barro - rational expectations and the role of monetary policy

8/13/2019 Barro - Rational Expectations and the Role of Monetary Policy

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Journal of onetaryEconomics 2 (1976) l-32. 0 North-Holland Publishing Company

RATIONAL EXPECTATIONS AND THE ROLE OFMONETARY POLICY

Robert J. BARRO*University of Rochester, Rochester, NY 14627, U.S.A.

1. IntroductionThe purpose of this paper is to analyze the role of monetary policy in a modelwith three major characteristics: (I) prices and quantities are competitivelydetermined by market-clearing relationships - that is, by the solution of acompetitive equilibrium system; (2) information is imperfect; and (3) expecta-tions of future variables are formed rationally, in the sense of being optimal

predictions based on the available information. The focus of the analysis ison the effects of monetary expansion on prices and outputs.Part 2 of the paper generates a Phillips-curve-type relation in a frameworkthat builds on the work of Friedman (1968) and Lucas (1973). The source ofthe Phillips curve is a lack of full current information that prevents individualsfrom dichotomizing unanticipated price movements into relative and absolutecomponents. Hence, although suppliers and demanders in any market formtheir expectations about future prices (in other markets) in a rational manner,the implied behavior of output in each market does not separate una,jticipatedsupply and demand shifts into relative and aggregate parts. In this frameworkchanges in money that are not fully perceived as nominal disturbances can lead tomovements in output. It also follows here that an increase in the variance of themonetary growth rate (which is one component of the variance of aggregateexcess demand) induces indihidtlals to attribute a larger fraction of observedprice movements to monetary fcrces, and thereby leads to a reduceG responsive-ness of output to a given monetary disturbance. Thus, as in Lucass model,the magnitude of the Phillips curve slope is inversely related to the varianceof the monetary growth rate.Part 2 of the paper also discusses the determination of the variance of relative,

*This research was supported by a grant from the Liberty Fund. I have benefited fromdiscussions of egtrlier versions of this paper at the Federal Reserve Bank of MinneapolisSeminar on Rational Expectations, and at seminars at Chicago, M.I.T., Rochester, and Penn-sylvania. I am particularly gratefui to Bob Lucas for a number of important suggestions.


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2 R.J. tmo, ational expectations and the role of monetarypolicyprices and the variance of future prices about their currently predictable values.One ir.teresting conclusion is that an increase in the variance of aggregate excessdem.and would lead to an increase in the variance of relative prices.

The third part of the paper follows Sargent and Wallace (1975) by inquiringinto the role of monetary policy in this type of rational expectations model.Pure variance of money leads to an increase in the variance of output about itsfull current information position and to an increased variance of future pricesabout their currently predictable values. Essentially, an additional amount ofmonetary noise makes it more difficult for individuals to isolate real shifts,and therefore tends to move output away from full information output. Ac-cordingly, to the extent that direct costs of controlling money are neglected, azero variance of money would be optimal.I then consider the implications of feedback effects from observed economicvariables to money. When the monetary authority lacks superior information,it turns out that this sort of feedback is irrelevant to the determination ofoutput. Essentially, when individuals know the form of the feedback rule andalso perceive the variables to which money is reacting, this type of monetarybehavior would be taken into account in the formation of expectations. Whenthe monetary au-i-hority possesses superior information there is the potentialfor beneficial cauntercyclical policy. However, the provision of the superiorinformation to the public has identical implications for output if the costs ofproviding this information are neglected.Finally, 1 ~~~~~~ a-c;d- the case where the monetary authority has superiorinformation about its own monetary rule. This situation might permit a formof systematic policy deception in the short run, when the public does notappreciate the nature of the deception. However, in my model where the policycriterion concerns the gap between actual and full information output, thistype of policy deception is not desirable.2. A rational expectations model with imperfect information2.1. Setup of the model

The model is an extension to the one developed by Lucas (1973). There is onetype of nondurable commodity, denoted by y, that can be viewed as a personalservice. With this view, the supply of the commodity corresponds to the supplyof factor services, and the demand for the commodity corresponds to the demandfor factor services. The commodity is transacted in various markets, indexed byZ I,...,: n, that are at physically separated locations. The variety of locationsfor a single good is intended to serve as a proxy for markets in a variety ofgoods, since the multilocation context seems easier to formalize. There isadsumed to be an instantaneous flow of information within any market, buta lag inI he flow of information across markets. Hence, at a given point m time,


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R.J. Barre, Rational expectations and the role of monetary policy 3

there can be a different commodity price across markets, but only a singleprice within each market.The model is constructed in a discrete time period framework, where thelength of the period signifies the time delay with which information travelsacross markets. In the present getup market participants possess full informationabout the relevant economy-wide variables with a one-period lag, During asingle period an individual can visit any of the n markets, but it is assumed to beimpossible to visit more than one market during a period. Further, it issupposed that there is sufficient information about last periods prices acrossmarkets so that current arbitrage insures that all markets offer the same exante distribution of price. In this respect the setup resembles the one used byMortensen (1974).

Aside from lagged knowledge of aggregate variables, a participant in market zalso possesses current information that is assumed to be limited to an observa-tion of the current price in that market, P,(z). The crucial idea is that certaintypes of local information are received more rapidly than some aspects ofglobal information - such as prices in other markets. It is this differentialinformation structure that allows for a confusion between relative and absoluteshifts, and thereby allows for temporary real effects of unpreceived moneymovements. Of course, the use of a fix -length information lag and the distinc-tion of only two types of information, local and global, are abstractions madesolely for technical convenience.Aside from the nondurable commodity, the only other good in the economyis fiat money, M.2 Money is held by individuals because it is the only availablestore of value. New money enters the economy as transfer payments from thegovernment. These transfers are received by individuals at the start of eachperiod in an amount that is ndependent of each individuals money holdingduring the previous period. It is assumed, for simplicity, that the governmentdoes not participate directly in the commodity markets.In order to keep the model analytscally manageable, I have constructed theequations in log-linear form. All of the variables used below in these equationsare to be interpreted in logarithmic terms.The supply of the commcdity at date t in market z, denoted by .J$(z), isassumed to depend on the following set of variables: (I) A systematic supplyterm, k:(z), that is intended to c.spture systematic changes in technology, popu-

IThe presentanalysis does not deal with optimal search for information across markets.Further, the manner in which an,gregate information is transmitted with a one-period lag)is not explored. Extensions to inc,Jrporate optimal search could be very interesting.ZSargent and Wallace (1975) have constructed a model that is similar in some respects,but which also includes a capital market. As Bob Lucas has pointed out to me, the existence fa single, economy-wide capital market implies that the observation of the price (rate ofreturn) on this market conveys important aggregate information. This sort of currentaggregate information is very different from the current local information that I assume isavailable in the present model. I plan to deal at a later time with the different type of informationstructure that is implied by the existence of an economy.-Sv 2c.eapital market.


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4 R.J. Bw ru, Rat i onal expect at i ons and t he rul e o monet ary poficy

lation, etc. (2) A term that measures the current price of output in market z,&(z), relative to the price that is expected to prevail next peri0d.j Because allof next periods markets have the same ex ante distribution of price, it can beassumed that this expectation applies to PI+1, the (geometric, unweighted)average of prices across the markets at date t+ 1. If I,(z) denotes the informationpossessed at date s by participants in market z,~ then EP,+&(z) is the relevantprice expectation. A positive response of supply to the term P,(z)- EP,, 1 &(z)can be viewed as an efIect of speculation over time associated with the inter-temporal substitutability of leisure. This type of effect has been discussed inLucas and Rapping (1970) and Lucas (1972). (3) A wealth variable, measured as[IV,+ EdMt+I I&(z) EP,+ 1 It(z)l,5 that is assumed to have a positive effecton desired leisure, and hence a negative effect on factor supply and a negativeeffect on g(z). The inclusion of the (log of the) aggregate money stock, M,,reflects a simplify:.ng assumption that the total money possessed by participantsin market z, M,(z), is always the same fraction of the aggregate money stock?The term EdM,+I l&(z), where AM,., = M,, 1 -Al,, accounts for the expectedgovernmental transfer at the start of the next period. (4) Random terms us ande:(z), where as is a shift term on aggregate supply, and E:(Z) s a shift term onrelative supply in market z. The sample mean of &S(z) cross the markets iszero by definition. Other properties of the distributions of these random vari-ables will be discus.sed below, after the introduction of the demand side of themodel.The specific form of the supply function (in log-linear terms) is

where 2, and B, are, respectively, the (absolute values of the) relative priceand wealth elasticities of current commodity supply. It should be noted thatthe wealth term in eq. (1) does not hold (constant the appropriate measure ofwealth when P, z)hanges. The price deflator for the wealth term should be a(weighted) price index that includes P,(z) as well as EP,. 1. The full effect ofP,(z) on y;(z) includes a positive substitution effect plus a reinforcing effectthat derives from the reduction in approprlately measured wealth. However,

The inclusion of expected prices at dates further into the future does not seem to have anyimportant effects in the present model.The present framework is sufficiently simple so that all participants in a single market at agiven point in time have the same information set. In this respect, Lucas (1975) considers amore complicated setup.Q would seem preferable to subtract off the expected desired real money holding at datet+ 1. However, this change would complicate the exposition of the model without affectingthe main results. See the discussion at the end of appendix 2.Lucas (i972) develops a model in which this fraction is a random variable. In my model therandom relative disturbance terms, discussed next, serve the same purpose.


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R.J. Barr-o,Rational expectations and he role of monetary policy 5this wealth effect would be negligible if the weight of the current period, duringwhich P,(z) applies, is small relative to the weight of the future period(s),during which EP,,, applies. Subsequently, the important issue concerns thenet efCect of EP,+1 on J#z), which depends from eq. (1) on the sign of /J-Q,.If the current period is viewed as short relative to the length of the future, thenthe substitution effect, as measured by cts, would tend to dominate over thewealth eftect & It is assumed below that the substitution effect is dominant,so that oc,> ps and the net effect of EP,, 1 on vi(z) is negative.The specification of the demand side of the model is parallel to that of thesupply side,

J:(Z) = k:(z)- z#,(z) - EP, +1 l,(z)]+~~[M,+E~M,+,)I,(;)-EP,+,II,(=)]+~~+E?(~). (2)

Price speculation by demanders implies a negative effect of [P,(z)- EP,+l 1It(z)] on y:(z), as measured by the elasticity -orold.Note that demanders inmarket z are assumed to possess the same information set, If(z), as suppliersto this market. The positive effect of wealth on commodity demand is measuredby the elasticity Pd. As discussed in the case of supply, it is assumed that thesubstitution effect of EP, + is dominant, so that did> /?d applies. Finally, upand E:(Z) arts stochastic shift terms that are analogous to those introduced intothe suppl;. function.2.2. Market-clear ir rg detemtinatior~ of pri ces and outputs

Before deriving the market-clearing conditions, it is useful to define theexcess demand variables,k,(z) = k:(z) k;(z),

E,(Z) = &f(Z) &f(Z).The determination of prices depends solely on excess demand measures, but thedetermination of output (below) requires also the specification of sepalatesupply and demand functions. 1 assume in the main text that U, is generated bya random walk process,

u, = up1 + l, 94 - NO, o,),

In the present setup an individual supplies and demands commodities simuhaneouslyin the same market. It would be possible to allow each individual to visit two markets in eachperiod, one for supply and one for demand, but the resulting complications in in;ormationsets are considerable. Separate concepts of supply and demand can be maintained here if onethinks of the commodity that an individual supplies as not being identical to those he demands(for example, back-scratching services?).


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6 R.J. .Barr o, Rat i onal xpectat i ons nd he ol e of monet ary ol i cy

where N refers to the normal distribution. The random variable O, is seriallyindependent and represents the current periods innovation to real aggregateexcess demand. Because U, has a one-to-one effect on u,+ l, the Annovationsare permanent in the sense of determining the most likely position of allfuture values of u. I consider in appendix 1 the implications of substituting afirst-order Markov process, u, = AU*_+ v,, where 0 /?.The price at date t in market z is determined to equate supply and demand inthat market. Equating the expressions in eqs. (1) and (2), and using the above

dlefinitions, leads to the market-clearing condition for market z,rP,(z) = (a-P)EP,,tlr,(z)+P[~,+EdM,,,[l,(r)l

+ k,(z) + I, + E,(Z)*Since the samp le mean of e,(z) is zero by definition, the distribution of E..\z)would actuallydepend cn the number of market


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R.J. Barr e, Rat i onal xpect at i ons nd he ol e of monet ary ol i cy 7

It is apparent from the form of eq. (3) and the assumed serial independence ofet(t) that the distribution of P,(z) can be independent of the market index, Z,only if k,(z) is constant across markets. That is, the arbitrage condition thatinsures that all markets have the same ex antz distribution of price is that theratio of systematic demand to supply, k,(r) = k:(z)-k:(z)_ be the same for allmarkets. o It is then permissible to drop the z subscript from the k,(z) term ineq* (3).Eq. (3) indicates that Pt(z) is determined by a set of demand-pull variablesthat include the money stock plus expected next periods transfer and the sum ofsystematic and random excess demand terms, k,+ u, +c~(z). There is also acost-push term, EP,+ 1 l,(z), that has an effect in the direction of the signof a-j?. Under the assumption of a dominant substitution effect, the impact ofEP,+ 1 on P,(z) is positive.The key element of the rational expectations approach is that the EP,+ 1 termin eq. (3) is not determined by an ad hoc expectations mechanism from outsideof the model, but is instead based on the knowledge - implied by an assumedknowledge of the model - that prices are determined by market-clearing condi-tions of the form of eq. (3). Hence, current market-clearing prices and (theset of) expectations about future prices are determined through a simultaneousprocess. In order to implement this approach, it is necessary to complete thespecification of the model by describing the processes that generate M, and k,.I assume, provisionally, that changes in money are generated by a constantgrowth rate, g, plus a random term, denoted by nr,. That is,

M,-M,_, E AAl, = g+m,,

where nt, is assumed to be serially independent, as well as uncorrelated with ~7,and the array of E,(Z). I examine the implications of more complicated moneysupply processes in a later part of the paper. In order to focus on the short-run,cyclical effects of money, 1 also abstract in the main text from long-term mone-tary growth - that is, g = 0 is assumed. This abstraction amounts to neglectingthe effects of systematic inflation. Appendix 2 deals with the case where g # 0.When g = 0, eq. (4) implies that ELM,, iI& = 0.I assume that the k, process takes the form,

k, = k,-$pt, (5)where k, = 0 can be assumed subsequently through an appropriate normaliza-tion of output units. It turns out, as shown in Appendix 2, that the form for k,

lAlternatively, if some serial dependence in E,(Z)had been introduced, then k,(z) could besuch as to just offset the implications of this serial dependence for P,(z).The terms on the right side of eq. (2) can be viewed equivalently as negative forces on thecurrent excess demand for money.


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8 R.J. Barr e, Rat i onal expect at i ons and t he rol e of monet ary pol i cy

in eq. (5) amounts to assuming that the systematic growth rate of output isequal to p. Again, it is convenient to abstract in the main text from the effectsof long-term growth so that p = 0 is assumed. Since k, = 0 in this case, thesystematic excess demand term no longer appears in the analysis. Appendix2 deals with the case where p # 0.The next step is to solve the model in the sense of determining prices andoutputs as functions of exogenous variables. The simplest procedure for solvingthe model involves, first, writing out the (log-linear) form of the solution forP,(z) in terms of a vector of unknown coefficients on the set of relevant inde-pendent variables. Second, the market-clearing condition expressed in eq. (3)is used to determine the values of the unknown coefficients. This solution methodhas been used before in a parallel context by Lucas (1972, 1973). The procedureis analogous to applying the method of undetermined coefficients to a trialsolution in the case of differential or difference equations. In the present situationPi(z) depends on the following variables (in a log-linear form), 2

Pt(z)= n,M,-,+~,m,+~,v,+~,~,(z)+~,u,-,, (6)where the ns are the unknown coefficients. Since M,_l is included in currentinformation sets, previous values of M do not appear in the price solution.Since m,, v, and ~~(2)are serially independent, past values of these variables donot appear. 3 Since, for a given value of v,, u, depends only on u,, 1, it followsthat valueF of u prior to c - 1 do not appear.If individuals know that prices in each period are determined by eq. (6),then the expected price for next period must be

since the expected values of m, +1, v,+ 1 and e,, 1(z), conditioned on I,(z), are allzero. The information set, It(z), is assumed to include observations (or sufficientdata to infer the values) of M,_l and u,_~. The additional information contri-but*ed by an observation of P,(z)~ amounts, from eq. (6) to an observationY121n the case where g and p are nonzero, the solution includes the additional terms &t+ L7,that is, a time trend and a constant term. See appendix 2.- 131.fa variable such as L+_~had been entered, it would eventually be determined that itsassociated LCcoefficient was zero.141 have not included an individuals own value of AM,, which arrives as a governmenttransfer, as an additional element of I&). This exclusion is satisfactory if the relation betweenindividual and aggregate transfers is sufficiently noisy so that the individual transfer provides anegligible increment of information over Pt(z). This assumption need not be inconsistentwith my earlier simplifying assumption that Aft(z) was a constant fraction of A&, since AC&(Z)refers to the total money contained in market z. If individual and aggregate M were alwaysproportionately related, then Mr would, itself, become an element of It(z), and the principalinfomation ap in the model would disappear.


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of the sum Jlr2nr,+ &P, + &cl(z). The key to the formation of price expectationsis then the calculatiti,sl of the two expectations, En?, and Er,, conditioned on theobservation of P,(z). fn effect, these two conditional expectations are obtainedby running regressions of IPI,and v,, respectively, on the observed sum mt +&tl, + &C,(Z). That is,

where1

8, = (w20:(n,)o~+(n3)2a5+(n,)2a,2 and 02Er,II,(z) = n En,m, j c, + & (z) ,3where

e2 = (n3)20,L(n2)20;+(n3)20,2(ns)2a,The Or-coefficient measures the fraction of the total price variance (of P,(z)about its best estimate given I, _ r) that is produced by (aggregate) money variance171, nd the O2 coefficient measures the fraction produced by aggregate realvariance v. The remaining fraction of price variance, 1 - 8, - 02, is attributableto relative real variance e. The expected price at i a yan then be written as

EP,+,II,(z) = n,bf,_, 44 n5e2V 1n+- n2mt ,t l , ,& ,(z)2 l7 IL 147su,_1. (8)

The n-coefficients must be such :hat the market-clearing condition, eq. (3),holds as an identity, given eqs. (6) and (8). This identity relation implies five(independent) conditions corresponding to term-by-term coefficient equalitiesfor the variables that appear in eq. (6). The algebra is straightforward and I willlimit the discussion here to a presentation and interpretation of the results.The five II-coefficients can be determined to ben, = 1,n2 = (4 +~,)+w)u -4 -e,hn, = n2/P,n4 = n,v,n, = /p. (9


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R.J. Bar re, Rational expectations and the role of monetary policy

The weighting term on the current demand shift depends on I -0, - 02, whichmeasures the fraction of total excess demand variance that is attributable torelative (hence, in this model, transitory) shifts.The price solutions from eqs. (13) and (14) can be substituted into eitherthe supply or demand function for commodities (eqs. (1) or (2)) to obtain anexpression for output. It is convenient to define here the parameterH = as/3d ad/?s.

Then, the result for output 1s 5

There are a number of interesting aspects of the output expression. First,(only) the tinperceived part of the current money stock, m,, has an impact onoutput. The sign of the effect depends on the substitution and wealth elasticitiesof the commodity supply and demand functions, as measured by the combina-tion H = as - zaf(. In LUG ss (1973) model, the substitution effect on demand,o(& nd the wealth effect on supply, ps, were both assumed to be zero. In that caseunperceived monetary expansion has, unambiguously, a positive effect onoutput. More generally, this result follows if the substitution effect on supply,a,, and the wealth effect on demand, /I&,are the dominant influences.6 I willtreat the case where H > 0 as the normal one, aithough there is nothing in mlparticular model that suggests that this case would typically arise. Second, the magnitude of the effect of nz, on J*,(Z) which could be called a(reverse) Phillips curve slope - depends, through the 1 -01 - O2 term, on therelation between the variances of relative and aggregate disturbances. Inparticular,

is the fraction of total excess demand variance that is attributable to relativedisturbances. For given varanccs of the real disturbances, CT: nd a:, the magni-tude of the Phillips-type response diminishes with the variance of the monetary Vhe output expression neglects any differences in the sizes of markets - that is, there are noremaining systematic effects on y,(z) that are associated with the z-in&x.16Barro and Grossman 1975, ch. 7) contains a related discussion for a model that hasseparate labor and commodity markets, but which treats expectations in an ad hoc manner.In an overlapping-generations model with a retirement period, this case may be typical.In this sort of model working households would have a small fraction of total wealth. so that/I, would be small. Further, the retired households, with a relatively large fraction of totalwealth, would have short time horizons, so that /Id would be large.


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12 R. . kzrro, Rational expectations and the role of monetary policy

growth rate, 6,. l 8 That is, when the monetary growth rate is less predictable, indi-viduals are more inclined to associate observed price fluctuations in their marketswith (aggregate) monetary movements. In that case, the reaction of output toa given monetary disturbance, m,, would be correspondingly smaller. This typeof effect has been discussed previously by Lucas (1973, p. 330), and it can beappropriately called the Lucas-hypothesis on the Phillips curve slope.lgGiven the negative effect of C: on the Phillips slope, there is a sense in whichmore variable monetary growth has a stabilizing effect on output. However,since this process reflects a monetary clouding that lessens the extent to whichobserved prices are a signal about relative prices, it seems intuitive that thistype of stabilization would not be desirable in a full sense. Section 3.1 of thispaper confirms that intuition.Third, this type of model does not yield real effects of monetary disturbancesthat persist beyond one period - that is, only the current value of m, enters intoeq. (15). Some elements that could result in persistent effects are (1) the recogni-tion that aggregate information is attained only gradually over time, ratherthan fully with a one-period lag; (2) elements of capital accumulation that wouldallow current changes in stocks to have a continued effect into subsequentperiods; (3) adjustment costs in the supply and demand functions. Lucass(1975) paper contains aspects of the first two of these elements. However, myanalysis in the pre:Gnt paper does not incorporate any of these effects.Fourth, the manner in which the current real shifts affect output brings outthe key aspect of the information structure of the model - namely, each aggre-gate shift, t p or z$ has the same effect as the corresponding relative shift,E:(Z) or E:(:). This behavior derives from the underlying assumption thatparticipants in market z cannot tell what fraction of the observed movementin P,(Z) reflects a relative price shift rather than an absolute shift. The preciseway in which individuals would like to discriminate between these two typesof shifts will be brought out below in section 3.1. It can also be noted here thatthe existence of an effect of unperceived monetary expansion on output, asdiscussed above, depends entirely on the inability of market participants todistinguish immediately between relative and absolute price shifts.2.3. Pri ce distr ibutions

Given the price solutions in eqs. (10) and (12), the model determines distri-butions of prices both cross markets and #over ime. It is convenient to focus1W monetary disturbances had differentialeffects across markets- either systematic orrandom - one would antisipate a positiveasso,c.iatian etweenu,,,~and ac2.However, if themovement in ac2 is much less than one-to-one with CT2, the qualitative conclusion about thePhillips curve slope would remain valid.I91 am currently attempting to test this hypothesis for the United States over the period1890 to 1973. Lucas (1973) has performed some related tests for a cross section of countriesduring the post-World War II period. Lucass results support the hypothesis, but his main evi-dence seems to rest on two outlying Latin American cases.


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R.J. Barre, Rcltional expectations and the role of monetary policy 13

the discussion of these distributions on the problem of preckting the futureprice in a (randomly-selected) market z, based on inforination currentlypossessed by participants in market z. That is, I focus on the gap betweenI,++) and EP,+,II,(z).~ This gap can be usefully broken down into threeindependent components,

&+,(+EP,,,(lt(z) = [~,+1w--P,+11+ [&+I- w+,p,1+ [EP,+*~I,-EP,,,11,(z)l, w

where I, denotes full current information. The information set It includesseparate observations of 111, nd u,, whereas I,(z) includes only the combinationof LIZ,, ,, and Ed that is implicit in an obszrvation of P,(z). It turns out thatthe three components in eq. (16) are independently, normally distributed withzero mean, so that the variance of' each component fully specifies it: -.istr ibution.1 will refer to these variances as T:. b2, and r& respectively, and will use thesymbol ?/to denote the sum of the three variances.The first component corresponds to the distribution of relative prices at apoint in time. Eqs. (10) and (12) (updated by one period) imply

C+ AZ)-C+r = (liP)[4 +&+(B3)(1-& -~,)I%+,(~),which has zero mean (conditioned on It(z)). Using the expression for 6, + e2in eq. (1 l), the variance of relative prices can then be determined as

r; = E[P,+I(=)-P,+1]2/1,(=)0,2[cJi+ a;12= jY?(crj+ 0;) (17)

Not surprisingly, a key determinant of the relative price variance is oz, thevariance of relative excess demand. 21 More interestingly, ihere is also an effectof ai. This effect is positive as long as r > /I .holds, as I have been assuming.Therefore, an increase in the variance of aggregate excess demand leads to anincrease in the variance of relative prices. 22 The reasoring for this effect isas follows. When 0: increases, the responsiveness of excess demand to locally-ORccall that EB, + (r) = EP, +1for all z in this model.zlHowever, the effe t is not unambiguously positive. Two sufficient conditions for a positive

effect arex k 3j?ora,z K. b12.2 2Vining (1974) has a preliminary, I believe inconclusive, discussion of some post-World WarII Umtcd States evidence on this issue. Graham (1930, p. 175) discusses some observationsfrom the German hyperinflation that appear to support this hypothesis. Cairncs (1873) dis-cusses the general idea that changes i? money (gold) would have short-run effects on the dis-persion of relative prices. His emphasis is on the (nonproportional) manner in which new moneyenters different parts of the economy, and on differences in the responsiveness of supply anddemand for various types of commodities. Mills (1927 pp. 252-69) calculates measures ofprice dispersion for the United States from 1891 to 1926.


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14 R.J. 3anq Rat@. al expect at i w and he ol e of monetary ol i cy

observed prices diminishes, because individuals are less inclined to associateprice movements with shifts in relative excess demand. Accordingly, a given-size relative disturbance, E,(Z), requires a larger price movement in order toachieve clearing of the local market. This accentuated response of P,(z) toat(z) implies the increase in relative price variance, r&The second component of eq. (16) is the future price net of the price that ispredictable based on full current information, It. Eqs. (12) and (13) imply

Note that this component has zero mean (conditioned on If(z)) and is inde-pendent of the first component. The variance of the future absolute price levelcan then be calculated as

The effect of ai on a2 is unambiguously positive if a > /3. The effect of a,:is negative when a > /?holds.Finally, the third component in eq. (16) involves the distribution of relativeinformation in terrus of its implications for EP,+ 1. Eqs. (12) and (13) imply

It can be verified that this expression has zero mean conditioned on I,(z). Thiscomponent is also independent of the first two components. The variance ofrelative information can then be calculated as

This variance is increasing in both 0; and at.The full variance of P,, I(z) about EP,, 1 I,(z) is the sum of the three com-ponent variances,

It can be shown by straightforward differentiation that V is unambiguously


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R.J. Barre, Rational expectations and he role of monetary policy 15

increasing in 0z,2 3 and is unambiguously increasing in 0: as long as x > /?.One aspect of the next part of the paper is an analysis of the impact of mone-tary policy on the predictability of future prices, as measured inversely by Yin eq. (20). That analysis would be more meaningful if price predictabilityplayed some direct role in the commodity supply and demand functions -perhaps by affecting the costs of long-term nominal contracting. However,the present treatment does not incorporate this type of effect.3. Monetary policy

Following Sargent and Wallace (1975), I now consider the role of monetarypolicy in a rational expectations framework. Monetary policy i; identified herewith a stochastic control rule for determining the time path of the money stock.My procedure differs from that of Sargent and Wallace in two major respects:first, the criterion for evaluating policy is different: and second, my analysisincorporates the dependence of certain coefficients of the model - in particular,the Phillips curve slope - on the underlying distributions of the excess demandshifts. Sargent and Wallace (1975, p. 5) evaluate policy by using a loss functionthat gives credit to stabilizing a measure of aggregate output, where this outputmeasure is an aggregate analogue to my eq. (15). Their model corresponds inessential respects to dealing with the (geometric) average of the ~,(z)s acrossthe markets, where this averaging of eq. (15) over the rz markets leads to anaggregate output expression in tihich the relative excess demand shifts, E:(Z)and E:(Z), do not appear. StabiKzing this measure of aggregate output wouldamount to giving no credit to changes in the composition of output that wereresponses to changes in relative supply and demand - that is, to changes in thecomposition of tastes, technology, etc. It seems clear that a loss function basedon this simple measure of aggregate output would not be appropriate.My earlier discussion of the output expression in eq. (15) stressed that thekey aspect of the partial information structure of the model is the confusionbetween aggregate and relative shifts. It is possible to determine the outputthat Hould arise in each market if all participants were able to discriminateperfectly between these shifts - that is, under full current information where1,(z) includes observarions on P, and M,. The output level under full currentinformation (subsequently called full information output) can be comparedwith the output level determilTed in eq. (15). My proposed criterion for morretarypolicy is to minimize the expected squared gap between actual and full inferma-tion output in each market.24

23That is, the positive effect on 722 in eq. (19) and the ambiguous (though likely positive)effect on z12 in eq. (17) dominate over the negative effect on o2 in eq. (18).24My basic idea for this measure is that it should serve as an approximation to the expectedloss of consumer surplus. Ideally, the criterion would be based directly on the behavior ofindividual expected utilities. Unfortunately, the present model is not set up to proceed in thatfashion.


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16 R.J, Barr e, Rational expectations and he role of monetary policy

3. I. Pri ces and out put s under ul l current i nformat i onThis model coincides with the one developed in part 2 except that P, and M,

(and, hence, nz,, v, and E,(Z))are now included in &(z). The analysis proceedsas in section 2.2 until the derivation of EP,+,ll,(z). Given the new informationassumption, eq. (8) is now replaced by the simpler expression,

The remainder of the analysis follows the form of section 2.2. Using an asteriskto denote the full (current) information situation, the price level in market zturns out to beP,*(G w-1 +ml+WP)(u,-, +vJ+(l/+,(z). (21)

It is convenient to rewrite here the price that arises under partial information,from eq. (IO),

In contrast with its effect on P,(z), the unanticipated change in the money stock,m,, has a one-to-one effect on P:(z). Further, the current real disturbances, v,and Ed, have different effects on P:(z). In particular, if oc> fl, the response ofP*(z) to the aggregate disturbance, v,, is larger than that to the relative distur-bance, Ed.The result for full information output is

where H = or,&, c&. Again, it is convenient to rewrite the partial informationresult, this time from eq. (15),

x [vd+EP(Z)I+(l/a)[Old+(HIP)(eI~,)l[~s+B:o1+ UWM- 1+ (Bs/P)u:.-i~

There are several interesting contrasts between the results for y,(z) and thosefor y:(z). First, HZ, as no effect on $(z), which corresponds to the one-to-oneeffect of m, on P,*(z>. Second, each aggregate shift, VP or vf, has a different


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R.3. Batto, Rational expectations and the role of monetary policy 17effect on yf(zj from the corresponding relative shift, &z) or E:(Z). From in-spection of the y,(z) and y,*(z) expressions, it is clear that the two responsesto the v,s would coincide if e1 +0, = 1. This result obtains because ( I1 02. = 1signifies 0: = 0, so that the aggregate - relative confusion cannot arise, andall aggregate shifts induce the appropriate output response. Note that the effectof m, on y&) is zero in this case. It also follows that the response of y,(z) and-y:(z) to the 6,s would coincide if e1 +O, = 0, since 0: = 0 in that case. WhenO1+O, is between zero and one, there will be divergences between the responsesof y&) and y:(z) to M,, v, and E,(Z). This observation can be seen more easilyby writing out an expression for the gap between actuai and full informationoutput,

YSZ)-YXZ = Was)Kl4 - e2)(pm, v,) - (e, + e2)Et z)j. (23)If H > 0 and 0 < e1 +0, < 1, it is clear from eq. (23) that (in relation to thefull information situation) y,(z) reacts too much to the aggregate shifts, nl, andv,, and not enough to the relative shifts, et(z). Eq. (23) also indicates again thatthe important informational division is between aggregate shifts, /?m, + tl ,, andrelative shifts, E,(Z). In a more general model it would also become relevantto separate the / l m, art of the aggregate shifts from the v, part - or, put anotherway, to separate the monetary shift, m,, from the real shift, V~ E,(z). For ex-ample, this other type of informational division would arise if u, were no longergenerated by a random walk. Appendix 1 deals with this case and clarifies someaspects of the two types of information divisions: aggregate versus relativeand monetary versus real.The proposed criterion for monetary policy is to minimize the expectedsquared gap between y,(z) and y,*(z), which is denoted by Q. Substituting forO1+ O2from eq. (11) and using eq. (23), the result is

l2 = E[y,(z) -J,(Z)] 2 &(-_)

This expression for the variance of output about its full information positionwill be used in the subsequent discussion of monetary policy.3.2. The optimal money variance

Before introducing the possibility of monetary policy through feedbackcontrol on observed values of prices, outputs, etc., I consider here the roleplayed by pure variance of money - that is, by o,$ First, it is clear from eq. (23)that, if all the coefficients including O1+O, were fixed, then an increase ii7 CT,:would lead to an increased variance of yl(z) about y:(z). Accordingly, in the


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18 R.J. l bro, Rat i onal xpect at i ons nd he ol e of monet ary ol i cy

Sargent and Wallace model, where all coefficients are fixed, it is trivial thattJ2 =m 0 would be optimal (and, hence, they do not discuss this issue). On theother hand, in my model an increase in a: has effects that operate throughthe O-coefficients. Specifically, the coefficient on the aggregate disturbanceterm in eq. (23) ins

and this coefficient declines with bm. As C: increases, individuals attribute alarger fraction of observed price movements to aggregate shocks and are,therefore, fooled less - in terms of the departure of vi(z) from u:(z) - for a givenvalue of the aggregate shock, /?Q+v~. In fact, as CJ~ + 00, the contribution ofthe: aggregate disturbance term in eq. (23) to the output variance R, as calculatedin eq. (24), approaches zero. 25 However, the contribution to Q of the relativedisturbance term in eq. (23), (0, +0,)&,(z), is an increasing function of ai, sothat the overall effect on s2 depends on two offsetting forces.The nature of the net effect is apparent from eq. (24). The form of thisexpression implie.: that Sz is an increasing function of both 0: (which equalsf120z+ ai) and 6;:. Hence, it is true in this model that the variance of outputabout its full information position is minimized by setting ai = 0.26 The reasonfor this result is that the policy criterion dictates getting output as close aspossible to its full information position. An increase in any of the underlyingvariances, t$ a:, or a,2, clouds the picture, in the sense of making currentprice information a less accurate signal for market participants, and thereforemakes it more difficult for individuals to get output close to full informationoutput. To the extent that the variance of money, ai, can be controlled,27 thesmallest possible value would be optimal. 2 iThe conclusion that 0: = 0 is optimal is basically in the spirit of the constactgrowth rate rule that has been advocated particularly by Friedman (for examr) rti,in Friedman, (1960, chapter 4)), and earlier by Simons (1948, pp. 1$I- ?).

93ecause (I-& - &)2 approaches zero faster than o,,,~approaches infinity.261n an earlier version of this paper I obtained the result that CJ,,,~ 0 would minimI. ? 0only under some configurations of the underlying parameters, and that am2 = 00 was optimalin some other cases. Those conclusions depended on a misspecification in which EP,, ratherthan EPt+1, entered into the supply and demand tPunctions. Another way to end up witham2 = m as an answer is to change the objective function to the minimization of the varianceof aggregate output yr about Ey,II,_ 1 (essentially the Sargent and Wallace criterion), wherethe aggregation eliminates the E,(Z) erms from the output expression of eq. (15). This objectivewould definitely call for a, 2 = co if aggregate real sh&ts were absent; that is, if uId = 11,~ 0.In the case where aggregate real shifts are present, the criterion would typically lead to apositive, but finite, value for ~7,~.271f there are significant money-control-type costs associated with reducing brn2, then thesecosts would have to be weighed against the benefits from a lower variance. This sort of trade-off would lead to the choice ofa pbsitivr: value for am2.28This result remains valid when the Usprocess is no longer a random walk. See appendix 1.


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R.J. Barr e, Rat i onal expect at i ons and the rol e of monet ary poli cy 19

The present result indicates that monetary policy is best when it is most pre-dictable. In particular, an increase in money variance is nonneutral and leadsto rn increased variance of output about its full information position becausemoney variance clouds the real picture and reduces the value of observed pricesas allocative signals.It is also useful to note here that the predictability of future prices is maxi-mized by setting 0: = 0. That is, the variance V of Pt+&) about E&+&(Z),which is indicated in eq. (20), is an increasing function of ai (and, hence, of~2) as long as a > / ?holds. Therefore, ;he introduction of a price varianceI=riterion into the objective function would 1101 lter the above result.

3.3. M onet ary poli cy as eedback cont rclI now consider the implications of complicating the money supply rule fromthe simple form of eq. (4) to include feedback effects from observed economicvariables. This extension would allow the monetary authority to performthe countercyclical function of increasing money more rapidly when outputis relatively low or prices are relatively high, and expanding money less rapidlyin the reverse situations. The implications of this sort of monetary behavior

depend crucially on the information set that is available to the monetaryauthority. There are two cases that have sharply divergent implications. Inthe first case, the monetary authority does not have more information than anyof the market participants. Formally, the authoritys current information setis It+, which includes all relevant information with a one-period lag, but doesnot include an observation on P,. 29 I n this situation monetarv policy can react(say, countercyclically) only to economic variables that have already beenperceived by market participants. In the second case, the monetary authorityhas superior information about (some) current economic variables. In anextreme case the authoritys information set would be I,, which in(Audes anobservation on P,. In this case the authoritys feedback rule for AM, can includesome economic varia Aes, such as aggregate values of current prices and out-puts, which are not yet fully perceived by market participants. Not surprisingly,it turns out that countercyclical policy can be more potent under the secondcase than under the first (and, further, that policy may have zero potency underthe first case). Finally, I assume in both cases that the market participants andthe monetary authority have the same information about the form of the mone-tary rule. That is, the form of the rule is, itself, assumed to be a part of theinformation set It-l (and, hence, of I&)). I consider in a later section someimplications of differential information about the form of the monetary rule.

291n his situation the monetarv authorit actually has less information than any of themarket participants since each individual has a current price observation, P,(z), in his informa-tion set, I,(z).


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20 R.J. B~tro, Rational expectations and he ole of monetary pol icy3.3.1. The monetary aut hori t y acks superi or i nformat i on about t he econom),.I consider first the situation where the monetary authoritys information set isI t_l. The feedback control problem can be illustrated in this case by prescribinga monetary rule of the form,

AM, = m,-yv,,,, (25)where, as before, m, m N(0, crz). Since v,+ is last periods real shift to aggre-gate excess demand, the rule described by eq. (25) amounts to a countercyclicalreaction to (one determinant of) last periods absolute price level if y > 0.The form of the rule could be complicated to include a separate reaction tolast periods aggregate output or money stock, which would amount to intro-ducing WZ,_, nd separate terms for vf_ 1 and I.$._ into eq. (25). The rule couldalsi:, be extended to incorporate observations from period t - 2 or earlier periods.However, these complications to the form of eq. (25) turn out to yield noadditional insights, as should become clear from the subsequent discussion. 3oWhen money is generated by the rule in eq. (25), the model can be solved Qutfor prices and outputs using the same type of procedure as in section 2.2.jSince the formal procedure involves no important new elements, I will confineattention here to a presentation and discussion of the results. The solutionsfor S,(z), EP,+ l jl,jz), and ELM,+ 1 It(z) turn out to be

x [mt+(1ID)~v,+~t(z))l+(~IP)U1-1 -w-19w +) 4i=) = w -1+ (6, + 02 ypw[nlt + (1 P)(v, E,(Z))]Ed +1 pm= rP~,~m,+ ~/P) v,+Et z))l*

In contrast to the earlier case in which there were no feedbacks to money(eqs. (4)) (lo), and (13), and EAM,.,Il,(z) = 0), the new elements concern they-terms. These terms are of two types: those pertaining to v,_~ and thoseassociated with v,. First, ;o,_~ s contained in the information set, It(z). Hence,the negative effect of o,_ 1 on M,, as implied by eq. (25) if y > 0, is fully per-ceived. As is generally the case for the perceived part of it ,, P,(z) moves inproportion to money - that is, the - YZ+_~erm appears in the P,(z) expression.Since eq. (25) implies that the effect of t,_1 on M, would also carry over to3oI have not discussed the possibility of monetary reaction to the array of E&:.). Since themonetary authority is assumed to possess only the aggregate instrument, AM,, one would notexpect the pattern of re ative excess demands to be an important input into policy decisions.In any event introducing the array of E&z) into eq. (25) would not change the basic results.31The form of the P,(z) solution in eq. (6) would now include the additional term, &v+~.


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R.J. Barr e, Rat i onal expectat i czrs and t he rol e of monet ary pol i cy 21M +l9 it follows that EPt+l I&(z) also moves in accordance with -yv,_ I. There-fore, the negative reaction of dM , to v,, 1 does not produce any gaps eitherbetween P,(z) and EP, +1 i,(z) or between M , + Ed M , + L(z) and EP, +1 l,(z).

A second type of effect arises because the fzurrent excess demand shift, v,,will have an effect next period on AMt+ l . Since v, is not contained in It(z),market participants form an estimate of the feedback effect on next periodsmoney based on the expectation yEv,(l,(z) = #O&z, + ( l//?)(vt +&))I. Thisterm appears in the above expressions for Ed M ,+$& \ , EPt+l I&), and P,(z).Again, the response of AMt+1 to v, does not produce sny gaps either betweenP,(z) and EP, +11 t(z)32 or between M , + EAh t 1 &(z) and EP, + 1The two feedback channels alter neither Pt(z) relative to EP,+i nor the wealthterm, Mt+EAMt+ l -EPt+l. It follows th L: there will be no effect on commoditysupply and demand, as given in eqs. (1) and (2), and therefore no effect onoutput, J+(Z). Because the market participants know the form of the money rule,and take this behavior into account in forming expectations of future pricesand monetary growth rates, the feedback from v,_ 1 to M , has no eFect on theentire distribution of output. 33 The level of output continues to be determinedby eq. (15). It follows trivially that the choice of the feedback parameter, 7, isirrelevant to the determination of the variance of output about its full informa-tion position, as determined in eq. (24). 343.3.2. The monet ary aut hori t y ossesses superi or nformat i on about he economy .The conclusions on the output effect of feedback control are radically differentwhen the monetary authority has superior information that can be includedin the money rule. The situation can be illustrated in the case where the authorityhas the information set It, which includes an observation of vt.35 In this case a

32Note that the suppy and dem; nd functions in eqs. (1) and (2) depend only on the expectedrealvalue of next periods money, MC+ EAM, + - EP, +1, which accords with the role of moneyas a store of value in this model. The current real money stock in market z, A& P,(Z), mightalso enter these functions if the model incorporated the role of money as a mechanism foreconomizing on transaction costs (or if current real balances were simply included as a directargument of individual utility functioris). In that case Pt(z) would not respond as much asEP,+#,(z) to the expected movement in LLV~+~.The implied gap between P,(z) and EP,, 1would then lead to effects on output, though the effects on actual and full information outputwould coincide. This sort of effect is analogous to the effect of systematic money growth onactual and full information output, as discussed in appendix 2.33This tvpc of result was first qresented by Sargent and Wallace (1975, section 4) Theirassumptio& about the monctaryauthoritys information set jre analogous to those that Imake in this section.

3*Gencrally, there will be a nonzero effect of changes in y on the predictability of futureprices. The main etrect is the following. When 7 is high, the effect of Pi+1 on P,+l is attenuatedbecause of the offsetting feedback effect on AM,+ 2. Hence (at least if y is not too large) P,can be made more predictable, based on 1,(z), by setting a positive value of y.351 do not consider here the possibility of superior information about the configurationof the B,s. Since the policymaker is assumed to possess only the aggregate instrument, AM,this sort of information would, in any case, be of only second-order use. Further, it seems muchless plausible that the policymaker would acually have superior information about the relativeshifts.


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22 R, . Barre, Rat i onal xpect at i ons nd he ol e of monet ary ol i cy

possible form of the monetary rule isAM, = m,- .+. (26)

Again, S > 0 describes a countercyclical monetary policy, but this time theresponse of AM, is to v,, which is not a part of the individual information sets,I,(z). Again, the solution for prices and outputs can be derived from a procedureof the type discussed in section 2.2. The price results are now 36P,(z) = M,_,+[e~+e,+(P/a)(l-e1-e~)]

x {m,+(l//N(l +)v,+st(Z)l} +(l/P)ut-19 (27)

The feedback from v, to AM, implies that pm, -t 1 - @)v, is now the aggregateexcess demand shift that affects P,(z) and EP,, 1 (Ii(z). Therefore, the varianceof aggregate demand is nowtJ; = P2a;+ l-pS)20;.

It is apparent that raising the feedback parameter, S, will reduce 0: as long asS < l/j? applies. Further, setting 6 = l/j? would minimize C: for a given valueof 02. (The combination of S = l/p and of = 0 would yield 0: = 0.)The formula for $2, the variance of output about its full information posi-tion,37 is still that given in eq. (24), and the formula for V, the variance of theabsolute future price level, is still that given in eq. (20). In particular, reductionsin 6: unambiguously reduce 0, and such reductions also unambiguouslyreduce v if a > /3 applies. It is then clear that S = l/p (along with cri = 0)yields the optimal money rule of the form of eq. (26). This parameter choiceimplies that the aggregate excess demand shift is ~,+ l - pS)v, = 0. That is,there \qould be sufficient feedback from v, to AM, so that the direct edict ofv, on excess demand would be fully offset by an inverse movement of Aki,.3aAlthough the above form of stabilization policy seems obvious under the

36Given eq. (26), t follows that ELM+ 1 I t = 0.37Th~ formula for J+(Z) from eq. (15) is modified only in the coefficients of uld and u,The new terms arew+w--w/B)K~ --bw, +~2)+861)~kdr(Go{% + WIP)[r~ - me4 + &I + Bsl); Is.The formula for y,(z)- yts(z) in eq. (23) is modified only by replacing ot with (I- Bs)u,.However, the Or+ & coefficient that appears in this expression now involves (1 - /~@)~a,~,rather than av2 (see eq. (11)).3gThis result can be generalized to a cast where the policymaker has only partial informationabout current variables. As long as the monetary authority possesses some information thatis not possessed by all market participants, there would be some potential role for counter-cyclical aojustments in money.


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R.J. Barr e Rat i onal xpect at i ons nd he ol e of monetary ol i cy 23

assumed superiority in the monetary authoritys information set, the way thatit works is somewhat subtle. In particular, the stabilization policy does notoperate to eliminate any output effects of shifts in vt or vi, but, rather, it worksby removing discrepancies between the movements of actual and full informa-tion output. Assume, for example, that there is no monetary feedback (6 = 0),and that VP s positive while 6 is zero. According to eq. (27), this unanticipatedaggregate demand shift would affect prices in all markets equiproportionately -that is, there would be sr shift in the absolute price level, but no shift in relativeprices. However, participants in market z would not be able fully to distinguishthis shift from a relative price change, and, therefore, the movement in outputwould depart from the movement in full information output. In the case whereH > 0, q. (23) indicates that actual output would increase too much in thissituation. Suppose, now, that a stabilization policy is adopted that implies anegative response of AM, to v, so that the net disturbance, (1 -/.?S)U,, is main-tained at zero. Eq. (27) indicates that neither relative nor absolute prices wouldthen be affected by the positive value of vf. In that case there is no possibilityof a confusion between absohte and relative shifts, and the movement in I.$cannot lead to a departure of actual from full information output. Further, asis clear from eq. (22), the movement in AM, itself does not affect the responseof full information output. Therefore, in this example, both actual and fullinformation output would increase with the positive value of vf in accordancewith the coefficient shown in eq. (22).Since the stabilization policy works by preventing a confusion betweenabsolute and relative price changes, it is also clear that an alternative to theactive stabilization policy would he the provision of the information about cur-rent economic variables. If thr zlonetary authority actually had more rapidobservations of v,, they could convey this information to the public. This in-formation would then augment the information set, It(z), that is used to formexpectations about P,, 1. Once v, is observable, it is clear that shifts in v,, canno longer lead to confusions between relative and absolute price changes.Hence, as in the case of the countercyclical monetary policy described above,movements in o, would not produce discrepancies between actual and fullinformation output. In other words, when the monetary authority has superiorinformation about the economy, the provision of the information to the publicis an alternative to an active stabilization policy. An argument for the superiktyof stabilization policy would have to be based on the costs of transmitting andusing the relevant information. 39 In particular, it could be argued that the

3qThe active stabilization policy and the information-provision policy do have differentimplications for the predictability of future prices. The information-provision policy (6 = 0)in eq. (X), but with ct contained in f,(z), would involve a higher variance of future prices.Essentially, the movements in V~and the associated movements in P, would be perceivedcurrently, but these movements would still not be predictable at date t- 1. On the other hand,the stabilization policy described above compPetely eliminates fluctuations in P, associated withmovements in L+, nd therefore makes P, more predictable at date t - 1.


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24 R.J. Barr e, Rat i onal xpect at i ons nd he ol e of monetary ol i cy

existence of an active stabilization policy motivates individuals to reduce ex-penditures that are aimed at augmenting their information sets. If there areeconomies-of-scale in information production, there could be a net social gainalong these lines.403.3.3. The monetary authority has superior information about the monetary rule.T@of (1975) has stressed the idea that individuals would not have perfectinformation about the form of the monetary rule. In this situation it is plausiblethat the monetary authority would have better information than the generalpublic about its own future actions. In fact, this situation seems most plausiblewhen the policymaker lacks a consistent objective function, such as the mini-mization of the variance of output about its full information position.41 In anycase, if the monetary authority has better information about its monetary rule,there is the possibility of controlling money so as to systematically fool thepublic. Taylor has pointed out that this sort of deception can be carried outduring transition -tiods during which individuals are modifying their beliefs(along Bayesian act+tation lines) about the form of policy.42 In Taylors modelthere is also an optimal, nonzero amount of this deception. His model appearsto support this typ? of action because the policymakers objective functiondoes not reflect individual preferences.43 In my model, there appears to be nobasis for policy deception as long as the policy-makers objective is based onminimizing the gap between actual and full information output.44A simple form of policy deception arises when individuals believe that AM, =m,, where m, - N(0, c , but where the monetary authority knows (determines)that m, is generated by a distribution other than N 0, 0:). Consider, for example,the case where m, can be set by the monetary authority at any desired level,while, in the short run, holding fixed peoples belief that m has zero mean andvariance t&45 In this case it is clear that the choice of m, has a systematic

400f course, once this sort of information externality is introduced, it is also natural toconsider the negative externalities associated with governmental incentive and control.41An unpredictable objective function would be one possible rationale for the existence ofm,, the stochastic part of money.42Sargent and Wallace (1974, p. 16) argue that there is no way for the monetary authorityto systematically fool the public, even in the short run.43His objective function gives positive credit to reducing unemployment throughout therelevant range. The analogy to my model would be to credit expansions of output even when itwas already above its full information position.44The normative case for policy deception could be based on external effects, such as incometaxation, unemployment compensation, etc., that are not incorporated into my model. Thisidea is discussed by Phelps (1972) and also by Hall (1973), who argues : . . . the benefits ofMation derive from the use of expansionary policy to trick economic agents into behavingin socially preferable ways even though their behavior is not in their own interest . . .. Prescott(19755 downplays the importance of external effects in this context. In any case the possibleexternal effects seem to have more pertinence for long-term allocative policies, such as thedesign of tax and welfare system, than for countercyclical monetary policy.45The monetary authority might, instead, be reacting to v~_~ by a feedback rule of theform of eq. (25), but individuals currently believe that y = 0.


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R.J. Bar re Rational expectations and the role ofmonetary policy 25effect on current output, as determined in eq. (15). However, it is also clearfrom eq. (23) that the expected squared gap between actual and full informationoutput would be minimized by choosing m, = 0.46 Given the objective ofminimizing gaps between actual and full information output, it is not surprisingthat optimal behavior rules out policy deception. In this sort of framework thebest monetary policy is always the policy that is most predictable.47 Theobvious policy implication is for the monetary authority to make known inadvance its intentions about money growth,48 which is again the basic philo-sophy behind the constant growth rate rule.

4. ConclusionsI will conclude by highlighting some of the main results that deal with theeffects of money variance and with the role of monetary policy. An increasedvariance of money makes it more difficult for individuals to react appropriatelyto the real shifts in the economy. There are two important types of responses toan increased money variance. First, since individuals react by attributing alarger fraction of observed price movements to monetary causes, there is asmaller effect of a given size monetary disturbance on output -that is, themagnitude of the Phillips curve slope is smaller. Second, the associated com-pounding of individual information problems leads both to a higher varianceof output about its full (current) information position and to a reduced pre-dictability of future prices. It also leads to an increase in the variance of rela-tive prices across markets.From the standpoint of monetary policy, it is clear that pure variance ofmoney is harmful, essentially because it clouds the real picture for individuals.The analysis of monetary pol;cy as feedback control is more complicated sincethe results hinge on the relative information positions of the monetary authorityand the public. When the authority ldcks superior information, the feedbackto money must be based on economic variables that hake already been per-ceived by the public. In this circumstance the choice of feedback control para-meters has no implications for the entire distribution of output. On the otherhand, if the monetary authority has superior information about the economy -

Slf tkc monetary authority sets 1~~= 0 continually, this action would also lead people tobeiicvc (along Baycsian lines) that o,,,~ = 0. I have not dealt explicitly with the etrects offooling people about the value of or,2. Presumably, the variance of actual about full informationoutput is minimized when perceptions about u,,,~are correct.*There is a sense in which this conclusion is violated for the case where the monetaryauthority has superior information about the economy. In particular, the feedback rule fromzyt o AM, described by eq. (26) would be ineffective if people fully perceived the counter-cJ . ical money resofinse - q=I9 while still remaining in the dark about u,. On the other hand,it i: desirable even in this case for people to kndw the form of the monetary rule.48More specifically, the Federal Reserve should publicize, as rapidly as possible, the pro-ceedings of its Open Market Committee.


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26 R.J. Burr o, Rat i onal expect at i ons and t he rol e of monet ary poli cy

which, for some reason, it does not provide to the public directly - then theappropriate feedback response to the extra information can move outputcloser to its full information position.

Basically, the conclusions for monetary policy are in accord with the philo-sophy behind Friedmans proposal for a constant growth rate rule. It is onlyto the extent that the monetary authority has superior economic information(as well as the appropriate objectives), and to the extent that providing informa-tion to the public is costly, that there is a call for departures from the constantgrowth rate rule. Further, if the attempt to use countercyclical policy to exploitthe superior informatibn results in a higher variance of money, c& there wouldbe a tradeoff between the beneficial effects from the countercyclical elements(the ne;gaitivecorrelation between v, and AM,) and the adverse effects from puremonetary variance.4gIt may be useful to discuss the role of feedback control of money in the caseof a concrete example. So The United States economy in 1974 was affected bytwo important real shocks: the oil cartel and the shortfall of agriculturalharvests. Although my model has been constructed to deal with a closed economy,it seems that either of these shocks can be represented by a downward movementin aggregate re:l supply, vs, and a lesser downward movement in aggregatereal demand, vf. (I am abstracting here from effects on relative supply anddemand, which would be quantitatively important for these shocks, but whichwlould not affect the essential parts of my story.) It follows that output (in atypical mark@ which experiences zero relative shifts) would fall while priceswould rise. What is the role for monetary policy in this situation? The presentanalysis suggests that there is a substantive role only to the extent that themonetary authority has better information than the public about the distur-bances, or, possibly, about their implications for the economy. Perhaps themlost obvious observation about the oil and agricultural shocks is the extent towhich they are perceived. Hence, the approach in this paper argues that thereis no role for monetary policy in offsetting these real shifts? 52 Adverseshifts like the oil and agricultural crises will reduce output and cause painfulrelative adjustments no matter what the reaction of the monetary authority.Added monetary noise would only complicate and lengthen the process ofadjustment.

4gThis ypeof tradeoff is discussedn Friedman (1953).S0Gordon (1974) discusses the same example. Yerhaps not surprisingly, he reaches verydifferent onclusions.51Further, o the extent that there is any role it would be a contraction of dMt in responseto the positive value of tr, = otd - v:.5zThe present analysis implies that having the monetary authority announce that there hadbeen an oil or agricultural crisis (or, perhaps, telling people that these crises meant loweroutput and higher prices) would be equivalent to the appropriate active response of money.In this case it seems that both the announcement and the active policy would have negligibleeffects. In fact, the announcement would be soimewhat prcierabie since it would not involvethe danger of introducing added variance into the money supply.


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R.J. Bar re, Rational expectations and he role of monetary poli y 27Appendix 1: Results when uI is a first-order Markov Process

I consider here the case where the real excess demand shift, u,, is generatedby a first-order Markov Process,

whereOSA j? then the 1 parameterasA-+O,and~+l asR-,l.prices and outputs are now

satisfies the conditions 0 s 1 5 A s 1, 1 - 0Recalling that H E as& a& , the results for


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28 R.J. Barro, Rat i onal xpect at i ons nd he & e of monetary olk y

YS4 dW = WldOWm, Xv, (4 +X02)(flm,v, + c,(z))],

where 0: = p2ci+ af in the last expression. The original results in section 2.2of the text correspond, in each case, to A = x = 1.The principal new results from allowing 2 # 1 are brought out in the above

expression for Q. When X = 1, the aggregate real shift, v,,, is permanent, inthe sense of affecting u + 1 on a one-to-one basis. More importantly, the mone-tary variable, M,, and the aggregate real shift, u,, are in this case generated byprocesses of the same form - that is, by random walks. In this situation thecurrent disturbance associated with money, pm,, and the current movement inthe aggregate real disturbance, v,, have identical implications for the future pricelevel, A?~+~. herefore, when 1 = 1, it is unnecessary for individuals who areinterested in forecasting P,+l to separate out the pm, part of the current excessdemand shift from the v, part. The only concern is with separating the totalaggregate shift, bmr +v t , rom the relative shift, et(z) (since E,(Z) is purelytransitory and has no impact on P,+J. In the Q-expression, 1 = 1 implies thatthe ~;a: interaction term vanishes, and the remaining terms can 5e combinedinto an interaction term between aez and /J20z+az = ai (as in eq. (24)). Inthis case the problem of separating permanent from transitory shifts in orderto forecast P, +1 amounts to separating aggregate from relative shifts.The other polar case is 2 = 0, which corresponds to the v, shifts being purelytransitory. In that case z?,and E,(Z)are generated by processes of the same formand the a$rf interaction term vanishes from the O-expression. The remainingterms can then be colmbined into an interaction term involving p2gi and a: + a~:.That is, the separation between permanent and transitory reduces in this caseto a separation between monetary and real.In the general case where 1 is in the interval between zero and one, all threeinteraction terms appear in the Q-expression. Individuals would then be con-cerned with the full separation of the current excess demand shift, pm, + v , +E, ( Z) ,nto its three components. The separation between permanent and transi-tory would entail two types of divisions of current excess demand shifts:aggregaie versus relative and monetary versusreal.

From the standpoint of monetary policy, the important aspect of the extendedmodel is that s2 is still a strictly increasing function of af. (This property can beverified from straightforward differentiation of the Q-expression.) Hence, thecompounding of the information problem to include a separation of monetaryversus real along with a separation of aggregate versus relative does not alterthe conclusion that monetary noise makes the information problem moredifficult.


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Finally, it can be noted that the extension of the model to a first-orderMarkov process for U, has been carried out within the framework where themonetary disturbance, m,, and the relative shift, e,(z), are purely white noiseprocesses. It would be possible to introduce some serial dependence into theseprocesses. However, it is already apparent from the above discussion of the U,process that the crucial consideration is the relation between the processesthat generate M,, U, and E,(Z). When these three processes assume differentforms there will be an information problem associated with dividing currentlyobserved excess demand shifts into its three components, The above case, inwhich the qprocess is first-order Markov (with 1 # 0 or I) and m, and E,(Z)are white noise, is r;ne way in which the processes for M,, u,, and E,(Z)can takeon different forms. Further alteration of the m, or e,(z) processes would notseem to change the basic picture, at least in terms of the implications for moneyvariance, 47:.Appendix 2: Systematic growth in money and output

This section extends rhe analysis of the text in two respects. First, the syste-matic growth rate of money, g in eq. (4), is allowed to be nonzero. Second, thegrowth rate of k,, the systematic part of excess demand which is defined as-&I in eq. (S), is allowed to be nonzero. It is clear that the introduction ofthese systematic growth elements (which are included in the information set,I,(Z)) would not affect the gap between actual and full information output.Therefore, the present discussion is limited to the effects of systematic growthon P,(z), W +1111w9 and J,(Z). The analysis here returns to the case where U,is generated by a random walk (1 = I, in the terminology of appendix 1).Formally, the extended mcjdel can be solved by the method of section 2.2 ofthe text if the solution form for P,(z) in eq. (6) is extended to include a timetrend and a canstant term - that is, R,t+&. Additional complications to thesystematic parts of M, and k, - foT example, io allow nonconstant growthrates - would be reflected as additional terms in the solution form for P,(z).Given the extended form of the solution, the procedure for solving the model 1;the same as that employed in section 2.2.The solution for P,(t) coincides with eq. (10) except for the inclusion ofsystematic effects associated with g and p. The extended result is

P,(Z) =: M,,,+I:+[0,+8,+(P/a)(l-01-82)][m,+(l/P)(u,+~t(z))]

Since AI,_ 1+g is now the fully perceived part of M,, this term has a one-to-oneeflect on P,(z). The -it term indicates that the systematic growth of k, atrate -Bp would generate a systematic growth in the price level at rate -pif 1M were constant. With IU growing steadily at rate g, the net systematic


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30 R.J. Elarr o, Ratio expectations and he role of monetary policy

growth rate of the price level is g- p. This systematic rate of inflation appearsadditionally in the term (c#)(g- p) as a positive effect on P,(z) for a givenvalue of the nominal money stock. Equivalently, systematic inflation reducesthe (expected) holding of real balances. I will discuss below the meaning of thefinal term, + p, in the P,(z) expression.The expected price level for next period is now

w+,p~~z) w-:+2g+(O*+e,)[m,+(l/P)(~,+&,(z))]

In particular, the gap between P,(z) and EP,+,[l,(z) now includes the term-(g-p), which is the negative of the systematic rate of inflation. In this modei,where commodity supply and demand depend on P,(z)- EP,,, l&(z). it is thiseffect of systematic growth that leads to influences on output.The solution for output is determined by substituting the price results intothe commodity supply or demand function, as given in eqs.-(1) and (2). Theresult for y,(z) coincides with eq. (15) except for the new systematic effects,

where the terms that appear in eq. (15) have been omitted. In determining out-put it is necessary to specify separately the syste,natic demand and supply,kf and kf, as well as the excess demand, k,. I assume that individuals plan thesystematic growth rate of real balances (real wealth) to equal the systematicgrowth rate of output. From the above expressions for P,(z) and EP,, #,(z),it is clear that the systematic growth rate of real balances is p. From the y,(z)expression it is clear that the systematic growth rate of output depends on thesystematic growth rates of kf and kf. The condition that the systematic growthof real balances coincides with the systematic growth of output thereforeimplies a condition on the time paths of kp and ki. Using also the conditionthat k, = -Bpt, and setting kd, = k, = 0 for convenience, it can be determinedthat

kf = PC1PA

Substitution into the above expression for us(z) yieldsY, r) = Pt - wlB)(g- p) + *

That is, the systematic growth rate of output is, indeed, equal to p.


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The other property of the output expression is that an increase in the syste-matic inflation rate, g-y, reduces output (both actual and full information)if H > 0. The mechanism is as follows. An increase in g-p implies a lower realrate of return on money, which is the only store ofvalue in the model. According-ly, there is a substitution effect that reduces current labor supply and raisescurrent consumption demand. 53 This shift raises output when H > 0 . Ofcourse, this scat of effect is operative here because money serves as the onlystore of value. Further, the present analysis does not deal with any benefitsof holding money that are associated with transaction costs. For these reasons,it seems that the present model is probably more useful for an analysis ofunperceived monetary change than for an analysis of systematic inflation.

Finally, I can now comment on the presence of the +p terms in the aboveprice expressions. In eqs. (1) and (2), excess commodity demand depends onexpected next periocis real balances, M, + EdM,+ 1 I,(z) - EP, +1 (l,(z). Thisformulation is reasonable as long as desired real balances are constant. Moregenerally, it is a gap between expected and desired real balances that wouldproduce an effect on excess commodity demand. It is now apparent that (desired)real balances grow at rate p in this model. If the effects of real balances onexcess commodity demand are adjusted to take account of this systematicgrowth in desired real balances, the +p terms would no longer appear in theabove price expressions. The expression for y,(z) would be unaffected by thisadjustment. Of course, no adjustment at all is required for the case in the textwhere p = 0 was assumed.s31n a life-cycle model these effects would also alter the distribution of wealth by age. 1have not dealt with this type of distribution effect.

ReferencesBarre, R-J., 1972,A theory of monopolistic price adjustment, Review of Economic Studies,January, 17-26.Barro, R.J. and H.I. Grossman, 1975, Money, employment, and inflation (Cambridge Univer-sity Press,Cambridge).Cairnes, J.E., 1873, The course of depreciation, in: Essays in political economy (Kelley,London).Friedman, M., 1953, The effects of a fu~l-employmcnt policy on economic stability: A formalanalysis, in: Essays n positive economics (University of Chicago Press, Chicago).Friedman, M., 1960, A program for monetary stability (Fordham, New York).Friedman, M., 1968, The role of monetary policy, American Economic Review, March, l-17.Gordon, R.J., 1975, Alternative responses of policy :o external supply shocks, Brookings Papers

on Economic Activity, no. 1.Graham, F.D., 1930, Exchange, prices and production in hyper-inflation: Germany, 19X-23 Princeton University Press, Princeton).Hall, R.E., 1975, The Phillips curve and macroeconomic policy, in : K. Brunner and A. Meltzer,eds., The Phillips curve and labor markets (North-Holland, Amsterdam).Lucas, R., 1972, Expectations and the neutrality of money, Journal of Economic Theory,April, 103-24.Lucas, R., 1973, Some international evidence on output-inflation tradeoffs, American EconomicReview, lune, 326-34.


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32 R.L Barr e, Rat i onal expectat rons and t he rol e of monet ary poli cyLucas, EL, 1975, An equilibrium model of the business cycle, Journal of Political Economy,December, 1113-44.Lucas, R. and L. Rapping, 1969, Real wages, employment, and inflation, Journal of PoliticalEconomy, September/October, 721-54.Mills, F.C., 1927, The behavior of prices (N.B.E.R., New York).Mortensen, D.T., 1975, Job matching under imperfect information, in: 0. Ashenfelter, ed.,Evaluating the labor market effects of social programs, forthcoming.Phelps, E.S., 1972, Inflation policy and unemployment theory (Norton, New York).Prescott, E.C., 1975, Efficiency of the natural rate, Journal of Political Economy, December.Sargent, T. and N. Wallace, 1974, Rational expectations and the theory of economic policy,presented at thz Seminar on Rational Expectations at the Federal Reserve Bank of Min-neapolis, October.Sargent, T. and N. Wallace, 1975, Rational expectations, the optimal monetary instrument,and the optimal money supply rule, Journal of Political Economy, April, 241-54.Simons, H., 1948, Economic policy ?or a free society (University of Chicago Press, Chicago).Taylor, J., 1975, Monetary policy during a transition to rational expectations, Journal ofPolitical Economy, October, 1009-22.Vining, D., 1974, The relationship between relative and general prices, unpublished.

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