inflation targeting in a st. louis model of the 21st century · 2019. 10. 17. · 1 andersen and...

1 Andersen and Carlson (1972)discuss the central role ofexpectations in the St. Louismodel. We further discuss theirmodeling of expectationsbelow.

FE D E R A L RE S E RV E BA N K O F ST. LO U I S

MAY/ JU N E 1 9 9 6

Inflation Targeting ina St. LouisModel of the 21st CenturyRobert G. King andAlexander L. Wolman

The St. Louis model of the early 1970s,as described by Andersen and Carlson(1972), was a small-scale monetarist

model of economic activity. Its structurewas sharply at variance with the frame-work of the major, larger scale macro-econometric models used for policyanalysis by the Federal Reserve, both at thetime of the inception of the St. Louismodel and today.

The St. Louis model had four majorfeatures:

• It was sufficiently small that onecould actually understand how itworked by looking at the model’sbehavioral equations and by con-ducting simulations of it.

• It could be used for policy analy-sis, specifically for studying the ef-fects of monetary and fiscal policyon inflation, output, and interestrates.

• The monetarist background of itsauthors meant that the model (1)focused on the quantity of moneyas the key measure of the stance ofmonetary policy and (2) containedstructural linkages from money toeconomic activity that are nowwidely accepted, including the cen-tral role of a long-run demand for

money that is a relatively stablefunction of a small number of variables.

• It combined short-run non-neutralityof changes in money with long-runneutrality, in line with the perspec-tive of Friedman and Schwartz(1963a and b).

With Lucas’ (1976) critique of policyevaluation, the St. Louis model was largelyabandoned by monetarists. The model fellvictim to the critique in a particularly rapidand complete manner because its buildershad stressed that it contained quantita-tively important effects of expectations.1

In this article, we construct a small-scale modern macroeconomic model thatcan be used to study the effects of alterna-tive monetary and fiscal policies in a man-ner consistent with Lucas’ recommenda-tions. That is, we build a rationalexpectations macroeconomic model inwhich the intertemporal optimizationproblems of households and firms are ex-plicitly described. We call this a St. Louismodel of the 21st century because we be-lieve it is the type of small-scale macro-economic model that will be systematicallyemployed for the purpose of policy analy-sis by central banks in the coming years.The model is monetarist in five specificways that it shares with the St. Louismodel:

• Our model contains a stable de-mand for money that is invariant toalternative monetary policies.

• It incorporates short-run non-neutrality of money with long-runneutrality.

• Frictions in the price-setting processyield a short-run non-neutrality ofmoney that is quantitatively andeconomically important.

Robert G. King is A. W. Robertson professor of economics at the University of Virginia. Alexander L. Wolman is with the Federal Reserve Bankof Richmond. The authors thank Marianne Baxter, Michael Dotsey, Marvin Goodfriend, and Peter Ireland for useful discussions during thepreparation of this article. We also received valuable comments during various presentations of it, particularly from Ben Bernanke, MichaelKiley, Preston McAfee, Edward Prescott, Julio Rotemberg, Christopher Sims, Mark Watson, and Michael Woodford.

MAY/ JU N E 1 9 9 6


84

• Once one takes into account antici-pated price change, these frictionslead to no quantitatively importantlong-run trade-off between inflationand real activity.

• Our model places a central empha-sis on expectations in consumptionchoices, investment decisions, assetvaluation, and price determinationin the tradition of Irving Fisher andMilton Friedman.

We use this model to study an impor-tant question in monetary economics thatis currently policy-relevant at centralbanks around the world: What are theconsequences of adopting an inflation-targeting rule for monetary policy? Weprovide detailed information on two ver-sions of this question. First, since mostcentral banks seek to target rates of infla-tion that are low by the historical stan-dards of their countries, we ask, What arethe benefits (or costs) of having a low rateof inflation? Second, since critics of infla-tion targets are frequently concerned thatthese may interfere with stabilization pol-icy, we ask, In a setting with sticky pricesand demand-determined output, how dothe responses of the economy to variousshocks differ from those which wouldoccur if prices were flexible?

Our model’s answers to these ques-tions are very monetarist. First, there aremajor benefits to setting low rates of in-flation. That is, Friedman’s prescriptionfor long-run monetary policy (setting thenominal interest rate to zero) approxi-mately holds in the long run of ourmodel economy even though we havesome imperfect market “frictions” of theform stressed by Tobin (1972a and b).Even if one does not go all the way to azero nominal interest rate, there are quan-titatively important long-run welfare gainsfrom moving from an inflation rate of 5percent to price stability (0 percent infla-tion). Second, under a regime of perfectinflation targeting (in which the path ofthe price level is specified exactly by themonetary authority), we find that the re-

sponses of our sticky price model are es-sentially identical to those of a flexibleprice economy.

Our analysis thus suggests that thereare major benefits to implementing an inflation-targeting regime with a low targetrate of inflation. To further explore issuesthat arise in the implementation of thisregime, we consider (1) the dynamic be-havior of the economy if a target path forthe price level is implemented with an in-terest rate rule and (2) the dynamic behav-ior of real activity if a credible, low infla-tion path is implemented immediately. Wefind that it is indeed feasible to implementa policy of targeting the path of the pricelevel with an interest rate rule. We alsofind that there is zero cost of immediatelyintroducing a credible low inflationprogram.

THE ST. LOUIS MODELCIRCA 1972

The St. Louis model of macroeconomicactivity was a small macroeconometricmodel containing five structural equations,as spelled out in Andersen and Carlson(1972): a total spending equation, a priceequation, a long-term interest rate equa-tion, a definition of anticipated pricechanges based on the long-term interestrate equation, and an Okun’s law (1962)link between an output gap and unem-ployment. In addition, in the back-ground, there were methods of measur-ing the trend level of real economicactivity and the normal level of unem-ployment.

Money Demand and ExpenditureThe centerpiece of the St. Louis

model was a total spending equation, putforward in Andersen and Jordan (1968),that linked the change in nominal grossnational product to four-quarter distrib-uted lags of changes in the nominalmoney stock and of high-employmentfederal government expenditures. Giventhat the effects of high-employment ex-penditures were small, this specification

MAY/ JU N E 1 9 9 6


85

was widely viewed as resulting from amonetarist specification of the demandfor money—one with an income elasticityof unity and an interest rate elasticity ofzero.

In the macroeconometric model, thisspecification was the econometric embodi-ment of the Friedman and Schwartz(1963a and b) method of taking nominalincome as proximately exogenous. It couldbe employed to discuss the effect of mone-tary changes on nominal income, as in Andersen and Jordan (1968), without dis-cussing the division of nominal incomeinto price level and real output.

Price AdjustmentAs elaborated in Andersen and

Carlson (1972), the St. Louis model em-ployed a price equation to describe the di-vision of nominal income into prices andoutput. That specification related thechange in the price level to two factors.First, anticipated changes in prices enteredwith a coefficient of 0.86, so that the priceequation was taken to be importantly in-fluenced by the beliefs of price setters. Sec-ond, a four-quarter distributed lag ofchanges in nominal income was includedas a measure of demand pressure in themacroeconomy.

The builders of the St. Louis modelcontrasted their approach with the ap-proach used to construct traditional priceequations, such as those presented byEckstein and Fromm (1968). Those whobuilt the St. Louis model emphasized thattheir tractable specification included im-portant expectations effects and permittedthe simultaneous determination of pricesand output. This latter feature was suffi-ciently novel, relative to the standardeconometric practice of relating pricechanges to real demand pressure measures,that it warranted extensive discussion byTobin (1972a and b) in his summary ofthe conference that led to the Eckstein(1972) volume. Since the coefficients onthe nominal demand variables summed to0.10, the model also implied a Phillipscurve—defined by Andersen and Carlson

(1972) to be the joint time paths of unem-ployment and inflation arising from theirmodel, which involved only a very smalleffect of sustained inflation on real activity.This small trade-off is contrasted withother contemporary studies such as de Menil and Enzler (1972), Klein (1972),Bodkin (1972), and Eckstein and Wyss(1972).

ExpectationsAn unusual feature of the St. Louis

model was its modeling of expectations.Andersen and Carlson (1972) stressed thatexpected prices played a key role in themodel and that their explicit specificationof an expectations mechanism allowedthem to explore the trade-off between in-flation and unemployment at various hori-zons. They used the long-term interest rateas an important empirical indicator of ex-pected inflation and, for this reason, alsoincluded a structural equation determiningthe long-term interest rate. The details oftheir expectations scheme were sharplycriticized by Gordon (1972) on theoreticaland empirical grounds, although manypractical macroeconomists now routinelyuse the long-term nominal interest rateas a guide to long-term inflation expec-tations.

A ST. LOUIS MODEL OFTHE 21ST CENTURY

Many of the structural equations ofour model economy are obtained bystudying the optimization problems ofhouseholds and firms. In addition, thestructural equations include resource con-straints and the policy rule of the centralbank.

Monetary Services andthe Demand for Money

In our model economy, there is a well-defined demand for money that one candetermine from a problem of cost mini-mization. That is, one can define a de-mand for money conditional on a pattern

of expenditure determined as part ofa more general utility maximizationproblem.

The demand for money stems from atransactions technology—a “shoppingtime technology” in the terminology ofMcCallum and Goodfriend (1987)—whichgoverns the amount of time that must bespent to undertake real consumption activ-ity within the period t of our discrete timesetup. This shopping time function speci-fies that time devoted to transactions activ-ity depends negatively on the ratio of theamount of real money balances (mt) tothe amount of real consumption expendi-ture (ct):

(1) ht = hmct

t .

Throughout, we use notation in whichlowercase letters refer to real variables anduppercase letters refer to nominal variablesso that mt is the quantity of real balancesand is equal to Mt /Pt, where Mt is the stockof money held during the period and Pt isthe price level.

The opportunity cost of a unit of timespent shopping is given by the real wagerate. The opportunity cost of choosing tohold a unit of money during period t is thediscounted value of interest forgone nextperiod, so that the rental price of a unit ofcash balances is

1+R

Rt

t

.2

Minimizing the flow real cost

wtht +1+

R

Rt

t

m t,

through selection of the quantity of realbalances accordingly requires that

(2) − wtDh ( m

ct

t ) (c1t) =

1+R

Rt

t

,

which implicitly defines the demand formoney. In this expression,

− Dh ( m

ct

t ),is the marginal time saving that arisesfrom holding an additional unit of cashbalances per unit of consumption expendi-ture. (We use Dh to denote the derivativeof the h function with respect to the ratiom/c, viewing it as a function of this singlevariable.) In our theoretical analysis, weassume that this time saving is diminish-ing in the ratio (m/c). Our empirical workjustifies this assumption.

Notice that if the real wage and realconsumption grow at the same rate andthe nominal interest rate is constant overtime, then our specification implies thatthere is constant “consumption velocity.”That is, there is no trend in the ratio m/c.In our empirical analysis below, we specifythat the function

Dh (m

ct

t ),takes a specific parametric form

Dh ( m

ct

t ) = − [ (m

ct

t ) / ]− 1_v ,

which then implies that

(3) ( m

ct

t ) = [ +1+

R

Rt

t(w

ct

t)] v.

This functional form for real moneydemand per unit of expenditure is close tothe constant elasticity structure that is fre-quently studied in the literature. Notably,if =0, then there is a loglinear money de-mand function,

log (mt) = log ( ) + (1−v) log (ct) − v log

+ vlog (wt ).

Rt

1+Rt

2 Our timing convention formoney demand embodies aview of the average cash bal-ance holdings as a durablegood (as in Friedman, 1969)and is best exposited as fol-lows. Suppose that the evolu-tion of bonds is

1+1Rt

Bt+1+Mt+Ptct =

Yt+Bt+Mt−1,

where Yt is some measure ofnominal income and Bt is thequantity of bonds maturing at t.Accordingly, the date t cost ofholding a unit of money from tto t +1(Mt ) is the discountedvalue of the interest foregone,

1+Rt

Rt

,

as in the text.

MAY/ JU N E 1 9 9 6


86

More generally, the parameter allowsthere to be a finite “satiation” level of realcash balances, m = [ ]−vc, which occurs asa limiting case when the nominal interestrate is zero. We choose this parametricform for the Dh(mt/ct) function because wewant to generate a demand for money thatis relatively conventional, while leavingopen the issue of whether there is a finitesatiation level of cash balances.

Consumption Demandand Labor Supply

Intertemporal utility maximizationleads to demand for consumption (ct) andsupply of labor (nt), given the allocationof time to shopping (ht) discussed above.Expected date t lifetime utility is given by

Et Ut Et

∞

∑j=0

ju(ct+j,lt+j),

where the momentary utility function im-plies that both consumption and leisure (lt)are goods. Later in the analysis we adopt aparametric specification of this functionthat has been much used in the real businesscycle literature.

Individuals choose contingency plansfor consumption, labor supply, real bal-ances, shopping time, and leisure to maxi-mize expected utility subject to a presentvalue budget constraint that links incomeand expenditure,

Et

∞

∑j=0

∆t, j Pt+jct+j ≤ Et

∞

∑j=0

∆t, jPt+j ×

[ wt jnt j 1

R

+t

Rj

t j

mt+j] + other wealth,

as well as a time constraint that restrictswork, shopping time, and leisure,

(4) nt+j + lt+j + ht+j =1.

In addition, as discussed above, thereis a technology linking shopping time tocurrent expenditure, ct and real cash bal-ances, mt. Since these specifications arestandard, we will review them relativelybriefly. First, in the present value budgetconstraint, we are discounting nominal

cash flows at date t+j by the discount factor∆t, j .3 Second, also in this expression, wehave real prices of work and cash balanceholding: wt is the real wage (Wt /Pt whereWt is the nominal wage) and the rentalprice of a unit of real cash is Rt /(1 + Rt),as discussed above. Third, the time con-straint includes time spent “shopping,” aswell as at working and at leisure: Marketwork is a residual given determination ofleisure demand from utility maximizationand time spent shopping from cost mini-mization.

Maximization of utility subject tothese constraints leads to the followingefficiency conditions for consumption,leisure, and money balances. These efficiency conditions are structural equa-tions of our small-scale macroeconomicmodel. Since they contain expectations,they must be evaluated as part of a complete rational expectations solution,but presentation of them provides uswith the opportunity to describe the main implications that they have, takingexpectations as exogenous. First, the efficient selection of consumption re-quires

(5) EtjD1u (ct+ j,lt+j ) =Λ t Et ∆ t , jPt+j

[1−wt + j Dh ( m

ct

t

+

+

j

j ) (mc2t

t

+j

j )],for j = 0, 1, . . . Second, the efficient selec-tion of labor requires

(6) Etj D2 u (ct+ j,lt+j ) =Λ tE t∆t , j [Pt+ jwt+j],

for j = 0, 1, . . . Third, the efficient patternfor cash balance holdings requires that

−wt+jDh ( m

ct

t

+

+

j

j )( c

1

t+j) =

1+R

Rt+j

t+j

,

for j = 0, 1, . . . In these expressions Λ t isthe Lagrange multiplier on the wealth con-straint and thus represents the lifetimeutility gain from an additional dollar ofwealth at t. We use the notation Diu to de-

3 In the interest of making themodel setup as simple as possi-ble notationally, we are being alittle cavalier about the role ofuncertainty. For certain cashflows, our discount factor islinked to one period interestrates by

t,j =[(1+Rt )...(1+Rt +j−1)]−1,where Rt is the nominal interestrate from t to t−1.

MAY/ JU N E 1 9 9 6


87

note the partial derivative of the utilityfunction with respect to its ith argument.

In the first of these efficiency condi-tions, notice that the shopping time tech-nology means that the Beckerian “fullprice” of a unit of consumption at date t+jinvolves a time cost of shopping,

∆t , jPt+j [−wt+j Dh (m

ct

t

+

+

j

j )( m

c2t

t

+

+

j

j )],as well as the standard market cost com-ponent ∆t, jPt+ j. In the second, notice thatthere is the standard equating of the costsand benefits of forgoing a unit of leisureand supplying it to the marketplace. To-gether with the lifetime budget constraint,these two equations implicitly determineconsumption and leisure demand at alldates in line with a “permanent income”approach to these two actions. The thirdcondition is the “money demand” costminimization condition discussed above.

Labor Demand, Investment, and Marginal Cost

As in Rotemberg (1987) and Blanchardand Kiyotaki (1987), we assume that firmshave some market power, behaving as mo-nopolistic competitors. (We contrast this toa perfect competition situation in someplaces below.) In this subsection, we focuson the structural equations arising from therepresentative firm’s decision problem thatconcern production, labor, and investmentdemand. In the next subsection, we focuson pricing implications. It is accordinglyuseful to think about breaking the firm intothree separate parts for planning purposes.

First, the production unit takes asgiven the output level of the firm and therental price of capital (a transfer pricefrom the investment unit): It determineslabor demand and capital demand so as tominimize cost. Second, the investmentunit takes as given the market prices of in-vestment goods and the rental price ofcapital: It determines investment so as tomaximize the value of the firm. The activi-ties of these two units are explored in this

section. Third, the pricing unit determinesthe price of the firm’s output, taking intoaccount demand conditions and costs.Throughout, the firm is taken to maximizethe expected present value of its profits,

E tVt = Et

∞

∑j=0

∆t , j [Pt+j yt+ j − Wt+j nt+j Pt+ j it+j],

subject to the production technology forits final product,

(7) yt+j = a t+j f (n t+j,kt+ j),

and the evolution equation for its capital,

(8) kt+j +1 − kt+ j = (it+j /kt+j)k t+ j kt+j,

where (i / k) is a positive, increasing andconcave function that embodies costs ofadjustment for the capital stock.

To describe decisions of the produc-tion unit, we employ standard microeco-nomic conditions for cost minimization.For this purpose, we assume that the out-put level is given at any arbitrary level

∧yt+j

and that capital can be rented at price Zt.Then, the static conditions for cost-minimization are:

(9) Ψt+ja t+jD1 f (n t+j,kt+ j )=Wt+j ,

and

(10) Ψt+jat+jD2 f (n t+ j,kt+j )=Zt+j ,

where Ψt+j is the Lagrange multiplier onthe constraint yt+j =

∧yt+ j and Ψt+ j accord-

ingly is interpretable as nominal marginalcost. The conventional solution to thisproblem implies that marginal cost is afunction of the level of output; the pro-ductivity shifter, a t+j ; and the factor prices,Wt+ j and Zt+j . It also depends on the formof the production function: We assumethat the production function (equation 7)is constant returns-to-scale, so that mar-ginal cost is independent of output andthus write Ψt+ j=Ψ (at+j ,Wt+j,Z t+j ) .

In terms of the decisions of the invest-ment unit, we assume that the firmchooses the optimal investment pattern tomaximize its present discounted value

MAY/ JU N E 1 9 9 6


88

given the rental price Z t+ j . This leads to apair of efficiency conditions,

(11) Pt =Qt D (it /kt),

and

(12) Qt =Et {∆t,1Zt+1+[ (ki t

t

+

+

1

1)−

ki t

t

+

+

1

1

×

D ( kit

t

+

+

1

1) +1 − ]∆t, 1Qt+1}.

In accord with the investment technol-ogy that Hayashi (1982) and others haveused to rationalize a Tobin’s q-theory of in-vestment, the first of these specificationsindicates that the investment rate it /kt isdetermined by the ratio of the (shadow)price of installed capital (Qt) to the price ofreplacement capital (Pt), that is, it is afunction of the ratio q = Q/P. The evolu-tion of Qt over time takes into account thediscounted value of rentals accruing in thefuture period, as well as the effect of capi-tal accumulation on next period’s capitalstock and adjustment costs.4

Price SettingThe price-setting structure that we em-

ploy follows Calvo (1983), in ways that arerecommended by Rotemberg (1987) and aresimilar to the recent work of Yun (1996).Firms are assumed to be able to change theirprices only in specific states of nature andmust otherwise satisfy all demand at thequoted price. As we will see, this latter re-quirement—that we treat as one of the insti-tutions of the marketplace—has importantconsequences for optimal price setting.

The price-adjustment event occurswith probability 1− so that with probabil-ity η the firm is stuck with a predeter-mined nominal price. Accordingly, the ex-pected time of price fixity is

(1− )1+ (1− )2+...+ n−1(1− ) + ... ,

which is equal to (1− ) −1. We assume thatthe average firm adjusts its price every

four quarters (once per year) so that=.75, but we also experiment with higher

values. The stochastic price-setting specifi-cation also implies a (stationary) distribu-tion of firms in terms of the time that theylast adjusted their price. The fraction offirms that last adjusted price j periods ago,

j, is given by j= (1− ) j.This price-setting specification cap-

tures two key features of price setting thathave been much emphasized by macro-economists working on price adjustment:The timing and magnitude of price adjust-ments vary widely across firms in waysthat appear stochastic to an outside ob-server. However, given that the probabilityof price adjustment η is exogenous in theCalvo setting, the frequency of price ad-justment cannot adjust to variations in thestate of the economy: It cannot change ei-ther with the average rate of inflation orwith the stage of the business cycle.5

We assume that firms are monopolisticcompetitors and that each faces a date tdemand schedule of the form

(13) ydj,t= dt (P∗

t−j /Pt ) − ,

if it last adjusted its price j periods agoand selected the price P∗

t−j .6 In this expres-sion, dt is a demand shifter that dependson the state of the economy and Pt is theaggregate price level that evolves accord-ing to

(14) Pt =[ ∞

∑j=0

j( ∗

Pt −j ) (1− )]( ).

Using the stationary fractions given above,the dynamics of the aggregate price level Pt

can be reduced to

(15) Pt = [(1− )(P∗t ) (1− )+ (Pt−1)

(1− )]( ),

where (Pt−1) (1− ) represents the influence ofthe prices ch a rged by the fraction of firm sthat do not currently change prices in periodt and (1− )(P∗

t) (1− ε) re p re sents the influence ofthe firms that do change prices in period t.

In this time-dependent price-adjust-ment framework, a firm that is rationally

11

11−

4 The introduction of investmentadjustment costs is not neces-sary to any of the main conclu-sions that follow from in ouranalysis below. However, as aconsequence of the evidencesummarized in Chirinko(1993), there is a good reasonfor incorporating this structuralaspect into a modern macroeco-nomic model.

5 Nevertheless, the Calvo setup isa natural starting point for ouranalysis: In Dotsey, King, andWolman (1996), we arguethat a somewhat more generaltime-dependent specification isformally a first-order approxima-tion to a richer state-dependentprice-adjustment model.

6 This specification requires thatwe view the consumption andinvestment goods as the sameconstant elasticity of substitu-tion “aggregator” of differenti-ated products. Blanchard andKiyotaki (1987) derive suchindividual product demand func-tions for a model with just aconsumption good.

MAY/ JU N E 1 9 9 6


89

setting its price in period t will choose to equate marginal revenue and mar-ginal cost in a discounted, expected value sense. Dynamic marginal revenuestemming from a change in the price isgiven by

Et

∞

∑j =0

∆t , j n j[(1− ) ydj, t+j ].

The form of this expression reflectsthe fact that the price at t j will remain atthe chosen level P∗

t with probability n j.Similarly, the dynamic marginal cost asso-ciated with a price change is

Et

∞

∑j=0

∆t , jj[(−ε)Ψt+j (P∗

t )− 1 ydj, t+j ].

We can simplify these expressions as inthe standard static case and then equatedynamic marginal cost and revenue to ob-tain a price that it is optimal to charge:

.

Three implications of this expressionare worth elucidating. First, if marginalcost were constant over time at the levelΨ, then we obtain

P∗= −1Ψ,

so that the ratio

= −1,

is interpretable as the markup just as inthe static case. Second, in the dynamicsetting, price setting is influenced by the scale of output (demand) unless theentire sequence of outputs in the numer-ator and denominator expressions arescaled by a common factor. Third, opti-mal price setting in the Calvo environ-ment involves forecasting both demandand costs.

Taking the price-setting rule (equation16) and the price index (equation 15) to-

gether, it is clear that there is long-run ho-mogeneity of nominal prices in terms ofnominal costs:

P=P∗= −1Ψ= −1 aD1

Wf (n,k)

.

Accordingly, as all of the other behavioralequations of our model are written in realterms, it follows that our model will dis-play long-run neutrality of money:Permanent changes in the quantity of Mwill ultimately affect prices and not output,even with short-run rigidity of prices.However, there will be a departure fromsuperneutrality, in that the same frictionsthat lead to (1) the demand for money and(2) the short-run rigidity of prices willmean that there will be real effects of sus-tained inflation. In the next section wequantify these real effects.

The Marginal and Average MarkupGiven that firms are charging different

prices in our setting, it is clear that therewill be different values of markups acrossfirms. We define the marginal markup asthat earned by firms which are currentlyadjusting price, that is,

∗t =P∗

t / Ψt .

We define the average markup as the ratioof the aggregate price level to marginalcost, that is,

t=Pt / Ψt .

In a steady state with zero inflation, bothof these constructions are equal to the sta-tic markup

=− 1

,

but in steady states with inflation or defla-tion, there will no longer be this equality.Similarly, in response to business fluctua-tions, the fact that part of the price level ispredetermined will lead to different time-series variation in the marginal and aver-age markup.

16( ) Pt* =

− 1

Etj =0

∞

∑ ∆t, jj Ψt + j dt + j t + jP

Etj =0

∞

∑ ∆ t, jj dt + j t+ jP

MAY/ JU N E 1 9 9 6


90

OPTIMAL INFLATIONPOLICY IN THE LONG RUN

A natural method for determining thetarget rate of inflation is to choose that rateof inflation which maximizes the welfare ofthe representative household. In this sectionwe conduct such an analysis for the “longrun,” defined as a steady-state situation inwhich all variables grow at constant rates inways that are consistent with the modeleconomy outlined in the previous section.We solve the equations of the model for thelink between inflation and welfare, isolatingthe factors that are important for determin-ing the long-run optimal inflation policy.

In models with perfect competitionand continuously adjusted prices, there isa presumption that the optimal inflationpolicy is that which makes the privatecost of holding money equal to the social cost of production, that is, a nominal in-terest rate of zero. Given a positive real interest rate, this condition represents aprescription for long-run deflation policythat was first made by Milton Friedman(1969). Friedman’s conclusion has beenreplicated in a wide range of theoreticalenvironments.

In particular, letting the rate of infla-tion be and the level of the real interestrate be r, it follows that the definition(1 + R) = (1 + r)(1 + ) and the Friedmanrule condition R = 0 together imply thatthe optimal rate of inflation should be

f = −1 +

r

r,

where the superscript indicates that this isthe Friedman rule level of the inflationrate. Long-term U.S. data compiled byIbbotson and Sinquefeld (1982) indicatesthat the average real return on Treasurybills is between 0 percent and 1 percent sothat this represents a recommendation forat most a small deflation.

Estimating the Welfare Gainsfrom Lower Inflation

One measure of the gains from lowerinflation may be computed as the time

savings generated as agents increase theircash balances, gains that are sometimesviewed as small. Following the provoca-tive work of Lucas (1993), there has beenmuch recent interest in the magnitudes ofthese gains. In this article, we use abenchmark estimate from Wolman(1996), the nature of which is displayedin Figure 1.

In the first step, the three-parametermoney-demand function (equation 3) is fit to annual U.S. time-series data over the 1915–92 period. Each annualobservation on the pair of ratios, m/cand (c/w)(R/(1 + R)), enters as a dot inthe top panel of Figure 1.7 The represen-tative individual holds cash balancesequal to 1.62 quarters of consumptionexpenditure at the sample mean (denotedby a “+” in the top panel of Figure 1).The values of , , and are chosen toprovide a best fit in a least squares sense,and the solid line in the top panel tracesout the fitted relationship. As it turnsout, the estimates indicate a satiationlevel of real cash balances. Cash balancesequal 2.7 quarters of consumption ex-penditure at the estimated satiation level,which is somewhat smaller than the maximum cash balances in the sample(about 3.3 quarters of consumption expenditure).

In the second step, we compute the time savings that arise as the infla-tion rate is lowered from a benchmarklevel of 5 percent per year. For this purpose, we employ the estimated param-eter values obtained in the first step andalso the sample average value of c/w over1915–92. That is, given the parameters,the marginal time savings at any level ofreal balances is

Dhm

ct

t = −m

ct

t /ζ− 1_

v .

Substituting in the formula for the realdemand for money from equation 3 andassuming that the real interest rate is in-variant to inflation, we can then deter-mine the time savings of moving from

7 The money stock is M1. Theinterst rate is a quarterly yieldon commercial paper. We formm/c as the ratio of nominalmoney to an annual nominalconsumption expenditure series(including durables). We thendivide by population andexpress the figure in terms ofquarterly time units by multiply-ing by 4. Similarly, we dividenominal quarterly per capitaconsumption by a nominalwage rate, measured as aver-age hourly earnings of produc-tion workers in manufacturing,in current dollars. The averagevalue of the resulting c/wseries indicates that a represen-tative worker requres 249hours of work per quarter topurchase consumption or about20 hours per week. In terms ofinterpreting Figure 1, however,the reader should know thatwe have rescaled c/w by divid-ing by average quarterly hoursworked. Additional details onthe data (and the data them-selves) are provided in a repli-cation diskette that you canrequest from the authors.

MAY/ JU N E 1 9 9 6


91

one inflation rate to another, which is theintegral of such time savings over the rel-evant range. The lower panel of Figure 1is the result of this computation. We findthat a movement from a 5 percent rate ofinflation to a 0 percent rate of inflationwould lead to a saving of about 5 hoursper quarter. Adopting the Friedman rulefrom an initial position of 5 percent infla-tion would lead to a saving of about 7 hours per quarter. For an individualworking 40 hours per week for 12 weeksin a quarter, these time savings representabout 1 percent of his time. Since the av-erage hours worked by an average work-age individual is lower, about 20 hoursper week, it follows that the time savingis roughly 2 percent.

The Markup and InflationIn models with monopolistic com-

petition and staggered price setting, econ-

omists have long suggested that the Friedman rule is not desirable. One argu-ment that is sometimes made for depart-ing from the Friedman rule is that themarkup of price over marginal cost may depend negatively on the inflationrate.8 Since higher levels of the markupdepress economic activity (acting like atax on factor supplies), the deflation envi-sioned by Friedman would have socialcosts, as well as social benefits. Thus,there is an open issue as to the level ofthe optimal rate of inflation within setupssuch as ours.

The average markup of price overmarginal cost that prevails in our economydepends on two factors,

(17)t=

Pt

t

=P

P*

t

t

P*t

t

.

These two factors are (1) the marginalmarkup (defined above as the ratio ofprice to marginal cost for firms that arefree to adjust their prices) and (2) theprice adjustment gap (defined as the ratioof the general price level to the pricecharged by firms that are free to adjust).

The price adjustment gap and inflation.In a steady-state situation, the price ad-justment gap is:

(18) PP

*t

t= .

This expression is obtained by evaluatingequation 15 in a situation where Pt and P *

t

are growing at the rate . If there is noinflation, then there is no price adjust-ment gap in the steady state—all firms arecharging P*. At a higher rate of inflation,it follows that Pt is less than P*

t: A priceadjustment gap emerges. This gap reflectsthe fact that higher inflation mechanicallyerodes the real value of markups and thuserodes relative prices set by firms in pastperiods.

We think of this price adjustment gapas a feature of sticky price models that is

(11

)

1 −

1 −1 +

1 (1− )

8 Several recent papers makethis point in differing settings.Benabou (1992) suggests thathigher inflation may raise theelasticity of demand in a searchmodel, thus lowering themarkup. In a model that sharesthe core neoclassical structureof this article, but uses a differ-ing pattern of price dynamics,Goodfriend (1995) also derivesa link between the markup andinflation.

MAY/ JU N E 1 9 9 6


92

Figure 1a,b

Time Cost of Inflation(a) Actual and Estimated Demand for Money

(b) Time Saved

emphasized by traditional econometricprice equations such as those developedin Eckstein and Fromm (1968). The im-plicit assumption in such studies is thatfirms set P*

t as a fixed markup over mar-ginal cost t. With such an assumption,there is a substantial effect of a sustainedinflation on the markup and on macro-economic activity (displayed in Figure 2).In the top panel, we display the implica-tions of equation 18 for the averagemarkup. To construct this diagram, we as-sume that there is a gross markup equalto 1.3 at zero inflation (so that the elas-ticity of demand , is 4.33). We also as-sume that = .75 (so that the averageduration of price fixity is a year). Higherrates of inflation erode the markup, whichapproaches zero at an annual rate of infla-tion of about 25 percent per year. Sincethe markup acts like a tax on real activity(as discussed in Blanchard and Kiyotaki,1987; Rotemberg and Woodford, 1991;and Goodfriend, 1995), declines in itslevel are associated with the substantialincreases in output shown in the lowerpanel of Figure 2.

Concretely, if the price adjustment gapwere the only structural feature of pricedynamics, then an increase in inflationfrom 5 percent to 10 percent would raiseoutput permanently by about 7 percent.

Effects of forward-looking price setting.In a situation of sustained inflation, how-ever, our model does not imply that priceadjusting firms behave in the manner thatunderlies Figure 2. In particular, the ratioof newly set prices to marginal cost—themarginal markup—is given by

(19)P*

t

t

=

−11 −

(1+(

r

1s)

+

(1

)

+ )1-×

1 −(1+

(

r

1s

+

)(1

)

+ )-

−1

.

This expression is a steady-state version ofequation 16 in which is the real growth

rate of the economy, rs is the real interest rate appropriate for discounting the firm’scash flows (given by the real rate of intereston the stock market, about 6.5 percent), and

−1,

is the markup that would prevail in the ab-sence of staggered price setting (that is,with = 0). The optimal pricing rulemakes this ratio depend positively on theinflation rate. A higher expected rate of in-flation leads firms to set a higher pricewhen they are free to adjust, principally be-cause they know that as long as their nomi-nal price remains fixed, inflation will erodeboth their relative price and the real valueof any markup established today. The for-mer erosion means there is increasing sub-

MAY/ JU N E 1 9 9 6


93

Figure 2a,b

Implications of the Price Adjustment Gap(a) Markup of Price over Marginal Cost

(b) Output Compared to Baseline of 5% Inflation

stitution toward a product as long as itsprice is fixed. The latter erosion means that per-unit profits fall for as long as aprice is fixed. Since firms must fill demandat posted prices, they attempt to counterthese two effects by setting higher markupsin the face of higher inflation rates.

The Approximate Optimalityof the Friedman Rule

A striking feature of our setup is thatthe Friedman rule is approximately opti-mal under a wide range of assumptionsabout the magnitude of price adjustment( ), the extent of the static markup

=−1

,

and the specification of the transactionstechnology. By approximate optimality, wemean the following. Since the transactionstechnology implies a satiation point for cashbalances, at the Friedman rule, there mustbe a zero loss to holding a slightly smalleramount of real cash balances. Thus, if themarkup can be reduced by slightly more in-flation at the Friedman rule (as it can for theparameters that we study), then there willbe an unambiguous welfare gain to increas-ing inflation from the Friedman rule.9 Al-though this point can be established for-mally, one needs a microscopic inspection ofthe welfare trade-off to find it in the experi-ments reported below: The maximum wel-fare point occurs very close to the Friedmanrule.

The benchmark case. To begin, thetop panel of Figure 3 shows the relation-ship between welfare in the steady stateand the rate of inflation for a benchmarkcase. In this benchmark case, we assumethat

= .75, =− 1

= 1.3,

and make other assumptions about thesteady state of the model presented in

Table 1. (These other parameter assump-tions are conventional in the quantitativebusiness cycle literature.) The referencepoint for our analysis is a situation of5 percent inflation, indicated by * inFigure 3.

In models that abstract from varia-tions in labor supply, a standard measureof welfare is the fraction of steady-stateconsumption that an individual wouldgive up to avoid a distortion (as in Lucas,1990). In our setting with variable laborsupply, we use the measure of welfare de-picted graphically in the lower panel ofFigure 3—the amount of additional con-sumption expenditure that could be pur-chased by an individual at an initial rela-tive price of consumption and leisure.10

Although we measure the change in fullincome along the vertical axis of thelower panel of Figure 3, valuing changesin leisure and consumption at a constantrelative price, we express the welfare ef-fect as a fraction of measured national in-come, so it is directly comparable toother measures of welfare losses ex-pressed as a fraction of steady-state na-tional income.

The salient features of Figure 3 aretwofold. First, as the rate of inflation fallstoward f = −1 percent from the referencelevel of = 5 percent there is a substan-tial increase in welfare. Fundamentally,this increase arises because there is a de-crease in shopping time when the nomi-nal interest rate falls and the associatedcost of money holding falls. Recent workby Lucas (1993) has documented themagnitude of these welfare gains ineconomies simpler than those studied inthis article, namely ones that abstractfrom variable labor supply, physical capi-tal accumulation, and staggered price setting. He finds gains on the order of 1.5 percent of national product, a usefulbenchmark for our discussion.

In our setting, the magnitude of the welfare gain to pursuing the Friedman ruleis 1.1 percent of national income. The gainto moving from 5 percent inflation to 0 per-cent inflation is about .8 percent of nationalincome. Second, Figure 3 also shows that

MAY/ JU N E 1 9 9 6


94

9 Michael Woodford and PrestonMcAfee each forcefully pointedout this conclusion to us duringpresentations of this paper.

10 This follows Baxter’s (1995)analysis of tax distortions in avariable labor supply setting.

there are quantitatively important welfarelosses from raising inflation from the bench-mark level of 5 percent: An increase in theinflation rate from 5 percent to 12 percentlowers welfare by 2 percent.

Interpretation. In Figure 1, there wasa gain from lowering inflation since thesociety economized on transactions time.In Figure 2, there was a gain from raisinginflation—inflation eroded markups andlower markups stimulated economic activi-ty. Given the magnitude of the real effectsin Figures 1 and 2, one would suspect astrong case for high inflation. Yet, whenthese two forces are combined (as inFigure 3), there is a strong case for low inflation.

The main reason for this striking finding is that the experiment displayed in Figure 2 leaves out the incentives firmshave to change their price-setting behaviorin a situation of sustained inflation. Thatis, in our model, a situation of positivesteady-state inflation involves two offset-ting displacements relative to price stabil-ity. The first is that inflation opens a priceadjustment gap, lowering the averagemarkup because

P

P*

t

t

<1.

The second is that the marginalmarkup rises with inflation as firms seekto avoid an erosion of their relative priceand markup. Figure 4 contrasts the overalleffect of inflation on the steady-statemarkup (dashed line) to the partial effectfrom Figure 2 that takes into account onlythe price adjustment gap (solid line).

There are two distinct regimes. Overthe range relevant for considering a de-crease in inflation relative to the bench-mark level of 5 percent, the averagemarkup is relatively unaffected by infla-tion: The incentives that firms have toraise the marginal markup are just offsetby the decline (via the price adjustmentgap) in the average markup.11 For thisreason, the welfare analysis of inflationcoincides with Friedman’s analysis. Overthe range relevant for considering in-creases in inflation relative to its bench-

MAY/ JU N E 1 9 9 6


95

Table 1

P a r a m e t e r s

Figure 3a,b

Steady State Welfare(a) Welfare Compared to Baseline of 5% Inflation

(b) The Welfare Measure

Own price demand elasticity 4.33Probability price does not change 0.75Multiplicative term in h ( ) function 0.01156Curvature of h ( ) function 0.8004Shift term in h ( ) function 0.0011

sn Labor share 2⁄3Quarterly depreciation rate 0.025Investment adj. cost parameter 2− ((i/k) ( ′′/ ′))(−1)

Quarterly real growth rate (3 percent annually) 0.0074Quarterly inflation rate (5 percent annually) 0.0122Utility discount factor (quarterly) 0.9917Utility function: u(c,l ) = ln(c ) + 2.47⋅ln(l )

mark level, significant increases occur inthe average markup. This response stemsfrom an even larger effect on the mar-ginal markup, that in turn reflects suffi-cient demand response to the real pricedeclines associated with inflation thatfirms choose to increase the marginalmarkup dramatically to avoid theprospect of satisfying unprofitable de-mand in the future.

Sensitivity analysis. We now present abrief sensitivity analysis. Six dimensions ex-ist along which it seems natural to explorethe robustness of the relationship betweenwelfare and inflation depicted in Figure 4.

• How different is the size of the costof inflation in our sticky price, mo-nopolistically competitive settingfrom that in a flexible price, per-fectly competitive setting?

• How would this cost be overesti-mated if one viewed price setters as myopic, in the same way we did in constructing Figure 1 and as was frequently done in traditionalKeynesian macroeconometric models?

• How different would the costs of in-flation be if the economy weremuch less competitive?

• How sensitive is the cost of inflationto higher values of , that is, tomore inertia in prices?

• How is the cost of inflation affectedby eliminating the inflation distor-tion between consumption andleisure?

• How sensitive is the cost of inflationto our assumption that there is a sa-tiation level of real cash balances?

The six panels of Figure 5 display theanswers to these questions. In each panel,we use the dashed line to re p resent the re s u l t sf rom the benchmark case and a solid line tore p resent those from the case under study.

Variations in competition, price rigidity,and forward-looking behavior. In conduct-ing the first four alterations in the model,we assumed that the economies were eachcalibrated at a 5 percent inflation rate, so that the new and old lines all rotatethrough the 5 percent inflation point. Inpanel A the effect of moving to perfectcompetition and flexible prices is shown:There is minimal difference. In panel B weprovide a case similar to that underlyingFigure 2 in which price setters are assumednot to be forward-looking: It is the singlecase we have found of a setting in whichthere is a case for increased inflation (avery strong one). In panel C we see the ef-fect of raising the static markup from 1.3 to3: The effect is to slightly increase the wel-fare benefit from reducing inflation. Theanalysis of Goodfriend (1995) can be usedto explain this result. With less competi-tion (higher ), the wage rate is a smallerfraction of labor’s marginal product andoutput is correspondingly further below its efficient level. Thus, when labor flowsout of transactions activity and into pro-ductive activity, there is a larger welfaregain. In panel D we see the effect of raisingthe expected duration of price setting from4 quarters to 10 quarters, that is, the effectsof an increase in from .75 to .8. There islittle effect on the benefits from lower infla-tion but a larger increase in costs of higherinflation.12

MAY/ JU N E 1 9 9 6


96

11 For the parameter values weuse, the markup is decreasingwith inflation in a neighborhoodof the Friedman rule. This leadsto the approximate optimalityresult discussed in the introduc-tion to this section.

12 The = .8 value is an upperbound for our analysis, givenour demand parameter ( or

). With higher values of ,there is a sufficiently large costof getting stuck with a fixedprice that it is optimal not toopen a firm. This example indi-cates an unfortunate tensionbetween matching short-runprice dynamics and longer runinflation responses in the Calvomodel, one reason for the gen-eralizations considered inDotsey, King, and Wolman(1996).

Figure 4

The Markup and Inflation

Variations in the money demand speci -fication. In panel E we show the effect ofeliminating the implications that themoney demand function has for the fullprice of consumption: We set the term

wt+jDhm

ct

t

+

+

j

j m

c2t

t

+

+

j

j ,

to zero in the expression (equation 5) foroptimal consumption. We view this as thetraditional neoclassical and monetarist procedure of ignoring the implications ofthe cost of money holding for the full price

of consumption—it is used, for example, inmost textbooks with strong neoclassical underpinnings, such as Bailey (1971), Barro (1990), and Abel and Bernanke(1992). However, this assumption is the polar opposite of that made in cash-in-advance models of money, where the trans-actions technology implicitly makes varia-tions in the ratio of consumption to moneyinfinitely expensive in terms of time. Thatis, in the cash-in-advance analysis of Cooley and Hansen (1992), there is only afull price effect of inflation, not a time re-

MAY/ JU N E 1 9 9 6


97

Figure 5 a–f

Sensitivity Analysis(a) Perfect CompetitionWelfare

(b) Price Adjustment Gap OnlyWelfare

(c) Static Markup 3Welfare

(d) Stickier PricesWelfare

(e) Full Price EffectWelfare

(f) No Satiation Level of RealBalancesWelfare

allocation effect associated with costly sub-stitutions in transactions activities designedto avoid the inflation tax. Panel E showssmall differences in our cost of inflationmeasure for small rates of inflation, butthese become more pronounced as the infla-tion rate increases. Thus, the traditionalneoclassical and monetarist procedure is agood approximation for small and moder-ate inflations, but it would likely not be forhyperinflations. In panel F, we investigatethe effect of ruling out satiation in real bal-ances (imposing the restriction = 0 whenestimating the money demand function).Lucas (1993) imposes such an assumptionthat has the effect of making the Friedmanrule exactly rather than approximately op-timal.13 However, in other ways it has little effect on our welfare computations.

INFLATION TARGETINGAND BUSINESS CYCLES

Having established that benefits to tar-geting a low rate of inflation exist in thelong run, we turn next to evaluating how apolicy of inflation targeting influences thedynamic response of our economy to vari-ous shocks. For this purpose, we use a per-fect inflation targeting scheme in which thecentral bank is presumed to manipulate themoney supply each period so as to achieveexactly the target rate of inflation (an an-nualized 5 percent rate of inflation in ourexperiments). Then we ask how real activ-ity responds to productivity and money de-mand shocks that we take to be two majorsources of disturbances. We model these asrandom walk shocks because we thinkthese are largely permanent in nature.

The motivation for this part of the in-vestigation is to see what gains or losseswould arise if the central bank could targetthe inflation rate accurately. In particular,we are concerned with whether price-leveltargeting introduces major gaps relative tothe real outcomes that would arise if therewere perfect price flexibility. The bottomline is that it does not, according to both“eyeball” and formal welfare measures. In fact, compared with a policy of money supply targeting, inflation targeting

succeeds in eliminating these gaps. To un-derstand this result, it is necessary to understand how real activity responds to shocks under money supply targeting.Our analyses of productivity and moneydemand shocks thus begin with this case.We subsequently discuss how and why re-sponses differ under inflation targeting.

Productivity ShocksFigure 6 displays the impulse response

functions to a permanent productivityshock of output, consumption, investment,hours, the average markup, the real wage,the real interest rate, and real balances, as-suming that the money growth rate is heldconstant.14 The dashed lines describe a flexible price economy ( = 0), and the solid lines describe a sticky price economy( = .75). To explain the marked differencesbetween the two sets of curves, it is helpfulto decompose the average markup as in thesection on estimating the welfare gains fromlower inflation. We can use the decomposi-tion (equation 17) at any date to write theaverage markup as,

(20)– t =

——1−

1 P*t

t

,

also recognizing that the price levelevolves according to equation 15 to describe the price adjustment gap as a function of the current and past pricelevel.

Productivity shock dynamics under afixed money supply rule. Under a fixedmoney supply rule, we find the intuitiveresult that a permanent productivity shockwill raise output (Figure 6, panel A) andlower the current price level from its trendwhen prices are flexible. Since capital andconsumption grow slowly toward the newsteady state, a situation of sustained defla-tion is shown in Figure 6: This is to be in-terpreted as the price level rising at lessthan the benchmark 5 percent rate.

If prices are sticky, there is also pres-sure for deflation. Accordingly, the firstterm in the markup expression (equation

1 −1 − (Pt−1/Pt)(1− )

13 That is, the slope of the solidline is infinitely negative at

f in Lucas’s analysis ratherthan slightly positive as in ouranalysis.

14 The impulse response functionsin Figures 6 to 10 were gener-ated by linearizing the modelaround its deterministic steady-state growth path, using thesingular linear system methodsdetailed in King and Watson(1995a and b).

MAY/ JU N E 1 9 9 6


98

MAY/ JU N E 1 9 9 6


99

Figure 6 a–h

Money Supply Targeting, Response to a Permanent Productivity Shock_ _ _ _ _ 0 _______ .75

(b) Investment% Deviations

(c) Consumption% Deviations

(d) Labor Input% Deviations

(e) Markup% Deviations

(f) Real Wage% Deviations

(g) Real Interest Rate% Deviations

(h) Real Balances% Deviations

(a) Output

20) rises when the price level falls, in-creasing the markup: This is the flip sideof the inflation erosion effect discussed inthe section on the price adjustment gapand inflation. Since the productivity shocklowers marginal cost at date t and in all fu-ture dates, there is a relatively small effecton the marginal markup component

P*t

t

.

The average markup rises in response to the productivity shock. A rise in themarkup (Figure 6, panel E) implies an in-crease in the wedge between the marginalproduct of labor and the real wage (Figure6, panel F). Since the wedge will eventu-ally return to its steady-state level, there isa strong substitution effect that causeslabor input (Figure 6, panel D) to fall inthe impact period.

The direction of the effect on laborcontrasts with the case in which prices areflexible and markups never deviate fromε/(ε−1). In this case, labor input rises asagents capitalize on the temporarily highreal interest rate. Thus under a moneysupply target, a sticky price economy re-sponds to shocks in a qualitatively differ-ent manner than a flexible price economy.

Productivity shock dynamics with a per -fect inflation target. The results differ sub-stantially when there is a policy of perfectlytargeting the inflation rate. Figure 7 displayscomparable impulse response functions inthis case (the target inflation rate is 5 per-cent). A glance at Figure 7 reveals that, un-like the money growth target case, there isno qualitative difference between the re-sponses under fixed and flexible prices. Theaverage markup decomposition is againhelpful in understanding this result. Be-cause inflation targeting prevents shocksfrom affecting the price level, it eliminatesthe price adjustment gap channel—the firstterm in the decomposition—so that there isno tendency for the markup to rise (Figure7, panel E). With the markup essentially un-changed, the real wage fully inherits the in-crease in productivity. Thus, a major com-ponent of the substitution effect acting to

decrease labor supply disappears and, as inthe flexible price model, hours rise in accordwith the opposing substitution effect of atemporarily high real interest rate (Figure 7,panels F, D, and G). Thus, perfect inflationtargeting effectively makes a sticky-priceeconomy behave like a flexible price econ-omy: The key is that inflation targeting in-troduces a monetary accommodation thatavoids the necessity for the price level to fallin response to permanent productivityshocks.15

Money Demand ShocksFigure 8 displays the results of a perma-

nent shock to the demand for money underfixed money supply and price level paths,with the latter being equivalent to the out-come under flexible prices just as it was inresponse to a technology shock. Our moneydemand shock corresponds to a change inthe cash balance efficiency condition suchthat there is a 1 percent higher demand forreal balances at given levels of consumption,the real wage rate and the nominal interestrate. An important difference is evident be-tween the two sets of results shown in Fig-ure 8: An increase in money demand pro-duces a decline in output if there is a fixedpath of money, whereas it has no effect onoutput if policy is geared toward a stabiliz-ing the price level.

IMPLEMENTATION ISSUESWe next discuss two sets of issues

that would be a necessary part of imple-menting a policy rule like that discussedabove. First, we ask whether it is possibleto use the nominal interest rate as an instrument to implement a policy of controlling the price level in our modeleconomy. Second, we investigate the con-sequences of immediately transiting to alower inflation rate.

Implementation with an InterestRate Instrument

Many central banks employ a short-term interest rate as the instrument by

15 A formal welfare comparisonsupports the conclusion thatsticky price and flexible priceeconomies are not very differ-ent under perfect inflation tar-geting. To produce this measurein an earlier draft of the article,we determined the welfareeffect of a shock using thedynamic equivalent of the mea-sure described in the section onoptimal inflation policy in thelong run and illustrated in thelower panel of Figure 2. Linearapproximation methods wereused to compute these welfarechanges that are related to themeasure of the Hicksian wealtheffects of shocks produced inKing (1993).

MAY/ JU N E 1 9 9 6


100

MAY/ JU N E 1 9 9 6


101

Figure 7 a–h

Inflation Targeting,Response to a Permanent Productivity Shock

0(o) .75(+)


(a) Output







MAY/ JU N E 1 9 9 6


102

Figure 8 a–h

Response to a Permanent Money Demand ShockInflation Target (o) Money Supply Target (+)


(a) Output







which monetary policy is implemented. Toconsider how our economy might respondto such an operating policy, we posit amonetary policy rule of the form:

Rt = f ⋅[log(Pt) − log(P t)],

log(P t) = log(P t t) + .

The first of these specifications indicatesthat the monetary authority raises theshort-term nominal interest rate in re-sponse to increases in the general pricelevel (Pt) relative to its trend path (P t),since we assume that the parameter f ispositive. The second of these specificationsis our earlier requirement that the pricelevel grow at a fixed target rate of infla-tion.16 In Figure 9, we reconsider the re-sponse of the macroeconomy to an in-crease in productivity under this rule,distinguishing between a strong and weakpattern of response.17

If the central bank follows a rule that requires it to respond strongly to deviationsof the price level from its target path, then it actually must respond very little, and theeconomy’s behavior closely resembles thatunder a perfect inflation target (these out-comes are the “o” path in Figure 9). Tounderstand this rule, it is important to recalla very small (maximum seven basis points)response of the real interest rate under per-fect price level targeting. Accordingly, bykeeping the nominal rate essentially con-stant, the central bank can accommodatethe productivity shock and keep the pricelevel close to its target path. In this case, the post–Lucas-critique structure of themodel is important. The interest rate policykeeps the price level close to the target be-cause agents understand that deviationsfrom the target would trigger large interestrate variations. This credible threat impliesthat such interest rate variations need neveroccur.

However, if the central bank respondsonly weakly to departures from the targetpath, then an overshooting of componentsof real activity may occur in response to aproductivity shock. Essentially, in this set-ting, the central bank allows a gap be-

tween the actual and target price level toemerge as a result of the productivityshock—given that the real interest ratewould rise under perfect inflation target-ing, the policy rule makes the price level(not shown) rise initially in response tothe shock, lowering the markup and rais-ing real quantities. Later the price levelfalls back to the target path, but this is oflittle consequence for real activity since itis largely forecasted by private agents.

Thus, when policy is implemented bymeans of an interest rate instrument, theeconomy’s response to shocks is highlysensitive to the specific form of the policyrule. Since rules involving interest ratesare inherently dynamic, understanding theimplications of different policy settings re-quires an understanding of the patterns ofexpectations generated by the rules in re-sponse to a shock.

Timing of ImplementationIf a central bank seeks to lower the in-

flation rate in the long run through an inflation targeting rule, are there importantcosts of immediate implementation? Inother words, should a gradual approach todisinflation be preferred to an immediateone within our model economy? Advo-cates of gradualism sometimes argue that a recession will result from abrupt disin-flation.

Figure 10 shows the results of an ex-periment of lowering the annual rate of in-flation from 5 percent to 3 percent undertwo alternative schemes. Under an infla-tion rule, there is no transitional outputloss from disinflation—there is simply asmall gain in real activity as labor flowsout of transactions activity and into theproduction of final goods. This outcomeresults from the structure of price dynam-ics in the Calvo model, as previously dis-cussed by Buiter and Miller (1985) andBall (1994). Inflation can readily jumpfrom one of the steady states (consideredabove) to another—there are no importantinertial forces governing the inflation rate,as opposed to the price level, within ourmodel economy.

MAY/ JU N E 1 9 9 6


103

16 McCallum (1981) makes itclear that such interest ratepolicies are a feasible mode ofcentral bank behavior so longas policy is conducted so as toproduce a nominal anchor forthe price level. Fang, Kerr, andKing (1995) show that aninterest rate policy will result inunique outcomes so long asf > 0.

17 We chose these values[ f = 500 (strong policy) andf = 0.1 (weak policy)] to pro-duce clear graphics that illus-trate the nature of the policyrule.

MAY/ JU N E 1 9 9 6


104

Figure 9 a–h

Interest Rate Rule, Feedback from Price Level, Response to a Permanent Productivity ShockStrong Feedback (o) Weak Feedback (+)








(a) Output% Deviations

However, as indicated by the pathsmarked money supply rule, there are im-portant consequences of a change in themoney growth rate—as distinguished froma change in the inflation rate—within themodel. Since a lower long-run inflation ratewill stimulate the demand for money, thepath of the price level must fall if there is adecline in the long-run rate of monetarygrowth. The process of transition from ahigh price level path to a lower one can beassociated with substantial declines in eco-nomic activity, as Figure 10 makes clear.

SUMMARY ANDCONCLUSIONS

We have explored the costs and benefits of inflation targeting in a mod-ern macroeconomic model of the link between nominal and real variables. Fromthe St. Louis model of 1972, we took an emphasis on monetarist specificationof money demand, as well as of the im-portance of expectations in price setting.From recent developments in macroecon-omics, we took the money demand func-tion as arising from a specific transac-tions technology, rational expectations,and explicit dynamic modeling of con-sumption, labor supply, investment, andprice setting. More specifically, we fol-lowed work by Calvo (1983), Rotemberg(1987), and Yun (1996) in modeling aneconomy that combines short-run pricestickiness with rational decisions of firms.We used our setup to evaluate the poten-tial costs and benefits of a policy of tar-geting the inflation rate.

Our conclusions are in line with thoseof earlier monetarists—Irving Fisher,Milton Friedman, and the builders of theSt. Louis model. We found that the targetrate of inflation should be set at a lowlevel. At current U.S. levels of inflation,the benefits from low inflation (that is, theeconomy reduces its time spent makingtransactions) are first order and the fric-tions associated with imperfect competi-tion and gradual price adjustment are sec-ond order. We also found this perfectinflation targeting policy produces re-

sponses to productivity and money de-mand shocks that are in line with thosewhich would arise in a flexible-price econ-omy. Finally, we briefly explored two is-sues associated with the implementation ofan inflation targeting policy, showing thatit can be implemented with an interest rateinstrument and that there can be an imme-diate disinflation without adverse conse-quences for real economic activity.

MAY/ JU N E 1 9 9 6


105

Figure 10 a–c

Permanent Disinflation(a) Output

(b) Money Stock

(c) Price Level

This study of an inflation-targetingpolicy leaves open many interesting ques-tions. First, our analysis of price dynamicsfollowing Calvo was relatively rudimentaryin terms of the stochastic structure ofprice adjustment. A more complete analy-sis would permit a richer time pattern ofanticipated adjustment and also permitthat time pattern to respond to the state of the economy, specifically to the averagerate of inflation. Second, our analysisleaves open the important question of howa regime of imperfectly credible inflationtargets would operate. Third, it would be useful to pose the counterfactual ques-tion, What would have been the welfaregains if the United States had been on aninflation-targeting regime during the post-war period? These topics are the subject ofour continuing research into inflation tar-gets within a St. Louis model of the 21stcentury.

REFERENCESAbel, Andrew B., and Ben S. Bernanke. Macroeconomics. Addison-

Wesley, 1992.

Andersen, Leonall C., and Keith M. Carlson. “An Econometric Analysis ofthe Relation of Monetary Variables to the Behavior of Prices andUnemployment,” in The Econometrics of Price Determination, OttoEckstein, ed. Board of Governors of the Federal Reserve System,1972, pp. 166–83.

_____ and Jerry Jordan. “Monetary and Fiscal Actions: A Test of theirRelative Importance in Economic Stabilization,” this Review (October1968), pp. 29–44.

Bailey, Martin J. National Income and the Price Level: A Study inMacroeconomic Theory, 2nd ed. McGraw Hill, 1971.

Ball, Laurence. “Credible Disinflation with Staggered Price Setting,” The American Economic Review (Vol. 84, 1994), pp. 282–89.

Barro, Robert J. Macroeconomics, 3rd ed. Wiley, 1990.

Benabou, Roland. “Inflation and Markups: Theories and Evidence fromthe Retail Trade Sector,” European Economic Review (Vol. 36, 1992),pp. 566–74.

Blanchard, O. J., and N. Kiyotaki. “Monopolistic Competition and theEffects of Aggregate Demand,” The American Economic Review(September 1987), pp. 647–66.

Bodkin, Ronald G. “Wage and Price Formation in Selected CanadianEconometric Models,” in The Econometrics of Price Determination, OttoEckstein, ed. Board of Governors of the Federal Reserve System,1972, pp. 369–85.

Buiter, Willem H., and Marcus H. Miller. “Costs and Benefits of an Anti-Inflationary Policy: Questions and Issues,” in Inflation and Unem-ployment: Theory, Experience, and Policymaking, Victor E. Argy andJohn W. Neville, eds. London: Allen and Unwin, 1985.

Calvo, G. A. “Staggered Prices in a Utility-Maximizing Framework,”Journal of Monetary Economics (September 1983), pp. 383–98.

Chirinko, Robert S. “Business Fixed Investment Spending: A CriticalSurvey of Modelling Strategies, Empirical Results, and PolicyImplications,” Journal of Economic Literature (Vol. 31, 1993),pp. 1,875–911.

Cooley, Thomas F., and Gary D. Hansen. “Tax Distortions in aNeoclassical Monetary Economy,” Journal of Economic Theory(December 1992), pp. 290–316.

de Menil, George, and Jared J. Enzler. “Prices and Wages in the FRMIT-Penn Econometric Model,” in The Econometrics of Price Determination,Otto Eckstein, ed. Board of Governors of the Federal Reserve System,1972, pp. 277–308.

Dotsey, Michael; Robert G. King; and Alexander L. Wolman. “StateDependent Pricing and the Dynamics of Business Cycles.” Manuscript,University of Virginia and Federal Reserve Bank of Richmond, 1996.

Eckstein, Otto, ed. The Econometrics of Price Determination, Board ofGovernors of the Federal Reserve System, 1972.

_____ and Gary Fromm. “The Price Equation,” The American EconomicReview (Vol. 58, 1968), pp. 1,159–83.

_____ and David Wyss. “Industry Price Equations,” in TheEconometrics of Price Determination, Otto Eckstein, ed. Board ofGovernors of the Federal Reserve System, 1972, pp. 133–65.

Fang, Justin; William Kerr; and Robert G. King. “Limits on Interest RateRules in the IS Model.” Manuscript, University of Virginia, 1995.

Friedman, Milton. The Optimum Quantity of Money, and Other Essays.Aldine Publishing Company, 1969.

_____ and Anna J. Schwartz. A Monetary History of the United States1867–1960. Princeton University Press, 1963a.

_____ and _____. “Money and Business Cycles,” Review ofEconomics and Statistics (February 1963b), pp. 32–78.

Goodfriend, Marvin S. “A Framework for the Analysis of ModerateInflations.” Manuscript, Federal Reserve Bank of Richmond, 1995.

Gordon, Robert J. “Discussion of Papers in Session II,” in TheEconometrics of Price Determination, Otto Eckstein, ed. Board ofGovernors of the Federal Reserve System, 1972, pp. 202–12.

Hayashi, Fumio J. “Tobin’s Marginal q and Average q: A NeoclassicalInterpretation,” Econometrica (January 1982), pp. 213–24.

Ibbotson, Roger, and Rex Sinquefeld. Stocks, Bonds, Bills and Inflation: ThePast and the Future. The Financial Analysts’ Research Foundation, 1982.

King, Robert G. “Value and Capital in the Equilibrium Business CycleProgram,” Value and Capital: Fifty Years Later, L. McKenzie and S. Zamagni, eds. London: MacMillan (1993), pp. 279–309.

MAY/ JU N E 1 9 9 6


106

_____ and Mark W. Watson. “The Solution of Singular LinearDifference Models Under Rational Expectations.” Manuscript, Universityof Virginia, 1995a.

_____ and _____. “System Reduction and Solution Algorithms forSingular Linear Difference Systems Under Rational Expectations.”Manuscript, University of Virginia, 1995b.

Lucas, Robert E., Jr. “Econometric Policy Evaluation: A Critique,”Carnegie-Rochester Conference Series on Public Policy (Vol. 1, no. 21976), pp. 19–46.

_____. “On the Welfare Cost of Inflation.” Manuscript, for theHitotsubashi International Symposium of Financial Markets and theChanging World, 1993.

_____. “Supply Side Economics: An Analytical Review,” OxfordEconomic Papers (April 1990), pp. 293–316.

McCallum, Bennett T. “Price Level Determinacy with an Interest Rate Ruleand Rational Expectations,” Journal of Monetary Economics (Vol. 8,1981), pp. 319–29.

_____ and Marvin S. Goodfriend. “Theoretical Studies of the Demandfor Money,” in The New Palgrave: A Dictionary of Economics; JohnEatwell, Murray Milgate, and Peter Newman, eds. Stockton Press,1987, pp. 775–81.

Okun, Arthur M. “Potential GNP: Its Measurement and Significance,”Proceedings of the Business and Economic Statistics Section of theAmerican Statistical Association, 1962, pp. 98–104.

Rotemberg, Julio J. “The New Keynesian Microfoundations,” NBERMacroeconomics Annual. MIT Press, 1987, pp. 69–104.

Tobin, James. “The Wage-Price Mechanism: Overview of theConference,” in The Econometrics of Price Determination, OttoEckstein, ed. Board of Governors of the Federal Reserve System,1972, pp. 5–15.

_____. “Inflation and Unemployment,” The American EconomicReview (March 1972b), pp. 1–18.

Wolman, Alexander L. “Three Essays on Monetary Economics.”Unpublished dissertation, University of Virginia, 1996.

Yun, Tack. “Nominal Price Rigidity, Money Supply Endogeneity, andBusiness Cycles,” Journal of Monetary Economics (Vol. 37,1996), pp. 345–370.

MAY/ JU N E 1 9 9 6


107

inflation targeting in a st. louis model of the 21st century · 2019. 10. 17. · 1 andersen and...

Documents