor (1999).
20. Also included are relevant transversality conditions.
21. No actual central bank has as yet publicly disclosed an explicit objective function, presumably because none has
been adopted.

23

an economy in which money is not important, in which there is no medium of
exchange that facilitates transactions and serves also as a medium of account? Is theimplied economy one in which inflation is a non-monetary phenomenon? Is it one inwhich the QTM does not hold? Let us consider these questions.
The final question can be answered quickly. Inspection of the model’s equations(3)–(5) indicates no departure from zero-degree homogeneity in nominal variables.
Also, the optimizing analysis that leads to (3) would in addition lead to a money
demand function of the form
mt − pt = 0 + 1yt + 2R t + t ,(6)

where mt is the log of (base) money and t is a shock affecting the function that
describes the transaction-facilitating properties of money. So it is evidently the casethat the QTM pertains to the modelled economy.
To address the other questions, it is useful to consider the RE solution to themodel at hand. On the basis of inspection, one can specify that the standard, bubblefree RE solution will be of the form
yt =
pt =
Rt =

y– +

+

10

20

30

11 t

+

+

y– +

21 t

y– +

31 t

R t−1 +

12

R t−1 +

22

R t−1 +

32

v +

13 t

v +

23 t

v +

33 t

u +

14 t

u +

24 t

u +

34 t

e,

(7a)

25 t

e,

(7b)

e.

(7c)

15 t

35 t

From (3), it can be seen that the average real rate of interest is −b0 /b1, so we presume
that the central bank sets its policy parameter 0 equal to that value. Let us also
assume that the price adjustment relation (4) satisfies the accelerationist hypothesis,
perhaps (but not necessarily) by being of form (2′). Then, in (7a), we know that
11 = 1 with
10 =12 = 0. Next, apply the unconditional expectation operator E to(5). Then substitution into the latter of 0 = ER t − Ept yields the implicationthat Ept =  *. Therefore, we find that the system implies that the long-run average
inflation rate is determined entirely by the central bank’s target value,  *. In thiscrucial sense, average inflation is—according to this model—determined entirely bymonetary policy. It is the case, moreover, that the central bank has the power to set
the one-period nominal interest rate, R t , basically because of its ability to control the
supply of base money.22 If the central bank did not have that ability, it might not beable to implement its interest rate rule (5).
Accordingly, I would judge that an economy depicted by the system (3)–(6) is one
that conforms in most important ways to traditional monetary analysis. While it may
or may not be optimal for central banks to conduct policy by means of interest rate
management, it is evidently the case that most of the leading central banks do so—and this conclusion does not have radical implications for monetary policy analysis.

22. For discussion of issues concerning the declining importance of base money, see McCallum (2004).

24 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004

Long-Run Monetary Neutrality and Contemporary Policy Analysis

One of the healthy aspects of the contemporary style of monetary policy analysis,as described above, is that it leads analysts to emphasize the effects of the systematiccomponent of monetary policy, as opposed to the effects of policy “shocks,” featuredin (for example) vector autoregression (VAR) analysis. This altered emphasis is healthy
partly because most of the variation in interest rate instrument values, such as thefederal funds rate in the United States, is evidently systematic (not random). Estimatesof quarterly Taylor rules, for example, typically indicate that only about 2–5 percent of
the variation in such rates is unexplained and therefore plausibly unsystematic.
Emphasis on the systematic rather than unsystematic portion of policy, moreover,leads naturally to the predominance of models that are designed to be structural, i.e.,
invariant to policy changes. Thus, analysis with VAR models has been de-emphasizedin recent years. To me this seems a healthy trend, most importantly because VAR
models—even “identified” or “structural” VAR models—are not structural in thesense of including equations that are designed to be invariant to alternative policy
rule specifications. Such models are not, therefore, appropriately specified for use in
the design of monetary policy (Lucas [1976]).
In addition, it seems to me that there are a number of fallacies which can easily result
from application of VAR methods to policy issues. Two of these can be illustrated by asystem just slightly different from the one in equations (3)–(6) and (7) above.
Specifically, I now assume that the relevant model of the economy is given by
yt = b 0 + b1(R t − Et pt +1) + Et yt +1 + vt b1 < 0(8)

pt = [ /(1 +  )]Et pt +1 + [1/(1 +  )]pt −1 + ( yt − y–t ) + u t
R t = (1 − 3)[0 + pt + 1(pt −  *) +  2( yt − y–t )] + et ,

>0

(9)
(10)

and
m t − pt = 0 + 1yt + 2R t + t .

(11)Here, I have eliminated interest rate smoothing from the policy rule (10) and havealtered the price adjustment equation (9) so as to reflect “inertia” that seems to be present for some theoretically impure reason. In this system, (8), (9), and (10) determine
yt , pt , and R t , so the solution for those three variables is given by equations of the form
yt =
pt =
Rt =

y– +

+

10

20

30

11 t

+

+

y– +

21 t

y– +

31 t

pt −1 +12pt−1 +

22

pt−1 +

32

v +

13 t

v +

23 t

v +

33 t

u +

14 t

u +

24 t

u +

34 t

e,

(12a)

25 t

e,

(12b)

e.

(12c)

15 t

35 t

With y–t exogenous, then it is clear that there is no Granger causality from the money
growth rate m t to inflation. In fact, there is no Granger causality from the interest
rate instrument, R t , to inflation. And if the variance of the random component of25

monetary policy, et , is small—it could in principle equal zero!—then a variancedecomposition analysis would find little effect on inflation of monetary policy
conducted via R t . In short, VAR-type analysis could easily lead to the idea that
inflation is not due to monetary policy, in an economy of the depicted type, although
the average inflation rate would be determined by the inflation target in the monetary
policy rule, as in the example above.
A very interesting development, due primarily to Woodford (1999b), is that of
the “timeless perspective” approach to policy rule formulation. The basic idea is thata central bank would commit itself not to a fixed algebraic rule for policy, but to a
fixed process of decision-making. Then the same type of optimization calculation could
be conducted each period without the internal dynamic inconsistency of standard“commitment” procedures, but with scope for updating the central bank’s model of theeconomy whenever new results indicate that such a change is needed. This approach
would not fully overcome the dynamic inconsistency “temptation” identified by
Kydland and Prescott (1977), but would feature full continuation on its own terms,
after a start-up period that avoids any attempt to exploit the conditions that happen
to prevail at the date at which this approach is first adopted. It would accordingly
stand a good chance of achieving credibility, and would in almost all circumstances
perform better on average than discretionary period-by-period reoptimization (see, e.g.,
McCallum and Nelson [2004]).

VIII. Conclusion
The last time that I gave a paper at this conference was in 1995, and my topic was“inflation targeting.” In that paper, I argued that a central bank’s main duty withregard to monetary policy was to keep nominal aggregate demand growing smoothly
at a rate consistent with its long-run inflation target, which should reflect a quite low
inflation rate. My preferred scheme involved nominal income growth targeting, but
I argued that this would in practice be very similar to inflation targeting, and that thelatter should be viewed as a highly attractive policy strategy. In the years since then,we have heard a great deal more about inflation targeting, but I do not know of any
development that would lead me to drastically change the basic contours of what
I wrote in 1995. In particular, I still believe that the most important thing that acentral bank can do, to encourage and support sustained economic growth, is to keep
nominal aggregate demand growing smoothly at a pace consistent with a small but
positive (and explicit) long-run inflation target.

References

Calvo, G., “Staggered Prices in a Utility-Maximizing Framework,” Journal of Monetary Economics, 12,1983, pp. 383–398.
Clarida, R., J. Gali, and M. Gertler, “The Science of Monetary Policy: A New Keynesian Perspective,”
Journal of Economic Literature, 37, 1999, pp. 1661–1707.

26 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004

Long-Run Monetary Neutrality and Contemporary Policy Analysis

Cuthbertson, K., and M. P. Taylor, “Money Demand, Expectations, and the Forward-Looking Model,”Journal of Policy Modelling, 12, 1990, pp. 289–315.
Fisher, I., The Purchasing Power of Money, New York: Macmillan, 1911.
Friedman, M., “The Quantity Theory of Money: A Restatement,” in M. Friedman, ed. Studies in the
Quantity Theory of Money, Chicago: University of Chicago Press, 1956.
———, “Comments,” in G. P. Schultz and R. Z. Aliber, eds. Guidelines, Informal Controls, and theMarket Place, Chicago: University of Chicago Press, 1966.
———, “The Role of Monetary Policy,” American Economic Review Papers and Proceedings, 58, 1968,
pp. 1–17.
———, The Optimum Quantity of Money, Chicago: University of Chicago Press, 1969.
———, “Comments on the Critics,” Journal of Political Economy, 80, 1972, pp. 906–950.
———, and A. J. Schwartz, A Monetary History of the United States, 1867–1960, Princeton: Princeton
University Press, 1963.
Hume, D., “Of Money,” in Political Discourses, Edinburgh: Fleming, 1752.
Keynes, J. M., The General Theory of Employment, Interest, and Money, London: Macmillan, 1936.
King, R. G., and A. Wolman, “Inflation Targeting in a St. Louis Model of the 21st Century,” Review,
78 (3), Federal Reserve Bank of St. Louis, 1996, pp. 83–107.
———, and ———, “What Should the Monetary Authority Do When Prices Are Sticky?” in J. B.
Taylor, ed. Monetary Policy Rules, Chicago: University of Chicago Press for the National
Bureau of Economic Research, 1999.
Kydland, F. E., and E. C. Prescott, “Rules Rather than Discretion: The Inconsistency of Optimal
Plans,” Journal of Political Economy, 85 (3), 1977, pp. 473–491.
Lucas, R. E., Jr., “Econometric Testing of the Natural Rate Hypothesis,” in The Econometrics of Price
Determination Conference, Washington, D.C.: Board of Governors of the Federal Reserve
System, 1972.
———, “Econometric Policy Evaluation: A Critique,” Carnegie-Rochester Conference Series on Public
Policy, 1, 1976, pp. 19–46.
———, “Two Illustrations of the Quantity Theory of Money,” American Economic Review, 70, 1980,
pp. 1005–1014.
McCallum, B. T., “Inflation: Theory and Evidence,” in B. M. Friedman and F. H. Hahn, eds. Handbookof Monetary Economics, Amsterdam: North-Holland, 1990.
———, “Theoretical Analysis Regarding a Zero Lower Bound on Nominal Interest Rates,” Journal of
Money, Credit and Banking, 32, 2000, pp. 870–904.
———, “Should Monetary Policy Respond Strongly to Output Gaps?” American Economic Review
Papers and Proceedings, 91, 2001, pp. 258–262.
———, “Monetary Policy in Economies with Little or No Money,” Pacific Economic Review, 9, 2004,
pp. 81–92.
———, and M. S. Goodfriend, “Demand for Money: Theoretical Analysis,” in The New Palgrave:
A Dictionary of Economics, London: Macmillan Press, 1987.
———, and E. Nelson, “Timeless Perspective vs. Discretionary Monetary Policy in Forward-Looking
Models,” Review, 86 (2), Federal Reserve Bank of St. Louis, 2004, pp. 43–56.
Nelson, E., “The Future of Monetary Aggregates in Monetary Policy Analysis,” Journal of Monetary
Economics, 50, 2003, pp. 1029–1059.
Patinkin, D., Money, Interest, and Prices, New York: Harper and Row, 1956.
———, “Friedman on the Quantity Theory and Keynesian Economics,” Journal of Political Economy,
80, 1972, pp. 883–905.
Rotemberg, J. J., and M. Woodford, “An Optimization-Based Econometric Framework for the Evaluationof Monetary Policy,” in B. S. Bernanke and J. J. Rotemberg, eds. NBER Macroeconomics Annual
1997, Cambridge, Massachusetts: MIT Press for the National Bureau of Economic Research,
1997.
Samuelson, P. A., “What Classical and Neoclassical Monetary Theory Really Was,” Canadian Journalof Economics, 1 (1), 1968, pp. 1–15.

27

Sargent, T. J., “A Note on the Accelerationist Controversy,” Journal of Money, Credit and Banking,3, 1971, pp. 50–60.
Taylor, J. B., “Discretion versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on
Public Policy, 39, 1993, pp. 195–214.
———, ed. Monetary Policy Rules, Chicago: University of Chicago Press for the National Bureau of
Economic Research, 1999.
Wicksell, K., Lectures on Political Economy, London: Routledge and Kegan Paul, 1935 (translated from
Vorlesungen über Nationalökonomie [1906]).
Woodford, M., “Optimal Monetary Policy Inertia,” NBER Working Paper No. 7261, National Bureau
of Economic Research, 1999a.
———, “Commentary: How Should Monetary Policy Be Conducted in an Era of Price Stability,” in
New Challenges for Monetary Policy, Federal Reserve Bank of Kansas City, 1999b.
———, Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton: Princeton
University Press, 2003.

28 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004