15
Long-Run Monetary Neutrality
and Contemporary Policy Analysis
Keynote Speech by Bennett T. McCallum
Arguments are developed concerning a number of topics including long-
run monetary neutrality, superneutrality, the natural-rate hypothesis, the
quantity 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 the
disagreement 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 is
argued that these models are consistent in most important ways with
highly 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 of
money; Cointegration
JEL Classification: E0, E4, E5
Carnegie Mellon University (E-mail: [email protected])
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.
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 talk
without being entirely wrong by just saying that there is no long-run relationship and
stopping with that, but presumably it would be better for me to go on a bit longer by
adding 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 empirical
tests 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 the
monetary base. This tendency by analysts reflects, of course, the actual policy practice
of 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 theory
of money (QTM), yet there exists substantial disagreement over the meaning of the
term. 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 level
with 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 of
velocity. Accordingly, the equation of exchange is consistent with any proposition
concerning monetary economics and therefore cannot play any essential role in
distinguishing 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 and
applications. 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
16 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004
1. The statement is ceteris paribus in the sense that it concerns effects of the single postulated change.
This proposition pertains to “long-run” effects, i.e., effects that would occur hypo-
thetically after all adjustments are completed. In real time, there will always be
changes 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 conduct
monetary 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 the
properties of actual economies, so that knowledge about the models’ behavior under
alternative policies can be obtained without having to undertake massive real-world
social 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 the
property known as long-run “neutrality of money.” Indeed, the latter concept is
defined 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 in
terms 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 be
homogenous of degree zero in nominal variables.
4
Since supply and demand relations
can be estimated econometrically, the QTM has empirical content—it requires that
all supply and demand equations have the stated homogeneity property. These equa-
tions, if properly formulated, are structural relations that do not depend upon the
policy rule in effect.
5
Their validity or invalidity therefore has nothing to do with the
operating 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 the
demand for real balances only to real variables (usually including a real rate of return
differential that is the opportunity cost of holding money
8
and a real transactions
quantity). This equation implies then that the steady-state inflation rate will equal
17
Long-Run Monetary Neutrality and Contemporary Policy Analysis
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, not
entirely 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 upon
some nominal variable; otherwise, nominal indeterminacy will prevail—i.e., the model will fail to determine the
value of any nominal variable. This is very different from the type of “indeterminacy” featured in recent writings
by, e.g., Woodford (2003).
5. Here I have in mind behavioral relations—e.g., Euler equations—rather than supply and demand functions under
some 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.
the steady-state rate of growth of the money stock minus a term pertaining to the
rate 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 of
real 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 of
the (log of the) price level, p
t
, with other variables including m
t
, the (log of the)
money stock. In particular, a frequently expressed contention is that if two or more
difference stationary (DS) variables are not cointegrated, then there exists no long-
run 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 m
t
must
be cointegrated” with p
t
, y
t
(the log of real income), and R
t
(the relevant nominal
interest 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, in
which the suggestions are correct: if z
t
and x
t
are both DS but not cointegrated, then
the disturbance term in any linear relationship between them must by definition
be nonstationary, implying that z
t
and x
t
can drift apart as time passes. I wish to
argue, 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
m
t
− p
t
=
0
+
1
y
t
+
2
R
t
+
t
. (1)
Suppose for the purpose of the present argument that m
t
, p
t
, y
t
, and R
t
are all
DS(1) variables that have been processed by the removal of deterministic trends.
10
Then the cointegration status of the four variables depends upon the properties
of the disturbance
t
; if its process is of the DS type, the variables in (1) will not
be cointegrated.
18 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004
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 covariance
stationary.
10. This step should not be at issue; the existence of technological change in the payments industry is generally
accepted by monetary analysts.
It is my contention, however, that traditional money demand theory—as described
by 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, further-
more, 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 such
that changes (shocks) are typically not reversed. Thus one would expect there to be
a significant permanent (i.e., unit root) component to the
t
process, making it one
of 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 p
t
would continue to be dominated by
m
t
values, provided that the variability of the latter is large relative to the variability
of the innovation component of
t
. In short, the failure of p
t
to be cointegrated with
m
t
, y
t
, and R
t
does not necessarily imply any violation of the messages of traditional
monetary 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 basis
of cointegration tests, that PPP fails to hold even as a long-run tendency. These tests
involve the relationship
s
t
= p
t
− p
*
t
+ q
t
,
where s
t
is the log of the price of foreign exchange while p
t
and p
*
t
are logs of the home-
country and foreign-country price levels. Then, s
t
will be cointegrated with p
t
− p
*
t
if
and only if q
t
is trend-stationary.
11
Several studies have found q
t
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 compo-
nent in the process generating q
t
, the real exchange rate, for the latter will be affected
by preference and technology shocks that would be likely to include permanent
components, implying that q
t
is not covariance stationary. That situation would
imply that s
t
and p
t
− 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 a
long-run neutrality proposition, then it is clearly not invalidated by the presence of a
permanent real component in the q
t
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.
19
Long-Run Monetary Neutrality and Contemporary Policy Analysis
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.
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 on
real 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 to
hold 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, there-
fore, they will utilize smaller amounts of these services. In many cases, the implied type
of portfolio readjustment will lead to changes in the steady-state levels of capital/labor
and capital/output ratios, which are important real variables. If no such changes in real
variables 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 the
context 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 to
hold in economies in which money provides transaction-facilitating services, as it
does normally in most actual economies. Departures from superneutrality are likely to
be small, however, for reasons discussed in McCallum (1990). Thus, for example, an
increase 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 when
superneutrality holds is the (e.g., one-period) real rate of interest. The absence of
superneutrality, 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 this
type of change does not imply any violation of the famous Fisher equation, r
t
=
R
t
− E
t
p
t +1
. The latter should be thought of, I would suggest, as a definition of r
t
.
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 altered
inflation rate having a (steady-state) effect on the real interest rate. In the Sidrauski-
Brock model, the steady-state real rate of interest is invariant to the steady-state rate
of inflation, but such is not the case in a typical overlapping-generations model, even
though the Fisher equation holds in both of them (McCallum [1990]).
20 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004
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 + r
t
)(1 + E
t
p
t +1
). In these expressions, E
t
z
t +j
reflects
the expectation formed in period t of z
t +j
.
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 some-
times confused with the latter. This is the “natural-rate hypothesis,” introduced by
Friedman (1966, 1968) and refined by Lucas (1972). Friedman’s version of this
hypothesis is that differing steady-state inflation rates will not keep output (or
employment) 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 and
superneutrality: an economy could be one in which superneutrality does not obtain,
in the sense that different permanent inflation rates lead to different steady-state
levels 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, not
by 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 Calvo
model posits that price adjustments can be made during any period by only a fraction
of 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, y
t
is the log of output, and y
–
t
is the natural rate (i.e.,
flexible price) level of output:
t
=
E
t
t +1
+
(y
t
− 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 of
y
t
− 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
−
=
(E
t
t +1
−
) +
(y
t
− y
–
t
). (2′)
21
Long-Run Monetary Neutrality and Contemporary Policy Analysis
15. I have used them several times myself, but mainly for illustrative purposes (as below).
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 relationship
would result if it is assumed that those sellers that do not have an opportunity (in a
given period) to reset their prices optimally have their prices rise at the ongoing infla-
tion rate (rather than held constant). From a steady-state perspective, (2′) would
imply y
t
− y
–
t
= 0, thereby satisfying the accelerationist hypothesis, Friedman’s weaker
version 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 of
traditional shoe-leather costs of inflation (due to transaction frictions that give
money its medium-of-exchange role).
17
Thus, with these frictions included, as in
Friedman (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 approach
that I find slightly disquieting, by and large the convergence and the general approach
both seem predominantly fruitful and encouraging. Let me briefly describe the
approach 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 a
quantitative macro model that is intended to be structural (invariant to policy changes)
and consistent with both theory and data. Then, by stochastic simulation or analytical
means, he determines how crucial endogenous variables (such as inflation and the
output 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. Evaluation
of 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,
22 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004
16. Other reference values for inflation yield similar results.
17. Also see King and Wolman (1999).
of course, but major advances have been made in the last 10–12 years in terms of
techniques, 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 a
simplified three-sector representation in which R
t
is a one-period interest rate while
p
t
and y
t
are logs of the price level and output, with y
–
t
the natural-rate value of y
t
:
y
t
= b
0
+ b
1
(R
t
− E
t
p
t +1
) + E
t
y
t +1
+ v
t
b
1
< 0 (3)
p
t
=
E
t
p
t +1
+
(y
t
− y
–
t
) + u
t
> 0 (4)
R
t
= (1 −
3
)[
0
+ p
t
+
1
(p
t
−
*
) +
2
(y
t
− y
–
t
)]
+
3
R
t−1
+ e
t
. (5)
Here, (3) represents an optimizing IS-type relation or set of relations, (4) a price
adjustment relation or set of relations such as (2) above, and (5) a Taylor-style mone-
tary policy rule for period-by-period (e.g., quarters) setting of the policy instrument
R
t
. Also, E
t
z
t +j
is the expectation of z
t +j
conditional on information available in t,
while v
t
, u
t
, and e
t
are exogenous shocks, v
t
reflecting tastes and fiscal policy. If capital
and therefore y
–
t
are treated as exogenous, as in the simplest versions, then (3)–(5)
determine time paths for y
t
, p
t
, and R
t
.
20
If investment is treated endogenously, then
capital 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 not
necessary 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 objective
function—which itself may or may not be explicitly based on the utility function of
private agents.
21
But it seems to me untrue that all worthwhile analysis presumes opti-
mization by the central bank; analysis of the differing effects of different hypothetical
rules 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
23
Long-Run Monetary Neutrality and Contemporary Policy Analysis
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.
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 the
implied economy one in which inflation is a non-monetary phenomenon? Is it one in
which 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
m
t
− p
t
=
0
+
1
y
t
+
2
R
t
+
t
, (6)
where m
t
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 case
that the QTM pertains to the modelled economy.
To address the other questions, it is useful to consider the RE solution to the
model at hand. On the basis of inspection, one can specify that the standard, bubble-
free RE solution will be of the form
y
t
=
10
+
11
y
–
t
+
12
R
t−1
+
13
v
t
+
14
u
t
+
15
e
t
, (7a)
p
t
=
20
+
21
y
–
t
+
22
R
t−1
+
23
v
t
+
24
u
t
+
25
e
t
, (7b)
R
t
=
30
+
31
y
–
t
+
32
R
t−1
+
33
v
t
+
34
u
t
+
35
e
t
. (7c)
From (3), it can be seen that the average real rate of interest is −b
0
/b
1
, 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
− Ep
t
yields the implication
that Ep
t
=
*
. 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 this
crucial sense, average inflation is—according to this model—determined entirely by
monetary 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 be
able 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.
24 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004
22. For discussion of issues concerning the declining importance of base money, see McCallum (2004).
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 systematic
component of monetary policy, as opposed to the effects of policy “shocks,” featured
in (for example) vector autoregression (VAR) analysis. This altered emphasis is healthy
partly because most of the variation in interest rate instrument values, such as the
federal funds rate in the United States, is evidently systematic (not random). Estimates
of 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-emphasized
in recent years. To me this seems a healthy trend, most importantly because VAR
models—even “identified” or “structural” VAR models—are not structural in the
sense 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 a
system 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
y
t
= b
0
+ b
1
(R
t
− E
t
p
t +1
) + E
t
y
t +1
+ v
t
b
1
< 0 (8)
p
t
= [
/(1 +
)]E
t
p
t +1
+ [1/(1 +
)]p
t −1
+
(y
t
− y
–
t
) + u
t
> 0 (9)
R
t
= (1 −
3
)[
0
+ p
t
+
1
(p
t
−
*
) +
2
(y
t
− y
–
t
)] + e
t
, (10)
and
m
t
− p
t
=
0
+
1
y
t
+
2
R
t
+
t
. (11)
Here, I have eliminated interest rate smoothing from the policy rule (10) and have
altered the price adjustment equation (9) so as to reflect “inertia” that seems to be pre-
sent for some theoretically impure reason. In this system, (8), (9), and (10) determine
y
t
, p
t
, and R
t
, so the solution for those three variables is given by equations of the form
y
t
=
10
+
11
y
–
t
+
12
p
t−1
+
13
v
t
+
14
u
t
+
15
e
t
, (12a)
p
t
=
20
+
21
y
–
t
+
22
p
t−1
+
23
v
t
+
24
u
t
+
25
e
t
, (12b)
R
t
=
30
+
31
y
–
t
+
32
p
t−1
+
33
v
t
+
34
u
t
+
35
e
t
. (12c)
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 of
25
Long-Run Monetary Neutrality and Contemporary Policy Analysis
monetary policy, e
t
, is small—it could in principle equal zero!—then a variance
decomposition 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 that
a 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 the
economy 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 with
regard 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 the
latter 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 a
central 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.
26 MONETARY AND ECONOMIC STUDIES (SPECIAL EDITION)/DECEMBER 2004
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