The Quantitative Analytics of the Basic Neomonetarist Model
Author(s): Miles S. Kimball
Source: Journal of Money, Credit and Banking, Vol. 27, No. 4, Part 2: Liquidity, Monetary
Policy, and Financial Intermediation (Nov., 1995), pp. 1241-1277
Published by: Blackwell Publishing
Stable URL: http://www.jstor.org/stable/2078048
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MILES S. KIMBALL
The QuantitativeAnalytics of the Basic
NeomonetaristModel
A GREAT DEAL OF MACROECONOMICRESEARCHin the last
decade or two has been motivatedby a lively debate over whetheror not prices are
sticky and whether and how much money matters. What are the lessons those who
have not been active partisanscan take away from this debate?I cannot claim true
impartiality,because of my saltwatergraduateschool backgroundon one side and
my attractionto the elegance of the Real Business Cycle pictureof an economy of
optimizing agents responding to the fundamentaleconomic forces of preferences
and technology on the other. But like a bystanderto the battlewho moves amongthe
dead and woundedto see what valuableshe can gather,I have triedto collect things
of worth from both sides. Thus, this paperis meant to stimulatediscussion, not to
be the final word on anything.
I will argue that a hybridmodel should be taken much more seriously a model
following the Real Business Cycle paradigmas closely as possible except for adding
what is logically necessary in orderto graft in sticky prices. In orderto avoid implicating either the New Keynesians or the New Classicals in my crimes, I will call
such a hybrid model grafting sticky prices into what would otherwise be a Real
Business Cycle model a "Neomonetarist"model. Such models are not unknown
in the literature for example, King (1991) and Cho and Cooley (1992) study models with both imperfect price flexibility and Real Business Cycle elements but
they have not been studied by as many people with as great intensity as other models. To justify more attentionto such hybridmodels, I must defend the assumption
of sticky prices and defend the essence of the Real Business Cycle approach.
The main reason to be interestedin sticky prices is that they provide one of the
few means of generatinglarge monetarynonneutralities.The basic evidence for the
MILESS. KIMBALL
is associateprofessorof economicsat the University
of Michigan.
Journalof Money,Credit,andBanking,Vol. 27, No. 4 (November 1995, Part2)
Copyright 1995 by The FederalReserve Bank of Cleveland
1242 : MONEY, CREDIT,AND BANKING
existence of large monetarynonneutralitiesis the evidence assembledby Friedman
and Schwartz(1963), togetherwith events afterthe end of their sample, such as the
Volcker deflation. The details of the historical record discussed by Friedmanand
Schwartz (1963) have persuadedmost macroeconomiststhat there has been a substantialexogenous componentto the timing of monetarypolicy and sometimeseven
the direction of monetarypolicy based on the personalitiesand the inner workings
of the FederalOpen MarketCommitteeandthe FederalReserve System more generally. The most exogenous shifts in monetarypolicy seem to have the clearesteffects.
Such historical evidence for the potency of monetarypolicy is also available for a
host of other countriesas well.
Despite considerableeffort, therehas been little success at generatinglarge monetary nonneutralitiesin flexible-price models using plausible parametersfor anything short of a hyperinflationarysituation. The basic problemis that, if prices are
perfectly flexible, the monetaryservices subsector(which is a small partof the financial services sector) looks a lot like any other type of service subsector in the
economy. Shortof massive bank failuresor hyperinflation,the fractionof a percent
share monetaryservices have in GDP1 is simply too small for what happensto this
sector to be a big deal if prices areperfectlyflexible. (Duringhyperinflations,monetary services as a share of GDP do become substantial,sometimes rising above 10
percent of GDP.) By contrast, if prices are sticky, what happens in the monetary
services sector can distortthe decisions of firms in all sectors of the economy that
have sticky prices.2
Real business cycle researchhas sometimes (thoughnot always) been pursuedin
opposition to the idea of sticky prices, but this approach has many important
strengthseven if one is willing to entertainthe idea thatprices are sticky. Real Business Cycle research has consistently taken dynamics, sensible anticipationof the
future, quantitativecalibrationand the welfare implications of models very seriously. As a result, even simple real business cycle models are rich in quantitative
dynamic implications. The agreementon the basic real business cycle model of
Prescott(1986) as a benchmarkallows researchersto comparetheirresultsandcommunicatein a productiveway as they modify one or two featuresof the basic model.
Explicit, disciplined modeling opens the possibility of unexpectedresults.
Real business cycle models may be oversimplified,but it is hardto dismiss the
forces identifiedin such models as importantcontributorsto what is going on. Firms
may not always minimize costs, but a tendency toward cost minimizationsurely
governs much of what happens in the economy. All households may not be rationally forwardlooking, but an importantfractionof households surely do condition
1. The amountpaid for monetaryservices in proportionto GDP is equal to the rate of foregone interest times MIPY = 1/V. An M1 velocity of 6, coupled with an averageforegone interestof 5 percentfor
the componentsof M 1 would lead to a shareof less than 1 percent(5/6 percentin this case) for monetary
services in GDP.
2. The literaturedoes give some examples of theoretical models that have large monetary nonneutralitieswith perfectly flexible prices and no informationproblems, but these are models with multiple equilibriaor very fragile equilibriain which small costs of price adjustmentwould have an even easier
time generatinglarge monetarynonneutralities.
MILESS. KIMBALL :
1243
their decisions in importantways on expectationsaboutthe future. Householdsmay
not be on their labor supply curves at every instant,but they surelyresist fluctuating
too far off their labor supply curves for too long. Thus, it seems folly to ignore the
economic forces highlightedin real business cycle models even if one wishes to add
othermechanismsto a model as well. It is particularlydifficultto thinkaboutinvestment in a sensible way without borrowingsome of the rationalexpectationsapparatus.
In additionto presentinga hybridmodel, I will try to hint at a joint researchprogram for New Keynesiansand real business cyclists. In both approaches,the key to
explaining economic fluctuationsis constructinga model with plausibleparameters
that allows for a strong response to shocks. In both approachesthe key model elements generatingresponsivenessof the economy to shocks are things like favorably
shapedfirmdemandand cost curves, positive externalities,and a fairlylarge macroeconomic elasticity of labor supply. The challenge of adequatelyjustifying such
roodel elements provides plenXty
of scope for a joint researchagenda.
1. THE MONETARYAND PRICE-ADJUSTMENTSIDE OF THE NEOMONETARISTMODEL
In this model I will use two kinds of approximationsin orderto focus on the most
importanteffects and to have a model that is easy to understand.First, I will make a
certainty-equivalenceapproximationthroughout,and focus on linearizing or loglinearizingaroundsteady-statevalues.3 I will use an asterisk(*) to denote a steadystate value, a tilde (-) to denote the deviationof a variablefrom its steady-statevalue, and a hacek (-) to denote the logarithmicdeviationof a variablefrom its steadystate value.
Second, I will look at a Taylorexpansion based on the typical length of time a
price is fixed being relatively short.4This greatly simplifies many expressions in a
very intuitiveway. In fact, this fast-price-adjustment
approximationis a formalway
to justify something akin to the classical dichotomy a way to justify separating
slower-moving growth and fluctuations induced by real factors from higherfrequency fluctuationsinduced by monetaryfactors. I will call the aspects of the
model that determineits short-runfluctuationsin response to monetaryfactors the
"monetaryand price adjustment"side of the neomonetaristmodel. In the light of
this approximateclassical dichotomy,I will call the otherside of the model based on
3. Although this is adequatefor a first pass at studying the responses of variables to shocks in the
Neomonetaristmodel, it precludes a serious welfare analysis of changes that affect the varianceof output. The fact thatunderimperfectcompetitionmore outputis typically beneficial socially means that the
influence of departuresfrom certaintyequivalence on mean outputmattersfor such a welfare analysis.
For instance, it is not inconceivablethat more variableoutputcould induce enough extra saving through
precautionaryeffects thatthe resultinglargermean capital stock and highermean outputcould more than
compensatefor the direct cost of higher varianceon welfare.
4. One advantageof working in continuoustime is that it highlightsthe questionof how long a price
is likely to be fixed. In discrete time models it is all too temptingto dodge this issue by assuming that
prices are set for "one period"without any serious thoughtgiven to whether"one period"is in fact the
likely length of time for which a price is fixed.
1244 : MONEY, CREDIT,AND BANKING
real relationshipsthatwould hold among symmetricallyacting firmsandhouseholds
the "classical"side of the model.
1.1. Money Demand and Supply
With velocity V assumed exogenous in the monetaristspirit, the identity
MV= PY
gets some real bite. M, of course, is the money supply, Y is aggregateoutput, andP
is the aggregateprice level. This equationdeterminesaggregateoutputas
y_
MV
P
'
or in logarithmicdeviations,
Y = M + V-P
.
(1)
I assume thatthe shareof money services in GDP is negligible, so thatthe money
market only really mattersbecause of its interactionwith sticky prices. This is a
situations.
reasonableassumptionin non-hyperinflationary
At this point, we alreadyhave an aggregatedemandcurve, (1), and a short-run
aggregatesupply curve, which is horizontalat the price P. The point of this paperis
to derive the dynamics of these curves and to study the action going on behind the
scenes of the aggregatesupply-aggregate demandgraph.
1.2. Price AdjustmentDynamics
I will use Calvo's (1982) model of price adjustmentin continuoustime. The biggest single reasonfor doing so is thathere, in a model thathas otherimportantcomo
plicating features, it seems wise to focus on the time-dependentsetting of fixed
prices for the sake of tractability.
Let me at least explain why I emphasize sticky prices ratherthan sticky wages.
The less importantreason is thatwage stickiness tends to yield counter-cyclicalreal
wages that are not apparentin the data. A deeper and much more importantreason
for the focus on price stickiness as opposed to wage stickiness is the view I share
with many other macroeconomists(both New Keynesian and New Classical) that
most employment takes place as partof a long-termimplicit contractin which the
wage observedat any given time is only an installmentpaymenton what the implicit
contractsays is due to a worker.Therefore,the observed wage does not accurately
representafirm's labor costs. Truemarginallaborcosts are a matterof the additional amounta firmis implicitlypromisingto pay a workersomedayin returnfor working an additionalhour. Given long-termimplicitcontracts,sticky-lookingwages are
a convenience for both workers and firms and can even have an insurancerole to
whichare technically first order, but these eSects wouldvanish as (x
w
MILESS. KIMBALL : 1245
play, but they have little bearing on true labor costs. Traditionalmodels of sticky
wages requirenot just sticky observed wages, which are easy to justify, but sticky
labor costs, which are very difficultto justify.
The Evolution of the Aggregate Price Level. In Calvo's (1982) model, each firm
gets the chance to consider and adjustits price at an intervaldeterminedby a Poisson process, with the chance to adjustthe firm'sprice arrivingwith probability(xper
unit time. Because all firms are identicalexceptfor thefixed prices they have at the
moment, each firm that gets the chance to change its price at a given time will
choose the same new price, which I will call the optimal resetprice and denote pt.
Firms that have fixed prices and can only change them at idiosyncraticrandom
intervalswill unavoidablyend up with differentprices wheneverthereare any fluctuations. The appropriateglobal aggregatefor these differentprices can be quite complex. But because of the underlying symmetry between the various firms, even a
complex price aggregate is equal, to a first-orderapproximation,to a simple, unweighted arithmeticaverage(and to a simple, unweightedgeometricaverage)of all
the prices. The interactionof a firm's change in its price and any departureof the
quantityweight for thatprice from symmetrywith the quantityweights for all of the
other firms' prices is a second-ordereffect. Thus,
.
Pt
=
(2)
S
(X[pt-Pt]
since price changes take place at the Poisson rate(x from variousprices averagingPt
to the optimal reset price pt. If the initial steady state has zero inflation,5 then
p* = P*, and all of the deviationsin (2) can be convertedto logarithmicdeviations
by dividing (2) throughby P*:
Pt=
(X[pt
Pt]
(3)
The Optimal Reset Price. Given the chance, a firm chooses its reset price p at
time t by maximizing the expected presentvalue of profits:
max Et ,( e f t (rg+(x)dt'H ( fC' t' ) dtt
where Et is an expectationover all the events other than the arrivalof the chance to
reset one's price, conditional on informationat time t, is the real interestrate at
time t", and II is the flow of real profitsas a functionof the firm's price relative to
the aggregate price at time t'. The dependenceof real profitson everythingelse is
representedby the second (time) argumentin II. The profitsare discountedby (x as
well as r because the currentreset price will last for a length of time t'-t only with
probabilitye-(x(t -t).
rt,,
5. Trendinflationcould result in interactionsbetween price changes and asymmetricquantityweights
o =(pt,
' (P#
t') t')'(1, '(1t') t')+ H"(1,
+ "(1 t')t') [pt[p# _ -1] 1] . (5)
(6)
Ht
1246 : MONEY, CREDIT,AND BANKING
Using Il' to denote the derivative of [I with respect to its first (relative price)
argument,the first-ordercondition for the optimalreset price IS
-It
Jw
(r +a)d1't
, t )
H (p
t'
t
The certainty-equivalenceapproximationmakes the impulse-responsefunctionsthe
same as in a perfect-foresightmodel, so I will drop the exp-ectationsign Et. Linearizing marginalprofits arounda relative price of 1,
It is helpful to define the "wishedfor"or "desired"pricept# the price that would
be optimal at a particularinstantif the firm could costlessly choose a price for just
that instantwithout affecting what its price would be at any othertime. The desired
condition
pricePt#satisfies the instantaneousfirst-ordher
Subtracting(6) from (5) yields the approximation
(Pt S t )
H
(1,t ) ( tp Pt )
(7)
Substituting(7) into the first-ordercondition (4) with the expectationsign omitted,
one can then solve for the optimal reset price pt
' (
tr
-r,(r+a)dG'
J
t
t')
)d{' "(1
II
(l,
t ) dtt
(8)
Pt2,
In words, the optimalreset price is (to a linearapproximation)a weighted averageof
the desired price over the length of time until the next price decision, appropriately
discounted. Other than the discounting, the weight is the curvatureof the profit
function with respect to the relative price, divided by the squareof the aggregate
price level. The aggregateprice level is part of the weight because the higher the
aggregate price level, the less effect the firm's own price will have on its relative
price level. Given the simplifying assumptionof zero inflationin the initial steady
MILESS. KIMBALL : 1247
state, one can differentiate(4) with respectto time using Leibniz' rule and divide by
p*=(p#)*=P*
to get the following differential equation in logarithmic
deviations:
pt
=
(t
+
r*)[t-Pt#]
(9)
S
where r* is the steady-statereal interestrate.6
Equation(3) indicatesthatwhat mattersfor price dynamicsis the ratiopIP. Combining (9) with (3) implies in turnthat the growth rate of pIP is given by
dt ln(p/P) =
pt-P
= r*(p-P)
+ (ot +
r*)(P-p#)
*
(10)
To interpret(10), combine it with (3) and integrateusing the steady state as a
terminalcondition to get
Pt
(X(t
Pt)
= oz(oz+ r*)
rw
1 e-r*(t-t)[pt#,-Pt,]
dt'
.
(11)
That is, to a first-orderapproximation,the rateof inflationis proportionalto a present discounted value of the (logarithmic) "inflationaryprice gap" p# - P
ln(p# / P). Since the discountingin (1 1) is only at the steady-staterateof interestr*,
the Calvo model of price adjustmentimpties that the expected size of the inflationary price gap in the fairly distantfuture(say ten years down the road) can mattera
lot for inflationnow. Thus, the model would allow the aggregateprice level to move
in apparentlymysteriousways that might not seem to accord with the currentstate
of the economy, much as stock prices often move in mysterious ways because of
their dependenceon expectationsof the fairly distantfuture.
1.3. MarketStructureand the Desired Price
The next orderof business is to look at what determinesthe desiredpricep# and
the (logarithmic)inflationaryprice gap p#-P
between the desired price and the
actual aggregateprice.
In addition to depending on the level of outputin relationto "full-employment"
output, the desired price p# depends on the model's market structure, broadly
construed.
Models with sticky prices also tend to have imperfectcompetitionand increasing
returnsfor good reason. Sticky prices require imperfect competition in order for
6. See Kimball (1995) for more details.
1248 : MONEY, CREDIT,AND BANKING
firms to be price-setters.(Underperfect competition, each firm is a price-takerand
the only price-setteris the Walrasianauctioneer.)
Imperfectcompetition, in turn, is intimatelyconnected by economic logic with
internalincreasingreturnsto scale. Internalincreasingreturnsto scale makes firms
likely to get large enough that perfect competitionbecomes doubtful. Conversely,
unless entry is artificiallyrestricted,constantreturnsto scale would allow firms to
enter imperfectly competitive markets(which are attractivebecause price is above
cost) until those marketsapproachbeing perfectlycompetitive.
The Role of Imperfect Competitionin Business Cycle Models. Besides making
sticky prices possible, imperfectcompetitionhas a numberof other importantand
attractiveimplicationsfor business cycle models. First, for some, the fact that imperfect competitionmakes increasingreturnsto scale possible is a virtue.
Second, imperfect competition capturesthe intuition that, over some very relevant range, more outputis better.As Weitzman(1984) notes, the eagernessof firms
to sell extraunits of theirproducts(as evidencedby the considerableefforts devoted
to marketing)is primafacie evidence of price being above marginalcost and therefore of imperfectcompetitionin a wide range of industries.The eagerness of firms
to provide more at the given price avoids,-for the most part, rationingof supply by
firms. The eagerness of firms to provide more at the given price (a price at which
households and otherfirmsare not averseto buying) indicatesthatoutputis likely to
be socially too low.
Third, the existence of a markupof price over marginalcost raises the possibility
that the markupmight vary over the business cycle.
A countercyclicalactual markupis a likely consequence of sticky prices if marginal cost is procyclical and prices (because of their stickiness) are fairly acyclical.
The importanceof even these undesiredfluctuationsin the actual markupcannotbe
overemphasizedbecause the only importanteffects of nominal things on the real
equations of a neomonetaristmodel operate throughthe fluctuationsin the actual
markup.In other words, to a first approximation,knowing the actualmarkupalone
tells one enough to solve the model in real terms without knowing anything else
from the monetaryside of the model.
The Flexible VarietyAggregator. In large part because of the things discussed
above macroeconomistshave been quite interestedin the effects of marketstructure
on economic fluctuations "marketstructure"including both the shape of an individual firm's demandcurve and how the shape of the firm'sdemandcurve changes
in response to aggregate forces. Specific macroeconomicinvestigationsof the effects of market structureabound in the literature.Ratherthan try to deal directly
with the greatvarietyof models in the literature,I will use a model of marketstructure for which the main virtues are simplicity and flexibility in a few importantdimensions. I will not make any particularclaim to realism for this model of market
structurein and of itself. I will merely express the hope that it can representreasonably well the kind of effects one would see in a more realistic, more cumbersome
model.
MILESS. KIMBALL : 1249
First, for simplicity, I will assume no entry and exit of the differentiatedfirms
producingvaried products.
Second, I will assume that the differentiatedgoods can be combined into an aggregate in essentially the same way in investmentand governmentpurchasesas in
consumption. The consumptionvariety aggregatorthat relates the quantitiesof the
difFerentiatedconsumptiongoods to overall consumptioncan be seen as a reflection
of the household's utility function. Similarly,the (mathematicallyidentical)government purchases variety aggregatorcan be seen as a reflectionof the government's
objective function. But the (mathematicallyidentical)investmentvarietyaggregator
has to be interpretedas a reflectionof the productionfunctionfor assemblingcapital
from differentiatedintermediateinvestmentgoods.
Having these three variety aggregatorsbe mathematicallyidenticalis only a convenience. There is no reason in principlenot to have a differentdegree and shape of
imperfect competition for consumption, investment and governmentpurchases. If
the consumption, investment, and governmentpurchasesvariety aggregatorswere
allowed to differ, the compositionof aggregateoutputwould interactwith the differing nature of imperfect competition for each type of good. Moreover, one could
then expect to find a differentrate of price adjustmentin each of these three sectors,
requiringone to keep trackof three differentimperfectlyflexible prices.
Third, in order to finesse the thorny question of how one would determinethe
scale at which substitutionamong differentiatedgoods operates, I will assume constantreturnsto scale for the variety aggregator.This simplifying assumptionmeans
that I cannot model a desired markupthat dependson the overall scale of the economy. But my setup does allow the elasticity of demand and thereforethe desired
markup to depend on the ratio of an individualfirm's outputto aggregateoutput.
variety aggregatorthat is
In orderto have a symmetric, constant-returns-to-scale
otherwise quite flexible, let the aggregatequantityY be given by the implicit relationship
1=
rl
J
Y(yelY) dt,
(12)
o
where the quantitiesy of the differentiatedgoods are indexedby f on the continuum
from Oto 1, and the functionY satisfiesY(1) = 1, Y'(g) > OandY"(g) < O, for all
By construction, this variety aggregatoris symmetric in the differentiated
t-O.
quantitiesYe,so thatthe aggregatequantityYis determinedin a symmetricway. The
variety aggregatorhas constantreturnsto scale since if the equationis satisfied for
one vector of quantitiesYeand Y?then the equationwill continueto be satisfiedafter
the vector of quantitiesYe and aggregatequantityY are all multipliedby the same
constant.
The l:)emandCurve Facing the Firm. The demandcurve each differentiatedfirm
faces can be derived by looking at the optimalchoice of differentiatedquantitiesby
1250
: MONEY, CREDIT,AND BANKING
the household, government,or investmentgood assembler.The household, government, or investment good assemblerminimizes the cost of the intermediategoods
necessary to produceany given amount:
rl
min J PeYedt
Ye
0
s.t.
rl
1 = J Y(Ye/Y)dt
S
o
for given Y. The first-ordercondition for this problemis
Pe =
y
Y (y/Y)
(13)
for some value of the LagrangemultiplierA that is constantfor all t.
Theimportance
of (13) is thatthemodelallowsoneto generateanydesiredshape
of demandcurvefacing the individualfirm.
The only restrictionsare that the firm
demandcurve must be downwardsloping and thatthe firmmust get its normalmarket share at a relativeprice of 1 (symmetricwith all of the other firms). With an eye
to generatingsufficient"realrigidity"in the sense of Ball andRomer(1990) to make
sticky prices plausible, I will be especially interestedin firm demand curves that
have a smoothed-outkink at the firm's normalmarketshare making it easier for
the firm to lose customersby raising its relativeprice above 1 thanit is to gain customersby lowering its relativeprice below 1. By contrast,the commonlyused model of Dixit and Stiglitz (1977) restricts one to constant-elasticityfirm demand
curves.
The key aspects of the firmdemandcurve can be summarizedby the behaviorof
the implied elasticity of demand at various points. Writingg = Ye/Y,the inverse
elasticity of demandfor a differentiatedfirm is
1
e(()
_
d ln(p)
Yt dYe
_ Ye Y (yelY)
Y Y (YtIY)
Y'(g)
(14)
The elasticity calculation depends on the firm being an infinitesimalpart of the
economy, so that a change in its own price has a negligible effect on Y and A. It is
MILESS. KIMBALL : 1251
easy to find a varietyaggregatorY to matchany desireddependenceof the elasticity
of demand e on the firm's relative output(marketshare) (. Viewed as a differential
equationfor the function Y'(g), (14) has the particularsolution
Y (g) = exp (-
d4)
4;f(g;)
J;
The elasticity of demand matters for two reasons. First, the desired markup
>(y/Y) that the firm would use in calculatingits desired price is given by
(15)
1
6(Ye/Y)-
Second, the elasticity relates movementsin relativeoutputYelY to movementsin the
relative price pelP. Log-linearizing(13) aroundthe steady state, whereYe = Y and
Pe = PX
ln(ye/Y)
( 16)
-e * ln(Pe/P) ,
with et = e(YelYt) = e(1). Using logarithmic deviations from the steady state
(treated like differentialsfrom calculus) one can rewrite (16) as the locally exact
equation
Ye-Y=
(17)
-68(Pe-P)
1.4. Full EmploymentOutputand Desired Output
At this stage, it is helpful to representa firm'sreal marginalcost as a functionof a
firm's own outputy, aggregateoutputY, and everythingelse " ":
MC
<t>(
y
)
Since, in the model, capital is rentedratherthanbeing a fixed factor, marginalcost
need not dependon firmoutputy, thoughit may. AggregateoutputY affects a firm's
marginalcost throughfactor prices and perhapsthroughproductionexternalitiesas
well. In this paper "everythingelse" affectingmarginalcost is the capital stock and
the marginalvalue of capital, but in principle"everythingelse" could include exogenous variablessuch as technology.
For stability, a key assumptionwill be that at the steady state, the elasticity
fi
= y(t)y + y(t)y 1
¢
(ys ys )=(y*sy*s
*)
1252 : MONEY, CREDIT,AND BANKING
is positive; that is, factor price pressuresare sufficientto make real marginalcost
increase when aggregate output and firm output increase by the same percentage
(such as when thereis a balancedexpansionof every firm'soutputat the same time).
The elasticity of real marginalcost with respectto a balancedexpansionof outputis
importantbecause, in the short run, with all firms having given prices, the homotheticity of the variety aggregatorguaranteesthat a monetaryexpansioncauses just
such a balanced expansion of output. If the elasticity were sometimes negative, it
would mean that a monetaryexpansioncould lower real marginalcost a situation
that would make it easy to generatemultipleequilibria,with Q negative at unstable
equilibriaand positive at stable equilibria.Even low positive values of Q could have
dramaticimplicationsfor the behaviorpredictedby the model, but I will arguethat
Q is likely to be a substantialpositive number.
The desired relative price p#lP, and the desired relative outputy#/Y that goes
equals
along with it, must satisfy the condition that marginalrevenuep#l>(y#lY)
marginalcost P¢@#, Y, *). Thus, the desired relative price must equal the desired
mark-upratio times real marginalcost:
(
p#
#ly)¢(
y
#
(18)
)
In conjunction with (16), which must hold in particularfor p#lP and y#/Y, (18)
determinesp#lP andy# as functionsof aggregateoutputY and the other arguments
of ¢ summarizedby " ". Let me define "full employmentoutput"Yf to be the level
of aggregateoutputat which the desiredrelativepricep#lP iS 1 . If the desiredrelative price is 1, all firms could have the desired price without alteringthe aggregate
price. By (16), if the desiredrelativepricep#/P is 1, then the desiredrelativeoutput
y#/Y iS also 1. Thus, full employmentoutputYf iS the solution to
1 = >(l)¢(Yt,
(19)
Yt, ) .
Clearly,full employmentoutputis a functionof " " variableslike the capitalstock
and the marginalvalue of capital.
Dividing (18) by (19), log-linearizingaroundthe steady-state,then combiningthe
result with (17) yields the equation
0=
1 [y<#-Y]+p<#-P
- Y] + Q[Y-
= ()[y
Yt],
where
r
1
V e(Y/Y)
+(YIY)A'(Y/y)+Y¢Y8l
A(YIY)
'I) / l (y y )=(y*y*
*)
MILES S. KIMBALL : 1253
1
+
>'(1)
Ye,
YtSy(Yts
+
Y*,
b(Y*,
>(1)
et
*8)
*e)
Solving for y#-Y (the logarithmicdeviationof desiredrelativeoutput)in termsof
(the logarithmicdeviation of actual output from full employmentoutput),
Y-Yf
(20)
- Y = - O) [Y - Yf] *
Y
1.5. The Desired Price
The Notional Short-RunAggregate SupplyCurve. As noted above, the short-run
aggregate supply curve is just a fixed aggregate price P. However, (20) and (17)
togetheryield the equation
=
P#-P
*
(21)
*
[Y-Yt]
In words, the inflationaryprice gap is equal to *
times the "inflationaryoutput
gap" Y-Yf. Since the inflationaryprice gap is proportionalto the inflationaryoutput gap, the rate of inflationis proportionalto a present discountedvalue of either
inflationarygap. Substituting(21) into (1 1),
P, = e(et + r*)
*
A
e-r*(' -')[Y, -Yf
] dt' .
(22)
Graphically,one can think of (21) as a notionalshort-runaggregatesupply curve,
giving the desired price p# as a function of output. With the logarithmsof output
and price on the axes, the notional short-runaggregatesupply curve intersectsthe
actual short-runaggregatesupply curve at (log) full employmentoutputln(Yf), but
the notional SRAS has an upwardslope of
*
insteadof being flat. The vertical
distance between the notional and actual short-runaggregate supply curves is the
inflationaryprice gap. The rate of inflationis cx(cx+ rt) times a presentdiscounted
value of this vertical distance.
Interpretingthe Eftectsof MarketStructureon the Desired Price. To interpret(20)
and (21), think of the firm's marginalrevenue and marginalcost curves.7 Near the
7. Forthe sake of interpretation,it is also helpful to put the curves for desiredoutputand desiredprice
into the frameworkof Cooper and John (1988), making allowances for the fact that Cooper and John
(1988) is essentially static. Equation(20) implies thatthe "reactionfunction"for desiredfirmoutputas a
function of actual aggregateoutputis
*
[l
Q I y + Q yf
)
(continued
1254 : MONEY, CREDIT,AND BANKING
steady state, (1/et) is the rate at which the demand curve falls, expressed as an
elasticity. Since the desiredmarkupratio > tells how far the marginalrevenuecurve
is below the demandcurve, (1/et) + [>'(1)/>(1)] is the rate at which the marginal
revenuecurve falls, expressedas an elasticity.On the marginalcost side, (YtSy/¢)
is the rate at which the firm's marginalcost curve rises, expressed as an elasticity.
Thus, X is the difference in the slopes of the marginalcost and marginalrevenue
curves expressed as an elasticity or equivalently,X is the elasticity of MC/MR
with respect to y. A 1 percent increase in firm outputy makes the ratio of marginal
revenue to marginalcost fall by X percent.
At the macroeconomiclevel, Q = [Yt(by + by)/¢] is the elasticity with which
a proportionalincrease in both firm and aggregateoutputraises the firm'sreal marginal cost. On the marginalrevenue side, the firm's real marginalrevenue is not
affected at all by a proportionalincrease in both aggregateoutputand firm output.
By (16) and (15), the real price at which a firm can sell its output, and the markup
that tells how much lower marginalrevenue is, are both functionsonly of relative
output y/Y. Thus, Q is the elasticity of MC/MR with respect to the proportional
increase in both aggregateoutputand firmoutputcaused by a monetaryexpansion.
Now, consideran averagefirmwithy = Y thathas marginalcost equal to marginal revenuewhen aggregateoutputis at the full employmentlevel. If monetaryforces
cause a 1 percent increase in aggregateoutputabove full employmentoutput, with
the firm's output going up proportionally,the average firm's marginalcost will be
pushed Q percent above its marginalrevenue. Because the firm's price is fixed,
there is no paradoxin this gap between marginalcost and marginalrevenue. However, by definition, desiredoutputmust equatemarginalrevenueand marginalcost.
Since the elasticity of MC/MR with respect to the firm's output is , firm output
QIX percent below what one would get from a balanced expansion would restore
equality between marginalrevenue and marginalcost. As for the desired relative
price, firm output Q/ percentbelow what one would get from a balancedexpansion would be associated with an *
percentincreasein the firm'sprice relative
to the actual aggregateprice.
The verbal definitionsof X (as the elasticity of MC/MR with respect to firmoutput, holding aggregateoutputfixed) and Q (as the elasticityof MCIMRwith respect
to aggregateoutput when firm outputmoves proportionally)are more general than
the particularmodel at hand. It is worth paying attentionto these elasticities in a
wide variety of models with imperfectlyflexible prices.
"RealRigidity" and the OutputElasticities of MCIMR.Following Ball and Ro-
The coefficient of Y is the slope of the reaction function, and implies a multiplierof 1/(1-slope)
=
/Q. To get the "reactionfunction"for desiredprice as a functionof the actualaggregateprice, definePf
= MV/YforPf = M + V-Yf, so thatP-Pf =-(Y-Yf). Then
P
[
e*
|
e*
with a correspondingmultiplierof e*X/Q. Since the optimalityof the firm'sprice in steady state implies
that e* > 1, the slope of the "reactionfunction"and the multiplier(both of which measurethe degree of
strategiccomplementarity)are greaterfor a price game thanfor an outputgame.
APFCPR * * [_
(y
_
yf)2
+
(o
4
(Ye-y)2
dW] (23)
MILESS. KIMBALL : 1255
mer (1990), it is easy to relate the elasticities Q and X to the cost of price rigidity.
Ball and Romer'sphrase"realrigidity"refersmost directlyto a change in aggregate
output having little effect on a firm's desired price, and so can be identified here
with a small value of * , ie elasticityof the desiredpnce with respectto aggregate
output.
The "deadweight loss" trianglegiving the approximateprivateflow cost of being
away from desired output has a base of length approximately[Ye-y#]Y*
and a
height of approximately[Q(Y-Yf) + (Ye-Y)]MRt.
Using (20) and averaging
over all firms, the average private flow cost of price rigidity (APFCPR) is
approximately
Of course, the averageprivate flow cost of price rigidity is second-order the one
second-order quantity that I will examine in this paper. The second part of the
APFCPR, involving the cross-sectionalvarianceof output, depends on the history
of the economy and so is difficult to analyze fully.8 However, I conjecture that
at least part of the cross-sectional variance in output will be related to the variance of movementsin y# - Y, which is proportionalto (Q/X)2 times the varianceof
[Y-Yf]. Thus, the second partof the APFCPRis likely to depend on Q and X in
much the same way as the first part.9In any case, a substantialpartof the average
private flow cost of price rigidity is proportionalto Q2/X. As Ball and Romer suggest, this means that a small privatecost of price rigidityis typically associatedwith
"realrigidity" a small elasticity of theSdesiredprice with respectto aggregateoutQ
put, * .
One fact that would not be apparentfrom readingBall and Romer (1990) is the
way in which a high initial elasticity of demandet lowers the elasticity of the desired price with respect to output. But in theirown terms, Ball and Romerdo make
clear the dependenceof both "realrigidity"and the privatecost of price rigidity on
Q and .
The macroeconomic elasticity Q incorporatesall of the effects of factor price
pressure on marginalcost as output increases. Ball and Romer (1990) look at the
possibility of lowering Q by increasingthe macroeconomiclabor supply elasticity
and therebyreducingfactor price pressurecaused by increasedoutput.
In general, the elasticity Q may also include a negative effect from production
8. Ball and Romer(1990) make the second partof the APFCPRinvolvingthe cross-sectionalvariance
of outputzero by using a static model in which all firms startoff at the same place.
9. Steady-stateinflation would introducean additionalreason for cross-sectional variance in prices
and outputs. The part of the cross-sectional variationin output due to steady-stateinflation should be
roughly proportionalto the elasticity of demande times the amountof inflationthat would take place in
the averagelength of time a price is fixed, all squared.This partof the cross-sectionalvarianceof output
could vary independentlyfrom the two elasticities Q and .
1256 : MONEY, CREDIT,AND BANKING
externalities and a negative effect from mechanisms that generate countercyclical
desiredmarkups.In the particularmodel at hand, the desiredmarkup> is acyclical,
but many models exist that generatecountercyclicaldesired markups.
The microeconomic elasticity X incorporatesall aspects of increasingmarginal
costs and decreasingmarginalrevenuethat are internalto the firm. Ball and Romer
(1990) show that having workers strongly attachedto firms ("the yeoman farmer
model") instead of being hired on the spot market leads to a lower privatecost
of price rigidity. This is because when workersare stronglyattachedto firms, labor
costs dependonfirm output- a dependencethataddsto X (as well as Q). If workers
are always hiredon the spot market,laborcosts dependonly on aggregateoutputa dependencethat adds only to Q, not . The same principlewould say that having
capital strongly attachedto a particularfirmratherthanbeing hiredon the spot market would also reduce the privatecost of having sticky prices.
The microeconomic elasticity X also includes any dependence of the desired
markupon the firm's relative output or marketsharey/Y. Ball and Romer (1990)
look at the possibility of using Woglom's (1982) model of customer marketsto
make the elasticity of demand(and thereforethe marginalrevenuecurve) fall sharply with the firm's marketshare (since it is harderto get new customersthanto drive
away old ones). This correspondsto a desired markupthat is sharplyincreasingin
the firm's marketsharey/Y- somethingthat could make X quite large. In the Neomonetaristmodel at hand, it is easy to find a variety aggregatorY that yields a desired markupthat is sharply increasing in each differentiatedfirm's marketshare,
reproducingthe most essential implicationof Woglom's (1982) model of customer
markets.
2. THE SHORT-RUNDYNAMICS OF THE NEOMONETARISTMODEL
Combining(10) with (21) and the QuantityEquationY = M + V-P
,-P
= r*(p-P)
+ (ot + r*)(P-p#)
= r*(f-P)
+ (ot + r*)
*
[P + Yf-M-V]
.
yields
(24)
The fast-price-adjustment
or high-cxapproximationimpliesthatthe endogenousmovements in full employmentoutput Yfare slow in comparisonto the price adjustment
dynamics. Therefore,treatingfull employmentYfas exogenous yields a reasonably
good approximationfor the short-rundynamicsof the model. The detailed analysis
of the fast-price-adjustmentapproximationcan be found in Kimball(1995). lO
With Yf, M and V treated as exogenous, (3) and (24) together form a dynamic
system in P and the (log) relative reset price p-P.
In matrixform,
10. Calculatedto a higherorderof approximationthanis neededhere, it involves takingthe derivative
of eigenvectors with respectto changes in the dynamicmatrix(in orderto make a Taylorapproximation).
MILESS. KIMBALL : 1257
[ p-P
(ot + rt) *
]
[ p-P
rt
]
_
_
(25)
( + r*) e*i) (Ft-M-V)
The absolute value of the negative eigenvalue of this matrixgives the convergence
rate s:
iC =
+
4(r4)
cx. N
Q
°f(°^+ rt) - 2
8
The approximationfor s on the second line ignores everythingthat is not at least of
ordercx. The most interestingaspect of this equationis that the convergence rate at
which the economy returnsto full employment after a permanentchange in M depends approximatelyon the squareroot of * , the elasticity of desiredprice with
respect to aggregate output. Thus, a high degree of "real rigidity" in Ball and
Romer's (1990) sense makes price adjustmentslow in comparisonto the frequency
cxat which individualfirmsadjusttheirprices. If *
is less than 1, aggregateprice
adjustmentwill be slower than cx, the microeconomic rate at which firms get a
chance to adjusttheir prices.1l
If cxis varied to hold the macroeconomicrate of price adjustments fixed, then a
fall in Q or an increase in X makes price stickiness more plausible not only by reducing the private flow cost of price rigidity caused by a given departureof output
from full employment output, but also by reducingthe length of time a given firm
incursthatprivateflow cost for each instanceof fixing its price. Even an increase in
et for given Q and X (which has no direct effect on the private flow cost of price
rigidity in (23)) would require an increase in cx to hold s fixed, thus implying a
shorterperiod of price-fixityat the firm level.
3. THE CLASSICAL SIDE OF THE NEOMONETARISTMODEL
The "classical" side of the neomonetaristmodel is importantfor three reasons.
First, the classical side of the model indicateswhat happensto variablesother than
P and Y. Second, the classical side of the model makes it possible to determinefull
11. This result is reminiscentof Blanchard(1983).
1258 : MONEY, CREDIT,AND BANKING
employmentoutputYf. Third,the classical side of the model determinesthe elasticity Q of marginalcost with respect to aggregateoutput.
3.1. lnvestmentAdjustmentCosts
Investmentadjustmentcosts are importantto business cycle analysis in orderto
allow a distinction between the real interest rate and the net marginalproduct of
capital. In the absence of some mechanismin a model to allow the relative price of
capitalrelativeto consumptiongoods to vary, the real interestrateand the rentalrate
for capital net of depreciationmust always be equal. Withouta distinctionbetween
the real interestrate and the net marginalproductof capital, virtuallyany stimulus
to the economy including a monetarystimulus must be associated with an increase in the real interestrate, since virtuallyevery business cycle model implies a
procyclical rentalrate for capital.
Due to space limitations,I will presentthe model here withoutinvestmentadjustment costs, then discuss what the effects of investmentadjustmentcosts would be.
The details of the model with investmentadjustmentcosts can be found in Kimball
(1995).
3.2. The Household
Although I am pushing trendgrowth of the economy into the background,I will
use the King-Plosser-Rebelo(1988) form for the utility functionin orderto make the
model consistentwith trendgrowth. An especially convenientway of expressingthe
King-Plosser-Rebeloutility function is
rx
J
N) dt,
e-Ptu(C,
o
where
u(C, N)
=
C
1 -
C
13
(26)
e(e-l)t(N)
or for @ = 1
u(C, N) = ln(C)-v(N)
.
(27)
This is the only type of additively time-separableutility function that allows income and substitutioneffects on laborsupplyto cancel out in the long runso thatthe
trendin the real wage W does not induce a trendin per capita laborN.
For simplicity, I will treathouseholds as owning all of the capital and renting it
out to the firms at the real rentalrateR, 12 and assume that each householdholds an
12. Whetherfirmsor householdsdo the investingdoes not matterfor outcomes as long as firmswould
also have to buy goods for investmentpurposesat the retail, markedup price.
MILESS. KIMBALL : 1259
identical cross-section of the sharesof the residualprofitsof the firms. (The households are identical in every other way, too.)
In addition to capital, a household can hold a real quantityof bonds B earning
interestat the real rate r. In additionto paying for consumptionC and investmentI,
it must pay lump-sumtaxes T.
Puttingeverythingtogether,the representativehousehold'sproblemis
C1-,B
rX
e(p-l)U(N)dt
max Z e-Pt
1 - 13
C,n,I Jo
s.t.
(28)
K = I-bK
B = rB + WN + RK + H-C-I-T
,
(29)
where v' ' O, v" c 0. If 13< 1, an additionalrestrictionis needed to guarantee
concavity of u(C,N), but I will arguethat the labor-constantintertemporalelasticity
of substitutions = (1/13)is less than 1, making 13' 1. II is residualprofits.
The current-valueHamiltonianH is
H=
C
C
e(C-l)t(N)
+
A[I-AK]
1 - 13
+ v[rB + WN+RK+
H-C-I-T],
where A is the marginalvalue of a unit of capital in utils and v is the marginalvalue
in utils of one real dollar's worthof bonds. The marginalvalue of capitalin dollars,
Q, is
Q
(30)
A
The first-ordercondition for I is
(31)
v= A
or equivalently, Q = 1. Therefore, the first-orderconditions for C and N boil
down to
(32)
C-e(Q-l}t(N) = A
Vt(ff)Cl-e(e-l+(N)=
WA
(33)
1260 : MONEY, CREDIT,AND BANKING
togetherimplying
(34)
W= Cv'(N) .
The Euler equationsfor A and v are
(35
A = [p + 8-R]A
v = (p-r)v
which, combined with the first-ordercondition A = v imply that
r
=
= P--
P-A
= R-8
.
(36)
3.3. The ProductionFunction
I will assume for each firm the same generalized Cobb-Douglas production
function:
Ye = F(xx,Y) = F(keone0, Y),
(37)
where x is a Cobb-Douglascomposite of the two inputs with a cost share of 0 for
capital and 1 -0 for labor as shown. The parameters0 and 1 -0 are the cost
sharesfor capital and laborbecause for any given composite inputxe, the firmminimizes costs by solving
min Wne + Rke
kt,,n+,
s.t.
ko 1->ene
-Xe
-implying among other things that
Wnf
Rke
1 -0
0
In the form ne = (R(1 -0)IW0)ke, this relationshipcan be neatly summed up to
the correspondingaggregaterelationship.Thus, in the aggregate,
K 1 -0
(38)
.
MILES S. KIMBALL : 1261
In words, capital-laborsubstitutionensures that the real rentalrateR is determined
in a straightforwardway by the capital stock and what is going on in the labor market, even when the economy is away from full employment.
The function F allows the possibility of both internaland externalincreasingreturns to scale (including fixed costs, as long as the factor compositionof the fixed
costs is the same as the factor compositionof the variablecosts). Omittingthe subscript on yf, the real total cost function for each firm is of the form
TC = R0W1-0C(y, Y) .
The real marginalcost MCIP = 4?(y,Y,) at the steady-statemarketsharey/Y = 1
(where the key elasticities are determined)is therefore
oCy(YY).
(1)= 4'(Y,Y,-) = [R(Y,--)]0[W(Y,-)]1
(39)
The size of the effect of factorprice pressureon real marginalcost will be calculated
below. In addition, there is a direct effect of aggregate output on marginal cost
throughboth argumentsof Cy(y,Y). In the neighborhoodof the steady state, with
y = Y = Y*, the elasticity X with which marginalcostfor givenfactor prices falls
as aggregateoutputand firmoutputincreasein the same proportionis
_ Y*[Cyy(Y*
X
Y*) + Cyy(y*
Cy(Y*,
Y*)]
Y*)
The degree of internalreturnsto scale Pyin the neighborhoodof the steady state
depends only on the level of marginalcost relativeto total cost, not to the derivative
of marginalcost:
_
7
TC _ C(Y*, Y*)
Y*MC Y*Cy(Y* Y*)
Similarly, the degree of returnsto scale r to a balancedexpansionof outputby all
nrms 1S
r_
Y*[cv(y*S
c(Y* Y*)
Y*) + Cy(Y*
Y*)]
3.4. Steady-StateRelationshipsUsefulfor Log-Linearizingaround
the Steady State
lnvestmentand the RentalRate in SteadyState. In the steady state, (28) becomes
1262 : MONEY, CREDIT,AND BANKING
and (36) becomes
R* = r* +
8
= p+
8
.
TheSteady-State
Composition
of Output.Let c = C*/Y*, 4 = l*lY* and G =
G*/Y* be the steady-statesharesof consumption,investment,and governmentpurchases in output. In the steady state, the real wage and the rentalrate are equal to
theirmarginalrevenueproducts.Since internalincreasingreturnsraise the marginal
product,while a markuplowers it, the steady-statepaymentsto capitalas a shareof
outputare equal to Py*/>*times capital's share in costs:
R*K*
(3 Py*
(40)
(This relationshipcan be derived by using the fact that
TR = P*Y* = >*MC * Y* = >*-.)
Thus,
g;
I*
I*
1
R*K*
8
y
(41)
0
Also,
(c=
y*
(W*N*) [
Y* ]
(T)
[>*
]
(42)
and
c
41
= P + 8 1 - 0
8
oT,
where the notationT for the ratio of laborincome to consumption
W*N*
T
=
*
will be used below as well.
3.5. Log-Linearizing
aroundtheSteadyState
Expressing some of the key equations above in terms of logarithmicdeviations
from the steady state yields the following block of key equations.
For the representativehousehold's first-orderconditions, one obtains
MILESS. KIMBALL : 1263
C = s(Q-A)
+ (1 -s)N
N
W= C + -
(43)
(44)
where
f
=
_
is the labor-constantelasticity of intertemporalsubstitutionfor consumptionand
_
n
v'(N*)
N*v"(N*)
is the consumption-constantelasticity of labor supply.
The Euler equationfor A and the accumulationequationfor K yield
(A)
(45)
= -r
=
-(p + 8)R
K= (l*lK*)[l-K]
(46)
= 8[l-K]
From the productionfunction,
Y = r[oK + (1 - o)M
(47)
Fromthe constantshares,
R = W+N-K,
(48)
and from (39), the logarithmicdeviationof real marginalcost + is given by
(>
= OR+ (1 -0)W-RY
(49)
Finally, with government purchases assumed constant, G = O and the closedeconomy accountingidentity Y = C + l + G can be log-linearizedas
Y= cC + 4,I .
(so)
1264 : MONEY, CREDIT,AND BANKING
Certainotherequationsare peripheralto the model. For example, given the material balance condition and the Ricardianequivalenceimplied by the model, it is not
necessaryto keep trackof the householdstock of bonds or the government'sbudget
constraint.
3.6. The Short-RunBehavior of the Classical Side of the Model
Recall the three things to be learnedfrom the classical side of the model: the behavior of variables other than P and Y in response to a monetaryexpansion, the
determinantsof full employmentoutput, and the determinantsof Q, the elasticity of
marginalcost with respect to a balancedexpansionin outputby all firms.
Using the equationsabove, it is a straightforwardmatterto express the behavior
of the key variablesin terms of Y, K, and A as follows:
N
r(l - 0)
c
r(l - o)
I
p + 8L.*r _ 1 + Sl
v(1
W
v(1 -
(1 - 0)
-s)
s) +
_
(1
-s)0
(
P ^ 8(1 - 5)
I
0 [T(1
-
r(l-o)
R
T(l
-S)
+
S)
K
re
A
(P + 8) [
+
L
T( t
m
s) +
5 (c
1]
1-0
m
+
0[T(t
l
-S)
r(l-o)
T(l
0
-y+-+
-A -
01
1-0
+
_
0
0
,, - 1 + Sl
S)
+
N +
[T(t
S)
N
1
-[s(P + a) - P]
l 1
(P
) [
(
m
^5(c
0 j
(
+
a)
-
(51)
Because of the log-linearizing, each element of the above matrix is in elasticity
form. Since Y = M + V-P, in the short-run,andP cannotjump, the firstcolumn
of elasticities with respect to Y are also the short-runelasticities with respect to M
and V. Moreover, in the high-cxapproximationin which prices adjust quickly, a
change in the money supply M or in velocity V will have only a small effect on K
and A. Therefore, as an approximation,we can take K and A fixed as we vary M or
V. That approximationis a formal version of the Classical Dichotomy.
Note that if the elasticity of intertemporalsubstitutionin consumptions is 1, as
many real business cycle models assume, (51) simplifiesquite a bit. However, I will
argue below that s < 1.
MILESS. KIMBALL : 1265
Here is the logic behindthe effects of a monetaryexpansionpredictedby the first
column of the matrix in (51): (O) Outputis determinedby the quantityequation.
With marginalrevenue above marginalcost in the neighborhoodof the steady state,
firmsare willing to supply all of the outputthatis demandedat theirfixed prices. ( 1)
Firms employ enough labor to producethe additionaloutput. (2) If s < 1, complementarityin the utility functionbetween laborand consumptionleads the household
to increase consumptionwhen it provides more labor. (3) Saving and thereforeinvestment increases because the additionalconsumptionis less than the increase in
output producedby the additionallabor input. (4) The increasedquantityof labor
moves the representativehousehold up its laborsupply curve, forcing the real wage
to rise. This increase in the real wage in conjunctionwith the increasedefficiency
of the economy as outputexpands from its suboptimalsteady-statevalue is what
guaranteesthat labor will increase enough in relation to consumptionthat saving
will increase. (S) The rentalrate of capitalincreases(even more thanthe real wage)
because the increase in the real wage makes firms want to substitutecapital for labor, but capital actually becomes scarcerrelativeto laboras N increases. In the absence of investmentadjustmentcosts, the increasein the rentalrate implies that the
real interestrate increases, since r = R-8. (6) Unless productiveexternalitiesor
downward-slopingmarginalcost at the firm level make X an elasticity to be reckoned with, the increase in the real wage and the rentalrate cause an increasein real
marginal cost, squeezing firms' actual markupsbelow their desired markups. (7)
The increased investment results in capital accumulation. (8) The above-normal
rental rate is associated with a temporarilyhigh and thereforefalling marginal
value of capital A.
Full employmentoutputis the level of outputat which real marginalcost is at its
steady-statevalue at which + = O. Thus,
yf
1 _
0
[T(1
(1
s)
-s)
+
+
N
n
+
r(l _ o)
+
1 ] K
+
sA
0
- X
Since K and A determinefull employmentoutput,the elasticityof marginalcost +
with respect to Y, holding K and A constant, is equal to Q:
(1
Q=
-s)
+-+
r(1-0)
0
-
Everythingin Q otherthanthe possible productiveexternalityeffects representedby
X is a matterof the real wage increasingas the economy moves up along the labor
supply curve and the rentalrate increasingas firmstry to substitutecapitalthat is in
fixed supply for more expensive labor. A high consumption-constantlabor supply
elasticity n or a high intertemporalelasticity of consumptions reduce Q because
1266 : MONEY, CREDIT,AND BANKING
they make the laborsupplycurve flatter.A high degree of economy-widereturns-toscale r and a high labor's share 1-0 reduceQ because they reducethe amountof
extra labor needed to producea given amountof extraoutput.
4. CALIBRATION
4.1. ParameterValues
Because the model has been solved algebraically,it is easy to plug in different
sets of parametervalues. Based on microeconomicevidence, I have a serious disagreement with two of the parametervalues traditionalin the real business cycle
literature the traditionalvalues for the elasticity of intertemporalsubstitutionand
for the labor supply elasticity. These parametersI discuss furtherbelow.
Based on Basu (1993), Basu and Fernald (1994a, b), and Basu and Kimball
(1995), I choose Py= 1.1 and >* = 1.1, implying e* = 11. (With />* = 1 the
steady state has zero pureprofits.) In the absenceof strongevidence againstconstant
marginal cost, and the absence of any strongevidence of productiveexternalities,I
choose X = 0 and r = w = 1.l. Thus, in tsheseparameters,I assumeonly a modest
departurefrom constantreturnsto scale and perfect competition.
The other, less controversial parametervalues are assigned as follows: 0 =
(A*/w)(p + 8)K*IY* = .3, 1 -0 = (>*I)W*N*IY* = .7, 8- .08/year, p =
= .7, 4 =
.02/year, and T = W*N*IC*= 1. These imply (c = C*/Y* = (1-0)/
= .06. (The value .06 is
I*IY* = 80/(p + 8) = .24 and (G = G*/Y* = 1-C-4,
too low for the share of all governmentpurchasesin output, but seems reasonable
for the shareof governmentpurchasesthatare not good substitutesfor eitherprivate
consumptionor privateinvestment.)
The two parametersmost difficultto calibrateare the microeconomicrateof price
adjustmentcxand >'(1)/>(1), the elasticity of the desired markupwith respect to a
firm's market share which is the key to calibrating. Given the assumptionof
constantmarginalcosts, making4)y = 0,
@ =
* +
A((1))
=
.09
+
A((1))
.
Therefore,cxand X should be viewed as unknownparameters.It is useful, however,
to rememberthat in order to make sticky prices plausible, large values of X are
needed. To get some sense of the possible values of , note that a value of 4.28 for
'(1)/>(1), making X = 4.37, would requirea 1% increase in marketshare g to
cause a fall in the elasticity of demandfrom 11 to about 8, so that > would increase
1. 1428.
from 1l/lo = 1. 1 to 8/7
The Elasticity of IntertemporalSubstitutionand Additive Nonseparability between Consumptionand Labor. A large shareof real business cycle models assume
an elasticity of intertemporalsubstitutions equal to 1, which is implausiblyhigh. 13
13. Some papers, notably King, Plosser, and Rebelo (1988) departfrom this default value of 1, but
the traditionalvalue of one continuallyreassertsitself.
MILESS. KIMBALL : 1267
Empirically,no one has been able to establishconclusively thatthe real interestrate
has any effect on the timing of consumption,much less that a one percentagepoint
increase in the real interestrate increases the expected growth rate of consumption
by 1 percent, as it would if the elasticity of intertemporalsubstitutionwere equal to
one. Given the standarderrorsin, say, Hall's (1988) regressions, the failure to find
intertemporalsubstitutionempiricallyis quite consistentwith some positive elasticity of intertemporalsubstitution,but it is not consistentwith an elasticity of intertemporal substitutionequal to 1. Responses to survey questions based on choices in
hypotheticalsituationsconfirmthese econometricresults. (See Barsky,Juster,Kimball, and Shapiro 1995). Even if the PermanentIncome Hypothesisor its auxiliary
assumptionsare failing to some extent, an elasticity of intertemporalsubstitutionas
large as one should be enough to cut througha lot of model noise.
The primaryjustification for assuming an elasticity of intertemporalsubstitution
equal to one is that this is the only value for which the King-Plosser-Rebelo(1988)
utility function yields additive separabilitybetween consumptionand labor. But I
see no compelling reason to assume additiveseparabilitybetween consumptionand
labor. Indeed, when tested, additive separabilityis often rejected. (See, for example, Garcia, Lusardi,and Ng 1994.) Withinthe class of King-Plosser-Rebelopreferences, an elasticity of intertemporalsubstitutionless than one implies that for any
given level of consumption, laboringmore raises the marginalutility of consumption. To me, this seems quite plausible. It means that, even in a permanentincome
setting, additionallabor induced by a temporaryincrease in the shadow real wage
tends to induce additionalconsumptionduringthat period of additionallabor. The
positive effect of labor on consumption implied by a King-Plosser-Rebeloutility
function with elasticity of substitutionless than one gives it a fighting chance at
explaining the business cycle fact that consumptionand labor tend to move in the
same direction. In a model with a smalEr elasticity of intertemporalsubstitution,
interestrate effects become less importantand effects inducedby fluctuationsin the
shadow real wage become more important.
Therefore, to be consistent with Hall (1988), let me try s = .2.
The Consumption-ConstantElasticity of Labor Supply. Typical microeconomic
estimates of the labor supply elasticity are quite low. However, the regressionsbehind these estimates either use high-frequencyvariationsin observed wages, confounding the observed real wage with the shadow real wage, or they rely on lifecycle variationsin the real wage. The effects of life-cycle variationsin the real wage
are difficultto disentanglefrom other age-linkedeffects.
In the absence of clear microeconomicevidence, the real business cycle literature
has traditionallychosen quite high values of the labor supply elasticity because
those large values make it easier to fit the macroeconomicdata. There is too little
space here to presentthe critiqueby Hall (1987) and others of the Rogerson (1984)
justificationfor high macroeconomiclabor supply elasticities. Instead, let me suggest a disciplined way of judging the appropriatesize of the consumption-constant
labor supply elasticity which is robustto the presence of Rogersoniannonconvexities at the microeconomiclevel.
Whatever its microeconomic underpinnings,to be consistent with steady-state
h
1268 : MONEY, CREDIT,AND BANKING
growth, the macroeconomiclabor supply relationshould imply thatthe income and
substitutioneffects of permanentlyhigher real wages cancel. This allows one to
gauge the size of the substitutioneffect by think1ngabout the size of the income
effect. Therefore, if one can constructa representativehousehold, it should have a
King-Plosser-Rebelo(1988) utility function, as above.
Given a King-Plosser-Rebeloutility function for the representativehousehold,
the slope of the income expansion path can be identified by looking at how consumption and labor are related when the (shadow) real wage is held constant. By
(44), when W = O,
N = -nC .
As income increases, the additionalexpenditureon consumptionis
w
C = C*C
while the additionalexpenditureon leisure is
-W*N = -C* ( C* ) N = -C*N
= C*TnC .
Thus, the marginalexpenditureshareof consumptionh is
1
C
1+ n '
C-W*N
and the marginalexpenditureshareof leisure 1-h
1 -h=
is
n
1 +TN
Given either of these marginalexpenditureshares, the consumption-constantlabor
supply elasticity can be calculatedas
1 -h
With the calibrationT = W*N*IC* = 1, the laborsupplyelasticity n is equal to the
ratio of the marginalexpenditureshareof leisure 1 -h to the marginalexpenditure
share of consumptionh. 14
14. As a note on the history of thought, this methodof calibratingthe laborsupply elasticity from the
marginal expenditureshares of leisure and consumption is closely akin to the way in which Prescott
(1986) calibratesthe laborsupplyelasticity. However, Prescott(1986) calibratesthe laborsupplyelasticity using the average expendituresharesof leisure and consumption,with the implicitassumptionthatthe
MILESS. KIMBALL : 1269
The thoughtexperimentto get these marginalexpendituressharesis to thinkhow
one would spend the proceedsof lotterywinnings. Whatpercentagewould be spent
on increased consumption and what percentage would be spent on reduced work
hours?If income and substitutioneffects are to cancel, anyone who wishes to argue
for a high labor supply elasticity must also be preparedto defend the idea that
people would spend a substantialfractionof such windfalls on reduced work. For
what it is worth, a sample of studentsasked to imagine a futuresituationin which
they were working had an average marginalexpenditureshare of leisure equal to
about .25. Even though the modal response was zero, many indicatedthey would
spend a substantialfraction of a windfall on reducing work hours. This implies a
consumption-constantlabor supply elasticity of about .25/.75 = .33. A marginal
expenditureshare of leisure of .5, which is as high as seems at all plausible to me,
would yield a consumption-constantlabor supply elasticity of about 1. The only
way to get the infinite labor supply elasticity that appearsin some Real Business
Cycle models and still have income and substitutioneffects cancel is to have a marginal expenditureshare of leisure equal to 1. That is, those models imply that a
household would spend 100 percentof a windfall on reducinglabor supply. Or, to
the extent that the high labor supply elasticity arises from mechanismsat a higher
level thanthatof the individualhousehold, they imply that 100 percentof a windfall
to the class of workersas a whole would be spent on reducinglabor. This is a typically unnoticed featureof these models. In orderto get the highest plausible value
of , take the somewhat extreme case in which half of a windfall is spent on consumptionand half on leisure (h = .5), so that n = 1.
4.2. General EquilibriumElasticities lmplied by These ParameterValues
Substitutingin the chosen parametervalues, the short-runbehaviorof the model
.
.
.
1S glVen
Dy
_
_
N
C
l
W _
R
+
K
_ A_
-
_
1.30
1.04
1.14
2.34
3.64
2.73
.091
_-.363
_
-.43
-.34
1
-.77
-2.20
-1.20
0
.220
0
-.20
.58
-.20
-.20
-.20
.047
.020
- y-
(52)
average and marginalexpenditureshares are equal. This gave rise to the question of how to deal with
sleep in calculatingthe averageexpenditureshareof leisure, an issue which made an enormousdifference
in the implied labor supply elasticity. But the question of how to deal with sleep can be seen for the red
herringit is once one focuses properattentionon the marginalexpendituresharesas opposed to the average expenditureshares.
1270 : MONEY, CREDIT,AND BANKING
The elasticity of + with respectto output,2.73, is equal to Q. Takinga stab in the
dark, if >t(1)/,u(1) is equal to the value 4.28 which I entertainabove, then X = 4.37
and
-
4
e*so
'
implying that macroeconomicprice adjustmentwould take more than four times as
long as it takes an individualfirmto adjustits price.
The Elasticity of IntertemporalSubstitutionand the Response of Saving and Investmentto a MonetaryStimulus. There is not space here to make a detailed comparisonof the generalequilibriumelasticities above with the data, but one elasticity
that seems at variancewith the data is the elasticity of saving and investmentwith
respect to output(in the context of a monetarystimulus): 1.14. The problemis that
with s = .2, labor and consumptionare such strong complementsthat most of the
additionaloutputproducedby additionallabor inputis eaten up as consumption,so
that there is little extra saving to be invested. Indeed, one can calculate that in response to a monetary stimulus, the general equilibrium marginal propensity to
consumein this model is (1-5)
sity to save is
7*r[ > r
_
Y*r and the generalequilibriummarginalpropen1 + S] .
Increasingeither the elasticity of intertem-
poral substitutions ar the steady-statemarkupratio >* can have a big effect in raising the marginalpropensityto save from the value of .27 impliedby the parameters
above. Consideran increase in the elasticity of intertemporalsubstitutionto s-.5.
Then the generalequilibriummarginalpropensityto save becomes .55, and the elasticity of investmentwith respect to output (in the context of a monetarystimulus)
becomes 2.27. The elasticity of consumptionwith respectto outputfalls to .65, but
neitherthe elasticities of N, W, R, and + with respectto outputnor the convergence
rate change much.
5. DOES THE REAL INTERESTRATE FALL IN RESPONSETO A PERMANENTINCREASEIN
THE MONEY SUPPLY?
As mentionedabove, as long as the relative price of capital is fixed at 1, so that
the real interestrate r must go up with output because the real rental
r = R-8,
rate R does. Therefore, in the model above, a monetaryexpansion raises the real
interest rate, just as in King's (1991) model, and for essentially the same reason.
To use the language of intermediatemacroeconomics,a relative price of capital
fixed at 1 leads to an upward-slopingIS curve, due to the positive effect of aggregate outputon the real rentalrate of capital. The quantityequationyields a vertical
LM curve, but one could easily combine a more general LM curve with this
upward-slopingIS curve.
When investmentadjustmentcosts allow the relativeprice of capitalQ to vary, it
MILESS. KIMBALL : 1271
becomes possible for a monetaryexpansionto cause the real interestrateto fall. But
movements in Q must be substantialto overcome the positive effect of the rentalrate
on the real interestrate. This section is devotedto discussing thatquantitativeissue.
Either of two differenttechnical tricks allow me to discuss the conditions for a
monetaryexpansion to lower the real interestrate without going throughthe entire
Q-theory neomonetaristmodel laid out in Kimball (1995). First, some simple inequalities relate the model with investmentadjustmentcosts to the model without
investment adjustmentcosts. Second, I look at an approximationin which the investment adjustmentcost parameterj goes to zero, butjof has a finite positive limit.
Then, in the limit, the behaviorof the classical side of the model becomes the same
as in the absence of investment adjustmentcosts, but the interactionbetween the
investmentadjustmentcosts and the convergence of the model to full employment
(which takes place at a rate proportionalto a) remains something to be reckoned
with.
5.1. Whythe AnswerDepends on the Size of the InvestmentAdjustmentCost and
the Rate of Price Adjustment
Q theory implies thatthe increasein investmentinducedby a monetaryexpansion
must be associated with an increasein Q, the relativeprice of capital. As the aggregate price adjustsand the economy returnsto full employment, investmentI and
thereforeQ falls back to its normallevel at the rate of price convergence K. The
capital loss from the falling price of capital lowers the rate of returnon capital,
which by arbitragemust equal the real interest rate r. The greaterthe investment
adjustmentcosts, the more Q will rise and then fall, and the bigger the downward
pressure on the real interest rate. The faster the economy returnsto full employment, the greaterthe rate of capital loss, and the more likely it is thatthe real interest determinedby arbitragewill fall.
To describe the same interest-rate-determination
mechanismin levels instead of
rates of change, consider the interactionbetween saving supply and investmentdemand. If with no change in the real interestrate the increase in investmentdemand would exceed the increase in saving supply induced by the expansion in
output, then the real interestrate must rise to choke off investmentdemandand restore equilibrium.If, on the otherhand, the increasein saving supply would exceed
the increasein investmentdemandwithouta change in the real interestrate, then the
real interestrate must fall to stimulateinvestmentdemandand restoreequilibrium.
In response to a monetaryexpansion, saving supply depends almost entirely on
currentoutput. To a first approximation,the elasticity of saving supply with respect
to a money-drivenincreasein outputdoes not dependon the rate at which the economy returnsto full employmentand is also not very sensitive to modest changes in
the size of the adjustmentcost. But the elasticity of investmentdemandwith respect
to a permanentincreasein the money supplydependsstronglyon both the size of the
adjustmentcost and the rate at which the economy returnsto full employment. A
largerinvestmentadjustmentcost reduces the elasticity of investmentdemandwith
1272 : MONEY, CREDIT,AND BANKING
respect to Q. Quicker convergence back to full employmentmeans that the rental
rate will only be high for a short time, leading to a smallermovement in Q. Thus,
high investmentadjustmentcosts and quick convergencerates make investmentdemand increaseless in relationto the increasein saving supply,makingit more likely
for the real interest rate to fall in response to a permanentincrease in the money
supply.
5.2. InvestmentAdjustmentCosts and the Real InterestRate
To make the logic of arbitrageor investmentdemandand saving supply quantitative, it is necessary to derive an equationrelating the real interestrate to the real
rentalrateR and the relativeprice of capitalQ when thereare investmentadjustment
costs.
With investment adjustmentcosts modeled as in Hayashi (1982), the owner of
capital, who rents it out to firms, solves
max J erOrdt [RK-I]
l
dtt
o
s.t.
K= KJ(IIK) .
(53)
The function J giving the rate of increase in the capital stock for a given investment/capitalratio satisfies J'( )-O, J"(@)s 0, J(8) = O, and J'(8) = 1, where 8
is defined as l*IK*. 15
The currentvalue Hamiltonianis
H = RK-I
+ QKJ(IIK).
The first-ordercondition for investmentis
1 = QJ'(IIK),
Since l*IK* = 8, in steady state the first-orderconditionimplies Q* = 1. The firstordercondition can be log-linearizedas
Q = j[l-K],
(54)
where
J
-(I *IK*)J"(I*IK*)
J '(I*IK*)
15. The model without investmentadjustmentcosts has J(llK) = (llK)-8,
so thatJ"(-) = O.
MILESS. KIMBALL : 1273
After using the first-ordercondition and dividing throughby Q, the Euler equation is
+ (IIK)-R
Q = r-j(IIK)
In the steady state, I*IK* = 8, Q* = 1 and J(l*IK*) = J(8) = O imply
r* + 8 = R* as in the absence of investmentadjustmentcosts. In log-linearizing
the Eulerequation, since J'(l*IK*) = (1/Q*) = 1, the derivativeof the second line
of (55) with respect to IIK is zero, and
.
Q = r-R + r*Q .
(56)
In integralform, using the steady state as a terminalcondition,
rx
(57)
Qt= J e-r*(t-t)[R-r-],
.
t
implying that expectationsof fairly distant futureevents have an importantimpact
on Q and thereforeon investment.
Finally, given (I*IK*) = 8 andJ'(8) = 1, the accumulationequation(53) can be
log-linearizedto
(58)
K= 8[1-K]
Note that (58) is identical to (46), since investment adjustmentcosts play only a
second-orderrole in the accumulationequationitself.
5.3. WhatIs Neededfor a PermanentIncrease in the Money Supplyto Lower the
Real InterestRate?
equation(56) can be rewritten
Since R = R*R = (r* + b)R, and Q = j[l-K],
(59)
r = (r* + 8)R + j[l-Kl-r*j[l-K]
As the rate of price adjustmenta gets large, the one big componentof I becomes
I
- Kl
-a
1T
&
Furthermore,K = b[1-K],
r = (r* + b)R-
e*l) I
while at time zero, K = O. Makingthese substitutions,
[r* +
8
+
K] jl
-
goes
aWith
oo
More
back
jthe
0,
formally,
necessary
to
(61)
fullis as
employment
consistent
jcondition
O andaafter
with
>for
oo,(60).
athe
the
permanent
monetary
only
Using
thing
the
increase
stimulus
in
parameter
(59)In
inthat
the
the
values
islimit
money
not
given
as
zeroed
supply
j above,
0 and
out
to
1274 : MONEY, CREDIT,AND BANKING
Therefore,an approximatenecessaryconditionfor a permanentincreasein the money supply to lower the real interestrate is
[r*
+
8
+
K]j
>
(r*
+
8)
I
|
>
(r*
yo
+
8)
l-
|
(60)
y=o
Why do I claim in (60) thatthe ratioRll of the rentalrateelasticity to the investment
elasticity is higher whenj > 0 thanwhenj = 0? First, investmentadjustmentcosts
lead to less of an outputexpansionbeing devotedto investment.Second, since more
of an output expansion is therefore spent on consumption, the relationship
W = Cv'(N) guaranteesthatthe real wage goes up more and capital/laborsubstitution guaranteesthat the real rentalrate goes up more as well. 16
when multipliedby j
is
the revision of investmentto its normallevel as the economy
lower the real interestrate is
-
lim
jK>(r*+8)
xm,jO
I
ao [ (1
=
j=O
- 5) +-+
n
(1- o)L>r
1]
(61)
1 + s]
using on the right-handside the movementsin R andI predictedby the model without investmentadjustmentcosts the elasticities given in the first column of (51).
the condition (61) becomes jK
> .32/year
when s = .2 and jK
> .14/year
when
s = .5.
Condition (60) looks the same as (61), but with j(r* + 8 + K) in place of jK.
Conditions (61) and (60) are related in much the same way as a x2 test based on
asymptotictheory and the correspondingF test which may be a better approximation even though it does not have as clean a formaljustification.
5.4. Calibrating
j and K
By (54), the elasticity of IIK with respect to Q is l/j. Regressions of IIK on Q
using stock and bond prices to measureQ have often found quite low coefficients,
implying quite high values of j. However, these high values of j give an implausibly
slow partialequilibriumadjustmentrate for the capital stock. Using a new method
16. Kimball (1995) provides more details.
MILES S. KIMBALL : 1275
of identificationbased on statutorytax changes, Cummins, Hassett, and Hubbard
(1994) find much larger elasticities of IIK with respect to Q on the order of 5,
implyingj = .2. This value for j is broadlyconsistent with the findingsof Shapiro
(1986), who estimates adjustmentcosts using an Euler equationthat implicitly defines Q in a way akin to (57) ratherthan using volatile stock and bond prices.
If j = .2, condition (61) for a monetarystimulus to lower the real interestrate
becomes K > 1 .60/year when s = .2 and K > .70/year when s = .5. Using (60)
would subtract10 percentper year from these necessaryconvergencerates. In other
words, for a permanentincrease in the money supply to lower the real interestrate,
the half-life for macroeconomicprice-adjustmentmust be less than2 quarterswhen
s = .2 or less than about 4 quarterswhen s = .5. This seems too fast if monetary
shocks are to be an importantcause of business cycles. Thus, by my judgment,
plausible parametervalues imply that a monetaryexpansion should lead to an increase in the real interestrate.17
To make things more concrete, even with s = .5, the model above says that a 1
percent increase in output raises the real rentalrate by about .32 percent/year(32
basis points), while the supply of saving and thereforethe level of investmentincreases by only about 2.27 percent. Givenj = .2, Q needs to rise by only about .47
percentto yield this increasein investmentdemand. Therefore,most of the increase
in Q must disappearin less than a year in orderto have a capital loss sufficientto
make the rate of returnon capital and the real interestrate fall.
In the language of intermediatemacroeconomics,the IS curve is stubbornlyupward sloping. It may be necessary to model any real-worldtendency for the real
interest rate to fall in response to a monetarystimulus as a result of output being
temporarilyoff the IS curve.
6. CONCLUSIONS
Though there is much more that could be said about the neomonetaristmodel
above, several things are apparent.
First, a kind of classical dichotomy separatingfluctuationscaused by monetary
forces from movements caused by real forces can be justified as an appropriateapproximationwhen prices adjustquickly.
Second, an elasticity of demandfalling sharplywith a firm'smarketshareis both
easy to model and effective at reducing the private cost of price rigidity, making
price stickiness more plausible.
Third, mechanisms that increase real rigidity and thereby make sticky prices
more plausible also tend to slow down the generalequilibriumadjustmentof prices.
This general equilibriumadjustmentrate is not the same as the ratea at which indi17. However, as can be seen from (61), increasingany of j, , or >* would slow down the necessary
convergence rate considerably.Increasingeitherj or n would make investmentdemandless sensitive to
money-drivenmovements in output, while saving supply would become more sensitive to money-driven
movements in outputif * increased.
1276
: MONEY, CREDIT,AND BANKING
vidual firms are assumed to change their prices. If there is enough real rigidity to
make sticky prices plausible, the generalequilibriumadjustmentrate is likely to be
significantlyslower than a.
Fourth,the exact natureof technology and preferences(includingthe elasticities
of labor supply and intertemporalsubstitution)has an importanteffect even on the
short-runbehaviorof the model before prices adjust.
Fifth, even when investmentadjustmentcosts are introducedto give the real interest rate a fightingchance to go down in responseto a monetaryexpansion, plausible
parametervalues imply thatthe real interestrate will increase in responseto a monetary expansion.
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