Testing Long-Run Monetary Neutrality Propositions: Lessons from … · 2019-10-09 · FEDERALRESERVEBANKOFST.LOUIS 57 NOVEMBER/DECEMBER1999 1 Not all papers dealing with neu- trality

FEDERAL RESERVE BANK OF ST. LOU IS

57

NOVEMBER/DECEMBER 1999

1 Not all papers dealing with neu-trality issues—an enormousamount of literature—can besurveyed here. Instead, atten-tion is restricted to those thatuse the newer techniques dis-cussed later.

Testing Long-Run MonetaryNeutralityPropositions:Lessons fromthe RecentResearchJames Bullard

M onetary economists long havethought that government injectionsof money into a macroeconomy

have a certain neutral effect. The mainidea is that changes in the money stockeventually change nominal prices andnominal wages, ultimately leaving impor-tant real variables, like real output, realconsumption expenditures, real wages,and real interest rates, unaffected. Sinceeconomic decision making is based on realfactors, the long-run effect of injectingmoney into the macroeconomy is oftendescribed as neutral—in the end, real vari-ables do not change and so economic deci-sion making is also unchanged. How longsuch a process takes, and what might hap-pen in the meantime, are hotly debatedquestions. But relatively few economistsdebate the merits of long-run neutrality.Indeed, long-run neutrality is insteadtaken as a given, almost an axiom, a logical consequence of suppositions made in economic theory.

Curiously, during most of the postwarperiod the empirical evidence on long-runmonetary neutrality has been in a state offlux. No doubt this is in part because it isdifficult to look at the data generated bythe world’s economies and come to any

firm conclusion about whether monetaryinjections had important real effects, in theshort run or in the long run. In addition,many of the empirical tests that weredevised ran into important criticisms thatseemed to invalidate their conclusions.These criticisms were based, at least inpart, on questionable handling or interpre-tation of the time-series properties of thedata. In recent years, however, economistshave devised new tests of long-run mone-tary neutrality, as well as related neutrality-type propositions. A fair amount of litera-ture has been written on the subject, andthe purpose of this paper is to review this literature.1

The next section provides more detailconcerning the background behind thecurrent empirical tests of neutrality propo-sitions. In the following sections, some ofthe recent research using the newer set oftests is reviewed, and a few related papersare discussed along with the results authorshave found using somewhat differentmethodologies. The final section offerssome comments about directions forfuture research.

SOME BACKGROUNDWhat is Long-Run Neutrality?

In discussing long-run monetaryneutrality, economists typically refer to aspecific, hypothetical experiment that nor-mally is not observed directly in actualeconomies. The experiment is a one-time,permanent, unexpected change in the levelof the money stock. If, for instance, themoney stock was $5 billion one day, andhad been $5 billion for a long time, thenwhat would the effect be of suddenlychanging it to $6 billion and keeping itthere for a long time? According to thequantity theory of money, prices shouldrise eventually in proportion to theincrease in the money stock, and all realvariables, perhaps after some transition

James Bullard is assistant vice president at the Federal Reserve Bank of St. Louis. The author thanks Patrick Coe, Mark Crosby, Mark Fisher,Phillip Jefferson, John Keating, Bob King, Chris Otrok, Bob Rasche, Trish Pollard, John Seater, Apostolos Serletis, Dan Thornton, and DavidRapach for helpful comments and suggestions. Nick Meggos and Stephen Majesky provided research assistance.



58

2 The phrase “standard economicassumptions” means maintain-ing assumptions that marketsclear at all times and that allagents behave rationally.

3 For a description of thesedepartures, see the survey byOrphanides and Solow (1990).

time, would return to their original valuesand stay there until some further distur-bance comes along. This is long-runmonetary neutrality.

In the hypothetical experiment, it isimportant that the new level of the moneystock be maintained for some, possiblylong, period of time, to allow the transi-tion effects to vanish. Theoretically, thechange in the money stock has to be “per-manent.” In the world’s economies, weobserve a high degree of persistence inmany macroeconomic variables, but it isgenerally difficult to tell the differencebetween “highly persistent” and “perma-nent.” In the empirical work surveyedbelow we will see the use of many tests—unit root diagnostic tests—intended tocategorize macroeconomic variables intothose that have been subject to permanentshocks and those that have not. It is impor-tant to bear in mind, however, that thesetests may not accurately distinguish betweenthe two cases—statistically speaking, thetests have limited power. The tests are usedbecause they offer the best available methodfor making the distinction between highlypersistent and permanent changes, but theyare far from perfect.

In the hypothetical experiment, it is alsoimportant that the change be unexpected,because if the economy’s participants knewthat the money stock was going to increase,and therefore, that prices were about toincrease, they might start changing theirpresent behavior. For example, they mightbuy consumption goods today, before theprice increase takes effect. Prices then mightbegin to rise in advance of the money stockchange. This complicates the story, andhence, we will think in terms of unantici-pated changes in the money stock level. In the discussion below, this will beapproximated by the notion of a “perma-nent shock” to the money supply.

In the world of monetary theory, nearlyall models based on standard economicassumptions embody some form of mone-tary neutrality.2 Most likely this is becausemonetary theorists generally think long-runmonetary neutrality is sensible, and, there-fore, they build it into their models.

Empirical tests that convincingly docu-mented departures from long-run monetaryneutrality therefore would be quite surprising(or quite suspect!) to monetary economists.

There is a second hypothetical experi-ment, related to the first, that more closelyresembles the types of monetary policyactions we see in actual economies. Thisexperiment says that the government ini-tially maintains a certain growth rate forthe money stock for a long period of time.At some date, that growth rate is adjustedunexpectedly to some new rate, say, from 3 percent to 5 percent on an annual basis,and is kept there for another long periodof time. What effect should this have onimportant real variables like the capital-labor ratio, real output, real consumptionexpenditures, and real interest rates? Ifthe answer is that after a long period oftime, nothing would happen to the realvariables, we have what is referred com-monly to as long-run monetary superneu-trality. Here again, one might expect animportant transition period (commonlyknown as “the short run”) when the econ-omy is adjusting to the new rate ofmonetary growth. Quite a lot couldhappen to real variables during this adjust-ment period. But the neutrality andsuperneutrality propositions discussed in this paper mainly concern long-run,limiting effects.

Perhaps surprisingly, there are manyplausible analyses that suggest that depar-tures from long-run monetary superneu-trality might be consistent with standardeconomic theory. It is, in fact, relativelyeasy to produce such theories. Moreover,these departures could go either way; thatis, a permanently higher rate of monetarygrowth might eventually either raise orlower the level of economic activity, orchange other important real variables ineither a positive or negative direction.3

Accordingly, whereas long-run neutralityis taken almost as an axiom of monetaryeconomics, long-run superneutrality isfar more circumspect. An empirical testthat convincingly showed departuresfrom long-run superneutrality would not be too surprising, since this result



59

4 The situation described is summarized by Canova (1994,p. 123), who states, “... thereare very few available modelswhich display superneutrality,while most existing models,both in the neoclassical andneoKeynesian tradition, possessneutrality of money.…”

5 See Marty (1994) for a discussion.

is consistent with a number of existingeconomic theories.4

It is important to note that whetherthe level of real output rises or falls, orwhether other real variables change in aparticular direction in response to a per-manent increase in the money growth rate,does not have any particular connotationsfor social welfare. In many theories, infla-tion distorts a Pareto optimal equilibrium,so that as a long-run proposition the popu-lation in the economy generally preferslower rates of money growth accompaniedby lower rates of inflation. Different theo-ries make different predictions in this regard,however, and to sort these out one wouldhave to consider various theories and theirunderlying assumptions in some detail.Since this would take us too far astray, socialwelfare will not be addressed in this survey.

There is another side to the superneu-trality question. Fischer (1996) suggeststhat the reason the central banks of theworld’s industrialized economies haveavidly pursued long-run price stability isbecause in the long run, inflation has dis-tortionary effects that adversely impact areal variable, or a group of real variables,that people care about. If monetary growthcauses inflation, and inflation has distor-tionary effects, then long-run monetarysuperneutrality should not hold in thedata. On the contrary, a permanent shockto the rate of monetary growth should havesome long-run effect on the real economy;why else should we worry about it? Careneeds to be taken, however, in definingwhich variables are supposed to be affectedand which are not—this is an area of someconfusion in the literature.5 In the currentpaper we will try to avoid this problemthrough use of the language “superneutralitywith respect to variable x.”

The above discussion has referred tochanges in real variables, meaning changesin the level of the variable, especially sowith respect to the level of real output. Ofcourse, real output in industrialized econ-omies generally grows over time. A shiftin the level would be a one-time movement,say from 100 to 90, whereupon the variablewould resume growing at its previous rate.

Thus permanent effects on the level of avariable need not imply permanent effectson the growth rate of that variable. Conse-quently, a natural question to ask is whe-ther permanent changes in the monetarygrowth rate affect a country’s rate of econ-omic growth; that is, is money superneu-tral with respect to economic growth?Many researchers in recent years have infact investigated questions of this type(mostly with methodology outside thefocus of this survey). There is much lesstheory concerning this issue, but some ofthe results I discuss later will have somebearing on this topic.

Prima Facie Evidence. In his NobelLecture, Lucas (1996) addresses the topicof monetary neutrality, both in the shortrun and the long run, and discusses theo-retical developments that might reconcilethe perceived short-run effects of an increasein the money supply with long-run mone-tary neutrality. Lucas mentions severalpieces of evidence as constituting the mainreasons that he would like a satisfactorytheory of the real effects of monetary policyto address. Among these, he cites Friedmanand Schwartz (1963) who argue that allmajor recessions in the United Statesbetween 1867 and 1960 were preceded by substantial contractions in the moneysupply, suggesting that monetary policymistakes were a primary contributor tobusiness cycle downturns during thisperiod. Lucas states that severe monetarycontraction seemed to play an importantrole especially during the Great Depressionof 1929-33. But he also cites work by Sar-gent (1986) who argues that huge reduc-tions in the rate of monetary expansion—reductions much larger than anythingexperienced in the post-Civil War UnitedStates—did not lead to any unusually largereduction in real output in the hyperinfla-tionary post-World War I European econ-omies. These reductions were carried outin conjunction with monetary reform.The hyperinflations ended abruptly whencredible reform was announced. But thesecitations are subsidiary to Lucas’s (1996,p. 668) main contention, that there is clear



60

evidence—even “decisive confirmation”—that long-run monetary neutrality holds.

Figure 1 shows the evidence thatLucas (1996) cites. This figure, fromMcCandless and Weber (1995), plots theaverage rates of monetary growth againstaverage rates of inflation for 110 countries.The averages are taken over 30 years,1960-90. Monetary growth is measured as the annual growth rate of M2 for acountry, and inflation is measured as theannual rate of increase in the consumerprice index for a country. The 45-degreeline is not fit to the data, but instead repre-sents a theoretical presumption based onthe quantity theory, that the rate of infla-tion should correspond to the rate of moneygrowth (adjusted for the real output growthrate in a particular economy). McCandlessand Weber report a simple correlation of.95 between money growth and inflationbased on this data. Lucas (1996, p. 666)asks “... how many specific economic

theories can claim empirical success at thelevel exhibited in figure 1? ... The kind ofmonetary neutrality shown in this figureneeds to be a central feature of any mone-tary or macroeconomic theory that claimsempirical seriousness.”

While Figure 1 is impressive, oneshould be careful to note that these resultsare different from the stories about long-runmonetary neutrality and superneutralityoutlined above. Evidently, the average rateof money growth is correlated highly withthe average rate of inflation in a country.But the story about long-run monetaryneutrality is about a permanent, unexpectedchange in the level of the money stock in asingle country, and the ultimate impact ofsuch a change. And, the story aboutsuperneutrality concerns the long-runeffect of a permanent, unexpected changein the rate of monetary expansion. Takingaverages over long periods of time, whileinformative at some level, masks the infor-mation about such events, to the extentthey might have occurred in the data. Tostudy long-run neutrality more directly,the time-series evidence on inflation andmonetary growth for individual countriesneeds to be considered. Can we isolatepermanent, or at least highly persistent,changes in the money stock (or the mone-tary growth rate), which are then corre-lated with persistent changes in the pricelevel (or the rate of inflation) and simulta-neously are uncorrelated with permanentmovements in important real variables?That is the challenge of testing monetaryneutrality propositions.

Time-Series Evidence. Some tests of long-run monetary neutrality during the 1960ssimply regressed the level of real output on a distributed lag of observations on themoney stock. In reaction to this practice,Sargent (1971) and Lucas (1972) arguedthat such evidence was circumspect for tworelated reasons. One is that Sargent andLucas built simple and plausible reduced-form models of the macroeconomy inwhich long-run monetary neutrality heldby construction, but which also wouldproduce data such that, if the standard

Figure 1

100

80

60

40

20

020 40 60

45°

80 100%

Money Growth and InflationInflation

Money Growth

%

Postwar average rates of money growth versus average inflation rates in 110 countries. Obser-vations near the 45 degree line, which is not fitted to the data, are consistent with the quantitytheory. This figure is from McCandless and Weber (1995).



61

practice was applied, the researcher wouldconclude that long-run monetary neutralityfailed. Thus, any evidence based on the(then) standard methodology was difficultto interpret.

The second reason—the one that is atthe heart of the methods used in the recentresearch—was that the story of monetaryneutrality involves permanent changes inthe level of the money stock, and that onecannot effectively test such a theory with-out evidence that the actual money stockhas been subject to a permanent change.The idea of permanent changes in econ-omic variables is statistically modeled as aunit root in the autoregressive representa-tion of a time series; a time series with aunit root has quite different propertiesfrom a stationary series.6 During the early1970s when Lucas and Sargent first wroteabout this topic, the implications of unitroots in economic time series were onlybeginning to be appreciated. Later, in aninfluential paper, Nelson and Plosser(1982) argued that many U.S. macroe-conomic time series were best characterizedby a unit root in their univariate, autoregres-sive representations. Their results broughtthe issue of how to handle these nonsta-tionary time series to the fore in macro-econometrics, and led to econometricmethodologies that respected the potentialfor nonstationarity in important macroeco-nomic variables.

The nonstationarity in economic vari-ables was viewed as something of a head-ache for much of macroeconometrics. Butin a remarkable turn of events, it actuallywas a boon to testing neutrality proposi-tions. As Lucas and Sargent had argued,one needs permanent changes in the moneystock as part of the historical record to testthe proposition of long-run neutrality in atime-series setting. But permanent shocksare exactly what macroeconomic timeseries provide.

This was exactly the line pursued byFisher (1988) and Fisher and Seater(1989, 1993), and also in a series of papersby King and Watson (1992, 1994, 1997).These authors provided new tests of long-run neutrality propositions that respected

the Lucas-Sargent critique and requiredlittle macroeconomic structure.

TESTING NEUTRALITYPROPOSITIONSRecent Tests Based (Mostly) on U.S. Data

Fisher and Seater (1993) work in termsof bivariate systems, with a measure ofmoney as one of the variables. Adoptingtheir notation, let m be the natural loga-rithm of the nominal money stock M. Lety be a second variable, expressed in eitherreal or nominal terms, which is the loga-rithm of a variable like the price level orreal output, and where the variable itself is Y.7 Denote the order of integration of avariable by ⟨x⟩ , so that if x is integrated oforder l, we write ⟨x⟩ = l. Sometimes wealso will use the phrase “x is I (l)” todescribe the order of integration. Denote a difference operator by D, so that Dy indi-cates the approximate growth rate of thevariable Y. Fisher and Seater study the following system

(1)

(2)

where a(L), b(L), c(L) and d(L) are lagpolynomials, and a0 = d0 = 1 and b0 and c0

are unrestricted. The error vector (ut,wt)'is iid with zero mean and covariance ∑ .Now let and with i, j= 0 or 1. Fisher and Seater define a certainlong-run derivative (LRD) that is central totheir findings. The LRD is a change in zwith respect to a permanent change in x,given by

(3)

provided otherwisethe LRD is undefined. Fisher and Seaterthen define long-run neutrality and long-run

lim / ,k t k tx→∞ +∂ ∂ ≠µ 0

LRDz u

x uz xk

t k t

t k t, lim

/

/,≡ ∂ ∂

∂ ∂→∞+

+

z ytj

t≡ ∆ ,x mti

t≡ ∆

d L y c L m wy

tm

t t( ) = ( ) +∆ ∆

a L m b L y um

ty

t t( ) = ( ) +∆ ∆6 One could use other methods

to statistically model a perma-nent shift in the level or growthrate of a monetary variable.One could, for instance, posit adiscrete shift in the mean of thevariable at a given date, T, andone could then check to seehow other variables respondedto such a permanent move-ment. Nothing here is rulingout such an approach, but theliterature surveyed in this paperfocuses on unit-root characteri-zations of variables of interestas measures of whether theseseries have permanent compo-nents or not.

7 To simplify the discussion in thissection, interest rates are leftout here, even though they areincluded in Fisher and Seater’s(1993) framework.

superneutrality in this framework, and foreach, discuss four cases that depend on theorder of integration of the variables.8

First of all, money is long-run neutralwith respect to y if LRDy,m= 1 when y is anominal variable, or if LRDy,m= 0 when yis a real variable. The four cases are: 1) ⟨m⟩ < 1. Here the LRD is not definedbecause there have been no permanentshocks to the level of the money stock,and the data are uninformative concerninglong-run monetary neutrality. 2) ⟨m⟩ ≥ ⟨y⟩+ 1 ≥ 1. Here the LRD is zero becausewhile there have been permanent shocksto the level of the money stock, there havebeen none to y. If y is a nominal variable,long-run neutrality is violated, otherwise itholds. 3) ⟨m⟩ = ⟨y⟩ ≥ 1. This case admitstests of long-run neutrality, in an effort tofind out if the permanent shocks to thelevel of the money stock are correlated withthe permanent shocks to the variable y. 4) ⟨m⟩ = ⟨y⟩ –1 ≥ 1. This case is morecomplicated. A necessary condition forlong-run neutrality is that the permanentshock to money does not change thegrowth rate of y.

Secondly, money is long-run superneu-tral with respect to y if LRDy, ∆m= 0. Thecases are 1) ⟨∆m⟩ < 1. Here the LRD is notdefined because there have been no perma-nent shocks to the growth rate of the moneystock, and the data are uninformative con-cerning long-run monetary superneutrality.2) ⟨∆m⟩ ≥ ⟨y⟩ + 1 ≥ 1. The LRD is zerobecause while there have been permanentshocks to the growth rate of the moneystock, there have been none to y. Long-runsuperneutrality holds. 3) ⟨∆m⟩ = ⟨y⟩ ≥ 1.This case admits tests of long-run superneu-trality, in an effort to find out if the perma-nent shocks to the level of the money stockare correlated with the permanent shocksto the variable y. 4) ⟨∆m⟩ = ⟨y⟩ –1 ≥ 1.Here LRD∆y, ∆m= 0 is testable; that is, onecan determine whether a permanentchange in the growth rate of money isassociated with a permanent change in the growth rate of y.

Fisher and Seater (1993) use theseresults to analyze previous research effortstesting long-run neutrality propositions,

efforts that, because of the time they werewritten, did not take such explicit accountof the time-series properties of the data.They interpret the evidence in Andersonand Karnovsky (1972), Kormendi andMeguire (1984), Lucas (1980), andGeweke (1986) mostly as consistent withlong-run neutrality and not very informa-tive about long-run superneutrality. Theyalso provide some evidence of their own.They use the Friedman and Schwartz(1982) data on money, prices, nominalincome, and real income from 1867 to1975 in the United States. All variables areviewed as I(1), making tests of long-runneutrality possible. With respect to nom-inal income and prices, long-run monetaryneutrality holds in this data, but withrespect to real output, long-run monetaryneutrality fails.

As mentioned earlier, evidence of thefailure of long-run monetary neutrality iseither surprising or suspect among mone-tary theorists; the Fisher and Seater findingwas no exception. In a note, Boschen andOtrok (1994) re-estimate the systemsstudied by Fisher and Seater, again usingthe Friedman and Schwartz (1982) data,but now updating the time series through1992. They split the data set into two sub-samples, 1869-1929 and 1940-92. Theyfind that long-run neutrality holds in bothof the subsamples using the Fisher andSeater methodology. They conclude thatthere may have been something specialabout the financial disruption during theGreat Depression era that causes the test tofail when that period is included.

Haug and Lucas (1997) comment fur-ther on these findings. They reason that,since Canada did not experience bank fail-ures during the Great Depression, theevidence on long-run neutrality usingCanadian data might provide furtherevidence that something unusual happenedin the United States during this period.Their data set includes real nationalincome and the M2 money supply from1914-94. They argue that pre-1914 data isinappropriate for this purpose becausechanges in the money supply were notexogenous in Canada at that time. They

8 In an appendix, Fisher andSeater (1993) argue that coin-tegration plays no role in theirbivariate tests of neutrality orsuperneutrality. This does notimply that one could not deviseother, similar tests based oncointegration, as (in fact) hasbeen done. See, for instance,the Boschen and Mills (1995)paper reviewed later in this section.



62

conclude, based on augmented Dickey-Fuller (ADF) tests, that both time series areI(1). And, according to the Fisher andSeater (1993) methodology, long-run mone-tary neutrality with respect to real outputcannot be rejected using the entire Canadiansample period. Haug and Lucas interpretthis finding as independent support for thearguments of Boschen and Otrok (1994).

Olekalns (1996) similarly explored analternative data set, 94 years of annualAustralian data. The downturn of the 1930swas less severe in Australia. Olekalns usesthe Fisher and Seater methodology, and twomeasures of money, M1 and M3, along withreal gross domestic product. All variablesare reasonably described as I(1) accordingto ADF tests. Olekalns finds that long-runmonetary neutrality cannot be rejectedusing the narrower money measure. How-ever, using the broader money measure,long-run neutrality can be rejected for this data set, and the rejection carries evenwhen dummy variables are used to controlfor the Depression period as well as theWWII period. Olekalns concludes thatresults can be sensitive to the measure of money used.

A recent paper by Coe and Nason (1999)also contributes to this literature. They usethe Fisher and Seater (1993) test for long-runneutrality, and they employ the same U.S.data as Fisher and Seater, except that theyupdate the data through 1997. When Coeand Nason use a broad measure of themoney stock (as Fisher and Seater did), theyreplicate the Fisher and Seater rejection oflong-run monetary neutrality with respect toreal output. But when they replace the broadmoney measure with the monetary base, theycan no longer reject long-run neutrality.They also consider about a century of datafrom the United Kingdom, and fail to rejectlong-run neutrality using either broad ornarrow measures of money. Coe and Nasonconclude that the Fisher and Seater rejectionof long-run neutrality is not robust to achange in either the measure of money or the country of study.9

An important work in this literature,King and Watson (1997) also use bivariatesystems, and they also take careful note of

the order of integration of the variablesinvolved when devising tests of neutralitypropositions. They study a “final form”model

(4)

(5)

where y is the logarithm of real output, the u coefficients are lag polynomials, εm

t isa serially independent, zero mean shock tomoney, and εη

t is a vector of nonmonetaryshocks that affect output. King and Watsonshow that

(6)

is the long-run elasticity of real outputwith respect to permanent shocks to themoney stock. Thus, long-run neutralityhere is analogous to the Fisher and Seaterdefinition: gym = 0. Again, long-run neutral-ity can be investigated only if there havebeen permanent shocks to the money stock.

Importantly, King and Watson (1997)emphasize identification issues. They ana-lyze long-run neutrality propositionsacross a range of possible identifications of their bivariate system, in an effort tounderstand the robustness of various con-clusions to differing assumptions. Theyrewrite the equations (4) and (5) as

(7)

(8)

and they assume that

They note that there are several plausibleways to complete their identification of thesystem. One could assume lym= 0, or that

cov , .ε εηtm

t( ) = 0

∆mj mm t j tm

j

p+ +∑ −

=α ε,

1

∆ ∆ ∆m y yt my t j my t jj

p= + ∑ −

=λ α ,

1

∆mj ym t j tj

p+ +∑ −

=α εη

,1

∆ ∆ ∆y m yt ym t j yy t jj

p= + ∑ −

=λ α ,

1

γθθym

ym

mm

=( )( )1

1

∆m L Lt m m t mm tm= + ( ) + ( )µ θ ε θ εη

η

∆y L Lt y y t ym tm= + ( ) + ( )µ θ ε θ εη

η

9 Coe and Nason also study theasymptotic power properties ofthe Fisher and Seater long-hori-zon regression test, and theyconclude that the test has lowpower against alternativehypotheses of monetary non-neutrality. For small samples,Monte Carlo experiments revealpoor size-adjusted power espe-cially at longer horizons. Coeand Nason conclude based onthis portion of their analysisthat the Fisher and Seaterapproach to testing long-runmonetary neutrality may not beinformative.



63



64

Figure 2

6

4

2

0

—2—0.6 —0.2 0.6 1.0 1.4 1.8 2.20.2

6

4

2

0

—2—10 —8 —4 —2 0 2—6

10

6

2

—2

—6—4—5 —2 —1 0 1 2 3—3

1.5

0.5

—0.5

—1.5

—2.5—0.2—0.4 0.2 0.4 0.6 0.80.0

Inflation and Unemployment

A. 95% Confidence Interval for gym as a Function of λ my

B. 95% Confidence Interval for gym as a Function of λ ym

C. 95% Confidence Interval for gym as a Function of gmy

D. 95% Confidence Ellipse when gym = 0

gym

gym

gym

λ ym

The evidence on long-run monetary neutrality according to King and Watson (1997). The panels show how the point estimate of gy m changes under the differing identifying restrictions, with the dotted lines indicating 95% confidence intervals. The bottom panel displays a 95% confidence ellipse for λ ym and λ my under the identifying restriction gym = 0.

λ my

λ ym

gmy

λ my

lmy= 0; this means that the impact elasticityof one variable on the other is zero. Alter-natively, one could simply assume long-runmonetary neutrality by imposing gym= 0.And finally, one could assume that gym= 1where gmy is the long-run elasticity of moneywith respect to a permanent shock to realoutput. King and Watson (1997, p.77)argue that this last assumption is consistentwith stable prices in an economy with con-stant velocity.

Because King and Watson wish toinvestigate the robustness of neutralityresults to alternative identifying assump-tions, they use all four of these possibilities.Furthermore, they allow a wide variety ofvalues for each elasticity, not just the zeroesand ones of the previous paragraph. Thus,the identifying assumptions are that eitherone of the impact elasticities is known tobe a certain value, or that one of the long-run elasticities is known to be a certainvalue. They then turn to estimation andreport results considering a number ofneutrality propositions. The quarterly data are for the United States and cover the sample period from 1949:1 to 1990:4;except for systems with unemployment, in which case the sample period is from1950:1 to 1990:4. The lag length p is setto six, although they experiment withvalues of four and eight at some points.Based on unit-root diagnostic tests, Kingand Watson conclude that all the seriesinvolved can reasonably be viewed as I(1),so that tests of neutrality propositions can be executed.

King and Watson (1997) first investi-gate the long-run neutrality of money inthe context of a bivariate system using realoutput and money (M2). They begin byestimating a value for gym using the identi-fying assumption that lmy is known. Theyfind that a 95-percent confidence intervalfor gym contains zero (and so supportslong-run monetary neutrality) so long aslmy > 1.4. If we interpret lmy the parameteras a short-run elasticity of money demand,a reasonable range is .1 ≤ lmy ≤ .6, so thatthe evidence is consistent with long-runneutrality. King and Watson complete sim-ilar calculations for identifying assumptions

involving lym and gmy. They also estimate95-percent confidence intervals for lmy,lym, and gmy using the identifying assump-tion that long-run neutrality holds, gym=0,in order to see if the confidence intervalsproduced contain the most reasonablevalues for these parameters. All of thisevidence comes down in favor of long-runneutrality, which is consistent with thefindings of Fisher and Seater (1993) andBoschen and Otrok (1994), because thesample period here covers the postwarUnited States.10 This evidence is summa-rized in Figure 2.

The superneutrality of money is inves-tigated using a bivariate system with moneygrowth (replacing the level of the moneystock) and real output, and the hypothesisis that the long-run elasticity of the level ofoutput to a permanent change in the growthrate of money, gy, ∆m , is zero. The evidenceon this question turns out to be mixed, inthat for some identification schemes thatKing and Watson consider reasonable, thehypothesis that gy, ∆m =0 can be rejected atthe 5-percent level. Moreover, the effectcan go either way: a permanently higherrate of money growth tending topermanently increase the level of realoutput, or to decrease the level of realoutput. For instance, if the identifyingassumption is l∆m, y =0 (which King andWatson again interpret as a short-runmoney demand elasticity), then the esti-mated value of gy, ∆m is positive and statis-tically significant, while if the identifyingassumption is that l∆m, y =.6, then the esti-mated value of gy, ∆m is negative and statis-tically significant. As mentioned earlier,theories exist that are consistent with both possibilities.

King and Watson go on to investigatea neutrality proposition associated withthe early 20th century economist IrvingFisher. The proposition is that nominalinterest rates move one-for-one withpermanent changes in inflation, leavingthe real interest rate unaffected. Using asystem with consumer price indexinflation, π, playing the role of the moneyvariable, and the nominal interest rate onthree-month Treasury bills, R, playing the

10 Jefferson (1997) also investi-gates monetary neutrality ques-tions using the King andWatson (1997) methodology,except that he considers mea-sures of both inside money(defined as nominal checkabledeposits, or M2 less currency)and outside money (defined asthe monetary base). He usesnearly a century of data fromthe United States and findssome departures (under someidentifying restrictions) fromlong-run neutrality when insidemoney is used.



65

role of the output variable, King andWatson (1997) investigate the hypothesisthat gRπ=1; that is, the long-run elasticityof the nominal interest rate with respect toa permanent inflation shock is one. Theevidence here again turns out to dependon the identification scheme. When statis-tically significant differences from thestandard Fisher relation occur, they occurin a negative direction, with nominalinterest rates rising less than one-for-onewith perma-nent shocks to inflation. Inother words, real interest rates are loweredpermanently by permanent, positive shocksto the inflation rate. King and Watson findthat identifying the model by assuminggRπ=1, and then estimating 95-percentconfidence intervals for the remainingparameters, leads to the conclusion thatthere are reasonable configurations ofparameters that are consistent with theFisher hypothesis. Nevertheless, the mainconclusion is that nominal interest ratesdo not adjust fully to permanent inflationshocks, and this conclusion holds across alarge set of identification schemes.

Finally, King and Watson turn to esti-mating the slope of a long-run Phillipscurve; that is, the long-run response ofunemployment to permanent shocks in theinflation rate. This particular test is dis-cussed in more detail in another paper,King and Watson (1994). The bivariatesystem now includes the CPI inflation ratein the role of the nominal variable, and theunemployment rate in the role of the realvariable. The hypothesis is that the long-run Phillips curve is vertical, which meansguπ=0 in this framework. King and Watsonreport that a statistically significant (nega-tive) slope for the long-run Phillips curvecan be obtained only if the identifyingassumption is that gπu>2.3, or alternativelythat guπ< –0.7. In particular, if either ofthese two impact elasticities are zero, thena vertical long-run Phillips curve cannot berejected. King and Watson conclude that areasonable estimate of the long-run Phillipscurve based on this data is either verticalor at least “very steep.”

While King and Watson’s strong suit isthat they can investigate the robustness of

results on neutrality for a wide variety ofidentification schemes, they do so only forbivariate systems, and they note the possi-bilities for exposure to omitted variablebias. One of the few multivariate studiesavailable using techniques related to thoseof Fisher and Seater (1993) for testingneutrality is by Boschen and Mills (1995).They use the notion of permanent shocksto the level of the money stock to testlong-run monetary neutrality in the U.S.data. They use a relatively high dimensionalsystem, and they organize their researcharound the idea that, if long-run neutralitydoes not hold, there would be a nonsta-tionary component of real output that isdetermined by long-term movements inthe money stock. They study a vector errorcorrection model (VECM) representation

(9)

where X' ≡ (y, m,υ )', and y is aggregateoutput, υ is a vector of real shocks, m is avector of monetary shocks, and ε is nor-mally distributed, iid, and has mean zero.Interest centers on the long-run impactcoefficient matrix ∏ that describes thelong-run relationships in the model. Foreach cointegrating relationship, this matrixwill have a nonzero row. If there is a coin-tegrating relationship between the mone-tary variables and output, then these varia-bles contribute to the trend shifts in output,and long-run neutrality is violated.11

Boschen and Mills (1995) use quarterlyU.S. data from 1951:4 to 1990:4. Theyinclude variables describing productivity,real oil prices, weighted foreign real GDPof major U.S. trading partners, real govern-ment purchases, taxes, labor supply, theM1 money stock, the M2 money stock,and the nominal three-month Treasury billrate. They use augmented Dickey-Fullertests as diagnostics for the presence ofnonstationarity in these data; they found(sometimes weak) evidence of a unit rootin all the series. They test for cointegratingrelationships among the blocks of real andnominal variables, and then between thenominal and real variables, as a means oftesting for long-run monetary neutrality.

∆ Γ ∆ ΠX X Xt i t i t k ti

k= + + +∑ − −

=

−µ ε

1

1,

11For a related approach andanalysis, see Hoffman andRasche (1996), Chapter 7.



66

Based on these tests, Boschen and Millsconclude that long-run monetary neutralityholds during the postwar period in the U.S.This result confirms the findings that Fisherand Seater (1993), Boschen and Otrok(1994), and King and Watson (1997)reported regarding long-run monetary neu-trality in the postwar U.S. data. This resultalso provides the best available evidencethat omitted variable bias did not contami-nate the previous results on this question.

Recent Tests Using International Data

So far, we have results that conform tothe suggestions of King and Watson andFisher and Seater only for U.S. data—cer-tainly a natural place to start but not thetrue extent of the available evidence. As afirst effort at generalization, Weber (1994)explicitly set out to apply the King andWatson testing procedures to G7 econo-mies: Canada, France, Germany, Italy,Japan, the United Kingdom, and theUnited States. The data is quarterly, fromthe postwar era, but the particular yearsvary across countries.

Weber begins with a battery of unit-root diagnostics—using a much moreelaborate procedure than the papersdiscussed so far—in an effort to makecareful statements about the evidence forthe presence of a unit root in the timeseries. For each country, he uses severaldifferent measures of the money stock, inpart to confront the question of whetherthe results are sensitive to how money isdefined. The combination of several diag-nostic tests and many different time seriesproduces a plethora of results that are notall the same. As a general rule, however,narrower monetary aggregates tended tobe I(1), while broader aggregates tended tobe I(2). Strictly speaking, according to themethodology outlined above, if money isI(2) then superneutrality can be tested,whereas neutrality cannot. In response tothis situation, Weber takes two approaches:In some cases, he performs neutrality testsanyway and warns the reader to interpretthe results with caution, while in other

cases he uses the I(1) aggregates to test forneutrality and the I(2) aggregates to testfor superneutrality. The remaining serieson output, inflation, interest rates, andunemployment rates, for the most part,can be reasonably interpreted as I(1).

Weber then turns to tests of long-runmonetary neutrality in these countries,using the same wide variety of possibleidentifying assumptions that King andWatson used. His general finding is thatfor broader monetary aggregates, such asM2 or M3, a wide variety of identifyingrestrictions are consistent with (fail toreject) long-run monetary neutrality in theG7 economies during the postwar era. Fornarrower measures of money, the range ofidentifying restrictions consistent withlong-run monetary neutrality is muchsmaller. Confidence ellipses for lym andlmy under the identifying assumption thatmoney is long-run neutral, gym=0, includethe plausible region of the space where lym

<0, (the short-run impact of money onoutput is positive) and lmy >0 (moneyreacts countercyclically to output in theshort run). This is true across the G7economies for both narrow and broadmeasures of money.

Superneutrality is examined using abivariate VAR in differenced money growthand differenced real output. In general,long-run superneutrality with respect tothe level of real output is rejected for awide variety of identifying restrictionsacross the G7 economies.

Considering the question of whetherthe long-run Phillips curve is vertical,Weber proceeds using the changes in infla-tion and unemployment in his bivariateVAR. For six of the seven G7 economies,the hypothesis that guπ=0 cannot berejected except in cases of rather extremeidentifying assumptions. The exception isItaly, where this hypothesis can be rejectedreadily. Weber also considers a “reverse”hypothesis, with causality running fromunemployment to inflation. In this casethe hypothesis gπu=0 can be rejected easilyacross the non-Italian economies. ForItaly this hypothesis is rejected only forextreme identification schemes. Weber



67

speculates that wage indexation in Italyduring much of this period accounts forthe differences between Italy and the otherindustrialized economies.

Finally, Weber goes on to test theFisher relation for the G7 economies usinga bivariate VAR in differenced inflation anddifferenced nominal interest rates. Hefinds that for Germany, a Fisher relationcan be rejected for a wide variety of identi-fying restrictions, although some importantbenchmark restrictions do not lead torejection. For the United States, Weberconfirms the findings of King and Watson(1997) that nominal interest rates do notadjust one-for-one with permanent shocksto inflation. Even stronger evidence in thisdirection is found for the United Kingdom.But for Japan, Canada, Italy, and France,

the evidence is much more favorable for a Fisher relation, grπ=1, to hold. The gen-eral finding in the previous literature (seefor instance, Lothian, 1985, for 20 OECDcountries) is that nominal interest ratesadjust less than one-for-one with inflation.

While Weber considered G7economies, Bullard and Keating (1995)consider virtually all of the countries inthe world where enough data existed toformulate tests of long-run neutralitypropositions in the spirit of Fisher andSeater (1993) and King and Watson (1997).In working with a large number of countries,data availability and quality impingesignificantly on the analysis. Accordingly,Bullard and Keating restrict attention tocountries that produce at least moderatelyhigh quality data (according to published



68

Figure 3

Long-Run Response of the Level of OutputTo a Permanent Increase in Inflation

Germany Austria

USAJapan

CyprusAustralia

FinlandUK

IrelandSpain

PortugalCosta Rica

IcelandMexico

ChileArgentina

—2.5

—1.5

0.5

—0.5

1.5

2.5

3.5

4.5

Countries ordered from lowest to highest average inflation in sample. Horizontal lines represent point estimates. Vertical lines represent 90 percent confidence bounds.

The point estimate of the long-run response of the level of real output to a permanent inflation shock is generally positive for the low inflation countries but zero or negative for high inflation countries. This figure is reproduced from Bullard and Keating (1995) and is reprinted with permission by the Journal of Monetary Economics.

Country

e

assessments) and have at least 25 years ofconsecutive annual observations (quarterlydata often is not available). This leavesthem with 58 countries. Bullard and Keatingfocus their analysis on one particular versionof a neutrality proposition: the effect of apermanent shock to inflation on the levelof output. If money is long-run neutral—and the evidence reported in this surveysuggests that this is a reasonable assump-tion—then this can be viewed as a test of monetary superneutrality with respectto the level of real output. Moreover, prob-lems with the definition of money withinand across countries are avoided.

Bullard and Keating also begin with abattery of unit-root diagnostic tests for thereal output and GDP deflator time seriesthey use. They divide countries intogroups based on the results of these tests,according to whether a country can becharacterized as having experiencedpermanent shocks to inflation or not, andsimilarly for the level of real output.Countries that experienced permanentshocks to inflation and also to the level ofoutput are candidates for a test based on abivariate VAR; there were 16 countries inthis group, dubbed Group A. There werealso nine Group B countries for which evidence of a unit root in inflation wasfound, but evidence of a unit root inoutput was lacking. A large number ofcountries, 31, showed no evidence of perma-nent shocks in the inflation series, and wereput into Group C. The two remainingcountries were special cases.

Bullard and Keating (1995) then ran atwo-variable VAR for the Group A countries,in differenced inflation and differencedoutput. They committed to the long-runidentifying restriction that money is long-run neutral, gπy=0 in the King and Watson(1997) notation, and did not attempt tosearch over alternative identifying restric-tions. They used the techniques of Blan-chard and Quah (1989) to decomposeshocks into permanent and transitorycomponents, and consequently they consi-dered the impulse-response functions ofreactions of the two variables to both permanent and transitory shocks.

The main results for the Group Acountries are as follows: The long-runresponse of the level of output to a perma-nent inflation shock was positive andstatistically significant for four countries,negative and statistically significant forone country, and not statistically differentfrom zero for the remainder. The pointestimate of this long-run response generallydeclined as the in-sample average inflationrate increased, as shown in Figure 3.

The Group B countries, which possesspermanent inflation shocks but no perma-nent output shocks, provide prima facieevidence of superneutrality. The Group Ccountries are uninformative because theydo not possess permanent inflation shocks.Altogether, the results appear to be consis-tent with superneutrality for most of thecountries that are informative.

However, as Figure 3 indicates, and as is borne out by the associated impulse-response functions, low-inflation countriesappear to react very differently to permanentinflation shocks than high-inflation coun-tries.12 In particular, for low-inflationcountries the point estimate of the long-run response is generally positive, whilefor high-inflation countries it is zero ornegative. This suggests that averagingresults from low and high-inflation coun-tries may be misleading.

Bullard and Keating also comment on the prospects for permanent inflationshocks to permanently alter rates of growthof real output in this sample. According to ADF and other diagnostic tests for unitroots, real output growth rates are stationaryin nearly all countries that experiencedpermanent shocks to inflation. This is directevidence for superneutrality with respectto output growth rates. This result doesnot seem like one that is likely to changewith data sets or countries, since the sta-tionarity of real output growth is likely toremain under most conceivable criteria.13

All of the Bullard and Keating data arefor postwar economies. Serletis and Krause(1996) use the Backus and Kehoe (1992)data set, which includes more than 100years of annual observations on real output,prices, and money for Australia, Canada,

12Other aspects of the impulse-response functions had naturalinterpretations according to con-ventional wisdom, and alsowere generally consistentacross countries.

13 This result conflicts with otherevidence from the cross-countrygrowth regression literature,such as Barro (1996).



69

Denmark, Germany, Italy, Japan, Norway,Sweden, the United Kingdom, and theUnited States.14 They test for unit rootsusing the procedures of Zivot and Andrews(1992), and they conclude that money isreasonably described as I(1) except inGermany and Japan where it is I(0); theselatter two countries are therefore uninfor-mative on neutrality questions in this dataset. Serletis and Krause (1996) find thatoutput is I(0) for Australia, Canada, Den-mark, Italy, the United Kingdom, and theUnited States. These countries, therefore,provide direct evidence in favor of long-run neutrality with respect to output.Serletis and Krause use the Fisher andSeater (1993) regression test to produceestimates for the remaining money-priceor money-output combinations. Theseresults generally support a hypothesis oflong-run monetary neutrality.

The same data set is used by Serletisand Koustas (1998), who apply the Kingand Watson methodology to study long-run neutrality and superneutrality issuesover a range of plausible identifying restric-tions. They use only the money and realoutput series, and apply a battery of tests todetermine the integration properties of thedata. Except for the money series for Italy,which is I(2), they conclude that all seriesare I(1) and hence provide a reasonabledataset with which to test long-run mone-tary neutrality (superneutrality for Italy).15

The results state that it is generally difficultto reject long-run monetary neutrality inthis dataset under plausible identifyingrestrictions. An exception is the UnitedKingdom, when the identifying restrictionis that 0 ≤ lmy ≤ .6. Superneutrality ofmoney with respect to real output in theItalian data can be rejected under plausibleidentifying restrictions.

The Serletis and Krause (1996) and Ser-letis and Koustas (1998) results may appearto impinge on the Fisher and Seater (1993)and Boschen and Otrok (1994) findings forthe United States, namely that the resultsfor long-run monetary neutrality in theUnited States over the last century dependcritically on inclusion or removal of theGreat Depression years from the sample.

Both Serletis and Krause (1996) and Serletisand Koustas (1998) fail to reject long-runneutrality even when this period is included(under a range of plausible identificationschemes in the latter case). However,Serletis and Koustas (1998) in fact rejectlong-run neutrality under the Fisher andSeater (1993) identifying restriction (gmy =0), but they do not reject under other, possibly more plausible, identifying restric-tions. Of course, differences in results couldalso be due to differences in the data setsemployed. Similar comments can be madeconcerning the results of Olekalns (1996)using a near-century of Australian data.

Crosby and Otto (1999) move awayfrom the money-inflation-output nexusdiscussed in many of the papers so far, inorder to analyze the long-run connectionbetween inflation and the capital stockusing the methods of Fisher and Seater(1993) and King and Watson (1997).Crosby and Otto consider a bivariate VARwith inflation playing the role of the nom-inal variable, and the capital stock playingthe role of the real variable. They use thelong-run identifying restriction that shocksto the capital stock do not have permanenteffects on the rate of inflation, which issimilar to the long-run restriction sometimesemployed in the papers discussed earlier.They construct an annual capital stockseries for 64 countries using postwar data,with differing sample periods for differentcountries. Their unit-root diagnostics(ADF tests) indicate that 34 of these coun-tries have both permanent shocks toinflation and to the capital stock. Forthese countries they test superneutralitywith respect to the capital stock usingtheir bivariate VAR. The Crosby and Ottoestimates indicate that a permanent infla-tion shock has no statistically significantlong-run impact on the capital stock for alarge majority of the countries. Departuresfrom this result are generally on the posi-tive side, with a permanent inflation shocktending to raise the stock of capital in acountry. Crosby and Otto argue that theseresults are robust to a number of changesin their analysis, including an alternativeidentifying restriction.

14 Some data are missing,notably 1914-24 and 1939-49for Germany and 1941-51 forJapan. Also missing are 1915-20 for Denmark, and 1940-45for Norway.

15 These results on orders of inte-gration are somewhat differentfrom those of the previousparagraph, even though thedata set is the same, becauseSerletis and Koustas (1998)use different (and more stan-dard) procedures to test for thepresence of unit roots thanSerletis and Krause (1996). In section four of their paper,Serletis and Koustas (1998)discuss the differences whenthe Zivot and Andrews (1992)methodology is used.



70

A real variable of interest to manyeconomists is productivity. In an attemptto understand the long-run relationshipbetween inflation and productivity,Sbordone and Kuttner (1994) devote aportion of their analysis to bivariate VARmethodology similar to that used by Kingand Watson (1997). They use data fromthe postwar United States, and theyconclude that both series are reasonablycharacterized as I(1). Sbordone and Kuttner use the King and Watson (1997)approach to identification, setting impactmultipliers and long-run multipliers tovarious values in an effort to learn aboutthe sensitivity of the results to alternativeidentification schemes. Under many ofthese schemes, the long-run impact of apermanent, positive shock to inflation onproductivity is negative. If the identifica-tion scheme is the monetarist one—thelong-run impact of a permanent shock toproductivity on inflation is zero—then theestimated effect of a permanent inflationshock on productivity is negative but isnot statistically different from zero.

Koustas and Serletis (1999) use theKing and Watson (1997) methodology ofsearching across alternative identificationschemes to study the Fisher relation betweennominal interest rates and inflation rates.They employ data from the postwar periodfor 11 industrialized countries: Belgium,Canada, Denmark, France, Germany, Greece,Ireland, Japan, the Netherlands, the UnitedKingdom, and the United States. Accordingto the authors’ unit root diagnostic tests, allof these countries except two (Denmarkand Japan) can reasonably be interpreted aspossessing the nonstationarity in interestrates and inflation rates required to use theKing and Watson techniques. The basicfinding is that the long-run Fisher relationcan be rejected across countries for a widerange of plausible identification assumptions.The authors also argue that taking tax effectsinto account accentuates this finding. The Koustas and Serletis results are moreconsistent across countries on this questionthan those of Weber (1994), who foundmore mixed results for a similar set of countries.

Rapach (1999a) is the first author toconsider a trivariate VAR in this literature.His variables are the inflation rate, thenominal interest rate, and the level of realoutput. The data is from the postwarperiod for 14 industrialized (OECD) coun-tries, where continuous observations on allthree variables are available starting fromthe 1960s and extending to the mid-1990s.16

Rapach (1999a) uses long-run identifyingrestrictions following Blanchard and Quah(1989); he needs three for the trivariatesystem. Rapach first extends the often-used monetarist restriction that permanentshocks to interest rates and output cannothave permanent effects on the inflationrate. Rapach’s third restriction, also moti-vated by theoretical considerations, is thatpermanent shocks to output (“permanenttechnology shocks”) leave the real interestrate unchanged. Since the long-runresponse of inflation to a permanent tech-nology shock is already set to zero, this lastrestriction is accomplished by making thelong-run response of the nominal interestrate to a permanent technology shockequal to zero.

Rapach uses unit-root diagnostic teststo conclude that the variables are reasonablydescribed as I(1) for these countries, andruns the trivariate VAR in an effort to esti-mate, primarily, the long-run responses ofthe level of real output to a permanentinflation shock, and of the real interest rateto a permanent inflation shock (the differ-ence between two estimated long-runresponses in this system). For all countries,the point estimates indicate that real interestrates fall in response to a permanent infla-tion shock. Moreover, these effects aregenerally statistically significant (or veryclose) at conventional significance levels.The point estimates also indicate that theresponse of the level of real output to apermanent inflation shock is positive for11 of 14 countries, and four of these arestatistically significant, or nearly so, atconventional significance levels. Theselatter results are generally consistent withthe findings of Bullard and Keating for lowinflation countries in a bivariate VARframework. The results on real interest

16 The countries are Australia,Austria, Belgium, Canada,Denmark, France, Ireland, Italy,Japan, the Netherlands, NewZealand, Sweden, the UnitedKingdom, and the United States.



71

rates are more strikingly in favor ofnonsuperneutrality than the findings ofWeber for G7 economies in bivariatesystems. Weber searched over identificationschemes while Rapach commits to a partic-ular scheme, but Rapach studies interactionsbetween three variables instead of two andanalyzes more countries.

Related Methodology Using U.S. Data

Ahmed and Rogers (1996, 1998) workon empirical issues related to the long-runimpact of permanent inflation shocks onreal variables, but with methods somewhatdifferent from those discussed earlier. Inparticular, Ahmed and Rogers construct atheoretical model economy and use thiseconomy to motivate restrictions imposedin their empirical work. The modelconsists of an infinitely-lived representativeagent who might hold money either becauseit enters the utility function or because of acash-in-advance constraint. The technologyfor production of private sector real outputis Cobb-Douglas, multiplied by a technologyshift variable and also by a function ofgovernment size. Special cases of thisframework (restrictions on theoreticalparameters) deliver the standard resultsfrom the theoretical literature on monetarysuperneutrality surveyed by Orphanidesand Solow (1990).

Ahmed and Rogers (1998) use annualU.S. data from 1889 to 1995 coveringinflation, real output, real consumptionexpenditures, real investment, and theratio of government spending to output.Much of the data is from Kendrick (1961).Based on diagnostic testing, Ahmed andRogers conclude that a reasonable descrip-tion of the data is that these series are I(1),with the exception of the size of govern-ment, which they sometimes treat as I(0).The authors then estimate cointegratingrelationships for two specifications of themodel. Based on these estimates, a perma-nent, positive shock to inflation is asso-ciated with a permanent drop in theconsumption-output ratio and a permanentincrease in the investment-output ratio.

These effects are large and statistically sig-nificant. The Fisher effect does not hold,as Ahmed and Rogers infer that real interestrates decline in the face of permanent, positive inflation shocks according to these estimates.

Ahmed and Rogers then turn to estima-tion of a VECM using the cointegratingrelationships implied by their theoreticalmodel, in an effort to find out what happensto the levels of the real variables followinga permanent inflation shock. For two dif-ferent specifications, the estimates indicatethat a permanent shock to inflation increasesthe level of output, consumption, andinvestment. Ahmed and Rogers also con-sider variance decompositions and notethat the inflation shock only accounts for asmall fraction of the forecast error variancein consumption, investment, and output.17

They interpret these results as follows:Permanent inflation shocks do not occurvery often, but when they do, they have a significant impact on the economy.Accordingly, when looking at the data historically, one might reasonably abstractfrom inflation in building a model, butwhen contemplating significant changes in inflation rates, one should not assumethe effects will be negligible.18

Bernanke and Mihov (1998a) testlong-run monetary neutrality, and, likeAhmed and Rogers (1998), they departfrom the methodology described in themain portion of this survey. In particular,Bernanke and Mihov use their own, largerVAR model of short-run monetary policywhich is described in more detail in anotherpaper (Bernanke and Mihov, 1998b) as astarting point. This model uses monthlydata for the United States during the postwarera, and has the following variables: totalbank reserves and nonborrowed reserves,both measured as deviations from a trendand the federal funds rate (collectively thepolicy variables); interpolated monthly realGDP and interpolated monthly GDP deflatorinflation, an index of spot commodityprices and real balances (with money mea-sured as M2). They use a semi-structuralapproach to derive identification restrictionsbased on relationships between the policy

17 Rapach (1999a) also com-putes variance decompositionsand concludes that inflationshocks do not explain a signifi-cant fraction of output forecasterror variance.

18Ahmed and Rogers (1998)also consider subsamples.They find that the effects ofinflation on real variables movein the same direction, but aremuch weaker, during the post-war period as opposed to thepre-WWI or the interwar period.



72

and nonpolicy variables, and among thepolicy variables, and they estimate theVAR. They do not examine the temporary-permanent dichotomy of the shocks to thevariables in their system; the focus insteadis on isolating an action that can reasonablybe termed “a shock to monetary policy.”Bernanke and Mihov’s evidence in favor oflong-run neutrality is based on the impulse-response functions of their estimated VAR:These functions show that the long-run(120-month) response of output to thepolicy shock is not significantly differentfrom zero, although positive. At the sametime, they find short-term impacts of thepolicy shock, such as a liquidity effect, thatare in accord with conventional wisdom.

Bernanke and Mihov (1998a) thenturn to an analysis of the robustness oftheir results, by considering alternativeidentification schemes in a manner analo-gous to the King and Watson (1997)methodology. They find that the evidenceon long-run neutrality is in a sense strongerwhen one is willing to accept an identifica-tion that produces a smaller liquidity effect.They also find that imposing long-run neu-trality as an identifying restriction does notimply that one can reject their specification.Bernanke and Mihov conclude that thesefindings inspire confidence in their VARmodel of monetary policy, since it is con-sistent with both a liquidity effect andlong-run monetary neutrality.

CONCLUSIONSThis survey has covered a fair amount

of territory. To avoid confusion about whatthe results actually say, this section includesa summary of the main findings organizedby the nature of the proposition.

Long-Run Monetary Neutrality. In thissurvey, we did not find much evidenceagainst the long-run neutrality of money.Fisher and Seater (1993) usefully reinter-preted some of the major time series studieson neutrality published in the 1970s and1980s as consistent with long-run monetaryneutrality, and uninformative regardinglong-run monetary superneutrality

(Geweke’s 1986 title notwithstanding!),once one takes proper account of the timeseries properties of the data. While Fisherand Seater (1993) found evidence againstlong-run neutrality with respect to realoutput for the United States during the lastcentury, Boschen and Otrok (1994) pointedout that such a result did not hold once theGreat Depression years were excluded fromthe sample. In another comment on thisquestion, Haug and Lucas (1997) could notreject long-run neutrality in a century ofCanadian data. Olekalns (1996) did findsome evidence against long-run neutralityin a near-century of Australian data using a broad money measure, but the neutralityhypothesis could not be rejected using anarrower money measure. Coe and Nason(1999) find that long-run neutrality cannotbe rejected for a century of U.S. data whenthe monetary base is the monetary variable,nor could they reject long-run neutralityfor a century of U.K. data.19

Long-run neutrality received supportfrom the studies focused exclusively on thepostwar U.S. data. King and Watson (1997)searched over a wide range of identificationschemes and found little evidence againstlong-run neutrality. Boschen and Mills(1995), studying a larger system of vari-ables with cointegration techniques, butwithout the extensive robustness checking,also found little reason to doubt long-runneutrality. Bernanke and Mihov (1998a)argue that their model is consistent withlong-run neutrality using the postwar U.S.data; like King and Watson (1997), theyexplore the robustness of their findings toan extensive range of alternative identifica-tion schemes.

The studies that used data from morethan one country also found general supportfor the long-run monetary neutrality pro-position. For instance, Weber (1994),using techniques similar to those of Kingand Watson (1997), generally supportslong-run neutrality for the G7 economiesduring the postwar period across a widevariety of identification schemes, especiallywhen money is measured using broadermonetary aggregates. Weber’s results alsoconfirm the findings of King and Watson

19Coe and Nason also raiseimportant questions concerningthe statistical properties of theFisher and Seater long-horizonregression test.



73

(1997) and Boschen and Mills (1995) forthe postwar U.S. data. Serletis and Krause(1996) use the Backus and Kehoe (1992)data set for 10 industrialized countries,including the United States and Australia,covering more than a century. They foundgeneral support for long-run monetaryneutrality, even in the United States andAustralia, where Fisher and Seater (1993)—for the United States—and Olekalns(1996)—for Australia—had cast doubt. In a more extensive study, Serletis andKoustas (1998), use the same data set and apply the King and Watson (1997)technology of searching over plausibleidentification schemes. Here, wide supportfor long-run monetary neutrality is foundacross industrialized countries and plausibleidentification schemes, even though the dataset is a very long-time series of the type thatsometimes displayed evidence against long-run monetary neutrality in previous studies.

Long-Run Monetary Superneutrality. Thissurvey has also shown that the evidence infavor of long-run monetary superneutralityis far more mixed. This is perhaps not toosurprising since, as was stressed in theintroduction, it is a relatively simple matterto write down neoclassical, market clearing,rational expectations theories in whichsuperneutrality does not hold. In addition,since inflation is generally regarded as adistortionary force in macroeconomic systems, we might reasonably expect realvariables to be altered in the face of perma-nent shocks to money growth and inflation.

Analyzing postwar U.S. data, King andWatson (1997) find that rejection of long-run monetary superneutrality with respectto real output is possible for a range ofidentification schemes they considerreasonable. Weber (1994) confirms thisresult using similar methodology acrossthe G7 economies during the postwarperiod. Bullard and Keating (1995) analyzedata from a number of countries worldwideduring the postwar period. They considerpermanent inflation shocks and the subse-quent reaction of the level of real output.The results generally support superneutrality,but Bullard and Keating note that in the

low inflation countries (such as the G7),point estimates tend to be positive and aresometimes statistically significant. Serletisand Koustas (1998) reject long-run mone-tary superneutrality for Italy over the lastcentury, in a bivariate system with moneyand real output, over a range of identifyingrestrictions. Crosby and Otto (1998) gen-erally find that permanent inflation shockshave little or no permanent effect on thelevel of the capital stock in a large sampleof countries during the postwar period.When they do find statistically significanteffects, permanently higher inflation isassociated with a permanently higher cap-ital stock. In Rapach’s (1999a) study of atrivariate VAR using postwar data from 14 OECD countries, permanent inflationshocks generally were associated with per-manently higher levels of real output and,more strikingly, with permanently lowerreal interest rates. Ahmed and Rogers(1998), using methodology that departssomewhat from the other studies in thesurvey, consider a century of U.S. data andconclude that permanent inflation shockshave permanent, positive effects on impor-tant real variables, including output,consumption, and investment. They alsostress that these shocks do not explain a large portion of the forecast errorvariance in the data.

While the overall evidence on thesequestions is mixed, considering only lowerinflation countries leads to the conclusionthat permanently higher money growth orinflation is associated with permanentlyhigher output and permanently lower realinterest rates. As Ahmed and Rogers (1998)stress, this result is inconsistent with many—almost all?—current quantitative busi-ness cycle models, which generally predictthat permanently higher inflation perma-nently lowers consumption and output.There is little support for such a predictionin the studies surveyed here. This is animportant empirical puzzle that stands as a challenge for future research.

Related Propositions. We have also seenin this survey a smattering of evidence onother, related neutrality propositions.



74

King and Watson (1994, 1997) analyze theslope of a long-run Phillips curve in thepostwar U.S. data, and find that a verticalcurve is a reasonable approximation.Weber (1994) reports generally similarfindings for the G7 economies.

King and Watson (1997) also studyFisher relations between interest rates and inflation, and conclude that nominalinterest rates do not adjust one-for-onewith permanent inflation shocks under a wide range of plausible identificationschemes. Weber (1994) finds more mixedresults for the G7 economies, but evidencepresented by Rapach (1999a) and Koustasand Serletis (1999) is squarely on the side of less than one-for-one adjustment acrossindustrialized nations.

Bullard and Keating (1995) comment onthe effect of permanent inflation shocks onlong-run economic growth. Because growthrates are generally stationary according todiagnostic tests, and inflation rates oftenare not, the methodology of Fisher andSeater (1993) and King and Watson (1997)suggests that permanent inflation shockshave no permanent effect on economicgrowth. Ahmed and Rogers (1998) includea comment in a similar vein.20

Areas for Further Research. Canova (1994),commenting on Weber (1994), stressed thatthe nature of the methodology of Fisher andSeater (1993) and King and Watson (1997)—however correct it may be from a logicalpoint of view—places heavy reliance onthe existence of (and on the number of)unit roots in the time series being studied.Canova comments that these tests of neu-trality propositions depend in an importantway on getting the inference on the unitroot correct, and yet, tests for unit rootsare known to have low power. Most authors,including Weber (1994), are well aware ofthis issue, and many use a battery of testsfor a unit root in a series or other measuresin an effort to be conservative about theirconclusions in this regard. But Canova(1994, p. 121) notes, nevertheless, that this procedure “... conditions the results of economic hypotheses on shakystatistical ground. ...”

One problem is in the nature of theunit-root diagnostic tests. Since time seriescharacterized by a unit root have such dif-ferent properties from stationary time series,the researcher is forced into a declarationof a unit root or not. Once this declarationis made, the researcher can proceed withfurther analysis. This brings to mind apossible role for fractional integration intesting neutrality propositions. In fact, thispossibility has been explored recently in astudy by Bae and Jensen (1998). More workin this area may be fruitful in the future.

Canova (1994) also comments thatWeber’s (1994) results are based on bivariateVAR systems, as are many others reportedhere. He worries that the results may notbe the same when larger systems areexplored. Some papers surveyed here havetaken steps in that direction, includingBoschen and Mills (1995), Ahmed andRogers (1998), Rapach (1999a), andBernanke and Mihov (1998a). Thesestudies generally have supported resultsfrom the bivariate VARs. However, muchmore could be done in multivariate systemsthan has been completed to date.

Even without turning to multivariatesystems, one notes that much of the worksurveyed has focused on real output, andthat less work has been done on the long-run bivariate relationship between money orinflation and other important real variables.One exception is Crosby and Otto (1999),who take a step in this direction, using thecapital stock instead of real output as theirprimary real variable.21 A good deal morecould be done by simply investigating thelong-run bivariate relationships more system-atically for variables other than real output.

All of the analyses surveyed considerone country at a time when testing neutralitypropositions. One would like to know if apanel approach, implemented for a groupof similar countries like the G7, wouldproduce results similar to the ones reportedin the studies surveyed here, or if importantinteractions between the countries are beingleft out. A simpler line would be to studymultivariate systems for a single countrythat attempt to account for cross-bordereffects by including an international

20This idea is also related to workby Jones (1995).

21For another exception seeRapach (1999b).



75

variable. This would seem to be particularlyimportant for some smaller, open economiessometimes included in these studies.22

While problems certainly remain, itseems that the 1990s have been quite fruit-ful in this area of empirical macroeco-nomics. Tests of neutrality propositions notsubject to the critique of Lucas (1972) andSargent (1971)—tests that have eludedeconomists during much of the postwarera—have been devised and executed for avariety of times and places. This body ofwork gives us economists what is perhapsour first glimpse at the evidence on long-runmonetary neutrality and superneutrality, andallows assessment of the merits of these pro-positions separate from the logical force oftheoretical arguments.

REFERENCESAhmed, Shaghil, and John H. Rogers. “Long-Term Evidence on the Tobin

and Fisher Effects: A New Approach,” International Finance DiscussionPaper #566, Board of Governors of the Federal Reserve System(September 1996).

__________, and __________ . “Inflation and the GreatRatios: Long-Term Evidence From the U.S.,” International FinanceDiscussion Paper #628, Board of Governors of the Federal ReserveSystem (October 1998).

Andersen, Leonall, and Denis Karnovsky. “The Appropriate Time FrameFor Controlling Monetary Aggregates: The St. Louis Evidence,” inControlling Monetary Aggregates II: The Implementation, FederalReserve Bank of Boston, 1972.

Backus, David K., and Patrick J. Kehoe. “International Evidence on theHistorical Properties of Business Cycles,” American Economic Review(September 1992), pp. 864-88.

Bae, Sangkun, and Mark J. Jensen. “Long-Run Neutrality in a Long-Memory Model,” working paper, University of Missouri at Columbia(December 1998).

Barro, Robert J. “Inflation and Growth,” this Review (May/June 1996),pp. 153-69.

Bernanke, Ben S., and Ilian Mihov. “The Liquidity Effect and Long-RunNeutrality,” National Bureau of Economic Research Working Paper#6608 (June 1998a).

__________, and __________ . “Measuring Monetary Policy,”Quarterly Journal of Economics (August 1998b), pp. 869-902.

Blanchard, Olivier J., and Danny Quah. “The Dynamic Effects ofAggregate Demand and Supply Disturbances,” American EconomicReview (September 1989), pp. 655-73.

Boschen, John F., and Leonard O. Mills. “Tests of Long-Run NeutralityUsing Permanent Monetary and Real Shocks,” Journal of MonetaryEconomics (February 1995), pp. 25-44.

__________, and Christopher M. Otrok. “Long-Run Neutrality andSuperneutrality in an ARIMA Framework: Comment,” AmericanEconomic Review (December 1994), pp. 1470-73.

Bullard, James, and John W. Keating. “The Long-Run RelationshipBetween Inflation and Output in Postwar Economies,” Journal ofMonetary Economics (December 1995), pp. 477-96.

Canova, F. “Testing Long-Run Neutrality: Empirical Evidence For G7Countries With Special Emphasis on Germany,” Carnegie-RochesterConference Series on Public Policy (1994), pp. 119-25.

Coe, Patrick J., and James M. Nason. “Long-Run Monetary Neutrality inThree Samples: The United Kingdom, the United States, and theSmall,” manuscript, University of Calgary and University of BritishColumbia (May 1999).

Crosby, Mark, and Glen Otto. “Inflation and the Capital Stock,” Journalof Money, Credit, and Banking, forthcoming (1999).

Fischer, Stanley. “Why are Central Banks Pursuing Long-Run PriceStability?” in Achieving Price Stability, Federal Reserve Bank ofKansas City Symposium, 1996.

Fisher, Mark E. “The Time Series Implications of the Long-Run Neutralityand Superneutrality of Money,” Ph.D. Dissertation, University ofChicago (1988).

__________, and John J. Seater. “Neutralities of Money,” manuscript, Board of Governors of the Federal Reserve System and North Carolina State University (1989).

__________, and __________. “Long-Run Neutrality andSuperneutrality in an ARIMA Framework,” American Economic Review(June 1993), pp. 402-15.

Friedman, Milton, and Anna Schwartz. A Monetary History of the UnitedStates, 1867-1960, Princeton University Press, 1963.

__________, and __________. Monetary Trends in the UnitedStates and the United Kingdom, University of Chicago Press, 1982.

Geweke, John F. “The Superneutrality of Money in the United States: An Interpretation of the Evidence,” Econometrica (January 1986), pp. 1-21.

Haug, Alfred A., and Robert F. Lucas. “Long-Run Neutrality andSuperneutrality in an ARIMA Framework: Comment,” AmericanEconomic Review (September 1997), pp. 756-59.

Hoffman, Dennis L., and Robert H. Rasche. Aggregate Money DemandFunctions, Kluner Academic Publishers, 1996.

Jefferson, Philip N. “On the Neutrality of Inside and Outside Money,”Economica (November 1997), pp. 567-86.

Jones, Charles I. “Time Series Tests of Endogenous Growth Models,”Quarterly Journal of Economics (May 1995), pp. 495-525.

Kendrick, J. Productivity Trends in the United States, Princeton UniversityPress, 1961.

22Nason and Rogers (1999) usemethodology related to thatdiscussed in this survey tostudy investment and currentaccount dynamics for Canada.



76

King, Robert G., and Mark W. Watson. “Testing Long-Run Neutrality,”working paper #4156, National Bureau of Economic Research(September 1992).

__________, and __________. “The Postwar U.S. PhillipsCurve: A Revisionist Econometric History,” Carnegie-RochesterConference Series on Public Policy (1994), pp. 157-219.

__________, and __________. “Testing Long-Run Neutrality,”Federal Reserve Bank of Richmond Economic Quarterly(Summer 1997), pp. 69-101.

Kormendi, Roger C., and Phillp G. Meguire. “Cross-Regime Evidence ofMacroeconomic Rationality,” Journal of Political Economy (October1984), pp. 875-908.

Koustas, Zisimos. “Canadian Evidence on Long-Run NeutralityPropositions,” Journal of Macroeconomics (Spring 1998), pp. 397-411.

__________, and Apostolos Serletis. “On the Fisher Effect,”Journal of Monetary Economics (August 1999), pp. 105-30.

Lothian, James R. “Equilibrium Relationships Between Money and OtherEconomic Variables,” American Economic Review (September 1985),pp. 828-35.

Lucas, Robert E., Jr. “Econometric Testing of the Natural RateHypothesis,” in The Econometrics of Price Determination, Board ofGovernors of the Federal Reserve System, 1972.

__________. “Two Illustrations of the Quantity Theory of Money,”American Economic Review (December 1980), pp. 1005-14.

__________. “Nobel Lecture: Monetary Neutrality,” Journal ofPolitical Economy (August 1996), pp. 661-82.

Marty, Alvin L. “What is the Neutrality of Money?” Economics Letters(April 1994), pp. 407-09.

McCandless, George T., and Warren E. Weber. “Some Monetary Facts,”Federal Reserve Bank of Minneapolis Quarterly Review(Summer 1995), pp. 2-11.

Nason, James M., and John H. Rogers. “Investment and the CurrentAccount in the Short Run and the Long Run,” manuscript, University ofBritish Columbia (September 1999).

Nelson, Charles R., and Charles I. Plosser. “Trends and Random Walks inMacroeconomic Time Series: Some Evidence and Implications,”Journal of Monetary Economics (September 1982), pp. 139-62.

Olekalns, Nilss. “Some Further Evidence on the Long-Run Neutrality ofMoney,” Economics Letters (March 1996), pp. 393-98.

Orphanides, Athanasios, and Robert M. Solow. “Money, Inflation andGrowth,” in Handbook of Monetary Economics, North-Holland, 1990.

Rapach, David E. “International Evidence on the Long-RunSuperneutrality of Money,” Working Paper, Trinity College (1999a).

__________. “Monetary Shocks and Real Exchange RateHysteresis: Evidence From the G-7 Countries,” Review of InternationalEconomics, (April 1999b).

Sargent, Thomas J. “A Note on the ‘Accelerationist’ Controversy,”Journal of Money, Credit, and Banking (August 1971), pp. 721-25.

__________. “The End of Four Big Inflations,” in RationalExpectations and Inflation, Harper and Row, 1986.

Sbordone, Argia M., and Kenneth Kuttner. “Does Inflation ReduceProductivity?” Federal Reserve Bank of Chicago Economic Perspectives(November/December 1994), pp. 2-14.

Serletis, Apostolos, and Zisimos Koustas. “International Evidence on theNeutrality of Money,” Journal of Money, Credit, and Banking(February 1998), pp. 1-25.

__________, and David P. Krause. “Empirical Evidence on the Long-Run Neutrality Hypothesis Using Low-Frequency International Data,”Economics Letters (March 1996), 323-27.

Weber, A. “Testing Long-Run Neutrality: Empirical Evidence For G7Countries With Special Emphasis on Germany,” Carnegie-RochesterConference Series on Public Policy (1994), pp. 67-117.

Zivot, Eric, and Donald W. K. Andrews. “Further Evidence on the GreatCrash, the Oil Price Shock and the Unit Root Hypothesis,” Journal ofBusiness and Economic Statistics (July 1992), pp. 251-70.



77



78

Documents

Testing Long-Run Monetary Neutrality Propositions: Lessons from … · 2019-10-09 · FEDERALRESERVEBANKOFST.LOUIS 57 NOVEMBER/DECEMBER1999 1 Not all papers dealing with neu- trality