1

Robert H. Rasche

Robert H. Rasche is a professor ot economics atMichigan State University.

•I Monetary Aggregates, MonetaryPolicy and Economic Activity

LMOST A QUARTER century has passed sincethe publication of the (in)famous Andersen-Jordan(AJ) equation.’ For a good portion of that time, TedBalbach has been associated with the researchdepartment of the Federal Reserve Bank ofSt. Louis, and for a significant fraction of theperiod directed the research efforts of thatdepartment.~Throughout that period the Bankconsistently advocated a rnonetarist approach tomonetary analysis and monetary policy. It isappropriate at this point to look back and exam-ine what lasting influence this perspective hascontributed, both to analysis and to policymaking.

This stud has three parts. The first is a re-examination of what monetarism and the St. Louisempirical representation thereof contributed. Inparticular, what controversies of the late limOsand 1970s now can be considered settled? Thesecond examines the empirical failures of the AJequation in the 1980s and argues that thesefailures represent specification problems of the“Lucas variety” and not a rejection of the under-lying theoretical framework. The implication ofsuch a “Lucas effect” for prominent monetaristpolicy prescriptions is then analyzed- ‘The third

part examines the monetarist proposition thathas remained most controversial in recentyears, namely the short-run impact of changesin nominal money growth on real economicactivity. In particular, the analysis attempts toaddress the question raised by Cagan—why dovector autoregressions (VARs) produce infer-ences about the impact of money on economicactivity that contrasts dramatically with the con-clusions of historical analyses?~

ST. LOUIS ON THE ROLE OF MONEY

Two aspects of the AJ equation seemed partic-ularly controversial in the late 1960s. First, theanalysis focused on the relationship betweennominal measures of fiscal and monetary policyand nominal income. Second, the analysis focusedon growth rates or first differences. Reduced tosimplest terms, the analysis stated that the growthin velocity of narrow money, defined as the ratioof nominal GNP to a weighted moving averageof Mi, fluctuated around a positive deterministictrend and that some fraction of these fluctuationswere correlated with fluctuations in the growth

1See Andersen and Jordan 0968).2A precusor of the AJ equation can be found in Brunnerand Balbach (1959). Michael Belongia is responsible forbringing this well known article to my attention.

asee Cagan (1989).

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of nominal government spending.~This contrastssharply with macroeconometric models that weredeveloped contemporaneously. The implicit reducedforms of the latter models specified relationshipsbetween the leve/ of nominal money balances andthe leve/ of real output. ‘the models also endogenizedthe price level or inflation rate, but the typicalreduced forms implied little if any price levelresponse over the time periods in the AJ specifi-cation.

The lightning rod in the AJ equation was theconclusion that a maintained change in nominalgovernment spending, unaccompanied by changesin the nominal money stock did not produce apermanent change in nominal income (or velocity)and that changes in high employment nominaltax receipts produced no statistically significantchanges in nominal income (or velocity). Theseimplications, which dramatically refuted thefixed-price Keynesian model, did not go un-challenged. Numerous counter regressions werepublished which reported that the implied fiscalpolicy implications of the AJ equation were arti-facts of measurement error and/or sample specific.~The point that seems to get lost in the back-ground of these challenges is the robustness ofthe long-run response of nominal income growthto monetary growth shocks: the conclusion thatmonetary shocks, in the absence of fiscal shocks,have only transitory impacts on velocity growthheld its ground in the face of repeated regres-sion attacks”.°

In retrospect it appears that in tivo significantrespects the macroeconomics profession has largelysurrendered and accepted the perspective of theAJ equation. First, velocity has been rehabilitatedas a useful theoretical device acrossa broad rangeof macroeconomic thought. Monetarists havesteadfastly maintained the usefulness of thisconcept. Two of Greg Mankiw’s (1991) “dubiousKeynesian propositions” speak directly to thepoints raised in the AJ equation: Point No. 2—

“[T]he lessons of classical economics are not help-ful in understanding how the world works”; andPoint No. 4—EFliscal policy is a powerful tool foreconomic stabilization and monetary policy isnot very important.” Mankiw further asserts“for purposes of analyzing economic policy, a stu-dent would be better equipped with the quantitytheory of money (together with the expectationsaugmented Phillips curve) than with the Keynesiancross.” Some new Keynesians may repudiateMankiw, since this statement could be paraphrasedthat a student would be better equipped withthe AJ equation (together with the St. Louismodel) than with the Keynesian cross.7 Never-theless, a statement such as this (original or par-aphrase) was heresy 25 years ago, and it canonly be said of the St. Louis view of monetaryanalysis and monetary policy “you’ve come along way baby’s

Most of the attention that real-business cycletheorists give to money has focused on the rela-tionship between money and real output in theshort run. Proponents of this approach generallydismiss any causal effect from money to realoutput, arguing that correlations between changesin money and changes in real output reflect feed-backs from real output onto an endogenousmoney stock. This is not a denial of all signifi-cant parts of the St. Louis position. Plosser (1991),for example, argues that “money, without ques-tion, plays the dominant role in determining therate of inflation.” Presumably money then alsohas important impacts on the path of nominalincome, though real shocks are also importantfr’om this perspective. Real—business cycle spec-ifications have recently expanded to include in-flation and nominal variables. At least sonic ofthese expanded specifications incorporate atraditional demand-for-real-balances function,with point estimates of long-run income elastici-ties that are fairly close to unity.°Thus thesemodels do not reject the usefulness of velocity

~Thisinterpretation of the AJ equation was not widelyrecognized at the time of publication, I suspect in partbecause the original specification was published in firstdifferences rather that log differences and also becausethe specification was never was presented as a hypothesisabout velocity. The original presentation was intended as asequel to the Friedman-Meiselman debate. See Jordan (1986).

5See, for example, deLeeuw and Kalchbrenner (1969), Cor-rigan (1970) and Davis (1969).

6For example, Benjamin Friedman (1977) argued that theoriginal Andersen-Jordan conclusion with respect to fiscalpolicy was sample specific. However, the permanent effectof money growth on velocity is robust to his changes insample periods.

‘See Andersen and Carlson (1970) for a discussion of theSt. Louis model.

8That the St. Louis view is still contested in discussions ofpublic policy is evidenced by the report ot March 31, 1992,that 100 economists, including six Nobel Memorial Prizelaureates, sent in an open letter to President Bush, ChairmanGreenspan and members of Congress calling for additionalgovernment spending, lower interest rates and tax creditsfor business investment to stimulate economic growth(“Top Economists Urge Officials to Boost Federal Spending toStimulate Growth”, Wall Street Journal, March 31, 1992,p. A2).

°SeeKing, Plosser, Stock and Watson (1991).

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as a long-run concept relating money to nominalincome.

The second aspect of the evolution of macro-economic thought toward the AJ equation involvesthe modeling of shocks to velocity. The AJ equa-tion was consistently estimated in differencedform, and thus the implicit assumption of thespecification is that shocks to the level of veloc-ity are permanent. At the time this analysis wasconstructed, the discussion of the role of per-manent and transitory shocks that is so prominentin recent analyses was unforeseen. Nevertheless,there is vindication for the St. Louis modelingapproach in the now conventional wisdom thatmany macroeconomic time series (includingvelocity) appear to be “difference stationary”and that there are serious problems of “spuri-ous regressions” in estimations involving levelsof such data series.’0

The conclusion from this discussion is that fromcurrent theoretical and econometric perspectivesthere are important ways in which the originalSt. Louis analyses “got things right.” Nevertheless,the AJ equation has disappeared from contem-porary discussions of monetary policy.” Whythen the demise of the AJ equation?

THE DEMISE OF THE AJ EQUATION:

ANALYSIS AND SOME IMPLICA-

TIONS FOR MONETARIST POLICY

PRESCRIPTIONS

The demise of the AJ equation is well illus-trated in figure 1. Two different measures ofvelocity are plotted there. The first is the con-ventional ratio of nominal GNP to Ml. The sec-

ond is the ratio of nominal GNP to a geometricmoving average of Mi, where the weights inthe moving average approximate the weights inthe lag polynomial of the log of differences inmoney in the AJ equation.” It is clear that thevelocity measure implicit in the AJ equationreplicates the behavior of the traditional Mlvelocity quite closely, both before and after1980. Both measures have a strong positivedeterministic trend that ends in the early l9SOs.This trend was captured in the AJ equation bya significant positive intercept on the order of2.5 percent to 3.0 percent per year. With thebreak in the trend in velocity in the l9SOs, it isclear that the AJ equation falls apart.

In Rasche (1987) I showed that essentially allnarrowly defined monetary aggregate velocitiesin the United States exhibit similar breaks intheir deterministic treads in the early 1980s butthat once these breaks are considered, the timeseries properties of the. various velocities arenot substantially different in the 1980s com-pared with the earlier period (see figure 2).”Thus to understand the demise of the AJ equa-tion, it is crucial to understand the origins ofthe trend in velocity.

A considerable number and variety of expla-nations have been advanced for the change invelocity behavior observed in the 1980s, butmost of these are not consistent with the pat-terns observed in the data.” Monetarism in gen-eral, and the AJ equation in particular, is basedon the proposition that a stable long-run demandfunction for money exists; that is, the demandfor real balances depends on relatively few vari-ables, including real income, or wealth, andvarious rates of return on nonmoney assets.

‘°SeeNelson and Plosser (1982) and Granger and Newbold(1974).

“Relatively few attempts to reestimate the St. Louis equationhave occurred in recent years. Batten and Thornton (1983)extend the sample period through third quarter 1982.Belongia and Chalfant (1989) estimate regressions usingM1A, Ml and divisia variants of both those aggregates(including variables for relative energy prices and strikedummies, but excluding fiscal policy variables) over a firstquarter 1976—third quarter 1987 sample. With the exceptionof Divisia M1A they find money growth elasticities that aresignificantly less than 1.0. They conclude the following:“Results indicate that the Ml and broad aggregates areall associated with significant structural change in themoney-income relationship around 1981.Gavin and Dewald (1989) estimated St. Louis equations(again omitting fiscal policy variables) over second quarter1961—third quarter 1980 and first quarter 1971—fourth quarter1982 samples. They conclude from out-of-sample forecastingexperiments that “Ml has done so poorly in the 1980s

that it does worse on average than the monetary baseover the entire postwar period, even though it performedbetter than the base for the 30 years before 1980.’

12The weights are taken from Appendix Table 2 in Carlson0982) as .40, .40 and .20 on nM1, lnM1, and lnM12respectively.

“These conclusions are not altered by updated data. Overthe sample period first quarter 1948—fourth quarter 1981the mean change in velocity (St. Louis velocity) is 3.45(3.46) percent per year, and the standard deviation is 4.74(4.74) percent per year. The mean for the first quarter1982—third quarter 1990 is — .72 (-.72) percent per yearand the standard deviation is 6.04 (5.75) per cent per year.The mean change in the second sample is not significantlydifferent from zero (p = .49 (.46)]. In Rasche (1990) I con-cluded that the velocities of the broadly defined monetaryaggregates M2 and Ma showed little if any changes intrends at this time.

“See Rasche (1987).

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Figure 1Velocity Measures First Quarter 1948 through Third Quarter 1990Velocity

Figure 2Growth Rate of St. Louis Equation Velocity Measures First Quarter 1948 through ThirdQuarter 1990

1

1948 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 1990

Percent

1948 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 1990

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The theory relates the level of real balances de-manded to the level of specific variables. How-ever, the AJ equation, proposed as a reducedform of a model containing such a money-demand specification, is estimated in differenceform. Such statistical methodology is correct inthat it properly adjusts for the apparent non-stationarities of the observed data series. Unfor-tunately, differencing data series maintains onlyshort-run relationships among the various seriesand overlooks any long-run relationships thatmay exist simultaneously.

In the last decade, particularly in the past fiveyears, innovations in econometric technique allowfor the simultaneous treatment of nonstationarydata and estimation of long-run relationshipsamong the levels of variables.” These techniques,namely cointegration analyses, maintain thespirit of the reduced form approach in differ-ences of the data, but permit the analysis toincorporate the specification of long-run rela-tionships among the levels of the variables, ifsuch relationships exist. If identifying restric-tions are satisfied, such a relationship can beinterpreted as the long-run money demand func-tion that is fundamental to the AJ analysis.16

Some studies have documented the existenceof such a cointegrating relationship among realbalances, real income and nominal interest rates.’7

The implied long-run income elasticity of moneydemand in such estimated equations is not sig-nificantly different from unity; hence there is along-run stationary relationship between the levelof velocity and the level of nominal interest rates.

What then of the changes in the mean growthrate of velocity in the 1980s relative to the meangrowth rate in previous decades? If a stable long-run money demand equation that relates thelevel of velocity to the level of nominal interestrates exists and if the deterministic trend (drift)in nominal interest rates changes, then the driftin velocity must change correspondingly to ac-commodate the stable money demand specifica-tion. Hence a reduced form in differences of

velocity such as the AJ equation, given a stablemoney demand function, implies an unchangedconstant only as long as there are no significantchanges in interest rate trends. Since during thei980s there is a complete break from the upwardtrend of nominal rates of the previous two decades,the break in velocity drift is completely consis-tent with stability of the money demand function.

Although the velocity break of the 1980s doesnot invalidate the theoretical propositions on whichthe AJ equation is based, it suggests that somerethinking of traditional monetarist policy pre-scriptions is in order. What forces are likely togenerate breaks in interest rate trends? A plau-sible candidate, and the one of most concern formonetary policy prescriptions, is inflation expec-tations. Assume that there is an established initialregime in which expected inflation has a positivetrend. Assume that the monetary authoritiestake successful actions to stabilize the inflationrate and that this regime change is reflected inthe expectation of future inflation at some con-stant rate.’8 The likely outcome of such a policyshift is that the drift in nominal interest rateswill disappear as will the drift in velocity.”

This suggests that the time series propertiesof velocity and the constants in reduced formequations specified in differences are dependenton specific monetary policy regimes throughexpected inflation trends specific to the policyregimes. If true, this stands as one of the fewclear-cut examples of a “Lucas effect” beyondthe original Phillips curve example.’°

One of the consequences of such a “Lucaseffect” is that straightforward application of no-feedback monetary growth rules for narrowlydefined monetary aggregates can lead to out-comes different from those predicted or desired.2’A monetary authority that desires to stabilize aninflation that has been drifting upward mightbe inclined to set a monetary growth objectiveequal to a projected growth rate for naturaloutput plus a desired stabilized inflation rate,minus the historically observed drift in the

“See Granger (1981); Engle and Granger (1987); Johansen(1988 and 1991); and Phillips (1991).

“See Hoffman and Rasche (1991b).“See Hoffman and Rasche (1991a, 1991c and 1992).“Survey data and inflation forecasts for the United States

are consistent with such an interpretation of the outcomeof the 1981—82 recession.

‘9The break in velocity drift as a result of a break inexpected inflation is the hypothesis advanced by MiltonFriedman, though to the best of my knowledge he did not

elaborate the mechanism described here.20See Lucas (1976).2’ln Milton Friedman’s defense it must be noted that he

originally proposed a no feedback rule in terms of a morebroadly defined aggregate, old M2. An aggregate such asnew M2, in a regime without interest rate ceilings, is unlikelyto suffer from the problem discussed here. For some evi-dence on the stationarity of new M2 velocity over the post-Accord period, see Hailman, Porter and Small (1991).

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velocity of a narrowly defined monetary aggre-gate. If the authority maintains this moneygrowth rate after expected inflation has stabi-lized, under the above “Lucas effect” the driftin velocity will have disappeared and the actualsteady rate of inflation will prove to be lowerthan the planned inflation rate. During the tran-sition period to the steady inflation regime, thedrift in velocity will be slowing and hence thegrowth of nominal income will drop below theplanned inflation rate plus the projected gi-owthrate of natural output.2’ If the aim of the mone-tary authorities is to reduce, as well as to stabi-lize, inflation and if actual and expected inflationadjust to the change in monetary policy slowlyso that p > p~%vhile the drift in velocity is intransition, then real output growth will fallbelow q* for some time during the transitionperiod.23

Meltzer [19871 and McCallum [19881 proposealternatives to a fixed money (base) growth rulethat allow feedback from velocity to the plannedgrowth in money (base). The rules are designedto account for permanent shocks to velocity,but not to respond to transitory velocity shocks.The rules set the growth rate of the monetarybase equal to a desired growth of nominalincome (p* + q8 in the above notation) less amoving average of the drift in base velocity.”The rules establish base growth consistent withthe planned stable inflation once stabilization isachieved, and the rules also adjust base growthto compensate for the declining velocity driftduring the transition period to the stabilizedinflation rate. Thus on the surface it appearsthat these feedback rules immunize monetarypolicy from the adverse consequences of the“Lucas effect” on velocity drift.

However, this conclusion depends critically onthe credibility of the monetary authority. As longas private agents believe that the monetary au-

thority is following the feedback rule consistently,inflation expectations should adjust either in antic-ipation of or with the observation over time of fall-ing inflation. The feedback mechanism will adjustbase growth as desired. Both the Meltzer and McCal-lum rules are deterministic. In practice, stochasticfluctuations around such deterministic rules will beobser-ved which may make diiect verification of therule difficult. If the monetary authority lacks credi-bility, feedback rules such as these could proveunstable. Suppose the rule is implemented by themonetary authority and inflation and inflationexpectations begin to stabilize. This lowers the driftin velocity, and the feedback rule calls forbase growth to be adjusted upward (see figure 3).The McCallum rule, which ultimately restoresnominal income to the specified path of nominalpotential income, requires that base growth andnominal income growth overshoot equilibriumbase growth during the transition period (seefigures 3 and 4). If private agents do not under-stand the rule well, or if the increase in baseand nominal income growth is interpreted bysuch agents as an abandonment of the rule,then inflation expectations could start adjustingupward. This would change the drift of veloc-ity, and the rule would then call for reductionsin base growth. It is not difficult to conceive ofa situation where the monetary authority lackscredibility, in which the Meltzer-McCallum rulessuffer from instrument instability (Holbrook [19721)if the observed behavior of the monetary baseaffects inflation expectations, and through thisthe drift in base velocity.”

The conclusions from Ihese obseivations on thereduced form behavior of velocity is that con-stant growth rules applied to narrowly definedmonetary aggregates ar-c unlikely to be success-ful in stabilizing a nonzero inflation trend. Thesuccess of feedback rules that depend on observedvelocity behavior can depend critically on thecredibility of the monetary authority. In the

“Set m1 = p’ +q’ — v, where m, is the maintained growthrate of the nominal money stock. p~is the planned steadyinflation rate, q* is the projected growth rate of naturaloutput and v is the historically observed drift of velocity.Then during a transition period (p1 + q1) = (m, + v1) =

(p* + q’) + (v1 — v). When the drift in velocity starts toreact to the change in expected inflation, (v1 — v) C 0 so(p

1+ q,) < (p* + q’).— q*) = (p* — p1) + (v1 —v) <0.

“McCallum’s rule provides an additional adjustment to basegrowth as nominal output is observed to deviate fromnominal natural output.

“See Holbrook (1972). Consider, for example, a feedbackrule of the form: b1 = O(L)LV1 + LX1 + ~, where b, is the

growth rate of base velocity, X1 is other factors to whichthe feedback rule responds, and r~are random fluctuationsgenerated by fluctuations of sources of monetary base out-side the control of the monetary authorities and that can-not be perfectly forecasted. Let inflation expectationsrespond to observed base growth p?,., = 3(L)b1. Finally,let velocity growth respond to trends in inflation expecta-tions: v1 = w(L)pr+,. Substituting the latter two equationsinto the first equation gives (1 —6(L)8(L)w(L)L] b1 X1 +

Invertibility of the polynomial (1 —O(L)8(L)co(L)L], and hencethe absence of instrument instability depends upon theexpectation formation mechanism, 8(L).

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Figure 3McCallum Rule: Nominal Income Growth

Percent

DYF

0012 -

0.01 -

:1:0:1 ~ll I I I I

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97

Figure 4

McCalIum Rule: Base and Base Velocity Growth

Percent

0_ol —

0.0075 -

/1 __

0.005 — DVF

0.0025—

I

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97

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absence of credibility, the adjustments to thegrowth of the aggregate required by the feed-back rule can provoke adjustments to inflationexpectations that introduce instrument instabil-ity into the feedback rule.

CAN THE TRANSITORY RESPONSEOF REAL OUTPUT TO MAINTAINEDCHANGES IN MONEY GROWTHBE INFERRED FROM REDUCED-FORM MODELS?

The Role of Ident4’ying Restrictions

‘l’he focus of much of the r-ecent discussion ofthe role of money and monetary policy is noton the response of nominal income, but ratheron the response of real output. Cagan (1989)summarizes a large body of recent empiricalresearch and reaches the conclusion that “latelymonetary research has turned again -. - and newstudies claim that money has little or no effecton output and other real variables.” VARs figureprominently in recent research and are thesource of much of the evidence from which thenegative conclusions about the impact of nominalmoney changes on real output are drawn. Caganfaults the VAR approach as follows: “The VARseems ... to be hopelessly unreliable arid low inpower to detect monetary effects of the kindthat we are looking for and believe, from otherkinds of evidence, to exist.” I will argue herethat Cagan’s skepticism about the conclusions ofVAR analysis is justified, but for reasons beyondthose he enumerated.

The most important aspect of VAR analysis isthe one most frequently slighted in drawing con-clusions about policy shocks from such analyses.VARs are reduced forms of some unspecifiedeconomic model; as such they have commonroots with the AJ equation. Reduced forms, inthemselves, provide no information about theimpact of nominal money shocks, or any otherpolicy shocks of interest to economists. To pro-vide such information, VABs must be supplementedwith sufficient identifying restrictions, derivedfrom some economic model, to uniquely extractinformation about the impact of monetary shockson real output within the economic structuredefined by the identifying restrictions.

Sims (1986) clearly explains the critical role of

identifying restrictions in VAR analysis. Sims definesthe economic model as follows:

(1) >i A(s)Y(t— s) = ~ B(s)e(t —s); Var(e(t)) = C)

and the corresponding VAR (reduced-form)model for Y as follows:

(2) Y(t) = ~ C(s)Y(t - s) + u(t); Var(uW) =

Sims notes the following:

The most str-aightforward example of iden-tifying restrictions on A(0), B(0) and C) is theWold causal chain. According to this idea, C)should be diagonal, B(0) = I and AU)) shouldbe triangular and normalized to have onesdown the main diagonal when the variablesare ordered according to causal priority.Using the fact that with B(0) = I, E = A(O) C)AU))’, the triangularity of A(0) implies that,once we have put the variables in properorder, we can recover A(0) and C) from ~ as~‘s unique LDL decomposition. That is, it isknown that there is a unique way to expressa positive definite matrix > in the form LDL’,where L is lower triangular with ones downits diagonal and U is diagonal. Applying thestandard LDL algorithm to E gives us A(0) asL arid C) as U. This triangular orthogonaliza-tion has become a standard practice as part ofthe interpretation of econometric models(emphasis added) (p. 10).

Though this set of identifying restrictions hasbecome so common in VAR analysis that onlyr-arely is it acknowledged explicitly, it is neitherunique nor’ uncontroversial. Criticisms of andar-guments against both the appropriateness andnecessity of the causal-chain (triangular) specifi-cation are longstanding.” A simple example ofthe nonuniqueness of this approach is given bythe three separate sets of identifying restrictionsthat Sims applies to his six-variable VAR. All ofthese identification schemes maintain the assump-tion that C) is diagonal, but they impose differ-ent exclusion restrictions on AU)), includingrestrictions that do not impose a triangularstructure on AU)).

Recently, attention has turned to identificationby restrictions on the steady-state coefficient

“See Basmann (1963) and Leamer (1985).

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able agreement over a broad range of macro-economic theories on identifying restrictions

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the past 10 years researchers have broadly

demand function, to the extent that alleged

problematic and at worst fall into a class of

If identification of a short-run money demand

will at best represent linear combinations ofmoney-demand and money-supply shocks.

“See Sernanke (1986); Blanchard and Quah (1989); andKing, Plosser, Stock and Watson 0991).

“See Hoffman and Rasche 11991c] for an illustration of howthe restrictions on the KPSW (1991) common trends modelare consistent with the identifying restrictions for the steady-state of a standard textbook macroeconomic model.

Under these conditions it is impossible to sepa-rate the impact effects of money on outputfrom the reaction of money to output throughwhatever reaction function characterizes thebehavior of the monetary authorities.

The Importance of Spec{ficationand Identjfying Assumptions

The questions discussed previously ar-c partic-ularly important in the discussion of the effectof nominal money shocks on real output. Toillustrate this, consider a four-variable VAR, thatincludes real output, inflation, nominal money(Ml) and a short-term nominal interest rate(Treasury bill rate).’°The general conclusionthat has emerged from the study of such VARsis that “most of the dynamic inter’actions amongthe key variables can best be explained as ar-is-ing from an economic structure in which mone-tary phenomena do not affect real variables.Thus ... monetary instability has not played an

“See Laidler (1982 and 1985); Cooley and LeRoy (1981);Carr and Darby (1981); Judd and Scadding (1981); andGordon (1984). See also Sims (1980).

“These VARs are in the form of Sims (1980) and Littermanand Weiss (1985).

matrix, A = ~ A(s), rather than by restrictionson AU)).” ThI~°latterapproach seems morepromising because there appears to be consider-

that apply to a steady-state macroeconomicmodel.” In contrast, economic theory provides

economic specifications. In particular, during

debated the identification of a short-run money-

short-m’un money demand functions are at best

“incredible” identifying restrictions.”

function is “incredible,” then any “shocks”extracted from VARs under these restrictions

MARCH/APRIL 1993

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N N~7Ø,N NSYN/w ~tt <“tSyeflG~ j~aS~s% N

‘P4* N “‘ass”” 4j ~ S ~V ““434 ~6øt / N N

“~ cN~J~ ~ ~/~‘,N NNT~~ INN Iimportant role in generating fluctuations.”

Estimates of this four-variable VAR are shownin table I and table 2, for sample periods thatbegin in second quarter 1955 and end in fourthquarter 1981 and third quarter 1990, respec-tively. The starting point for both samples ischosen to avoid the pre-Accord data. The firstsample ends before the apparent break in thetrend of Ml velocity discussed previously. Thesecond sample includes the 1980s. The VAR issupplemented with three dummy variables cho-sen to define roughly four inflation regimeswith different trends.”

The implications of these VARs for the responseof real output to “money shocks” identified bythe Wold causal chain structure with variablesordered as real output, inflation, money andinterest rates are quite sensitive to the choice ofthe sample period (figure 3). Closer examinationreveals that this is associated with dramatically

different long-run responses of the nominalmoney stock to the “money shock” (figure 6).Both samples show the real output response tothe “money shock” rises to a peak and then trailsoff. However, the nominal interest rate exhibitsa transitory positive response to the “moneyshock” in both samples which is difficult toreconcile with the identification of the “moneyshock” as a monetary policy action (figure 7).33

Two other variables of interest are implicit inthe VAR menu: real money balances and veloc-ity. The impulse response function for velocityto a “money shock” is shown in figure 8. Theimplicit velocity response is almost uniformlynegative in both sample periods, and in thethird quarter 1990 sample has the peculiarcharacteristic of having a response below -1.0even after 40 periods.

The realization that the four-variable VAR

‘1See Litterman and Weiss (1985).

“The dummy variables are as follows: D67 = 1.0 for 67:4and subsequent observations; D79 = 1.0 for 79:3 andsubsequent observations; and D82 = 1.0 for first quarter1982 and subsequent observations.

“It is also difficult to reconcile the “interest rate shock”

identified by the Wold causal chain specification with amonetary policy action because although the immediateimpact of such a shock on interest rates is positive, thepermanent effects of this shock on nominal rates, inflation,money and real output are all negative in both sampleperiods.

FEDERAL RESERVE BANK OF ST. LOUIS

Figure 6Nominal Money iii to Nominal Money Shock2.75-

2.5-

2.25-

2-

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1—

— 081

- - - 090

I II I II I II I II I II I II I II I II I II I II I II I II I II024681012141618202224262830323436 39

11

Figure 5Real Output irt to Nominal Money Shock

0.9-

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0 2 4 6 81012141618202224262830323436 39

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Figure 7Inflation iii to Nominal Money Shock

Figure 8Velocity iii to Money Growth Shock0i36—

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I I II I II I II I II I II I II I II I II I II I II I II I II I II024681012141618202224262830323436 39

FEDERAL RESERVE BANK OF ST. LOUIS

13

NN N N’ “N NN N

N ,, •~ ~‘N, ,,\N N —~ “, ‘N N N’,

N “‘~kiiwa~ N / NN N ‘N I N, N~ N “NN lift iumtlkàlUh a ~Sma*ow*t N N N N N

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N LSt~4Vfl*” ~~“‘N //S W~’ £4””’ NNN it as

N /N NN / NN /N/ ;NNK N I,’ N N NN “

N N’~ ~—1t~,M~ ~~N5 ~ N * N~t ~ N,~ Nfl*N NN N /‘ N / N ~‘ N”N U t4mfl~NtNfltS

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defines additional interesting economic meas-

Clearly if the degree of diffem-encing of the vari-ables in the VAR were the same, the OLS esti-mates would produce the same results regardlessof the particular linear combinations explicitlychosen. l’Iowever, the degree of differencingvaries among the variables in the typical VARstudy as log levels of real output and nominalmoney appear along with log differences of theprice level (inflation). An alternative menu is toenter real balances along with either inflation ornominal money growth. The advantage of thesechoices is that the three variables that are tradi-tionally included in money-demand specifications—’real balances, real output and nominal interestm’ates—now explicitly appear in the VAR.’4

In table 3, some results are reported from the

estimation of a VAR with real output, inflation,real money balances and the Treasum’y bill i-ate.These results indicate the tests for’ stationarylinear combinations (cointegrating vector-s)among the four variables using the Johansenmaximum likelihood estimator under the restric-tion that the log of real balances and the log ofreal output enter’ any such coinlegrating vectorswith equal and opposite signs.” Both of the like-lihood ratio tests—the trace test and the maximumeigenvalue test—typically reject the hypothesisof one or fewer cointegrating vectors at the Spercent level, and in some samples at the 1 per-cent level. In every case the tests fail to rejectthe hypothesis that two or fewer cointegratingvectors exist. Thus we conclude that amongthese four variables there are two permanentand two transitory shocks.

To obtain a unique (to a scalar multiple) eco-nomic interpretation of the two cointegrating

‘4Such a VAR is an expanded version of the VAR used byHoffman and Rasche 11992] to investigate long-run moneydemand.

“See Johansen (1988 and 1991). This restriction was im-posed because it was never rejected in the three variable

menus investigated by Hoffman and Rasche (1992) andbecause in that study the unrestricted long-run incomeand interest elasticities were found to be quite impreciseand sensitive to the choice of the sample period.

ures as linear combinations of the menu entriesraises the following question: Are the resultsinvariant to the explicit choice of menu entries?

MARCH/APRIL 1993

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,NN, /N’ ,N K /~ N N N’ N I ~N’’’” N NN ‘ / N ,N

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N, ‘N”” N NN” //NK”~ “N’ ““a ~‘N’,, N,N/NKN,NK ‘,,“NNK ,N ‘N/””’~N “’~,~~‘N /

vectors present among these four variables,identifying restrictions must be imposed on theestimated matrix of cointegration vectors.” Inthis case the exclusion of one variable fromeach cointegrating vector is sufficient to achieveidentification. The exclusion restrictions intro-duced here eliminate the inflation rate from onecointegrating vector and real balances from theother. The resulting identified cointegrating vec-tors, normalized for real balances and inflationrespectively, are reported as fl~in table 3. Theremaining unconstrained coefficients in thesematrices are quite stable across sample periods.The estimated interest rate coefficient in thecointegrating vector with real balances is closeto the estimate that Hoffman and Rasche ob-tained for the long-run interest semielasticity ofmoney demand in the United States.’7 The esti-mated interest rate coefficient in the cointegrat-ing vector with the inflation rate ranges from-0.9 to -0.7 and is not significantly different from-1.0 consistent with a long-run Fisher effect,which implies a stationary real interest rate.”

The difficulty in interpreting results from thisspecification of the VAR is that nominal moneyor its growth rate does not appear explicitlyamong the variables in the VAR. An alternativespecification is to replace the inflation rate withthe growth rate of nominal money and allowthe inflation rate to be determined implicitly bythe identity relating nominal money growth andreal balances to inflation. Some results from theestimation of this VAR are presented in table 4using the same sample periods as in table 1 andtable 2. These results are basically the same asthose in table 3. The Johansen likelihood ratiotests again reject the hypotheses that one orfewer cointegrating vectors exist. When theidentifying exclusion restrictions and normaliza-tion are applied to the two estimated cointegrat-ing vectors (fl’,), the interest semielasticity in thevelocity vector is approximately 0.11 and theinterest coefficient in the vector error with themoney growth rate is between -0.8 and -0.9.The latter estimates are not significantly differ-ent from -1.0 on the basis of a Wald test.”

“See Hoffman and Rasche (1991c).

“See Hoffman and Rasche (1992).

“Significance is examined using Wald tests developed byJohansen (1991). Stock and Watson (1991) also report evi-dence for a stationary real interest rate.

“See Johansen (1991).

FEDERAL RESERVE BANK OF ST. LOUIS

15

N N’ NNNNNN “N N~NN,NNN NNN’~N ~N N’3C’ N/ ,N ‘ NN ~>NN~ /N N JN”” N” N”~~/~ N”’ N N” N NN NN N N N

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~ ~ N

/ ‘N N ‘~‘ ‘~ “‘ / ~“ N’ N ‘‘‘ ‘“’, ‘~ ‘ ‘‘N NN /,N’ N> /N’,’ / N N“N N” / /“NN N ~ N N N N N

N N “ NN N NNN N “ N’ N

The vector error cormection model (VECM) intable 4 can be reestimated with the ovem’ident-ifying restriction J3~{,4, -1.0 imposed. The con-strained estimates of J3~are obtained using thetwo-step estimator’ in Rothenberg and theasymptotic covariance matrix for !3~derived byJohansen.~°The restricted estimates of ji’ aregiven at the bottom of table 4. These estimatesare used to construct two linear combinationsof the levels of the four different variables toobtain estimates of the remaining parameters ofthe restricted VECM. The estimated coefficientsof the restricted VECM are shown in table S forthe ll/19.$5—lll/1990 sample.~’

The interesting question that these resultsraise is: Can the two permanent shocks amongthese four’ variables be associated with individ-

ual variables? Or in the terminology of King,Plosser, Stock and Watson (KPSW) (1991): Canwe derive a structural model from the reduced-form model with steady-state character-istics suggested by economic theory? ‘The interest-ing hypotheses to test are as follows:

• One permanent shock corresponds to areal-output (productivity) shock as sug-gested by real—business cycle theories; and

• The second permanent shock correspondsto a money growth—inflation—nominal inter-est rate shock consistent with a broad spec-trum of macroeconomic theories.

The common-trends modeling approach ofKPSW identifies the permanent components ofeach time series by restricting them to be ran-dom walks. A common-trends model exists if

4cRothenberg (1973) proves that his two-step estimator is arestricted maximum likelihood estimator when the unres-tricted estimator is asymptoticly normal and coverges atrate T’½.Johansen (1991) shows that his estimator of fi’is asymptotic normal, but converges at rate T’’. The max-imum likelihood properties of the restricted estimator havenot been established for this case.

41The dummy variables are not important for the estimationof the cointegrating vector (CIV) involving real balances.The separation of the shift in the constant of the VECMinto components representing shifts in the deterministictrend and shifts in the mean of this cointegrating vector

indicates that the mean of the CIV is little changed in the80s compared with the previous 25 years. (See Yoshidaand Rasche [1990].) The dummy variables are importantfor the estimation of the second (real interest rate) coin-tegrating vector. They suggest a large increase in themean real interest rate during fourth quarter 1979—fourthquarter 1981 followed by a substantial, though not fully off-setting reduction in the mean real rate after 1981. This isconsistent with the work of Clarida and Friedman (1984),Huizinga and Mishkin (1986) and Roley (1986) all of whomfound shifts in the relationship of nominal rates and infla-tion in 1979 and 1962.

MARCH/APRIL 1993

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the permanent components of each time seriesare equal to linear combinations of the orthogonalpermanent shocks that are suggested by eco-nomic theory. In the case under considerationhere, the existence of the hypothesized common-trends model requires that the permanent com-ponents of real output and money growth areequal to the two permanent shocks and henceare orthogonal. These correlations are 0.047and -0.065 for the samples ending in fourthquarter’ 1981 and thim-d quarter 1990, respec-tively. The extent that the pernianent compo-nents of real output and money growth violatethe necessary conditions for the existence of acommon-trends model can be judged by thesize of the off-diagonal element of the fl matrixas defined by KPSW.42 In the sample endingfourth quarter 1981 the estimated restrictedVECM implies that fl,, — 0.107 and in the sam-ple ending third quarter 1990 the estimated res-tricted VECM implies that fl,, = -0.007 underthe identifying restrictions that the permanentcomponents ar-c random walks. Because theabsolute values of these estimates are both closeto zero, we conclude that the data are consis-tent with a common-trends representation withindependent, permanent real-output and perma-nent money-growth shocks.

KPSW (1991) show how impulse responsefunctions are constructed for permanent shocksin such a common-trends mnodel. Graphs ofthese impulse response functions ar’e shown infigures 5—18. ‘I’he long-run properties of theseimpulse r-esponse functions are completelydetermined by the cointegrating vectors and thenear orthogonality of the permanent compo-nents of real output and money growth. Thelong-run responses of velocity, inflation, moneygrotvth and nominal interest rates (figures 14,16, 17 and 18) to a permanent shock to realoutput are all identically equal to zero. This fol-lows from the orthogonalization of the commontrends when real output is ordered beforemoney growth. The long-run responses of realoutput to a pernianent nioney growth shock arenot idenlically zero (figure TO), reflecting thesmall correlations between the permanent com-ponents of real output and money growth. Thelong-run responses of inflation and nominalinterest rates to a permanent money-growth

shock (figures 11 and 13) are identically equalto 1.0 as determined by the values of the esti-mated coefficients in the cointegrating vectors.In the long run, the level of velocity is increasedslightly by the permanent increase in moneygrowth in response to the permanently highervalue of nonminal rates (figure 8). The long-runresponses are consistent with the steady-stateproperties of most macroeconomnic models, butthis is not “news” once the elements of the coin-tegrating vectors have been estimated.

Additional interesting information can be foundin these figures. Estimates for both samples sug-gest that the transitory responses to either per-manent shock die out after two to three years.‘fhese implied lags in the adjustment to thesteady state seem quite short relative to muchof the conventional wisdom, though the lengthof the transitory reaction of velocity to a perma-nent money-growth shock is surprisingly similarto that in the AJ equation.

The reactions to a real-output shock are notexactly those implied by a pure m’eal—husinesscycle model because output effects from thistype of shock build only gradually (figure 15),during which period there are highly seriallycor’related negative impacts on the inflation rate(figure 16). The l’eal output response hereis quite similar to the output response to abalanced-growth” shock obtained by KPSW in

their six-variable restricted VAR model (figure6).~’There is a transitory money-gr’owthresponse (figure 17) associated with the outputshock, but because the money measure here,Ml, includes inside money, this response is con-sistent with the pictur-e drawn by some real—business cycle theorists.”

At first glance, it appears that the variancedecomposition of real output in this model isconsistent with the conclusion that “monetaryinstability has not played an important role ingenerating fluctuations.”~’The variance decom-position of real output from the fourth quarter1981 sample indicates that the permanentmoney-growth” shock accounts for’ about 23

percent of the variance of real output at all fore-cast horizons. In contrast, the permanent real-output” shock accounts for only 7 percent ofthe variance of real output at a one-period hori-

425ee King, Plosser, Stock and Watson (1991).4’See King, Plosser, Stock and Watson (1991).445ee Plosser (1991).455ee Litterman and Weiss (1985).

FEDERAL RESERVE BANK OF ST. LOUIS

17

Figure 9T-bill Rate irf to Nominal Money Shock

Figure 10Real Output hf to Money Growth Shock

— 081

090

024681012141618202224262830323436 39

0.12

0.1 —

0M8—

0.06—

0.04—

0.02—+

‘F

-0.02 Ill 1111111111 liii 11111111 I I I liii I II I I I I I024681012141618202224262830323436 39

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Figure 11Inflation u-f to Money Growth Shock

Figure 12

12.5

024681012141618202224262830323436 39

Money Growth hi to Money Growth Shock

FEDERAL RESERVE BANK OF ST. LOUIS

19

Figure 13T-bilI Rate iii to Money Growth Shock

Figure 14Velocity iii to Real Output Shock

024681012141618202224262830323436 39

0246 81012141618202224262830323436 39

MARCH/APRIL 1993

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Figure 15Real Output it-f to Real Output Shock

— Q81Y

Q90v

Figure 16Inflation in to Real Output Shock

20—

0

I 1111111111111111 1111111 11111111 1111 1111024681012141618202224262830323436 39

1.12—

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024681012141618202224252830323436 39

-20-

-40—

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I

— INF81Y

INF9OY

-100-

-120

FEDERAL RESERVE BANK OF ST. LOUIS

21

Figure 17Money Growth h-f to Real Output Shock

70—e

60—

50—— MG81Y

40—- - - - - MG9OY

30— /20—

10—

0— .. .— --

S. -

-10—

-20— I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

024681012141618202224262830323436 39

Figure 18T-bill Rate it-f to Real Output Shock

8—

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zon but increases to 66 percent of the varianceat a 12-period horizon. When the sample isextended through third quarter 1990, the per-manent “money-growth” shock accounts foronly 7 percent of the forecast variance at a one-quarter horizon, and this declines steadily toone percent of the forecast variance at a12-quarter horizon. In this sample the perma-nent “real output” shock accounts for 31 per-cent of the forecast variance of real output at aone-quarter horizon, and this increases steadilyto 87 percent of the variance at a 12-quarterhorizon. From this information and the impulseresponse functions in figure 10, it is tempting toconclude that monetary shocks have little short-run effect on real output.

The variatice decomposition of each cointegrat-ing vector’ can also be computed. At a one-quarter horizon 6 (32) percent of the varianceof real balances around equilibrium real bal-ances is attributable to the permanent “money-growth” shock, 27 (24) percent is attributable tothe permanent “real-output” shock, and 67 (44)pemcent is attributable to the two transitoryshocks. At a 12-quarter horizon the corr’espond-ing decomposition is 4 (21) percent and 71 (48)percent. At a one-quarter horizon the cor-responding decomposition of the variance of thereal interest rate around the equilibrium realinterest rate is 41(3) percent, 1 (1) percent and58 (96) percent. At a 12-quarter horizon thedecomposition is 24 (10) percent, 20 (27) percentand 56 (63) percent. ‘These decompositions arebased on the third quarter 1990 (fourth quarter1981) sample estimates.

It is also possible to allocate the deviation ofactual real balances from equilibrium real bal-ances (or the actual real rate from the equilibriumreal rate) at any point in the sample period tothe history of the permanent and i-cal shocks.Following KPSW (1991) write X, —fit + Ar, +where rj is a vector of “structural” disturbances.”Let fl~be the matrix of cointegrating vectors.Then 13’,.X, measures the deviations of actual realbalances from equilibrium real balances and theactual real rate from the equilibrium real rate.But fl~X,= fl~1it+ j3~A-r, + p’r~(L)~,=because /3~is orthogonal to M and A.

The fallacy of concluding that monetary insta-bility is not important for economic fluctuationsfromn this system under this class of restrictions

involves the interpretation of the “tnoney-growth”shock (figum-e 12). Ultimately this shock becomesa maintained change in the growth of nominalmoney. However this is not the case initially.For the first two to three years, the moneygrowth response to the permanent “money-growth” shock contains a large transitory com-ponent and the net effect is frequently of theopposite sign to the permnanent effect. Thisresponse pattern certainly does not conform tothe traditional monetarist policy experiment. Inthe latter case, the policy intervention involves ashift from one maintained growth rate of money(or the monetary base) to a different maintainedmonetary growth rate. Under these conditionsthe traditional monetarist hypothesis is that theinitial impact of the policy intervention willlargely affect real output, but that over timethis effect will disappear as the inflation rateapproaches its new steady-state rate.47

The only identifying characteristic of a mone-tary shock in this analysis is the steady-staterestriction that the impulse response of moneygrowth to such a shock is one. However, thisrestriction does not define a unique monetaryshock, but rather a whole class of such shocks.This is clear from the impulse responses ofmoney growth to the two “transitory shocks”that are plotted in figures 19 and 20. By con-struction, in both samples the steady-stateresponse of money growth (and all other- varia-bles defined by the VAR) is zero. Thus it is pos-sible to define the class of monetary shocksequal to the permanent “monetary shock” plusany weighted sum of the two transitory shocksand satisfy the identifying restriction for amonetary shock. Within this class of monetaryshocks it is impossible to determine the short-run impact of monetary policy on real output.For example, consider- defining the response ofreal output as the sum of the responses to thepermanent “money-growth” shock and the twotmansitory shocks. Such a composite shock hasthe identical steady-state response as the perma-nent “money-growth” shock and so satisfies theidentifying restrictions for’ a permanent mone-tary intervention imposed by our model. Yet ona one-quarter forecasting horizon such a com-posite shock accounts for 69 (93) percent of thevariance in real output for the sample periodending third quarter 1990 (fourth quarter 1981). Ona 12-quarter- horizon the fraction of the forecast

“See Appendix B.47See Friedman (1974) and Andersen and Carlson (1970).

FEDERAL RESERVE BANK OF ST. LOUIS

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Figure 19Money Growth iif to Transitory Output Shock

1—

0.8-

0.6-

0.4-

0.2 -

111111111111111111111111111111111111111102468101214161820222426283032343639

Figure 20Money Growth iif to Second Transitory Shock

1

0.5

0

-0.5

—1

-1.5

-2

-2.5

— MDOT81

- - --- MDOT9O

MARCH/APRIL 1993

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variance in real output attributable to such acomposite shock decreases to 13 (34) percentfor the sample period ending in third quarter1990 (fourth quarter 1981).

The fraction of the variance of deviations ofreal balances from equilibrium real balancesattributable to this composite shock is 73 (76)percent at a one-quarter horizon and 75 (66)percent at a 12-quarter horizon for the sampleperiod ending third quarter- 1990 (fourth quar-ter 1981). The fraction of the variance of devia-tions of the real interest rate attributable to thiscomposite shock is 99 (99) percent at a one-quarterhorizon and 80 (73) percent at a 12-quarter hori-zon for the sample periods ending third quarter1990 (fourth quarter 1981).

In contrast, the tnonetary intervention oftraditional monetarist analysis is not containedin the general class of monetary shocks definedas the permanent “monetary shock” plus aweighted sum of the transitory shocks. Considera regression of the following form:

(IMPMP — 1.0) = J3,IMPMTI + (J2IMPMT2 +

where 1MPMP~is the impulse response of moneygrowth to the permanent “money shock” andIMPMT1~and IMPM’F2~are the impulse responsesof money growth to the transitory shocks. Thetraditional monetarist policy experiment isdefined in the class of identified monetaryshocks if there are J3~sthat produce an esti-mated impulse response pattern that replicatesthe deviations of the impulse response functionto the permanent “money shock” from unity.This result does not hold for either sample period.For the sample ending fourth quarter 1981,

(IMPMP — 1.0) = —11.39(IMPMT11)--(— 10.56)

6.19 IMPMT2) +

H2= 0.81 SEE = 1.15(—9.28)

while for the sample period ending third quar-ter 1990,

(IMPMP — 1.0) = —9.06(IMPMT1~) —

(—4.31)0.94(IMPMT2) +

(—1.0)112 = 0.23 SEE = 2.47

The weighted-sum impulse response functionsfor money growth ar-c shown in figures 21 and22 for the two sample periods. Large transitorydeviations from unity remain in both cases.

The lack of identification of the short-run r’ealoutput response in the absence of a specificationof the monetary rule, or monetary policy reactionfunction, that prevails during the sample periodcan be shown easily using a simple macroeconomicmodel that satisfies all of the steady-state iden-tifying restrictions imposed on the VECM. Con-sider the following:

(1) lnP = ,_,lnP + y[lnQ, — lnQ~]+

(2) lnMR, = lnQ, — flu, +

(3) i, = r, + ,lnP~, — lnP,(4) lnQ, = k + InA, — or, +

where equation (1) is an expectations-augmentedPhillips curve (Lucas supply function) that relatesdeviations of real output (Q,) from natural out-put (Q) to inflation expectation errors (lnP, —

,lnP~.Equation (2) is a money-demand functionthat relates real money balances (MR,; InMR, =

lnM, — lnP,) to real output and nominal interestrates (i) with a unitary income elasticity ofmoney demand. Equation (3) defines nominalinterest rates as the sum of the real rate (r-,) andthe expected future rate of inflation (,lnP’~, —

lnP,). Equation (4) defines the demand for realoutput in terms of the real interest rate andautonomous planned expenditures (A,). Thismodel is closed by two additional specifications.First, we assume that expectations are gener-ated by adaptive expectations of inflation:”

(5) ,-,p~= ,,pç, + A(R, —

where p,=lnP,— lnp,_, and ~ =, lnP~,÷,— lnP,~

Second, a stochastic monetary rule (policyreaction function) is specified as follows:

(6) AInM, = p + #,Ai, + #2

(AInM,, — p) +

This rule allows for contemporaneous interestrate smoothing (#~>0)and for offsetting of pastdeviations from the steady-state money growth

“Adaptive expectations in the inflation rate are chosen asan algebraicly convenient way of generating a model thatpotentially has transitory real output responses to perma-nent nominal money growth shocks and has the steady-state characteristics of the estimated VECM. This is onlyfor illustration of the identification problem. In particular,the type of inflation expectation shift discussed in the sec-

tion beginning on p. 3 as the root cause of the shift invelocity drift is not consistent with an adaptive expecta-tions mechanism.

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Figure 21Weighted Sum of Permanent and Transitory iii

111111111 1111111 I II 11110246 81012141618202224262830323436 39

Figure 22Weighted Sum of Permanent and Transitory iii

4—

3—

2—

1—

0—

—l —

-2—

-3—

-4-

-5—

MGF81

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FEDERAL RESERVE BANK OF ST. LOUIS

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path (#~>0).Thus with appropriate parametervalues this specification can accommodate arange of central bank behavior from nominal—interest rate smoothing to a stochastic no-feedbackmoney growth regime. This model can bereduced to a four-variable VAR in ln(4, lnMR,, i,and AInM,, driven by the exogenous variableslnQ’, lnA, and the shocks &~,.

algebra, the moving averagethe model êan be expressed

lnq, — ylnQ +

(7) lnMR, [.i.oJ*~ E2

,

i, k + InA, +

AlnM, p(1+#,) +

where the polynomial matrix A* and the poly-nomial det are given in table 6. In the deter-ministic steady state, the impulse responsefunctions are independent of the parameters ofthe monetary rule (#,, ~,) and real outputresponds only to changes in lnqn, (1.0). Simi-larly in the deterministic steady-state AlnM,responds only to p (1.0). However, the transitoryresponses of real output to money-growth shocksare not zero. In particular, the greater is theinterest-rate smoothing (#,), the smaller are thetransitory responses of real output to monetaryshocks. Thus estimation of VARs in this type ofmodel will produce different impulse responsefunctions based on different behaviors of themonetary authorities, and it is not possible toinfer- from those impulse response functions theshort-run impact of a change in money growthunder’ a rio-feedback rule, without prior knowl-edge of the form and parameter values of thesample period monetary rule(s).

A recent analysis by Strongin (1991) is an attemptat defining a monetai-y policy disturbance. Hisidentifying restriction is that monetary policyshocks have exactly offsetting impacts on non-borrowed reserves and borrowed reserves andhence have no effect on total reserves. In con-trast he assumes that “reser-ve-demand” shocksin principle affect all three aggregates. Much ofStrongin’s discussion of historical Federal Reserveoperating procedures focuses on the likely dis-

tribution of reserve-demand shocks (his # para-meter) between nonborr’owed and borrowedreserves. The size of this parameter is not rele-vant to his identification problem, though it isimportant for estimation if the parameter valuediffers across subsamples.~°The identifying res-triction allows him to construct a measure ofmonetary policy shocks but does not addressthe structure of the monetary rule or policyreaction function. Strongin implicitly assumesthat there is no contemporaneous feedbackfrom interest rates onto his monetary-policyshock because both total and nonborrowedreserves precede the fed funds i-ate in his Woldcausal chain. Thus his identifying restriction doesnot address all of the problems raised here.

Unfortunately, inference about monetary regimes(policy reaction functions) using regi-ession tech-niques has proved illusory. Khoury (1990) reviews42 attempts at the estimation of reaction func-tions for the Fed over various sample periods.He concludes that “the results wet-c in disarray”and “the specification search showed that veryfew variables ivere robust in a reaction function

consistent with the lack of robustness in theliterature.” The additional attempts at developingreaction functions that are included in Mayerdo not overturn this conclusion.~°Thus it appearsappropriate to conclude that at present we lackadequate information to make infeiences fromtime series analyses on the vexing question ofthe short-i-un impact of nominal shocks on realoutput -

CONCLUSIONS

Significant elements of the St. Louis researchagenda ar-c now widely accepted, at least in U.S.academic circles and to some extent within theFederal Reserve System. Nevertheless, issues ofshort-run impacts of monetary policy remainunresolved. Among these are the following twocritical topics: 1) changes in the drift of velocityand the extent to which such changes ar-cgenerated by changes in inflation expectationsand 2) the short-run in pacts of nominal moneyshocks on i-cal output.

The first of these questions is critical to thedesign of monetary rules and/or operating pro-cedures that will retain credibility during the

“The exclusion of monetary policy disturbances from totalreserve shocks is analogous to identifying the supply functionby the exclusion of income in a classical demand/supplymodel.

50See Mayer (1990).

With some tediousrepresentation ofas follows:

MARCH/APRIL 1993

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transition to an alternative inflation regime. Thesecond question has longbeen debated and appearsto be i-c-emerging as a focus of time series anal-ysis. The analysis presented here suggests thatthe information necessary to pursue this agendasuccessfully is not yet available. One criticalprecondition to such analysis is a reasonablespecification of the monetary regime(s) duringthe sample period. In this respect, Cagan’s(1989) appeal for more “historical” researchwarrants careful consideration.

A potential application of such a historicalanalysis is a test of Strongin’s (1991) identifyingrestriction for monetary policy shocks. His res-triction provides an estimated time series forsuch shocks. We can infer from publishedRecords of Policy Actions of the FOMC the tim-ing and to some extent the magnitude of policyinterventions to change the fed funds rate and/orborrowed reserves targets.5’ If the identifyingrestriction is valid, time series estimates of themnonetary policy shocks should correlate wellwith the data extracted from these historicalrecords.

REFERENCES

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Andersen, Leonall C., and Jerry L. Jordan. “Monetary andFiscal Actions: A Test of their Relative Importance in EconomicStabilization,” this Review (November 1968), pp. 11—24.

Basmann, R.L. “The Causal Interpretation of Non-TriangularSystems of Economic Relations,” Econometrica (July 1963),pp. 439—48.

Batten, Dallas S., and Daniel L. Thornton. “Polynomial DistributedLags and the Estimation of the St. Louis Equation,” thisReview (April 1983), pp. 13—25.

Belongia, Michael T., and James A. Chalfant. “The ChangingEmpirical Definition of Money: Some Estimates From aModel of the Demand for Money Substitutes,” Journal ofPolitical Economy (April 1989), pp. 387—97.

Bernanke, Ben S. “Alternative Explanations of the Money-Income Correlation,” Carnegie-Rochester ConferenceSeries on Public Policy (Autumn 1986), pp. 49—99.

Blanchard, Olivier Jean, and Danny Ouah. “The DynamicEffect of Aggregate Demand and Supply Disturbances,”American Economic Review (September 1989), pp. 655—73.

Brunner, Karl, and Anatol B. Balbach. “An Evaluation of TwoTypes of Monetary Theories,” Proceedings of the Thirty-FourthAnnual Conference of the Western Economic Association,September 2—4, 1959 (Santa Barbara, California), pp. 78—84.

Brunner, Karl, and Meltzer, Allan H. The Federal Reserve’s Attach-ment to the Free Reserve Concept Subcommittee onDomestic Finance, U.S. House of Representatives, Com-mittee on Banking and Currency, May 7, 1964.

Cagan, Phillip. “Money-Income Causality—A Critical Reviewof the Literature Since A Monetary History,” in Michael D.Bordo, ed., Money, I-listonj, and International Finance:Essays in Honor of Anna J. Schwartz (Chicago: Universityof Chicago Press for the NBER, 1989).

Carlson, Keith M. “A Monetary Analysis of the Administration’sBudget and Economic Projections,” this Review (May 1982),pp. 3—14.

Carr, Jack, and Michael R. Darby. “The Role of Money SupplyShocks in the Short-Run Demand for Money,” Journal ofMonetary Economics (September 1981), pp. 183—99.

Clarida, Richard H., and Benjamin M. Friedman. “The Behaviorof U.S. Short-Term Interest Rates Since October, 1979,”Journal of Finance (July 1984), pp. 671 —82.

Cooley, Thomas F., and Stephen F. LeRoy. “Identificationand Estimation of Money Demand,” American EconomicReview (December 1981), pp. 825—44.

Corrigan, E. Gerald. “The Measurement and Importance ofFiscal Policy Changes,” Federal Reserve Bank of New YorkMonthly Review (June 1970), pp. 133—45.

Davis, Richard 6. “How Much Does Money Matter: A Look atSome Recent Evidence,” Federal Reserve Bank of New YorkMonthly Review (June 1969), pp. 119—31.

DeLeeuw, Frank, and John Kalchbrenner. “Monetary andFiscal Actions: A Test of Their Relative Importance in Eco-nomic Stabilization—Comment,” this Review (April 1969),pp. 6—lI.

Doan, Thomas A. User’s Manual RATS Version 3.10 (Evanston,IL: VAR Econometrics, 1990).

Engle, Robert F., and Clive W.J. Granger. “Cointegration andError Correction: Representation, Estimation and Testing,”Econometrica (March 1987), pp. 257—76.

Friedman, Benjamin M. “Even the St. Louis Model NowBelieves in Fiscal Policy,” Journal of Money, Credit andBanking (May 1977), pp. 365—67.

Friedman, Milton. “A Theoretical Framework for MonetaryAnalysis,” in Robert J. Gordon, ed., Milton Friedman’sMonetary Framework- A Debate With His Critics (Universityof Chicago Press, 1974).

Gavin, William T., and William 0. Dewald. “The Effect ofDisinflationary Policies on Monetary Velocity,” The CatoJournal (SpringlSummer 1989), pp. 149—64.

Gordon, Robert J. “The Short-Run Demand for Money: AReconsideration,” Journal of Money, Credit and Banking,Part 1 (November 1984), pp. 403—34.

Granger, Clive W.J. “Some Properties of Time Series Data andTheir Use in Econometric Model Specification,” Journal ofEconometrics (May 1981), pp. 121—30.

Granger, Clive W.J., and P. Newbold. “Spurious Regressionin Econometrics,” Journal of Econometrics (July 1974),pp. 111—20.

Hallman, Jeffrey J., Richard D. Porter, and David H. Small.‘Is the Price Level Tied to the M2 Monetary Aggregate inthe Long Run?” American Economic Review (September1991), pp. 841—58.

Hoffman, Dennis L., and Robert H. Rasche. “Long-RunIncome and Interest Elasticities of Money Demand in theUnited States,” Review of Economics and Statistics(November, 1991a), pp. 665—74.

- “The Demand for Money in the U.S. During theGreat Depression and Post War Period: Identifying theSource of Shifts in Velocity,” mimeo (1991b).

515ee Brunner and Meltzer (1964) and Rasche (1987).

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- “Identification and Inference in Cointegrated Systems:A Synthesis of Recent Developments,” mimeo (1991c).

“Money Demand in the U.S. and Japan: Analysis ofStability and the Importance of Transitory and PermanentShocks,” mimeo (1992).

Holbrook, Robert S. “Optimal Economic Policy and the Prob-lem of Instrument Instability,” American Economic Review(March 1972), pp. 56—65.

Huizinga, John, and Frederic S. Mishkin. “Monetary PolicyRegime Shifts and the Unusual Behavior of Real InterestRates,” Carnegie-Rochester Conference Series on PublicPolicy (Spring 1986), pp. 231—74.

Johansen, Soren. “Statistical Analysis of Cointegration Vectors,”Journal ofEconomic Dynamics and Control (June—September1988), pp. 231—54.

_______ “Estimation and Hypothesis Testing of CointegrationVectors in Gaussian Vector Autoregressive Models,”Econometrica (November 1991), pp. 1551—80.

Jordan, Jerry L. “The Andersen-Jordan Approach After Nearly20 Years,” this Review (October 1986), pp. 5—8.

Judd, John P., and John L. Scadding. “Liability Management,Bank Loans and Deposit ‘Market’ Disequilibrium,” FederalReserve Bank of San Francisco Economic Review (Summer1981), pp. 21—44.

King, Robert, Charles I. Plosser, James H. Stock, and Mark W.Watson. “Stochastic Trends and Economic Fluctuations,”American Economic Review (September 1991), pp. 819—40.

Khoury, Salwa S. “The Federal Reserve Reaction Function:A Specification Search,” in Thomas A. Meyer, ed., ThePolitical Economy of American Monetary Policy (New York:Cambridge University Press, 1990).

Laidler, David E.W. The Demand for Money: Theories, Evidenceand Problems (New York: Harper and Row, 1985).

_______- Monetarist Perspectives (Cambridge, Massachusetts:Harvard University Press, 1982).

Leamer, Edward E. “Vector Autoregressions for Causal Infer-ence?” Carnegie-Rochester Conference Series on PublicPolicy (Spring 1985), pp. 255—303.

Litterman, Robert B., and Laurence M. Weiss. “Money, RealInterest Rates, and Output: A Reinterpretation of PostwarU.S. Data,” Econometrica (January 1985), pp. 129—56.

Lucas, Robert E. Jr. “Econometric Policy Evaluation: A Critique,”Journal of Monetary Economics (Supplementary Series,Volume 1, 1976) pp. 19—46.

Mankiw, N.G. “The Reincarnation of Keynesian Economics,”NBER Working Paper 3885 (October 1991).

McCalIum, Bennett T. “Robustness Properties of a Rule forMonetary Policy,” Carnegie-Rochester Conference Serieson Public Policy (Autumn 1988), pp. 173—203.

Meltzer, Allan H. “Limits of Short-Run Stabilization Policy,”Economic Inquiry (January 1987), pp. 1—14.

Meyer, Thomas A. The Political Economy ofAmerican MonetaryPolicy (New York: Cambridge University Press, 1990).

Nelson, Charles R., and Charles I. Plosser, “Trends andRandom Walks in Macroeconomic Time Series: SomeEvidence and Implications,” Journal of Monetary Economics(September 1982), pp. 139—62.

Osterwald-Lenum, Michael. “Recalculated and Extended Tablesof the Asymptotic Distribution of Some Important MaximumLikelihood Cointegration Test Statistics,” Institute of Eco-nomics, University of Copenhagen, mimeo, (January 1990).

Phillips, P.C.B. “Optimal Inference in Cointegrated Systems,”Econometrica (March 1991), pp. 283—306.

Plosser, Charles I. “Money and Business Cycles: A Real

Business Cycle Interpretation,” in Michael T. Belongia,ed., Monetary Policy on the 75th Anniversary of the FederalReserve System (Boston: Kluwer Academic Publishers,1991), pp. 245—74.

Rasche, Robert H. “Mi-Velocity and Money-Demand Functions:Do Stable Relationships Exist?” Carnegie-Rochester Con-ference Series on Public Policy (Autumn 1987), pp. 9—88.

_______- “Demand Functions for Measures of U.S. Moneyand Debt,” in Peter Hooper et. al., eds., Financial Sectorsin Open Economies: EmpiricalAnalysis and Policy Issues(Washington: Board of Governors of the Federal ReserveSystem, 1990).

Roley, V. Vance. “The Response of Interest Rates to MoneyAnnouncements Under Alternative Operating Proceduresand Reserve Requirement Systems,” NBER Working Paper1812 (January 1986).

Rothenberg, Thomas J. Efficient Estimation With Apriori Infor-mation (New Haven: Yale University Press, 1974).

Sims, Christopher A. “Macroeconomics and Reality,”Econometrica (January 1980), pp. 1—48.

_______ “Are Forecasting Models Usable for Policy Analysis?”Federal Reserve Bank of Minneapolis Quarterly Review(Winter 1988), pp. 2—16.

Stock, James H., and Mark W. Watson. “A Simple Estimator ofCointegrating Vectors in Higher Order Integrated Systems,”mimeo (1991).

Strongin, Steven. “The Identification of Monetary Policy Dis-turbances: Explaining the Liquidity Puzzle,” FederalReserve Bank of Chicago Working Paper WP—91—24,(December 1991).

Yoshida, Tomoo, and Robert H. Rasche. “The M2 Demandin Japan: Shifted and Unstable?” Bank of Japan Monetaryand Economic Studies (September 1990), pp. 9—30.

Appendix ATechnical Descriptionof the Assumptions inthe Simulation of theMeCallum Rule

The initial regime (periods 1-19) in figures 3and 4 before the implementation of the McCallumrule are base velocity growth at t~ = .0075 perperiod. The monetary base is assumed to growat a rate that increases at tr = .0001563 perpetiod. Thus nominal income growth is increas-ing at a rate of tr = .0001563 per period. Therate of increase in nominal income growth isassumed to reflect the trend in inflation, whichin turn is assumed to reflect the trend in norni-nal interest rates. The trend in nominal interestrates and the trend in velocity must satisfy therestriction t~ —e,tr 0 where Cr 15 the interestsernielasticity of velocity if base velocity andinterest rates are cointegrated. er is assumed tobe 48, using the estimated semielasticity of Ml

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velocity from Hoffman and Rasche [1992]. Nominalincome and nominal potential income areassumed equal throughout this period.

The regime switch to the McCallum rule is an-nounced and implemented in period 20. The desiredgrowth rate of nominal income in the newregime is .0075 per period. It is assumed thatthe announcement of the new policy results in animmediate elimination of base velocity growth.

It should be noted that the path of nominalincome growth once the McCallum regime isimplemented is independent of the assumptionsabout growth in the prior regime. Nominal incomegrowth in the McCallum regime is totally deter-mined by the assumed growth of velocity start-ing 16 periods prior to the implementation ofthe rule, and the reaction of velocity growth tothe institution of the new regime. l’he particu-lar initial conditions for base growth used hereare chosen strictly for consistency with theassumed initial growth rate of base velocity.

Appendix BConfidence Intervals forImpulse ResponseFunctions

Estimates of the precision of the impulseresponse functions from the sample ending in90:3 were constructed from a Monte Carlointegration. The estimated coefficients and co-variance matrix of residuals from a VAR aug-mented by two error correction variables wereshocked using the algorithm described in Doan[1990], example 10.1. The elements of the coin-tegrating vectors were held constant at theirestimated values, since Johansen [1991], The-orem 5.5, proves that the estimated asymptoticcovariance matrix of 11 = & fi’ depends only onthe estimated asymptotic covariances of & andthe estimated j3 and_not on the estimated asymp-totic covariance of fi- 1000 replications on theparameter values were constructed and theparameters of the KPSW common trends modelwere recomputed for each replication. Themean value of KPSW’s critical 117 parameteracross all replications is -.0057 with a standarddeviation of .0371. These parameters were usedto derive impulse response functions. The meansof various impulse responses across the 1000

replications are plotted in Figures Al—AlO,together with confidence bands of ±1.96*(standard deviations of the impulse responsesacross replications). The graphs suggest that theshort-run responses of real output and velocity withrespect to both permanent shocks are measuredwith considerable precision, in particular that thereal output response to a permanent “moneygrowth” shock is initially significantly positiveand that the real output response of a perma-nent “ real output” shock is significantly lessthan 1.0 for about 10 quarters. In contrast, themeasurement of the short-run responses ofinflation, money growth, and interest rates toboth permanent shocks is highly imprecise.

Appendix CSources of DataAll data series were extracted from Citibase.The primary sources are as follows:

Treasury Bill Rate: Three month secondary marketrate. Federal Reserve Bulletin. Table 1.35, hne 15.

Seasonally adjusted monthly data.January 1947—December 1958 con-structed following Rasche (1987),Appendix A.January 1959—December 1989 Boardof Governors of the Federal ReserveSystem, Money Stock Revisions,March 1990, Table 1.January 1990—March 1990 FederalReserve Bulletin, July 1990, Table1.21, line 1.

April 1990—June 1990 FederalReserve Bulletin, October 1990, Table1.21, line 1.July 1990 Federal Reserve Bulletin,January 1991, Table 1.21, hne 1.August 1990 Federal Reserve Bulletin,February 1991, Table 1.21, line 1.

Seasonally adjusted quarterly data.January 1947—April 1987 Survey ofCurrent Business, July 1990January 1988—March 1990 EconomicReport of the President, February1991, Table B-i.

Real GNP: Seasonally adjusted quarterly data.January 1947—April 1987 Survey ofCurrent Business, July 1990

January 1988—March 1990 EconomicReport of the President, February1991, Table B-2.

Mi:

GNP:

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Appendix Figure 1Velocity iii to Money Growth Shock

0.12

0.11—

0_i —

0.09—

0.08—

0.07—

0.06—

Appendix Figure 2Real Output id to Money Growth Shock

0.021 —

0.018-

0.015-

0.012-

0.009—

0.006—

0.003—

0—

-0.003—

-0.006—

IIIIIIIIIIIIIIIIIIIIIIIFT1lIIIIIIIIIIIII024681012141618202224262830323436 39

4~~~4

4

If 1IIIII1IIIIIFI 111111 III I [11111 fIll fill

024681012141618202224262830323436 39

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Appendix Figure 3Inflation it-f to Money Growth Shock

17.5—

14—

105—

I II II I I I 1 I I I II II II II0 2 4 6 81012141618202224262830323436 39

Appendix Figure 4Money Growth it-f to Money Growth Shock

12

6

0~

-6

-12

-18

-24~

-30-

-36024681012141618202224262830323436 39

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Appendix Figure 5T-bill Rate irf to Money Growth Shock

I

- S.

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I —

024681012141618202224262830323436 39

4

3

2-

1

0

—1 —

-2

-3-

-4-

-5.

Appendix Figure 6Velocity it-f to Real Output Shock

0.24—

0.16—

0.08—

-0.08—

-0.16—

-0.24—

-0~32

0

S.,

I I I I I I I II I I [I1TJ I I I I I I II II II I I I I I I I I I I I0 2 46 81012141618202224262830323436 39

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Appendix Figure 7Real Output it-f to Real Output Shock

1.1—

1—S.,’...

OS —

0.8— / ..•“~

0j-

0.6-

0.5— 55

0.4— : 5S

0.3—’~111111111 I 1111 I I 1111111 I I III I 111111 I III

024681012141618202224262830323436 39

Appendix Figure 8Inflation it-f to Real Output Shock

800—

600—

400—

200—

0— __:::::.;;~~~~tn

-200—

-400—

-600— -

-800—

—1000— I 1 I II I 1 1 Il I I II I I II 1 1 II I I 1 II I I I I I I II I I I I I

024681012141618202224262830323436 39

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Appendix Figure 9Money Growth it-f to Real Output Shock

2700— -

1800—

900—S

S

,,., ,~tt- --—-—-

4S

-900—

-1800— -

—2700— I II I II II II II II III II II II II II I II I I II II II II

0 2 4 681012141618202224262830323436 39

Appendix Figure 10T-Bill Rate iii to Real Output Shock

300— ~

200—

5—

100—

0——5-—---—— :5_S.-, - S - - - - - - - - - - - -

-100— /-200— j

-300—S

-400— I I I II I II I II I II I II I II I I I I II I II II I If I If I If

024681012141618202224262830323436 39

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